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control speeds” set by these factors rather than
simple stall speeds based on C&,.
When a wing of a given planform has various
high lift devices added, the lift distribution and
stall pattern can be greatly affected. Deflec-
tion of trailing edge flaps increases the local
lift coe5cients in the flapped areas and since
the stall angle of the flapped section is de-
creased, initial stall usually begins in the
flapped area. The extension of slats simply
allows the slatted areas to go to higher lift
coe5cients and angles of attack and generally
delays stall in that vicinity. Also, power
effects may adversely affect the stall pattern of
the propeller powered airplane. When the
propeller powered airplane is at high power
and low speed, the flow induced at the wing
root by the slipstream may cause considerable
delay in the stall of the root sections. Hence,
the propeller powered airplane may have its
most undesirable stall characteristics during the
power-on stall rather than the power-off stall.
PARASITE DRAG
In addition to the drag caused by the de-
velopment of lift (induced drag) there is the
obvious drag which is nor due to the develop
ment of lift. A wing surface even at zero lift
will have “profile” drag due to skin friction
and form. The other components of the air-
plane such as the fuselage, tail, nacelles, etc.,
contribute to drag because of their own form
and skin friction. Any loss of momentum of
the airstream due to powerplant cooling, air
conditioning, or leakage through construction
or access gaps is, in effect, an additional drag.
When the various components of the airplane
are put together the total drag will be greater
than the sum of the individual components
because of “interference” of one surface on the
other.
The most usual interference of importance
occurs at the wing-body intersection where the
growth of boundary layer on the fuselage re-
duces the boundary layer velocities on the wing
root surface. This reduction in energy allows
NAVWEPS OO-ROl-80
BASIC AERODYNAMICS
the wing root boundary layer to be more easily
separated in the presence of an adverse pressure
gradient. Since the upper wing surface has the
more critical pressure gradients, a low wing
position on a circular fuselage would create
greater interference drag than a high wing
position. Adequate filleting and control of
local pressure gradients is necessary to mini-
mize such additional drag due to interference.
The sum of all the drags due to form, fric-
tion, leakage and momentum losses, and inter-
ference drag is termed “parasite” drag since
it is not directly associated with the develop-
ment of lift. While this parasite drag is not
directly associated with the production of lift
it is a variable with lift. The variation of
parasite drag coefficient, C+, with lift coef-
ficient, C,, is shown for a typical airplane in
figure 1.34. The minimum parasite drag co-
efficient, CDpmi,, usually occurs at or near zero
lift and parasite drag coefficient increases
above this point,in a smooth curve. The in-
duced drag coefficient is shown on the same
graph for purposes of comparison since the
total drag of the airplane is a sum of the
parasite and induced drag.
In many parts of airplane performance it is
necessary to completely distinguish between
drag due to lift and drag not due to lift. The
total drag of an airplane is the sum of the para-
site and induced drags.
G=c++cD;
where
C, = airplane drag coefficient
C+=parasite drag coefficient
C,,= induced drag coeaicient
From inspection of figure 1.34 it is seen that
both CD, and CD, vary with lift coefticient.
However, the usual variation of parasite drag
allows a simple correlation with the induced
drag term. In effect, the part of parasite drag
above the minimum at zero lift can be “lumped”
a7 | 104 | 104 | 00-80T-80.pdf |
NAVWEPS 00-801-80
BASIC AERODYNAMICS
1.4
1.2
iL
i 0.4
0.2
0
0 .05 ;!O .!5
DRAG COEFFICIENT, CD
I.4
I.2
j 1.0
^
5
t 0.6
ii
kl $ 0.6
t
i 0.4
0.2
0
DRAG COEFFICIENT, CD
Figure 1.34. Airplane Parasite and Induced Drag | 105 | 105 | 00-80T-80.pdf |
NAVWEPS 00-8OT-80
BASIC AERODYNAMICS
ure is not too accurate because of the sharper
variation of parasite drag at high angles of
attack. In a sense, the airplane efficiency fac-
tor would change from the constant value and
decrease. The deviation of the actual airplane
drag from the approximating curve is quite
noticeable for airplanes with low aspect ratio
and sweepback. Another factor to consider is
the effect of compressibility. Since compressi-
bility effects would destroy this relationship,
the greatest application is for subsonic perform-
ance analysis.
The total airplane drag is the sum of the
parasite and induced drags.
where
D= D,+D<
Di= induced drag
in with the induced drag coefficient by a con-
stant factor which is defined as the “airplane
e5ciency factor”, c. By this method of ac-
counting the airplane drag coe5cient is ex-
pressed as :
where
C DPmB=
minimum parasite drag
coefficient
CD;= induced drag coe5cient
e = airplane e5ciency factor
In this form, the airplane drag coefficient is
expressed as the sum of drag not due to lift
F%d” ) and drag due to lift (G). The air-
plane efficiency factor is some co&ant (usually
less than unity) which includes parasite drag
due to lift with the drag induced by lift.
C Dpmr” is invariant with lift and represents the
parasite drag at zero lift. A typical value of
C r,Pmin would be 0.020, of which the wing may
account for 50 percent, the fuselage and nacelles
40 percent, and the tail 10 percent. The term
of ( 0.318 g > accounts for all drag due’ to
lift-the drag induced by lift and the extra
parasite drag due to lift. Typical values of
the airplane efficiency factor range from 0.6 to
0.9 depending on the airplane configuration
and its characteristics. While the term of
drag due to lift does include some parasite
drag, it is still generally referred to as induced
drag.
The second graph of figure 1.34 shows that
the sum of CD, and G can approximate the -mm e
actual airplane CD through a large range of lift
coefficients. For airplanes of moderate aspect
ratio, this representation of the airplane total
drag is quite accurate in the ordinary range of
lift coefficients up to near 70 percent of CL,,.
At high lift coefficients near CL-, the proced-
and
=(0.318 $+S
D,= parasite drag
When expressed in this form the induced drag,
Di, includes all drags due to lift and is solely
a function of lift. The parasite drag, D,, is
the parasite drag and is completely independent
of lift-it could be called the “barn door”
drag of the airplane.
An alternate expression for the parasite drag
is:
R=fq
where
f = equivalent parasite area, sq. ft.
f = CDPmi,S
q= dynamic pressure, psf
UP =-
295
or
DpEfg
In this form, the equivalent parasite area, f,
is the product of CDPml” and S and relates an
89 | 106 | 106 | 00-80T-80.pdf |
B I Y | 107 | 107 | 00-80T-80.pdf |
impression of the “barn door” size. Hence,
parasite drag can be appreciated as the result
of the dynamic pressure, 4, acting on the
equivalent parasite area, j. The “equivalent”
parasite area is defmed by this relationship as
a hypothetical surface with a C,=l.O which
produces the same parasite drag as the air-
plane. An analogy would be a barn door in
the airstream which is equivalent to the air-
plane. Typical values for the equivalent para-
site area range from 4 sq. ft. for a clean fighter
type airplane to 40 sq. ft. for a large transport
type airplane. Of course, when any airplane
is changed from the clean configuration to the
landing configuration, the equivalent parasite
area increases.
EFFECT OF CONFIGURATION. The par-
asite drag, D,, is unaffected by lift, but is
variable with dynamic pressure and equivalent
parasite area. This principle furnishes the
basis for illustrating the variation of parasite
drag with the various conditions of flight.
If all other factors are held constant, the para-
site drag varies directly with the equivalent
parasite area.
D,,= b C) D,, I
where
D,,= parasite drag corresponding to some orig-
inal parasite area, fi
D,,==parasite drag corresponding to some new
parasite area, fi
(V and (r are constant)
As an example, the lowering of the landing
gear and flaps may increase the parasite area
80 percent. At any given speed and altitude
this airplane would experience an 80 percent
increase in parasite drag.
EFFECT OF ALTITUDE. In a similar man-
ner the effect of altitude on parasite drag may
NAVWEK OD-BOT-BO
BASIC AERODYNAMICS
be appreciated. The general effect of altitude
is expressed by:
where
D,, = parasite drag corresponding to some orig-
inal altitude density ratio, 0,
D,,=parasite drag corresponding to some new
altitude density ratio, (ra
(and f, V are constant)
This relationship implies that parasite drag
would decrease at altitude, e.g., a given air-
plane in flight at a given T.4.Y at 40,COO ft.
(e=O.29 would have one-fourth the parasite
drag when at sea level (u=l.OO). This effect
results when the lower air density produces
less dynamic pressure. However, if the air-
plane is flown at a constant EAS, the dynamic
pressure and, thus, parasite drag do not vary.
In this case, the TASwould be higher at altitude
to provide the same EAS.
EFFECT OF SPEED. The effect of speed
alone on parasite drag is the most important.
If all other factors are held constant, the effect
of velocity on parasite drag is expressed as:
&, V, * -=- (3 D,, V
where
D,,=parasite drag corresponding to some orig-
inal speed, Vi
D,,=parasite drag corresponding to some new
speed, VS
(j and o are constant)
This relationship expresses a powerful effect
of speed on parasite drag. As an example, a
given airplane in flight at some altitude would
have four times as much parasite drag at twice
91 | 108 | 108 | 00-80T-80.pdf |
NAVWEPS 00-801-80
BASIC AERODYNAMICS
as great a speed or one-fourth as much parasite
drag at half the original speed. This fact may
be appreciated by the relationship of dynamic
pressure with speed-twice as much V, four
times as much 4, and four times as much D,.
This expressed variation of parasite drag with
speed points out that parasite drag will be of
greatest importance at high speeds and prac-
tically insignificant in flight at low dynamic
pressures. To illustrate this fact, an airplane
in flight just above the stall speed could have a
parasite drag which is only 25 percent of the
total drag. However, this same airpfane at
maximum level flight speed at low altitude
would have a parasite drag which’ is very
nearly 100 percent of the total drag. The
predominance of parasite drag at high flight
speeds emphasizes the necessity for great aero-
dynamic cleanness (low j) to obtain high speed
performance.
In the subsonic regime of flight, the ordinary
configuration of airplane has a very large por-
tion of the equivalent parasite area determined
by skin friction drag. As the wing contrib-
utes nearly half of the total parasite drag, the
profile drag of the wing can be minimized by
the use of the airfoil sections which produce
extensive laminar flow. A subtle effect on
parasite drag occurs from the influence of the
wing area. Since the wing area (S) appears
directly in the parasite drag equation, a reduc-
tion in wing area would reduce the parasite
drag if all other factors were unchanged.
While the exact relationship involves con-
sideration of many factors, most optimum
airplane configurations have a strong preference
for the highest practical wing loading and
minimum wing surface area.
As the flight speeds of aircraft approach the
speed of sound, great care must be taken to
delay and alleviate compressibility effects.
In order to delay and teduce the drag rise
associated with compressibility effects, the
components of the airplanes must be arranged
to reduce the early formation of shock waves
on the airplane. This will generally require
fuselage and nacelles of high fineness ratio,
well faired canopies, and thin wing sections
which have very smooth uniform pressure dis-
tributions. -Low aspect ratios and sweepback
are favorable in delaying and reducing the
compressibility drag rise. In addition, inter-
ference effects are quite important in transonic
and supersonic flight and the airplane cross
section area distribution must be controlled
to minimize local velocity peaks which could
create premature strong shock wave formation.
The modern configuration of airplane will
illustrate the features required to effect very
high speed performance-low aspect ratio,
sweepback, thin low drag sections, etc. These
same features produce flight characteristics at
low airspeeds which necessitate .proper flying
technique.
AIRPLANE TOTAL DRAG
I%,- rn+ql Jr,, nf ~ln eimlooe in fl.jght is the AI&C CYCYl Y Ye v YIL L”y’““c
sum of the induced and parasite drag. Figure
I.35 illustrates the variation of toral drag
with speed for a given airplane in level flight
at a particular weight, configuration, and alti-
tude. The parasite drag increases with speed
varying as the square of the velocity while the
induced drag decreases with speed varying in-
versely as the square of the velocity. The
total drag of the airplane shows the predomi-
nance of induced drag at low speed and parasite
drag at high speed. Specific points of interest
on the drag curve are as follows:
(A) Stall of this particular airplane occurs
at 100 knots and is indicated by a sharp rise
in the actual drag. Since the generalized iqua-
tions for induced and parasite do not account
for conditions at stall, the actual drag of the
airplane is depicted by the “hook” of the
dotted line.
(B) At a speed of 124 knots, the airplane
would incur a minimum rate of descent in
power-off flight. Note that at this speed the
induced drag comprises 75 percent of the total
drag. If this airplane were powered with a
reciprocating-propeller type powerplant, maxi-
mum endurance would occur at this airspeed.
92 | 109 | 109 | 00-80T-80.pdf |
NAVWEPS OO-ROT-80
BASIC AERODYNAMICS
VELOCITY KNOTS
Figure 9.35. Typical Airplane Drag Curves
93 | 110 | 110 | 00-80T-80.pdf |
NAVWEPS OO-BOT-80
BASIC AE,RODYNAMlCS
(C) The point of minimum total drag occurs
at a speed of 163 knots. Since this speed in-
curs the least total drag for lift-equal-weight
flight, the airplane is operating at (L/D)ma,.
Because of the particular manner in which
parasite and induced drags vary with speed
(parasite drag directly as the speed squared;
induced drag inversely as the speed squared)
the minimum total drag occurs when the in-
duced and parasite drags are equal. The speed
for minimum drag is an important reference for
many items of airplane performance. One
item previously ,presented related glide per-
formance and lift-drag ratio. At the speed of
163 knots this airplane incurs a total drag of
778 lbs. while producing 12,000 lbs. of lift.
These figures indicate a maximum lift-drag
ratio of 15.4.and relate a glide ratio of 15.4.~
In addition, if this airplane were jet powered,
the airplane would achieve maximum en-
durance at this airspeed for ‘the specified alti-
tude. If this airplane were propeller powered,
the airplane would achieve maximum range at
this airspeed for the specified altitude.
(D) Point (D) is at an airspeed approxi-
mately 32 percent greater than the speed for
(L/D),.,. Note that the parasite drag com-
prises 75 percent of the total drag at a speed of
215 knots. This point on the drag curve pro-
duces the highest proportion between velocity
and drag and would be the point for maximum
range if the airplane were jet powered. Be-
cause of the high proportion of parasite drag
at this point the long range jet airplane has
great preference for great aerodynamic clean-
ness and less demand for a high aspect ratio
than the long range propeller powered airplane.
(E) At a speed of 400 knots, the induced
drag is an extremely small part of the total
drag and parasite drag predominates.
(P) As the airplane reaches very high flight
speeds, the drag rises in a very rapid fashion
due to compressibility. Since the generalized
equation for parasite drag does not account for
compressibility effects, the actual drag rise is
typified by the dashed line.
The airplane drag curve shown in figure 1.34
is particular to one weight, configuration, and
altitude in level flight. Any change in one of
these variables will affect the specific drags at
specific velocities.
The airplane drag curve is a major factor in
many items of airplane performance. Range,
endurance, climb, maneuver, landing, takeoff,
etc., performance are based on some relation-
ship involving the airplane drag curve.
94 | 111 | 111 | 00-80T-80.pdf |
NAVWEPS 00-8OT-80
AIRPLANE PERFORMANCE
The performance of an aircraft is. the most operating limitations and insight to obtain
important feature which defines its suitability the design performance of his aircraft. The
for specific missions. The principal items of performance section of the flight handbook
airplane performance deserve detailed consid- provides the specific information regarding the
eration in order to better understand and capabilities and limitations of each airplane.
appreciate the capabilities of each airplane.
Knowledge of the various items of airplane
Every Naval Aviator must rely upon these
handbook data as the guide to safe and effec-
performance will provide the Naval Aviator rive operation of his aircraft.
with a more complete appreciation of the
95 | 112 | 112 | 00-80T-80.pdf |
NAVWEPS 00-ROT-80
AIRPLANE PER,FORMANCE
REQUIRED THRUST AND POWER
DEFINITIONS
All of the principal items of flight perform-
ance involve steady state flight conditions and
equilibrium of the airplane. For the airplane
to remain in steady level flight, equilibrium
must be obtained by a lift equal to the air-
plane weight and a powerplant thrust equal to
the airplane drag. Thus, the airplane drag
defines the thrust required to maintain steady
level flight.
The total drag of the airplane is the sum of
the parasite and induced drags: Parasite drag
is the sum of pressure and friction drag which
is due to the basic configuration and, as de-
fined, is independent of lift. Induced drag is
the undesirable but unavoidable consequence
of the development of lift. In the process of
creating lift by the deflection of an airstream,
the actuai iift is inclined and a coimponcn: of
lift is incurred parallel to the flight path direc-
tion. This component of lift combines with
any change in pressure and friction drag due
to change in lift to form the induced drag.
While the parasite drag predominates at high
speed, induced drag predominates at low speed.
Figure 2.1 illustrates the variation with speed
of the induced, parasite, and total drag for a
specific airplane configuration in steady level
flight.
The power required for flight depends on the
thrust required and the flight velocity. By
definition, the propulsive horsepower required
is related to thrust required and flight velocity
by the following equation:
pr= Trv
3%
where
Pr=power required, h.p.
Tr= thrust required (total drag), Ibs.
V= true airspeed, knots
By inspection of this relationship, it is appar-
ent that each’pound of drag incurred at 325
knots requires one horsepower of propulsive
power. However, each pound of drag at 650
knots requires two horsepower while each
pound of drag at 162.5 knots requires one-half
horsepower. The term “power” implies work
rate and, as such, will be a function of the speed
at which a particular force is developed.
Distinction between thrust required and
pawcr required is necessary for several reasons.
For the items of performance such as range and
endurance, it is necessary to relate powerplant
fuel flow with the propulsive requirement for
steady IeveI flight. Some powerplants incur
fuel flow rate according to output thrust while
other powerplants incur fuel flow rate depend-
ing on output power. For example, the turbo-
jet engine is principally. a thrust producing
machine and fuel flow is most directly related
to thrust output. The reciprocating engine is
principally a power producing machine and
fuei flow is most directiy reiated to power
output. For these reasons the variation of
thrust required wil1 be of greatest interest in
the performance of the turbojet powered air-
plane while the variation of power required
will be of greatest interest in the performance
of the propeller powered airplane. Also, dis-
tinction between power and thrust required is
necessary in the study of climb performance.
During a steady climb, the rate of climb will
depend on excess power while the angle of
climb is a function of excess thrust.
The total power required for flight can be
considered as the sum of induced and parasite
effects similar to the total drag of the airplane.
The induced power required is a function of the
induced drag and velocity.
p,,,!g
where
Pri= induced power required, h.p.
D<=induced drag, lbs.
V= true airspeed, knots
96 | 113 | 113 | 00-80T-80.pdf |
Thus, induced power required will vary with
lift, aspect ratio, altitude, etc., in the same
manner as the induced drag. The only differ-
ence will be the variation with speed. If all
other factors remain constant, the induced
power required varies inversely with velocity
while induced’drag varies inversely with the
square of the velocity.
where
Pri,=induced power required corresponding to
some original speed, Vi
I+;,= induced power required corresponding to
some different speed, V,
For example, if an airplane in steady level flight
is operated at.twice as great a speed, the in-
duced drag is one-fourth the original value but
the induced power required is one-half the
original value.
The parasite power required is a function
of the parasite drag and velocity.
where
Pr,=parasite power required, h.p.
D,=paraSite drag, lbs.
V= true airspeed, knots
Thus, parasite power required will vary with
altitude and equivalent parasite area ( f) in the
same manner as ‘the parasite drag. However,
the variation with speed will be different. If
all other factors are constant, the parasite drag
varies as the square of velocity but parasite
power varies as the cube of velocity.
Pb% v* 3
-=(-I Ph VI
where
Prpl= parasite power required corresponding to
some original speed, Vi
NAVWEPS 00-8OT-80
AIRPLANE PERFORMAN:CE
PrPs=parasite power required corresponding to
some different speed, I’,
For example, if an airplane in steady flight is
operated at twice as great a speed, the parasite
drag is four times as great but the parasite
~;;zr required is eight times the original
Figure 2.1 presents the thrust required and
power required for a specific airplane configu-
ration and altitude. The curves of figure 2.1
are applicable for the following airplane data:
gross weight, W= 15,000 Ibs.
span, b=40 ft.
equivalent parasite area, f=7.2 sq. ft.
airplane efficiency factor, c= ,827
sea level altitude, C= 1.000
compressibility corrections neglected
The curve of drag or thrust required versus
velocity shows the variation of induced, para-
site, and total drag. Induced drag predomi-
nates at low speeds. When the airplane is
operated at maximum lift-drag ratio, (L/D)-,
the total drag is at a minimum and the induced
and parasite drags are equal. For the specific
airplane of figure 2.1, (,L/D),, and minimum
total drag are obtained at a speed of 160 knots.
The curve of power required versus velocity
shows the variation of induced, parasite, and
total power required. As before, induced
power required predominates at low speeds and
parasite power required predominates at high
speeds and the induced and parasite power are
equal at (L/D),,. However, the condition of
(L/D&- defines only the point of minimum
drag and does not define the point of minimum
pozver required. Ordinarily, the point of mini-
mum power required will occur at a speed
which is 76 percent of the speed for minimum
drag and, in the case of the airplane configura-
tion of figure 2.1, the speed for minimum power
required would be 122 knots. The total drag
at the speed for minimum power required is 15
percent higher than the drag at (L/D)- but the
minimum power required is 12 percent lower
than the power required at (L/D)-.
97 | 114 | 114 | 00-80T-80.pdf |
NAVWEPS OO-ROT-80
AIRPLANE PERFORMANCE
Figure 2.1. Airplane Thrust and Power Required
96 | 115 | 115 | 00-80T-80.pdf |
NAVWEPS OO-.ROT-80
AtRPlANE PERFORMANCE
Induced drag predominates at speeds below
the point of minimum total drag. When the
airplane is operated at the condition of mini-
mum power required, the total drag is 75
percent induced drag and 25 percent parasite
drag. Thus, the induced drag is three times as
great as the parasite drag when at minimum
power required.
VARIATIONS OF THRUST REQUIRED AND
POWER REQUIRED
The curves of thrust required and power
required versus velocity provide the basis for
comprehensive analysis of all the major items
of airplane performance. The changes in the
drag and power curves with variations of air--
plane gross weight, configuration, and altitude
furnish insight for the ‘variation of range,
endurance, climb performance, etc., with these
same items.
The effect of a change in weight on the thrust
and power required is illustrated by figure 2.2.
1 The primary effect of a weight change is a
change in the induced drag and induced power
required at any given speed. Thus, the great-
est changes in the curves of thrust and power
required will take place in the range of low
speed flight where the induced effects pre-
dominate. The changes in thrust and power
required in the range of high speed flight are
relatively slight because parasite effects pre-
dominate at high speed. The induced effects
at high speed are relatively small and changes
in these items produce a small effect on the
total thrust or power required.
In addition to the general effect on .the in-
duced drag and power required at particular
speeds, a change in weight will require that the
airplane operate at different airspeeds to main-
tain conditions of a specific lift coefficient and
angle of attack. If the airplane is in steady
flight at a particular C,,, the airpseed required
for this CL will vary with weight in the fol-
lowing manner :
v, Tg -=J VI E
where
Vi = speed corresponding to a specific C,
and weight, W,
Va=speed corresponding to the same C,
but a different weight, Ws
For the example airplane of figure 2.2, a change
of gross weight from 15,000 to 22,500 lbs. re-
quires that the airplane operate at speeds which
are 22.5 percent greater to maintain a specific
lift coefficient. For example, if the 15,000-lb.
airplane operates at 160 knots for (L/D)-, the
speed for (L/D)mz at 22,500 lbs. is:
v, = VI@
=I&) 22,500
-\i- 15,000
= (160) (1.225)
= 196 knots
The same situation exists with respect to the
curves of power required where a change in
weight requires a change of speed to maintain
flight at a particular CL. For example, if the
15,000-lb. airplane achieves minimum power
required at 122 knots, an increase in weight to
22,500 Ibs. increases the speed for minimum
power required to 149 knots.
0f course, the thrust and power required at
specific lift coefficients are altered by changes in
weight. At a specific C,, any change in weight
causes a like change in thrust required, e.g., a
50-percent increase in weight causes a 50-per-
cent increase in thrust required at the same C,.
The effect of a weight change on the power re-
quired at a specific CL is a bit more complex be-
cause a change in speed accompanies the change
99
Revised January 1965 | 116 | 116 | 00-80T-80.pdf |
NAVWEPS OO-ROT-80
AIRPLANE PERFORMANCE
Figure 2.2. Effect of Weight on Thrust and Power Required | 117 | 117 | 00-80T-80.pdf |
in drag and there is a two-fold effect. A 50-
percent increase in weight produces an increase
of 83.8 percent in the power required to main-
tain a specific CL. This is the result of a 50-
percent increase in thrust required coupled with
a 22.5-percent increase in speed. The effect of a
weight change on thrust required, power re-
quired, and airspeed at specific angles of attack
and lift coefficients provides an important basis
for various techniques of cruise and endurance
conditions of flight.
1 Figure 2.3 illustrates the effect on the curves
of thrust and power required of a change in the
equivalent parasite area,!, of the configuration.
Since parasite drag predominates in the region
of high flight speed, a change in f will produce
the greatest change in thrust and power re-
quired at high speed. Since parasite drag is
relatively small in the region of low speed
flight, a change in f will produce relatively
small changes in thrust and power required at
low speeds. The principal effect of a change in
equivalent parasite area of the configuration is
to change the parasite drag at any given air-
speed.
The curves of figure 2.3 depict the changes in
the curves of thrust and power required due
to a 50 percent increase in equivalent parasite
area of the configuration. The minimum total
drag is increased by an increase in f and the
GWL is reduced. ‘Also, the increase in f
will increase the CL for (L/D)- and require a
reduction in speed at the new, but decreased,
(L/D)-. The point of minimum power re-
quired occurs at a lower airspeed and the value
of the minimum power required is increased
slightly. Generally, the effect on the mini-
mum power required is slight because the para-
site drag is only 25 percent of the total at this
specific condition of flight.
An increase in the equivalent parasite area
of an airplane may he brought about by the
deflection of flaps, extension of landing gear,
extension of speed brakes, addition of external
stores, etc. In such instances a decrease in the
airplane efficiency factor, c, may accompany
NAVWEPS 00-501-50
AMPLANE PERFORMANCE
an increase in f to account for the additional
changes in parasite drag which may vary with
C‘.
A change in altitude can produce signifi-
cant changes in the curves of thrust and power
required. The effects of altitude on these
curves providea great part of the explanation of
the effect of altitude on range and endurance.
Figure 2.4 illustrates the effect of a change in
altitude on the curves of thrust and power re-
quired for a specific airplane configuration and
gross weight. As long as compressibility
effects are negligible, the principal effect of
increased altitude on the curve of thrust re-
quired is that specific aerodynamic conditions
occur at higher true airspeeds. For example,
the subject airplane at sea level has a minimum
drag of 1,250 lbs. at 160 knots. The same
airplane would incur the same drag at altitude
if operated at the same cqthdcnt airsprcd of 160
knots. However, the equivalent airspeed of
160 knots at 22,000 ft. altitude would produce
a true airspeed of 227 knots. Thus, an in-
crease in altitude will cause the curve of thrust
required to flatten out and move to the direc-
tion of higher velocity. Note that altitude
alone will not alter the value of minimum drag.
The effect of altitude on the curve of power
required can best be considered from the effect
on true airspeed to achieve a specific aero-
dynamic condition. The sea level power re-
quired curve of figure 2.4 indicates that
CW>mz occurs at 160 knots and requires 615
h.p. If this same airplane is operated at
WD)ma at an altitude of 22,000 ft., the same
drag is incurred at a higher velocity and re-
quires a higher power. The increase in ve-
locity to 227 knots accounts for the increase
in power required to 872 hp. Actually, the
various points on the curve of power required
can be considered affected in this same fashion.
At specific lift coefficients and angles of attack,
a change in altitude will alter the true airspeed
particular to these points and cause a change
in power required because of the change in
true airspeed. An increase in altitude will
101
Revised Januaty 1965 | 118 | 118 | 00-80T-80.pdf |
NAVWEPS 00-8OT-80
AIRPLANE PERFORMANCE
VELOCITY-KNOTS
VELOCITY-KNOTS
Figure 2.3. Effect of Equivalent Parasite Area, f, on Thrust and Power Required | 119 | 119 | 00-80T-80.pdf |
NAVWEPS Oo-8oT-80
AIRPLANE PERFORMANCE
THRUST
REQUIRED
(LB9
VELOCITY-KNOTS (TAS)
POWER
REK?
:D
VELOCITY-KNOTS (TAS)
Figure 2.4. Ekf of Altitude on Thrust and Power Required
103 | 120 | 120 | 00-80T-80.pdf |
NAVWEPS 00-8OT-80
AIRPLANE PERFORMANCE
cause the power required curve to flatten out
and move to higher velocities and powers
required.
The curves of thrust and power required and
their variation with weight, altitude, and con-
figuration are the basis of all phases of airplane
performance. These curves define the require-
lnent~ of the airplane and must be considered
with the power and thrust available from the
powerplants to provide detailed study of the
various items of airplane performance.
AVAILABLE THRUST AND POWER
PRINCIPLES OF PROPULSION
All powerplants have in common certain
general principles. Regardless of the type of
propulsion device, the development of thrust is
related by Newton’s laws of motion.
or
where
F=ma
F-d(mV)
df
$=force or thrust, lbs.
m=mass, slugs
a=acceleration, ft. per sec.%
d=derivative with respect to time, e.g.,
dr rate of change with time
mV=momentum, lb.-sec., product of mass
and velocity
The force of thrust results from the accelera-
tion provided the mass of working fluid. The
magnitude of thrust is accounted for by the
rate of change of momentum produced by the
powerplant. A rocket powerplant creates
thrust by creating a very large change in veloc-
ity of a relatively small mass of propellants.
A propeller produces thrust by creating a com-
paratively small change in velocity of a rela-
tively large mass of air.
The development of thrust by a turbojet or
ramjet powerplant is illustrated by figure 2.5.
Air approaches at a velocity, Vi, depending on
the flight speed and the powerplant operates
on a certain mass flow of air, Q, which passes
through the engine. Within the powerplant
the air is compressed, energy is added by the
burning of fuel, and the mass flow is expelled
from the nozzle finally reaching a velocity,
V;. The momentum change accomplished bv
this action produces the thrust,
where
Ttz=Q (V,V,)
Ta= thrust, lbs.
Q= mass flow, slugs per sec.
Vi= inlet (or flight) velocity, ft. per sec.
V,= jet velocity, ft. per sec.
The typical ramjct or turbojet powerplane de-
rives its thrust by working with a mass flow
relatively smaller than that of a propeller but
a relatively greater change of velocity. From
the previous equation it should be appreciated
that the jet thrust varies directly with the mass
flow Q, and velocity change, Va-Vi. This
fact is useful in accounting for many of the
performance characteristics of the jet power-
plant.
In the process of creating thrust by mo-
mentum change of the airstream, a relative
velocity, Vz-V1, is imparted to the airstream.
Thus, some of the available energy is essen-
tially wasted by this addition of kinetic energy
to the airstream. The change of kinetic energy
per time can account for the power wasted in
the airstream.
Pw=KE/t | 121 | 121 | 00-80T-80.pdf |
NAVWEPS Oo-ROT-80
AIRPLANE PERFORMANCE
F=mo
F=$(mV)
T, = Q (V,-V,)
Pa= T,, V,
Pw=Q/,(v2-v,)2
2VI 7)p=-
v2 +v,
1.0
.9
.6
.7
.6
7p .5
.4
.3
.2
.I
0
0 .I .2 .3 .4 .5 .6 .? .6 .9 1.0
%f2
Figure 2.5. Principles of Propulsion
105 | 122 | 122 | 00-80T-80.pdf |
NAWEPS 0040140
AlRPLANE PERFORMANCE
Of course, the development of thrus,t with
some finite mass flow will require some finite
velocity change and there will be the inevita-
ble waste of power in the airstream. In order
to achieve high efficiency of propulsion, the
thrust should be developed with a minimum
of wasted power.
The propulsion efficiency of the jet power-
plant can be evaluated by comparing the
propulsive output power with the input power.
Since the input power is the sum of the output
power and wasted power, an expression for
propulsion efficiency can be derived.
Pa
vp=Pa+Pw
zv,
')p= v*+v1
where
trp = propulsion efficiency
9=“eta”
Pa = propulsive power available
= TCZV~
Pw= power wasted
The resulting expression for propulsion effi-
ciency, v,,, shows a dependency on the flight
velocity, V,, and the jet velocity, VZ. When
the flight velocity is zero, the propulsion
efficiency is zero since all power generated is
wasted in the slipstream and the propulsive
power is zero. The propulsion efliciency would
be I.00 (or 100 percent) only when the flight
velocity, Vi, equals the jet velocity, Vz.
Actually, it would not be possible to produce
thrust under such conditions with a finite mass
flow. While 100 percent efficiency of propul-
sion can not be attained practically, some
insight is furnished to the means of creating
high values of propulsion efficiency. To ob
tain high propulsion efficiency it is necessary
to produce the required thrust with the highest
possible mass flow and lowest possible velocity
change.
The graph of figure 2.5 shows the variation
of propulsion efficiency, qP, with the ratio of
flight speed to jet velocity, VJV,. To achieve
a propulsion efficiency of 0.85 requires that the
flight velocity be approximately 75 percent of
the slipstream speed relative to the airplane.
Such a propulsive efficiency could be typical
of a propeller powered airplane which derives
its thrust by the propeller handling a large
mass flow of air. The typical turbojet power-
plant cannot achieve such high propulsive
ethciency because the thrust is derived with a
relatively smaller mass flow and larger vcloc-
ity change. For example, if the jet velocity is
1,200 ft. per sec. at a flight velocity of 600 ft.
per sec., the propulsion efficiency is 0.67. The
ducted fan, bypass jet, and turboprop are vari-
aCon -which impiove tliC propulsive efIiciency
of a type of powerplant which has very high
power capability.
When the conditions of range, endurance, or
economy of operation are predominant, high
propulsion efhciency is necessary. Thus, the
propeller powered airplane with its inherent
high propulsive efliciency will always find ap
plication. The requirements of very high
speed and high altitude demand very high
propulsive power from relatively small powcr-
plants. When there are practical limits to the
increase of mass flow, high output is obtained
by large velocity changes and low propulsive
efficiency is an inevitable consequence.
TURBOJET ENGINES
The turbojet engine has foundwidespread USC
in aircraft propulsion because of the relatively
high power output per powerplant weight and
size. Very few aircraft powerplants can com-
pare with the high output, flexibility, simplic-
ity, and small size of the aircraft gas turbine.
The coupling of the propeller and recipro-
cating engine is one of the most efficient means
106 | 123 | 123 | 00-80T-80.pdf |
known for converting fuel energy into propul-
sive energy. However, the intermittent action
of the reciprocating engine places practical
limits to the airflow that can be processed and
restricts the development of power. The con-
tinuous, steady flow feature of the gas turbine
allows such a powerplant to process consider-
ably greater airflow and, thus, utilize a greater
expenditure of fuel energy. While the pro-
pulsive efficiency of the turbojet engine is con-
siderably below that of the reciprocating en-
gine-propeller combination, the specific power
output of the turbojet at high speeds is quite
superior.
compressor pressure ratio should be high to
produce a high thermal efliciency in the engine
The area XCDZ represents the work done by
the compressor during the compression of the
unit weight of air. Of course, certain losses
and inefliciencies are incurred during the com-
pression and the power required to operate the
compressor will be greater than that indicated
by the work done on the engine airflow.
The operation of the turbojet engine involves
a relatively large change in velocity being im-
parted to the mass flow through the engine.
Figure 2.6 illustrates the operation of a typical
turbojet engine by considering the processing
given a unit weight of inlet airflow. Consider
a unit weight of ambient air approaching the
inlet to the engine then experiencing the
changes in pressure and volume as it is proc-
essed by’the turbojet. The chart of pressure
versus volume of figure 2.6 shows that the unit
weight of airflow at atmospheric condition A
is delivered to the inlet entrance at condition
B. The purpose of the inlet or diffuser as to
reduce the velocity and increase the pressure
of the flow entering the compressor section.
Thus, the aerodynamic compression produces
an increase in pressure and decrease in volume
of the unit weight of air and delivers air to
the compressor at condition C. The work done
by the aerodynamic compression of the inlet
ot diffuser is represented by the area ABCX.
Generally, most conventional turbojet engines
require that the compressor inlet flow be sub-
sonic and supersonic flight will involve con-
siderable aerodynamic compression in the inlet.
Compressed air is discharged from the com-
pressor to the combustion chamber at condition
D. Fuel is added in the combustion chamber,
and the combustion of fuel liberates consider-
able heat energy. The combustion process in
the gas turbine differs from that of the recipro-
cating engine in that the process is essentially
a constant pressure addition of heat energy.
As a result, the combustion of fuel causes a
large change in temperature and large change
of volume of the unit weight of airflow. The
process in the combustion chamber is repre-
sented by the change from point D to point E of
the pressure-volume diagram of figure 2.6.
Air delivered to the compressor inlet at con-
dition C is then subject to further compression
through the compressor section. As a result
of the function of the compressor, the unit
weight of air is subject to a decrease in volume
and increase in pressure to condition D. The
107
NAVWEPS 00-801-80
ARPLANE PERFORMANCE
The combustion products are delivered to the
turbine section where sufficient work must be
extracted to power the compressor section.
The combustion chamber discharges high tem-
perature, high pressure gas to the turbine where
a partial expansion is accomplished with a drop
in pressure and increase in volume to point F
on the pressure-volume diagram. The work
extracted from the unit weight of air by the
turbine section is represented by the area
ZEFY. As with the compressor, the actual
shaft work extracted by the turbine will differ
from that indicated by the pressure-volume
diagram because of certain losses incurred
through the turbine section. For steady, sta-
bilized operation of the turbojet engine the
power extracted by the turbine will equal the
power required to operate the compressor. If
the turbine power exceeds the compressor
power required, the engine will accelerate; if
the turbine power is less than the compressor
power required, the engine will decelerate. | 124 | 124 | 00-80T-80.pdf |
NAVWEPS 00-807-80
AIRPLANE PERFORMANCE
INLET OR
DIFFUSER COMPRESSOR
COMBUSTION TAILPIPE
CHAMBER TURBINE NOZZLE
TURBOJET ENGINE CYCLE
2
iiT! TURBINE WORK .
E
2
E Y
it
COMPRESSOR
I 1 c
VOLUME. CU. FT.
Figure 2.6. Turbojet Engines
108 | 125 | 125 | 00-80T-80.pdf |
The partial expansion of the gases through
the turbine will provide the power to operate
the engine. As. the gases are discharged from
the turbine at point F, expansion will continue
through the tailpipe nozzle. until atmospheric
pressure is achieved in the exhaust. Thus,
continued expansion in the jet nozzle will re-
duce the pressure and increase the volume of
the unit weight of air to point G on the pressure
volume diagram. As a result, the final jet
velocity is greater than the inlet velocity and
the momentum change necessary for the .de-
velopment of thrust ha~s’been created. The
area YFGA represents the work remaining to
provide the expansion to jet velocity after the
turbine has extracted the work requited to
operate the compressor.
Of course, the combustion chamber discharge
could be more completely expanded through a
larger turbine section and the net power could
be used to operate a propeller rather than pro-
vide high exhaust gas velocity. For certain
applications, the gas turbine-propeller combi-
nation could utilize the high power capability
of the gas turbine with greater propulsive
efficiency.
FUNCTION OF THE COMPONENTS.
Each of the engine components previously de-
scribed will contribute some function affecting
the efficiency and output of the turbojet engine.
For this reason, each of these components
should be analyzed to determine the requite-
ments for satisfactory operating characteristics.
The i&t or &@er must be matched to the
powerplant to provide the compressor entry
with the required airflow. Generally, the
compressor inlet must receive the required air-
flow at subsonic velocity with uniform dis-
tribution of velocity and direction at the
compressor face. The diffuser must capture
high energy air and deliver it at low Mach
number uniformly to the compressor. When
the inlet is along the sides of the fuselage, the
edges of the inlet must be located such that
the inlet receives only high energy air and
provision must be made to dispose of the
NAVWEPS OO-ROT-RO
AtRPlANE PERFORMANCE
boundary layer along the fuselage surface. At
supersonic flight speeds, the diffuser must slow
the air to subsonic with the least waste of
energy in the inlet air and accomplish the
process with a minimum of aerodynamic drag.
In addition, the inlet must be efIicient and
stable in operation throughout the range of
angles of attack and Mach numbers of which
the airplane is capable.
The operation of the compressor can be af-
fected greatly by the uniformity of flow at the
compressor face. When large variations in
flow velocity and direction exist at the face of
the axial compressor, the efficiency and stall-
surge limits are lowered. Thus, the flight
conditions which involve high angle of attack
and high sideslip can cause deterioration of
inlet performance.
The compreJ.ror s&on is one of the most im-
portant components of the turbojet engine.
The compressor must furnish the combustion
chamber with large quantities of high pressure
air in a most efficient manner. Since the com-
pressor of a jet engine has no direct cooling,
the compression process takes place with a
minimum of heat Ioss of the compressed air.
Any friction loss or inefficiency of the com-
pression process is manifested as an undesirable
additional increase in the temperature of the
compressor discharge air. Hence, compressor
efficiency will determine the compressor power
necessary to create the pressure rise of a given
airflow and will affect the temperature change
which can take place in the combustion
chamber.
The compressor section of a jet engine may
be an axial flow or centrifugal flow compressor.
The centrifugal flow compressor has great util-
ity, simplicity, and flexibility of operation.
The operation of the centrifugal compressor
requires relatively low inlet velocities and a
plenum chamber or expansion space must be
provided for the inlet. The impeller rotating
at high speed receives the inlet air and pto-
vides high acceleration by virtue of centrifugal
force. As a result, the air leaves the impeller
109 | 126 | 126 | 00-80T-80.pdf |
NAVWEPS GOdOT-
AIRPLANE PERFORMANCE
DWGLE ENTRY
CENfRlFuGAL COMPRESSCR
f-~&ARGE
CENTRIFUGAL COMPRESSOR
9A
AXIAL FLOW COMPRESSOR
STA’VM BLADES7
INLET
SHAFT7
COMPRESSOR BLADING
USCHARGE
ROTATING
Rows
Figure 2.7. Compressor Types
110 | 127 | 127 | 00-80T-80.pdf |
at very high velocity and high kinetic energy.
A pressure rise is produced by subsequent ex-
pansion in the diffuser manifold by converting
the kinetic energy into static pressure energy.
The manifold then distributes the high pres-
sure discharge to the combustion chambers.
A double entry impeller allows a given diam-
eter compressor to process a greater airflow.
The major components of the centrifugal com-
pressor are illustrated in figure 2.7.
The centrifugal compressor can provide a
relatively high pressure ratio per stage but the
provision of more than one or two stages is
rarely feasible for aircraft turbine engines.
The single stage centrifugal compressor is
capable of producing pressure ratios of about
three or four with reasonable efficiency. &es-
sure ratios greater than four require such high
impeller tip speed that compressor efficiency
decreases very rapidly. Since high pressure
ratios are necessary to achieve low fuel con-
sumption, the centrifugal compressor finds
greatest application to the smaller engines
where simplicity and flexibility of operation are
the principal requirements rather than high
efficiency.
The axial flow compressor consists of altet-
nate rows of rotating and stationary airfoils.
The major components of the axial flow com-
pressor ate illustrated in figure 2.7. A pressure
rise occurs through the row of rotating blades
since the airfoils cause a decrease in velocity
relative to the blades. Additional pressure
rise takes place through the row of stationary
blades since these airfoils cause a decrease in
the absolute velocity of flow. The decrease
I in velocity, relative or absolute, eEeLts a com-
1 ptession of the flow and causes the increase in
static pressure. While the pressure rise pet
stage of the axial compressor is relatively Jo%-,
the efficiency is very high and high pressure
ratios can be obtained efficiently by successive
axial stages. Of course, the eficient pressure
rise in each stage is limited by excessive gas
velocities. The multistage axial flow com-
pressor is capable of providing pressure ratios
NAWEPS 00-8OT-80
AIRPLANE PERFORMANCE
from five to ten (or greater) with efficiencies
which cannot be approached with a multi-
stage centrifugal compressor.
The axial flow compressor can provide
efficiently the high. pressure ratios necessary
for low fuel consumption. Also, the axial
compressor is capable of providing high air-
flow with a minimum of compressor diameter.
When compared with the centrifugal com-
pressor, the design and construction of the
axial compressor is relatively complex and
costly and the high efficiency is sustained over
a much narrower range of operating conditions.
For these reasons, the axial compressor finds
greatest application where rhe demands of
efficiency and output predominate over con-
siderations. of cost, simplicity, flexibility of
operation, etc. Multispool compressors and
variable statot blades serve to improve the
operating characteristics of the axial com-
pressor and increase the flexibility of operation.
The combustion chamber must convert the fuel
chemical energy into heat energy and cause a
large increase in the total energy of the engine
airflow. The combustion chamber will opet-
ate with one principal limitation: the dis-
charge from the combustion chamber must be
at temperatures which can be tolerated by the
turbine section. The combustion of liquid
hydrocarbon fuels can produce gas temperatures
which are in excess of 1,700 to 1,800° C.
However, the maximum continuous turbine
blade operating temperatures rarely exceed
NO0 to J,OOO” C and considerable excess air
must be used in the combustion chamber to
prevent exceeding these temperature limits.
While the combustion chamber design may
.take various forms and configurations, the
main features of a typical combustion chamber
ate illustrated by figure 2.8. The combustion
chamber receives the high pressure discharge
from the compressor and introduces apptoxi-
mately one half of this air into the immediate
area of the fuel spray. This primary combus-
tion air must be introduced with relatively
high turbulence and quite low velocities to
111
Revised Januwy 1965 | 128 | 128 | 00-80T-80.pdf |
NAVWEPS 00-80T-80
AIRPLANE PERFORMANCE
PRIMARY
COMBUSTION
AIR7
TYPICAL COMBUSTION CHAMBER
SECONDARY Al R
OR COOLING FLOW
FUEL
SPRAY
NOZZLE
DISCHARGE
TO TURBINE
NOZZLES
COMBUsTlON
NUCLEUS
TURBINE SECTION
TUR’BINE NOZZLE VANES
r / 11 TmaiNt BLADES
TURBINE WHEEL SHAFT
TURBIhE BLADING
(STATIONARY)
(ROTATING) TURBINE BLADES
Figure 2.8. Combustion Chamber and Turbine Components
112 | 129 | 129 | 00-80T-80.pdf |
maintain a nucleus of combustion in the com-
bustion chamber. In rhe normal combustion
process, the speed of flame propagation is quite
low and, if the local velocities are too high at
the forward end of the combustion chamber,
poor combustion will result and it is likely
rhar the flame will blow out. The secondary
air-or cooling flow-is introduced downstream
from the combustion nucleus to dilute the com-
bustion products and lower the discharge gas
temperature.
The fuel nozzle must provide a finely
atomized, evenly distributed spray of fuel
through a wide range of flow rates. Very
specialized design is necessary to provide a
nozzle with suitable characteristics. The
spray parrern and circulation in the combustion
chamber must make efficient use of the fuel by
complete combustion. The temperatures in
the combustion nucleus can exceed 1,700” to
1,SW’ C but the secondary air will dilute the
gas and reduce the temperature to some value
which can be tolerated in the turbine section.
A pressure drop will occur through the com-
bustion chamber to accelerate the combustion
gas rearward. In addition, turbulence and
fluid friction will cause a pressure drop but this
loss must be held to the minimum incurred by
providing complete combustion. Heat trans-
ferred through the walls of the combustion
chamber constitutes a loss of thermal energy
and should be held to a minimum. Thus, the
combustion chamber should enclose the com-
bustion space with a minimum of surface area
to minimize heat and friction losses. Hence,
the “annular” typ: combustion chamber offers
certain advantages over the multiple “can”
type combustion chamber.
The tur6inc section is the most critical element
of the turbojet engine. The function of the
turbine is to extract energy from the combus-
tion gases and furnish power to drive the com-
pressor and accessories. In the case of the
turboprop engine, the turbine section must ex-
tract a very large portion of the exhaust gas
NAVWEPS O(L8OT-80
AIRPLANE PERFORMANCE
energy to drive the propeller in addition to the
compressor and accessories.
The combustion chamber delivers high en-
ergy combustion gases to the turbine section at
high pressure and tolerable temperature. The
turbine nozzle vanes are a row of stationary
blades immediately ahead of the rotating tur-
bine. These blades form the nozzles which
discharge the combustion gases as high ve-
locity jets onto the rotating turbine. In this
manner, the high pressure energy of the com-
bustion gases is converted into kinetic energy
and a pressure and temperature drop takes
place. The function of the turbine blades
operating in these jets is to develop a tangen-
tial force along the turbine wheel thus extract-
ing mechanical energy from the combustion
gases. This is illustrated in figure 2.8.
The form of the turbine blades may be a com-
bination of two distinct types. The imp&c
type turbine relies upon the nozzle vanes to
accomplish the conversion of combustion gas
static pressure to high velocity jets. The
impulse turbine blades are shaped to produce
a large deflection of the gas and develop the
tangential force by the flow direction change.
In such a design, negligible velocity and pres-
sure drop occurs with the flow across the tur-
bine rotor blades. The reaction type turbine
differs in that large velocity and pressure
changes occur across the turbine rotor blades.
In the reaction turbine, rhe stationary nozzle
vanes serve only to guide the combustion gas
onto the turbine rotor with negligible changes
in velocity and pressure. The reaction tur-
bine rotor blades are shaped to provide a pres-
sure drop and velocity increase across the
blades and the reaction from this velocity in-
crease provides the tangential force on the
wheel. Generally, the turbine design is a
form utilizing some feature of each of the two
types.
The turbine blade is subjected to high
centrifugal stresses which vary as the square
of the rorative speed. In addition, the blade
113
Revised January 1965 | 130 | 130 | 00-80T-80.pdf |
NAVWEPS 00-801-80
AIRPLANE PERFORMANCE
is subjected to the bending and torsion of
the tangential impulse-reaction forces. The
blade must wirhstand these stresses which are
generally of a vibratory and cyclic nature
while at high temperatures. The elevated
temperatures at which the turbine must func-
tion produce extreme conditions for struc-
tural creep and fatigue considerations. Conse-
quently, the engine speed and temperature op-
erating limits demand very careful considera-
tion. Excessive engine temperatures or speeds
may produce damage which is immediately
apparent. However, creep and fatigue damage
is cumulative and even though damage may
not be immediately apparent by visual inspec-
tion, proper inspection methods (other than
visual) must be utilized and proper records
kept regarding the occurrence.
Actually, the development of high tempera-
ture alloys for turbines is a critical factor in the
develop,mcnt of high ei%ciciicy, high output
aircraft gas turbines. The higher the tem-
peratute of gases entering the turbine, the
higher can be the temperature and pressure of
the gases at discharge from the turbine with
greater exhaust jet velocity and thrust.
The function of the t&pipe or exhaust no?&
is to discharge the exhaust gases to the atmos-
phere at the highest possible velocity to pro-
duce the greatest momentum change and thrust.
If a majority of the expansion occurs through
the turbine section, there remains only to con-
duct the exhaust gases rearward with a mini-
mum energy loss. However, if the turbine
operates against a noticeable back pressure, the
nozzle must convert the remaining pressure
energy into exhaust gas velocity. Under ideal
conditions, the nozzle would expand the flow
to the ambient static pressure at the exhaust
and the area distribution in the nozzle must
provide these conditions. When the ratio af
exhaust gas pressure to ambient pressure is
relatively low and incapable of producing sonic
flow, a converging nozzle provides the expan-
sion. The exit area must be of proper size to
bring about proper exit conditions. If the exit
114
area is too large, incomplete expansion will
take place; if the exit area is too small, an over
expansion tendency results. The exit area can
affect the upstream conditions and must be
properly proportioned for overall performance.
When the ratio of exhaust gas pressure to
ambient pressure is greater than some critical
due, sonic flow can exist and the nozzle will
be choked or limited to some maximum flow.
When supersonic exhaust gas velocities are re-
quired to produce the necessary momentum
change, the expansion process will require the
convergent-divergent nozzle illustrated in fig-
ure 2.9. With sui?icient pressure available the
initial expansion in the converging portion is
subsonic increasing to sonic velocity at the
throat. Subsequent expansion in the divergent
portion of the nozzle is supersonic and the re-
sult is the highest exit velocity for a given
pressure ratio and mass flow. When the pres-
sure ratio is very high the final exit diameter
required to expand to ambient pressure may be
very large but is practically. limited to the
fuselage or nacelle afterbody diameter. If the
exhaust gases exceed sonic velocity, as is porsi-
ble in a ramjet combustion chamber or after-
burner section, only the divergent portion of
the nozzle may be necessary.
Figure 2.9 provides illustration of the func-
tion of the various engine components and the
changes in static pressure, temperature, and
velocity through the engine. The conditions
at the inlet provide the initial properties of the
engine airflow. The compressor section fur-
nishes the compression pressure rise with a
certain unavoidable but undesirable increase in
temperature. High pressure air delivered to
combustion chamber receives heat from the
combustion of fuel and experiences a rise in
temperature. The fuel flow is limited so that
the turbine inlet temperature is within limits
which can be tolerated by the turbine structure.
The combustion takes place at relatively con-
stant pressure and initially low velocity. Heat
addition then causes large increases in gas vol-
ume and flow velocity. | 131 | 131 | 00-80T-80.pdf |
NAVWEPS 00-801-80
AIRPLANE PERFORMANCE
NOZZLE TYPES
CONVERGENT NOZZLE CONMRGPIT-DDMRGENT NOZZLE
--3- ~--
ENGINE OPERATING CONOITIONS
COMPRESSOR TURBlElE EXHAUST
NOZZLE
STATIC
PRESSURE
INLET
TEMPERATURE
CHANGE
INLET
VELOCITY
CHANGE
INLEl
Figure 2.9. Exhaust Nozzle Types and Engine Operating Conditions
115 | 132 | 132 | 00-80T-80.pdf |
NAVWEPS 00-801-80
AIRPLANE PERFORMANCE
Generally, the overall fuel-air ratio of the
turbojet is quite low because of the limiting
turbine inlet temperature. The overall air-
fuel ratio is usually some value between 80 to
40 during ordinary operating conditions be-
cause of the large amount of secondary air or
cooling flow.
High temperature, high energy combustion
gas is delivered to the turbine section where
power is extracted to operate the compressor
section. Partial or near-complete expansion
can take place through the turbine section with
the accompanying pressure and tempcratute
drop. The exhaust nozzle completes the ex-
pansion by producing the final jet velocity and
momentum change necessary in the develop-
ment of thrust.
TURBOJET OPERATING CHARACTER-
ISTICS. The turbojet engine has many oper-
ating characteristics which are of great im-
portance to the various items of jet airp!ane
performance. Certain of these operating char-
acteristics will provide a strong influence on
the range, endurance, etc., of the jet-powered
airplane. Other operating characteristics will
require operating techniques which differ
greatly from more conventional powerplants.
The turbojet engine is essentially a thrust-
producing powerplant and the propulsive
power produced is a result of the flight speed.
The variation of available thrust with speed is
relatively small and the engine output is very
nearly constant with flight speed. The mo-
mentum change given the engine airflow de-
velops thrust by the following relationship:
where
Ta= thrust available, lbs.
Q=mass flow, slugs per sec.
vi=inlet or flight velocity, ft. per sec.
Va= jet velocity, ft. per see.
Since an increase in flight speed will increase
the magnitude of Vi, a constant thrust will be
obtained only if there is an increase in mass
flow, Q, or jet velocity, Vs, When at low
velocity, an increase in velocity will reduce
the velocity change through the engine with-
out a corresponding increase in mass flow and
the available thrust will decrease. At higher
velocity, the beneficial ram helps to overcome
this effect and the available thrust no longer
decreases, but increases with speed.
The propulsive power available from the
turbojet engine is the roduct of available
thrust and velocity. t T e propulsive horsc-
power available from the turbojet engine’is
related by the following expression:
pyav --
325
where
Pa=propulsive power available, h.p.
T.-*Le..;- ;--;11.1*~ LC‘--LL,IlLSL ‘t”.uiaOK, ibs.
V= flight velocity, knots
The factor of 321 evolves from the use of the
nautical unit of velocity and implies that
each pound of thrust developed at 325 knots
is the equivalent of one horsepower of propul-
sive power. Since the thrust of the turbojet
engine is essentially constant with speed, tht
power available increases almost linearly with
speed. In this sense, a turbojet with 5000 Ibs.
of thrust available could produce a propulsive
power of 3,ooO h.p. at 325 knots or 10,000
h.p. at 650 knots. The tremendous propulsive
power at high velocities is one of the principal
features of the turbojet engine. When the
engine RPM and operating altitude arc fixed,
the variation with speed of turbolet thrust and
power available is typified by the first graph
of figure 2.10.
The variation of thrust output with engine
speed is a factor of great importance in the
operation of the turbojet engine. By reason-
ing that static pressure changes depend on the
square of the flow velocity, the changer of
pressure throughout the turbojet engine would
116 | 133 | 133 | 00-80T-80.pdf |
be expected to vary as the square of the rota-
tive speed, N. However, since a variation in
rotative speed will alter airflow, fuel flow,
compressor and turbine efficiency, etc., the
thrust variation will be much greater than
just the second power of rotative speed. In-
stead of thrust being proportional to iV2, the
typical fixed geometry engine develops thrust
approximately proportional to N3.6. Of course,
such a variation is particular to constant alti-
tude and speed.
Figure 2.10 illustrates the variation of per-
cent maximum thrust with percent maximum
RPM for a ‘typical fixed geometry engine.
Typical values from this graph are as follows:
P<m#r ma%. RPM Pmwit IMX. tlJrw,r
100 loo (of course)
99 96.5
95 83.6
90 69.2
80 45.8
70 28.7
Note that in the top end of power output, each
1 percent RPM change causes a 3.5-percent
change in thrust output. This illustrates the
power of variation of thrust with rotative
speed which, iii this example, is N3.“. Also
note that the top 20 percent of RPM controls
more than half of the output thrust.
While the fixed geometry engine develops
thrust approximately proportional to Na.“, the
engine with variable geometrywill demonstrate
a much more powerful effect of rotative speed.
When the jet engine is equipped with a vari-
able nozzle, multispool compressor, variable
stator blades, etc., the engine is more likely
to develop thrust proportional to rotative
speed from values of N4.6 to N6.0. For ex-
ample, if a variable geometry engine develops
thrust proportional to Ns.‘, each one per cent
RPM change causes a 5.0-percent thrust change
at the top end of power output. Also, the
top 13 percent of RPM would control the top
50 percent of thrust output.
The powerful variation of thrust with engine
speed has certain ramifications which should
NAVWEPS 00-801-80
AlR,PlANE PERFORMANCE
be appreciated. If the turbojet powerplant
operates at less than the “trimmed” or adjusted
speed for maximum thrust, the deficiency of
thrust for takeoff may cause a considerable
increase in takeoff distance. During approach,
an excessively low RPM may cause very low
thrust and produce a very steep glide path.
In addition, the low RPM range involves the
much greater engine acceleration time to pro-
duce thrust for a waveoff. Another compli-
cation exists when the thrust is proportional
to some large power of rotative speed, e.g.,
Nb.O. The small changes in RPM produce
such large variations in thrust that instruments
other than the tachometer must be furnished
for accurate indication of thrust output.
The “specific fuel consumption, ci’ is an
important factor for evaluating the perform-
ance and efficiency of operation of a turbojet
engine. The specific fuel consumption is the
proportion between the fuel flow (in lbs. per
hr.) and the thrust (in lbs.). For example,
an engine which has a fuel flow of 14,000 lbs.
per hr. and a thrust of 12,500 lbs. has a specific
fuel consumption of:
Fuel flow
“= Thrust
14,000 lbs./hr.
‘I= 12,500 lbs.
c,=1.12 lbs./hr./lb.
Thus, each unit pound of thrust requires 1.12
lbs. per hr. fuel flow. Obviously, high engine
efficiency would be indicated by a low value of
c,. Typical values for turbojet engines with
relatively high pressure ratios range from 0.8
to 1.2 at design operating conditions in sub-
sonic flight. High energy fuels and greater
pressure ratios tend to produce the lower values
of ct. Supersonic flight with the attendant in-
let losses and high compressor inlet air tem-
peratures tend to increase the specific fuel con-
sumption to values of 1.2 to 2.0. Of course,
the use of an afterburner is quite inefficient | 134 | 134 | 00-80T-80.pdf |
NAVWEPS 00-801-80
AIRPLANE PERFORMANCE
VARIATION OF THRUST AN0 POWER WITH VELOCITY
/
/STATIC THRUST
.
THRUST
AvA’&?eLE
POWER
AVAILABLE
1
THRUST
AVAILABLE
/
/ AV!$%EHp’ E
(CONSTANT ALTITUDE 8 RPM)
VELOCITY, KNOTS
100
90
80
i-cl
PERCENT 6o
mmlgTM 50
40 1
30
20
IO 1
VARIATION OF THRUST WITH RPM
(CONSTANT ALTITUDE
a VELOCITY)
ThrN3.5
04 I I 1 0 1
0 IO 20 30 40 50 SO 70 80 90 100
PERCENT MAXIMUM RPM
I VARIATION OF SPECIFIC FUEL
CONSUMPTION WITH RPM
3.0
(CONSTANT ALTITUDE
8 VELOCITY)
sEzc 2.0
CONSUMPTION
ct 1.0
.T, * I I I I I I I I.
0 IO 20 30 40 50 60 70 80 90 100
PERCENT MAXIMUM RPM
Figure 2.10. Turbojet Performance
118 | 135 | 135 | 00-80T-80.pdf |
due to thc~ low combustion pressure and values
of c, from 2.0 to 4.0 are typical with aftet-
burner operation.
The turbojet engine usually has a strong
preference fot high RPM to produce low specif-
ic fuel consumption. Since the normal rated
thrust condition is a particular design point
for the engine, the minimum value of c, will
occur at or near this range of RPM. The
illustration of figure 2.10 shows a typical vati-
ation of c, with percent maximum RPM where
values of RPM less than 80 to 85 percent pro-
duce a specific fuel consumption much greater
than the minimum obtainable. This pref-
erence for high.RPM to obtain low values of
C, is very pronounced in the fixed geometry
engine. Turbojet engines with multispool
compressors tend to be less sensitive in this
respect and are more flexible in their operating
characteristics. Whenever low values of cI ate
necessary to obtain range or endurance, the
preference of the turboiet engine for the design
operating RPM can be a factor of great
influence.
Altitude is one factor which strongly affects
the performance of the turbojet engine. An
increase in altitude produces a decrease in
density and pressure and, if below the tropo-
pause, a decrease in temperature. If a typical
nonaftcrbutning turbojet engine is operated at
a constant RPM and true airspeed, the vatia-
tion of thtust and specific fuel consumption
with altitude can be approximated from figure
221. The variation of density in the standard
atmosphere is shown by the values of density
ratio at vatious altitudes. Typical values of
the density ratio at specific altitudes are as
follows:
Altitude, ft.: Dews@ ra#ie
scaleeel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Loo0
5,ooo.. :. . .a617
lO,coo.............................. .7385
.?2#XQ. .4976
35,cao . . . . . . . . . . . . . . . . . . . . . .3099
40,oal.. . . . .2462
~,OUO. . . . .lS32
NAVWEPS 00-8OT-80
AtRPlANE PERFORMANCE
If the fixed geometry engine is operated at a
constant V (TAS) in subsonic flight and con-
stant N (RPM) the inlet velocity, inlet ram,
and compressor pressure ratio are essentially
constant with altitude. An increase in alti-
tude then causes the engine air mass flow to
decrease in a manner very nearly identical to
the altitude density ratio. Of coutsc, this de-
crease in mass flow will produce a significant
e&ct on the output thrust of the engine.
Actually, the variation of thrust with altitude
is not quite as severe as the density variation
because favorable decreases in temperature
occut. The decrease in inlet air temperature
will provide a relatively greater combustion
gas &ergy and allow a greater jet velocity.
The increase in jet velocity somewhat offsets
the decrease in mass flow. Of course, an in-
crease in altitude provides lower temperatures
below the tropopause. Above the tropopause,
no further favorable decrease in temperature
takes place so a more rapid variation of thrust
will take place. The approximate variation
of thrust with altitude is represented by figure
2.11 and some typical values at specific alti-
tudes ate as follows :
RIrio of Tbrvrt at dri14 Altitude, ft. : ( ) Thi ti I,‘ bwl
Scalevel............................. 1.m
5,ooo................................ ,888
lO,ooo............................... .785
2o,ooo............................... ,604
35,Mx)............................... .392
40,Ko. .315
=Jo,ocQ ._._..,...._....._,.,.__.,..... .180
Since the change in density with altitude is
quite rapid at low altitude turbojet takeoff pet-
formance wil1 Abe greatly affected at high alti-
tude. Also note that the thrust at 35,000 ft.
is approximately 39 percent of the sea level
value.
The thrust added by the afterburner of a
turbojet engine is not affected so greatly by
altitude as the basic engine thrust. The use of
afterburner may provide a thrust increase of 50
percent at low altitude or as much as 100 per-
cent at high altitude.
119 | 136 | 136 | 00-80T-80.pdf |
kAVWEPS OO-EOT-80
AIRPLANE PERFORMANCE
50,ooc
45,ooc
40,ooc
35,ooc
30.000
t
I
0” 2 25,000
5 a
20,000
SEA
LEVEL’
\ I
\\ !
\ \\
CONSUMPTION
,FIXED GEOMETRY
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.6 0.9 1.0
RATIO OF WANTITY) AT ALTITUDE
(QUANTIT’I) AT SEA LEVEL
Figure 2.7 1. Approximate Eftect of Altitude on Engine Performance
120 | 137 | 137 | 00-80T-80.pdf |
When the inlet ram and compressor pressure
ratio is fixed, the principal factor affecting the
specific fuel consumption is the inlet air temp-
erature. When the inlet air temperature is
lowered, a given heat addition can provide
relatively greater changes in pressure or vol-
ume. As a result, a given thrust output
requires less fuel flow and the specific fuel con-
sumption, c,, is reduced. While the effect of
altitude on specific fuel consumption does not
compare with the effect on thrust output, the
variation is large enough to strongly influence
range and endurance conditions. Figure 2.11
illustrates a typical variation of specific fuel
consumption with altitude. Generally, the
specific fuel consumption decreases steadily
with altitude until the tropopause is reached
and the specific fuel consumption at this point
is approximately 80 percent of the sea level
value.
Above the tropopause the temperature is con-
stant and altitudes slightly above the tropo-
pause cause no further decrease in specific fuel
consumption. Actually, altitudes much above
the tropopause bring about a general deteriora-
tion of overall engine efficiency and the~spkific
fuel consumption begins an increase with
altitude. The extreme altitudes above the
tropopause produce low combustion chamber
pressures, low compressor Reynolds Numbers,
low fuel flow, etc. which are notconduci,ve to
high engine efficiency.
Because of the variation of c, with altitude,
the majority of turbojet engines achieve maxi-
mum efficiency at or above 35,000 ft. For this
reason, the turbojet airplane will find optimum
range and endurance conditions at. or above
35,000 ft. provided the aircraft is not thrust
or compressibility limited at these altitudes.
The governing apparatus of the turbojet engine
consists primarily of the, items which control
the flow of fuel to the engine. In addition,
there may be included certain functions which
operate variable nozzles, variable stator vanes,
variable inlets, etc. Generally, the fuel con-
trol and associated items should regulate fuel
NAVWEPS 00-8OT-80
AIRPLANE PERFORMANCE
flow, nozzle area, etc. to provide engine per-
formance scheduled by the throttle or power
lever. These regulatory functions provided
must account for variations in altitude, tem-
perature, and flight velocity.
One principal governing factor which must
be available is that a selected power setting
(RPM) must be maintained throughout a wide
range of flight conditions. Figure 2.12 illus-
trates the sariation of fuel flow with RPM for
a turbojet operating at a particular set of
flight conditions. Curve 1 depicts the varia-
tion with RPM of the fuel flow required for
stabilized, ste,ady state operation of the engine.
Each point along this curve 1 defines the fuel
flow which is necessary to achieve equilib-
rium at a given RPM. The steady state fuel
flow produces a turbine, power to equal the
compressor power requirement at a particular
RPM. The throttle position primarily com-
mands .a given, engine speed and, as changes
occur in the ambient pressure, temperature,
and flight speed, the .steady state fuel flow will . vary. The governing’ apparatus must account
for these variations in flight conditions and
maintain the power setting scheduled by
throtrle position.
In addition to the maintenance of steady
state operation, the fuel control and associ-
ated engine control itemsmust provide for the
transient conditions of engine acceleration and
deceleration. In order to accelerate the en-
gine, the fuel control must supply a fuel flow
greater than that required for steady state
operation to ,produce a’ turbine power greater
than the compressor power requirement. How-
ever, the additional fuel flow to accelerate the
engine must be controlled and regulated to
prevent any one or combination of the follow-
ing items:
(1) compressor stall or surge
(2) excessive turbine inlet temperature
(3) excessively rich fuel-air ratio which
may not sustain combustion
Generally, the stall-surge and turbine tem-
perature limits predominate to form an ac-
celeration fuel flow boundary typified by curve
121 | 138 | 138 | 00-80T-80.pdf |
NAVWEPS 00-807-80
AIRPLANE PERFORMANCE
ALL CURVES APPROPRIATE
FOR A PARTICULAR:
r
ALTITUDE
M&N NUMBER
BOUNDARY A&
DECELEFlATlON
BOUNDARY
MAFfGIN
w
E I (IDLE) N-RPM (MA%)
EXHAUST GAS
TEMPERATURE
RPM c
PRESSURE . _ . _ _ - - -
TEMPERATURE
rAILPIPE TOTAL
PRESSURE
Figure 2.12. Engine Governing and Instrumentation
122 | 139 | 139 | 00-80T-80.pdf |
2 of figure 2.12. Curve 2 of this illustration
defines an upper limit of fuel flow which can
be tolerated within stall-surge and tempera-
ture limits. The governing apparatus of the
engine must limit the acceleration fuel flow
within this boundary.
To appreciate the governing requirements
during the acceleration process, assume the
engine described in figure 2.12 is in steady state
stabilized operation at point A and it is desired
to acceler&the engine to maximum RPM and
stabilize:at point C. As the throttle is placed
at the position for maximum RPM, the fuel
control will increase the fuel flow to point B
to provide acceleration fuel flow. As the
engine accelerates and increases RPM, the fuel
control will continue to increase the fuel flow
within the acceleration boundary until the
engine speed approaches the controlled maxi-
mum RPM at point C. As the engine speed
nears the maximum at point C, the fuel contrcl’
will reduce fuel flow to produce stabilized oper-
ation at this point and prevent the engine
overspeeding the commanded RPM. Of course,
if the throttle is opened very gradually, the
acceleration fuel flow is barely above the steady
state condition and the engine does not ap-
proach the acceleration fuel flow boundary.
While this technique is recommended for
ordinary conditions to achieve trouble free
operation and good service life, the engine must
be capable of good acceleration to produce
rapid thrust changes for satisfactory flight
control.
In order for the powerplant to achieve mini-
mum acceleration times, the fuel control must
provide acceleration fuel flow as close as
practical to the acceleration boundary. Thus,
a maximum controlled acceleration may pro-
duce limiting turbine inlet temperatures or
slight incipient stall-surge of the compressor.
Proper maintenance and adjustment of the
engine governing apparatus is essential to
produce minimum acceleration times without
incurring excessive temperatures or heavy stall-
surge conditions.
NAVWEPS 00-8OT-30
AIRPLANE PERFORMANCE
During deceleration conditions, the mini-
mum allowable fuel flow is defined by the lean
limit to support combustion. If the fuel flow
is reduced below some critical value at each
RPM, lean blowout or flameout will occur.
This condition is illustrated by curve 3 of
figure 2.12 which forms the deceleration fuel
flow boundary. The governing apparatus must
regulate the deceleration fuel flow within this
boundary.
To appreciate the governing requirements
during the deceleration process, assume the
engine described in figure 2.12 is in stabilized,
steady state operation at point C and it is
desired to decelerate to idle conditions and
stabilize at point E. As the throttle is placed
at the position for idle RPM, the fuel control
will decrease the fuel flow to point D to provide
the deceleration fuel flow. As the engine
decelerates and decreases RPM, the fuel gov-
erning will continue to decrease the fuel flow
within the deceleration boundary until the idle
fuel flow is reached and RPM is established at
point E. Of course, if the throttle is closed
very slowly, the deceleration fuel flow is barely
below the steady state condition and the engine
does not approach the deceleration fuel flow
boundary. The fuel control must provide a
deceleration flow close to the boundary to
provide rapid decrease in thrust and satisfactory
flight control.
In most cases, the deceleration fuel flow
boundary is considerably below the steady
state fuel flow and no great problem exists in
obtaining satisfactory deceleration character-
istics. In fact, the greater problem is con-
cerned with obtaining proper acceleration
characteristics. For the majority of centrifu-
gal flow engines, the acceleration boundary is
set usually by temperature limiting conditions
rather than compressor surge conditions. Peak
operating efficiency of the centrifugal com-
pressor is obtained at flow conditions which
are below the surge limit, hence acceleration
fuel flow boundary is determined by turbine
temperature limits. The usual result is that
123 | 140 | 140 | 00-80T-80.pdf |
NAVWEPS 00-801-80
AIRPLANE PERFORMANCE
the centrifugal flow engine has relatively large
acceleration margins and good acceleration
characteristics result with the low rotational
inertia. The axial flow compressor must oper-
ate relatively close to the stall-surge limit to
obtain peak efficiency. Thus, the acceleration
fuel flow boundary for the axial flow engine is
set by these stall-surge limits which are more
immediate to steady state conditions than tur-
bine temperature limits. The fixed geometry
axial flow engine encounters relatively small
acceleration margins and, when compared to
the centrifugal flow engine with larger accel-
eration margins and lower rotational inertia,
has inferior acceleration characteristics. Cer-
tain variation of the axial flow engine such as
variable nozzles, variable stator blades, multi-
ple-spool compressors, etc., greatly improve
the acceleration characteristics.
A note of caution is appropriate at this
point. If the main fuel control and govern-
ing apparatus should malfunction or become
inoperative and an unmodulated secondary or
emergency system be substitued, extreme care
must be taken to avoid abrupt changes in
throttle position. In such a case, very gradual
movement of the throttle is necessary to ac-
complish changes in power setting without
excessive turbine temperatures, compressor
stall or surge, or flameout.
There are various instruments to relate irnr
portant items of turbojet engine performance.
Certain combinations of these instruments are
capable of immediately relating the thrust
output of the powerplant in a qualitative man-
ner. It is difficult to provide an instrument or
combination of instruments which immedi-
ately relate the thrust output in a ~arrantitativ~
manner. As a result, the pilot must rely on
a combination of instrument readings and judge
the output performance according to standard
values particular to the powerplant. Some of
the usual engine indicating instruments are as
follows :
(1) The tachometer provides indication of
engine speed, N, by percent of the maximum
RPM. Since the variation of thrust with
RPM is quite powerful, the tachometer in-
dication is a powerful reference.
(2) The exhaust gas temperature gauge
provides an important reference for engine
operating limitations. While the tempera-
ture probe may be located downstream from
the turbine (tailpipe or turbine discharge
temperature) the instrument should provide
an accurate reflection of temperatures up-
stream in the turbine section. The exhaust
gas temperature relates the energy change
accomplished by fuel addition.
(3) The fuel flowmeter can provide a fair
reflection of thrust output. and operating
efficiency. Operation at high density alti-
tude or high inlet air temperatures-reduces
the output thrust and this effect is related by
a reduction of fuel flow.
(4) The’ tailpipe total pressure (p+q in
the tailpipe) can be correlated with the jet
thrust for a given engine geometry and set of
operating conditions. The output thrust
can be related accurately with various com-
binations of compressor inlet total pressure,
tailpipe total pressure, ambient pressure and
temperature. Hence; pressure differential
(Ap), pressure ratio, and ,tailpipe total pres-
sure instruments can provide more accurate
immediate indications of output thrust than
combined indications of RPM and EGT.
This is especially true with variable geom-
etry or multiple spool engines.
Many other specialized instruments furnish
additional information for more detailed items
of engine performance. Various additional
engine information is realized from fuel pres-
sure, nozzle positions, compressor inlet air
temperature, etc.
TURBOJET OPERATING LIMITATIONS.
The operating characteristics of the turbojet
engine provide various operating limitations
which must be given due respect. Operation
of the powerplant within the specified limita-
tions is absolutely necessary in order to obtain | 141 | 141 | 00-80T-80.pdf |
the design service life with trouble-free opera-
tion. The following items describe the critical
areas encountered during the operational use
of the turbojet engine:
(1) The limiting exhaust gag tcmpcra;wcs pro-
vide the most important restrictions to the op-
eration of the turbojet engine. The turbine
components are subject to centrifugal loads of
rotation, impulse and reaction loads on the
blades, and various vibratory loads which may
be inherent with the design. When the turbine
components are subject to this variety of stress
in the presence of high temperature, two types
of structural phenomena must be considered.
when a part is subject to a certain stress at some
high temperature, weep failure will take place
after a period of time. Of course, an increase
in .tcmperature or stress will increase the rate
at which creep damage is accumulated and
reduce the time required to cause failure. An-
other problem results when a part is subjected
to a repeated or cyclic stress. F&&e failure
will occur after a number of cycles of a varying
stress. An increase in temperature or magni-
tude of cyclic stress will increase the rate of
fatigue damage and reduce the number of cycles
necessary to produce failure. It is important
to note that both fatigue and creep damage are
cumulative.
A gross overstress or overtemperature of the
turbine section will produce damage that is
immediately apparent. However, the creep
and fatigue damage accumulated through pe-
riods of less extreme’ overstress or overtem-
perature is more subtle. If the turbine is
sibject to repeated excessive temperatures, the
greatly increased rate of creep and fatigue
damage wiIl produce failure early within the
anticipated service life.
Generally, the operations which produce
the highest exhaust gas temperatures are
starting, acceleration, and maximum thrust
at high altitude. The time spent at these
temperatures must be limited arbitrarily to
prevent excessive accumulation of creep and
fatigue. Any time spent at temperatures in
NAVWEPS OO-SOT-RO
AIR.PLANE PERFORMANCE
excess of the operational limits for these con-
ditions will increase the possibility of early
failure of the turbine components.
While the turbine components are the most
critically stressed high temperature elements
they are not the only items. The combustion
chamber components may be critical at low
altitude where high combustion chamber pres-
sures exist. Also, the airframe structure and
equipment adjacent to the engine may be sub-
ject to quite high temperatures and require
provision to prevent damage by excess time at
high temperature.
(2) The c~mprcs~or Jtall or surge has the pos-
sibility of producing damaging temperatures
in the turbine and combustion chamber or un-
usual transient loads in the compressor. While
the stall-surge phenomenon is possible with
the centrifugal compressor, the more common
.occurrence is with the axial flow compressor.
Figure 2.13 depicts the pressure distribution
that may exist for steady state operation of
the engine. In order to accelerate the engine
to a greater speed, more fuel must be added to
increase the turbine power above that required
to operate the compressor.
Suppose that the fuel flow is increased be-
yond the steady state requirement without a
change in rotative speed. The increased com-
bustion chamber pressure due to the greater
fuel flow requires that the compressor dis-
charge pressure be higher. For the instant
before an engine speed change occurs, an in-
crease in compressor discharge pressure will be
accompanied by a decrease in compressor flow
velocity. The equivalent effect is illustrated
by the flow components onto the rotating com-
pressor blade of figure 2.13. One component
of velocity is due to rotation and this compo-
nent remains unchanged for a given rotative
velocity of the single blade. The axial flow
velocity for steady state operation combines
with rotational component to define a result-
ant velocity and direction. If the axial flow
component is reduced, the resultant velocity
and direction provide an increase in angle of
125 | 142 | 142 | 00-80T-80.pdf |
NAVWEPS 00-BOT-80
AIRPLANE PERFORMANCE
COMPRESSOR STALL
COMPRESSOR
COMBUSTION EXHAUST
CHAMBER T”RB,NE NOZZLE
PRESSURE RISE
LIMITED BY
STATIC
PRESSURE
CHANGE
INLET
INCREASED
BLADE ANGLE
ROTATING
COMPRESSOR
,STEADY STATE
AXIAL FLOW VEL
/ VELOCITY COMPONENT
DUE TO ROTATION
EFFECT OF INLET TEMPERATURE
-REDUCED AXIAL
FLOW VELOCITY
TEMPERATURE EXHAUST
CHANGE TEMPERATURE RISE
THROUGH COMBUSTION
-- CHAMBER
INLET
.OCITY
COMPRESSOR COMBUSTION TURBINE EXHAUST
CHAMBER NOZZLE
Figure 2.13. Effect of Compressor Stall ond Inlet Temperature on Engine Operation
126 | 143 | 143 | 00-80T-80.pdf |
attack for the rotating blade with a subsequent
increase in pressure rise. Of course, if the
change in angle of attack or pressure rise is
beyond some critical value, stall will occur.
While the stall phenomenon of a series of
rotating compressor blades differs from that
of a single airfoil section in a free airstream,
the cause and effect are essentially the same.
If an excessive pressure rise is required
through the compressor, stall may occur with
the attendant breakdown of stable, steady flow
through the compressor. As stall occurs, the
pressure rise drops and the compressor does not
furnish discharge at a pressure equal to the
combustion chamber pressure. As a result, a
flow reversal or backfire takes place. If the
stall is transient and intermittent, the indica-
tion will be the intermittent “bang” as back-
fire and flow reversal take place. If the stall
develops and becomes steady, strong vibration
and a loud (and possibly expensive) roar
develops from the continuous flow reversal.
The increase in compressor power required
tends to reduce RPM and the reduced airflow
and increased fuel flow cause rapid, immediate
rise in exhaust gas temperature. The pos-
sibility of damage is immediate with the steady
stall and recovery must be accomplished
quickly by reducing throttle setting, lowering
the airplane angle of attack, and increasing
airspeed. Generally, the compressor stall is
caused by one or a combination of the fol-
lowing items:
(ti) A malfunctioning fuel control or gov-
erning apparatus is a common cause. Proper
maintenance and adjustment is a necessity for
stall-free operation. The malfunctioning is
most usually apparent during engine
acceleration.
(6) Poor inlet conditions are typical at
high angles of attack and sideslip. These
conditions reduce inlet airflow and create
nonuniform flow conditions at the com-
pressor face. Of course, these conditions are
at the immediate control of the pilot.
NAVWEPS 00-801-80
AIRMANE Pl?RFORMANCE
(c) Very high altitude flight produces low
compressor Reynolds numbers and an effect
similar to that of airfoil sections. As a
decrease to low Reynolds numbers reduces
the section c&, very high altitudes reduce
the maximum pressure ratio of the com-
pressor. The reduced stall margins increase
the likelihood of compressor stall.
Thus, the recovery from a compressor stall
must entail reduction of throttle setting to
reduce fuel flow, lowering angle of attack and
sideslip and increasing airspeed to improve
inlet condition, and reducing altitude if high
altitude is a contributing factor.
(3) While the j7ameout is a rare occurrence
with modern engines, various malfunctions
and operating conditions allow the flameout to
remain a possibility. A uniform mixture of
fuel and air will sustain combustion within a
relatively wide range of fuel-air ratios. Com-
bustion can be sustained with a fuel-air ratio
as rich as one to five or as lean as one to twenty-
five. Fuel air ratios outside these limits will
not support combustion due to the deficiency
of air or deficiency of fuel. The characteristics
of the fuel nozzle and spray pattern as well as
the governing apoaratus must insure that the
nucleus of combt .,on is maintained through-
out the range of engine operation.
If the rich limit of fuel-air ratio is exceeded
in the combustion chamber, the flame will
blow out. While this condition is a pos-
sibility the more usual cause of a flameout is
exceeding the lean blowout limit. Any con-
dition which produces some fuel-air ratio
leaner than the lean limit of combustion will
produce a flameout. Any interruption of the
fuel supply could bring on this condition.
Fuel system failure, fuel system icing, or pro-
longed unusual attitudes could starve the flows
of fuel to the engine. It should be noted the
majority of aviation fuels are capable of
holding in solution a certain small amount of
water. If the aircraft is refueled with rela-
tively w&m fuel then flown to high altitude,
127 | 144 | 144 | 00-80T-80.pdf |
NAVWEPS OO-BOT-80
AIRPLANE PERFORMANCE
the lower temperatures can precipitate this
water out of solution in liquid or ice crystal
form.
High altitude flight produces relatively small
air mass flow through the engine and the rela-
tively low fuel flow rate. At these conditions
a malfunction of the fuel control and governing
apparatus could cause flameout. If the fuel
control allows excessively low fuel flow during
controlled deceleration, the lean blow out limit
may be exceeded. Also, if the governed idle
condition allows any deceleration below the
idle condition the engine will usually continue
to lose speed and flameout.
Restarting the engine in flight requires sufli-
cient RPM and airflow to allow stabilized op-
eration. Generally, the extremes of altitude
are most critical for attempted airstart.
(4) An increased compressor inlet air tcmpcra-
tare can have a profound effect on the output
tbLrust of 2 rnrhniet m&n,= ---“-,-- --o---. As shown in
figure 2.13, an increase in compressor inlet
temperature produces an even greater increase
in the compressor discharge temperature. Since
the turbine inlet temperature is limited to
some maximum value, any increase in com-
pressor discharge temperature will reduce the
temperature change which can take place in
the combustion chamber. Hence, the fuel flow
will be limited and a reduction in thrust is
incurred.
The effect of inlet air temperature on thrust
output has two special ramifications. At rakc-
off, a high ambient air temperature at a given
pressure altitude relates a high density altitude.
Thus, the takeoff thrust is reduced because of
low density and low mass flow. In addition
to the loss of thrust due to reduced mass flow,
thrust and fuel flow are reduced further be-
cause of the high compressor inlet temperature.
In flight at Sigh Mach number, the aerodynamic
heating will provide an increase in compressor
inlet temperature. Since the compressor inlet
temperature will reflect the compressor dis-
charge temperature and the allowable fuel
flow, the compressor inlet air temperature may
provide a convenient limit to sustained high
speed flight.
(5) The effect of engine overspeed or critical vi-
bration speed ranger is important in the service
life of an engine. One of the principal sources
of turbine loads is the centrifugal loads due to
rotation. Since the centrifugal loads vary as
the square of the rotative speed, a 5 percent
overspeed would produce 10.25 percent over-
stress (1.05*= 1.1025). The large increase in
stress with rorative speed could produce very
rapid accumulation of creep and fatigue dam-
age at high temperature. Repeated overspeed
and, hence, overstress can cause failure early
in the anticipated service life.
Since the turbojet engine is composed of
many different distributed masses and elastic
structure, there are certain vibra~tory modes
and frequencies for the shaft, blades, etc.
While it is necessary to prevent any resonant
conditions from existing within the normal
operating range, there may be certain vibra-
tory modes encountered in the low power range
common to ground operation, low altitude
endurance, acceleration or deceleration. If
certain operating RPM range restrictions are
specified due to vibratory conditions, opera-
tions must be conducted with a minimum of
time in this area. The greatly increased
stresses common to vibratory conditions are
quite likely to cause fatigue failures of the
offending components.
The operating limitations of the engine are
usually specified by various combinations of
RPM, exhaust gas temperature, and allowable
time. The conditions of high power output
and acceleration have relatively short times
allowable to prevent abuse of the powerplant
and obtain good service life. While the al-
lowable times at various high power and
acceleration condition appear arbitrary, the
purpose is to reduce the spectrum of loading
which contributes the most rapid accumulation
of creep and fatigue damage. In fact, in some
instances, the arbitrary time standards can be
set to suit the particular requirements of a
128 | 145 | 145 | 00-80T-80.pdf |
certain type of operation. Of course, the
effect on service life of any particular load
spectrum must be anticipated.
One exception to the arbitrary time standard
for operation at high temperatures or sus-
tained high powers is the case of the after-
burner operation. When the cooling flow is
only that necessary to prevent excessive tem-
peratures for adjacent structure and equipment,
sustained operation past a time limit may cause
damage to these items.
THRUST AUGMENTATION. Many op-
erating performance conditions may require
that additional thrust be provided for short
periods of time. Any means of augmenting
the thrust of the turbojet engine must be ac-
complished without an increase in engine speed
or maximum turbine section temperature. The
various forms of afterburning or water injection
allow the use of additional fuel to provide
thrust augmentation without increase in engine
speed or turbine temperature.
The aftsrbumer is a relatively simple means
of thrust augmentation and the principal fea-
tures are light weight and large thrust increase.
A typical afterburner installation may add only
10 to 20 percent of the basic engine wei,ght but
can provide a 40- to 60-percent increase in the
static sea level thrust. The afterburner con-
sists of an additional combustion area aft of
the turbine section with an arrangement of
fuel nozzles and flameholders. Because the
local flow velocities in the afterburner are
quite high, the flameholders are necessary to
provide the turbulence to maintain combustion
within the afterburner section. The turbojet
engine operates with airflows greatly in excess
of that chemically required to support combus-
tion of engine fuel. This is necessary because
of cooling requirements and turbine tempera-
ture limitations. Since only 15 to 30 percent
of the engine airflow is used in the combustion
chamber, the large excess air in the turbine
discharge can support combustion of large
amounts of additional fuel. Also, there are
no highly stressed, rotating members in the
NAVWEPS OO-EOT-80
AIRPLANE PERFORMANCE
afterburner and very high temperatures can be
tolerated. The combustion of fuel in the after-
burner brings additional increase in tempera-
ture and volume and\ adds considerable energy
to the exhaust. gases producing increased jet
velocity. The major components of the after-
burner are illustrated in figure 2.14.
One necessary feature of the turbojet engine
equipped with afterburner is a variable nozzle
area. As the afterburner begins functioning,
the exit nozzle area must increase to accom-
modate the increased combustion products.
If the afterburner were to begin functioning
without an increase in exit area, the mass flow
through the engine would drop and the tem-
peratures would increase rapidly. The nozzle
area must be controlled to increase as after-
burner combustion, begins. As a result, the
engine mass flow is given a large increase in
jet velocity with the corresponding increase in
thrust. .,
The combustion of fuel in the afterburner
takes place at low pressures and is relatively
inefficient. This basic inefficiency of the low
pressure combustion is given evidence by the
large increase in specific fuel combustion.
Generally, the use of afterburner at least will
double the specihtfuel consumption. As an
example, consider a turbojet engine capable
of producing 10,000 lbs. of thrust which can
develop 15,ooO lbs.. of thrust with the use of
afterburner. Typical values for specific fuel
consumption would. be c,= 1.05 for the basic
engine or t,= 2.1 when the afterburner is in
use. The fuel flow during operation would be
as follows:
fuel flow = (thrust) (specific fuel consump-
tion)
without afterburner,
fuel flow=(10,000) (1.05)
= 10,500 lbs./hr.
with afterburner,
fuel flow=(15,COO) (2.1)
=31,500 lbs./hr.
The low efficiency of the afterburner is illus-
trated by the additional 21,CCO lbs./hr. of fuel
flow to create the additional 5,ooO lbs. of
129 | 146 | 146 | 00-80T-80.pdf |
NAVWEPS 0040T-80
AIRPLANE PERFORMANCE
AFTERBURNER COMPONENTS
AFTt$lRNRNER
HOLDERS
PRE -COMPRESSOR
WATER INJECTION
WATER INJECTION
NOZZLES
CHAMBER NOZZLE
INJECTION
TURBINE-PROPELLER COMBINATION
REDUCTION
TURBINES
CHAMBER NOZZLE
Figure 2.14. Thrust Augmentation and the Gas Turbine-Propeller Combination
130 | 147 | 147 | 00-80T-80.pdf |
thrust. Because of the high fuel consumption
during afterburner operation and the adverse
effect on endurance, the use of the afterburner
should be limited to short periods of time.
In addition, there may be limited time for the
use of the afterburner due to critical heating
of supporting or adjacent structure in the vicin-
ity of the afterburner.
The specific fuel consumption of the basic
engine will increase with the addition of the
afterburner apparatus. The losses incurred by
the greater fluid friction, nozzle and flame-
holder pressure drop, etc. increase the specific
fuel consumption of the basic engine approxi-
mately 5 to 10 percent.
The principal advantage of afterburner is the
ability to add large amounts of thrust with
relatively small weight penalty. The applica-
tion of the afterburner is most common to the
interceptor, fighter, and high speed type
aircraft.
The use of wafer injection in the turbojet en-
gine is another means of thrust augmentation
which allows the combustion of additional fuel
within engine speed and temperature limits.
The most usual addition of water injection de-
vices is to supplement takeoff and climbout
performance, especially at high ambient tem-
peratures and high altitudes. The typical
water injection device can produce a 25 to 35
percent increase in thrust.
The most usual means of water injection is
direct flow of the fluid into the combustion
chamber. This is illustrated in figure 2.14.
The addition of the fluid directly into the com-
bustion chamber increases the mass flow and
reduces the turbine inlet temperature. The
drop in temperature reduces the turbine power
and a greater fuel flow is required to maintain
engine speed. Thus, the mass flow is increased,
more fuel flow is allowed within turbine limits,
and greater, energy is imparted to the exhaust
gases.
The fluid injected into the combustion cham-
bers is generally a mixture of water and alco-
hol. The water-alcohol solution has one
NAVWEPS 00-30T-30
AIRPLANE PERFORMAPJCE
immediate advantage in that it prevents fouling
of the plumbing from the freezing of residual
fluid at low temperatures. In addition, a large
concentration of alcohol in the mixture can
provide part of the additional chemical energy
required to maintain engine speed. In fact,
the large concentration of alcohol in the in-
jection mixture is a preferred means of adding
additional fuel energy. If the added chemical
energy is included with the water flow, no
abrupt changes in governed fuel flow are
necessary and there is less chance of underspeed
with fluid injection and overspeed or over-
temperature when fluid flow is exhausted. Of
course, strict proportions of the mixture are
necessary. Since most water injection devices
are essentially an unmodulated flow, the use
of this device is limited to high engine speed
and low altitude to prevent the water flow
from quenching combustion.
THE GAS TURBINE-PROPELLER COM-
BINATION. The turbojet engine utilizes the
turbine to extract suflicient power to operate
the compressor. The remaining exhaust gas
energy is utilized to provide the high exhaust
gas velocity and jet thrust. The propulsive
efficiency of the turbojet engine is relatively
low because thrust is produced by creating a
large velocity change with a relatively small
mass flow. The gas turbine-propeller combin-
ation is capable of producing higher propulsive
efficiency in subsonic flight by having the pro-
peller operate on a much greater mass flow.
The turboprop or propjet powerplant re-
quires additional turbine stages to continue
expansion in the turbine section and extract
a very large percent of the exhaust gas energy
as shaft power. In this sense, the turboprop
is primarily a power producing machine and
the jet thrust is a small amount of the output
propulsive power. Ordinarily, the jet thrust
of the turboprop accounts for 15 to 25 percent
of the total thrust output. Since the turbo-
prop is primarily a power producing machine,
131 | 148 | 148 | 00-80T-80.pdf |
3~PWbWtlOdWd 3NVldUlV
08-108-00 SdSMAVN | 149 | 149 | 00-80T-80.pdf |
the turboprop powerplant is rated by an
“equivalent shaft horsepower.”
T,y ESHP= BHP+325vp
where
ESHP=equivalent shaft horsepower
EHP= brake horsepower, or shaft horse-
power applied to the propeller
T,= jet thrust, lbs.
V=flight velocity, knots, TAS
‘1s = propeller efficiency
The gas turbine engine is capable of processing
large quantities of air and can produce high
output power for a given engine size. Thus,
the principal advantage of the turboprop
powerplant is the high specific power output,
high power per engine weight and high power
per engine size.
The gas turbine engine must operate at quite
high rotative speed to process large airflows
and produce high power. However, high
rotative speeds are not conducive to high
propeller efficiency because of compressibility
effects. A large reduction of shaft speed must
be provided in order to match the powerplant
and the propeller. The reduction gearing must
provide a propeller shaft speed which can be
utilized effectively by the propeller and, be-
cause of the high rotative speeds of the turbine,
gearing ratios of 6 to 15 may be typical. The
transmission of large shaft horsepower with
such high gearing involves considerable desi,gn
problems to provide good service life. The
problems of such gearing were one of the
greatest difficulties in the development of
turboprop powerplants.
The governing apparatus for the turboprop
powerplant must account for one additional
variable, the propeller blade angle. If the
propeller is governed separately from the tur-
bine, an interaction can exist between the
engine and propeller governers and various
“hunting,” overspeed, and overtemperature
conditions are possible. For this reason, the
NAVWEPS Oo-ROT-30
AIRPLANE PERFORMANCE
engine-propeller combination is operated at a
constant RPM throughout the major range of
output power and the principal variables ofcon-
trol are fuel flow and propeller blade angle.
In the major range of power output, the
throttle commands a certain fuel flow and the
propeller blade angle adjusts to increase the
propeller load and remain at the governed
speed.
The operating limitations of the turboprop
powerplant are quite similar in nature to the
operating limitations of the turbojet engine.
Generally, the turbine temperature limnations
are the most critical items. In addition, over-
speed conditions can produce overstress of the
gearing and propeller as well as overstress of
the turbine section.
The performance of the turboprop illustrates
the typical advantages of the propeller-engine
combination. Higher propulsive efficiency
and high thrust and low speeds provide the
characteristic of range, endurance, and takeoff
performance superior to the turbojet. As is
typical of all propeller equipped powerplants,
the power available is nearly constant with
speed. Because the power from the jet thrust
depends on velocity, the power available in-
creases slightly with speed. However, the
thrust available decreases with speed. The
equivalent shaft horsepower, ESHP, of the
turboprop is affected by mass ,flow and inlet
temperature in fashion similar to that of the
turbojet. Thus, the ESHP will vary with
altitude much like the thrust output of the
turbojet because the higher altitude produces
much lower density and engine mass flow.
The gas turbine-propeller combination utilizes
a number of turbine stages to extract shaft
power from the exhaust gases and, as high
compressor inlet temperatures reduce the fuel
flow allowable within turbine temperature
limits, hot days will cause a noticeable loss of
output power. Generally, the turboprop is
just as sensitive, if not more sensitive, to com-
pressor inlet air temperature as the turbojet
engine.
133 | 150 | 150 | 00-80T-80.pdf |
151 | 151 | 00-80T-80.pdf |
|
The specific fuel consumption of the turbo-
prop powerplant is defined as follows :
specific fuel consumption=
engine fuel flow
equivalent shaft horsepower
c=lbs. per hr.
ESHP
Typical values for specific fuel consumption, c,
range from 0.5 to 0.8 lbs. per hr. per ESHP.
The variation of specific fuel consumption with
operating conditions is similar to that of the
turbojet engine. The minimum specific fuel
consumption is obtained at relatively high
power setting and high altitudes. The low
inlet air temperature reduces the specific fuel
consumption and the lowest values of c are ob-
tained near altitudes of 25,ooO to 3900 ft.
Thus; the turboprop as well as the turbojet has
a preference for high altitude operation.
THE RECRIPROCATING ENGINE
The reciprocating engine is one of the most
efficient powerplants used for aircraft power.
The combination of the reciprocating engine
and propeller is one of the most efficient means
of converting the chemical energy of fuel into
flying time or distance. Because of the in-
herent high efficiency, the reciprocating engine
is an important type of aircraft powerplant.
OPERATING CHARACTERISTICS. The
function of the typical reciprocating engine in-
volves four strokes of the piston to complete
one operating cycle. This principal operating
cycle is illustrated in figure 2.15 by the varia-
tion of pressure and volume within the cylin-
der. The first stroke of the operating cycle is
the downstroke of the piston with the intake
valve open. This stroke draws in a charge of
fuel-air mixture along AB of the pressure-
volume diagram. The second stroke accom-
plishes compression of the fuel-air mixture
along line EC. Combustion is initiated by a
spark ignition apparatus and combustion takes
place in essentially a constant volume. The
combustion of the fuel-air mixture liberates
NAVWEPS 00-8OT-80
AlR,Pl.ANE PERFORMANCE
heat and causes the rise of pressure along line
CD. The power stroke utilizes the increased
pressure through the expansion along line DE.
Then the exhaust begins by the initial rejection
along line EB and is completed by the upstroke
along line BA.
The net work produced by the cycle of opera-
tion is idealized by the area BCDE on the
pressure-volume diagram of figure 2.15. Dur-
ing the actual rather than ideal cycle of op-
eration, the intake pressure is lower than the
exhaust pressure and the negative work repre-
sents a pumping loss. The incomplete expan-
sion during the power stroke represents a basic
loss in the operating cycle because of the re-
jection of combustion products along line EB.
The area EFB represents a basic loss in the
operating cycle because of the rejection of
combustion products along line EB. The area
EFB represents a certain amount of energy of
the exhaust gases, a part of which can be ex-
tracted by exhaust turbines as additional shaft
power to be coupled to the crankshaft (turbo-
compound engine) or to be used in operating a
supercharger (turbosupercharger). In addi-
tion, the exhaust gas energy may be utilized to
augment engine cooling flow (ejector exhaust)
and reduce cowl drag.
Since the net work produced during the op-
erating cycle is represented by the enclosed area
of pressure-volume diagram, the output of the
engine is affected by any factor which influences
this area. The weight of fuel-air mixture will
determine the energy released by combustion
and the weight of charge can be altered by
altitude,supercharging,etc. Mixturestrength,
preignition, spark timing, etc., can affect the
energy release of a given airflow and alter the
work produced during the operating cycle.
The mechanical work accomplished during
the power stroke is the result of the gas pres-
sure sustained on the piston. The linkage of
the piston to a crankshaft by the connecting
rod applies torque to the output shaft. During
this conversion of pressure energy to mechani-
cal energy, certain losses are inevitable because | 152 | 152 | 00-80T-80.pdf |
NAVWEPS 00-801-80
AIRPLANE PERFORMANCE
INTAKE COMPRESSION COMBUSTION POWER EXHAUST
RECIPROCATING ENGINE
OPERATING CYCLE
E
\ \
‘. -. -\
B ------==.f=
EXHAUST
4
VOLUME
Figure 2.15. Reciprocating Engines
136 | 153 | 153 | 00-80T-80.pdf |
of friction and the mechanical output is less
than the available pressure energy. The power
output from the engine will be determined by
the magnitude and rate of the power impulses.
In order to determine the power output of the
reciprocating engine, a brake or load device is
attached to the output shaft and the operating
characteristics are determined. Hence, the
term “brake” horsepower, BHP, is used to
denote the output power of the powerplant.
From the physical definition of “power” and
the particular unit of “horsepower” (1 h.p. =
33,ooO ft.-lbs. per min.), the brake horsepower
can be expressed in the following form.
BHP=G
or
TN
BHP= 5255
where
BHP= brake horsepower
T=output torque, ft.-lbs.
N=output shaft speed, RPM
In this relationship, the output power is ap-
preciated as some direct variable of torque, T,
and RPM. Of course, the output torque is
some function of the combustion gas pressure
during the power stroke. Thus, it is helpful
to consider the mean effective gas pressure
during the power stroke, the “brake mean
effective pressure” or BMEP. With use of
this term, the BHP can be expressed in the
following form.
BHP=@MEP)(D)(N) 792,m
where
BHP= brake horsepower
BMEP= brake mean effective pressure, psi
D=engine displacement, cu. in.
N= engine speed, RPM
The BMEP is not actual pressure within the
cylinder, but an effective pressure representing
the mean gas load acting on the piston during
NAVWEPS 00401-30
AlRPlANE PERFORMANCE
the power stroke. As such, BMEP is a con-
venient index for a majority of items of recip-
rocating engine output, efficiency, and operat-
ing limitations.
The actual power output of any reciptocat-
ing engine is a direct function of the combina-
tion of engine torque and rotative speed.
Thus, output brake horsepower can be related
by the combination of BMEP and RPM or
torque prc~surc and RPM. No other engine
instruments can provide this immediate indi-
cation of output power.
If all other factors are constant, the engine
power output is directly related to the engine
airflow. Evidence of this fact could be appre-
ciated from the equation for BHP in terms of
BMEP.
BHP = @M.W(DXN)
792,000
This equation relates that, for a given BMEP,
the BHP is determined by the product of en-
gine RPM, N, and displacement, D. In a
sense, the reciprocating engine could be con-
sidered primarily as an air pump with the
pump capacity directly affecting the power
output. Thus, any engine instrumems which
relate factors affecting airflow can provide some
indirect reflection of engine power. The pres-
sure and temperature of the fuel-air mixture
decide the density of the mixture entering the
cylinder. The carburetor air temperature will
provide the temperature of the inlet air at the
carburetor. While this carburetor inlet air
is not the same temperature as the air in the
cylinder inlet manifold, the carburetor inlet
temperature provides a stable indication inde-
pendent of fuel flow and can be used as a stand-
ard of performance. Cylinder inlet manifold
temperature is difficult to determine with the
same degree of accuracy because of the normal
variation of fuel-air mixture strength. The
inlet manifold pressure provides an additional
indication of the density of airflow entering the
combustion chamber. The manifold absolute
pressure, MAP, is affected by the carburetor
137 | 154 | 154 | 00-80T-80.pdf |
NAVWEPS 00-801-80
AIRPLANE PRRFORMANCE
inlet pressure, throttle position, and super-
charger or impeller pressure ratio. Of course,
the throttle is the principal control of mani-
fold pressure and the throttling action controls
the pressure of the fuel-air mixture delivered
to the supercharger inlet. The pressure re-
ceived by the supercharger is magnified by
the supercharger in some proportion depend-
ing on impeller speed. Then the high pressure
mixture is delivered to the manifold.
Of course, the engine airflow is a function of
RPM for two reasons. A higher engine speed
increases the pumping rate and the volume flow
through the engine. Also, with the engine
driven supercharger or impeller, an increase in
engine speed increases the supercharger pres-
sure ratio. With the exception of near closed
throttle position, an increase in engine speed
will produce an increase in manifold pressure.
The many variables affecting the character
,.F the romL.,*r;nn :...^---” “1 L..,, c YYU”Cl”Y process a:e an I.n~“Lrant
subject of reciprocating engine operation.
Uniform mixtures of fuel and air will support
combustion between fuel-air ratios of approxi-
mately 0.04 and 0.20. The chemically correct
proportions of air and hydrocarbon fuel would
be 15 lbs. of air for each lb. of fuel, or a fuel-
air ratio of 0.067. This chemically correct, or
“stoichiometric,” fuel-air ratio would provide
the proportions of fuel and air to produce
maximum release of heat during combustion of
a grven weight of mixture. If the fuel-air
ratio were leaner than stoichiometric, the ex-
cess of air and deficiency of fuel would produce
lower combustion temperatures and reduced
heat release for a given weight of charge. If
the fuel-air ratio were richer than stoichio-
metric, the excess of fuel and deficiency of air
would produce lower combustion temperatures
and reduced heat release for a given weight of
charge.
The stoichiometric conditions would pro-
duce maximum heat release for ideal conditions
of combustion and may apply quite closely for
the individual cylinders of the low speed re-
ciprocating engine. Because of the effects of
flame propagation speed, fuel distribution,
temperature variation, etc., the maximum
power obtained with a fixed airflow occurs at
fuel-air ratios of approximately 0.07 to 0.08.
The first graph of figure 2.16 shows the varia-
tion of output power with fuel-air ratio for a
a constant engine airflow, i.e., constant RPM,
MAP, and CAT (carburetor air temperature);
Combustion can be supported by fuel-air ratios
just greater than .0.04 but the energy released
is insufficient to overcome pumping losses and
engine mechanical friction. Essentially, the
same result is obtained for the rich fuel-air
ratios just below 0.20. Fuel-air ratios be-
tween these limits produce varying amounts of
output power and the maximum power output
generally occurs at fuel-air ratios of approxi-
mately 0.07 to 0.08. Thus, this range of fuel-
air ratios which produces maximum power for
a given airflow is termed ,the “best power”
range. At jo,me lower range of f-ue;-air rariop,
a maximum of power per fuel-air ratio is ob-
tained and this the “best economy” range.
The best economy range generally occurs be-
tween fuel-air ratios of 0.05 and 0.07. When
maximum engine power is required for take-
off, fuel-air ratios greater than 0.08 are neces-
sary to suppress detonation. Hence, fuel-air
ratios of 0.09 to 0.11 are typical during this
operation.
The pattern of combustion in the cylinder is
best illustrated by the second graph of figure
2.16. The normal combustion process begins
by spark ignition toward the end of the com-
pression stroke. The electric spark provides
the beginning of combustion and a flame front
is propagated smoothly through the com-
pressed mixture. Such normal combustion is
shown by the plot of cylinder pressure versus
piston travel. Spark ignition begins a smooth
rise of cylinder pressure to some peak value
with subsequent expansion through the power
stroke. The variation of pressure with piston
travel must be controlled to achieve the great-
est net work during the cycle of operation.
138 | 155 | 155 | 00-80T-80.pdf |
PERCENT
POWEFI
CONSTANT
AIRFLOW
BEST
OVERLEAN WER-RICH
NAVWEPS 00-307-80
AIRPLANE PERFORMANCE
I FUEL-AIR RATIO
NORMAL COMBUSTION
SPARK
PLUG
DETONATION
FLAME PROPAGATION
BURNJNG IGNITION
FROM HOT SFfYT
NORMAL CCMBUSTION
COMPRESSION STROKE POWER STROKE
TOP CENTER :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::~:::::::::::::::::::::::::::~:::::::::::::::::::::::::::::::::::::::::::::::::::::::::~.:::::::~::::::::::::::~~~~~~~~~~~~~~~~~~~~~~ ::::::::::::::::::::::::::::::::::::::::::~::::~:::::::::::::::::::::::::::::::::::::::::::::::::::~::::::::::::::::::::::::::::~:::::::::::::::::::::::::::::::::::::::::::::::::::...~.............., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ .._..______._.,,.,.,,...................,......................,,...............,..... . . . . . . . . . . . . . . .
MAXIMUM
1 RATED TAKEOFF
CRUISE POWER 1 1 POWER
DETONATION
ENGINE AIRFLOW, LBS. PER HR.
Figure 2.16. Reciprocating Engine Operation
139 | 156 | 156 | 00-80T-80.pdf |
NAVWEPS 00-8OT-RO
AIRPLANE PERFORMANCE
Obviously, spark ignition timing is an impor-
tant factor controlling the initial rise of pres-
sure in the combustion chamber. The ignition
of the fuel mixture must begin at the proper
time to allow flame front propagation and the
release of heat to build up peak pressure for the
power stroke .
The speed of flame front propagation is a
major factor affecting the power output of the
reciprocating engine since this factor controls
the rate of heat release and rate of pressure rise
in the combustion chamber. For this reason,
dual ignition is necessary for powerplants of
high specific power output. Obviously, nor-
mal combustion can be accomplished more
rapidly with the propagation of two flame
fronts rather than one. The two sources of
ignition are able to accomplish the combus-
tion heat release and pressure rise in a shorter
period of time. Fuel-air ratio is another factor
affecting the flame propagation speed in the
combustion chamber. The maximum flame
propagation speed occurs near a fuel-air ratio
of 0.08 and, thus, maximum power output for
a given airflow will tend to occur at this value
rather than the stoichiometric value.
Two aberrations of the combustion process
are preignition and detonation. Preignition
is simply a premature ignition and flame f&t
propagation due to hot spots in the combustion
chamber. Various lead and carbon deposits
and feathered edges on metal surfaces can sup-
ply a glow ignition spot and begin a flame
propagation prior to normal spark ignition.
As shown on the graph of figure 2.16, pre-
ignition causes a premature rise of
pressure during the piston travel. As a result,
preignition combustion pressures and tempera-
tures will exceed normal combustion values and
are very likely to cause engine damage. Be-
cause of the premature rise of pressure toward
the end of the compression stroke, the net work
of the operating cycle is reduced. Preignition
is evidenced by a rise in cylinder head tempera-
ture and drop in BMEP or torque pressure.
Denotation offers the possibility of immedi-
ate destruction of the powerplant. The nor-
mal combustion process is initiated by the
spark and beginning of flame front propaga-
tion As the flame front is propagated, the
combustion chamber pressure and temperature
begin to rise. Under certain conditions of
high combustion pressure and temperature,
the mixture ahead of the advancing flame front
may suddenly explode with considerable vi-
olence and send strong detonation waves
through the combustion chamber. The result
is depicted by the graph of figure 2.16, whete:a
sharp, explosive increase in pressure takes place
with a subsequent reduction of the mean pres;
sure during the power stroke. Detonation
produces sharp explosive pressure peaks many
times greater than normal combustion1 Also,
the exploding gases radiate considerable heat
and cause excessive temperatures for many local
parts of the engine. The effects of heavy
detonation are so severe that structural damage
is the immediate result. Rapid rise of cylinder
head temperature, rapid drop in BMEP, and
loud, expensive noises are evidence of detona-
tion.
Detonation is not necessarily confined to. a
period after the beginning of normal flame front
propagation. With extremely low grades of
fuel, detonation can occur before normal igni-
tion. In addition, the high temperatures and
pressure caused by preignition will mean that
detonation is usually a corollary of preigniticn.
Detonation results from a sudden, unstable de-
composition of fuel at some critical combina-
tion of high temperature and pressure. Thus,
detonation is most likely to occur at any op
erating condition which produces high com-
bustion pressures and temperatures. Gener-
ally, high engine airflow and fuel-air ratios for
maximum heat release will produce the critical
conditions. High engine airflow is common
to high MAP and RPM and the engine is most
sensitive to CAT and fuel-air ratio in this
region.
140 | 157 | 157 | 00-80T-80.pdf |
NAVWEPS 00-8OT-80
AIRPLANE PERFORMANCE
cruise power is the upper limit of power that
can be utilized for this operation. Higher air-
flows and higher power wirhout a change in
fuel-air ratio will intersect the knee of the
detonation envelope.
The primary factor relating the efficiency of
operation of the reciprocating engine is the
brake specific fuel consumption, iWE%, or
simply c.
Brake suecific fuel consumution
The detonation properties of a fuel are de-
termined by the basic molecular structure of
the fuel and the various additives. The fuel
detonation properties are generally specified
by the antidetonation or antiknock qualities of
an octane rating. Since the antiknock proper-
ties of a high quality fuel may depend on the
mixture strength, provision must be made
in. the rating of fuels. Thus, a fuel grade of
IIS/ would relate a lean mixture antiknock
rating of 115 and a rich mixture antiknock
rating of 145. One of the most common opera-
tional causes of detonation is fuel contamina-
tion. An extremely small contamination of
high octane fuel with jet fuel can cause a serious
,decrease in the antiknock rating. Also, the
contamination of a high grade fuel with the
next lower grade will cause a noticeable loss of
antiknock quality.
The fuel metering requirements for an engine
are illustrated by the third graph of figure 2.16
which is a plot of fuel-air ratio versus engine
airflow. The carburetor must provide specific
fuel-air ratios throughout the range of engine
airflow to accommodate certain output power.
Most modern engines equipped with auto-
matic mixture control provide a scheduling of
fuel-air ratio for automatic rich or automatic
lean operation. The auto-rich scheduling usu-
ally provides a fuel-air ratio at or near the
maximum heat release value for the middle
range of airflows. However, at high airflows
a power enrichment must be provided to sup-
press detonation. The auto-rich schedule gen-
erally will provide an approximate fuel-air
ratio of 0.08 which increases to 0.10 or 0.11 at
the airflow for takeoff power. In addition,
the low airflow and mixture dilution that oc-
curs in the idle power range requires enrich-
ment for satisfactory operation.
The schedule of fuel-air ratios with an auto-
matic lean fuel-air ratio will automatically
provide maximum usable economy. If manual
leaning procedures are applicable a lower fuel-
air ratio may be necessary for maximum possi-
ble efficiency. The maximum continuous
I
engine fuel flow
= brake horsepower
C= lbs. per hr.
BHP
Typical minimum values for c range from 0.4
to 0.6 lbs. per hr. per BHP and most aircraft
powerplaots average 0.5. The turbocompound
engine is generally the most efficient because
of the power recovery turbines and can ap-
proach values of c=O.38 to 0.42. It should be
noted that the minimum values of specific fuel
consumption will be obtained only within the
range of cruise power operation, 30 to 60 per-
cent of the maximum power output. Gen-
erally, the conditions of minimum specific fuel
consumption are achieved with auto-lean or
manual lean scheduling of fuel-air ratios and
high BMEP and low RPM. The low RPM is
the usual requirement to minimize friction
horsepower and improve output efficiency.
The effect of &it&c is to reduce the engine
airflow and power output and supercharging
is necessary to maintain high power output
at high altitude. Since the basic engine is
able to process air only by the basic volume
displacement, the function of the supercharger
is to compress the inlet air and provide a
greater weight of air for the engine to process.
Of course, shaft power is necessary to operate
the engine driven supercharger and a tempera-
ture rise occurs through the supercharger com-
pression. The effect of various forms of super-
charging on altitude performance is illustrated
in figure 2.17.
The unsupercharged-or naturally aspi-
rated-engine has no means of providing a
141 | 158 | 158 | 00-80T-80.pdf |
NAVWEPS OO-ROT-RO
AIRPLANE PERFORMANCE
EFFECT OF SUPERCHARGING ON ALTITUDE
PERFORMANCE
UNAVAILABLE
\
J
LOW SLOWER
\ LIMIT MAP
_c U&Q f-
HIGH SLOWER
LIMIT MAf
\ b CONSTANT
N,D
Figure 2.17. Fffect of Supercharging on Altitude Performonce
142 | 159 | 159 | 00-80T-80.pdf |
manifold pressure any greater than the induc-
tion system inlet pressure. As altitude is
increased with full throttle and a governed
RPM, the airflow through the engine is
reduced and BHP decreases. The first forms of
supercharging were of relatively low pressure
ratio and the added airflow and power could
be handled at full throttle within detonation
limits. Such a “ground boosted” engine
would achieve higher output power at all
altitudes but an increase in altitude would
produce a decrease in manifold pressure, air-
flow, and power output.
More advanced forms of supercharging with
higher pressure ratios can produce very large
engine airflow. In fact, the typical case of
altitude supercharging will produce such high
airflow at low altitude operation that full
throttle operation cannot be utilized within
detonation limits. Figure 2.17 illustrates this
case for a typical two-speed engine driven
altitude supercharging installation. At sea
level, the limiting manifold pressure produces
a certain amount of BHP. Full throttle oper-
ation could produce a higher MAP and BHP
if detonation were not the problem. In this
case full throttle operation is unavailable
because of detonation limits. As altitude is
increased with the supercharger or “blower”
at low speed, the constant MAP is maintained
by opening the throttle and the BHP increases
above the sea level value because of the re-
duced exhaust back pressure. Opening the
throttle allows the supercharger inlet to re-
ceive the same inlet pressure and produce the
same MAP. Finally, the increase of altitude
will require full throttle to produce the con-
stant MAP with low blower and this point is
termed the “critical altitude” or “full throttle
height.” If altitude is increased beyond the
critical altitude, the engine MAP, airflow, and
BHP decrease.
The critical altitude with a particular super-
charger installation is specific to a given com-
bination of MAP and RPM. Obviously, a
lower MAP could be maintained to some
NAVWEPS OO-ROT-RO
AWIANE PERFORMANCE
higher altitude or a lower engine speed would
produce less supercharging and a given MAP
would require a greater throttle opening.
Generally, the most important critical alti-
tudes will be specified for maximum, rated,
and maximum cruise power conditions.
A change of the blower to a high speed will
provide greater supercharging but will require
more shaft power and incur a greater tempera-
ture rise. Thus, the high blower speed can
produce an increase in altitude performance
within the detonation limitations. The vari-
ation of BHP with altitude for the blower at
high speed shows an increase in critical alti-
tude and greater BHP than is obtainable in low
blower. Operation below the high blower
critical altitude requires some limiting mani-
fold pressure to remain within detonation
limits. It is apparent that the shift to high
blower is not required just past low blower
critical altitude but at the point where the
transition from low blower, full throttle to
high blower, limit hiAP will produce greater
BHP. Of course, if the blower speed is
increased without reducing the throttle
opening, an “overboost” can occur.
Since the exhaust gases have considerable
energy, exhaust turbines provide a source of
supercharger power. The turbosupercharger
(TB.S) allows control of the supercharger
speed and output to very high altitudes with
a variable discharge exhaust turbine (PDT).
The turbosupercharger is capable of providing
the engine airflow with increasing altitude by
increasing turbine and supercharger speed.
Critical altitude for the turbosupercharger is
usually defined by the altitude which produces
the limiting exhaust turbine speed.
The minimum specific fuel consumption of
the supercharged engine is not greatly affected
by altitudes less than the critical altitude. At
the maximum cruise power condition, specific
fuel consumption will decrease slightly with
an increase in altitude up to the critical
altitude. Above critical altitude, maximum
,cruise power cannot be maintained but the
143 | 160 | 160 | 00-80T-80.pdf |
NAVWEPS O&ROT-SO
AIRPLANE PERFORMANCE
specific fuel consumption is not adversely
affected as long as auto-lean or manual lean
power can be used at the cruise power setting.
One operating characteristic of the recipro-
cating engine is distinctly different from that
of the turbojet. Water vapor in the air will
cause a significant reduction in output power of
the reciprocating engine but a negligible loss
of thrust for the turbojet engine. This basic
difference exists because the reciprocating
engine operates with a fixed displacement and
all air processed is directly associated with the
combustion process. If water vapor enters the
induction system of the reciprocating engine,
the amount of air available for combustion is
reduced and, since most carburetors do not
distinguish water vapor from air, an enrich-
ment of the fuel-air ratio takes place. The
maximum power output at takeoff requires
fuel-air ratios richer than that for maximum
-haezt re1m.e rn ,, C,I+P- nnr:rLmm.c . . ..I1 *-IF- --A-“-\- “W . A....A c. b.IIA.cIIIIICIIL “1111 La&C
place with subsequent loss of power. The
turbojet operates with such great excess of air
that the combustion process essentially is
unaffected and the reduction of air mass flow
is the principal consideration. As an example,
extreme conditions which would produce high
specific humidity may cause a 3 percent thrust
loss for a turbojet but a 12 percent loss of BHP
for a reciprocating engine. Proper accounting
of the loss due to humidity is essential in the
operation of the reciprocating engine.
OPERATING LIMITATIONS. Recipro-
cating engines have achieved a great degree of
refinement and development and are one of the
most reliable of all types of aircraft power-
plants. However, reliable operation of the re-
ciprocating engine is obtained only by strict
adherence to the specific operating limitations.
The most important operating limitations of
the reciprocating engine are those provided to
ensure that detonation and preignition do not
take place. The pilot must ensure that proper
fuel grades are used that limit MAP, BMEP,
RPM, CAT, etc., are not exceeded. Since
Revised January 1965
144
heavy detonation or preignition is common to
the high airflow at maximum power, the most
likely chance of detonation or preignition is at
takeoff. In order to suppress detonation or
allow greater power for takeoff, water injec-
tion is often used in the reciprocating engine.
At high power’settings, the injection of the
water-alcohol mixture can replace the excess
fuel required to suppress detonation, and de-
richment provisions can reduce the fuel-air
ratio toward the value for maximum heat re-
lease. Thus, an increase in power will be ob-
tained by the better fuel-air ratio. In some
instances, a higher manifold pressure can be 1
utilized to produce additional power. The in-
jection fluid will require proportions of alcohol
and water quite different from the injection
fluid for jet engine thrust augmentation.
Since derichment of the fuel-air ratio is de-
sired, the anti-detonant injection (AOZ) will
rr\n+l;n ,Ir,.Le, :.. -.....^*;*:- r-^--..-.*--.:J..-l b”IICLIALI PlC”ll”l111 yu‘a”c’l’L~ L” pC”LuL Ic>luual
fluid from fouling the plumbing.
When the fuel grades are altered during oper-
ation and the engine must be’operated on a
next lower fuel grade, proper account must be
made for the change in the operating limita-
tions. This accounting must be made for the
maximum power for takeoff and the maximum
cruise power since both of these operating con-
ditions are near the detonation envelope. In
addition, when the higher grade of fuel again
becomes available, the higher operating,limits
cannot be used until it is sure chat no contamina-
tion exists from the lower grade fuel remaining
in the tanks.
Spark plug fouling can provide certain high
as well as low limits of operating temperatures.
When excessively low operating temperatures
are encountered, rapid carbon fouling of the
plugs will take place. On the other hand,
excessively high operating temperatures will
produce plug fouling from lead bromide de-
posits from the fuel additives.
Generally, the limited periods of time at
various high power settings are set to mini-
mize the accumulation of high rates of wear | 161 | 161 | 00-80T-80.pdf |
and fatigue damage. By minimizing the
amount of total time spent at high power
setting, greater overhaul life of the powerplant
can be achieved. This should not imply that
the-takeoff rating of the engine should not be
used. Actually, the use of the full maximum
power at takeoff will accumulate less total
engine wear than a reduced power setting at
the same RPM because of less time required to
climb to a given altitude or to accelerate to a
given speed.
The most severe rate of wear and fatigue
damage occurs at high RPM and low MAP.
High RPM produces high centrifugal loads
and reciprocating iuertia loads. When the
large reciprocating inertia loads are not cush-
ioned by high compression pressures, critical
resultant loads can be produced. Thus, op-
erating time at maximum RPM and MAP must
be held to a minimum and operation at mari-
mum RPM and low MAP must be avoided.
AIRCRAFT PROPELLERS
.The aircraft propeller functions to convert
the powerplant shaft horsepower into propul-
sive horsepower. The basic principles of pro-
pulsion apply to the propeller in that thrust is
produced by providing the airstream a mo-
mentum change. The propeller achieves high
propulsive ef?iciency by processing a relatively
large mass flow of air and imparting a rela-
tively small velocity change. The momentum
change created by propeller is shown by the
illustration of figure 2.18.
The action of the propeller can be idealized
by the assumption that the rotating propeller
is simply an actuating disc. As shown in fig-
ure 2.18, the inflow approaching the propeller
disc indicates converging streamlines with an
increase in velocity and drop in pressure. The
converging streamlines leaving the propeller
disc indicate a drop in pressure and increase in
velocity behind the propeller. The pressure
change through the disc results from the distri-
bution of thrust over the area of the propeller
NAVWEPS OO-EOT-80
AIRPLANE PERFORMANCE
disc. In this idealized propeller disc, the pres-
sure difference is uniformly distributed over the
disc area but the actual case is rather different
from this.
The final velocity of the propeller slipstream,
V,, is achieved some distance behind the pro-
peller. Because of the nature of the flow pat-
tern produced by the propeller, one half of the
total velocity change is produced as the flow
reaches the propeller disc. If the complete
velocity increase amounts to Za, the flow veloc-
ity has increased by the amount II at the pro-
peller disc. The propulsive e$icien~, vp, of the
ideal propeller could be expressed by the fol-
lowing relationship:
output power ?%I= . mput power
TV
‘I’= T(V+a)
where
v,=propulsive efficiency
T=thrust, lbs.
V=fligkt velocity, knots
IJ = velocity increment at the
propeller disc, knots
Since the final velocity, Vs, is the sum of total
velocity change 2a and the initial velocity,
V,, the propulsive efliciency rearranges to a
form identical to that for the turbojet.
2 VP’
1+ k 0
So, the same relationship exists as with the
turbojet engine in that high efficiency is de-
veloped by producing thrust with the highest
possible mass flow and smallest necessary
velocity change.
The actual propeller must be evaluated in a
more exact sense to appreciate the effect of
nonuniform disc loading, propeller blade drag
forces, interference flow between blades, etc.
With these differences from the ideal Propeller,
145 | 162 | 162 | 00-80T-80.pdf |
NAVWEPS 00-801-80
AIRPLANE PERFORMANCE
-- r PROPELLER DISC
--
---
“1 *-
~3
_ =“,.?*a
--- -
-- --
PRESSURE CHANGE
P;;;lW;;E THROUGH DISC
1 ,
DISTRIBUTION OF
ROTATIONAL FLOW COMPONENT
mDAT TIP
VORTEX
ii- 2.18. Rhuiples of Ropellerr
146 | 163 | 163 | 00-80T-80.pdf |
it is more appropriate to define propeller effi-
ciency in the following manner:
‘)~= output propulsive power
mput shaft horsepower
where
vP= propeller efficiency
T= propeller thrust
V= flight velocity, knots
BHP= brake horsepower applied to the
propeller
Many di,fferent factors govern the efficiency of
a propeller. Generally, a large diameter pro-
peller favors a high propeller efficiency from
the standpoint of large mass flow. However,
a powerful adverse effect on propeller efficiency
is produced by high tip speeds and conipressi-
bility effects. Of course, small diameter pro-
pellers favor low tip speeds. In addition, the
propeller and powerplant must be matched for
compatibility of output and efficiency.
In order to appreciate some of the principal
factors controlling the efficiency of a given
propeller, figure 2.18 Uustrates the distribu-
tion of rotative velocity along the rotating
propeller blade. These rotative velocities add
to the local inflow velocities to produce a
variation of resultant velocity and direction
along the blade. The typical distribution of
thrust along the propeller blade is shown with
the predominating thrust being located on the
outer portions of the blade. Note that the
propeller producing thrust develops a tip
vortex similar to the wing producing lift.
Evidence of this vortex can be seen by the con-
densation phenomenon occurring at this Ioca-
tion under certain atmospheric conditions.
The component velocities at a given propeller
blade section are shown by the diagram of
figure 2.18. The inflow velocity adds vec-
torially to the velocity due to rotation to pro-
duce an inclination of the resultant wind with
respect to the planes of rotation. This incli-
nation is termed + (phi), the effective pitch
NAVWEPS 00-8OL80
AiRPlANE PERFORMANCE
angle, and is a function of some proportion of
the flight velocity, V, and the velocity due to
rotation which is mD at the tip. The pro-
portions of these terms describe the propeller
“advance ratio”, J.
where
J=propeller advance ratio
V=flight velocity, ft. per sec.
n=propeller rotative speed, revolutions
per sec.
D = propeller diameter, ft.
The propeller blade angle, fi (beta), varies
throughout the length of the blade but a
representative value is measured at 75 percent
of the blade length from the hub.
Note that the difference between the effec-
tive pitch angle, 4, and the blade angle, 8,
determines an effective angle of attack for the
propeller blade section. Since the angle of
attack is the principal factor affecting the
efficiency of an airfoil section, it is reasonable
to make the analogy that the advance ratio, J,
and blade angle, 8, are the principal factors
affecting .propeller efficiency. The perform-
ance of a propelleris typified by the chart of
figure 2.19 which- illustrates the variation of
propeller efficiency, ~a, with advance ratio, J,
for various values of blade angle, 8. The
value of vP for each fl increases with J
until a peak is reached, then decreases. It is
apparent that a fixed pitch propeller may be
selected to provide suitable performance in a
narrow range of advance ratio but efficiency
would suffer considerably outside this range.
In order to provide high propeller efficiency
through a wide range of operation, the pro-
peller blade angle must be controllable. The
most convenient means of controlling the
propeller is the provision of a constant speed
governing apparatus. The constant speed gov-
erning feature is favorable from the standpoint
of engine operation in that engine output and
efficiency is positively controlled and governed.
147 | 164 | 164 | 00-80T-80.pdf |
NAVWEPS OO-ROT-RO
AIRPLANE PERFORMANCE
The governing of the engine-propeller combi-
nation will allow operation throughout a wide
range of power and speed while maintaining
efficient operation.
If the envelope of maximum propeller dfi-
ciency is available, the propulsive horsepower
available will appear as shown in the second
chart of figure 2.19. The propulsive power
available, Pa, is the product of the propeller
efficiency and applied shaft horsepower.
The propellers used on most large reciprocating
engines derive peak propeller efficiencies on the
order of s,=O.85 to 0.88. Of course, the peak
values are designed to occur at some specific
design condition. For example, the selection
of a propel!er for a !ong rasge transport wsuld
require matching of the engine-propeller com-
bination for peak efhciency at cruise condjtion.
On the other hand, selection of a propeller for
a utility or liaison type airplane would require
matching of the engine-propeller combination
to achieve high propulsive power at low speed
and high power for good takeoff and climb
performance.
Several special considerations must be made
for the application of aircraft propellers. In
the event of a powerplant malfunction or
failure, provision must be made to streamline
the propeller blades and reduce drag so that
flight may be continued on the remaining op-
erating engines. This is accomplished by
feathering the propeller blades which .stops
rotation and incurs a minimum of drag for the
inoperative engine. The necessity for feather-
ing is illustrated in figure 2.19 by the change
in equivalent parasite area, Af, with propeller
blade angle, 8, of a typical instaliation. When
the propeller blade angle is in the feathered
position, the change in parasite drag is at a
minimum and, in the case of a typical multi-
engine aircraft, the added parasite drag from
a single feathered propeller is a relatively small
contribution to the airpfane total drag.
At smaller blade angles near the Rat pitch
position, the drag added by the propeller is
very large. AC these small blade angles, the
propeller windmilling at high RPM can create
such a tremendous amount of drag that the
airplane may be uncontrollable. The propel-
ler windmilling at high speed in the low range
of blade angles can produce an increase in para-
site drag which may be as great as the parasite
drag of the basic airplane. An indication of
this powerful drag is seen by the hclieopter in
autorotation. The windmilling rotor is ca-
pable of producing autorotation rates ofdcscent
which approach that of a parachute canopy
with the identical disc area laading. THUS,
the propeller windmilling at high speed and
small blade angle can produce an cffccti+e
drag coefficient of the disc area which compares
with tha~t of a parachute canopy. The drag
and yawing moment caused by loss of power
at high engine-propeller speed is considerable
and the transient yawing displaccmcnt of the
aircraft’ may produce critical loads for the
vertical tail. For this reason, automatic
feathering may be a necessity rather than a
luxury.
The large drag which can be produced by
the rotating propeller can be utilized to im-
prove the stopping performance of the air-
plane. Rotation of the propekr blade to
small positive values or negative values with
applied power can produce large drag or re-
verse thrust. Since the thrust capability of the
propeller is quite high at low speeds, very
high deceleration can be provided by reverse
thrust alone,
The qs&zg limitatiar of the pmpcllcr are
closely associated with those of the Rower-
plant. Overspeed conditions are critical be-
cause of the large centrifugal loads and blade
twisting moments produced by an excessive
rotative speed. In addition, the propeller
blades will have various vibratory modes and
certain operating limitations may hc necessary
to prevent exciting resonant conditions. | 165 | 165 | 00-80T-80.pdf |
PRO~‘ELLER EFFICIENCY
ENVELOPE OF MAXIMUM EFFICIENCY
NAVWEPS 00-801-80
AIRPLANE PERFORMANCE
PROPELLER
EFFICIENCY
-lP
-I PROPELLER ADVANCE RATIO, J . . . . . . . . . . . . . . . . . . . . . ...... . . -.-................::::::::: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..~.~~.................................... . . . . . .._.........._................ ::::::::::::::::::::::::::::::::::::::::::::~~:~~~~~~~~~~~~~~~~~~~~::::::::~::::::: liiiiiii!lililliiiiiiiliiiii8iiliili::::::::::::::::::::::::::::~~~~~~~~~~~ ::::::::::: ::::::::::::::~~::::::::::::: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .,............._............................................. I..
--.
POWER AVAILABLE
\ \ BHP
---
POWER
AVAILABLE
HP
VELOCITY, KNOTS :::::::::::::::::::::::::::::::::::::::~:::::::::::::::::::::::::::::~::::::::::::::::::::::::::::::::.::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::~~~~~~~~~~.~: ::::::::::::::::::::::::::::::::::::::::::::::::::::::~::::::::::::::::::::::::::::::::::::::::::::::l::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::............~...,..~..~
PROPELLER DRAG CONTRIBUTION
CHANGE IN
EQUIVALENT
PARASITE
AREA
Af
-
FEATHEREO
POSITION
0 I5 30 45 60 90
PROPELLER BLADE ANGLE,P
Figure 2.79. Propeller Operation
149 | 166 | 166 | 00-80T-80.pdf |
MAWEPS 00-801-80
AIRPLANE PERFORMANCE
The various items of airplane performance
result from the combination of airplane and
powerplant characteristics. The aerodynamic
characteristics of the airplane generally define
the power and thrust requirements at various
conditions of flight while the powerplant
characteristics generally define the power and
thrust available at various conditions of flight.
The matching of the aerodynamic configura-
tion with the powerplant will be accomplished
to provide maximum performance at the speci-
fic design condition, e.g., range, endurance,
climb, etc.
STRAIGHT AND LEVEL FLlGHT
When the airyJane is in steady, level flight,
the condition of equilibrium must prevail.
The unaccelerated condition of flight is
achieved with the airplane trimmed for lift
equal to weight and the powerplant set for a
thrust to equal the airplane drag. In certain
conditions of airplane performance it is con-
venient to consider the airplane requirements
by the thnr$t required (or drag) while in other
cases it is more applicable to consider the
power re@red. Generally, the jet airplane will
require consideration of the thrust required
and the propeller airplane will require consid-
eration of the power required. Hence, the
airplane in steady level flight will require lift
equal to weight and thrust available equal to
thrust required (drag) or power available equal
to power required.
The variation of power required and thrust
required with velocity is illustrated in figure
2.20. Each specific curve of power or thrust
required is valid for a particular aerodynamic
configuration at a given weight and altitude.
These curves define the power or thrust re-
quired to achieve equilibrium, Jift-equal-
weight, constant altitude flight at various
airspeeds. As shown by the curves of figure
2.20, ifit is desired to operate the airplane at
the airspeed corresponding to point A, the
power or thrust required curves define a par-
ticular value of thrust or power that must be
made available from the powerplant ~to achieve
equilibrium. Some different airspeed such as
that corresponding to point B changes the
value of thrust or power required to achieve
equilibrium. Of course, the change of air-
speed to point B also would require a change
in angle of attack to maintain a constant lift
equal to the airplane weight. Similarly, to
establish airspeed and achieve equilibrium at
point C will require a particular angle of attack
and powerplant thrust or power. In this case,
flight at point C would be in the vicinity of
the minimum flying speed and a major portion
of the ,thrust or power required would be due
to induced drag.
The maximum level flight speed for the air-
plane will be obtained when the power :or
thrust required equals the maximum power or
thrust available from the powerplant. The
minimum level flight airspeed is not usually
defined by thrust or power requirement since
conditions of, stall or stability and control
problems generally predominate.
CLIMB PERFOLWANCE
During climbing flight, the airplane gains
potential energy by virtue of elevation. This
increase in potential energy during a climb is
provided by one, or a combination, of two
means: (1) expenditure of propulsive energy
above that required to maintain level flight or
(2) expenditure of airplane kinetic energy, i.e.,
loss of velocity by a zoom. Zooming for alti-
tude is a transient process of trading kinetic
energy for potential energy and is of considera-
ble importance for airplane configurations
which can operate at very high levels of kinetic
energy. However, the major portions of climb
performance for most airplanes is a near steady
process in which additional propulsive energy
is converted into potential energy. The funda-
mental parts of airplane climb performance in-
volve a flight condition where the airplane is
in equilibrium but not at constant altitude.
150 | 167 | 167 | 00-80T-80.pdf |
NAVWEPS OO-ROT-80
AIRPLANE PERFORMANCE
THRUST
c
1 WEIGHT
THRUST
REQUIRED
I
-MAXIMUM LEVEL
FLIGHT SPEED
VELOCITY
POWER
REQUIRED
- MAXIMUM LEVEL
FLIGHT SPEED
VELOCITY
Figure 2.20. Level Right Pedormancc
151 | 168 | 168 | 00-80T-80.pdf |
NAVWEPS OO-SOT-80
AIRPLANE PERFORMANCE
The forces acting on the airplane during a
climb are shown by the illustration of figure
2.21. When the airplane is in steady flight
with moderate angle of climb, the vertical
component of lift is very nearly the same as the
actual lift. Such climbing flight would exist
with the lift very nearly equal to the weight.
The net thrust of the powerplant may be in-
clined relative to the flight path but this effect
will be neglectec! for the sake of simplicity.
Note that the weight of the aircraft is vertical
but a component of weight will act aft along
the flight path.
If it is assumed that the aircraft is in a steady
climb with essentially small inclination of the
flight path, the summation of forces along the
flight path resolves to the following:
Forces forward= Forces aft
where
T= thrust available, lbs.
D= drag, lbs.
W= weight, lbs.
v=flight path inclination or angle ,of
climb, degrees (“gamma”)
This basic relationship neglects some of the
factors which may be of importance for air-
planes of very high climb performance. For
example, a more detailed consideration would
account for the inclination of thrust from the
flight path, lift not equal to weight, subse-
quent change of induced drag, etc. However,
this basic relationship will define the principal
factors affecting climb performance. With
this relationship established by the condition
of equilibrium, the following relationship
exists to express the trigonometric sine of the
climb angle, y:
T-D sin y=- W
This relationship simply states that, for a
given weight airplane, the angle of climb (7)
depends on the difference between thrust and
drag (T-D), or excess thrust. Of course,
when the excess thrust is zero (T-D=0 or
T=D), the inclination of, the flight path is
zero-and the airplane is in steady, level flight.
When the thrust is greater than the drag, the
excess thrust will allow a climb angle depend-
ing on the value of excess thrust. Also, when
the thrust is less than the drag. the deficiency
of thrust will allow an angle ~of descent.
The most immediate interest in the climb
angle performance involves obstacle clearance.
The maximum angle of climb would occur
where there exists the greatest difference be-
tweenthrust available and thrust required, i.e.,
maximum (T-D). Figure 2.21 illustrates the
climb angle performance with the curves of
thrust available and thrust required versus
velocity. The thrust required, or drag, curve
is nss,~pued to be ppw=n*~r;.rP nc CnmP +-+a! y.“- ..I‘..&. c “I ““IILL ‘, y
airplane configuration which could be powered
by either a turbojet or propeller type power-
plant. The thrust available curves included
are for a characteristic propeller powerplant
and jet powerplant operating at maximum
output.
The thrust curves for the representative pro-
peller aircraft show the typical propeller thrust
which is high at low velocities and decreases
with an. increase in velocity. For the pro-
peiler powered airplane, the maximum excess
thrust and angle of climb will occur at some
speed just above the stall speed. Thus, if it
is necessary to clear an obstacle after takeoff,
the propeller powered airplane will attain
maximum angle of climb at an airspeed con-
veniently close to-if not at-the takeoff
speed.
The thrust curves for the representative jet
aircraft show the typ~ical turbojet thrust which
is very nearly constant ~with speed. If the
thrust available is essentially constant with
speed, the maximum excess thrust and angle
of climb will occur where the thrust required
152 | 169 | 169 | 00-80T-80.pdf |
NAVWEPS OD-80T-80
AIRPLANE PERFORMANCE
w SIN ,-- COMPONENT OF WEIGHT
ALONG FLIGHT PATH
THRUST - - -- __---- AVAILABLE AVAILABLE
AND JET ACFT
THRUST
REOUIRED
LBS.
POWER
AVAILABLE
AND
POWER
REolYLRED
VELOCITY, KNOTS
l=‘a JET
Pr, POWER REOUIRED
POWER AVAILABLE
PROP ACFT
SPEED FOR MAX R.C., JET
SPEED FOR MAX R.C., PROP
I VELOCITY, KNOTS
Figure 2.21. Climb Performance
153 | 170 | 170 | 00-80T-80.pdf |
NAVWEPS 00-801-80
AIRPLANE PERFORMANCE
is at a minimum, (LID),. Thus, for maxi-
mum steady-state angle of climb, the turbojet
aircraft would be operated at the speed ,for
(L/D),. This poses somewhat of a problem
in determining the proper procedure for ob-
stacle clearance after takeoff. If the obstacle
is a considerable distance from the takeoff
point, the problem is essentially that of a long
term gain and steady state conditions will pre-
dominate. That is, acceleration from the take-
off speed to (L/D), speed will be favorable
because the maximum steady climb angle can
be attained. However, if the obstacle is a rela-
tively short distance from the takeoff point,
the additional distance required to accelerate
to (L/D),, speed may be detrimental and the
resulting situation may prove to be a short
term gain problem. In this case, it may prove
necessary to begin climb out at or near the take-
off speed or hold the aircraft on the runway
for extra speed and a subsequent zoom. The
problem is su&ciently varied that no general
conclusion can be applied to all jer aircraft and
particular procedures are specified for each air-
craft in the Flight Handbook.
Of greater general interest in climb per-
formance are the factors which affect the rate of
climb. The vertical velocity of an airplane
depends on the flight speed and the inclination
of the flight path. In fact, the rate of climb
is the vertical component of the flight path
velocity. By the diagram of figure 2.21, the
following relationship is developed:
since
RC- 101.3 V sin y
then
RC=101.3 V
a&
2-v with Pa=%
and Pr=&
where
RC=rate of climb, f.p.-.
P11=power available, h.p.
Pr=power re
W=weight, 1 %
uired, h.p.
s
and
V=true airspeed, knots
33,000 is the factor converting horsepower
to ft-lbs/min
101.3isthefactorconvertingknocstof.p.m.
The above relationship states that, for a given
weight airplane, the rate af climb (RC) depends
on the difference between the power available
and the power required (Pd- Pr), or excess
power. Of course, when the excess power is
zero (Pa-Pr=O or Pa== PI), the rate of climb
is zero and the airplane is in steady level flight.
When the power available is greater than the
power required, the excess power will, allow a
rate of climb specific to the magnitude of excess
power. Also, when the power available is
less than the power required, the deficiency of
power produces a rate of descent. This rela-
tionship provides the basis for an important
axiom of flight technique: “For the conditions
of steady flight, the power setting is the pri-
mary control of rate of climb or descent”.
One of the most important items of climb
performance is the maximum rate of climb.
By the previous equation for rate of climb,
maximum rate of climb would occur where
there exists the greatest difference between
power available and power required, i.e.,
maximum (Pa- Pr). Figure 2.21 illustrates
the climb rate performance with the curves of
power available and power required versus
velocity. The power required curve is again a
representative airplane which could be powered
by either a turbojet or propeller type power-
plant. The power available curves included
are for a characteristic propeller powerplant
and jet powerplant operating at maximum
output.
The power curves for the representative pro-
peller aircraft show a variation of propulsive
power typical of a reciprocating engine-pro-
peller combination. The maximum rate of
climb for this aircraft will occur at some speed
154
RevId J4mwy 1ws | 171 | 171 | 00-80T-80.pdf |
172 | 172 | 00-80T-80.pdf |
|
NAVWEPS 06801-80
AIRPLANE PERFORMANCE
near the speed for (L/D&-. There is no direct
relationship which establishes this situation
since the variation of propeller efficiency is the
principal factor accounting for the variation
of power available with velocity. In an ideal
sense, if the propeller efficiency were constant,
maximum rate of climb would occur at the
speed for minimum power required. How-
ever, in the actual case, the propeller efficiency
of the ordinary airplane will produce lower
power available at low velocity and cause the
maximum rate of climb to occur at a speed
greater than that for minimum power required.
The power curves for the representative. jet
aircraft show the near linear variation of power
available with velocity. The maximum rate
of climb for the typical jet airplane will occur
at some speed much higher than that for max-
imum rate of climb of the equivalent propeller
powered airplane. In part, this is accounted
for by the continued increase in power avail-
able with speed. Note that a 50 percent in-
increase in thrust by use of an afterburner may
cause an increase in rate of climb of approxi-
mately 100 percent.
The climb performance of an airplane is
affected by many various factors. The con-
ditions of maximum climb angle or climb rate
occur at specific speeds and variations in speed
will produce variations in climb performance.
Generally, there is sufficient latitude that small
variations in speed from the optimum do not
produce large changes in climb performance
and certain operational items may require
speeds slightly different from the optimum.
Of course, climb performance would be most
critical at high weight, high altitude, or dur-
ing malfunction of a powerplant. Then, opti-
mum climb speeds are necessary. A change
in airplane weight produces a twofold effect
on climb performance. First, the weight, W,
appears directly in denominator of the equa-
tions for ,both climb angle and climb rate.
In addition, a change in weight will alter the
drag and power required. Generally, an in-
crease in weight will reduce the maximum rate
156
of climb but the airplane must be operated at
some increase of speed to achieve the ,smaller
peak climb rate (unless the airplane is compres-
sibility limited).
The effect of altitude on climb performance
is illustrated by the composite graphs of figure
2.22. Generally, an increase in altitude will
increase the power required and decrease the
power available. Hence, the climb perform-
ance of an airplane is expected to be greatly
affected by altitude. The composite chart of
climb performance depicts the variation with
altitude of the speeds for maximum rate of
climb, maximum angle of climb, and maximum
and minimum level flight airspeeds. As alti-
tude is increased, these various speeds finally
converge at the absolute ceiling of the airplane.
At the absolute ceiling, there is no excess of
power or thrust and only one speed will allow
steady level flight. The variation of rate of
climb and maximum level flight’ speed’ with
altitude for the typical propeller powered air-
plane give evidence of the effect of supercharg-
ing. Distinct aberrations in these curves take
place at the supercharger critical altitudes and
~blower shift points. The curve of time to
climb is the result of summing.up the incre-
ments of time spent climbing through incre-
ments of altitude. Note that approach to the
absolute ceiling produces tremendous increase
in the time curve.
Specific reference points are established by
these composite curves of climb performance.
Of course, the absolute ceiling of the airplane
produces zero rate of climb. The service ceiling
is specified as the altitude which produces a
rate of climb of 100 fpm. The altitude which
produces a rate of climb of 500 fpm is termed
the combat ceiling. Usually, these specific refer-
ence points are provided for the airplane at
the combat configuration or a specific design
configuration.
The composite curves of climb performance
for the typical turbojet airplane are shown in
figure 2.22. One particular point to note is
the more rapid decay of climb performance | 173 | 173 | 00-80T-80.pdf |
NAVWEPS C&801-80
AIRPLANE PERFORMANCE
TYPICAL PROPELLER AIRCRAFT ALTlTUOE PERFORMANCE
. RATE OF,CL!MB_, _-
.
tiAXlMUM LEVEL FLIGHT SPEED
HIGH BLOWER CRITICAL ALTITUDE
FEE0 FOR MA% R c
LOW BLOWER CRITICAL ALTITUDE
= y$y VELOCITY, KNOTS
-e-*--
TROPOPAUSE
t-
\ MAXIMUM LEVEL
\
\ FLIGHT SPEED
-RATE OF CLIMB
\
\
\
\
I I I I b
-8
VELOCITY, KNOTS
POWER OFF DESCENT PERFORMANCE
POWER
REQUIRED
HP
MINIMUM POWER REP’D
I VELOCITY, KNOTS
Figure UP, Climb ad Desceni Pedormome
lS7 | 174 | 174 | 00-80T-80.pdf |
NAVWEPS 00-8OT-80
AIRPLANE PERFORMANCE
with altitude above the tropopause. This is
due in great part to the more rapid decay of
engine thrust in the stratosphere.
During a power off descent the deficiency of
thrust and power define the angle of descent
and rate of descent. TWO particular points
are of interest during a power off descent:
minimum angle of descent and minimum rate
of descent. The minimum angle of descent
would provide maximum glide distance through
the air. Since no thrust is available from the
power plant, minimum angle of descent would
be obtained at (L/D)-. At (L/D),, the
deficiency of thrust is a minimum and, as
shown by figure 2.22, the greatest proportion
between velocity and power required is ob-
tained. The minimum rate of descent in
power off flight is obtained at the angle of
attack and airspeed which produce minimum
power required. For airplanes of moderate
aspect ratio, the speed for minimum rate of
descent is approximately 75 percent of the
speed for minimum angle of descent
RANGE PERFORMANCE
The ability of an airplane to convert fuel
energy into flying distance is one of the most
important items of airplane performance. The
problem of eficient range operation of an air-
plane appears of two general forms in flying
operations: (1) to extract the maximum flying
distance from a given fuel load or (2) to fly a
specified distance with minimum expenditure
of fuel. An obvious common denominator for
each of these operating problems is the “spe-
cific range, ” nautical miles of flying distance
per lb. of fuel. Cruise flight for maximum
range cond.itions should be conducted so that
the airplane obtains maximum specific range
throughout the flight.
GENERAL RANGE PERFORMANCE.
The principal items of range performance can
be visualized by use of the illustrations of figure
2.23. From the characteristics of the aero-
dynamic configuration and the powerplant, the
conditions of steady level flight will define
various rates of fuel flow throughout the range
of flight speed. The first graph of figure 2.23
illustrates a typical variation of fuel flow versus
velocity. The specific range can be defined by
the following relationship:
nautical miles
specific raw= lbs, of fuel
nautical miles/hr.
‘pecific range= lbs. of fuel/hr.
thus,
specific range = velocity, knots
fuel flow, lbs. per hr.
If maximum specific range is desired, the flight
condition must provide a maxinium of velocity
fuel flow. This particular point would be
located by drawing .a straight line from the
origin tangent to the curve of fuel flow versus
velocity.
The general item of range must be clearly
distinguished from the item of endurance. The
item of range involves consideration of flying
distance while endurance involves consideration
of flying time. Thus, it is appropriate to define
a separate term, “specific endurance.”
specific endurance= flight hours
lb. of fuel
specific endurance = flight hours/hr.
lbs. of fuel/hr.
then,
specific endurance= 1
fuel flow, lbs. per hr.
By this definition, the specific endurance is
s&ply the reciprocal of the fuel ~flow. Thus,
.ifl.maximum endurance is desired, the flight
condition ‘must provide a minimum of fuel
flow. This point is readily appreciated as the
lowest point of the curve of fuel flow versus
velocity. Generally, in subsonic performance,
the speed at which maximum endurance is
158 | 175 | 175 | 00-80T-80.pdf |
NAVWEPS 00-501-50
AIRPLANE PERFORMANCE
FUEL
FLOW
I APPLICABLE FOR A
PARTICULAR: WEIGHT
MAXIMUM ALTITUDE
ENDURANCE CONFIGURATION
LINE FROM ORIGIN
TANGENT TO CURVE
VELOCITY, KNOTS
100%
MAXIMUM
-- 99% MAXIMUM RANGE
SPECIFIC
RANGE APPLICABLE FOR A PARTICLAR
-CONFIGURATION
-ALTITUDE
-WEIGHT
VELOCITY, KNOTS
AREA REPRESENTS
Figure 2.23. Geneml Range Performance
159 | 176 | 176 | 00-80T-80.pdf |
NAVWEPS oo-80~~80
AIRPLANE PERFORMANCE
obtained is approximately 75 percent of the
speed for maximum range.
A more exact analysis of range may be ob-
tained by a plot of specific range versus velocity
similar to the second graph of figure 2.23. Of
course, the source of these values of specific
range is derived by the proportion of velocity
and fuel flow from the previous curve of fuel
flow versus velocity. The maximum specific
range of the airplane is at the very peak of the
curve. Maximum endurance point is located
by a straight line from the origin tangent to
the curve of specific range versus velocity.
This tangency point defines a maximum of
(nmi/lb.) per (nmi/hr.) or simply a maximum
of (hrs./lb.).
While the very peak value of specific range
would provide maximum range operation, long
range cruise operation is generally recom-
mended at some slightly higher airspeed.
Most long range cruise operation is conducted
at the flight condition which provides 99 per-
cent of the absolute maximum specific range.
The advantage of such operation is that 1
percent of range is traded for 3 to 5 percent
higher cruise. velocity. Since the higher cruise
speed has a great number of advantages, the
small sacrifice of range is a fair bargain. The
curves of specific range versus velocity are
affected by three principal variables: airplane
gross weight, altitude, and the external aero-
dynamic configuration of the airplane. These
curves are the source of range and endurance
operating data and are included in the per-
formance section of the flight handbook.
“Cruise control” of an airplane implies that
the airplane is operated to maintain the recom-
mended long range cruise condition through-
out the flight. Since fuel is consumed during
cruise, the gross weight of the airplane will
vary and optimum airspeed, altitude, and
power setting can vary, Generally, “cruise
control” means the control of optimum air-
speed, altitude, and power setting to maintain
the 99 percent maximum specific range condi-
tion. At the beginning of cruise, the high
initial weight of the airplane will require spe-
cific values of airspeed, altitude,’ and power
setting to produce the recommended cruise
condition. As fuel is consumed and the air-
plane gross weight decreases, the optimum ai,r-
speed and power setting may decrease or the
optimum altitude may increase. Also, the
optimum specific range will increase. The
pilot must provide the proper cruise control
technique to ensure that the optimum condi-
tions are maintained.
The final graph of figure 2.23 shows a typical
variation of specific range with gross weight
for some particular cruise operation. At the
beginning of cruise the gross weight is high
and the specific range is low. As fuel is con-
sumed, and the gross weight reduces, the
specific range increases. .This’ type of curve
relates the range obtained by the expenditure
of fuel .by the crosshatched area between the
gross weights at beginning and end of cruise.
For example, if the airplane begins cruise at
18,500 Jbs. and ends cruise at 13,000 lbs., 5,500
lbs. of fuel is expended. If the average spe-
cific range were 0.2 nmi/Jb., the total range
would be:
range=(0.2)$ (5,500) lb.
= 1,100 nmi.
Thus, the total range is dependent on both
the fuel available and the specific range. When
range and economy of operation predominate,
the pilot must ensure that the airplane will be
operated at the recommended long range cruise
condition. By this procedure, the airplane
will be capable of its,maximum design operat-
ing radius or flight distances less than the
maximum can be achieved with a maximtim of
fuel reserve at the destination.
RANGE, PROPELLER DRIVEN AIR-
PLANES. The propeller driven airplane com-
bines the propeller with the reciprocating
engine or the gas turbine for propulsive power.
In the case of either the reciprocating engine or
the gas turbine combination, powerplant fuel | 177 | 177 | 00-80T-80.pdf |
NAVWEPS OS80140
AIRPLANE PERFORMANCE
flow is determined mainly by the shaft poluet
put into the propeller rather than thrust. Thus,
the powerplant fuel flow could be related di-
rectly to power required to maintain the air-
plane in steady, level flight. This fact allows
study of the range of the propeller powered
airplane by analysis of the curves of power
required versus velocity.
Figure 2.24 illustrates a typical curve of
power required versus velocity which, for the
propeller powered airplane, would be analo-
gous to the variation of fuel flow versus veloc-
ity. Maximum endurance condition would be
obtained at the point of minimum power re-
quired since this would require the lowest fuel
flow to keep the airplane in steady, level flight.
Maximum range condition would occur where
the proportion between velocity and power re-
quired is greatest and this point is located by
a straight line from the origin tangent to the
curve.
The maximum range condition is obtained
at maximum lift-drag ratio and it is important
to note that (L/D),, for a given airplane
configuration occurs at a particular angle of
attack and li5t coefficient and is unaffected by
weight or altitude (within compressibility
limits). Since approximately 50 percent of
the total dra.g a’t (L/D)* is induced drag, the
propeller powered airplane which is designed
specifically i3r IJong range will have a strong
preference for rbe thigh aspect rario planform.
The effect ,df tihe variation of airplane gross
weight is illustrated by the second graph of
figure 2.24. ‘The flight condition of (L/D),.,
is achieved a’t,one-particular value of lift coefIi-
cient for a given airplane configuration.
Hence, a variation of gross weight will alter
the values of airspeed, power required, and spe-
cific range obtained at (L/D)m.r. If a given
configuration ‘of airplane is operated at con-
stant altitude and the lift coefficient for
WDL the following relationships will
awb :
-4 v*- E VI K
pr* w* s’*
-=H PC WI
where
SRs WI -=-
SRI W,
condition (1) applies to some known condi-
tion of velocity, power required, and
specific range for (L/D),., at some basic
weight, WI
condition (2) applies to some new values of
velocity, power required, and specific
range for (L/D),., at some different
weight, WI
and,
V= velocity, knots
W= gross weight, Jbs.
Pr=power required, h.p.
SK= specific range, nmi/lb.
Thus a 10 percent increase in gross weight
would create:
a 5 percent increase in velocity
a 15 percent increase in power required
a 9 percent decrease in specific range
when flight is maintained at the optimum con-
ditions of (L/D),.,. The variations of veloc-
ity and power required must be monitored by
the pilot as part of the cruise control to main-
tain .(L/D),.+ When the airplane fuel weight
is a small part of the gross-weight and the range
is small, then cruise control procedure can be
simplified to essentially a constant speed and
power setting throughout cruise. However,
the long range airplane has a fuel weight which
is a conside’rable part of the gross weight and
cruise control procedure must employ sched-
uled airspeed and power changes to maintain
optimum range conditions.
The effect of altitude on the range of the
propeller powered airplane may be appreciated
by inspection of the final graph of figure 2.24.
If a given configuration of airplane is operated
at constant gross weight and the lift coefficient
161 | 178 | 178 | 00-80T-80.pdf |
NAVWEPS OO-ROT-RO
AIRPLANE PERFORMANCE
GENER,AL. RANGE CONDITIONS
PROPELLER AIRPLANE
POWER
REO’D
HP
APPLICABLE FOR
A PARTICULAR
MAXIMUM -WEIGHT
ENDURANCE -ALTITUDE
-CONFIGURATION
VELOCITY, KNOTS
POWER
REO’D
EFFECT OF GROSS WEIGHT
HlGHER WT.
CONSTANT
ALTITUDE
VELOCITY, KNOTS
HP HP
A t
EFFECT OF ALTITUDE EFFECT OF ALTITUDE
AT ALTITUDE AT ALTITUDE
SEA LEVEL SEA LEVEL
CONSTANT CONSTANT
WEIGHT WEIGHT
I VELOCITY, KNOTS
Figure 2.24. Range Performance, Propeller Aircraft | 179 | 179 | 00-80T-80.pdf |
for WD)m.z, a change in altitude will produce
the following relationships:
where
condition (I) applies to some known condi-
tion of velocity and power required for
W’),,,,,z at some original, basic altitude
condirion (2) applies to some new values of
velocity and power required for (L/D),,
at some different altitude
and
V= velocity, knots (TAX, of course)
Pr=power required, h.p.
o=altitude density ratio (sigma)
Thus, if flight is conducted at 22,000 ft.
(o=O.498), the airplane will have:
a 42 percent higher velocity
a 42 percent higher power required
than when operating at sea level. Of course,
the greater velocity is a higher TAS since the
airplane at a given weight and lift coefficient
will require the same PAS independent of
altitude. Also, the drag of the airplane at
altitude is the same as the drag at sea level but
the higher TAS causes a proportionately
greater power required. Note chat the same
straight line from the origin tangent to the sea
level power curve also is tangent to the
altitude power curve.
The effect of altitude on specific range can be
appreciated from the previous relationships.
If a change in altitude causes identical changes
in velocity and power required, the proportion
of velocity to power required would be un-
changed. This fact implies that the specific
range of the propeller powered airplane would
be unaffected by altitude. In the actual case,
this is true to the extent that powerplant specif-
ic fuel consumption (c) and propeller efficiency
(qp) are the principal factors which could
cause a variation of specific range with altitude.
NAWEPS oo-EOT-80
AWPLANE PERFORMAhlCE
If compressibility effects are negligible, any
variation of ~peci)c range with altitude is strictly a
function of engine-propeller pcrformanCC.
The airplane equipped with the reciprocating
engine will experience very little, if any,
variation of specific range with altitude at low
altitudes, There is negligible variation of
brake specific fuel consumption for values of
BHP below the maximum cruise power rating
of the powerplant which is the auto-lean or
manual lean range of engine operation. Thus,
an increase in altitude will produce a decrease
in specific range only when the increased power
requirement exceeds the maximum cruise power
rating of the powerplants. One advantage of
supercharging is that the cruise power may be
maintained at high altitude and the airplane
may achieve the range at high altitude with
the corresponding increase in TAS. The prin-
cipal differences in the high altitude cruise and
low altitude cruise are the true airspeeds and
climb fuel requirements.
The airplane equipped with the turboprop
powerplant will exhibit a variation of specific
range with altitude for two reasons. First,
the specific fuel consumption (c) of the turbine
engine improves with the lower inlet tem-
peratures common to high altitudes. Also,
the low power requirements to achieve opti-
mum aerodynamic conditions at low altitude
necessitate engine operation at low, inefficient
output power. The increased power require-
ments at high .altitudes allow the turbine
powerplant to operate in an efficient output
range. Thus, while the airplane has no
particular preference for altitude, the power-
plants prefer the higher altitudes and cause
an increase in specific range with altitude.
Generally, the upper limit of altitude for
efficient cruise operation is defined by airplane
gross weight (and power required) or com-
presslbility effects.
The optimum climb and descent for the
propeller powered airplane is affected by
many different factors and no general, all-
inclusive relationship is applicable. Hand-
book data for the specific airplane and various
163 | 180 | 180 | 00-80T-80.pdf |
NAVWEPS OO-SOT-80
AIRPLANE PERFORMANCE
operational factors will define operating pro-
cedures.
RANGE, TURBOJET AIRPLANES. Many
different factors influence the range of the
turbojet airplane. In order to simplify the
analysis of the overall range problem, it is
convenient to separate airplane factors from
powerplant factors and analyze each item
independently. An analogy would be the
study of “horsecart” performance by separat-
ing “cart” performance from “horse” per-
formance to distinguish the principal factors
which affect the overall performance.
In the case of the turbojet airplane, the
fuel flow is determined mainly by the thrust
rather than power. Thus, the fuel flow could
be most directly related to the thrust required
to maintain the airplane in steady, level flight.
.This fact allows study of the turbojet powered
airplane by analysis of the curves of thrust
required versus velocity. Figure 2.25 illu-
strates a typical curve of thrust required versus
velocity which would be (somewhat) analo-
gous to the variation of fuel flow versus veloc-
ity. Maximum endurance condition would
be obtained at (L/D)- since this would incur
the lowest fuel flow to keep the airplane in
steady, level flight. Maximum range condition
would occur where the proportion between
velocity and thrust required is greatest and
this point is located by a straight line from
the origin tangent to the curve.
The maximum range is obtained at the aero-
dynamic condition which produces a maximum
proportion between the square root of the
lift coefficient (CJ and the drag coe&cient
(CD), or (&/CD)-. In subsonic perform-
ance, (G/C > D - occurs at a particular value
angle of attack and lift coefficient and is un-
affected by weight or altitude (within com-
pressibility limits). At this specific aerody-
namic condition, induced drag is approxi-
mately 25 percent of the total drag so the
turbojet airplane designed for long range does
not have the strong preference for high aspect
ratio planform like the propeller airplane.
On the other hand, since approximately 75
percent of the total drag is parasite drag, the
turbojet airplane designed specifically for long
range has the special requirement for great
aerodynamic cleanness.
The effect of the variation of airplane gross
weight is illustrated by the second graph
of figure 2.25. The flight condition of
(mc 1 D IMI is achieved at one value of lift
coefbcient for a given airplane in subsonic
flight. Hence, a variation of gross weight will
alter the values of airspeed, thrust required,
and specific range obtained at ,(&/CD)-. If
a given configuration is operated at constant
altitude and lift coefficient the following re-~
lationships will apply:
SR2 -=
SRI (constant .altitude)
where
condition (1) applies to some! known condi-
tion of velocity, thrust required, and
specific range for (&/CD)- at some
basic weight, Wi
condition (2) applies to some new values of
velocity, thrust required, and specific
range for (&/CD)- at some different
weight, W,
and
V= velocity, knots
W=gross weight, lbs.
Tr= thrust required, lbs.
.SR= specific range, nmi/lb.
Thus, a 10 percent increase in gross weight
would create:
a 5 percent increase in velocity
a 10 percent increase in thrust required
a 5 percent decrease in specific range
when flight is maintained at the optimum con-
ditions of (&/CD)-. Since most jet airplanes
164 | 181 | 181 | 00-80T-80.pdf |
NAVWEPS 00-8OT-80
AIRPLANE PERFORMANCE
GENERAL RANGE CONDITIONS
TURBOJET
THRUST
REO’D
LBS
THRUST
REO’D
LBS
THRUST
REP’0
LBS
MAXIMUM
ENDURANCE
MAXIMUM
APPLICABLE FOR
A PARTICULAR
-WEIGHT
-ALTITUDE
-CONFIGURATION
VELOCITY, KNOTS
EFFECT OF GROSS WEIGHT
CONSTANT
ALTITUDE
t
EFFECT OF ALTITUDE
.%A LEVEL SEA LEVEL AT ALTITUDE
/
CONSTANT
WEIGHT
7 VELOCITY. KNOTS
c
VELOCITY. KNOTS
Ftgure P.25. Rangt Performoncr, Jet Aircraft | 182 | 182 | 00-80T-80.pdf |
NAVWEPS 00-801-80
AIRPLANE PERFORMANCE
have a fuel weight which is a large part of the
gross weight, cruise control procedures will be
necessary to account for the changes in opti-
mum airspeeds and power settings as fuel is
consumed.
The effect of altitude on the range of the
turbojet airplane is of great importance be-
cause no other single item can cause such large
variations of specific range. If a given con-
figuration of airplane is operated at constant
gross weight and the lift coefficient for
(JCL/CDL, a change in altitude will produce
the following relationships:
vz - -= 3
J VI .Y*
Tr=constant (neglecting compressibility
effects)
JR.2 - -=
J
3
JR1 rJ*
(neglecting factors affecting en-
gine performance)
where
condition (I) applies some known condition
of velocity, thrust required, and specific
range for (&QCD),, at some original,
basic altitude.
condition (2) applies to some new values of
velocity, thrust required, and specific
range for (fi/CD)mm at some different
altitude.
and
V= velocity, knots (TAX, of course)
Tr= thrust required, lbs.
JR= specific range, nmi/lb.
a=altitude density ratio (sigma)
Thus, if flight is conducted at 40,000 ft.
(u=O.246), the airplane will have:
a 102 percent higher velocity
the same thrust required
a 102 percent higher specific range
(even when the beneficial effects of altitude
on engine performance are neglected)
than when operating at sea level. Of course,
the greater velocity is a higher TAJ and the
same thrust required must be obtained with a
greater engine RPM.
At this point it is necessary to consider the
effect of the operating condition on powerplant
performance. An increase in altitude will im-
prove powerplant performance in two respects.
First, an increase in altitude when below the
tropopause will provide lower inlet Gr tem-
peratures which redqce the specific fuel con-
sumption (c~). Of course, above the tropo-
pause the specific fuel consumption tends to
increase. A; low altitude, the engine RPM
necessary to produce the required thrust is low
and, generally, well below the normal rated
value. Thus, a second benefit of altifude on
engine performance is due to the increased
RPM required to furnish cruise thrust. An
increase in engine speed to the normal rated
value will reduce the specific fu,el consumption.
The increase in specific range with altitude
of the turbojet airplane can be attributed to
these three factors:
(1) An increase in altitude will increase the
proportion of (V/Tr) and provide a greater
TAS for the same TY.
(2) An increase in altitude in the tropo-
sphere will produce lower inlet air temperature
which reduces the specific.fuel consumption.
(3) An increase in altitude requires in-
creased engine RPM to provide cruise thrust
and the specific fuel consumption reduces as
normal rated RPM is approached.
The combined effect of these three factors de-
fines altitude as the one most important item
affecting the specific range of the turbojet air-
Pl ane. As an example of this combined’effect,
the typical turbojet airplane obtains a specific
range at 40,ooO ft. which is approximately 150
percent greater than that obtained at sea leirel.
The increased TAS accounts for approxi-
mately two-thirds of this benefit while in-
creased engine performance (reduced cJ ,~ ‘ac-
counts for the other one-third of the benefit.
For example, at sea level the maximum spe-
cific range of a turbojet airplane may be 0.1
nmi/lb. but at 40,000 ft. the maximum specific
range would be approximately 0.25 nmi/lb.
166 | 183 | 183 | 00-80T-80.pdf |
From the previous analysis, it is apparent
that the cruise altitude of the turbojet should
be as high as possible within compressibility
or thrust limits. Generally, the optimum alti-
tude to begin cruise is the highest altitude at
which the maximum continuous thrust can
provide the optimum aerodynamic conditions.
Of course, the optimum altitude is determined
mainly by the gross weight at the begin of
cruise. For the majority of turbojet airplanes
this altitude will be at or above the tropopause
for normal cruise configurations.
Most turbojet airplanes which have rran-
sonic or moderate supersonic performance will
obtain maximum range with a high subsonic
cruise. However, the airplane designed spe-
cifically for high supersonic performance will
obtain maximum range with a supersonic
cruise and subsonic operation will cause low
lift-drag ratios, poor inlet and engine perform-
ance and redute the range capability.
The cruise control of the turbojet airplane
is considerably ~different from that of the pro-
peller driven airplane. Since the specific range
is so greatly affected by altitude, the optimum
altitude for begin of cruise should be attained
as rapidly as is consistent with climb fuel re-
quirements. The range-climb program varies
considerably between airplanes and the per-
formance section of the flight handbook will
specify the appropriate procedure. The de-
scent from cruise altitude will employ essen-
tially the same feature, a rapid descent is
necessary to minimize the time at low altitudes
where specific’ range is low and fuel flow is high
for a given engine speed.
During cruise flight of the turbojet airplane,
the decrease of gross weight from expenditure
of fuel can result in two types of cruise control.
During a constant altitlrdc C&SC, a reduction in
gross weight will require a reduction of air-
speed and engine thrust ‘to maintain the opti-
mum lift coefhcient of subsonic cruise. While
such a cruise may be necessary to conform to
the flow of traffic, it constitutes a certain in-
efficiency of operation. If the airplane were
NAVWEPS OO-BOT-RO
AIRPLANE PERFORMANCE
not restrained to a particular altitude, main-
taining the same lift coeAicient and engine
speed would allow the airplane to climb as the
gross weight decreases. Since altitude gen-
erally produces a beneficial effect on range, the
climbing C&SC implies a more efficient flight
path.
The cruising flight of the turbojet airplane
will begin usually at or above the tropopause
in order to provide optimum range conditions.
If flight is conducted at (a/&)-, optimum
range will be obtained at specific values of lift
coefficient and drag coefficient. When the air-
plane is fixed at these values of CL and C, and
the TAS is held constant, both lift and drag are
directly proportional to the density ratio, (T.
Also, above the tropopause, the thrust is pro-
portional to .J when the TAS and RPM are con-
stant. As a result, a reduction of gross weight
by the expenditure of fuel would allow the
airplane to climb but the airplane would re-
main in equilibrium because lift, drag, and
thrust all vary in the same fashion. This re-
lationship is illustrated by figure 2.26.
The relationship of lift, drag, and thrust is
convenient for, in part, it justifies the condi-
tion of a constant velocity. Above the tropo-
pause, rhe speed of sound is constant hence a
constant velocity during the cruise-climb
would produce a constant Mach number. In
this case, the optimum values of (&,/CD), C,
and C, do not vary during the climb since the
Mach number is constant. The specific fuel
consumption is initially constant above the
tropopause but begins to increase at altitudes
much above the tropopause. If the specific
fuel consumption is assumed to be constant
during the cruise-climb, the following rela-
tionships will apply:
V, M, CL and C, are constant
62 wz
61 w,
FR 02
FFI ~1
JR2-W, (cruise climb above tropopause,
x-W9 constant M, c,)
167 | 184 | 184 | 00-80T-80.pdf |
NAVWEPS oo-801-80
AIRPLANE PERFORMANCE
where
condition (1) applies to some known condi-
tion of weight, fuel flow, and specific
range at some original basic altitude
during cruise climb.
con&&r (2) applies to some new values of
weight, fuel flow, and specific range at
some different altitude along a partic-
ular cruise path.
and
V= velocity, knots
M = Mach number
W= gross weight, lbs.
FF=fuel flow, lbs./hr.
JR= specific range, nmi./lb.
e=altitude density ratio
Thus, during a cruise-climb flight, a 10 percent
decrease in gross weight from the consumption
of fuel would create:
no change in Mach number or ‘TAS
a 5 percent decrease in EAS
a 10 percent decrease in C, i.e., higher
altitude
a 10 percent decrease in fuel flow
an 11 percent increase in specific range
An important comparison can be made between
the constant altitude cruise and the cruise-
climb with respect to the variation of specific
range. From the previous relationships, a
2 percent reduction in gross weight durmg
cruise would create a 1 percent increase in
specific range in a constant altitude cruise but
a 2 percent increase in specific range in a cruise-
climb at constant .Mach number. Thus, a
higher average specific range can.be maintained
during the expenditure of a given increment of
fuel. If an airplane begins a cruise at optimum
conditions at or above the tropopause with a
given weight of fuel, the following data
provide a comparison of the total range avail-
able from a constant altitude or cruise-climb
0.0 Loo0
.I 1.026
.2 1.057
.3 1.92
.4 1.136
.5 1.182
.6 1.248
.7 1.331
For example, if the cruise fuel weight is 50 per-
cent of the gross weight, the climbing cruise
flight path will provide a range 18.2 percent
greater than cruise at constant ,altitude. This
comparison does not include consideration of
any variation of specific fuel consumption dur-
ing cruise or the effects of compressibility in
defining the optimum aerodynamic conditions
for cruising flight. However, the comparison
is generally applicable for aircraft which have
subsonic cruise.
When the airplane has a supersonic cruise for
maximum range, the optimum flight path is
generally one of a constant Mach number.
The optimum flight path is generally-but not
necessarily-a climbing cruise. In this case of
subsonic. or supersonic cruise, a Machmeter is
of principal importance in cruise control of the
jet airplane.
The @ct of wind on nznge is of considerable
importance in flying operations. Of course,
a headwind will always reduce range and a
tailwind will always increase range. The
selection of a cruise altitude with the most
favorable (or least unfa:vorable) winds is a rel-
atively simple matter for the case of the
propeller powered airplane. Since the range of
the.propeller powered airplane is relatively un-
affected by altitude, the altitude with the most
favorable winds is selected for range. However,
the range of the turbojet airplane is greatly
affected by altitude so the selection of an op-
timum altitude will involve considering the
wind profile ‘with the variation of range with
altitude. Since the turbojet range increases
168 | 185 | 185 | 00-80T-80.pdf |
NAVWEPS 00-801-80
AIRPLANE PERFORMANCE
TURBOJET CRUISE-CLIMB
t-
IF CL AND TAS ARE CONSTANT,
LIFT IS PROPORTIONAL TOE
IF co AND T/h ARE CONSTANT,
DRAG IS PROPORTIONAL TO a
(SPEEDS FOR MAXIMUM
FUEL GROUNO NAUTICAL ,MlLES
FLOW PER LB. OF FUEL)
LBS/HR I HEADWIND I /
I
IF RPM AND TAS ARE CONSTANT,
THRUST IS PROPORTIONAL TO”
(APPROXIMATE)
t-
WEIGHT DECREASES AS FUEL IS
CONSUMED
EFFECT OF WIN0 ON RANGE
-I-
VELOCITY, KNOTS
VELOCITY VELOCITY
Figure 2.26. Range Performance
169 | 186 | 186 | 00-80T-80.pdf |
NAVWEPS 00401-60
AIRPLANE PERFORMANCE
greatly with altitude, the turbojet can tolerate
less favorable (or more unfavorable) winds
with increased altitude.
In some cases, large values of wind may
cause a significant change in cruise velocity to
maintain maximum ground nautical miles per
lb. of fuel. As an example of an extreme con-
dition, consider an airplane flying into a head-
wind which equals the cruise velocity. In this
case, ““9 increase in velocity would improve
range.
To appreciate the changes in optimum speeds
with various winds, refer to the illustration of
figure 2.26. When zero wind conditions exist,
a straight line from the origin tangent to the
curve of fuel flow versus velocity will locate
maximum range conditions. When a head-
wind condition exists, the speed for maximum
ground range is located by a line tangent drawn
from a velocity offset equal to the headwind
velocity. This will locate maximum range at
some higher velocity and fuel flow. Of course,
the range will be less than when at zero wind
conditions but the higher velocity and fuel flow
will minimize the range loss due to the head-
wind. In a similar sense, a tailwind will re-
duce the cruise velocity to maximize the
benefit of the tailwind.
The procedure of employing different cruise
velocities to account for the effects of wind is
necessary only at extreme values of wind
velocity. It is necessary to consider the
change in optimum cruise airspeed when the
wind velocities exceed 25 percent of the zero
wind cruise velocity.
ENDURANCE PERFORMANCE
The ability of the airplane to convert fuel
energy into flying time is an important factor
in flying operations. The “specific endurance”
of the airplane is defined as follows:
specific endurance==1
specific endurance= 1
fuel flow, Ibs. per hr.
The specific endurance is simply the reciprocal
of the fuel flow, hence maximum endurance
conditions would be obtained at the lowest
fuel flow required to hold the airplane in steady
level flight. Obviously, minimum fuel flow
will provide the maximum flying time from a
given quantity of fuel. Generally, in subsonic
performance, the speed at which maximum en-
durance is achieved is approximately 75 per-
cent of the speed for maximum range.
While many different factors can affect the
specific endurance, the most important factors
at the control of the pilot are the configuration
and operating altitude. Of course, for maxi-
mum endurance conditions the airplane must
be in the clean configuration and operated at
the proper aerodynamic conditions.
EFFECT OF ALTITUDE ON ENDUR-
ANCE, PROPELLER DRIVEN AIRPLANES.
Since the fuel flow of the propeller driven air-
plane is proportional to power required, the
propeller powered airplane will achieve maxi-
mum specific endurance when operated at mini-
mum power required. The point of minimum
power required is obtained at a specific value
of lift coefficient for a particular airplane con-
figuration and is essentially independent of
weight or altitude. However, an increase in
altitude will increase the value of the minimum
power required as illustrated by figure 2.27.
If the specific fuel consumption were not in-
fluenced by altitude or engine power, the spe-
cific endurance would be directly proportional
to ji, e.g., the specific endurance at 22,000 ft.
(a=O.498) would be approximately 70 percent
of the value at sea level. This example is very
nearly the case of the airplane with the recipro-
cat&g engine since specific fuel consumption and
propeller efficiency are not directly affected by
altitude. The obvious conclusion is that
maximum endurance of the reciprocating en-
gine airplane is obtained at the lowest practical
altitude.
The variation with altitude of the maximum
endurance of the turboprop airplane requires
consideration of powerplant factors in addition
im | 187 | 187 | 00-80T-80.pdf |
NAV’iiEPS Oo-801-80
AIRPLANE PERFORMANCE
EFFECT OF ALTlTUOE ON MINIMUM
POWER REO’D
b
AT ALTITUDE
SEA.LEVEL /
/
MINIMUM /
/
/
CONSTANT
WEIGHT 8
CONFIGURATION
lm-
VELOCITY, KNOTS
EFFECT OF ALTITUDE ON MINIMUM
t
THRUST REO’D
SEA LEVEL AT ALTITUDE
T;;;g MINIMUM THRUST REO’D
LBS /’
A’
,’
CONSTANT
-- WEIGHT 8
I
CONFIGURATION
VELOCITY, KNOTS
Figure 2.27. Endurance Performance
171 | 188 | 188 | 00-80T-80.pdf |
NAVWEPJ OO-ROT-80
AIRPLANE PERFORMANCE
to airplane factors. The turboprop power-
plant prefers operation at low inlet air tem-
peratures and relatively high power setting to
produce low specific fuel consumption. While
an increase in altitude will increase the mini-
mum power required for the airplane, the
powerplant achieves more efficient operation.
As a result of these differences, maximum en-
durance of the multiengine turboprop airplane
at low altitudes may require shutting down
some of the powerplants in order to operate
the remaining powerplants at a higher, more
efficient power setting.
EFFECT OF ALTITUDE ON ENDUR-
ANCE, TURBOJET AIRPLANES. Since the
fuel flow of the turbojet powered airplane is
proportional to thrust required, the turbojet
airplane will achieve maximum specific endur-
ance when operated at minimum thrust re-
quired or (L/D),. In subsonic flight,
(L/D)m~ occurs at a specific value of lift
coefBcient for a given airplane and is essentially
independent of weight or altitude. If a given
weight an~d configuration of airplane is oper-
ated at various altitudes, the value of the
minimum thrust required is unaffected by the
curves of thrust required versus velocity shown
in figure 2.27. Hence, it is apparent that the
aerodynamic configuration has no prefeience
for altitude (within compressibility limits)
and specific endurance is a function only of
engine performance.
The specific fuel consumption of the turbojet
engine is strongly affected by operating RPM
and altitude. Generally, the turbojet engine
prefers the operating range near normal rated
engine speed and the low temperatures of the
stratosphere to produce low specific fuel con-
sumption. Thus, increased altitude provides
the favorable lower inlet air temperature and
requires a greater engine speed to provide the
thrust required at (L/D)-. The typical
turbojet airplane experiences an increase in
specific endurance with altitude with the peak
values occurring at or near the tropopausc.
For example, a typical single-engine turbojet
airplane will have a maximum specific endur-
ance at 35,ooO ft. which is at least 40 percent
greater than the maximum value at sea level.
If the turbojet airplane is at low altitude and
it is necessary to hold for a considerable time,
maximum time in the air will be obtained by
beginning a climb to some optimum altitude
dependent upon the fuel quantity available.
Even though fuel is expended during the climb,
the higher altitude will provide greater total
endurance. Of course, the use of afterburner
for the climb would produce a prohibitive re-
duction in endurance.
OFl4X’TIMUM RANGE AND ENDUR-
ANCE
There are many conditions of flying oper-
ations in which optimum range or endurance
conditions are not possible or practical. In
many instances, the off-optimum conditions
result from certain operational requirements
or simplification of operating procedure. In
addition, off-optimum performance may be the
result of a powerplant malfunction or failure.
The most important conditions are discussed
for various airplanes by powerplant type.
RECIPROCATING POWERED AIR-
PLANE. In the majority of cases, the recipro-
cating powered airplane is operated at’an engine
dictated cruise. Service use will most probably
define some continuous power setting which
will give good service life and trouble-free
operation of the powerplant. When range or
endurance is of no special interest, the simple
expedient is to operate the powerplant at the
recommended power setting and accept what-
ever speed, range, or endurance that results.
While such a procedure greatly simplifies the
matter of cruise control, the practice does not
provide the necessary knowledge required for
operating a high performance, long range
airplane.
The failure of an engine on the multiengine
reciprocating powered airplane has interesting
ramifications. The first problem appearing is
to produce sufficient power from the remaining
engines to keep the airplane airborne. The
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problem will be most .critical if the airplane is
at high altitude, high gross weight, and with
gaps and gear extended. Lower altitude,
jettisoning of weight items, and cleaning up
the airplane will reduce the power required for
flight. Of course, the propeller on the in-
operative engine must be feathered or the
power required may exceed that available from
the remaining operating powerplants.
The effect on range is much dependent on
the airplane configuration. When the pro-
peller on the’inoperative engine is feathered,
the added drag is at a minimum, but there is
added the trim drag ,required to balance
the unsymmetrical power. When both these
sources of added drag are accounted for, the
(L/D)- ,is reduced but not by significant
amounts. Generally, if the specific fuel con-
sumption and propeller efficiency do not deteri-
orate, the maximum specific range is not greatly
reduced. On the twin-engine airplane the
power required must .be furnished by the one
remaining engine and this. usually requires
more than the,maximum cruise-rating of the
powerplant.i As a result the powerplant can-
not be operated in the auto-lean or manual
lean, power range and the specific ,fuel con-
sumption increasesgreatly! Thus, noticeable
loss of range must be anticipated when one
engine fails on the twin-engine airplane. The
failure of oneengine on the four (or more)
engine airpla,W may allow the required, power
to be,develo,ped:by.the three remaining power-
plants operating in an economical power range.
If the airplane is clean, at low altitude, and
low gross weight, ,the failure of one engine is
not likely to cause a, loss of range. However,
then loss. of ‘two engines is likely ‘to cause a
considerable loss of range.
When engine failure produces a critical
power or range situation, improved perform-
ance is possible with- theairplane in ;the clean
configuration at low altitude. Also, jetti-
soning of expendable weight items will reduce
the power required and improve the specific
range.
NAVWEPS OO-ROT-RO
AtRPLANE PERFORMANCE
TURBOPROP POWERED AIRPLANE.
The turbine engine has the preference for
relatively high power settings and high alti-
tudes to provide low specific fuel consumption.
Thus, the off-optimum conditions of range or
endurance can be concerned with altitudes
less than the optimum. Altitudes less than
the optimum can reduce the range but the
loss can be minimized on the multiengine
airplane by shutting down some powerplants
and operating the remaining powerplants at a
higher, more efficient output. In this case
the change of range is confined to the variation
of specific fuel consumption with altitude.
Essentially the same situation exists in the
case of engine failure when cruising at optimum
altitude. If the propeller on the inoperative
engine is feathered, the loss of range will be
confined to the change in specific fuel con-
sumption from the reduced cruise altitude. If
a critical power situation exists due to engine
failure, a reduction in altitude provides im-
mediate benefit because of the reduction of
power required and the increase in power
available from the power plants. In addition,
the jettisoning of expendable weight items
will improve performance and, of course, the
clean configuration provides minimum parasite
drag.
Maximum specific endurance of the turbo-
prop airplane does not vary as greatly with
altitude as the turbojet airplane. While each
configuration has its own particular operating
requirements, low altitude endurance of the
turboprop airplane requires special considera-
tion. The single-engine turboprop will gen-
eraBy experience an increase in specific endur-
ance with an increase in altitude from sea level.
However, if the airplane is at low altitude and
must hold or endure for a period of time, the
decision to begin a climb or hold the existing
altitude will depend on the quantity of fuel
available. The decision depends primarily on
the climb fuel,requirements and the variation of
specific endurance with altitude. A somewhat
similar problem exists with the multiengine
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turboprop airplane but additional factors are
available to influence the specific endurance at
low altitude. In other words, low altitude
endurance can be improved by shutting down
some powerplants and operating the remaining
powerplants at higher, more efbcient power
setting. Many operational factors could decide
whether such procedure would be a suitable
technique.
TURBOJET POWERED AIRPLANE. In-
creasing altitude has a powerful effect on both
the range and endurance of the turbojet air-
plane. As a result of this powerful effect, the
typical turbojet airplane will achieve maxi-
mum specific endurance at or near the tropo-
pause. Also, the maximum specific range will
be obtained at even higher altitudes since the
peak specific range generally occurs at the
highest altitude at which the normal rating of
the engine can sustain the optimum aero-
dynamic conditions. At low altitude cruise
conditions, the engine speed necessary to sus-
tain optimum aerodynamic conditions is very
low and the specific fuel consumption is rela-
tively poor. Thus, at low altitude, the air-
plane prefers the low speeds to obtain
(&/CD)- but the powerplant prefers the
higher speeds common to higher engine effi-
ciency. The compromise results in maximum
specific range at flight speeds well above the
optimum aerodynamic conditions. In a sense,
low altitude cruise conditions are engine
dictated.
Altitude is the one most important factor
affecting the specific range of the turbojet
airplane. Any operation below the optimum
altitude will have a noticeable effect on the
range capability and proper consideration
must be given to the loss of range. In addi-
tion, turbojet airplanes designed specifically for
long range will have a large percent of the
gross weight as fuel. The large changes in
gross weight during cruise will require partic-
ular methods of cruise control to extract the
maximum flight range. A variation from the
optimum flight path of cruise (constant Mach
NAVWEPS OO-EOT-80
AIRPLANE PERFORMANCE
number, cruise-climb, or whatever the appro-
priate technique) will result in a loss of range
capability.
The failure of an engine during the optimum
cruise of a multiengine turbojet airplane will
cause a noticeable loss of range. Since the
optimum cruise of the turbojet is generally a
thrust-limited cruise, the loss of part of the
total thrust means that the airplane must
descend to a lower altitude. For example, if a
twin-engine jet begins an optimum cruise at
35,000 ft. (e=O.31) and one powerplant fails,
the airplane must descend to a lower altitude
so that the operative engine can provide the
cruise thrust. The resulting altitude would be
approximately 16,030 ft. (~=0.61). Thus, the
airplane will experience a loss of the range
remaining at the point of engine failure and
loss could be accounted for by the reduced
velocity (TM) and the increase in specific fuel
consumption (c~) from the higher ambient air
temperature. In the case of the example air-
plane, engine failure would cause a 30 to 40
percent loss of range from the point of engine
failure. Of course, the jettisoning of expend-
able weight items would allow higher altitude
and would increase the specific range.
Maximum endurance in the turbojet air-
plane varies with altitude but the variation is
due to the changes in ‘fuel flow necessary to
provide the thrust required at (I./D),... The
low inlet air temperature of the tropopause
and the greater engine speed reduce the specific
fuel consumption to a minimum. If the single-
engine turbojet airplane is at low altitude
and must hold or endure for a period of time,
a climb should begin to take advantage of the
higher specific endurance at higher altitude.
The altitude to which to climb will be deter-
mined by the quantity of fuel remaining. In
the case of the multiengine turbojet at low
altitude, some slightly different procedure
may be utilized. If all powerplants are oper-
ating, it is desirable to climb to a higher
altitude which is a function of the remaining
fuel quantity. An alternative at low altitude
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NAVWEPS oo-80mo
AIRPLANE PERFORMANCE
would be to provide the endurance thrust with
some engine(s) shut down and the remaining
engine(s) operating at a more efficient power
output. This technique would cause a mmi-
mum loss of endurance if at low altitude. The
feasibility of such a procedure is dependent
on many operational factors.
In all cases, the airplane should be in the
cleanest possible external configuration because
the specific endurance is directly proportional
to the (L/D).
MANEUVERING PERFORMANCE ,...s’ .i :.,cyz’
When the airplane is’in turning flight, the
airplane is not in static equilibrium for there
must be developed the unbalance of force to
produce the acceleration of the turn. During
a steady coordinated turn, the lift is inclined
to produce a horizontal component of force to
equal the centrifugal force of the turn. In
addition, the steady turn is achieved by pro-
ducing a vertical component of lift which is
equal to the weight of the airplane. Figure
2.28 illustrates the forces which act on the
airplane in a steady, coordinated turn.
For the case of the steady, coordinatedturn,
the vertical component oft lift must equal the
weight of the aircraft so that there will be no
acceleration in the vertical direction. This
requirement leads to the following relation-
ship:
L *=- W
where
1 BE-- cos q5
n=sec $6
rz= load factor or “G”
L=lift, lbs.
W= weight, Ibs.
+= bank angle, degrees (phi)
From this relationship it is apparent that the
steady, coordinated turn requires specific values
of load factor, n, at various angles of bank, 6.
For example, a bank angle of 60’ requires a
load factor of 2.0 (cos 60’=0.5 or set 60’=2.0)
to provide the steady, coordinated turn. If
the airplane were at a 60’ bank and lift were
not provided to produce the exact load factor
of 2.0, the aircraft would be accelerating in the
vertical direction as well as the horizontal di-
rection and the turn would not be steady.
Also, any sideforce on the aircraft due to
sideslip, etc., would place the resultant aero-
dynamic force out of the plane of symmetry
perpendicular to the lateral axis and the turn
would not be coordinated.
As a consequence of the increase lift re-
quired to produce the steady turn in a bank,
’ ihe induced drag is increased above that in-
curred by steady, wing level, lift-equal-weight
flight. In a sense, the increased lift required
in a steady turn will increase the total drag or
power required in the same manner as increased
gross weight in level flight. The curves of
figure 2.28 illustrate the general effect of turn-
ing flight on the total thrust and power re-
quired. Of course, the change in thrust re-
quired at any given speed is due to the change
in induced drag and the magnitude of change
depends on the value of induced drag in level
flight and the angle of bank in .turning flight.
Since the induced drag generally varies as the
square of C,, the following data provide an
illustration of the effect of various degrees of
bank :
Load factor, Pcrccnt incrcaw in
n induced drag from
lcvcl flight
Since the, induced drag predominates at low
speeds, steep turns at low speeds can produce
significant increases in thrust or power required
to maintain altitude. Thus, steep turns must
be avoided after takeoff, during approach, and
especially during a critical power situation
from failure or malfunction of a powerplant.
The greatly increased induced drag is just as
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NAVWEPS 00-801-80
AIRPLANE PERFORMANCE
CENTRIFUGAL FORCE
iRUST
I I TURNING FLIGHT&
\ \
I VELOCITY, KNOTS
LEVEL FLIGHT
VELOCITY, KNOTS
Figure 2.28. Effect of Turning Flight
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NAVWEPS 00-8OT-80
AIRPLANE PERFORMANCE
important-if not more important-as the
increased stall speed in turning flight. It is
important also that any turn be well coordi-
nated to prevent the increased drag attendant
to a sideslip.
TURNING PERFORMANCE. The hori-
zontal component of lift will equal the centrif-
ugal force of steady, turning flight. This fact
allows development of the following relation-
ships of turning performance:
turn radius
P
r= 11.26 tan 6
where
r= turn radius, ft.
I’= velocity, knots (TAX)
ti = bank angle, degrees
ttrrn rate
ROT= 1,091 tan rb
V
where
ROT=rate of turn, degrees per sec.
$= bank angle, degrees
v=velocity, knots, TAS
These relationships define the turn radius, I,
and rate of turn, ROT, as functions of the two
principal variables: bank angle, +, and velocity,
I’ (TAX). Thus, when the airplane is flown
in the steady, coordinated turn at specific
values of bank angle and velocity, the turn
rate and turn radius are fixed and independent
of the airplane type. As an example, an air-
plane in a steady, coordinated turn at a bank
angle of 45’ and a velocity of 250 knots (TAS)
would have the following turn performance:
= 5,550 ft.
and
ROT=(I,091)(1.000)
250
-4.37 deg. per sec.
If the airplane were to hold the same angle of
bank at 500 knots (TAS), the turn radius
would quadruple (r=22,200 ft.) and the turn
rate would be one-half the original value
(ROT=2.19 deg. per sec.).
Values of turn radius and turn rate versus
velocity are shown in figure 2.29 for various
angles of bank and the corresponding load
factors. The conditions are for the steady,
coordinated turn at constant altitude but the
results are applicable for climbing or descend-
ing flight when the angle of climb or descent
is relatively small. While the effect of alti-
tude on turning performance is not immediately
apparent from these curves, the principal effect
must be appreciated as an increased true air-
speed (TAX) for a given equivalent airspeed
(EAS).
TACTICAL PERFORMANCE. Many tac-
tical maneuvers require the use of the maxi-
mum turning capability of the airplane. The
maximum turning capability of an airplane will
be defined by three factors:
(1) Maximum lift capability. The combi-
nation of maximum lift coefIicient, C,,=,
and wing loading, W/S, will define the
ability of the airplane to develop aero-
dynamically the load factors of maneuvering
flight.
(2) Optrating ftrcngth limits will define the
upper limits of maneuvering load factors
which will not damage the primary struc-
ture of the airplane. These limits must not
be exceeded in normal operations because of
the possibility of structural damage or
failure.
(3) Thwt or power limits will define the
ability of the airplane to turn at constant
altitude. The limiting condition would al-
low increased load factor and induced drag
until the drag equals the maximum thrust
available from the powerplant. Such a case
would produce the maximum turning capa-
bility for maintaining constant altitude.
The first illustration of figure 2.30 shows
how the aerodynamic and structural limits
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NAVWEPS 00-801-80
AIRPLANE PERFORMANCE
define the maximum turning performance.
The acrodynomic limir describes the minimum
turn radius available to the airplane when
operated at C,,,,. When the airplane is at the
stall speed in level flight, all the lift is neces-
sary to sustain the aircraft in flight and none
is available to produce a steady turn. Hence,
the turn radius at the stall speed is infinite.
As speed is increased above the stall speed, the
airplane at C,,, is able to develop lift greater
than weight and produce a finite turn radius.
For example, at a speed twice the stall speed,
the airplane at CL,,,,= is able to develop a load
factor of four and utilize a bank angle of 75.5’
(cos 75.~~ = 0.25). Continued increase in
speed increases the load factor and bank angle
which is available aerodynamically but, be-
cause of the increase in velocity and the basic
effect on turn radius, the turn radius approaches
an absolute minimum value. When C,,, is
unaffected by velocity, the aerodynamic mini-
mum turn radius approaches this absolute
value which is a function of C,,,,,,,, W/S, and 6.
Actually, the one common denominator of
aerodynamic turning performance is the wing
level stall speed.
The aerodynamic limit of turn radius requires
that the increased velocity be utilized to pro-
duce increasing load factors and greater angles
of bank. Obviously, very high speeds will
require very high load factors and the absolute
aerodynamic minimum turn radius will require
an infinite load factor. Increasing speed above
the stall speed will eventually produce the
limit load factor and continued increase in
speed above this point will require that load
factor and bank angle be limited to prevent
structural damage. When the load factor and
bank angle are held constant at the structural
limit, the turn radius varies as the square of
the velocity and increases rapidly above the
aerodynamic limit. The intersection of ‘the
aerodynamic limit and structural limit lines
is the ‘*maneuver speed.” The maneuver
speed is the minimum speed necessary to
develop aerodynamically the limit load factor
180
and it produces the minimum turn radius
within aerodynamic and structural limitations.
At speeds less than the maneuver speed, the
limit load factor is not available aerodynami-
cally and turning performance is aerody-
namically limited. At speeds greater than
the maneuver speed, CL- and maximum
aerodynamic load factor are not available and
turning performance is structurally limited.
When the stall speed and limit load factor
are known for a particular configuration, the
maneuver speed is related by the following
expression:
where
V,=maneuver speed, knots
V.=stall speed, knots
n limit = limit load factor
For example, an airplane with a limit load
factor of 4.0 would have a maneuver speed
which is twice the stall speed.
The aerodynamic limit line of the first
illustration of figure 2.30 is typical of an air-
plane with a CL, which is invariant with
speed. While this is applicable for the ma-
jority of subsonic airplanes, considerable differ-
ence would be typical of the transonic or
supersonic airplane at altitude. Compressi-
bility effects and changes in longitudinal
control power may produce a maximum avail-
able CL which varies with velocity and an
aerodynamic turn radius which is not an
absolute minimum at the maximum of velocity.
The second illustration of figure 2.30 describes
the constant altitude turning performance
of an airplane. When an airplane is at high
,altitude, the turning performance at the high
speed end of the flight speed range is more
usually thrust limited rather than structurally
limited. In flight at constant altitude, the
thrust must equal the drag to maintain equilib-
rium and, thus, the constant altitude turn
radius is infinite at the maximum level flight
speed. Any bank or turn at maximum level
flight speed would incur additional drag and | 197 | 197 | 00-80T-80.pdf |
NAVWEPS 00-801-80
AIRPLANE PERFORMANCE
A
TURN
RADIUS
F:
A-- I t
VELOCITY, KNOTS (TAS)
EFFECT OF AERODYNAMIC AND
STRUCTURAL LIMIT ON TURNING
PERFORMANCE
ABSOLUTE MINIMUM
L
TURN
RADIUS
F:
CONSTANT ALTITUDE TURNING
PERFORMANCE
I
,-INCREASING
BANK ANGLE
THRUST OR
t
VELOCITY, KNOTS (TAS)
figure 2.30. Maneuvering Performance
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NAVWEPS OO-EOT-80
AIRPLANE PERFORMANCE
cause the airplane to descend. However, as
speed is reduced below the maximum level
flight speed, parasite drag reduces and allows
increased load factors and bank angles and
reduced radius of turn, i.e., decreased parasite
drag allows increased induced drag to accom-
modate turns within the maximum thrust
available. Thus, the considerations of con-
stant altitude will increase the minimum turn
radius above the aerodynamic limit and define
a particular airspeed for minimum turn radius.
Each of the three limiting factors (aero-
dynamic, structural, and power) may combine
to define the turning performance of an air-
Pl ane. Generally, aerodynamic and structural
limits predominate at low altitude while aero-
dynamic and power limits predominate at high
altitude. The knowledge of this turning per-
formance is particularly necessary for effective
operation of fighter and interceptor types of
airplanes.
TAKEOFF AND LANDING PERFORMANCE
The majority of pilot caused airplane acci-
dents occur during the takeoff and landing
phase of flight. Because of this fact, the
Naval Aviator must be familiar with all the
many variables which influence the takeoff and
landing performance of an airplane and must
strive for exacting, professional techniques of
operation during these phases of flight.
Takeoff and landing performance is a con-
dition of accelerated motion, For instance,
during takeoff the airplane starts at zero veloc-
ity and accelerates to the takeoff velocity to
become airborne. During landing, the air-
plane touches down at the landing speed and
decelerates (or accelerates negatively) to the
zero velocity of the stop. In fact, the landing
performance could be considered as a takeoff
in reverse for purposes of study. In either
case, takeoff or landing, the airplane is ac-
celerated between zero velocity and the takeoff
or landing velocity. The important factors of
takeoff or landing performance are:
(1) The takeoff or landing velocity which
will generally be a function of the stall
speed or minimum flying speed, e.g., 15 per-
cent above the stall speed.
(2) The accclcration during the takeoff or
landing roll. The acceleration experienced
by any object varies directly with the un-
balance of force and inversely as the mass of
the object.
(3) The takeoff or landing roll distance is
a function of both the acceleration and
velocity.
In the actual case, the takeoff and landing dis-
tance is related to velocity and acceleration in
a .very complex fashion. The main source of
the complexity is that the forces acting on the
airplane during the takeoff or landing roll are
“difficult to define wit,h simple relationships.
Since the acceleration is a function of these
forces, the acceleration is difficult to define in
a simple fashion and it is a principal variable
affecting distance. However, some simplifica-
tion can be made to study the basic relatiomhip
of acceleration, velocity, and distance While
the acceleration is not necessarily constant or
uniform throughout the takeoff or landing
roll, the assumption of uniformly acceler-
ated motion will facilitate study of the princi-
pal variables. affecting takeoff and landing
distance.
From basic physics, the relationship of
velocity, acceleration, and distance for uni-
formly accelerated motion is defined by the
following equation:
s=g
where
S= acceleration distance, ft.
V= final velocity, ft. per sec., after accel-
erating uniformly from zero velocity
a= acceleration, ft. per sec.*
This equation ‘could relate the takeoff distance
in terms of the takeoff velocity and acceleration
when the airplane is accelerated uniformly
from zero velocity to the final takeoff velocity.
Also, this expression could relate the landing
distance in terms of the landing velocity and
deceleration when the airplane is accelerated
(negatively) from the landing velocity to a
complete stop. It is important to note that
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AIRPLANE PERFORMANCE | 200 | 200 | 00-80T-80.pdf |
NAVWEPS 00-801-80
AIRPLANE PERFORMANCE
the distance varies directly as the square of the
velocity and inversely as the acceleration.
As an example of this relationship, assume
that during takeoff an airplane is, accelerated
uniformly from zero velocity to a takeoff
velocity of 150 knots (253.5 ft. per sec.) with
an acceleration of 6.434 ft. per sec.* (or, 0.2g,
since g=32.17 ft. per sec.*). The takeoff
distance would be:
= (253.5)*
(2)(6.434)
=5,ooo ft.
If the acceleration during takeoff were reduced
10 percent, the takeoff distance would increase
11.1 percent; if the takeoff velocity were
increased 10 percent, the takeoff distance
would increase 21 percent. These relation-
ships point to the fact that proper accounting
must be made of altitude, temperature, gross
weight, wind, etc. because any item affecting
acceleration or takeoff velocity will have a
definite effect on takeoff distance.
If an airplane were to land at a velocity of
150 knots and be decelerated uniformly to a
stop with the same acceleration of 0.2g, the
landing stop distance would be 5,000 ft.
However, the case is not necessarily that an
aircraft may have identical takeoff and landing
performance but the principle illustrated is that
distance is a function of velocity and accelera-
tion. As before, a 10 percent lower accelera-
tion increases stop distance Il.1 percent, and a
10 percent higher landing speed increases
landing distance 21 percent.
The general relationship of velocity, accel-
eration, and distance for uniformly accelerated
motion is illustrated by figure 2.31. In this
illustration., acceleration distance is shown as
a function of velocity for various values of
acceleration.
TAKEOFF PERFORMANCE. The mini-
mum takeoff distance is of primary interest in
the operation of any aircraft because it defines
the runway requirements. The minimum take-
off distance is obtained by takeoff at some
minimum safe velocity which allows sufficient
margin above stall and provides satisfactory
control and initial rate of climb. Generally,
the takeoff speed is some fixed percentage of
the stall speed or minimum control speed for
the airplane in the takeoff configuration. As
such, the takeoff will be accomplished at some
particular value of lift coefficient and angle of
attack. Depending on the airplane character-
istics, the takeoff speed will be anywhere from
1.05 to 1.25 times the stall speed or minimum
control speed. If the takeoff speed is specified
as 1.10 times the stall speed, the takeoff lift
coefficient is 82.6 percent of CL- and the angle
of attack and lift coeticient for takeoff are
fixed values independent of weight, altitude,
wind, etc. Hence, an angle of attack indicator
can be a valuable aid during takeoff.
To obtain minimum takeoff distance at the
specified takeoff velocity, the forces which act
on the aircraft must provide the maximum
acceleration during the takeoff roll. The
various forces acting on the aircraft may or
may not be at the control of the pilot and
various techniques may be necessary in certain
airplanes to maintain takeoff acceleration at
the highest value.
Figure 2.32 illustrates the various forces
which act on the aircraft during takeoff roll.
The powerplant thrust is the principal force to
provide the acceleration and, for minimum
takeoff ,distance, the output thrust should be
at a maximum. Lift and drag are produced as
soon as the airplane has speed and the values
of lift and drag depend on the angle of attack
and dynamic .pressure. Rolling friction results
when there is a normal force on the wheels
and the friction force is the product of the
normal force and the coefficient of rolling
friction. The normal force pressing the wheels
against the runway surface is the net of weight
and lift while the rolling friction coefficient is
a function of the tire type and runway surface
texture. | 201 | 201 | 00-80T-80.pdf |
The acceleration of the airplane at any
instant during takeoff roll is a function of the
net accelerating force and the airplane mass.
From Newton’s second law of motion:
or
where
a=acceleration,~fr. per set
Fn- net accelerating force,
W=weight, lbs.
g? gravitational accelerat
=32.17 ft. per sec.*
M= mass, slugb
= WE
The riet aicelerating fdrce on ‘the airplane,
F,, is the net of thiust, T, drag, D, and rolling
friction, F. Thus, the acceleration -at any
instant during takeoff roll is:
a=&T-D-F)
Figure 2.32 illustrates the typical variation of
the various fbrces acting on the aircraft
throughout the takeoff roll: If ‘it is assumed
that the aircraft is at essentially constant
angle of attack during takeoff roll, CL and Co
are constant and the forces of lift and drag
vary as the square of the speed. For the case
of uniformly accelerated motion, distance
along the takeoff roll is proportional also to
the square bf the velocity hence velocity
squared and distance can be used almost synon-
omously. Thus, lift and drag will vary lint
arly with dyriamic pressure (4) or P from
the point of beginning takeoff roll. As the
rolling friction coefficient -is esscnti&y un-
affected by velocity, the rolling ftiction will
vary as the normal force on the wheels. At
zero velocity, the normal force on the wheels
is equal to the airplane weight but, at takeoff
velocity, the lift is equal to the weight and
the normal force is zero. Hence, rolling fric-
tion decreases linearly with 4 or Vz from the
beginning of takeoff roll and reaches zero at
the point of takeoff.
NAVWEPS 00-801-80
AIRPLANE PERFORMANCE
The total retarding for& on the aircraft is
the sum of drag and rolling friction (D+F)
and, for the majority of configurations, this
sum is nearly Constant or changes only slightly
during the takeoff roll. The net accelerating
force is then the difference between the power-
plant thrust and the total retarding force,
Fn=T-D-F
The variation of the net accelerating force
throughout the takeoff roll is shown in figure
2.32. The typical propeller airplane demon-
strates a net accelerating force which decreases
with velocity and the resulting acceleration is
initially high but decreases throughout the
takeoff roll. The typical jet airplane demon-
strates a net accelerating force which is essen-
tially constant throughout the takeoff roll.
As a result, the takeoff performance of the
typical turbojet airpiane will compare closely
with the case for uniformly accelerated motion.
The pilot technique required to achieve peak
acceleration throughout takeoff roll can vary
considerably between airplane configurations.
In some instances, maximum acceleration will
be obtained by allowing the airplane to remain
in the three-point attitude throughout the roll
until the airplane simply reaches lift-equal-to-
weight and flies off the ground. Other air-
planes may require the three-point attitude
until the takeoff speed is reached then rotation
to the takeoff angle of attack to become air-
borne. Still other configurations may require
partial or complete rotation to the takeoff
angle of attack prior to reaching the takeoff
speed. In this case, the procedure may be
necessary to provide a smaller retarding force
(D+F) to achieve peak acceleration. When-
ever any form of pitch rotation is necessary the
pilot must provide the proper angle of attack
since an excessive angle of attack will cause
excessive drag and hinder (or possibly pre-
clude) a successful takeoff. Also, irisufficient
rotation may provide added rolling resistance
or require that the airplane accelerate to some
excessive speed prior to becoming airborne.
185
Revised January 1965 | 202 | 202 | 00-80T-80.pdf |
NAVWEPS O&601-80
AIRPLANE PERFORMANCE
FORCES ACTING ON THE AIRPLANE DURING
TAKEOFF ROLL
LlFT,L7
/’
,-THRUST (PROPELLER), T ,/
/
THRUST (JETI,T /
/’ ‘\
(T-D-F) / ‘1
NET
ACCELERATING /’
FORCE
(PROPELLER)- , I ’
(T;&F)
CONSTANT
a 1
ACCELERATING
INNING WHICH IS ESSENTIALLY POINT OFF
OF TAKEOFF PROPORTIONAL TO DISTANCE TAKEOFF
ROLL IN UNIFORMLY ACCELERATED
MOTION
Figure 2.32. Forces Acting on the Airplane During Takeoff Roll
186 | 203 | 203 | 00-80T-80.pdf |
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