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In this sense, an angle of attack indicator is
especially useful for night or instrument takeoff
conditions as well as. the ordinary day VFR
takeoff conditions. Acceleration errors of the
attitude gyro usually preclude accurate pitch
rotation under these conditions.
FACTORS AFFECTING TAKEOFF PER-
FORMANCE. In addition to the important
factors of proper technique, many other vari-
ables affect the takeoff performance of an air-
plane. Any item which alters the takeoff
velocity or acceleration during takeoff roll will
affect the takeoff distance. In order to evalu-
ate the effect of the many variables, the prin-
cipal relationships of uniformly accelerated
motion,will be assumed and consideration will
be given to those effects due to any nonuni-
formity of acceleration during the process of
takeoff. Generally, in the case of uniformly
accelerated motion, distance varies directly
with the square of the takeoff velocity and in-
versely as the takeoff acceleration.
where
S= distance
V= velocity,
a= acceleration
;’ con&&‘(I) applies to some known takeoff
distance, Si, which was common to
some original takeoff velocity, Vi, and
acceleration, ai.
condition (2) applies to some new takeoff
distance, Sa, which is the result of some
different value of takeoff velocity, Vs, or
acceleration, aa.
With xhis basic relationship, the effect of the
many variables on takeoff ‘distance can be
approximated.
The effect of gross weight on takeoff distance is
large and proper consideration of this item
must be made in predicting takeoff distance.
Increased gross weight can be considered to
produce a threefold effect on takeoff perform-
ance: (1) increased takeoff velocity, (2) greater
NAVWEPS 00401-80
AIRPLANE PERFORMANCE
mass to accelerate, and (3) increased retarding
force (D+F). If the gross weight increases,
a greater speed is necessary to produce the
greater lift to get the airplane airborne at the
takeoff lift coefficient. The relationship of
takeoff speed and gross weight would be as
follows:
where
VI= takeoff velocity corresponding to
some original weight, Wi
V2= takeoff velocity corresponding to
some different weight, W,
Thus, a given airplane in the takeoff configura-
tion at a given gross weight will have a specific
takeoff speed (EAS or CAS) which is invariant
with altitude, temperature, wind, etc. because
a certain value of 4 is necessary to provide lift
equal to weight at the takeoff CL. As an ex-
ample of the effect of a change in gross weight
a 21 percent increase in takeoff weight will
require a 10 percent increase in takeoff speed to
support the greater weight.
A change in gross weight will change the
net accelerating force, Fn, and change the
mass, M, which is being accelerated. If the
airplane has a relatively high thrust-to-weight
ratio, the change in the net accelerating force
is slight and the principal effect on accelera-
tion is due to the change in mass.
To evaluate the effect of gross weight on
takeoff distance, the following relationship
are used :
the effect of weight on takeoff velocity is
if the change in net accelerating force~is
neglected, the effect of weight on accelera-
tion is
187 | 204 | 204 | 00-80T-80.pdf |
NAVWEPS 00-801-80
AIRPLANE PERFORMANCE
the effect of these items on takeoff dis-
tance is
or
g+?)x(Z)
J-2 WY2 a -= - J-1 ( ) WI
(ut 1eaJt this effect because weight will
alter the net accelerating force)
This result approximates the e5ect of gross
weight on takeoff distance for airplanes with
relatively high thrust-to-weight ratios. In
effect, the takeoff distance will vary at least
as the square of the gross weight. For ex-
ample, a 10 percent increase ,in takeoff gross
weight would cause:
a 5 percent increase in takeoff velocity
at least a, 9 percent decrease in acceleration
at least a 21 percent increase in takeoff
distance
For the airplane with a high thrust-to-weight
ratio, the increase in takeoff distance would
be approximately 21 to 22 percent but, for
the airplane with a relatively low thrust-to-
*eight ratio, the increase in takeoff distance
would be approximately 25 to 30 percent.
Such a powerful effect requires proper con-
sideration of gross weight in predicting takeoff
distance.
The effect of wind on takeoff distance is large
and proper consideration also must be provided
when predicting takeoff distance. The effect
of a headwind is to allow the airplane to reach
the takeoff velocity at a lower ground velocity
while the effect of a tailwind is to require the
airplane to achieve a greater ground velocity
to attain the takeoff velocity. The effect of
the wind on acceleration is relatively small
and, for the most part, can be neglected. To
evaluate the effect of wind on takeoff distance,
the following relationships are used:
the effect of a headwind is to reduce the
takeoff ground velocity by the amount of
the headwind velocity, VW
the effect of wind on acceleration is
negligible,
the effect of these items on takeoff distance
is
where
Xi= zero wind takeoff distance
Sa=takeoff distance into the head-
wind
V,= headwind velocity
VI= takeoff ground velocity with zero
wind, or, simply, the take05
airspeed
As a .result of this relationship, a headwind
wh,ich is 10 percent of the takeoff airspeed will
reduce the takeoff distance 19 percent. How-
ever, a tailwind (or negative headwind) which
is 10 percent of the take05 airspeed will in-
crease the takeoff distance 21 percent. In the
case where the headwind velocity is 50 percent
of the takeoff speed, the takeoff distance would
be approximately 25 percent of the zero wind
takeoff distance (75 percent reduction).
The e5ect of wind on landing distance is
identical to the effect on takeoff distance.
Figure 2.33 illustrates the general dfect of
wind by the percent change in takeoff or land-
ing distance as a function of the ratio of wind
velocity to takeoff or landing speed.
188 | 205 | 205 | 00-80T-80.pdf |
NAVWEPS 00-801-80
AIRPLANE PEkFORMANCE
Figure 2.33. Approximate Effect of Wind Velocity on Takeoff or Landing Distance
189 | 206 | 206 | 00-80T-80.pdf |
NAVWEPS 00-8OT-80
AIRPLANE PERFORffANCE
The cffcct of nrnzuay slope on takeoff distance
is due to the component of weight along the
inclined path of the airplane. A runway
slope of 1 percent would provide a force com-
ponent along the path of the airplane which is
1 percent of the gross weight. Of course, an
upslope would contribute a retarding force
component while a downslope would contri-
bute an accelerating force component. For
the case of the upslope, the retarding force
component adds to drag and rolling friction to
reduce the net accelerating force. Ordinarily,
a 1 percent runway slope can cause a 2’tO 4
percent change in takeoff distance depending
on rhe airplane characrerisrics. The airplane
with the high thrust-to-weight ratio is least
affected while the airplane with the low thrust-
to-weight ratio is most affected because the
slope force component causes a relatively
greater change in the net accelerating force.
The effect of runway slope must be consid-
ered when predicting the takeoff distance but
the effect is usually minor for the ordinary run-
way slopes and airplanes with moderate
thrust-to-weight ratios. In fact, runway slope
considerations are of great significance only
when the runway slope is large and the airplane
has an intrinsic low acceleration, i.e., low
thrust-to-weight ratio. In the ordinary case,
the selection of the takeoff runway will favor
the direction with an upslope and headwind
rather than the direction with a downslope
and tailwind.
The effect of proper takeoff t&city is important
when runway lengths and takeoff distances are
critical. The takeoff speeds specified in the
flight handbook are generally the minimum
safe speeds at which the airplane can become
airborne. Any attempt to take 05 below the
recommended speed may mean that the air-
craft may stall, be difficult to control, or have
very low initial rate of climb. In some cases,
an excessive angle of attack may not allow
the airplane to climb out of ground effect. On
the other hand, an excessive airspeed at takeoff
may improve the initial rare of climb and
“feel” of the airplane but will produce an un-
desirable increase in takeoff distance. Assum-
ing that the acceleration is essentially un-
affected, the takeoff distance varies as the
square of the takeoff velocity,
s* vz.2 -= -
0 J-1 v,
Thus, 10 percent excess airspeed would increase
the takeoff distance 21 percent. In most criti-
cal takeoff conditions, such an increase in
takeoff distance would be prohibitive and the
pilot must adhere to the recommended takeoff
speeds.
The effect of prcs~wc altitude and ambient
rcmpcraturc is to define primarily the density
altitude and its effect on takeoff performance.
While subsequent corrections are appropriate
for the effect of temperature on certain items
of powerplant performance, density altitude
defines certain effects on takeoff performance.
An increase in density altitude can produce a
two-fold effect on takeoff performance: (I) in-
creased takeoff velocity and (2) decreased
thrust and reduced net accelerating force. If
a given weight and configuration of airplane is
taken to altitude above standard sea level, the
airplane will still require the same dynamic
pressure to become airborne at the takeoff lift
coefficient. Thus, the airplane at altitude will
take 05 at the same equivalent airspeed (EAS)
as at sea level, but because of the reduced
density, the true airspeed (TAS) will be
greater. From basic aerodynamics, the rela-
tionship between true airspeed and equivalent
airspeed is as follows:
TAS 1
EAS=F
where
TAS= true airspeed
EAS= equivalent airspeed
n=altitude density ratio
0 = Plpo
190 | 207 | 207 | 00-80T-80.pdf |
The effect of density altitude on powerplant
thrust depends much on the type of power-
plant. An increase in altitude above standard
sea level will bring an immediate decrease in
power output for the unsupercharged or ground
boosted reciprocating engine or the turbojet
and turboprop engines. However, an increase
in altitude above standard sea level will not
cause a decrease in power output for the super-
charged reciprocating engine until the altitude
exceeds the critical altitude. For those power-
plants which experience a decay in thrust with
an increase in altitude, the effect on the net
accelerating force and acceleration can be ap-
proximated by assuming a direct variation
with density. Actually, this assumed vari-
ation would closely approximate the effect on
airplanes with high thrust-to-weight ratios.
This relationship would be as follows:
a2 Fm P -=-=-En
al Frill PO
where
ai, Fn, = acceleration and net accelerating
force corresponding to sea level
aa, Fn, = acceleration and net accelerating
force corresponding to altitude
~=altitude density ratio
In order to evaluate the effect of these items on
takeoff distance, the following relationships
are used :
if an increase in altitude does not alter ac-
celeration, the principal effect would be
due to the greater TAS
;=(g,yxe)
where
f2 1 -=-
$1 (T
Si=standard sea level takeoff distance
St= takeoff distance at altitude
o-altitude density ratio
if an increase in altitude reduces accelera-
tion in addition to the increase in TAS, the
NAVWEPS 00-805-80
AIRPLANE PERFORMANCE
combined effects would be approximated
for the case of the airplane with high in-
trinsic acceleration by the following:
g=(gyx(~)
g=(i)x(;)
s2 12 -= -
0 J-1 a
where
S,= standard sea level takeoff distance
Ja= takeoff distance at altitude
o=altitude density ratio
As a result of these relationships, it should.
be appreciated that density altitude will affect
takeoff performance in a fashion depending
much on the powerplant type. The effect of
density altitude on takeoff distance can be
appreciated by the following comparison:
sealevel....
I.cmft.....
Z,cmfC.....
,,mfi.....
4.@JJfc.....
5.Ccnft.....
6.-xafC.....
--
1
1
I
I
1
I
-
..om
.0?.98
..c605
L. wls
L. 126
L. 1605
1.1965
L.cca
L.oa5
1.125
1.191
1.264
1.347
1.431
-
P
--
-
drirude
--
0 0
2.98 6.05
6.05 12.5
9.28 19.5
12.6 26.4
16.05 34.7
19.65 0.1
0
9.8
19.9
30.1
40.6
52.3
65.8
-
From the previous table, some approximate
rules of thumb may be derived to illustrated
the differences between the various airplane
types. A 1,ooo-ft. increase in density altitude
191 | 208 | 208 | 00-80T-80.pdf |
NAVWEPS 00-801-80
AIRPLANE PERFORMANCE
will cause these approximate increases in
takeoff distance:
3% percent for the supercharged recipro-
cating airplane when below critical
altitude
7 percent for the turbojet with high thtust-
to-weight ratio
10 percent for the turbojet with low
thrust-to-weight ratio
These approximate relationships show the
turbojet airplane to be much more sensitive to
density altitude than the reciprocating powered
airplane, This is an important fact which
must be appreciated by pilots in transition
from propeller type to jet type airplanes.
Proper accounting of pressure altitude (field
elevation is a poor substitute) and temperature
is mandatory for accurate prediction of takeoff
roll distance.
The most critical conditions of takeoff
performance are the result of somecombination
of high gross weight, altitude, temperature
and unfavorable wind. In a11 cases, ir be-
hooves the pilot to make an accurate prcdic-
tion of takeoff’ distance from the performance
data of the Flight Handboo& regardless of the
runway available, and to strive for.2 polished,
professional takeoff technique.
In the prediction of takeoff distance from
the handbook data, the following primary
considerations must be given:
Reciprocating powered airplane
(1) Pressure altitude and temperature-
to define the effect of density altitude on
distance.
(2) Gross weight-a large effect on dis-
tance.
(3) Specific humidity-to correct cake-
off distance for the power loss associated
with water vapor.
(4) Wind-a large effect due to the wind
or wind component along the runway.
Turbine powered airplane
(I) Pressure altitude and temperature-
to define the effect of density altitude.
(2) Gross weight.
(3) Temperature--an additional correc-
tion for nonstandard temperatures to ac-
count for the thrust loss associated with
high compressor inlet air temperature.
For this correction the ambient tempera-
ture at the runway conditions is appro-
priate rather than the ambient temperature
at some distant location.
(4) Wind.
In addition, corrections are necessary to ac-
count for runway slope, engine power defi-
ciencies, etc.
LANDING PERFORMANCE. In many
cases, the landing distance of an airplane will
define the runway requirements for flying
operations. This is particularly the case of
high speed ‘jet airplanes at low altitudes where
landing distance is the problem rather than
takeoff performance. The minimum landing
distance is obtained by landing at some mini-
mum safe velocity which allows sufficient mar-
gin above stall and provides satisfactory, con-
trol and capability for waveoff Generally,
the landing speed is some fixed percentage of
the stall speed or minimum control speed for
the airplane in the landing configuration. As
such, the landing will be accomplished at
some particuIar value of ~lift coefficient and
angle of attack. The exact value of CL and
P for landing will depend on the airplane
characteristics but, once defined, the values are
independent of weight, altitude, wind, etc.
Thus, an angle of attack indicator can be a
valuable aid during approach and landing.
To obtain minimum landing distance at the
specified landing velocity, the forces which
act on the airplane must provide maximum
deceleration (or negative.acceIeration) during
the landing roll. The various forces actin~g.
on the airplane during the landing roll may
require various techniques to maintain landing
deceleration at the peak value.
Figure 2.34 illustrates the forces acting on
the aircraft during landing roll. The power-
plant thnrJt should be a minimum positive
192 | 209 | 209 | 00-80T-80.pdf |
value, or, if reverse thrust is available, a maxi-
mum negative value for minimum landing dis-
tance. Lift and drag are produced as long as
the airplane has speed and the values of lift
and drag depend on dynamic pressure and
angle of attack. Braking friction results when
there is a normal force on the braking wheel
surfaces and the friction force is the product of
the normal force and the coe&cient of braking
friction. The normal force on the braking
surfaces is some part of the net of weight and
lift, i.e., some other part of this net may be
distributed to wheels which have no brakes.
The maximum coefficient of braking friction is
primarily a function of the runway surface con-
dition (dry, wet, icy, etc.) and rather inde-
pendent of the type of tire for ordinary condi-
tions (dry, hard surface runway). However,
the operating coefficient of braking friction is
controlled by the pilot by the use of brakes.
The acceleration of the airplane during the
landing roll is negative (deceleration) and will
be considered to be in that sense. At any in-
stant during the landing roll the acceleration
is a function of the net retarding force and the
airplane mass. From Newton’s second law of
motion:
B = Fr/M
or
where
a=g 0+/W)
a= acceleration, ft. per seca (negative)
Fr=net retarding force, lbs.
g= gravitational acceleration, ft. per sec.’
W=weight, lbs.
M= mass, slugs
= Wig
The net retarding force on the airplane, Fr, is
the net of drag, D, braking friction, F, and
thrust, T. Thus, the acceleration (negative)
at any instant during the landing roll is :
d=$ (Df F--T)
NAVWEPS OO-EOT-RO
AtRPtANE PERFORMANCE
Figure 2.34 illustrates the typical variation
of the various forces acting on the aircraft
throughout the landing roll. If it is assumed
that the aircraft is at essentially constant angle
of attack from the point of touchdown, CL and
CD are constant and the forces of lift and drag
vary as the square of the velocity. Thus, lift
and drag will decrease linearly with 4 or V’
from the point of touchdown. If the braking
coefficient is maintained at the maximum
value, this maximum value of coefficient of
friction is essentially constant with speed and
the braking friction force will vary as the
normal force on the braking surfaces. As the
airplane nears a complete stop, the velocity
and lift approach zero and the normal force on
the wheels approaches the weight of the air-
plane. At this point, the braking friction
force is at a maximum. Immediately after
touchdown, the lift: is quite large and the
normal force on the wheels is small. As a re-
sult, the braking friction force is small. A
common error at this point is to apply exces-
sive brake pressure without sufficient normal
force on the wheels. This may develop a skid
with a locked wheel and cause the tire to blow
out so suddenly that judicious use of the brakes
is necessary.
The coefficient of braking friction can reach
peak values of 0.8 but ordinarily values near
0.5 are typical for the dry hard surface runway.
Of course, a slick, icy runway can reduce the
maximum braking friction coefficient to values
as low as 0.2 or 0.1: If the entire weight of
the airplane were the normal force on the brak-
ing surfaces, a coefficient of braking friction of
0.5 would produce a deceleration of %g, 16.1 ft.
per sec.a Most airplanes in ground effect
rarely produce lift-drag ratios lower than 3 or
4. If the lift of the airplane were equal to the
weight, an L/D = 4 would produce a decelera-
tion of xg, 8 ft. per sec.* By this comparison
it should be apparent that friction braking
offers the possibility of greater deceleration
than airplane aerodynamic braking. To this
end, the majority of airplanes operating from | 210 | 210 | 00-80T-80.pdf |
NAVWEPS 00-801-80
AIRPLANE PERFORMANCE
FORCES ACTING ON THE AIRPLANE
DURING LAUDING ROLL
I-- LIFT
DRAG + BRAKING
POINT FINAL
OF LANDING STOP
TOUCHDOWN
Figure 2.34. Forces Acting on Airplane During Landing Roll
194 | 211 | 211 | 00-80T-80.pdf |
dry hard surface runways will require particular
techniques to obtain minimum landing dis-
tance. Generally, the technique involves low-
ering the nose wheel to the runway and retract-
ing the flaps to increase the normal force on
the braking surfaces. While the airplane drag
is reduced, the greater normal force can pro-
vide greater braking friction force to com-
pensate for the reduced drag and the net retard-
ing force is increased.
The technique necessary for minimum land-
ing distance can be altered~ to some extent in
certain situations. For example, low aspect
ratio airplanes with high longitudinal control
power can create very high drag at the high
speeds immediate to landing touchdown. If
the landing gear configuration or flap or
incidence setting precludes a large reduction
of CL, the normal force on the braking surfaces
and braking friction force capability are rela-
tively small. Thus, in the initial high speed
part of the landing roll, maximum deceleration
would be obtained by creating the greatest
possible aerodynamic drag. By the time the
aircraft has slowed to 70 or 80 percent of the
touchdown speed, aerodynamic drag decays
but braking action will then be effective.
Some form of this technique may be necessary
to achieve minimum distance for some con-
figurations when the coefficient of braking
friction is low (wet, icy runway) and the
braking friction force capability is reduced
relative to airplane aerodynamic drag.
A distinction should be made between the
techniques for minimum landing distance and
an ordinary landing roll with considerable
excess runway .available. Minimum landing
distance will be obtained from the landing
speed by creating a continuous peak decelera-
tion of the airplane. This condition usually
requites extensive use of the brakes for maxi-
mum deceleration. On the other hand, an
ordinary landing roll with considerable excess
runway may allow extensive use of aero-
dynamic drag to minimize wear and tear on
the tires and brakes. If aerodynamic drag is
NAVWEPS 00-ROT-80
AIRPLANE PERFORMANCE
sufficient to cause deceleration of the airplane
it can be used in deference to the brakes in the
early stages of the landing roll, i.e., brakes
and tires suffer from continuous, hard use but
airplane aerodynamic drag is free and does not 1
wear out with use. The use of aerodynamic
drag is applicable only for deceleration to 60
ot 70 percent of the touchdown speed. At
speeds less than 60 to 70 percent of the touch-
down speed, aerodynamic drag is so slight as
to be of little use and braking must be utilized
to produce continued deceleration of the
airplane.
Powerplant thrust is not illustrated on
figure 2.34 for there are so many possible
variations. Since the objective during the
landing toll is to decelerate, the powerplant
thrust should be the smallest possible positive
value or largest possible negative value. In
the case of the turbojet aircraft, the idle
thrust of the engine is nearly constant with
speed throughout the landing roll. The idle
thrust is of significant magnitude on cold days 1
because of the low compressor inlet air temper-
ature and low density altitude. Unfortu-
nately, such atmospheric conditions usually
have the corollary of poor braking action be-
cause of ice or water on the runway. The
thrust from a windmilling propeller with the
engine at idle can produce large negative thrust
early in the landing roll but the negative force
decreases with speed. The .large negative
thrust at high speed is valuable in adding to
drag and braking friction to increase the net
retarding force.
Various devices can be utilized to provide
greater deceleration-of the airplane or to mini-
mize the wear and teat on tires and brakes.
‘The drag parachute can provide a large retatd-
ing force at high 4 and greatly increase the de-
celeration during the initial phase of landing
toll. It should be noted that the contribution
of the drag chute is important only during the
high speed portion of the landing roll. For
maximum effectiveness, the drag chute must be
deployed immediately after the airplane is in
contact with the runway. Reverse thrust of
195
Revised January 1965 | 212 | 212 | 00-80T-80.pdf |
NAVWEPS 00-EOT-80
AIRPLANE PERFORMANCE
propellers is obtained by rotating the blade
angle well below the low pitch stop and
applying engine power. The action is to ex-
tract a large amount of momentum from the
airstream and thereby create negative thrust.
The magnitude of the reverse thrust from pro-
pellets is very large, especially in the case of
the turboprop where a very large shaft power
can be fed into the propeller. In the case of
reverse propeller thrust, maximum effective-
ness is achieved by use immediately after the
airplane is in contact with the runway. The
reverse thrust capability is greatest at the
high speed and, obviously, any delay in pro-
ducing deceleration allows runway to pass by
at a rapid rate. Reverse thrust of turbojet
engines will usually employ some form of
vanes, buckets, or clamshells in the exhaust to
turn or direct the exhaust gases forward.
Whenever the exit velocity is less than the in-
let velocity (or negative), a negative momen-
tum change occurs and negative thrust is
produced. The reverse jet thrust is valuable
and effective but it should not be compared
with the reverse thrust capability of a com-
parable propeller powerplant which has the
high intrinsic thrust at low velocities. As
with the propeller reverse thrust, jet reverse
thrust must be applied immediately after
ground contact for maximum effectiveness in
reducing landing distance.
FACTORS AFFECTING LANDING PER-
FORMANCE. In addition to the important
factors of proper technique, many other vari-
ables affect the landing performance of an air-
plane. Any item which alters the landing
velocity or deceleration during landing toll
will affect the landing distance. As with
takeoff performance, the relationships of uni-
formly accelerated motion will be assumed
applicable for studying the principal effects on
landing distance. The case of uniformly ac-
celerated motion defines landing distance as
varying directly as the square of the landing
velocity and inversely as the acceleration dur-
ing landing toll.
where
Si = landing distance resulting from certain
values of landing velocity, Vi, and
acceleration, 6zi
S2=landing distance resulting from some
different values of landing velocity,
V2, or acceleration, a2
With this relationship, the effect of the many
variables on landing distance can be apptoxi-
mated.
The effect of gross wclght on landing distance
is one of the principal items determining the
landing distance of an airplane One effect
of an increased gross weight is that the airplane
will require a greater speed to support the
airplane at the landing angle of attack
and lift coefficient. The relationship of land-
ing speed and gross weight would be as
follows:
where
Vi=landing velocity corresponding to
some original weight, W,
Vs = landing velocity corresponding to
some different weight, W,
Thus, a given airplane in the landing con-
figuration at a given gross weight will have a
specific landing speed (MS ot CAS) which is
invariant with altitude, temperature, wind,
etc., because a certain value of 4 is necessary
to provide lifr equal to weight at the landing
C,. As an example of the effect of a change in
gross weight, a 21 percent increase in landing
weight will require a 10 percent increase in
landing speed to support the greater weight.
When minimum landing distances are con-
sidered, braking friction forces predominate
during the landing toll and, for the majority
of airplane configurations, braking friction is
the main source of deceleration. In this case,
an increase in gross weight provides a greater | 213 | 213 | 00-80T-80.pdf |
214 | 214 | 00-80T-80.pdf |
|
NAVWEPS OO-ROT-80
AIRPLANE PERFORMANCE
normal force and increased braking friction
force to cope with the increased mass. Also,
the higher landing speed at the same CL and
CD produce an average drag which increased in
the same proportion as the increased weight.
Thus, increased gross weight causes like in-
creases in the sum of drag plus braking friction
and the acceleration is essentially unaffected.
To evaluate the effect of gross weight on
landing distance, the following relationships
are used:
the effect of weight on landing velocity is
if the net retarding force increases in the
same proportion as the .weight, the accel-
eration is unaffected.
the effect of these items on landing dis-
tance is,
or
$2 w*
s,=w,
In effect, the minimum landing distance will
vary directly as the gross weight. For ex-
ample, a 10 percent increase in gross weight
at landing would cause:
a 5 percent increase in landing velocity
a 10 percent increase in landing distance
A contingency of the previous analysis is the
relationship between weight and braking ftic-
tion force. The maximum coefficient of brak-
ing friction is relatively independent of the
usual range of normal forces and rolling speeds,
e.g., a 10 percent increase in normal force would
create a like 10 percent increase in braking
friction force. Consider the case of two air-
planes of the same type and c.g. position but
of ~diffetent gross weights. If these two air-
planes are rolling along the runway at some
speed at which aerodynamic forces are negli-
gible, the use of the maximum coefficient of
braking friction will bring both airplanes to
a stop in the same distance. The heavier ait-
plane will have the gteater mass to decelerate
but the greater normal force will provide a
greater retarding friction force. As a result,
both airplanes would have identical accelera-
tion and identical stop distances from a given
velocity. However, the heavier airplane
would have a greater kinetic energy to be dis-
sipated by the brakes and the principal differ-
ence between the two airplanes as they reach
a stop would be that the heavier airplane
would have the hotter brakes. Therefore,
one of the factors of braking performance is the
ability of the brakes to dissipate energy with-
out developing excessive temperatures and
losing effectiveness.
To appreciate the effectiveness of modern
brakes, a 30,000-lb. aircraft landing at 175
knots has a kinetic energy of 41 million ft.-lbs.
at the instant of touchdown. In a minimum
distance landing, the brakes must dissipate
most of this kinetic energy and sach brake must
absotb an input power of approximately 1,200
h.p. for 25 seconds. Such requirements for
brakes are extreme but the example serves to
illustrate the ptoblems of brakes for high
performance airplanes.
While a 10 percent increase in landing
weight causes :
a 5 percent higher landing speed
a 10 percent greater landing distance,
it also produces a 21 percent increase in the
kinetic energy of the airplane to be dissipated
during the landing roll. Hence, high landing
weights may approach the energy dissipating
capability of the brakes.
The s&t of wind on landing distance is large
and deserves proper consideration when pre-
dicting landing distance. Since the airplane
will land at a particular airspeed independent
of the wind, the principal effect of wind on
landing distance is due to the change in the
ground velocity at which the airplane touches
down. The effect of wind on acceleration
duting the landing distance is identical to the
198 | 215 | 215 | 00-80T-80.pdf |
NAVWEPS OO-ROLRO
AIRPlANE PERFORMANCE
effect on takeoff distance and is approximated
by the following relationship:
$2 v 2 ..-.= Sl c 1 13
where
Si= zero wind landing distance
Sa=landing distance into a headwind
I’, = headwind velocity
Vi=landing ground velocity with zero
wind or, simply, the landing airspeed
As a result of this relationship, a headwind
which is 10 percent of the landing airspeed will
reduce the landing distance 19 percent but a
tailwind (or ‘negative headwind) which is 10
percent of the landing speed will increase the
landing distance 21 percent. Figure 2.33 illus-
trates this general effect.
The effect of ranway slope on landing distance
is due to the component of weight along the
inclined path of the airplane. The relation-
ship is identical to the case of takeoff per-
formance but the magnitude of the effect is
not as great. While account must be made
for the effect, the ordinary values of runway
slope do not contribute a large effect on landing
distance. For this reason, the selection of the
landing runway will ordinarily favor the direc-
tion with a downslope and’headwind rather
than an upslope and tailwind.
The effect of pressure altitude and ambient tem-
perature is to define density altitude and its effect
on landing performance. An increase in dens-
ity altitude will increase the landing velocity
but will not alter the net retarding force. If
a given weight and configuration of airplane
is taken to altitude above standard sea level,
the airplane will still require the same 4 to
provide lift equal to weight at the landing C,.
Thus, the airplane at altitude will land at the
same equivalent airspeed (EAS) as at sea level
but, because of the reduced density, the true
airspeed (TM) will be greater. The relation-
ship between true airspeed and equivalent air-
speed is as follows:
TAS 1
E-33=5
where
TAS= true airspeed
EAS= equivalent airspeed
a=altitude density ratio
Since the airplane lands at altitude with the
same weight and dynamic pressure, the drag
and braking friction throughout the landing
toll have the same values as at sea level. As
long as the condition is within the capability
of the brakes, the net retarding force is un-
changed and the acceleration is the same as
with the landing at sea level.
To evaluate the effect of density altitude on
landing distance, the following relationships
are used :
since an increase in altitude does not alter
acceleration, the effect would be due to
the greater TAS
where
S1= standard sea level landing dis-
tance
Sa=Ianding distance at altitude
c=altitude density ratio
From this relationship, the minimum land-
ing distance at 5,OCO ft. (u=O.8617) would be
16 percent greater than the minimum landing
distance at sea level. The approximate increase
in landing distance with altitude is approxi-
mately 3% percent for each 1,ooO ft. of altitude.
Proper accounting of density altitude is neces-
sary to accurately predict landing distance.
The effect of proper landing velocity is impor-
tant when runway lengths and landing dis-
tances are critical. The landing speeds specified
in the flight handbook ate generally the mini-
mum safe speeds at which the airplane can be
landed. Any attempt to land at below the | 216 | 216 | 00-80T-80.pdf |
NAVWEPS O&ROT-R0
AIRPLANE PERFORMANCE
specified speed may mean that the airplane may
stall, be difhcult to control, or develop high
rates of descent. On the other hand, an exces-
sive speed at landing may improve the control-
lability (especially in crosswinds) but will
cause an undesirable increase in landing dis-
tance. The principal effect of excess landing
speed is described by:
& v2 * -= - h 0 VI
Thus, a 10 percent excess landing speed would
cause a 21 percent increase in landing distance.
The excess speed places a greater working load
on the brakes because of the additional kinetic
energy to be dissipated. Also, the additional
speed causes increased drag and lift in the nor-
mal ground attitude and the increased lift will
reduce the normal force on the braking sur-
faces. The acceleration during this range of
speed immediately after touchdown may suffer
and it will be more likely that a tire can be
blown out from braking at this point. As a
result, 10 percent excess landing speed will
cause at JUJ; 21 percent greater landing dis-
tance.
The most critical conditions of landing per-
formance are the result of some combination of
high gross weight, density altitude, and un-
favorable wind. These conditions produce the
greatest landing distance and provide critical
levels of energy dissipation required of the
brakes. In all cases, it is necessary to make an
accurate prediction of minimum landing dis-
tance to compare with the available runway.
A polished, professional landing technique is
necessary because the landing phase of flight
accounts for more pilot caused aircraft acci-
dents than any other single phase of flight.
In the prediction of minimum landing dis-
tance from the handbook data, the following
considerations must be given:
(1) Pressure altitude and temperature-to
define the effect of density altitude.
(2)’ Gross weight-which define the CAS
or EAS for landing.
(3) Wind-a large effect due to wind or
wind component along the runway.
(4) Runway slope-a relatively small cor-
rection for ordinary values of runway slope.
IMPORTANCE OF HANDBOOK PER-
FORMANCE DATA. The performance sec-
tion or supplement of the flight handbook con-
tains all the operating data for the airplane.
For example, all data specific to takeoff, climb,
range, endurance, descent and landing are in-
cluded in this section. The ordinary use of
these data in flying operations is mandatory
and great knowledge and familiarity of the air-
plane can be gained through study of this
material. A complete familiarity of an air-
plane’s characteristics can be obtained only
through extensive analysis and study of the
handbook data.
200 | 217 | 217 | 00-80T-80.pdf |
NAVWEPS 00-801-80
HIGH SPEED AERODYNAMICS
Chapter 3
HIGH SPEED AERODYNAMICS
Developments in aircraft and powerplants
have produced high performance airplanes
with capabilities for very high speed flight.
The study of aerodynamics at these very high
flight speeds has many significant differences
from the study of classical low speed aero-
dynamics. Therefore, it is quite necessary
that the Naval Aviator be familiar with the
nature of high speed airflow and the charac-
teristics of high performance airplane
configurations.
GENERAL CONCEPTS AND SUPERSONIC
FLOW PATTERNS
NATURE OF COMPRESSIBILITY
At low flight speeds the study of aero-
dynamics is greatly simplified by the fact
that air may experience relatively small
changes in pressure with only negligible
changes in density. This airflow is termed
incompressible since the air may undergo changes
201 | 218 | 218 | 00-80T-80.pdf |
NAVWEPS 00-601-60
HIGH SPEED AERODYNAMICS
in pressure without apparent changes in den-
sity. Such a condition of airflow is analogous
to the flow of water, hydraulic fluid, or any
other incompressible fluid. However, at high
flight speeds the pressure changes that take
place are quite large and significant changes
in air density occur. The study of airflow at
high speeds must account for these changes
1 in air density and must consider that the
1 air is compressible and that there will be
“compressibility effects.”
A factor of great importance in the study of
high speed airflow is the speed of sound.
The speed of sound is the rate at which small
pressure disturbances will be propagated
through the air and this propagation speed
is solely a function of air temperature. The
accompanying table illustrates the variation
of the speed of sound in the standard
atmosphere.
TABLE 3-I. V.r;afIm <
Altitude in
,I T<
the -
--
-
D F. - c. K?uI,
59.0 15.0 661.7
41.1 5.1 650.3
23.3 -4.8 6%. 6
5.5 -14.7 6X6.7
--12., --24.6 614.6
--30.2 -34.5 602.2
-48.0 -44.4 589.6
-65.8 --w.3 516.6
-69.7 -56.5 573:s
-69.1 -56.5 573.8
-69.7 -56.5 573.8
As an object moves through the air mass,
velocity and pressure changes occur which
create pressure disturbances in the airflow sur-
rounding the object. Of course, these pressure
disturbances are propagated through the air
at the speed of sound. If the object is travel-
ling at low speed the pressure disturbances are
propagated ahead of the object and the airflow
immediately ahead of the object is influenced
by the pressure field on the object. Actually,
these pressure disturbances are transmitted in
all directions and extend indefinitely in all
directions. Evidence of this “pressure warn-
ing’ ’ is seeii in the typical subsonic flow
pattern of figure 3.1 where there is upwash
and flow direction change well ahead of the
leading edge. If the object is travelling at
some ,speed above the speed of sound the air-
flow ahead of the object will not be influenced
by the pressure field on the object since pres-
-sure disturbances cannot. be propagated ahead
of the object. Thus, as the flight speed nears
the speed of sound a compression wave will
form at the leading edge and all changes in
velocity and pressure will take place quite
sharply and suddenly. The airflow, ahead of
the object is not influenced until the air par-
ticles are suddenly forced out .of the way by
the concentrated pressure wave set up by the
object. Evidence of this phenomenon is seen
in the typical supersonic flow pattern of
figure 3.1.
The analogy of surface waves on the water
may help clarify these phenomena. Since a
surface wave is simply the propagation of a
pressure disturbance, a ship moving at a speed
much less than the wave speed will not form
a “bow wave.” As the. ship’s speed nears
the wave pro$agation speed the bow wave
will form and become stronger as speed is
increased beyond the wave speed.
At this point it should become apparent
that all compressibility effects depend upon
the relationship of airspeed to the speed of
sound. The term used to describe this rela-
tionship is the Mach number, M, and this
term is the ratio of the true airspeed to the
speed of sound. ,-I
M=;
where
M=Mach number
V= true airspeed, knots
d= speed of sound, knots
=a&
aO=speed of sound at standard sea level
conditions, 661 knots
e= temperature ratio
= T/T,
Revised January 1965 | 219 | 219 | 00-80T-80.pdf |
NAVWEPS OD-8OT-80
HIGH SPEED AERODYNAMICS
TYPICAL SUBSONIC FLOW PATTERN
FLOW DIRECTION CHANGES WELL AHEAD
OF LEADING EDGE
TYPICAL SUPERSONIC FLOW PATTERN
APPARENT AHEAD OF LEADING EDGE
Figure 3.1. Comparison of Subsonic and Supersonic Now Patterns
203 | 220 | 220 | 00-80T-80.pdf |
NAVWEPS OCMOT-60
HIGH SPEED AERODYNAMICS
It is important to note that compressibility
effects are not limited to flight speeds at and
above the speed of sound. Since any aircraft
will have some aerodynamic shape and will
be developing lift there will be local flow
velocities on the surfaces which arc greater
than the flight speed. Thus, an aircraft can
experience compressibility effects at flight
speeds well below the speed of sound. Since
there is the possibility of having both subsonic
and supersonic flows existing on the aircraft
it is convenient to define certain regimes of
flight. These regimes are defined approxi-
mately as follows:
Subsonic-Mach numbers below 0.75
Transonic-Mach numbers from 0.75 to
1.20
Supersonic-Mach numbers from 1.20 to
5.00
Hypersonic-Mach numbers above 5.00
While the flight Mach numbers used to define
these regimes of flight are quite approximate,
it is important to appreciate the types of flow
existing in each area. In the subsonic regime
it is most likely that pure subsonic airflow
exists on all parts of the aircraft. In the
transonic regime it is very probable that flow
on the aircraft components may be partly sub-
sonic and partly supersonic. The supersonic
and hypersonic’ flight regimes will provide
definite supersonic flow velocities on all parts
of the aircraft. Of course, in supersonic flight
there will be some portions of the boundary
layer which are subsonic but the predominating
flow is still supersonic.
The principal differences between subsonic
and supersonic flow are due to the cmprrs-
Jibi& of the supersonic flow. Thus, any
change of velocity or pressure of a supersonic
flow will produce a related change of density
which must be considered and accounted for.
Figure 3.2 provides a comparison of incom-
pressible and compressible flow through a
closed tube. Of course, the condition of con-
tinuity must exist in the flow through the
closed tube; the mass flow at any station along
the tube is constant. This qualification must
exist in both compressible and incompressible
cases.
The example of subsonic incompressible flow
is simplified by the fact that the density of
flow is constant throughout the tube. Thus,
as the flow approaches a constriction and the
streamlines converge, velocity increases and
static pressure decreases. In other words, a
convergence of the tube requires an increasing
velocity to accommodate the continuity of
flow. Also, as the subsonic incompressible
flow enters a diverging section of the tube,
velocity decreases and static pressure increases
but density remains unchanged. The behavior
of subsonic incompressible flow is that a con-
vergence causes expansion (decreasing pressure)
while a divergence causes compression (in-
creasing pressure).
The example of supersonic compressible flow
is complicated by the fact that the variations
of flow density are related to the changes
in velocity and static pressure. The behavior
of supersonic compressible flow is that a con-
vergence causes compression while a divergence
causes expansion. Thus, as the supersonic
compressible flow approaches a constriction
and the streamlines converge, velocity dc-
creases and static pressure increases. Con-
tinuity of mass flow is maintained by the
increase in flow density which accompanies the
decrease in velocity. As the supersonic com-
pressible flow enters a diverging section of the
tube, velocity increases, static pressure de-
creases, and density decreases to accommodate
the condition of continuity.
The previous comparison points out three 1
significant differences between supersonic corn- 1
pressible and subsonic incompressible flow.
(a) Compressible flow includes the addi-
tional variable of flow density.
(b) Convergence of flow causes expansion
of incompressible flow but compression of
compressible flow.
(c) Divergence of flow causes compression
of incompressible flow but expansion of
compressible flow.
Revised January 1965
204 | 221 | 221 | 00-80T-80.pdf |
NAVWEPS OD-8OT-80
HIGH SPEEO AERODYNAMICS
INCOMPRESSIBLE
(SUBSONIC)
//------
--
--- -- ---- --- -- --_-__-- ------
__--__----- -------
---- --- ---_ ---
-- ---_ -----
_---- ---__-
.,,,,,,,,,,l--~-
CONVERGING
INCREASING VELOCITY DECREASING VELOCITY
DECREASING PRESSURE INCREASING PRESSURE
CONSTANT DENSITY CONSTANT DENSITY
COMPRESSIBLE
(SUPERSONIC)
CONVERGING DIVERGING
DECREASING VELOCITY INCREASING VELOCITY
INCREASING PRESSURE DECREASING PRESSURE
JNCI~EASJ~~G DENSITY DECREASING DENSITY
figure 3.2. Comparison of Compressible and lncomprossible Flow Through a Closed Tube
205 | 222 | 222 | 00-80T-80.pdf |
NAVWEPS OD-SOT-80
HIGH SPEED AERODYNAMICS
OBLIQUE SHOCK WAVE-,
SUPERSONIC FLOW INTO A CORNER
SERfES OFOBLIOUE SHOCK WAVES
r\
SUPERSONIC FLOW INTO A ROUNDED CORNER
Figure 3.3. Oblique Shock Wave Formotion
206 | 223 | 223 | 00-80T-80.pdf |
‘I-YPICAL SUPERSONIC FLOW PATTERNS
When supersonic flow is clearly established,
all changes in velocity, pressure, density, flow
direction, etc., take place quite suddenly and
in relatively confined areas. The areas of flows
change are generally distinct and the phenom-
ena are referred to as “wave” formations. All
compression waves occur suddenly and are
wasteful of energy. Hence, the compression
waves are distinguished by the sudden “shock”
type of behavior. All expansion waves are not
so sudden in their occurrence and are not waste-
ful of energy like the compression shock waves.
Various types of waves can occur in supersonic
flow and the nature of the wave formed depends
upon the airstream and the shape of the object
causing the flow change. Essentially, there
are three fundamental types of waves formed
in supersonic flow: (1) the oblip shock wave
(compression), (2) the normal shock wave
(compression), (3) the expansion wave (no
shock).
OBLIQUE SHOCK WAVE. Consider the
case where a supersonic airstream is turned
into the preceding airflow. Such would be
the case of a supersonic flow “into a comer”
as shown in figure 3.3. A supersonic airstream
passing through the oblique shock wave will
experience these changes:
(1) The airstream is slowed down; the
velocity and Mach number behind the wave
are reduced but the flow is still supersonic
(2) The flow direction is changed to flow
along the surface
(3) The static pressure of the airstrea:m
behind the wave is increased
(4) The density of the airstream behind
the wave is increased
(5) Some of the available energy of the
airstream (indicated by the sum of dynamic
and static pressure) is dissipated and turned
into unavailable heat energy. Hence, the
shock wave is wasteful of energy.
A typical case of oblique shock wave forma-
tion is that of a wedge pointed into a super-
sonic airstream. The oblique shock wave
NAVWEPS OD-807-80
HIGH SPEED AERODkNAMlCS
will form on each surface of the wedge and the
inclination of the shock wave will be a func-
tion of the free stream Mach number and the
wedge angle. As the free stream Mach number
increases, the shock wave angle decreases; as
the wedge angle increases the shock wave
angle increases, and, if the wedge angle is in-
creased to some critical amount, the shock
wave will detach from the leading edge of the
wedge. It is important to note that detach-
ment of the shock wave will produce sub$onic
flow immediately after the central portion of
the shock wave. Figure 3.4 illustrates these
typical flow patterns and the effect of Mach
number and wedge angle.
The previous flow across a wedge in a
supersonic airstream would allow flow in ;UU
dimensions. If a cone were placed in a super-
sonic airstream the airflow would occur in
three dimensions and there would be some
noticeable differences in flow characteristics.
Three-dimensional flow for the same Mach
number and flow direction change would pro-
duce a weaker shock wave with less change in
pressure and density. Also, this conical wave
formation allows changes in airflow that con-
tinue to occur past the wave front and the
wave strength varies with distance away from
the surface. Figure 3.5 depicts the typical
three-dimensional flow past a cone.
Oblique shock waves can be reflected like
any pressure wave and this effect is shown in
figure 3.5. This reflection appears logical and
necessary since the original wave changes the
flow direction toward the wall and the reflected
wave creates the subsequent flow change to
cause the flow to remain parallel to the wall
surface. This reflection phenomenon places
definite restrictions on the size of a model in a
wind tunnel since a wave reflected back to the
model would cause a pressure distribution not
typical of free flight.
NORMAL SHOCK WAVE. If a blunt-
nosed object is placed in a supersonic airstream
the shock wave which is formed will be de-
tached from the leading edge. This detached | 224 | 224 | 00-80T-80.pdf |
NAVWEPS 00-8OT-80
HIGH SPEED AERODYNAMICS
DETACHED
M = 3.0
M = 3.0 \
Figure 3.4. Shock Waves Formed by Various Wedge Shapes
208 | 225 | 225 | 00-80T-80.pdf |
NAVWEPS 00-BOT-80
HIGH SPEED AERODYNAMICS
CONE IN SUPERSONIC FLOW
CONICAL WAVE
REF:LECTED OBLIOUE WAVES
MODEL IN WIND
TUNNEL WITH wows
REFL\Cmg FROM
Figure 3.5. Three Dimensional and Reflected Shock Waves
209 Revised Januaty I%5 | 226 | 226 | 00-80T-80.pdf |
NAVWEPS 00-8OT-80
HIGH SPEED AERODYNAMICS
OBLlOuE SHOCK
WAVES
NORMAL
/
,SHOCK WAVE
Figure 3.6. Normal ShockWave Formation | 227 | 227 | 00-80T-80.pdf |
wave also occurs when a wedge or cone angle
exceeds some critical value. Whenever the
shock wave forms perpendicular to the up-
stream flow, the shock wave is termed a
“normal” shock wave and the flow immediately
behind the wave is subsonic. Any relatively
blunt object in a supersonic airstream will form
a normal shock wave immediately ahead of the
leading edge slowing the airstream to subsonic
SO the airstream may feel the presence of the
blunt nose and flow around it. Once past the
blunt nose the airstream may remain subsonic
or accelerate back to supersonic depending on
the shape of the nose and the Mach number of
the free stream.
In addition to the formation of normal
shock waves described above, this same type
of wave may be formed in an entirely different
manner when there is no object in the super-
sonic airstream. It is particular that whenever
a supersonic airscream is slowed to subsonic
without a change in direction a normal shock
wave will form as a boundary between the
supersonic and subsonic regions. This is an
important fact since aircraft usually encounter
some “compressibility effects” before the flight
speed is sonic. Figure 3.6 illustrates the man-
ner in which an airfoil at high subsonic speeds
has local flow velocities which are supersonic.
As the local supersonic flow moves aft, a
normal shock wave forms slowing the flow
to subsonic. The transition of flow from
subsonic to supersonic is smooth and is not
accompanied by shock waves if the transition
is made gradually with a smooth surface. The
transition of flow from supersonic to subsonic
without direction change always forms a
normal shock wave.
A supersonic airstream passing through a
normal shock wave will experience these
changes:
(1) The airstream is slowed to subsonic;
the local Mach number behind the wave is
approximately equal to the reciprocal of the
Mach number ahead of the wave-e.g., if
NAVWEPS OD-EOT-80
HIGH SPEED AERODYNAMICS
Mach number ahead of the wave is 1.25,
the Mach number of the flow behind the
wave is approximately 0.80.
(2) The airflow direction immediately
behind the wave is unchanged.
(3) The static pressure of the airstream
behind the wave is increased greatly.
(4) The density of the airstream behind
the wave is increased greatly.
(5) The energy of the airstream (indi-
cated by total pressure-dynamic plus static)
is greatly reduced. The normal shock wave
is very wasteful of energy.
EXPANSION WAVE. If a supersonic air-
stream were turned away from the preceding
flow an expansion wave would form. The
flow “around a corner” shown in figure 3.7
will not cause sharp, sudden changes in the
airflow except at the corner itself and thus is
not actually a “shock” wave. A supersonic
airstream passing through an expansion wave
will experience these changes:
(1) The airstream is accelerated; the ve-
locity and Mach number behind the wave
are greater.
(2) The flow direction is changed to
flow along the surface-provided separa-
tion does not occur.
(3) The static pressure of the airstream
behind the wave is decreased.
(4) The density of -the airstream behind
the wave is decreased.
(5) Since the flow changes in a rather
gradual manner there is no “shock” and
no loss of energy in the airstream. The
expansion wave does not dissipate air-
stream energy.
The expansion wave in three dimensions is
a slightly different case and the principal
difference is the tendency for the static pres-
sure to continue to increase past the wave.
The following table is provided to summa-
rize the characteristics of the three principal
wave forms encountered with supersonic flow.
21’1 | 228 | 228 | 00-80T-80.pdf |
NAVWEPS 00-807-80
HIGH SPEED AERODYNAMICS
EXPANSION WAVE,
SUPERSONIC FLOW
AROUND A CORNER
SERIES OF EXPANSION WAVES7
SUPERSONIC FLOW
AROUND A SMOOTti CORNER
Figure 3.7. Expansion Wove Formation
212 | 229 | 229 | 00-80T-80.pdf |
NAVWEPS 00-8OT-80
HIGH SPEED AERODYNAMICS
TABLE 3-P. Suprnonk Wave Charactwiltks
Type of wave formation
Flow direction change.
Efkct cm velociry and Mach
number.
Effect on static pressure and
density.
_-
Oblique shock wave
“Flow into a corner,”
turned into preceding
flow.
Decreased but still supcr-
sonic.
Increase. :.
DKICaSe
_-
__
__
__
-
Normal shock wave.
No change.
Great increase,
Great decrease
-
__
-.
-.
-.
-
Expansion wwc.
‘/ //
<
- ,/$y
“Flow around a corner,”
turned away from pre-
ceding flow.
Increased to higher super-
sonic.
DeCrWSe.
No change (no shock).
SECTIONS IN SUPERSONIC FLOW
In order to appreciate the effect of these
various wave forms on the aerodynamic char-
acteristics in supersonic flow, inspect figure 3.8.
Parts (a) and (b) show the wave pattern and
resulting pressure distribution for a thin flat
plate at a positive angle of attack. The air-
stream moving over the upper surface passes
through an expansion wave at the leading edge
and then an oblique shock wave at the trailing
edge. Thus, a uniform suction pressure exists
over the upper surface. The airstream moving
underneath the flat plate passes through an
oblique shock wave at the leading edge then an
expansion wave at the trailing edge. This pro-
duces a uniform positive pressure on the under-
side of the section. This distribution of pres-
sure on the surface will produce a net lift and
incur a subsequent drag due co lift from the in-
clination of the resultant lift from a perpen-
dicular co the free stream.
Parts (c) and (d) of figure 3.8 show the
wave pattern and resulting pressure distribu-
tion for a double wedge airfoil at zero lift.
The airstream moving over the surface passes
through an oblique shock, an expansion wave,
and another oblique shock. The resulting
pressure distribution on the surfaces produces
no net lift, but the increased pressure on the
forward half of the chord along with the de-
creased pressure on the aft half of the chord
produces a “wave” drag. This wave drag is
caused by the components of pressure forces
which are parallel to the free scream direction.
The wave drag is in addition to the drag due
to friction, separatien, lift, etc., and can be
a very considerable part of the total drag at
high supersonic speeds.
Parts (e) and (f) of figure 3.8 illustrate the
wave pattern and resulting pressure distribu-
tion for the double wedge airfoil at a small
positive angle of attack. The net pressure
213 | 230 | 230 | 00-80T-80.pdf |
NAVWEPS 00-8oT-80
HIGH SPEED. AERODYNAMlCS
0 a FLAT PLATE WAVE PATTERN
0 c DOUBLE WEDGE WAVE PATTERN
AT ZERO LIFT
ANGLE
ATTAC
O e DOUBLE WEDGE WAVE PATTERN
AT POSITIVE ANGLE OF ATTACK
NOTE: CENTER OF PRESSURE
IS AT 50% CHORD
v b FLAT PLATE PRESSURE DISTRIBUTION
NO NET LIFT BUT
HAVE “WAVE DRAG”
0 d REDOUBLE WEDGE PRESSURE
DISTRIBUTION AT ZERO LIFT
DRAG DUE TO LIFT
‘CLEFT
L-WAVE DRAG
0 f DOUBLEWEDGEPRESSURE
DISTRIBUTION AT POSITIVE LIFT
0 9 CIRCULAR ARC TYPE AIRFOIL 0 b CONVENTIONAL BLUNT NOSE
AIRFOIL
Figure 3.8. Typical Supersonic Flow Patterns and Distribution of Pressure
214 | 231 | 231 | 00-80T-80.pdf |
distribution produces an inclined lift with
drag due to lift which is in addition to the
wave drag at zero lift. Part (g) of figure 3.8
shows the wave pattern for a circular arc air-
foil. After the airflow traverses the oblique
shock wave at the leading edge, the airflow
undergoes a gradual but continual expansion
until the trailing edge shock wave is en-
countered. Part (h) of figure 3.8 illustrates
the wave pattern on a conventional blunt nose
airfoil in supersonic flow. When the nose is
blunt the wave must detach and become a
normal shock wave immediately ahead of the
leading edge. Of course, this wave form
produces an area of subsonic airflow at the
leading edge with very high pressure and
density behind the detached wave.
The drawings of figure 3.8 illustrate the
typical patterns of supersonic flow and point
out these facts concerning aerodynamic surfaces
in two dimensional supersonic flow:
(1) All changes in velocity, pressure,
density and flow direction will take place
quite suddenly through the various. wave
forms. The shape of the object and the
required flow ,direction change dictate the
type and strength of the wave formed.
(2) As always, lift results from the distri-
bution of pressure on a surface and is the net
force perpendicular to the free stream direc-
tion. Any component of the lift in a direc-
tion parallel to the windstream will be
drag due to lift.
(3) In supersonic flight, the zero lift drag
of an airfoil of some finite thickness will
include a “wave drag.” The thickness of
the airfoil will have an extremely powerful
effect on this wave drag since the wave drag
varies as the square of the thickness ratio-
if the thickness is reduced 50 percent, the
wave drag is reduced 73 percent. The lead-
ing edges of supersonic shapes must be sharp
or the wave formed at the leading edge will
be a strong detached shock wave.
(4) Once the flow on the airfoil is super-
sonic, the aerodynamic center of the surface
NAWEPS 00-80T-80
HIGH SPEED AERODYNAMICS
will be located approximately at the SO per-
cent chord position. As this contrasts with
the subsonic location for the aerodynamic
center of the 23 percent chord position, sig-
nificant changes in aerodynamic trim and
stability may be encountered in transonic
flight.
CONFIGURATION EFFECTS
TRANSONIC AND SUPERSONIC PLIGHT
Any object in subsonic flight which has some
finite thickness or is producing lift will have
local velocities on the surface which are
greater than the free stream velocity. Hence,
compressibility effects can be expected to
occur at flight speeds less than the speed of
sound. The transonic regime of flight pro-
vides the opportunity for mixed subsonic and
supersonic flow and. accounts for the first 1
significant effects of compressibility.
Consider a conventional airfoil shape as
shown in figure 3.9. If this airfoil is at a
flight Mach number of 0.50 and a slight posi-
tive angle of attack, the maximum local
velocity on the surface will be greater than
the flight speed but most likely less than
sonic speed. Assume that an increase in
flight Mach number to 0.72 would produce
lfrst cvidmc of local son@ flow. This condition
of flight would be the highest flight speed
possible without supersonic flow and would
be termed the “critical Mach number.” Thus,
critical Mach number is the bouodary between
subsonic and transonic flight and is an im-
portant ~point of reference for all compressi- 1
bility effects encountered in transonic flight.
By delinition, critical Mach number is the
“free stream Mach number which produces
6rst evidence of local sonic flow.” Therefore,
shock waves, buffet, airflow separation, etc.,
take place above critical Mach number.
As critical Mach number is exceeded an
area of ~uprrronic airflow is created and a normal
215
Revised January 1965 | 232 | 232 | 00-80T-80.pdf |
NAVWEPS 00-8OY-60
HIGH SPEED AERODYNAMICS
MAXIMUM LOCALVELOCITY
M=.50 IS LESS THAN SONIC
MAXIMUM LOCAL VELOCITY
EOUALTO SONIC
M =.72
(CRITICAL MACH NUMB
NORMAL SHOCK WAVE
POSSIBLE SEPARATION
su NORMAL SHOCK
\\I NORMAL SHOCK
NORMAL SHOCK
Figure 3.9. Transonic Flow Patterns (sheet 1 of 2)
216 | 233 | 233 | 00-80T-80.pdf |
NAVWEPS OD-801-80
HIGN SPEED AEQODYNAMICJ
WING IN TRANSONIC FLOW
I M = .700 a= +2O CL= ,370
NO SHOCK WAVES
I
I M-.800 a=+2O CL=.442
SHOCK FORMATION IS APPARENT AT
25 TO 30 % CHORD POSITION
I M=.075 a=+20 CL=.450
SHOCK INDUCED SEPARATION ALONG
AFT PORTION OF WING PLAPJFORM
Figure 3.9. Transonic Flow Patterns (sheet 2 of 2) | 234 | 234 | 00-80T-80.pdf |
NAVWEPS 00-8OT-80
HIGH SPEED AERODYNAMICS
shock wave forms as the boundary between
the supersonic flow and the subsonic flow on
the aft portion of the airfoil surface. The
acceleration of the airflow from subsonic to
supersonic is smooth and unaccompanied by
shock waves if the surface is smooth and the
transition gradual. However, the transition
of airflow from supersonic to subsonic is
always accompanied by a shock wave and,
when there is no change in direction of the
airflow, the wave form is a normal shock
wave.
Recall that one of the principal effects of
th,e normal shock wave is to produce a large
increase in the static pressure of the airstream
behind the wave. If the shock wave is
strong, the boundary layer may not have
sufficient kinetic energy to withstand the
large, adverse pressure gradient and separation
will occur. At speeds only slightly beyond
critical Mach number the shock wave formed
is not strong enough to cause spearation or
any noticeable change in the aerodynamic
force coefficients. However, an increase in
speed above critical Mach number sufhcient
to form a strong shock wave can cause sepa-
ration of the boundary layer and produce
sudden changes in the aerodynamic force
coefficients. Such a flow condition is shown
in figure 3.9 by the flow pattern for M=O.n.
Notice that a further increase in Mach number
to 0.82 can enlarge the supersonic area on the
upper surface and form an additional area of
supersonic flow and normal shock wave on the
lower surface.
As the flight speed approaches the speed of
sound the areas of supersonic flow enlarge and
the shock waves move nearer the trailing
edge. The boundary layer may remain sepa-
rated or may reattach depending much upon
the airfoil shape and angle of attack. When
the flight speed exceeds the speed of sound
the “bow” wave forms at the leading edge and
this typical flow pattern is illustrated in
figure 3.9 by the drawing for M= 1.05. If the
speed is increased to some higher supersonic
value all oblique portions of the waves incline
more greatly and the detached normal shock
portion of the bow wave moves closer to the
leading edge.
Of course, all components of the aircraft
are affected by compressibility in a manner
somewhat similar to that of basic airfoil.
The tail, fuselage, nacelles, canopy, etc. and
the efkct of the interference between the
various surfaces of the aircraft must be
considered.
FORCE DIVERGENCE. The airflow sepa-
ration induced by shock wave formation can
create significant variations in the aerody-
namic force coefficients. When the free stream
speed is greater than critical Mach number some
typical effects on an airfoil section are as
follows :
(1) An increase in the section drag coeffi-
cient for a given section lift coe5cient.
(2) A decrease in section lift coefficient
for a given section angle of attack.
(3) A change in section pitching moment
coe5cient.
A reference point is usually taken by a plot
of drag coe5cient versus Mach number for
a constant lift coefficient. Such a graph is
shown in figure 3.10. The Mach number
which produces a sharp change in the drag
coe5cient is termed the “force divergence”
Mach number and, for most airfoils, usually
exceeds the critical Mach number at least 5
to 10 percent. This condition is also referred
to as the “drag divergence” or “drag rise.”
PHENOMENA OF TRANSONIC FLIGHT.
Associated with the “drag rise” are buffet,
trim and stability changes, and a decrease
in control surface effectiveness. Conventional
aileron, rudder, and elevator surfaces sub
jetted to this high frequency buffet may
“buzz,” and changes in hinge moments may
produce undesirable control forces. Of course,
if the buffet is quite severe and prolonged,
structural damage may occur if this operation
is in violation of operating limitations. When
airflow separation occurs on the wing due to
218 | 235 | 235 | 00-80T-80.pdf |
NAVWEPS OO-EOT-80
HIGH SPEED AERODYNAMICS
CD
DRAG
COEFFICIENT
FORCE DIVERGENCE
MACH NUMBER
CRITICAL
MACH NUMBER.
I
I I c
0.5 1.0
ht,MACH NUMBER
Figure 3ilO. Compressibility Drag Rise
shock wave formation, there will be a loss of
lift and subsequent loss of downwash aft of
the affected area. If the wings shock unevenly
due to physical shape differences or sideslip,
a rolling moment will be created in the
direction of the initial loss of lift and con-
tribute to control difficulty (“wing drop”).
If the shock induced separation occurs sym-
metrically near the wing root, a decrease in
downwash behind this area is a corollary of
the loss of lift. A decrease in downwash on
the horizontal tail will create a diving moment
and the aircraft will “tuck under.” If these
conditions occur on a swept wing. planform,
the wing center of pressure shift contributes
to the trim change-root shock first moves
the wing center of pressure aft and adds to the
diving moment; shock formation at the wing
tips first moves the center of pressure forward
and the resulting climbing moment and tail
downwash change can contribute to “pitch
up.”
Since most of the dificulties of transonic
flight are associated with shock wave induced
flow separation, any means of delaying or
alleviating the shock induced separation will
improve the aerodynamic characteristics. An
aircraft conhguration may utilize thin surfaces
of low aspect ratio with sweepback to delay
and reduce the magnitude of transonic force
divergence. In addition, various methods of
boundary layer control, high lift devices,
vortex generators, etc., may be applied to
improve transonic characteristics. For exam-
ple, the application of vortex generators to a
surface can produce higher local surface veloci-
ties and increase the kinetic energy of the
boundary layer. Thus, a more severe pressure
gradient (stronger shock wave) will be neces-
sary to produce airflow separation.
219 | 236 | 236 | 00-80T-80.pdf |
NAVWEPS 00-801-80
HIGH SPEEO AERODYNAMICS
Once the configuration of a transonic air-
craft is fixed, the pilot must respect the effect
of angle of attack and altitude. The local flow
1 velocities on any upper surface increase with an
increase in angle of attack. Hence, local sonic
flow and subsequent shock wave formation
can occur at lower free stream Mach numbers.
A pilot must appreciate this reduction of force
divergence Mach number with lift coefficient
since maneuvers at high speed may produce
compressibility effects which may not be en-
countered in unaccelerated flight. The effect
of altitude is important since the magnitude
of any force or moment change due to com-
pressibility will depend upon the dynamic
pressure of the airstream. Compressibility
effects encountered at high altitude and low
dynamic pressure may be of little consequence
in the operation of a transonic aircraft. How-
ever, the same compressibility effects en-
countered at low altitudes and high dynamic
pressures will create greater trim changes,
heavier buffet, etc., and perhaps transonic
flight restrictions which are of principal inter-
est only to low altitude.
can be quite weak, the pressure waves can be
of sufficient magnitude to create an audible
disturbance. Thus, “sonic booms” will be a
simple consequence of supersonic flight.
The aircraft powerplant: for supersonic flight
must be of relatively high thrust output.
Also, in many cases it may be necessary to
provide the air breathing powerplant with
special inlet configurations which will slow
the airflow to subsonic prior to reaching the
compressor face or combustion chamber. Aero-
dynamic heating of supersonic flight can pro-
vide critical inlet temperatures for the gas
turbine engine as well as critical structural
temperatures.
The density variations in airflow may be
shown by certain optical techniques. Schlieren
photographs and shadowgraphs can define the
various wave patterns and their effect on the
airflow. The Schlieren photographs presented
in figure 3.11 define the flow conditions on an
aircraft in supersonic flight. I
TRANSONIC AND SUPERSONIC CONFIGU-
RATIONS
PHENOMENA OF SUPERSONIC FLIGHT.
While many of the particular effects of super-
sonic flight will be presented in the detail of
later discussion, many general effects may be
anticipated. The airplane configuration must
have aerodynamic shapes which will have low
drag in compressible flow. Generally, this will
require airfoil sections of low thickness ratio
and sharp leading edges and body shapes of
high fineness ratio to minimize the supersonic
wave drag. Because of the aft movement of the
aerodynamic center with supersonic flow, the
increase in static longitudinal stability will
demand effective, powerful control surfaces to
achieve adequate controllability for super-
sonic maneuvering.
Aircraft configurations developed for high
speed flight will have significant differences in
shape and planform when compared with air-
craft designed for low speed flight. One of
the outstanding differences will be in the
selection of airfoil profiles for transonic or
supersonic flight.
As a corollary of supersonic flight the shock
wave formation on the airplane may create
special problems outside the immediate vicinity
of the airplane surfaces. While the shock
waves a great distance away from the airplane
no
AIRFOIL SECTIONS. It should be ob-
vious that airfoils for high speed subsonic
flight should have high critical Mach num-
bers since critical Mach number defines the
lower limit for shock wave formation and
subsequent force divergence. An additional
complication to airfoil selection in this
speed range is that the airfoil should have
a high maximum lift coefficient and sufficient
thickness to allow application of high lift
devices. Otherwise an excessive wing area
would be required to provide maneuverability
and reasonable takeoff and landing speeds. | 237 | 237 | 00-80T-80.pdf |
NAVWEPS DG-RDT-RD
HIGH SPEED AERODYNAMICS
FE!4 MODEL AT VARIOUS
MACH NUMBERS
a-O0 pee
M* 1.2 W 1.6
Figure 3.11. Schliemn Photographs of Supersonic Flight (sheet 1 of 2)
221 | 238 | 238 | 00-80T-80.pdf |
Figure 3.7 1. Schlieren Photographs of Supersonic Flight (sheet 2 of 2) | 239 | 239 | 00-80T-80.pdf |
However, if high speed flight is the primary
consideration, the airfoil must be chosen to
have. the highest practical critical Mach
number.
Critical Mach number has been defined as
the flight Mach number which produces first
evidence of local sonic flow. Thus, the air-
foil shape and lift coe&ient-which determine
the pressure and velocity distribution-will
have a profound effect on critical Mach number.
Conventional, low speed airfoil shapes have
relatively poor compressibility characteristics
because of the high local velocities near the
leading edge. These high local velocities are
inevitable if both the maximum thickness and
camber are well forward on the chord. An
improvement of the compressibility character-
istics can be obtained by moving the points of
maximum camber and thickness aft on the
chord. This would distribute the pressure and
velocity more evenly along the chord and
produce a lower peak velocity for the same
lift coefficient. Fortunately, the airfoil shape
to provide extensive lamiaar flow and low
profile drag in low speed, subsonic flight will
provide a pressure distribution which is favor-
able for high speed flight. Figure 3.12
illustrates the pressure distributions and
variation of critical Mach number with lift
coefficient for a conventional low speed airfoil
and a high speed section.
In order to obtain a high critical Mach
number from an airfoil at some low lift
coefficient the section must have:
(u) Low thickness ratio. The point of
maximum thickness should be aft to smooth
the pressure distribution.
(6) Low camber. The mean camber line
should be shaped to help minimize the
local velocity peaks.
In addition, the higher the required lift
coefficient the lower the critical Mach number
and more camber is required of the airfoil.
If supersonic flight is a possibility the thick-
ness ratio and leading edge radius must be
small to decrease wave drag.
NAVWEPS 00-801-80
HIGH SPEED AERODYNAMICS
Figure 3.13 shows the flow patterns for
two basic supersonic airfoil sections and pro-
vides the approximate equations for lift,drag,
and lift curve slope. Since the wave drag is
the only factor of difference between -the two
airfoil sections, notice the configuration fac-
tors which affect the wave drag. For the
same thickness ratio, the circular arc airfoil
would have a larger wedge angle formed
between the upper and lower surfaces at the
leading edge. At the same flight Mach num-
ber the larger angle at the leading edge would
form the stronger shock wave at the nose and
cause a greater pressure change on the circular
arc airfoil. This same principle applies when
investigating the effect of airfoil thickness.
Notice that the wave drag coefficients for
both airfoils vary as the SQUARE of the
thickness ratio, e.g., if the thickness ratio
were doubled, the wave drag coefhcient would
he four times as great. If the thickness were
increased, the airflow at the leading edge will
experience a greater change in direction and
a stronger shock wave will be formed. This
powerful variation of wave drag with thick-
ness ratio necessitates the use of very thin air-
foils with sharp leading edges for supersonic
flight. An additional consideration is that
thin airfoil sections favor the use of low aspect
ratios and high taper to obtain lightweight
structures and preserve stiffness and rigidity.
The parameter JMz-l appears in the
denominator of each of the equations for the
aerodynamic coefficients and indicates a de-
crease in each of these coefficients with an
increase in Mach number. Essentially, this
means that any aerodynamic surface becomes
less sensitive to changes in angle of attack at
higher Mach numbers. The decrease in lift
curve slope with Mach number has tremendous
implications in the stability and control of
high speed aircraft. The vertical tail becomes
less sensitive to angles of sideslip and the
directional stability of the aircraft will deteri-
orate with Mach number. The horizontal
tail of the airplane experiences the same | 240 | 240 | 00-80T-80.pdf |
NAVWEPS DD-801-80
HIGH SPEED AERODYNAMICS
-1.0
PRESSURE
COEFFICIENT 0
PP, 4
1.0
SAME Cl LOW PEAK FOR
HIGH SPEED SECTION
(LAMINAR FLOW)
SECTION LIFT COEFFICIENT
Figure 3.72. High speed Section Characteristics
224 | 241 | 241 | 00-80T-80.pdf |
NAVWEPS 00-BOT-80
HIGH SPEED AERODYNAMICS
DOUBLE WEDGE SECTION
WAVE DRAG COEFFICIENT:
LIFT COEFFICIENT:
DRAG DUE .TO LIFT:
LIFT CURVE SLOPE:
CIRCULAR ARC SECTION
WHERE
( +/c ) = AIRFOIL THICKNESS RATIO
a 2 ANGLE OF ATTACK (IN RADIANS)
M = MACH NUMBER
Figure 3.73. Approximate Equations for Supersonic Section Characteristics
225 | 242 | 242 | 00-80T-80.pdf |
NAWEPS OD-ROT-RO
HIGH SPEEO AERODYNAMICS
general effect and contributes less damping to
longitudinal pitching oscillations. These ef-
fects can become so significant at high Mach
numbers that the aircraft might require com-
plete synthetic stabilization.
PLANFORM EFFECTS. The development
of surfaces for high speed involves considera-
tion of many items in addition to the airfoil
sections. Taper, aspect ratio, and sweepback
can produce major effects on the aerodynamic
characteristics of a surface in high speed flight.
Sweepback produces an unusual effect on the
high speed characteristics of a surface and has
basis in a very fundamental concept of aero-
dynamics. A grossly simplified method of
visualizing the effect of sweepback is shown in
figure 3.14. The swept wing shown has the
streamwise velocity broken down to a com-
ponent of velocity perpendicular to the leading
edge and a component parallel to the leading
edge. The component of speed perpendicular
to the leading edge is less than the free.stream
speed (by the cosine of the sweep angle) and
it is this velocity component which determines
the magnitude of the pressure distribution.
The component of speed parallel to the lead-
ing edge could be visualized as moving across
constant sections and; in doing so, does not
contribute to the pressure distribution on the
swept wing. Hence, sweep of a surface pro-
duces a beneficial e&ct ‘in high speed flight
since higher flight speeds may be obtained be-
fore components of speed perpendicular to the
leading edge produce critical conditions on the
wing. This is one of the most important ad-
vantage of sweep since there is an increase in
critical Mach number, force divergence Mach
number, and the Mach number at which the
drag rise will peak. In other words, sweep will
delay the onset of compressibility effects.
Generally, the effect of wing sweep will
apply to either sweep back or sweep forward.
While the swept forward wing has been used
1 in rare instances, the aeroelastic instability of
such a wing creates such a problem that sweep
back is more practical for ordinary applica-
tions.
In addition to the delay of the onset of com-
pressibility effects, sweepback will reduce the
magnitude of the changes in force coefficients
due to compressibility. Since’ the component
of velocity perpendicular to the leading edge is
less than the free stream velocity, the magni-
tude of all pressure forces on the wing will be
reduced (approximately by the square of the
cosine of the sweep angle). Since compressi-
bility force divergence occurs due to changes in
pressure distribution, the use of sweepback will
“soften” the force divergence. This effect is
illustrated by the graph of figure 3.14 which
shows the typical variation of drag coeiIicient
with Mach number for various sweepback
angles. The straight wing shown begins drag
rise at M=O.lO, reaches a peak near M=l.O,
and begins a continual drop past M= 1.0. Note
that the use of sweepback then deh+y~ the drag
rise to some~ higher Mach number and wdms
the magnitude of the drag rise.
In view of the preceding discussion, sweep-
back will have the following principal ad-
vantages :
(1) Sweepback will delay the onset of all
compressibility effects. Critical Mach num-
ber and force divergence Mach number will
increase since the velocity component affect-
ing the pressure distribution is less than the
free stream velocity. Also, the peak of drag
rise is delayed to some higher supersonic
speed-approximately the speed which pro-
duces sonic flow perpendicular to the leading
edge. Various sweeps applied to wings of
.moderate aspect ratio will produce these
approximate effects in transonic flight:
Sweep angle(k)
Revised Jaanuar~ 1965
226 | 243 | 243 | 00-80T-80.pdf |
NAVWEPS 00-80T-80
HIGH SPEED AERODYNAMICS
FREE STREAM
/
VELOCITY
VELOCITY COhlPONENT
PARALLEL TO LEADING
EDGE
\
SWEEP ANGLE, 11
VELOCITY COMPONENT
PERPENDICULAR TO
LEADING EDGE
DFf AG
COEFFICIENT
cD
c
0 I.0 2.0 3.0
MACH NUMBER, M
UM
t IlC.IT ,STRAIGHT
MAXIM’
MACH NUMBER, M MACH NUMBER, M
Figure 3.14. General Effects of Sweepbock
227 | 244 | 244 | 00-80T-80.pdf |
NAVWEPS DD-ROT-80
HIGH SPEE’D AERODYN,AMlCS
EFFECT OF SWEEPBACK ON LOW SPEED LIFT CURVE
LIFT
COEFFICIENT
CL
SWEPT
t
ANGLE OF ATTACK,O
EFFECT OF SWEEPBACK ON YAW AND ROLL MOMENTS /
YAW MOMENT
SWEPT WING AT SWEPT WING IN A
ZERO SIDESLIP SIDESLIP TO THE RIGHT
SWEPT WING
IN LEVEL FLIGHT
SWEPT WING IN A
S IDESLIP TOWARD
THE DOWN WING
Figure 3.15. Aerodynamic Effects Due to Sweepbach
228 | 245 | 245 | 00-80T-80.pdf |
NAVWEPS 00-801-80
HIGH SPEED AERODYNAMICS
(1) The wing lift curve slope is reduced
for a given aspect ratio. This is illustrated
by the lift curve comparison of figure 3.15
for the straight and swept wing. Any
reduction of lift curve slope implies the
wing is less sensitive to changes in angle of
attack. This is a beneficial effect only when
the effect of gusts and turbulence is con-
sidered. Since the swept wing has the
lower lift curve slope it will be less sensitive
to gusts and experience less “bump” due
to gust for a given aspect ratio and wing
loading. This is a consideration particular
to the aircraft whose structural design shows
a predominating effect of the gust load
spectrum, e.g., transport, cargo, and patrol
types.
(2) “Divergence” of a surface is an aero-
elastic problem which can occur at high
dynamic pressures. Combined bending and
twisting deflections interact with aerody-
namic forces to produce sudden failure of
the surface at high speeds. Sweep forward
will aggravate this situation by “leading”
the wing into the windstream and tends to
lower the divergence speed. On the other
hand, sweepback tends to stabilize the
surface by “trailing” and tends to raise the
divergence speed. By this tendency, sweep-
back may be beneficial in preventing di-
vergence within the anticipated speed range.
(3) Sweepback contributes slightly to the
static directional-or weathercock-stability
of an aircraft. This effect may be appre-
ciated by inspection of hgure 3.13 which
shows the swept wing in a yaw or sideslip.
The wing into the wind has less sweep and
a slight increase in drag; the wing away
from the wind has more sweep and less
drag. The net effect of these force changes is
to produce a yawing moment tending to
retarn the nose into the relative wind.
This directional stability contribution is
usually small and of importance in tailless
aircraft only.
(2) Sweepback will reduce the magnitude
of change in the aerodynamic force coeffi-
cients due to compressibility. Any change
in drag, lift, or moment coefbcients will be
reduced by the use of sweepback. Various
sweep angles applied to wings of moderate
aspect ratio will produce these approximate
effects in transonic flight.
00 ............................... 0
150. ............. ................ 5
M” .............................. 15
45’.............................. 35
600 .............................. 60
-
-_
-
These advantages of drag reduction and preser-
vation of the transonic maximum lift coefficient
are illustrated in figure 3.14.
Thus, the use of sweepback on a transonic
aircraft will reduce and delay the drag rise and
preserve the maneuverability of the aircraft
in transonic flight. It should be noted that a
small amount of sweepback produces very
little benefit. If sweepback is to be used at all,
at least 30’ to 33’ must be used to produce any
significant benefit. Also note from figure 3.14
that the amount of sweepback required to
d&y drag rise in supersonic flight is very large,
e.g., more than 60° necessary at M=2.0. By
comparison of the drag curves at high Mach
numbers it will be appreciated that extremely
high (and possibly impractical) sweepback is
necessary to delay drag rise and that the lowest
drag is abtained with zero sweepback. There-
fore, the planform of a wing designed to operate
continuously at high Mach numbers will tend
to be very thin, low aspect ratio, and unswept.
An immediate conclusion is that sweepback is
a device of greatest application in the regime of
transonic flight.
A few of the less significant advantages of
sweepback are as follows:
229
Revised January l%S | 246 | 246 | 00-80T-80.pdf |
i | 247 | 247 | 00-80T-80.pdf |
(4) Sweepback contributes to lateral sta-
bility in rhe same sense as dihedral. When
the swept wing aircraft is placed in a side-
slip, the wing into the wind experiences an
increase in lift since the sweep is less and
the wing away from the wind produces less
lift since rhe sweep is greater. As shown in
figure 3.15, the swept wing aircraft in a
sideslip experiences lift changes and a sub-
sequent rolling moment which tends to
right the aircraft. This lateral stability
conrribution depends on the sweepback and
the lift coefficient of the wing. A highly
swept wing operating at high lift coeflicient
usually experiences such an excess of this
lateral stability contribution that adequate
controllability may be a significant problem.
As shown, the swept wing has certain im-
portant advantages. However, the use of
sweepback produces certain inevitable disad-
vantages which are important from the stand-
point of both airplane design and flight oper-
ations. The most important of these disad-
vantages are as follows:
(1) When sweepback is combined with
taper there is an extremely powerful tendency
for the wing to stall tip first. This pattern
of stall is very undesirable since there would
be little stall warning, a serious reduction
in lateral control effectiveness, and the for-
ward shift of the center of pressure would
contribute to a nose up moment (“pitch up”
or “stick force lightening”). Taper has its
own effect of producing higher local lift
coefhcients toward the tip and one of the
effects of sweepback is very similar. All
outboard wing sections are affected by the
upwash of the preceding inboard sections
and the lift distribution resulting from sweep-
back alone is similar to that of high taper.
An additional effect is the tendency to
develop a strong spanwise flow of the bound-
ary layer toward the tip when the wing is at
high lift coefficients. This spanwise flow
produces a relatively low energy boundary
layer near the tip which can be easily sep-
NAVWEPS 00-801-80
HIGH SPEED AERODYNAMICS
arated. The combined effect of taper and
sweep present a considerable problem of tip
stall and this is illustrated by the flow pat-
terns of figure 3.16. Design for high speed
performance may dictate high sweepback,
while structural efficiency may demand a
highly tapered planform. When such is the
case, the wing may require extensive aero-
dynamic tailoring to provide a suitable stall
pattern and a lift distribution at cruise condi-
tion which reduces drag due to lift. Wash-
out of the tip, variation of section camber
throughout span, flow fences, slats, leading
edge extension, etc., are typical devices used
to modify the stall pattern and minimize
drag due to lift at cruise condition.
(2) As shown by the lift curve of figure
3.15 the use of sweepback will reduce the lift
curve slope and the subsonic maximum lift
coefficient. It is important to note this
case is definitely subsonic since sweepback
may be used to improve the transonic ma-
neuvering capability. Various sweep angles
applied to wings of moderate aspect ratio
produce these approximate effects on the
subsonic lift characteristics:
sweep Angle (A):
O”................................. 0
w................................ 4
300. 14
450.......... 30
M)Q................................ yl
The reduction of the low speed maximum
lift coefficient (which is in addition to that
lost due to tip stall) has very important
implications in design. If wing loading is
not reduced, stall speeds increase and sub-
sonic maneuverability decreases. On the
other hand, if wing loading is reduced, the
increase in wing surface area may reduce
the anticipated benefit of sweepback in the
transonic flight regime. Since the require-
ments of performance predominate, certain
increases of stall speeds, takeoff speeds,
251 | 248 | 248 | 00-80T-80.pdf |
NAVWEPS OO-EOT-80 NAVWEPS OO-EOT-80
HIGH SPEED AERODYNAMICS HIGH SPEED AERODYNAMICS
5
SPANWISE LIFT O~STR~BUT~ON SPANWISE LIFT DISTRIBUTION
WC
26
TIP STALL TENDENCY TIP STALL TENDENCY
OF UNMOOIFIEO WING OF UNMOOIFIEO WING
::G
g:: - - - - - - - - 1.0 1.0
Ot+ ,s
- I.0 - I.0
t ” 3
it
zi WING MODIFIED BY WING MODIFIED BY
OCJ WASHOUT, CAMBER, WASHOUT, CAMBER,
;$
SECTION VARIATION, ETC. SECTION VARIATION, ETC.
v) 0 0 0 f ! 0
ROOT TIP
TYPICAL STALLSEQUENCE
SPANWISE FLOW OF
BOUNDARY LAYER
DEVELOPS AT HIGH CL
STALL AREA
Figure 3.16. Stall Characteristics of Tapered Swept Wing
232 | 249 | 249 | 00-80T-80.pdf |
NAVWEPS 00-8OT-80
HIGH SPEED AERODYNAMICS
STRIJ;U;RAL
STRAIGHT WING OF SAME
AREA, ASPEC&ATIO, AN0
I
AEROD&AMIC
WING BENDING PRODUCES
-/TIP ROTATION
---
TIP VIEW TRAILING EDGE VIEW
figure 3.17. Structurd Complications Due to Sweephk
233 | 250 | 250 | 00-80T-80.pdf |
NAVWEPS 00-ROT-80
HIGH SPEED AERODYNAMICS
and landing speeds usually will be accepted.
While the reduction of lift curve slope may
be an advantage for gust considerations,
the reduced sensitivity to changes in angle
of attack has certain undesirable effects in
subsonic flight. The reduced wing lift
curve slope tends to increase maximum lift
angles of attack and complicate the problem
of landing gear design and cockpit visi-
bility. Also, the lower lift curve slope
would reduce the contribution to stability
of a given tail surface area.
(3) The use of sweepback will reduce
the effectiveness of trailing edge control
surfaces and high lift devices. A typical
example of this effect is the application of
a single slotted flap over the inboard 60
percent span to both a straight wing and a
wing with 35” sweepback. The flap applied
to the straight wing produces an increase
in maximum lift coefficient of approxi-
mately 50 percent. The same type flap
applied to the swept wing produces an
increase in maximum lift coefficient of
approximately 20 percent. To produce some
reasonable maximum lift coefficient one a
swept wing may require unsweeping the
flap hinge line, application of leading edge
high lift devices such as slots or slats, and
possibly boundary layer control.
(4) As described previously, sweepback
contributes to lateral stability by producing
stable rolling moments with sideslip. The
lateral stability contribution of sweepback
varies with the amount of wing sweepback
and wing lift coefficient-large sweepback
and high lift coefficients producing large
contribution to lateral stability. While sta-
bility is desirable, any excess of stability will
reduce controllability. For the majority of
airplane configurations, high lateral sta-
bility is neither necessary nor desirable, but
adequate control in roll is absolutely neces-
sary for good flying qualities. An excess of
lateral stability from sweepback can aggra-
vate “Dutch roll” problems and produce
marginal control during crosswind takeoff
and landing where the aircraft must move in
a controlled sideslip. Therefore, it is not
unusual to find swept wing aircraft with
negative dihedral and lateral control de-
vices designed principally to meet cross wind
takeoff and landing requirements.
(5) The structural complexity and aero-
elastic problems created by sweepback are of
great importance. First, there is the effect
shown in figure 3.17 that swept wing has a
greater structural span than a straight wing
of the same area and aspect ratio. This effect
increases wing structural weight since
greater bending and shear material must be
distributed in the wing to produce the same
design strength. An additional problem is
created near the wing root and “carry-
through” structure due to the large twisting
loads and the tendency of the bending stress
distribution to concentrate toward the trail-
ing edge. Also shown in figure 3.17 is the
influence of wing deflection on the spanwise
lift distribution. Wing bending produces
tip rotation which tends to unload the tip
and move the center of pressure forward.
Thus, the same effect which tends to allay
divergence can make an undesirable contri-
bution to longitudinal stability.
EFFECT OF ASPECT RATIO AND TIP
SHAPE. In addition to wing sweep, plan-
form properties such as aspect ratio, and tip
shape, can produce significant effects on the
aerodynamic characteristics at high speeds.
There is no particular effect of aspect ratio on
critical Mach number at high or medium
aspect ratios. The aspect ratio must be less
than four or five to produce any apparent
change in critical Mach number. This effect
is shown for a typical 9 percent thick sym-
metrical airfoil in the graph of figure 3.18.
Note that very low aspect ratios are required
to cause a significant increase in critical Mach
number. Very low aspect ratios create the
extremes of three dimensional flow and sub-
sequent increase in free stream speed to create
134 | 251 | 251 | 00-80T-80.pdf |
NAVWEPS 00-801-80
HIGH SPEED AERODYNAMICS
APPROXIMATE VARIATION OF CRITICAL
i.oo- MACH NUMBER WITH ASPECT RATIO FOR
A 9% THICK AIRFOIL SECTION
.95-
CRITICAL .90-
MACH .85-
NUMBER
MCR .80-
.75 -
.7od I 1 1 I 1 9 I
01 2 3 4 5 6 7 8 9 IO II I2
ASPECT RATIO, AR
MACH CONES FORMED AT
TIPS OF RECTANGULAR
\-
WING IN SUPERSONIC FLOW
PRESSURE DISTRIBUTION
AT THE TIP OF THE
RECTANGULAR WING
Y- MACH CONE
VORTEX CREATED WITHIN
THE MACH CONE AT THE TIP
OF THE RECTANGULAR WING
WING WITH TIPS
“RAKED” OUTSIDE
THE TIP CONES
Figure 3.18. Generd Pknform Effects
235 | 252 | 252 | 00-80T-80.pdf |
NAVWEPS 00-ROT-80
HIGH SPEED AERODYNAMICS
local sonic flow. Actually, the extremely
low aspect ratios required to produce high
critical Mach number are not too practical.
Generally, the advantage of low aspect ratio
must be combined with sweepback and high
speed airfoil sections.
The thin rectangular wing in supersonic
flow illustrates several important facts. AS
shown in figure 3.18, Mach cones form at the
tips of the rectangular wing and affect t~he
pressure distribution on the area within the
cone. The vortex develops within the tip
cone due to the pressure differenti,al and the
resulting average pressure on the area within
thecone is approximately one-half the pressure
between the cones. Three-dimensional flow
on the wing is then confined to the area within
the tip cones, while the area between the
cones experiences pure two-dimensional flow.
It is important to realize that the three-
dimensional flow on the rectangular wing in
supersonic flight differs greatly from that of
subsonic flight. A wing of finite aspect ratio
in subsonic flight experiences a three-dimen-
sional flow which includes the tip vortices,
downwash behind the wing, upwash ahead of
the wing, and local induced velocities along
the span. Recall that the local induced veloc-
ities along the span of the wing would incline
the section lift aft relative to the free stream
and result in “induced drag.” Such a flow
condition cannot be directly correlated with
the wing in supersonic flow, ~ The flow pattern
for the rectangular wing of figure 3.18 dem-
onstrates that the three-dimensional flow is
confined to the tip, and pure two-dimensional
flow exists on the wing area between the tip
cones. If the wing tips were to be “raked”
outside the tip cones, the entire wing flow
would correspond to the two-dimensional (or
section) conditions.
Therefore, for the wing in supersonic flow,
no upwash exists ahead of the wing, three-
dimensional effects are confined to the tip
cones, and no local induced velocities occur
along the span between the tip cones. The
supersonic drag due to lift is a function of the
section and angle of attack while the subsonic
induced drag is a function of lift coefficient
and aspect ratio. This comparison makes it
obvious that supersonic flight does not demand
the use of high aspect ratio planforms typical
of low speed aircraft. In fact, low aspect
ratios and high taper are favorable from the
standpoint of structural considerations if very
thin sections are used to minimize wave drag.
If sweepback is applied to the supersonic
wing, the pressure distribution will be affected
by the location of the Mach cone with respect
to the leading edge. Figure 3.19 illustrates the
pressure distribution for the delta wing plan-
form in supersonic flight with the leading edge
behind or ahead of the Mach cone. When the
leading edge is behind the Mach cone the com-
ponents of velocity perpendicular to the leading
edge are still subsonic even though the free
stream flow is supersonic and the resulting
pressure distribution will greatly resemble the
subsonic pressure distribution for such a plan-
form. Tailoring the leading edge shape and
camber can minimize the components of the
high leading edge suction pressure which are
inclined in the drag direction and the drag due
to lift can be reduced. If the leading edge
is ahead of the h4ach cone, the flow over this
area will correspond to the two-dimensional
supersonic flow and produce constant pressure
for that portion of the surface between the
leading edge and the Mach cone.
CONTROL SURFACES. The design of con-
trol surfaces for transonic and supersonic flight
involves many important considerations. This
fact is illustrated by the typical transonic and
supersonic flow patterns of figure 3.19. Trail-
ing edge control surfaces can be affected ad-
versely by the shock waves formed in flight
above critical Mach number. If the airflow
is separated by the shock wave the resulting
buffet of the control surface can be very objec-
tionable. In addition to the buffet of the sur-
face, the change in the pressure distribution due
to separation and the shock wave location can
236 | 253 | 253 | 00-80T-80.pdf |
NAVWEPS 00-801-60
HIGH SPEED AERODYNAMICS
DELTA WING PLANFORM
-PRESSURE
DISTRIBUTION
MACH CONE MACH CONE
AHEAD OF LEADING
EDGE
CONTFOL SURFACE
FLOW PATTERNS
SONIC FLOW ON
G EDGE CONTROLS
M=.85
SUPERSONIC FLOW CONDITIONS
TRAILING ED
CONTROLSURFACE
Figure 3.19. Planform Effects and Control Surfaces | 254 | 254 | 00-80T-80.pdf |
NAVWEPS 00-ROT-80
HIGH SPEED AERODYNAMICS
create very large changes in control surface
hinge moments. Such large changes in hinge
moments create very undesirable control forces
and present the need for an “irreversible” con-
trol system. An irreversible control. system
would employ powerful hydraulic or electric
actuators to move the surfaces upon control by
the pilot and the airloads developed on the
surface could not feed back to the pilot. Of
course, suitable control forces would be syn-
thesized by bungees, “4” springs, bobweights,
etc.
Transonic and supersonic flight can cause a
noticeable reduction in the effectiveness of
trailing edge control surfaces. The deflection
of a trailing edge control surface at low sub-
sonic speeds alters the pressure distribution on
the fixed portion as well as the movable portion
of the surface. This is true to the extent that a
l-degree deflection of a 40 percent chord eleva-
tor produces a lift change very nearly the
equivalent of a l-degree change in stabilizer
setting. However, if supersonic flow exists on
the surface, a deflection of the trailing edge
control surface cannot influence the pressure
distribution in the supersonic area ahead of the
movable control surface. This is especially
true in high supersonic flight where supersonic
flow exists over the entire chord and the change
in pressure distribution is limited to the area of
the control surface. The reduction in effective-
ness of the trailing edge control surface at tran-
sonic and supersonic speeds necessitates the use
of an all movable surface. Application of the
all movable control surface to the horizontal
tail is most usual since the increase in longi-
tudinal stability in supersonic flight requires a
high degree of control effectiveness to achieve
required controllability for supersonic maneu-
vering.
SUPERSONIC ENGINE INLETS. Air
which enters the compressor section of a jet
engine or the combustion chamber of a ramlet
usually must be slowed to subsonic velocity.
This process must be accomplished with the
least possible waste of energy. At flight speeds
just above the speed of sound only slight modi-
fications to ordinary subsonic inlet design pro-
duce satisfactory performance. However, at
supersonic flight speeds, the inlet design must
slow the air with the weakest possible series-or
combination of shock waves to minimize en-
ergy losses and temperature rise. Figure 3.20
illustrates some of the various forms of super-
sonic inlets or “diffusers.”
One of the least complicated types of inlet
is the simple normal shock type diffuser. This
type of inlet employs a single normal shock
wave at the inlet with a subsequent internal
subsonic compression. At low supersonic Mach J
numbers the strength of the normal shock wave
is not too great and this type of inlet is quite
practical. At higher supersonic Mach num-
bers, the single normal shock wave is very
strong and causes a great reduction in the total
pressure recovered by the inlet. In addition,
it is necessary to consider that the wasted 1
energy of the airstream will appear as an addi-
tional undesirable rise in temperature of the
captured inlet airflow.
If the supersonic’airstream can be captured,
the shock wave formations tiill be swallowed
and a gradual contraction will reduce the speed
to just above sonic. Subsequent diverging flow 1
section can then produce the normal shock
wave which slows the airstream to subsonic.
Further expansion continues to slow the air to
lower subsonic speeds. This is the convergent-
divergent type inlet shown in figure 3.20. If
the initial contraction is too extreme for the
inlet Mach number, the shock wave formation
will not be swallowed and will move out in
front of the inlet. The external location of the
normal shock wave will produce subsonic flow
immediately at the inlet. Since the airstream
is suddenly slowed to subsonic through the
strong normal shock a greater loss of airstream
energy wiIl occur.
Another form of diffuser employs an external
oblique shock wave which slows the super-
sonic airstream before the normal shock occurs.
Ideally, the supersonic airstream could be
Revised January 1965
238 | 255 | 255 | 00-80T-80.pdf |
NAVWEPS 00-8OT-80
HIGH SPEED AERODYNAMICS
NORMALSHOCKINLET CONVERGENT-DIVERGENT INLET
SINGLEOBLIOUE SHOCK IPLE OBLIOUE SHOCK
NORMAL SHOCK WAVE
NEAR DESIGN RANGE BELOW DESIGN RANGE
EFFECT OF DIFFUSER DESIGN AND
MACH NUMBER ON DIFFUSER PERFORMANCE
1.00
.90 -
.BO -
.70 -
.60 -
.50 - -
.40 -
.30 -
.20 -
.I0 7 0 I
I 1.5 2.5 3.5
1.0 2.0 3.0 4.0
MACH NUhl6ER
Figure 3.20. Various Types of Supersonic Mets
239 | 256 | 256 | 00-80T-80.pdf |
NAVWEPS 00-8OT-80
HIGH SPEED AERODYNAMICS
slowed gradually through a series of very
weak oblique shock waves to a speed just
above sonic velocity. Then the subsequent
normal shock to subsonic could be quite weak.
Such a combination of the weakest possible
waves would result in the least waste of energy
and the highest pressure recovery. The ef-
ficiency of various types of diffusers is shown
in figure 3.20 and illustrates this principle.
An obvious complication of the supersonic
inlet is that the optimum shape is variable with
inlet flow direction and Mach number. In
other words, to derive highest efficiency and
stability of operation, the geometry of the
inlet would be different at each Mach number
and angle of attack of flight. A typical super-
sonic military aircraft may experience large
variations in angle of attack, sideslip angle,
and flight Mach number during normal oper-
ation. These large variations in inlet flow
conditions create certain important design
considerations.
(1) The inlet should provide the highest
practical efficiency. The ratio of recovered
total pressure to airstream total pressure is
an appropriate measure of this efficiency.
(2) The inlet should match the demands
of the powerplant for airflow. The airflow
captured by the inlet should match that
necessary for engine operation.
(3) Operation of the inlet at flight condi-
tions other than the design condition should
not cause a noticeable loss of efficiency or
excess drag. The operation of the inlet
should be stable and not allow “buzz”
conditions (an oscillation of shock location
possible during off-design operation).
In order to develop a good, stable inlet design,
the performance at the design condition may
be compromised. A large variation of inlet
flow conditions may require special geometric
features for the inlet surfaces or a completely
variable geometry inlet design,
SUPERSONIC CONFIGURATIONS. When
all the various components of the supersonic
airplane are developed, the most likely general
configuration properties will beas follows:
(1) The wing will be of low aspect ratio,
have noticeable taper, and have sweepback
depending on the design speed range. The
wing sections will be of low thickness ratio
and require sharp leading edges.
(2) The fmelagc and naceller will be of
high fineness ratio (long and slender). The
supersonic pressure distribution may create
significant lift and drag and require con-
sideration of the stability contribution of
these surfaces.
(3) The t&Z surfaces will be similar to
the wing-low aspect ratio, tapered, swept
and of thin section with sharp leading edge.
The controls will be fully powered and ir-
reversible with all movable surfaces the
most likely configuration.
(4) In order to reduce interference drag
in transonic and supersonic flight, the gross
cross section of the aircraft may be “area
ruled” to approach that of some optimum
high speed shape.
One of the most important qualities of high
speed configurations will be the low speed
flight characteristics. The low aspect ratio
swept wing planform has the characteristic
of high induced drag at low flight speeds.
Steep turns, excessively low airspeeds, and
steep, power-off approaches can then produce
extremely high rates of descent during landing.
Sweepback and low aspect ratio can cause
severe deterioration ‘of handling qualities at
speeds below those recommended for takeoff
and landing. On the other hand, thin, swept
wings at high wing loading will have rela-
tively high landing speeds. Any excess of
this basically high airspeed can create an im-
possible requirement of brakes, tires, and arrest
ing gear. These characteristics require that
the pilot account for the variation of optimum
speeds with weight changes and adhere to the
procedures and techniques outlined in the
flight handbook. | 257 | 257 | 00-80T-80.pdf |
NAVWEPS Do-Sd-eD
“,G” SPEED AERODYNAMICS
EFFECT OF SPEED AND ALTITUDE
ON AERODYNAMIC HEATING
STAGNATION
TEMPERATURE
AT
SEA LEVEL
RAM TEMPERATURE
;;I
Z STAGNATION
w TEMPERATURE I- IN THE
STRATOSPHERE
500-
0, --I 0 500 1000 1500 2000 2500 3000
TRUE AIRSPEED, KNOTS
APPROXIMATE EFFECT OF TEMPERATURE
ON TENSILE ULTIMATE STRENGTH, l/2 HR, EXPOSURE
IOO-
go-
00-
70-
60-
50-
40-
30- ,-ALUMINUM
20- ALLOY
IO- L Or I
0 100 200 300 400 500 600 700 SO0 900 ~000
TEMPERATURE, “F
Figure 3.21. Aerodynamic Heating
241 | 258 | 258 | 00-80T-80.pdf |
NAVWEPS 00-BOT-80
H,lGH SPEED AERODYNAMICS
AERODYNAMIC HEATING
When air flows over any aerodynamic surface
certain reductions in velocity occur with cor-
responding increases in temperature. The
greatest reduction in velocity and increase in
temperature will occur at the various stagna-
tion points on the aircraft. Of course, similar
changes occur at other points on the aircraft
but these temperatures can be related to the
ram temperature rise at the stagnation point.
While subsonic flight does not produce temper-
atures of any real concern, supersonic flight
can produce temperatures high enough to be
of major importance to the airframe and power-
plant structure. The graph of figure 3.21 il-
1 lustrates the variation of ram temperature rise
with airspeed in the standard atmosphere.
The ram temperature rise is independent of
altitude and is a function of true .airspeed.
Actual temperatures would be the sum of the
temperature rife and the ambient air temper-
ature. ~Thus, low altitude flight at high Mach
numbers will produce the highest temperatures.
In addition to the effect on the crew member
environment, aerodynamic heating creates
special problems for the airplane structure
and the powerplant. The effect of tempera-
ture on the short time strength of three typical
structural materials is shown in figure 3.21.
Higher temperatures produce definite reduc-
tions in the strength of aluminum alloy and
require the use of titanium alloys, stainless
steels, etc., at very high temperatures. Con-
tinued exposure at elevated temperatures effects
further reductions of strength and magnifies the
problems of “creep” failure and structural
stiffness.
The turbojet engine is adversely affected by
high compressor inlet air temperatures. Since
the thrust output of the turbojet is some func-
tion of the fuel flow, high compressor inlet air
temperatures reduce the fuel flow that can be
used within turbine operating temperature
limits. The reduction in performance of the
turbojet engines with high compressor inlet
air temperatures requires that the inlet design
produce the highest practical efficiency and
minimize the temperature rise of the air
delivered to the compressor face.
High flight speeds and compressible flow
dictate airplane configurations which are much
different from the ordinary subsonic airplane.
To achieve safe and efficient operation, the pilot
of the modern, high speed aircraft must under-
stand and appreciate the advantages and dis-
advantages of the configuration. A knowledge
of high speed aerodynamics will contribute
greatly to this understanding.
Revised January 1965
242 | 259 | 259 | 00-80T-80.pdf |
NAVWEPS 00-80T-80
STABILITY AND CONTROL
Chapter 4
STABILITY AND CONTROL
An aircraft must have satisfactory handling
qualities in addition to adequate performance.
‘lYhe aircraft must have adequate stability to
maintain a uniform flight condition and recover
from the various disturbing influences. It is
necessary to provide sufficient stability to
minimize the workload of the pilot. Also, the
aircraft must have proper response to the
controls so that it may achieve the inherent
performance. There are certain conditions of
flight which provide the most critical require-
ments of stability and control and these condi-
tions must be understood and respected to
accomplish safe and efficient operation of the
aircraft.
DEFINITIONS
STATIC STABILITY
An aircraft is in a state of equilibrium when
the sum of all forces and all moments is equal
243 | 260 | 260 | 00-80T-80.pdf |
NAVWEPS 00-8OT-80
STABILITY AND CONTROL
POSITIVE STATIC STABILITY
TENDENCY TO RETURN
TO EOUILIBRIUM
L EOUILIBRIUM
TENDENCY TO CONTINUE
IN/DISPLACEMENT DIRECTION
\
NEGATIVE STATIC STABILITY
EOulLlBRlUM ENCOUNTERED
AT ANY POINT OF DISPLACEMENT
1
(-1
Figure 4.1. Static Stability | 261 | 261 | 00-80T-80.pdf |
to zero. When an aircraft is in equilibrium,
there are no accelerations and the aircraft
continues in a steady condition of flight. If
the equilibrium is disturbed by a gust or deflec-
tion of the controls, the aircraft will experi-
ence acceleration due to unbalance of moment
or force.
The static stability of a system is defined by
the initial tendency to return to equilibrium
conditions following some disturbance from
equilibrium. If an object is disturbed from
equilibrium and has the tendency to return
to equilibrium, positive .rtatic Jtability exists.
If the object has a tendency to continue in the
direction of disturbance, negative static stability
or static instability exists. An intermediate
condition could occur where an object dis-
placed from equilibrium remains in equilibrium
in the displaced position. If the object subject
to a disturbance has neither the tendency to
return nor the tendency to continue in the dis-
placement direction, ncutrnl Jtatic stability ex-
ists. These three categories of static stability
are illustrated in figure 4.1. The ball in a
trough illustrates the condition of positive
static stability. If the ball is displaced from
equilibrium at the bottom of the trough, the
initial tendency of the ball is to return to the
equilibrium condition. The ball may roll
back and forth through the point of equilib-
rium but displacement to either side creates
the initial tendency to return. The ball on a
hill illustrates the condition of static insta-
bility. Displacement from equilibrium at the
hilltop brings about the tendency for greater
displacement. The ball on a flat, level surface
illustrates the condition of neutral static sta-
bility. The ball encounters a new equilibrium
at any point of displacement and has neither
stable nor unstable tendencies.
The term “static” is applied to this form of
stability since the resulting motion is not
considered. Only the tendency to return to 1. eqmlibrtum conditions is considered in static
stability. The static longitudinal stability of
an aircraft is appreciated by displacing the
NAVWEPS 00-802-80
STABILITY ,AND CONTROL
aircraft from some trimmed angle of attack.
If the aerodynamic pitching moments created
by this displacement tend to return the air-
craft to the equilibrium angle of attack the
aircraft has positive static longitudinal
stability.
DYNAMIC STABILITY
While static stability is concerned with the
tendency of a displaced body to return to
equilibrium, dynamic stability is defined by
the resulting motion with time. If an object is
disturbed from equilibrium, the time history
of the resulting motion indicates the dynamic
stability of the system. In general, the system
will demonstrate positive dynamic stability
if the amplitude of motion decreases with
time. The various condirions of possible
dynamic behavior are illustrated by the time
history diagrams of figure 4.2.
The nonoscillatory modes shown in figure
4.2 depict the time histories possible without
cyclic motion. If the system is given an initial
disturbance and the motion simply subsides
without oscillation, the mode is termed “sub-
sidence” or “deadbeat return.” Such a motion
indicates positive static stability by the tend-
ency to return to equilibrium and positive dy-
namic stability since the amplitude decreases
with time. Chart B illustrates the mode of
“divergence” by a noncyclic increase of ampli-
tude with time. The initial tendency to con-
tinue in the displacement direction is evidence
of static instability and the increasing ampli-
tude is proof of dynamic instability. Chart C
illustrates the mode of pure neutral stability.
If the original disturbance creates a displace-
ment which remains constant thereafter, the
lack of tendency for motion and the constant
amplitude indicate neutral static and neutral
dynamic stability.
The oscillatory modes of figure 4.2 depict the
time histories possible with cyclic motion.
One feature common to each of these modes is
that positive static stability is demonstrated in
the cyclic motion by tendency to return to
245 | 262 | 262 | 00-80T-80.pdf |
NAVWEPS 00-EOT-80
STABILITY AND CONTROL
NON-OSCILLATORY MODES
(OR DEAD BEAT RETURN)
5 (POSITIVE STATIC) (NEGATIVE STATIC)
0 (POSITIVE DYNAMIC) (NEGATIVE DYNAMIC)
(NEUTRAL STATIC)
(NEUTRAL DYNAMlc)
OSCILLATORY h
5 g E 1: 0. (POSITIVE STATIC) ;
(POSITIVE DYNAMIC)
0 E
UNDAMPED OSCILLATION
(POSITIVE STATIC)
(NEUTRAL DYNAMIC)
(P0slTl~E
(NEGATIVE
STATIC)
DYNAMIC)
Figure 4.2. Dynamic Sfabihty
246 | 263 | 263 | 00-80T-80.pdf |
quilibrium conditions. However, the dy-
namic behavior may be stable, neutral, or un-
stable. Chart D illustrates the mode of a
damped oscillation where the amplitude de-
creases with time. The reduction of amplitude
with time indicates there is resistance to mo-
tion and that energy is being dissipated. The
dissipation of energy-or “damping’‘-is nec-
essary to provide positive dynamic stability.
If there is no damping in the system, the mode
of chart E is the result, an undamped oscilla-
tion. Without damping, the oscillation con-
tinues with no reduction of amplitude with
time. While such an oscillation indicates posi-
tive static stability, neutral dynamic stability
exists. Positive damping is necessary to elimi-
nate the continued oscillation. As an example,
an automobile with worn shock absorbers (or
“dampers”) lacks sufficient dynamic stability
and the continued oscillatory motion is neither
pleasant nor conducive to safe operation. In
the same sense, the aircraft must have sufficient
damping to, rapidly dissipate any oscillatory
motion which would affect the operation of
the aircraft. When natural aerodynamic damp-
ing cannot be obtained, a synthetic damping
must be furnished to provide the necessary
positive dynamic stability.
Chart F of figure 4.2 illustrates the mode of
a divergent oscillation. This motion is stat-
ically stable since it tends to return to the
equilibrium position. However, each subse-
quent return to equilibrium is with increasing.
velocity such that amplitude continues to
increase with time. Thus, dynamic insta-
bility exists. The divergent oscillation occurs
when energy is supplied to the motion rather
than dissipated by positive damping. The
most outstanding illustration of the divergent
oscillation occurs with the short period pitch-
ing oscillation of an aircraft. If a pilot un-
knowingly supplies control functions which
are near the natural frequency of the airplane
in pitch, energy is added to the system, nega-
tive damping exists, and the “pilot induced
oscillation” results.
NAVWEPS OO-ROT-80
STABILITY AND CONTROL
In any system, the existence of static sta-
bility does not necessarily guarantee the
existence of dynamic stability. However,
the existence of dynamic stability implies
the existence of static stability.
Any aircraft must demonstrate the required
degrees of static and dynamic stability. If
the aircraft were allowed to have static in-
stability with a rapid rate of divergence, the
aircraft would be very difficult-if not impos-
sible-to fly. The degree of difficulty would
compare closely with learning to ride a uni-
cycle. In addition, positive dynamic stability
is mandatory in certain areas to preclude
objectionable continued oscillations of the
aircraft.
TRIM AND CONTROLLABILITY
An aircraft is said to be trimmed if all
moments in pitch, roll, and yaw are equal to
zero. The establishment of equilibrium at
various conditions of flight is the function of
the controls and may be accomplished by
pilot effort, trim tabs, or bias of a surface
actuator.
The term “controllability” refers to the
ability of the aircraft to respond to control
surface displacement and achieve the desired
condition of flight. Adequate controllability
must be available to perform takeoff and
landing and accomplish the various maneuvers
in flight. An important contradiction exists
between stability and controllability since
adequate controllability does not necessarily
exist with adequate stability. In fact, a high
degree of stability tends to reduce the controlla-
bility of the aircraft. The general relation-
ship between static stability and controlla-
bility is illustrated by figure 4.3.
Figure 4.3 illustrates various degrees of
static stability by a ball placed on various
surfaces. Positive static stability is shown by
the ball in a trough; if the ball is displaced
from equilibrium at the bottom of the trough,
there is an initial tendency to return to equilib-
rium. If it is desired to “control” the ball
247 | 264 | 264 | 00-80T-80.pdf |
NAVWEPS 00-ROT-80
STABILITY AND CONTROL
POSITIVE STATIC
STABILITY
CREASED POSIT,VE
TIC STABILITY
NEUTRAL STATIC STABILITY
NEGATIVE
STATIC STABILITY
Figure 4.3. Stability and Control/ability
248 | 265 | 265 | 00-80T-80.pdf |
and maintain it in the displaced position, a
force must be supplied in rhe direction of
displacement co balance the inherent tendency
to return to equilibrium. This same stable
tendency in an aircraft resists displacement
from trim by pilot effort on the controls or
atmospheric disturbances.
The effect of increased stability on con-
trollabilicy is illustrated by rhe ball in a
steeper trough. A greater force is required to
“control” the ball to the same lateral dis-
placement when the stability is increased.
In this manner, a large degree of stability tends
to make the aircraft less controllable. It is
necessary to achieve the proper balance be-
tween stability and tontrollability during rhe
design of an aircraft because the ~ppcr limits
of stability arc set by the lower 1imitJ of controlla-
bility.
The effect of reduced stability on .controlla-
bility is illustrated by the ball on a flat surface.
When neutral static stability exists, the ball
may be displaced from equilibrium and there
is no stable tendency to return. A new point
of equilibrium is obtained and no force is
required to maintain the displacement. As
the static stability approaches zero, controlla-
bility increases to infinity and the only resist-
ance to displacement is a resistance to the
motion of displacement-damping. For this
reason, the lower Limits of stability may be Set
by the upper limits of controllability. If the
stability of the aircraft is too low, control
deflections may create exaggerated displace-
ments of the aircraft.
The effect of static instability. on controlla-
bility is illustrated by the ball on a hill. If
the ball is displaced from equilibrium at the
top of the hill, the initial tendency is for the
ball td continue in the displaced direction.
In order to “control”~the ball to some lateral
displacement, a force must be applied oppo&
to the direction of displacement. This effect
would be appreciated during flight of an un-
stable aircraft by an unstable “feel” of the air-
craft. If the controls were deflected co in-
NAVWEPS DD-8OT-80
STABILITY AND CONTROL
&ease the angle of attack, the aircraft would
be trimmed at the higher angle of attack by
a push force to keep the aircraft from con-
tinuing in the displacement direction. Such
control force reversal would evidence the aii-
plane instability; the pilot would be supply-
ing the stability by his attempt to maintain
the equilibrium. An unstable aircraft can be
flown if the instability is slight with a low
rate of divergence. Quick reactions coupled
with effective controls can allow the pilot to
cope with some degree of static instability.
Since such flight would require constant at-
tention by the pilot, slight instability can be
tolerated only in airships, helicopters, and
certain minor motions of the airplane. How-
ever, the airplane in high speed flight will
react rapidly to any disturbances and any in-
stability would create unsafe conditions. Thus,
it is necessary to provide some positive static
stability to the major aircraft degrees of
freedom.
AIRPLANE REFERENCE AXES
In order to visualize the forces and moments
on the aircraft; it is necessary to establish a
set of mutually perpendicular reference axes
originating at the center of gravity. Figure
4.4 illustrates a conventional right hand axis
system. The longitudinal or X axis is located
in a plane of symmetry and is given a positive
direction pointing into the wind. A moment
about this axis is a rolling moment, L, and the
positive direction for a positive rolling moment
utilizes the right hand rule. The vertical or 2
axis also is in a plane of symmetry and is estab-
lished positive downward. A moment about
the vertical axis is a yawing moment, N, and a
positive yawing moment would yaw the air-
craft co the right (right hand rule). The
lateral or Y axis is perpendicular to the plane
of symmetry and is given a positive direction
out the right side of the aircraft. A moment
about the lateral axis is a pitching moment, M,
and a positive pitching moment is in the nose-
up dlrection.
249 | 266 | 266 | 00-80T-80.pdf |
NAVWEPS 00-8OT-80
STABELITY AND CONTROL
CENTER OF ..-.. ,.-.. _
1 VERTICAL AXIS
2
Figure 4.4. Airplane Rekre&e Axes
LONGITUDINAL STABILITY AND
CONTROL
STATIC LONGITUDINAL STABILITY
GENERAL CONSIDERATIONS. An air-
craft will exhibit positive static Iongitudinal
stability if it tends to return to the trim angle
of attack when displaced by a gust or control
movement. The aircraft which is unstable will
continue to pitch in the disturbed direction
until the displacement is resisted by opposing
control forces. If the aircraft is neutrally
stable, it tends to remain at any displacement
to which it is disturbed. It is most necessary
to provide an airplane with positive staric
longitudinal stability. The stable airplane is
safe and easy to fly since the airplane seeks and
tends to maintain a trimmed condition of
flight. It also follows that control deflec-
tions and control “feel” are logical in direction
and magnitude. Neutral static longitudinal
stability usually defines the lower limit of
airplane stability since it ‘is the boundary
between stability and instability. The air-
plane with neutral static stability’ may be
excessively responsive to controls and the
aircraft has no tendency to return to trim fol-
lowing a disturbance. The airplane with
negative sradc longitudinal stability is in-
herently divergent from any intended trim
condition. If it is at all possible to fly the
aircraft, the aircraft. cannot be trimmed and
illogical control forces and deflections are rc-
quired to provide equilibrium with a change
of attitude and airspeed.
Since static longitudinal stability depends
upon the relationship of angle of attack and
pitching moments, it is necessary to study the
pitching moment contribution of each com-
ponent of the aircraft. In a manner similar
to all other aerodynamic forces, the pitching
250 | 267 | 267 | 00-80T-80.pdf |
moment about the lateral axis is studied in
the coefficient form.
or
M = C,qS(MAC)
M
&= qS(MAC)
where
M=pitching moment about the c.g., ft.-
lbs., positive if in a nose-up direction
q= dynamic pressure, psf
S= wing area, sq. ft.
MAC=mean aerodynamic chord, ft.
C,= pitching moment coefficient
The pitching moment coefficients contributed
by all the various components of the aircraft
are summed up and plotted versus lift coeffi-
cient. Study of this plot of C, versus C,
will relate the static longitudinal stability
of the airplane.
Graph A of figure 4.5 illustrates the variation
of pitching moment coefficient, C,, with lift
coefficient, C,, for an airplane with positive
static longitudinal stability. Evidence of
static stability is shown by the tendency to re-
,t,urn to equilibrium-or “trim”- upon dis-
.,placement. The airplane described by graph A
is in trim or equilibrium when C,=O and, if the
‘airplane is disturbed to some different C,, the
pitching moment change tends to return the
aircraft to the.point of trim. If the airplane
‘were disturbed to some higher C, (point Y), a
negative or nose-down pitching moment is de-
veloped which tends to decrease angle of attack
back to the trim point. If the airplane were
disturbed to some lower C,, (point X), a posi-
tive, or nose-up pitching moment is developed
which tends to increase the angle of attack
back to the trim point. Thus, positive static
longitudinal stability is indicated by a negative
slope of C, versus C,, i.e., positive stability is
evidenced by a decrease in CM with an increase
in C,.
The degree of static longitudinal stability is
indicated by the slope of the curve of pitching
moment coefficient with lift coefficient. Graph
NAVWE,PS OO-ROT-80
STABILITY AND CONTROL
B of figure 4.5 provides comparison of the
stable and unstable conditions. Positive sta-
bility is indicated by the curve with negative
slope. Neutral static stability would be the
result if the curve had zero slope. If neutral
stability exists, the airplane could be dis-
turbed to some higher or lower lift coefficient
without change in pitching moment coefficient.
Such a condition would indicate that the air-
plane would have no tendency to return to
some original equilibrium and would not hold
trim. An airplane which demonstrates a posi-
tive slope of the C, versus C, curve would be
unstable. If the unstable airplane were subject
to any disturbance from equilibrium at the
trim point, the changes in pitching moment
would only magnify the disturbance. When
the unstable airplane is disturbed to some
higher CL, a positive change in C, occurs which
would illustrate a tendency for continued,
greater displacement. When the unstable air-
plane is disturbed to some lower C,,, a negative
change in C, takes place which tends to create
continued displacement.
Ordinarily, the static longitudinal stability
of a conventional airplane configuration does
not vary with lift coefficient. In other words,
the slope of C, versus CL does not change with
CL. However, if the airplane has sweepback,
large contribution of power effects to stability,
or significant changes in downwash at the
horizontal tail, noticeable changes in static
stability can occur at high lift coefficients.
This condition is illustrated by graph C of
figure 4.5. The curve of C, versus CL of this
illustration shows a good stable slope at low
values of CL. Increasing CL effects a slight
decrease in the negative slope hence a decrease
in stability occurs. With continued increase
in C,, the slope becomes zero and neutral
stability exists. Eventually, the slope be-
comes positive and the airplane becomes un-
stable or “pitch-up” results. Thus, at any
lift coefficient, the static stability of the air-
pl.ane is depicted by the slope of the curve of
CM versus CL.
251 | 268 | 268 | 00-80T-80.pdf |
NAVWEPS 00-8OT-80
STABILITY AND CONTROL
TRIM
CM=0
LIFT COEFFICIENT
CL
-I
0 0
+
CM ---- b CL
-
-
LESS STABLE -NEUTRAL
Figure 4.5. Airphmc Static Longitudinal Stability
252 | 269 | 269 | 00-80T-80.pdf |
CONTRIBUTION OF THE COMPONENT
SURFACES. The net pitching moment about
the lateral axis is due to the contribution of
each of the component surfaces acting in their
appropriate flow fields. By study of the con-
tribution of each component the effect of each
component on the static stability may be ap-
preciated. It is necessary to recall that the
pitching moment coefficient is defined as:
M
‘“=qS(MAC)
Thus, any pitching moment coefficient-re-
gardless of source-has the common denomi-
nator of dynamic pressure, q, wing area, S, and
wing mean aerodynamic chord, MAC. This
common denominator is applied to the pitch-
ing moments contributed by the fuselage and
nacelles, horizontal tail, and power effects
as well as pitching moments contributed by
the wing.
WING. The contribution of the wing to
stability depends primarily on the location
of the aerodynamic center with respect to the
airplane center of gravity. Generally, the
aerodynamic center-or a.c.-is defined as the
point on the wing mean aerodynamic chord
where the wing pitching moment coefficient
does not vary with lift coefficient. All changes
in lift coefficient effectively take place at the
wing aerodynamic center. Thus, if the wing
experiences some change in lift coefficient, the
pitching moment created will be a direct
function of the relative location of the a.c. and
c.g.
Since stability is evidenced by the develop-
ment of restoring moments, the c.g. must be
forward of the a.c. for the wing to contribute
to positive static longitudinal stability. As
shown in figure 4.6, a change in lift aft of the
c,g. produces a stable restoring moment de-
pendent npon the lever arm between the a.c.
and c.g. In this case, the wing contribution
would be stable and the curve of CM versus CL
for the wing alone would have a negative slope.
If the c.g. were located at the a.c., C, would
NAVWEPS OO-BOT-BO
STABILITY AND CONTROL
not vary with C, since all changes in lift would
take place at the c.g. In this case, the wing
contribution to stability would be neutral.
When the c.g. is located behind the a.c. the
wing contribution i,s unstable and the curve
of C, versus CL for the wing alone would have
a positive slope.
Since the wing is the predominating aero-
dynamic surface of an airplane, any change in
the wing contribution may produce a sig-
nificant change in the airplane stability. This
fact would be most apparent in the case of the
flying wing or tailless airplane where the wing
contribution determines the airplane stability.
In order for the wing to achieve stability, the
c.g. must be ahead of the a.c. Also, the wing
must have a positive pitching moment about
the aerodynamic center to achieve trim at
positive lift coefficients. The first chart of
figure 4.7 illustrates that the wing which is
stable will trim at a negative lift coefficient if
the C,,, is negative. If the stable wing has a
positive C,,, it will then trim at a useful posi-
tive CL. The only means available to achieve
trim at a positive CL with a wing which has a
negative C,,, is an unstable c.g. position aft of
the ax. As a result, the tailless aircraft
cannot utilize high lift devices which incur
any significant changes in C,,,.
WhiIe the trim lift coefficient may be altered
by a change in c.g. position, the resulting
change in stability is undesirable and is unsat-
isfactory as a primary means of control. The
variation of trim CL by deflection of control
surfaces is usually more effective and is less
inviting of disaster. The early attempts at
manned flight led to this conclusion.
When the aircraft is operating in subsonic
flight, the a.c. of the wing remains fixed at the
25 percent chord station. When the aircraft
is flown in supersonic flight, the ax. of the
wing will approach the 50 percent chord sta-
tion. Such a large variation in the location
of the a.c. can produce large changes in the
wing contribution and greatly alter the air-
plane longitudinal stability. The second chart
252 | 270 | 270 | 00-80T-80.pdf |
NAVWEPS 00-801-80
STABILITY AND CONTROL
t CHANGE IN LIFT
~AERODYNAMIC CENTER
CENTER OF GRAVITY
-
CL
Figure 4.6. Wing Contribution
254 | 271 | 271 | 00-80T-80.pdf |
NAVWEPS 00-BOT-80
STABILITY AND CONTROL
4 STABLE, POSITIVE CyAC
CM .ICl-2A-rI\,C C~ I IDIIETAIPI e
I ai*
STABLE, NEGATIVE f&AC
) =3=Ez.,.
CM + CL
\
SUBSONIC -
\
SUPERSONIC
Figure 4.7. Effect of CM~~ C. G. Position and Mach Nimber
255 | 272 | 272 | 00-80T-80.pdf |
NAVWEPS DD-807-80
STABILITY AND CONTROL
of figure 4.7 illustrates the change of wing
contribution possible between subsonic and
supersonic flight. The large increase in static
stability in supersonic flight can incur high
trim drag or require great control effectiveness
to prevent reduction in maneuverability.
FUSELAGE AND NACELLES. In most
cases, the contribution of the fuselage and
nacelles is destabilizing. A symmetrical body
of revolution in the flow field of a perfect fluid
develops an unstable pitching moment when
given an angle of attack. In fact, an increase
in angle of attack produces an increase in the
unstable pitching moment without the devel-
opment of lift. Figure 4.8 illustrates the pres-
sure distribution which creates this unstable
moment on the body of revolution. In the
actual case of real subsonic flow essentially
the same effect is produced. An increase in
angle of attack causes an increase in the
unstable pitching moment but a negligible
increase in lift.
An additional factor for consideration is the
influence of the induced flow field of the wing.
As illustrated in figure 4.8, the upwash ahead
of the wing increases the destabilizing influence
from the portions of the fuselage and nacelles
ahead of the wing. The downwash behind
the wing reduces the destabilizing influence
from the portions of the fuselage and nacelles
aft of the wing. Hence, the location of the
fuselage and nacelles relative to the wing is
important in determining the contribution to
stability.
The body of revolution in supersonic flow
can develop lift of a magnitude which cannot
be neglected. When the body of revolution in
supersonic flow is given an angle of attack, a
pressure distribution typical of figure 4.8 is the
result. Since the center of pressure is well
forward, the body contributes a destabilizing
influence. AS is usual with supersonic con-
figurations, the fuselage and nacelles may be
quite large in comparison with the wing area
and the contribution to stability may be large.
Interaction between the wing and fuselage and
nacelles deserves consideration in several in-
stances. Body upwash and variation of local
Mach number can influence the wing lift while
lift carryover and downwash can effect the fu-
selage and nacelles forces and moments.
HORIZONTAL TAIL. The horizontal tail
usually provides the greatest stabilizing influ-
ence of all the components of the airplane. To
appreciate the contribution of the horizontal
tail to stability, inspect figure 4.9. If the air-
plane is given a change in angle of attack, a
change in tail lift will occur at the aerody-
namic center of the tail. An increase in lift
at the horizontal tail produces a negative
moment about the airplane c.g. and tends to
return the airplane to the trim condition.
While the contribution of the horizontal tail
to stability is large, the -magnitude of the
contribution is dependent upon the change in
tail lift and the lever arm of the surface. It is
obvious that the horizontal tail will produce a
stabilizing effect only when the surface is aft
of the c.g. For this reason it would be inap-
propriate to refer to the forward surface of a
canard (tail&St) configuration as a horizontal
“stabilizer.” In a logical sense, the horizontal
“stabilizer” must be aft of the c.g. and-
generally speaking-the farther aft, the greater
the contribution to stability.
Many factors influence the change in tail
lift which occurs with a change in airplane
angle of attack. The area of the horizontal
tail has the obvious effect that a large surface
would generate a large change in lift. In a
similar manner, the change in tail lift would
depend on the slope of the lift curve for the
horizontal tail. Thus, aspect ratio, taper,
sweepback, and Mach number would deter-
mine the sensitivity of the surface to changes
in angle of attack. It should be appreciated
that the flow at the horizontal tail is not of
the same flow direction or dynamic pressure as
the free stream. Due to the wing wake, fuse-
lage boundary layer, and power effects, the q
at the horizontal tail may be greatfy different
from the 4 of the free stream. In most in-
256 | 273 | 273 | 00-80T-80.pdf |
NAVWEPS oo-BDT-BD
STABILITY AND CONTROL
BODY OF REVOLUTION IN PERFECT FLUID
INDUCED FLOW FIELD FROM WING
BODY OF REVOLUTION INSUPERSONIC FLOW
Figure 4.8. Body or Nacelle Contribution
257 | 274 | 274 | 00-80T-80.pdf |
NAVWEPS 00-BOT-BO
STABILITY AND CONTROL
_--- -. CHANGE IN LIFT
ON HORIZONTAL TAlL
OF HORIZONTAL TAIL
DOWNWASH AT
FUSELAGE CROSS FLOW
SEPARATION VORTICES
Figure 4.9. Contribution of Tail and Downwash Effects
258 | 275 | 275 | 00-80T-80.pdf |
stances, the 4 at the tail is usually less and this
reduces the efficiency of the tail.
When the airplane is given a change in angle
of attack, the horizontal tail does not expe-
rience the same change in angle of attack as
the wing. Because of the increase in down-
wash behind, the wing, the horizontal tail will
experience a smaller change in angle of attack,
e.g., if a 10" change in wing angle of attack
causes a 4O increase in downwash at the hori-
zontal tail, the horizontal tail experiences
only a 6’ change in angle of attack. In this
manner, the downwash at the horizontal tail
reduces the contribution to stability. Any
factor which alters the rate of change of down-
wash at the horizontal tail will directly affect
the tail contribution and airplane stability.
Power effects can alter the downwash at the
horizontal tail and affect the tail contribution.
Also, the ~downwash at the tail is affected by
the lift distribution on the wing and the flow
condition ,on the fuselage. The low aspect
ratio airplane requires large angles of attack
to achieve high ,lift coefficients and this posi-
tions the fuselage at high angles of attack.
The change in the wing downwash can be
accompanied by crossflow separation vortices
on the fuselage. It is possible that the net
effect obviates or destabilizes the contribu-
tion of the horizontal tail and produces air-
plane instability.
POWER-OFF STABILITY. When the in-
trinsic stability of a configuration is of interest,
power effects are neglected and the stability
is considered by a buildup of the contributing~
components. Figure 4.10 illustrates a typical
buildup of the components of a conventional
airplane configuration. If the c.g. is arbi-
trarily set at 30 percent MAC, the contribu-
tion of the wing alone is destabilizing as indi-
cated by the positive slope of CM versus C,.
The combination of the wing and fuselage
increases the instability. The contribution
of the tail alone is highly stabilizing from
the large negative slope of the curve. The
contribution of the tail must be sufficiently
NAVWEPS OO-BOT-80
STABILITY AND CONTROL
stabilizing so that the complete configuration
will exhibit positive static stability at the
anticipated c.g. locations. In addition, the tail
and wing incidence must be set to provide a
trim lift coefficient near the design condition.
When the configuration of the airplane is
fixed, a variation of c.g. position can cause
large changes in the static stability. In the
conventional airplane configuration, the large
changes in stability with c.g. variation are
primarily due to the large changes in the wing
contribution. If the incidence of all surfaces
remains fixed, the effect of c.g. position on
static longitudinal stability is typified by the
second chart of figure 4.10. As the cg. is
gradually moved aft, the airplane static sta-
bility’ decreases, then becomes neutral then
unstable., The c.g. position which produces
zero ,slope and neutral static stability is re-
ferred to asp the ~“neutral point.” The neutral
point may be imagined as the effective aerody-
namic center of the entire airplane configura-
ration, i.e., with the c.g. at this position, all
changes in net lift effectively occur at this
point and no change in pitching moment
results. The neutral point defines the most
aft c.g. position without static instability.
POWER EFFECTS. The effects of power may
cause significant changes in trim lift coefficient
and static. longitudinal stability. Since the
contribution to stability is evaluated by the
change in moment coefficients, power effects
will be most significant when the airplane
operates at high power and low airspeeds such
as the power approach or waveoff condition.
The effects of power are considered in two
main categories. First, there are the direct
effects resulting from the forces created by the
propulsion unit. Next, there are the indirect
effects of the slipstream and other associated
flow which alter the forces and moments of the
aerodynamic surfaces. The direct effects of
power are illustrated in figure 4.11. The ver-
tical location of the thrust line defines one of
the direct contributions to stability. If the
259 | 276 | 276 | 00-80T-80.pdf |
NAVWEPS OD-BOT-80
STABILITY AND CONTROL
TYPICAL GUILD-UP 0F tzci~m~ENTs
CM ,-WING+ FUSELAGE
WING ONLY/.
- -
CL
-
C.G. @ 30% MAC .
t
EFFECT OF C.G. WsITION
CM 50% MAC
40% MAC (NEUTRAL pOlNn ---
Figure 4.10. Stability Build-up and Effect of C.G. Positim | 277 | 277 | 00-80T-80.pdf |
NAVWEPS 00-BOT-80
STABILITY ,AND CONTROL
slipstream creates a normal force at the plane
of the propeller similar to a wing creating lift
by deflecting an airstream. As this normal
force will increase with an increase in airplane
angle of attack, the effect will be destabilizing
when the propeller is ahead of the cg. The
magnitude of the unstable contribution de-
pends on the distance from the c.g. to the
propeller and is largest at high power and low
dynamic pressure. The normal force created
thrust line is below the c.g., thrust produces a
positive or noseup moment and the effect is de-
stabilizing. On the other hand, if the thrust
line is ,located above the c.g., a negative
moment is created and the effect is stabilizing.
A propeller or inlet duct located ahead of
the c.g. contributes a destabilizing effect. As
shown in figure 4.11, a rotating propeller in-
clined to the windstream causes a deflection
of the airflow. The momentum change of the
261 | 278 | 278 | 00-80T-80.pdf |
NAVWEPS OD-BOT-80
S-lABlLlTY AND CONTROL
EFFECT OF VERTICAL LOCATION OF THRUST LINE
d DESTABILIZING
STABILIZING
DESTABILIZING INCRE
IN NORMAL FORCE
DESTABILIZING INCREASE
IN DUCT INLET NORMAL
FORCE
Figure 4.11. Direct Power Effects | 279 | 279 | 00-80T-80.pdf |
NAVWEPS GO-BOT-BO
STABILITY AND CONTROL
n f WING.NACELLE,AND FUSELAGE
MOMENTS AFFECTED BY
SLIPSTREAM
-DYNAMIC PRESSURE
AT TAIL AFFECTED
BY SLIPSTREAM
WING LIFT AFFECTED
BY SLIPSTREAM
FLOW INDUCED BY
JET EXHAUST
DOWNWASH AT TAIL
Figure 4.12. Indirect Power Effects.
263 | 280 | 280 | 00-80T-80.pdf |
NAVWEPS 00-8OT-90
STABHITY AND CONTROL
at the inlet of a jet engine contributes a similar
destabilizing effect when the inlet is ahead
of the c,g. As with the propeller, the magni-
tude of the stability contribution is largest at
high thrust and low flight speed.
The indirect effects of power are of greatest
concern in the propeller powered airplane
rather than the jet powered airplane. As
shown in figure 4.12, the propeller powered
airplane creates slipstream velocities on the
various surfaces which are different from the
flow field typical of power-off flight. Since
the various wing, nacelle, and fuselage surfaces
are partly or wholly immersed in this slip-
stream, the contribution of these components
to stability can be quite different from the
power-off flight condition. Ordinarily, the
change of fuselage and nacelle contribution
with power is relatively small. The added
lift on the portion of the wing immersed in
the slipstream requires that the airplane oper-
ate at a lower angle of attack to produce the
same effective lift coefficienr. Generally, this
reduction in angle of attack to effect the same
CL reduces the tail contribution to stability.
However, the increase in dynamic pressure at
the tail tends to increase the effectiveness of
the tail and may be a stabilizing effect. The
magnitude of this contribution due to the
slipstream velocity on the tail will depend on
the c.g. position and trim lift coefficient.
The deflection of the slipstream by the nor-
mal force at the propeller tends to increase the
downwash at the horizontal tail and reduce
the contribution to stability. Essentially the
same destabilizing effect is produced by the
flow induced at the exhaust of the jet power-
plant. Ordinarily, the induced flow at the
horizontal tail of a jet airplane is slight and is
destabilizing when the jet passes underneath
the horizontal tail. The magnitude of the
indirect power effects on stability tends to be
greatest at high Cr, high power, and low flight
speeds.
The combined direct and indirect power
effects contribute to a general reduction of
static stability at high power, high CL, and
low 4. It is generally true that any airplane
will experience the lowest level of static longi-
tudinal stability under these conditions. Be-
cause of the greater magnitude of both direct
and indirect power effects, the propeller pow-
ered airplane usually experiences a greater
effect than the jet powered airplane.
An additional effect on stability can be from
the extension of high lift devices. The high
lift devices tend to increase downwash at the
tail and reduce the dynamic pressure at the tail,
both of which are destabilizing. However,
the high lift devices may prevent an unstable
contribution of the wing at high CL. While
the effect of high lift devices depends on the
airplane configuration, the usual effect is de-
stabilizing. Hence, the airplane may experi-
ence the most critical forward neutral point
during the power approach or waveoff. Dur-
ing these conditions of flight the static stability
is usually the weakest and particular attention
must be given to precise control of the air-
plane. The power-on neutral point may set
the most aft limit of c.g. position.
CONTROL FORCE STABILITY. The static
longitudinal stability of an airplane is defined
by the tendency to return to equilibrium upon
displacement. In otherwords, the stable air-
plane will resist displacement from the trim or
equilibrium. The control forces of the air-
plane should reflect the stability of the air-
plane and provide suitable reference for precise
control of the airplane.
The effect of elevator deflection on pitching
moments is illustrated by the first graph of
figure 4.13. If the elevators of the airplane are
fixed at zero deflection, the resulting line of
CM versus C’s for 0’ depicts the static stability
and trim lift coefficient. If the elevators are
fixed at a deflection of 10” up, the airplane
static stability is unchanged but the trim lift
coefficient is increased. A change in elevator
or stabilizer position does not alter the tail
contribution to stability but the change in
pitching moment will alter the lift coeflicient
264 | 281 | 281 | 00-80T-80.pdf |
NAVWEPS 00-SOT-80
STABILITY AND CONTROL
EFFECT OF ELEVATOR DEFLECTION
I
CM -L ELEVATOR nre, CCTl,-..,
TRIM FOR
CG@20% MAC
TRIM C, VERSUS ELEVATOR DEFLECTION
A TRIM AIRSPEED VS ELEVATOR DEFLECTION
z
F
ii
ii UP ’ X~SLE
:
oz EQUIVALENT
2
/ ~RSPEED
t
a /
2 DOWN /
ii /
Figure 4.13. Longitudinal Control
265 | 282 | 282 | 00-80T-80.pdf |
NAVWEPS 00-BOT-80
STABILITY AND CONTROL
at which equilibrium will occur. As the ele-
vator is fixed in various positions, equilibrium
(or trim) will occur at various lift coefficients
and the trim CL can be correlated with elevator
deflection as in the second graph of figure 4.13.
When the c,g. position of the airplane is
fixed, each elevator position corresponds to a
particular trim lift coefficient. AS the c.g. is
moved aft the slope of this line decreases and
the decrease in stability is evident by a given
control displacement causing a greater change
in trim lift coefficient. This is evidence that
decreasing stability causes increased controlla-
bility and, of course, increasing stability de-
creases controllability. If the c.g. is moved
aft until the line of trim CL versus elevator de-
flection has zero slope, neutral static stability
is obtained and the “stick-fixed” neutral point
is determined.
Since each value of lift coefhcient corresponds
to a particular value of dynamic pressure re-
quired to support an airplane in level flight,
uim airspeed can be correlated with elevator
deflection as in the third graph of figure 4.13.
If the c.g. location is ahead of the stick-fixed
neutral point and control position is directly
related to surface deflection, the airplane will
give evidence of stick podion mbility. In
other words, the airplane will require the
stick to be moved aft to increase the angle
of attack and trim at a lower airspeed and to
be moved forward to decrease the angle of
attack and trim at a higher airspeed. To be
sure, it is desirable to have an airplane demon-
strate this feature. If the airplane were to
have stick position instability, the airplane
would require the stick to be moved aft to trim
at a higher airspeed or to be moved forward to
trim at a lower airspeed.
There may be slight differences in the static
longitudinal stability if the elevators are
allowed to float free. If the elevators are
allowed to float free as in “hands-off” flight,
the elevators may have a tendency to “float”
or streamline when the horizontal tail is given
a change in angle of attack. If the hot&ma1
tail is subject to an increase in angle of attack
and the elevators tend to float up, the change
in lift on the tail is less than if the elevators
remain fixed and the tail contribution to
stability is reduced. Thus, the “stick-free”
stability of an airplane is usually less than the
stick-fixed stability. A typical reduction of
stability by free elevators is shown in figure
4.14(A) where the airplane. stick-free demon-
strates a reduction of the slope of CM versus Cs.
While aerodynamic balance may be provided
tu reduce control forces, proper balance of the
surfaces will reduce floating and prevent great
differences between stick-fixed and stick-free
stability. The greatest floating tendency oc-
curs when the surface is at a high angle of
attack hence the greatest difference between
stick-fixed and stick-free stability occurs when
the airplane is at high angle of attack.
If the controls are fully powered and actu-
ated by an irreversible mechanism, the sur-
faces are not free to float and there is no differ-
ace between the stick-fixed and stick-free
static stability.
The control forces in a conventional air-
plane are made up of two components. First,
the basic stick-free stability of the airplane
contributes an incremem of force which is
independent of airspeed.. Next, there. is an
increment of force dependent on the trim tab
setting which varies with-the dynamic pres-
sure or the square of ‘equivalent airspeed.
Figure 4.14(B) indicates the variation of
stick force with airspeed and illustrates the
effect of tab setting on stick force. In order
te trim the airplane at point (1) a certain
amount of up elevator is required and zero
stick force is obtained~ with’the nse of the tab.
To trim the airplane for higher speeds corre-
sponding to points (2) and (3) less and less
nose-up tab is required. Note that when the
airplane is properly trimmed, a push force is
required to increase airspeed and a pull force
is required to decrease airspeed. In this man-
ner, the airplane would indicate positive stick
force stability with a stable “feel” for air-
246 | 283 | 283 | 00-80T-80.pdf |
)
a,,, I,
-- F
TAB FORCE INCREMENT
NAVWEPS 00-BOT-80
STABILITY AND CONTROL
STICK -FIXED
PULL
PUSH
INCREMENT EQUIVALENT
CG AT 20% MAC I
CG POSITION
10% MAC
p-z; ,/’ EQUlVALENT
PULL
w
E
,o T
5
0
D -
FRICTION FORC
BAND
Figure 4.74. Control Force Stability
267 | 284 | 284 | 00-80T-80.pdf |
NAVWEPS 00-801-80
STABILITY AND CONlRO’L
speed, If the airplane were given a large nose
down tab setting the pull force would in-
crease with airspeed. This fact points out the
possibility of “feel” as not being a true indi-
cation of airplane static stability.
If the c.g. of the airplane were varied while
maintaining trim at a constant airspeed, the
effect of c.g. position on stick force stability
could be appreciated. As illustrated in figure
4,14(C), moving the c,g. aft decreases the
slope of the line of stick force through the
trim speed. Thus, decreasing stick force
stability is evident in that smaller stick forces
are necessary to displace the airplane from
the trim speed. When the stick force gradient
(or slope) becomes zero, the c.g. is at the
stick-free neutral point and neutral stability
exists. If the c.g. is aft of the stick-free
neutral point, stick force instability will
exist, e.g. the airplane will require a push
force at a lower speed or a pull force at a higher
speed. It should be noted that the stick force
gradient is low at low airspeeds and when
the airplane is at low speeds, high power,
and a c.g. position near the aft limit, the
“feel” for airspeed will be weak.
Control system friction can create very un-
desirable effects on control forces. Figure
4.14(D) illustrates that the control force
versus airspeed is a band rather than a line.
A wide friction force band can completely
mask the stick force stability when the stick
force stability is low. Modern flight control
systems require precise maintenance to mini-
mize the friction force band and preserve
proper feel to the airplane.
MANEUVERING STABILITY. When an
airplane is subject to a normal acceleration,
the flight path is curved and the airplane is
subject to a pitching velocity. Because of
the pitching velocity in maneuvering flight,
the longitudinal stability of the airplane is
slightly greater than in steady flight condi-
tions. When an airplane is subject to a pitch-
1 ing velocity at a given lift coefficient, the air-
plane develops a pitching moment resisting
the pitch motion which adds to the restoring
moment from the basic static stability. The
principal source of this additional pitching
moment is illustrated in figure 4.15.
During a pull-up the airplane is subject to
an angular rotation about the lateral axis and
the horizontal tail will experience a component
of wind due to the pitching velocity. The
vector addition of this component velocity to
the flight velocity provides a change in angle
of attack for the tail and the change in lift on
the tail creates a pitching moment resisting
the pitching motion. Since the pitching mo-
ment opposes the pitching motion but is due
to the pitching motion, the effect is a damping
in pitch. Of course, the other components of
the airplane may develop resisting moments
and contribute to pitch damping but the
horizontal tail is usually the largest contri-
bution. The added pitching moment from
pitch damping will effect a higher stability
in maneuvers than is apparent in steady flight.
From this consideration, the neutral point for
maneuvering flight will be aft of the neutral
point for unaccelerated flight and in most cases
will not be a critical item. If the airplane
demonstrates static stability in unaccelerated
flight, it will most surely demonstrate stability
in maneuvering flight.
The most direct appreciation of the ma-
neuvering stability of an airplane is obtained
from a plot of stick force versus load factor
such as shown in figure 4.15. The airplane
with positive maneuvering stability should
demonstrate a steady increase in stick force
with increase in load factor or “G”. The
maneuvering stick force gradient-or stick
force per G-must be positive but should be
of the proper magnitude. The stick force
gradient must not be excessively high or the
airplane will be difficult and tiring to maneuver.
Also, the stick force gradient must not be too
low or the airplane may be overstressed in-
advertently when light control forces exist.
A maneuvering stick force gradient of 3 to 8
lbs. per G is satisfactory for most fighter and | 285 | 285 | 00-80T-80.pdf |
NAVWEPS 00-801-80
STABILITY AND CONTROL
CHANGE IN TAIL LIFT
RELATIVE WIND
FROM ANGULAR ROTATION
CHANGE IN TAIL ANGLE OF
ATTACK DUE TO PITCHING
VELOCITY
co
!!I 30
8
; 20 MANEUVERING STICK
:: FORCE GRADIENT
g IO
w
I 2 3 4 5 6 7 8
LOAD FACTOR, n
(OR G)
CG POSITION
% MAC /
LOAD FACTOR
Figure 4.15. Maneuvering Stability
269 | 286 | 286 | 00-80T-80.pdf |
NAVWEPS 00-8’X-60
STABILITY AND CONTROL
attack airplanes. A large patrol or transport
type airplane would ordinarily show a much
higher maneuvering stick force gradient be-
cause of the lower limit load factor.
When the airplane has high static stability,
the maneuvering stability will be high and
a high stick force gradient will result. A
possibility exists that the forward c.g. limit
could be set to prevent an excessively high
maneuvering stick force gradient. As the
c.g. is moved aft, the stick force gradient de-
creases with decreasing maneuvering stability
and the lower limit of stick force gradient
may be reached.
The pitch damping of the airplane is obvi-
ously related to air density. At high altitudes,
the high true airspeed reduces the change in
tail angle of attack for a given pitching velocity
and reduces the pitch damping. Thus, a de-
crease in maneuvering stick force stability can
be expected with increased altitude.
TAILORING CONTROL FORCES. The
control forces should reflect the stability of
the airplane but, at the same time, should be
of a tolerable magnitude. The design of the
surfaces and control system may employ an
infinite variety of techniques to provide satis-
factory control forces.
Aerodynamic balance must be thought of in
two different senses. First, the control surface
must be balanced to reduce hinge moments due
to changes in angle of attack. This is necessary
to reduce the floating tendency of the surface
which reduces the stick-free stability. Next,
aerodynamic balance can reduce the hinge
moments due to deflection of the control sur-
face. Generally, it is difficult to obtain a high
degree of deflection balance without incurring
a large overbalance of the surface for changes
in angle of attack.
Some of the types of aerodynamic balance
are illustrated in figure 4.16. Thesimple horn
type balance employs a concentrated balance
area located ahead of the hinge line. The
balance area may extend completely to the
leading edge (unshielded) or partway to the
leading edge (shielded). Aerodynamic balance
can be achieved by the provision of- a hinge
line aft of the control surface leading edge.
The resulting overhang of surface area ahead
of the hinge line will provide a degree of
balance depending on the amount of overhang.
Another variation of aerodynamic balance is
an internal balance surface ahead of the hinge
line which is contained within ,the surface.
A flexible seal is usually incorporated to in-
crease the effectiveness of the balance area.
Even the bevelling of the trailing edge..of the
control surface is effective also as a balancing
technique. The choice of the type of aerody-
namic balance will depend on many factors
such as required degree of balance, simplicity,
drag, etc.
Many devices can be added to a control
system to modify or tailor the stick force
stability to desired levels. If a spring is added
to the control system as shown in figure 4.16,
it will tend to center the stick and provide a
force increment depending on stick displace-
ment. When the control system has a fixed
gearing between stick position and surface
deflection, the centering spring will provide a
contribution to stick force stability according
to stick position. The contribution to stick
force stability will be largest at low flight
speeds where relatively large control deflec-
tions are required. The contribution will be
smallest at high airspeed because of the smaller
control deflections required. Thus, .the stick
centering bungee will increase the airspeed
and maneuvering stick force stability but the
contribution decreases at high airspeeds. A
variation of this device would be a spring
stiffness which would be controlled to vary
with dynamic pressure, 4. In this case, the
contribution of the spring to stick force
stability would, not diminish with. speed.
A “downspring” added to a control system
is~ a means ~of increasing airspeed stick force
stability without a change in airplane static
2,70 | 287 | 287 | 00-80T-80.pdf |
NAVWEPS 00-8OT-80
STABILITY AND CONTROL
TYPES OF AERODYNAMIC BALANCE
OVERHANGORLEADINGEDGE
BALANCE BY OFFSET HINGE 7
INTERNAL BALANCE
WITH FL’XlBLESE& <I
HORN TYPE BALANCE
---‘I “1G EDGE BEVEL -,
EFFECT LaF STICK CENTERING SPRING
TICK CENTERING
RING OR BUNGEE
A PULL FORCE INCREMENTADDED
8 y
BY SPRING
E EQUIVALENT e
i5 \ AIRSPEED
I=
m PUSH
LOAD FACTOR
figure 4.16. loiloring Control forces | 288 | 288 | 00-80T-80.pdf |
NAVWEPS 00-801-80
STABILITY AND CONTROL
EFFECT OF DOWNSPRING
u P*RELO+DED SPRING
PULL
EQUIVALENT
lRSPEED
EFFECT OF BOBWEIGHT
1
PULL
EQUIVALENT
PUSH
RETRIMMED
FORCE INCREMENT
PROVIDED
BY BOBWEIGHT
LOAD FACTOR c
Figure 4.77. Tailoring Control Forces
272 | 289 | 289 | 00-80T-80.pdf |
stability. As shown in figure 4.17, a down-
spring consists of a long preloaded spring at-
tached to the control system which tends to
rotate the elevators down. The effect of the
downspring is to contribute an increment of
pull force independent of control deflection or
airspeed. When rhe downspring is added to
the control system of an airplane and the air-
plane is retrimmed for the original speed, the
airspeed stick force gradient is increased and
there is a stronger feel for airspeed. The down-
spring would provide an “ersatz” improve-
ment to an airplane deficient in airspeed stick
force stability, Since the force increment from
the downspring is unaffected by stick position
or normal acceleration, the maneuvering stick
force stability would be unchanged.
The bobweight is an effective device for im-
proving stick force stability. As shown in
figure 4.17, the bobweight consists of an eccen-
tric mass attached to the control system
which-in unaccelerated flight--contributes
an increment of pull force identical to the
downspring. In fact, a bobweight added to
the control system of an airplane produces an
effect identical to the downspring. The bob-
weight will increase the airspeed stick force
gradient and increase the feel for airspeed.
A bobweighr will have an effect on the
maneuvering stick force gradient since the bob-
weight mass is subjected to the same accelera-
tion as the airplane. Thus, the bobweight will
provide an increment of stick force in direct
proportion to the maneuvering acceleration of
the airplane. Because of the linear contribu-
tion of the bobweight, the bobweight can be
applted to Increase the maneuvering stick force
stability if the basic airplane has too low a
value or develops a decreasing gradient at high
lift coefficients.
The example of the bobweight is useful to
point out the effect of the control system dis-
tributed masses. All carrier aircraft must have
the control system mass balanced to prevent
undesirable control forces from the longi-
tudinal accelerations during catapult launching.
NAVWEPS 00-EOT-80
STABILITY AND CONTROL
Various control surface tab devices can be
utilized to modify control forces. Since the de-
flection of a tab is so powerful in creating hinge
moments on a control surface, the possible
application of tab devices is almost without
limit, The basic trim tab arrangement is
shown in figure 4.18 where a variable linkage
connects the tab and the control surface. Ex-
tension or contraction of this linkage will de-
flect the tab relative to the control surface and
create a certain change in hinge mon~ent coef-
ficient. The use of the trim tab will allow the
pilot to reduce the hinge moment to zero and
trim the control forces to zero for a given flight
condition. Of course, the trim tab should have
adequate effectiveness so that control forces
can be trimmed out throughout the flight speed
range.
The lagging tab arrangement shown in figure
4.18 employs a linkage between the fixed sur-
face and the tab surface. The geometry is
such that upward deflection of the control
surface displaces the tab down relative to the
control surface. Such relative displacement
of the tab will aid in deflection of the control
surface and thus reduce the hinge moments due
to deflection. An obvious advantage of this
device is the reduction of deflection hinge
moments without a change in aerodynamic
balance.
The leading tab arrangement shown in figure
4.18 also employs a linkage between the fixed
surface and the tab surface. However, the
geometry of the linkage is such that upward
deflection of the control surface displaces the
tab up relative to the control surface. This
relationship serves to increase the control sur-
face hinge moments due to deflection of the
surface.
The servo tad shown in figure 4.18 utilizes a
horn which has no direct connection to the
control surface and is free to pivot about the
hinge axis. However, a linkage connects this
free horn to the tab surface. Thus, the control
system simply deflects the tab and the resulting
hinge moments deflect the control surface. | 290 | 290 | 00-80T-80.pdf |
NAVWEPS 00-EOT-80
STABILITY AND CONTROL
TRIM TAB
VARIABLE LINKAGE
LAGGING TAB
LEAOING TAB
SERVO TAB
HORN FREE TO
PIVOT ON HINGE 13X6
SPRING TAB
ON HINGE AXIS
FIXED TO SURFACE
SPRING LLADED TAB
ROTATES TAB UP
Figure 4.18. Various Tab Devices
274 | 291 | 291 | 00-80T-80.pdf |
Since the only control forces are those of the
tab, this device makes possible the deflection
of large surfaces with relatively small control
forces.
A variation of the basic servo tab layout is
the sprirzg tab arrangement of figure 4.18.
When the control horn is connected to the
control surface by springs, the function of the
tab is to provide a given portion of the required
control forces. The spring tab arrangement
can then function as a boost to reduce control
forces. The servo tab and spring tab are
usually applied to large or high speed subsonic
airplanes to provide tolerable stick forces.
The spring Zoadcd tab of figure 4.18 cotisists
of a free tab preloaded with a spring which
furnishes a constant moment about the tab
hinge line. When the airplane is at zero air-
speed, the tab is rotated up to the limit of
deflection. As airspeed is increased, the aero-
dynamic hinge moment on the tab will finally
equal the spring torque and the tab will begin
to streamline. The effect of this arrangement
is to provide a constant hinge moment to the
control system and contribute a constant push
force requirement at speeds above the preload
speed. Thus, the spring loaded tab can im-
prove the stick force gradient in a manner
similar to the downspring. Generally, the
spring loaded tab may be more desirable
because of greater effectiveness and the lack of
undesirable control forces during ground
operation.
The various tab devices have almost un-
limited possibilities for tailoring control forces.
However, these devices must receive proper
care and maintenance in order to function
properly. In addition, much care must be
taken to ensure that no slop or play exists in
the joints and fittings, otherwise destructive
flutter may occur.
LONGITUDINAL CONTROL
To be satisfactory, an airplane must have
adequate controllability as well as adequate
NAVWEPS OtWOT-80
STABILITY AND CONTROL
stability. Ati airplane with high static longi-
tudinal stability will exhibit great resistance
to displacement from equilibrium. Hence,
the most critical conditions of controllability
will occur when the airplane has high sta-
bility, i.e., the lower limits of controllability
will set the upper limits of stability.
There are three principal conditions of
fli~ght which provide the critical requirements
of longitudinal control power. Any one
or combination of these conditions can de-
termine the longitudinal control power and
set a limit to forward c.g. position.
MANEUVERING CONTROL REQUIRE-
MENT. The airplane should have sufficient
longitudinal control power to attain the maxi-
mum usable lift coefficient or limit load factor
during maneuvers. As shown in figure 4.19,
forward movement of the c.g. increases the
longiturjinal stability of an airplane and
requires larger control deflections to produce
changes in trim lift coefficient. For the
example shown, the maximum effective de-
flection of the elevator is not capable of trim-
ing the airplane ‘at C,,,, for c.g. positions
ahead of 18 percent MAC.
This particular control requirement can be
most critical for an airplane in supersonic
flight. Supersonic flight is usually accom- . panied by large increases in static longltu-
dinal stability and a reduction in the effective-
ness of control surfaces. In order to cope with
these trends, powerful all-movable surfaces
must be used to attain limit load factor or
maximum usable C, in supersonic flight. This
requirement is so important that once satis-
fied, the supersonic configuration usually has
sufficient longitudinal control power for all
other conditions of flight.
TAKEOFF CONTROL REQUIREMENT.
At takeoff, the airplane must have sufficient
control power to assume the takeoff attitude
prior to reaching takeoff speed. Generally,
for airplanes with tricycle landing gears, it
is desirable to have at least sufficient control
power to attain the takeoff attitude at 80
275 | 292 | 292 | 00-80T-80.pdf |
NAVWEPS 00-80’1-80
SlABILITY AND CONTROL
MAXIMUM MOST FORWARD
DEFLECTION CG FOR MANEUVERING
CONTROLLABILITY
DOWN POSITION
TAIL
LOAD
!'.',i:'.
WEIGHT
TAKE OFF CONTROL
REDUCED DOWNWASH
DUE TO GROUND EFFECT
. .:,.,. ‘,:::.;,y ,;,,.,,>: ::..‘~~,‘i;,:,‘,,:.~,,‘: y: :, ,: ,/. :“‘J.:;:‘j:~!,.: : :., :, .‘. ;. ~.. i... .,-: -, :,.: ~, :,., :.:, :~’
LANDING CONTROL
Figure 4.19. Longitudinal Control Requirements
176 | 293 | 293 | 00-80T-80.pdf |
percent of the stall speed for propeller air-
planes or 90 percent of the stall speed for jet
airplanes. This feat must be accomplished on
a smooth runway at all normal service takeoff
loading conditions.
Figure 4.19 illustrates the principal forces
acting on an airplane during takeoff toll.
When the airplane is in the three point attitude
at some speed less than the stall speed, the
wing lift will be less than the weight of the
airplane. As the elevators must be capable
of rotating to the takeoff attitude, the critical
condition will be with zero load on the nose
wheel and the net of lift and weight supported
on the main gear. Rolling friction resulting
from the normal force on the main gear creates
an adverse nose down moment. Also, the
center of gravity ahead of the main gear
contributes a nose down moment and this
consideration could decide the most aft loca-
tion of the main landing gear during design.
The wing may contribute a large nose down
moment when flaps are deflected but this
effect may be countered by a slight increase
in downwash at the tail. To balance these
nose down moments, the horizontal tail
should be capable of producing sufficient nose
up moment to attam the takeoff attitude. at
the specified speeds.
The propeller airplane at takeoff power may
induce considerable slipstream velocity at the
horizontal tail which can provide an increase
in the e&iency of the surface. The jet
airplane does not experience a similar magni-
tude of this effect since the induced velocities
from the jet are relatively small compared
to the slipstream velocities from a propeller.
LANDING CONTROL REQUIREMENT
At landing, the airplane must have suthcient
control power to ensure adequate control at
specified landing speeds. Adequate landing
control is usually assured if the elevators are
capable of holding the airplane just off the
runway at 105 percent of the stall speed. Of
course, the most critical requirement will exist
when the c.g. is in the most forward position,
NAVWEPS 00-BOT-80
STABILITY AND CONTROL
flaps are fully extended, and power is set at
idle. This configuration will provide the
most stable condition which is most demand-
ing of controllability. The full deflection of
flaps usually provides the greatest wing diving
moment and idle power will produce the most
critical (least) dynamic pressure at the hoti-
zontal tail.
The landing control requirement has one
particular difference from the maneuvering
control requirement of free flight. As the
airplane approaches the ground surface, there
will be a change in the three-dimensional flow
of the airplane due to ground effect. A wing in
proximity to the ground plane will experience
a decrease in tip vortices and downwash at
a given lift coefficient. The decrease in down-
wash at the tail tends to increase the static
stability and produce a nosedown moment from
the reduction in download on the tail. Thus,
the airplane just off the runway surface will
requite additional control deflection to trim
at a given lift coefficient and the landing con-
trol requirement may be critical in the design
of longitudinal control power.
As an example of ground effect, a typical
propeller powered airplane may requite as
much as 15” more up elevator to trim at CL-
in ground effect than in free flight away from
the ground plane. Because of this effect, many
aitplaneshavesufIicientcontrolpowertoachieve
full stall out of ground effect but do not have
the ability to achieve full stall when in close
proximity to the ground.
In some cases the effectiveness of the control
surface is adversely affected by the use of trim
tabs. If trim tabs are used to excess in ttim-
ming stick forces, the effectiveness of the
elevator.may be reduced to hinder landing or
takeoff control.
Each of the three principal conditions re-
quiting adequate longitudinal control are ctit-
ical for high static stability. If the forward
c.g. limit is exceeded, the airplane may en-
counter a deficiency of controllability in any
of these conditions. Thus, the forward c.g.
177 | 294 | 294 | 00-80T-80.pdf |
295 | 295 | 00-80T-80.pdf |
|
limit is set by the minimum permissible con-
trollability while the aft c.g. limit is set by
the minimum permissible stability.
LONGITUDINAL DYNAMIC STABILITY.
All previous considerations of longitudinal
stability have been concerned with the initial
tendency of the airplane to return to equilib-
rium when subjected to a disturbance. The
considerations of longitudinal dynamic sta-
bility ate concerned with time history response
of the airplane to these disturbances, i.e., the
variation of displacement amplitude with time
following a disturbance. From previous deli-
nition, dynamic stability will exist when the
amplitude of motion decreases with time and
dynamic instability will exist if the amplitude
increases with time.
Of course, the airplane must demonstrate
positive dynamic stability for the major longi-
tudinal motions. In addition, the airplane
must demonstrate a certain degree of longitu-
dinal stability by reducing the amplitude of
motion at a certain rate. The requited degree
of dynamic stability is usually specified by
the time necessary for the amplitude to reduce
to one-half the original value-the time to
damp to half-amplitude.
The airplane in free flight has six degrees of
freedom: rotation in roll, pitch, and yaw and
translation in the horizontal, vertical, and
lateral directions. In the case of longitudinal
dynamic stability, the degrees of freedom can
be limited to pitch rotation, vertical and
horizontal translation. Since the airplane is
usually symmetrical from port to starboard,
there will be no necessity for consideration of
coupling between longitudinal and lateral-
directional motions. Thus, the principal vari-
ables in the longitudinal motion of an airplane
will be:
(1) The pitch attitude of the airplane.
(2) The angle of attack (which will differ
from the pitch attitude by the inclination of
the flight- path).
(3) The flight velocity.
NAVWEPS DD-801-80
STABILITY AND CONTROL
(4) The displacement or deflection of the
elevator when the stick-free condition is
considered.
The longitudinal dynamic stability of an
airplane generally consists of three basic modes
(or manners) of oscillation. While the longi-
tudinal motion of the airplane may consist of a
combination of these modes, the characteristics
of each mode are sufficiently distinct that each
oscillatory tendency may be studied separately.
The first mode of dynamic longitudinal sta-
bility consists of a very long period oscillation
referred to as the phagoid. The phugoid or long
period oscillation involves noticeable vatia-
tions in pitch attitude, altitude, and airspeed
but nearly constant angle of attack. Such an
oscillation of the airplane could be considered
as a gradual interchange of potential and
kinetic energy about some equilibrium airspeed
and altitude. Figure 4.20 illustrates the char-
acteristic motion of the phugoid.
The period of oscillation in the phugoid is
quite large, typical values being from 20 to 100
seconds. Since the pitching rate is quite low
and only negligible changes in angle of attack
take place, damping of the phugoid is weak and
possibly negative. However, such weak or
negative damping does not necessarily have any
great consequence. Since the period of oscilla-
tion is so great, the pilot is easily able to
counteract the oscillatory tendency by very
slight and unnoticed control movements. In
most cases, the necessary corrections ate so
slight that the pilot may be completely un-
aware of the oscillatory tendency.
Due to the nature of the phugoid, it is not
necessary to make any specific aerodynamic
provisions to contend with the oscillation.
The inherent long period of the oscillation al-
lows study to be directed to more important
oscillatory tendencies. Similarly, the diffet-
ences between the stick-fixed and stick-free
phugoid are not of great importance.
The second mode of longitudinal dynamic sta-
bility is a relatively short period motion that | 296 | 296 | 00-80T-80.pdf |
NAVWEPS OO-BOT-80
STABILITY AND CONTROL
IST MODE OR PHUGOID
ANGLE OF ATTACK AT EACH
INS%; ,,“L&blSG$~,lGH~ &
5 LoNG PERIOD ------I kw a0 f 2 -
g: *a
2 0
2ND MODE OR SHORT PERIOD OSCILLATION
MOTION OCCURS AT ESSENTIALLY CONSTANT SPEED
L TIME TO DAMP TO
HALF AMPLITUDE
Lb-- TIME
/
/
-6.HORT PERIOD -
UNSTABLE OSCILLATION
Figure 4.20. Longiitudinal Dynamic Sttxbility
280 | 297 | 297 | 00-80T-80.pdf |
can be assumed to take place with negligible
changes in velocity. The second mode consists
of a pitching oscillation during which the air-
plane is being restored to equilibrium by the
static stability and the amplitude of oscillation
decreased by pitch damping. The typical mo-
tion is of relatively high frequency with a
period of oscillation on the order of 6.5 to 5
seconds.
For the conventional subsonic airplane, the
second mode stick-fixed is characterized by
heavy damping with a time to damp to half
amplitude of approximately 0.5 seconds. IJsu-
ally, if the airplane has static stability stick-
fixed, the pitch damping contributed by the
horizontal tail will assume sufficient dynamic
stability for the short period oscillation. How-
ever, the second mode stick-free has the possi-
bility of weak damping or unstable oscilla-
tions. This is the case where static stability
does not automatically imply adequate dy-
namic stability. The second mode stick-free is
essentially a coupling of motion between the
airplane short period pitching motion and ele-
vator in rotation about the hinge line. Ex-
treme care must be taken in the design of the
control surfaces to ensure dynamic stability for
this mode. The elevators must be statically
balanced about the hinge line and aerodynamic
balance must be within certain limits. Control
system friction must be minimized as it con-
tributes to the oscillatory tendency. If insta-
bility were to exist in the second mode, “por-
poising” of the airplane would result with
possibility of structural damage. An oscilla-
tion at high dynamic pressures with large
changes in angle of attack could produce severe
flight loads.
The second mode has relatively short periods
that correspond closely with the normal pilot
response lag time, e.g., 1 or 2 seconds or less.
There is the possibility that an attempt to
forceably damp an oscillation may actually re-
inforce the oscillation and produce instability.
This is particularly true in the case of powered
controls where a small input energy into the
NAVWEPS 00-BOT-80
STABILITY AND CONTROL
control system is greatly magnified. In addi-
tion, response lag of the controls may add to
the problem of attempting to forceably damp
the oscillation. In this case, should an oscilla-
tion appear, the best rule is to release the con-
trols as the airplane stick-free will demonstrate
the necessary damping, Even an attempt to
fix the controls when the airplane is oscillating
may result in a small unstable input into the
control system which can reinforce the oscilla-
tion to produce failing flight loads. Because
of the very short period of the oscillation, the
amplitude of an unstable oscillation can reach
dangerous proportions in an extremely short
period of time.
The third mode occurs in the elevator free case
and is usually a very short period oscillation.
The motion is essentially one of the elevator
flapping about the hinge line and, in most
cases, the oscillation has very heavy damping.
A typical flapping mode may have a period of
0.3 to 1.5 seconds and a time to damp to half-
amplitude of approximately 0.1 second.
Of all the modes of longitudinal dynamic
stability, the second mode or porpoising oscil-
lation is of greatest importance. The por-
poising oscillation has the possibility of
damaging flight loads and can be adversely
affected by pilot response lag. It should be
remembered that when stick-free the airplane
will demonstrate the necessary damping.
The problems of dynamic stability are acute
under certain conditions of flight. Low static
stability generally increases the period (de-
creases frequency) of the short period oscil-
lations and increases the time to damp to half-
amplitude. High altitude-and consequently
low density-reduces the aerodynamic damp-
ing. Also, high Mach numbers of supersonic
flight produce a decay of aerodynamic damping.
MODERN CONTROL SYSTEMS
In order to accomplish the stability and
control objectives, various configurations of
control systems are necessary. Generally, the
?Bl | 298 | 298 | 00-80T-80.pdf |
NAVWEPS 00-BOT-BO
STABILITY AND CONTROL
type of flight control system is decided by the
size and flight speed range of the airplane.
The conventional control system consists of
direct mechanical linkages from the controls
to the control surfaces. For the subsonic
airplane, the principal means of producing
proper control forces utilize aerodynamic bal-
ance and various tab, spring, and bobweight
devices. Balance and tab devices are capable
of reducing control forces and will allow the
use of the conventional control system on large
airplanes to relatively high subsonic speeds.
When the airplane with a conventional
control system is operated at transonic speeds,
the great changes in the character of flow
can produce great aberrations in control sur-
face hinge moments and the contribution of
tab devices. Shock wave formation and
separation of flow at transonic speeds will
limit the use of the conventional control
system to subsonic speeds.
The power-boosted control system employs a
‘mechanical actuator in parallel with the
mechanical linkages of a conventional control
system. The principle of operation is to pro-
vide a fixed, percentage of the required control
forces thus reducing control forces at high
speeds. The power-boosted control system
requires a hydraulic actuator with a control
valve which supplies boost force in fixed
proportion to control force. Thus, the pilot
is given an advantage by the boost ratio to
assist in deflecting the control surface, e.g.,
with a boost ratio of 14, the actuator provides
14 lbs. of force for each 1 lb. of stick force.
The power-boosted control system has the
obvious advantage of reducing control forces
at high speeds. However, at transonic speeds,
the changes in control forces due to shock
waves and separation still take place but to a
lesser degree. The “feedback” of hinge
moments is reduced but the aberrations in
stick forces may still exist.
The power-opsrdted, irreversible control system
consists of mechanical actuators controlled
by the pilot. The control surface is deflected
by the actuator and none of the hinge moments
are fed back through the controls. In such
a control system, the control position decides
the deflection of the control surfaces regardless
of the airloads and hinge moments. Since the
power-operated control system has zero feed-
back, control feel must be synthesized other-
wise an infinite boost would exist.
The advantages of the power-operated COR-
trol system are most apparent in transonic and
supersonic flight. In transonic flight, none of
the erratic hinge moments are fed back to the
pilot. Thus, no unusual or erratic control
forces,will be encountered in transonic flight.
Supersonic flight generally requires the use of
an all-movable horizontal surface to achieve
the necessary control effectiveness. Such con-
trol surfaces must then be actuated and posi-
tively positioned by an irreversible device.
The most important item of an artificial feel
system is the stick-centering spring or bungee.
The bungee develops a stick force in proportion
to stick displacement and thus provides feel
for airspeed and maneuvers. A bobweight
may be included in the feel system to develop
a steady positive maneuvering stick force
gradient which is independent of airspeed for
ordinary maneuvers.
The gearing between the stick position and
control surface deflection is not necessarily a
linear relationship. The majority of powered
control systems will employ a nonlinear gear-
ing such that relatively greater stick deflection
per surface deflection will occur at the neutral
stick position. This sort of gearing is to
advantage for airplanes which operate at flight
conditions of high dynamic pressure. Since
the airplane at high 4 is very sensitive to small
deflections of the control surface, the nonlinear
gearing provides higher stick force stability
with less sensitive control movements than
the ‘system with a linear gearing. Figure 4.21
illustrates a typical linear and nonlinear control
system gearing.
The second chart of figure 4.21 illustrates
the typical control system stick force variation
282 | 299 | 299 | 00-80T-80.pdf |
NAVWEPS 00-ROT-80
STABILITY AND CONTROL
CONTROL SYSTEM GEARING
CONTROL SYSTEM STICK FORCE
-40
STICK FORCE LBS.
-30
PULL
-20
-10
STABILIZER DEFLECTION
LEADING EDGE DOWN LEADING EDGE UP
25O 200 I50 100 50 50 I00
Figure 4.27. Longitudinal Control System | 300 | 300 | 00-80T-80.pdf |
NAVWEPS OO-ROT-80
STABILITY AND CONTROL
with control surface deflection. While it is
desirable to have a strong centering of the
stick near the neutral position, the amount of
force required to create an initial displacement
must be reasonable. If the control system
“break-out” forces are too high, precise control
of’the airplane at high speeds is diflicult. As
the solid friction of the control system con-
tributes to the break-out forces, proper mainte-
nance of the control system is essential. Any
increase in control system friction can create
unusual and undesirable control forces.
The trim of the powered control system is
essentially any device to produce zero control
force for a given control surface deflection.
One system may trim off bungee force at a
given stick position while another system may
trim by returning the stick to neutral position.
Flight at high supersonic Mach numbers
might require a great variety of devices in the
longitudinal control system. The deteriora-
tion of pitch damping with Mach-number may
require that dynamic stability be obtained
synthetically by pitch dampers in the control
system. The response of the airplane to
longitudinal control may be adversely affected
by flight at high dynamic pressures. In such
conditions of flight stick forces must be ade-
quate to prevent an induced oscillation. Stick
forces must relate the transients of flight as
well as the steady state conditions. Such a
contribution to control system forces may be
provided by a pitching acceleration bobweight
and a control system viscous damper.
DIRECTIONAL STABILITY AND CONTiOL
DIRECTIONAL STABILITY
The directional stability of an airplane is
essentially the “weathercock” stability and
involves moments about the vertical axis and
their relationship with yaw or sideslip angle.
An airplane which has static directional sta-
bility would tend to return to an equilibrium
when subjected to some disturbance from equi-
librium. Evidence of static directional sta-
bility would be the development of yawing
moments which tend to restore the airplane
to equilibrium.
DEFINITIONS. The axis system of an air-
plane will define a positive yawing moment,
N, as a moment about the vertical axis which
tends to rotate the nose to the right. As in
other aerodynamic considerations, it is con-
venient to consider yawing moments in the
coefficient form so that static stability can be
evaluated independent of weight, altitude,
speed, etc. The yawing moment, N, is de-
fined in the coefficient form by the following
equation:
or
N = C,qSb
C,=N 0 where
N=yawing moment, ft.-lbs;
positive to the right
q= dynamic pressure, psf
S=wing area, sq. ft.
b=wing span, ft.
C,=yawing moment coefficient, positive
to the right
The yawing moment coefficient, C,, is based on
the wing dimensions $ and 6 as the wing is the
characteristic surface of the airplane.
The yaw angle of an airplane relates the dis-
placement of the airplane centerline from some
reference azimuth. and is assigned the short-
,hand notation I& (psi). A positive yaw angle
occurs when the nose of the airplane is dis-
placed to the right of the azimuth direction.
The definition of sideslip angle involves a sig-
nificant difference. Sides&p angle relates the
displacement of the airplane centerline from
the relative wind rather than some reference
azimuth., Sideslip angle is’provided the short-
hand notation p (beta) and is positive when
ihe rela&e wind is displaced to the right of
the,airplane centerline. Figure 4.22 illustrates
the definitions of sideslip and yaw angles.
The sideslip angle, 8, is essentially the di-
rectional angle of attack of the airplane and
284 | 301 | 301 | 00-80T-80.pdf |
is the primary reference in lateral stability as
well as directional stability considerations.
The yaw angle, #, is a primary reference for
wind tunnel tests and time history motion of
an airplane. From the definitions there is no
direct relationship between @ and # for an
airplane in free flight, e.g., an airplane flown
through a 360° turn has yawed 360” but side-
slip may have been zero throughout the entire
turn. Since the airplane has no directional
sense, static directional stability of the air-
plane is appreciated by response to sideslip.
The static directional stability of an airplane
can be illustrated by a graph of yawing moment
coe&cient, C., versus sideslip angle, 8, such as
shown in figure 4.22. When the airplane is
subject to a positive sideslip angle, static direc-
tional stability will be evident if a positive
yawing moment coefficient results. Thus,
when the relative wind comes from the right
(+p), a yawing moment to the right (+C.)
should be created which tends to weathercock
the airplane and return the nose into the wind.
Static directional stability will exist when the
curve of C,, versus fi has a positive slope and the
degree of stability will be a function of.the
slope of this curve. If the curve has zero slope,
there is no tendency to return to equilibrium
and neutral static directional stability exists.
When the curve of C. versus /3 has a negative
slope, the yawing moments developed by side-
slip tend to diverge rather than restore and
static directional instability exists.
The final chart of figure 4.22 illustrates the
fact that the instantaneous slope of the curve of
C,, versus @ will describe the static directional
stability of the airplane. At small angles of
sideslip a strong positive slope depicts strong
directional stability. Large angles of sideslip
produce zero slope and neutral stability. At
very high sideslip the negative slope of the
curve indicates directional instability. This
decay of directional stability with increased
sideslip is not an unusual condition. However,
directional instability should not occur at the
angles of sideslip of ordinary flight conditions.
NAVWEPS 00-ROT-80
STABILITY AND CONTROL
Static directional stability must be in evi-
dence for all the critical conditions of flight.
Generally, good directional stability is a ftm-
damental quality directly affecting the pilots’
impression of an airplane.
CONTRIBUTION OF THE AIRPLANE
COMPONENTS. The static directional sta-
bility of the airplane is a result of contribution
of each of the various airplane components.
While the contribution of each component is
somewhat dependent upon and related to other
components, it is necessary to study each
component separately.
The vertical tail is the primary source of
directional stability for the airplane. As
shown in figure 4.23, when the airplane is in
a sideslip the vertical tail will experience a
change in angle of attack. The change in
lift-or side force-on the vertical tail creates
a yawing moment about the center of gravity
which tends to yaw the airplane into the
relative wind. The magnitude of the vertical
tail contribution to static directional stability
then depends on the change in tail lift and the
tail moment arm. Obviously, the tail moment
arm is a powerful factor but essentially dic-
tated by the major configuration properties of
the airplane.
When the location of the vertical tail is set,,
the contribution of the surface to directional
stability depends on its ability to produce
changes in lift-or side force-with changes in
sideslip. The surface area of the vertical tail
is a powerful factor with the contribution of
the vertical tail being a direct function of the
area. When all other possibilities are ex-
hausted, the required directional stability may
be obtained by increases in tail area. How-
ever, increased surface area has the obvious
disadvantage of increased drag.
The lift curve slope of the vertical tail
relates how sensitive the surface is to changes
in angle of attack. While it is desirable to
have a high lift curve slope for the vertical
surface, a high aspect ratio surface is not
necessarily practical or desirable. The stall | 302 | 302 | 00-80T-80.pdf |
NAVWEPS 00-ROT-80
STABILITY AND CONTROL
+N,YAWlNG MOMENT
YAWING MOMENT
COEFFICIENT,Cn
t
+Cn
p SIDESLLANGLE,
Figure 4.22. Static Directional Stability
286 | 303 | 303 | 00-80T-80.pdf |
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