Chapter 1 — Part 8

Excess airspeed at landing is just as undesira-

ble as a deficiency of airspeed. An cxccssivc

airspeed at landing will produce an undesirable

increase in landing distance and the energy to

be dissipated by the brakes for the field landing

or excessive arresting loads for theshipboard

landing. In addition, the excess airspeed is a

corollary of too low an angle of attack and the

airplane may contact the deck or runway nose

wheel first and cause damage to the nose wheel

or begin a porpoising of the airplane. During

a flare to landing, any excess speed will be

difficult to dissipate due to the reduction of

drag due to ground effect. Thus, if the air-

plane is held off with excess airspeed the air-

plane will “float” with the consequence of a

barrier engagement, barricade engagement,

bolter, or considerable runway distance used

before touchdown.

A fundamental requirement for a good land-

ing is a well planned and executed approach.

The possibility of errors during the landing

process is minimized when the airplane is

brought to the point of touchdown with the

proper glide path and airspeed. With the

proper approach, there is no need for drastic

changes in the flight path, angle of attack, or

power setting to accomplish touchdown at the

intended point on the deck or runway. Late

corrections to line up with the deck or diving

for the deck are common errors which eventu-

ally result in landing accidents. Accurate

control of airspeed and glide path are ab-

solutely necessary and the LSO, angle of attack

indicator, and the mirror landing system pro-

vide great assistance in accurate control of the

airplane.

THE TAKEOFF

As in the case of landing, the specific tech-

niques necessary may vary greatly between

various types of airplanes and various oper-

ations but certain fundamental principles will

be common to all airplanes and all operations.

The specific procedures recommended for each

airplane type must be followed exactly to

MAVWEPS OD-BOT-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

insure a consistent, safe takeoff flying tech-

nique.

TAKEOFF SPEED AND DISTANCE. The

takeoff speed of any airplane is some mini-

mum practical airspeed which allows sufficient

margin above stall and provides satisfactory

control and initial rate of climb.. Depending

on the airplane characteristics, the takeoff

speed will be some value 5 to 25 percent above

the stall or minimum control speed. As such,

the takeoff will be accomplished at a certain

value of lift coefficient and angle of attack

specific to each airplane configuration. As

a result, the takeoff airspeed (FAX or CM) of

any specific airplane configuration is a function

of the gross weight at takeoff. Too low an

airspeed at takeoff may cause stall, lack of

adequate control, or poor initial climb per-

formance. An excess of speed at takeoff may

provide better control and initial rate of climb

but the higher speed requires additional dis-

tance and may provide critical conditions for

the tires.

The takeoff distance of an airplane is affected

by many different factors other than technique

and, prior to takeoff, the takeoff distance

must be determined and compared with the

runway length available. The principal factors

affecting the takeoff distance are as follows:

(1) The gross weight of the airplane has

a considerable effect on takeoff distance be-

cause it affects both takeoff speed and ac-

celeration during takeoff roll.

(2) The surface winrls must be considered

because of the powerful effect of a headwind

or tailwind on the takeoff distance. In the

case of the crosswind, the component of

wind along the runway will be the effective

headwind or tailwind velocity. In addi-

tion, the component of wind across the run-

way will define certain requirements of lateral

control power and the limiting compo-

nent wind must not be exceeded.

(3) Pressure altitude and temperature can

cause a large effect on takeoff distance, es-

pecially in the case of the turbine powered

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APPLICATION OF AERODYNAMICS,

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airplane. Density altitude will determine

the true airspeed at takeoff and can affect

the takeoff acceleration by altering the

powerplant thrust. The effect of tempeta-

ture alone is important in the case of the

turbine powered aircraft since inlet air tem-

perature will affect powerplant thrust. Ic

should be noted that a typical turbojet ait-

plane may he approximately twice as sensi-

tive to density altitude and five to ten times

as sensitive to temperature as a representa-

cive reciprocating engine powered airplane.

(4) Specific humidity must be accounted

for in the case of the reciprocating engine

powered airplane. A high water vapor

content in the air will cause a definite reduc-

tion in takeoff power and takeoff acceler-

ation.

(5) The runluay condition will deserve con-

sideration when the takeoff acceleration is

basically low. The runway slope must be

compared carefully with the surface winds

because ordinary values of runway slope will

usually favor choice of the runway with

headwind and upslope rather than down-

slope and tailwind. The surface condition

of the runway has little bearing on takeoff

distance as long as the runway is a hard

surface.

Each .of these factors must be accounted

for and the takeoff distance properly com-

puted for the existing conditions. Since

obstacle clearance distance is generally a

function of the same factors which affect

takeoff distance, the obstacle clearance dis-

tance is usually related as some proportion

of the takeoff distance. Of course, the take-

off and obstacle clearance distances related

by the handbook data will be obtained by

the techniques and procedures outlined in the

handbook.

TYPICAL ERRORS. The takeoff distance

of an airplane should be computed for each

takeoff. A most inexcusable error would be to

attempt takeoff from a runway of insufficient

length. Familiarity with the airplane hand-

book performance data and proper accounting

of weight, wind, altitude, temperature, etc.,

are necessary parts of flying. Conditions of

high gross weight, high pressure altitude and

temperature, and unfavorable winds create the

extreme requirements of runway length, espe-

cially for the turbine powered airplane. Under

these conditions, use of the handbook data is

mandatory and no guesswork can be tolerated.

One typical.etror of takeoff technique is the

premature or excess pitch rotation of the air-

plane. Premzture or excm pitch rotation of the

airplane may seriously reduce the takeoff accel-

eration and increase the takeoff distance. In

addition, when the airplane is placed at an

excessive angle of attack during takeoff, the

airplane may become airborne at too low a

speed and the result may be a stall, lack of ade-

quate control (especially in a crosswind), or

poor initial climb performance. In fact. there

are certain low aspect ratio configurations of

airplanes which, at an excessive angle of ar-

tack, will not fly out of ground effect. Thus,

over-rotation of the airplane ,during takeoff

may hinder takeoff acceleration or the.initial

climb. It is quite typical for an airplane to be

placed at an excess angle of attack and become

airborne prematurely then settle back fo rhe

runway. When the proper angle of attack is

assumed, the airplane simply accelerates to the

takeoff speed and becomes airborne wirh suf-

ficient initial rate of climb. In this sense, the

appropriate rotation and takeoff speeds or an

angle of attack indicator must be used.

If the airplane is subject to a sudden pull-up

or Jteep tzzra after becoming airborne, rhe,resulr

may be a stall, spin, or reduction in initial rate

of climb. The increased angle of attack may

exceed the critical angle of attack or the in-

crease in induced drag may be quite large. For

this reason, any clearing turns made immedi-

ately after takeoff or deck launch must be slight

and well within the capabilities of the air-

plane.

In order to obviate some of the problems

of a deficiency of airspeed at takeoff, usual

result can be an excess of airspeed at takeoff.

The principal effect of an BXCBJS takeoff air@pssd

is the greater takeoff distance which results.

The general effect is that each 1 percent excess

takeoff velocity incurs approximately 2 per-

cent additional takeoff distance. Thus, excess

speed must be compared with the additional

runway required to produce the higher speed.

In addition, the aircraft tires may be subject

to critical loads when the airplane is at very

high rolling speeds and speeds in excess of a

basically high takeoff speed may produce

damage or failure of the tires.

As with the conditions of landing, excess

velocity or deficiency of velocity at takeoff

is undesirable. The proper takeoff speeds and

angle of attack must be utilized to assure

satisfactory takeoff performance.

GUSTS AND WIND SHEAR

The variation of wind velocity and direction

throughout the atmosphere is important be-

cause of its effect on the aerodynamic forces

and moments on an airplane. As the airplane

traverses this variation of wind velocity and

direction during flight, the changes in airflow

direction and velocity create changes in the

aerodynamic forces and moments and produce

a response of the airplane. The variation of

airflow velocity along a given direction exists

with shear parallel to the flow direction.

Hence, the velocity gradients are often re-

ferred to as the wind “shear.”

The effect of the vertical gust has important

effects on the airplane at high speed because

of the possibility of damaging flight loads.

The mechanism of vertical gust is illustrated

in figure 6.5 where the vertical gust velocity

is added vectorially to the flight velocity to

produce some resultant velocity. The principal

effect of the vertical gust is to produce a change

in airplane angle of attack, e.g., a positive

(up) gust causes an increase in angle of attack

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APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

while a negative (down) gust causes a de-

crease in angle of attack. Of course, a change

in angle of attack will effect a change in lift

and, if some critical combination of high gust

intensity and high flight speed is encountered,

the change in lift may be large enough to

cause structural damage.

At low flight speeds during approach, land-

ing, and takeoff, the effect of the vertical gust

is due to the same mechanism of the change

in angle of attack. However, at these low

flight speeds, the problem is one of possible

incipient stalling and sinking rather than

overstress. When the airplane is at high

angle of attack, a further increase in angle of

attack due to a gust may exceed the critical

angle of attack and cause an incipient stalling

of the airplane. Also, a decrease in angle

of attack due to a gust will cause a loss of lift

and allow the airplane to sink. For this

reason, any deficiency of airspeed will be quite

critical when operating in gusty conditions.

The effect of the hori<oonral gust differs from

the effect of the vertical gust in that the im-

mediate effect is a change of airspeed rather

than a change in angle of attack. In this

sense, the horizontal gust is of little conse-

quence in the major airplane airloads and

strength limitations. Of greater significance

is the response of the airplane to horizontal

gusts and wind shear when operating at low

flight speeds. The possible conditions in

which an airplane may encounter horizontal

gusts and wind shear are illustrated in figure

6.5. As the airplane traverses a shear of wind

direction, a change in headwind component

will exist. Also, a climbing or descending

airplane may traverse a shear of wind velocity,

i.e., a wind profile in which the wind velocity

varies with altitude.

The response of an airplane is much de-

pendent upon the airplane characteristics but

certain basic effects are common to all ait-

planes. Suppose that an airplane is estab-

lished in steady, level flight with lift equal to

weight, thrust equal to drag, and trimmedso

NAVWEPS OG-8OT-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

EFFECT OF VERTICAL GUST

CHANGE IN ANGLE OF ATTACK

OF WIND

-1

VERTICAL VARll

TRANSIENT

CONDITION FROM

WIND SHEAR

STEADY

LEVEL LIFT

FLIGHT

OR HORIZONTAL GUST 1 LIFT I

Figure 6.5. Effect of Wind Shear

there is no unbalance of pitching, yawing, or

rolling moment. If the airplane traverses a

sharp wind shear equivalent to a horizontal

gust, the resulting change in airspeed will

disturb such an equilibrium. For example, if

the airplane encounrers a sharp horizontal

gust which reduces the airspeed 20percent,the

new airspeed (80 percent of the original value)

produces lift and drag at the same angle of

attack which are 64 percent of the original

value. The change in these aerodynamic forces

would cause the airplane to accelerate in the

direction of resultant unbalance of force.

That is, the airplane would accelerate down

and forward until a new equilibrium is

achieved. In addition, there would be a

change in pitching moment which would

produce a response of the airplane in pitch.

The response of the airplane to a horizontal

gust will differ according to the gust gradient

and airplane characccristics. Gmcrally, if the

airplane encounters a sharp wind shear which

reduces the airspeed, the airplane tends to sink

and incur a loss of altitude ‘before equilibrium

conditions are achieved. Similarly, if the

airplane encounters a sharp wind shear which

increases the airspeed, the airplane tends to

float and incur a gain of altitude before equilib-

rium conditions are achieved.

Significant vertical and horizontal gusts may

be due to the terrain or atmospheric conditions.

The proximity’of an unstable front or thunder-

storm activity’in the vicinity of the airfield is

likely to create significant wind shear and gust

activity at low altitude. During gusty condi-

tions every effort must be made for precise con-

trol of airspeed and flight path and any changes

due to gusts must be corrected by proper con-

trol action. Under extreme gusts conditions,

it may be advisable to utilize approach, land-

ing, and takeoff speeds slightly greater than

normal to provide margin for adequate control.

POWER-OFF GLIDE PERFORMANCE

The gliding performance of an airplane is of

special interest for the single-engine airplane

NAVWEPS O&ROT-80

APPLICATION OF AERODYNAMICS

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in the case of powerplant failure or malfunc-

tion. When a powerplant failure or malfunc-

tion occurs, it is usually of interest to obtain a

gliding flight path which results in the mini-

mum glide angle. The minimum glide angle

will produce the greatest proportion of glide

distance to altitude loss and will result in

maximum glide range or minimum expendi-

ture of altitude for a specific glide distance.

GLIDE ANGLE AND LIFT-DRAG RATIO.

In the study of climb performance, the forces

acting on the airplane in a steady climb (or

glide) produce the following relationship:

where

Y=: angle of climb, degrees

T-thrust, lbs.

D-drag, lbs.

W=: lbs.

In the case of power-off glide performance, the

thrust, T, is zero and the relationship reduces

to:

D sin y= -- W

By this relationship it is evident that the mini-

mum angle of glide-or minimum negative

climb angle-is obtained at the aerodynamic

conditions which incur the minimum total

drag. Since the airplane lift is essentially equal

to the weight, the minimum angle of glide

will be obtained when the airplane is operated

at maximum lift-drag ratio, (L/D)ma,. When

the angle of glide is relatively small, the ratio

of glide distance to glide altitude is numeri-

cally equal to the airplane lift-drag ratio.

glide ratio= glide distance, ft.

glide altitude, ft.

glide ratio = (L/D)

Figure 6.6 illustrates the forces acting on the

airplane in a power-off glide. The equilibrium

of the steady glide is obtained when the sum-

mation of forces in the vertical and horizontal

directions is equal to zeta.

NAVWEPS 00-801-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

+Y

l--J-@$!?e

DRAG

\ SIN 7 = - j WEIGHT

LIFT-OR&G

RATIO

L4l

GLIDE RATIO * L/o

r )M

-CLEAN CONFIGURATION

!

A <LANDING CONFIGURATION

LIFT COEFFICIENT, CL

RATE OF

DESCENT,

FPM

CLEAN CONFIGURATION

POWER OFF

VELOCITY, KNOTS

Figure 6.6. Glide Performance

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APPLICATION OF AERODYNAMICS

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speed will not cause any significant reduction

of glide ratio. This is fortunate and allows the

specifying of convenient glide speeds which

will be appropriate for a range of gross weights

at which power-off gliding may be encoun-

tered, e.g., small quantities of fuel remaining.

An attempt to stretch a glide by flying at

speeds above or below the best glide speed will

prove futile. As shown by the illustration of

figure 6.6, any C, above or below the optimum

will produce a lift-drag ratio less than the

maximum. If the airplane angle of attack is

increased above the value for (L/D),,, a tran-

sient reduction in rate of descent will take place

but this process must be reserved for the land-

ing phase. Eventually, the steady-state condi-

tions would be achieved and the increased

angle of attack would incur a lower airspeed

and a reduction in (L/D) and glide ratio.

The effect of gross weight on glide performance

may be difficult to appreciate. Since (L/D)-

of a given airplane configuration will occur at a

specific value of C,, the gross weight of the air-

plane will not affect the glide ratio if the air-

plane is operated at the optimum C,. Thus,

two airplanes of identical aerodynamic con-

figuration but different gross weight could

glide the same distance from the same altitude.

Of course, this fact would be true only if both

airplanes are flown at the specific C, to produce

(L/D),,. The principal difference would be

that the heavier airplane must fly at a higher

airspeed to support the greater weight at the

optimum C,. In addition, the heavier airplane

flying at the greater speed along the same flight

path would develop a greater rate of descent.

The relationship which exists between gross

weight and velocity for a particular C, is as

follows:

In order to obtain maximum glide ratio, the

airplane must be operated at the angle of at-

tack and lift coefficient which provide maxi-

mum lift-drag ratio. The illustration of figure

6.6 depicts a variation of lift-drag ratio, L/D,

with lift coeficient, C,, for a typical airplane

in the clean and landing configurations. Note

that (LID),,, for each configuration will occur

at a specihc value of lift coefficient and, hence,

a specific angle of attack. Thus, the maximum

glide performance of a given airplane configu-

ration will be unaffected by gross weight and

altitude when the airplane is operated at

(L/D),az. Of course, an exception occurs at

very high altitudes where compressibility ef-

fects may alter the aerodynamic characteristics.

The highest value of (L/D) will occur with the

airplane in the clean configuration. As the

airplane is changed to the landing configura-

tion, the added parasite drag reduces (L/D)_nz

and the C, which produces (L/D),, will be in-

creased. Thus, the best glide speed for the

landingconhguration generallywill be lessthan

the best glidespeed .for theclean configuration.

The power-off glide performance may be

appreciated also by the graph of rate of descent

versus velocity shown in figure 6.6. When a

straight line is drawn from the origin tangent

to the curve, a point is located which produces

the maximum proportion of velocity to rate

of descent. Obviously, this condition provides

maximum glide ratio. Since the rate of descent

is proportional to the power required, the

points of tangency define the aerodynamic

condition of (L/D)m.z.

FACTORS AFFECTING GLIDE PER-

FORMANCE. In order to obtain the mini-

mum glide angle through the air, the airplane

must be operated at (L/D)mor. The subsonic

(LIDL of a given airplane configuration will

occur at a specific value of lift coefficient and

angle of attack. However, as can be noted

from the curves of figure 6.6, small deviations

from the optimum C, will not cause a drastic

reduction of (L/D) and glide ratio. In fact, a

5 percent deviation in speed from the best glide

-4 VT- w, VI w, (constant C,>

where

VI= best glide speed corresponding to

some original gross weight. WI

V,=best glide speed corresponding to

some new gross weight, IV2

NAVWEPS OD-ROT-80

APPLICATION OF AERODYNAMICS

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As a result of this relationship, a IO percent

increase in gross weight would require a 5 per-

cent increase in glide speed to maintain

(L/D),,. While small. variations in gross

weight may produce a measurable change in

best glide speed, the airplane can tolerate small

deviations from the optimum C, without signif-

icant change in (L/D) and glide ratio. For this

reason, a standard, single value of glide speed

may be specified for a small range of gross

weights at which glide performance can be of

importance. A gross weight which is con-

siderably different from the normal range will

require a modification of best glide speed to

maintain the maximum glide ratio.

The effect a! &it.& on glide performance is

insignificant if there is no change in (L/D),.,.

Generally, the glide performance of the major-

ity of airplanes is subsonic and there is no

noticeable variation of (L/D),, with altitude.

Any specific airplane configuration at a partic-

ular gross weight will require a specific value

of dynamic pressure to sustain flight at the

C, for (L/D),,. Thus, the airplane will have

a best glide speed which is a specific value of

equivalent airspeed (EAS) independent of

altitude. For convenience and simplicity, this

best glide speed is specified as a specific value

of indicated airspeed (IAS) and compressibility

and position errors are neglected. The prin-

cipal effect of altitude is that at high altitude

the true airspeed (TAX) and rate of descent

along the optimum glide path are increased

above the low altitude conditions. However,

if WD),.z is maintained, the glide angle and

glide ratio are identical to the low altitllde

conditions.

The effect of configura+~n has been noted pre-

viously in that the addition of parasite drag by

flaps, landing gear, speed brakes, external

stores, etc. will reduce the maximum lift-drag

ratio and cause a reduction of glide ratio. In

the case where glide distance is of great im-

portance, the airplane must be maintained in

the clean configuration and flown at (L/D),=,

The eficct aj wind on gliding performance is

similar to the effect of wind on cruising range.

That is, a headwind will always reduce the

glide range and a tailwind will always increase

the glide range. The maximum glide range

of the airplane in still air will be obtained by

flight at (L/D),,,,. However, when a wind is

present, the optimum gliding conditions may

not be accomplished by operation at (L/D)ma.

For example, when a headwind is present,

the optimum glide speed will be increased to

obtain a maximum proportion of ground dis-

tance to altitude. In this sense, the increased

glide speed helps to minimize the detrimental

effect of the headwind. In the case of a tail-

wind, the optimum glide speed will be reduced

to maximize the benefit of the tailwind. For

ordinary wind conditions, maintaining the

glide speed best for zero wind conditions will

suffice and the loss or gain in glide distance

must be accepted. However, when the wind

conditions are extreme and the wind velocity

is large in comparison with the glide speed,

e.g., wind velocity greater than 25 percent of

the glide speed, changes in the glide speed must

be made to obtain maximum possible ground

distance.

THE FLAMEOUT PATTERN. In the case

of failure of the powerplant, every effort

should be made to establish a well-planned,

stabilized approach if a suitable landing area

is available. Generally a 360’ overhead ap-

proach is specified with the approach begin-

ning from the “high key” point of the flameout

pattern. The function of a standardized

pattern is to provide a flight path well within

the capabilities of the airplane and the abilities

of the pilot to judge and control the flight

path. The flight handbook will generally

specify the particulars of the flameout pattern

such as the altitude at the high key, glide

speeds, use of flaps, etc. Of course, the par-

ticulars of the flameout pattern will be de-

termined by the aerodynamic characteristics

of the airplane. A principal factor is the

effect of glide ratio, or (L/D),,, on the alti-

tude required at the high key point at the ~ _

beginning of the flameour pattern. The air-

plane with a low value of (L/D),,* will require

a high altitude at the high key point.

The most favorable situation during a

flameout would be for the airplane to in posi-

tion to arrive over the intended landing area

the altitude for the high key point. In this

case, the standard flameout pattern could be

utilized. If the airplane does not have s&i-

cient glide range to arrive at the landing

area with the altitude for the high key point,

it is desirable to fit the approach into the

lower portions of the standard flameout ap-

proach. If it is not possible to arrive at the

intended landing area with sufficient altitude

to “play” the approach, serious considera-

tion should be given to ejection while suffi-

cient altitude remains. Deviations from a

well-planned approach such as the standard

flameout pattern may allow gross errors in

judgment. A typical error of a non-standard

or poorly executed flameout approach is the

use of excessive angles of bank in turns to

correct the approach. Because of the great

increase ‘in induced drag at large angles of

bank, excessive rates of descent will be incurred

and there will be further deviations from a

desirable flight path.

The power-off gliding characteristics of the

airplane can be simulated in power on flight by

certain combinations of engine power setting

and position of the speed brake or dive Rap.

This will allow the pilot to become familiar

with the power-off glide performance and the

flameopt landing pattern. In addition, the

simulated flameout pattern is useful during a

precautionary landing when the powerplant is

malfunctioning and there is the possibility of

an actual flarneout.

The final approach and landing flare will be

particularly critical for the airplane which has*

a low glide ratio but a high best glide speed.

These airplane characteristics are typical of the

modern configuration of airplane which has

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APPLICATION OF AERODYNAMICS

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low aspect ratio, sweepback, and high wing

loading. Since these airplane characteristics

also produce marginal flare capability in power-

off flight, great care should be taken to follow

the procedure recommended for the specific

airplane.

As an example of the power-off glide per-

formance of an airplane with low aspect ratio,

sweepback, and high wing loading, a best

glide speed of 220 knots and a glide ratio of 6

may be typical. In such a case, the rate of

descent during the glide at low altitude would

be on the order of 3,700 FPM. Any deviations

from the recommended landing technique can-

not be tolerated because of the possibility of an

excessive rate of descent. Either premature

flare or delayed flare may allow the airplane to

touch down at a rate of descent which would

cause structural failure. Because of the mar-

ginal flare characteristics in power-off flight,

the best glide speed recommended for the land-

ing configuration may be well above the speed

corresponding to the exact maximum lift-drag

ratio. The greater speed reduces induced drag

and provides a greater margin for a successful

power-off landing flare.

In the extreme case, the power-off glide and

landing flare characteristics may be very criti-

cal for certain airplane configurations. Thus,

a well-planned standard flameout pattern and

precise flying technique are necessary and, if

very suitable conditions are not available, the

recommended alternative is simple: eject!

EFFECT OF ICE AND FROST ON AIRPLANE

PERFORMANCE

Without exception, the formation of ice or

frost on the surfaces of an airplane will cause a

detrimental effect on aerodynamic performance.

The ice or frost formation on the airplane sur-

faces will alter the aerodynamic contours and

affect the nature of the boundary layer. Of

course, the most important surface of the air-

plane is the wing and the formation of ice or

frost can create significant changes in the aero-

dynamic characteristics.

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APPLICATION OF AERODYNAMICS

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EDGE ICE FOR_“ATlON

UPPER SURFACE FROST

BASIC SMOOTH WING

WING WITH FROST

LIFT

COEFFICIENT WITH ICE

ANGLE OF ATTACK, a

Figure 6.7. Effect of ice and Frost

A large formation of ice on the leading edge

of the wing can produce large changes in the

local contours and severe local pressure gra-

dients. The extreme surface roughness common

to some forms of ice will cause high surface

friction and a considerable reduction of bound-

ary layer energy. As a result of these effects,

the ice formation can produce considerable in-

crease in drag and a large reduction in maxi-

mum lift coefficient. Thus, the ice formation

will cause an increase in power required and

stall speed. In addition, the added weight of

the ice formation on the airplane will provide

an undesirable effect. Because of the detri-

mental effects of ice formation, recommended

anti-icing procedures must be followed to

preserve the airplane performance.

The effect of frost is perhaps more subtle

than the effect of ice formation on the aero-

dynamic characteristics of the wing. The ac-

cumulation of a hard coat of frost on the wing

upper surface will provide a surface texture of

considerable roughness. While the basic shape

and aerodynamic contour is unchanged, the

increase in surface roughness increases skin-

friction and reduces the kinetic energy of the

boundary layer. As a result, there will be an

increase in drag but, of course, the magnitude

of drag increase will not compare with the

considerable increase due to a severe ice forma-

tion. The reduction of boundary layer kinetic

energy will cause incipient stalling of the wing,

i.e., separation will occur at angles of attack

and lift coefficients lower than for the clean,

smooth wing. While the reduction in C,,,,

due to frost formation ordinarily is not as great

as that due to ice formation, it is usually un-

expected because it may be thought that large

changes in the aerodynamic shape (such as

due to ice) are necessary to reduce CL,az. How-

ever, the kinetic energy of the boundary layer

is an important factor influencing separation

of the airflow and this energy is reduced by an

increase in surface roughness.

The general effects of ice and frost formation

NAVWEPS OD-BOT-80

APP,LlCATlON OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

on the lift characteristics is typified by the il-

lustration of figure 6.7.

The effect of ice or frost on takeoff and land-

ing performance is of great importance. The

effects are so detrimental to the landing and

takeoff that no effort should be spared to keep

the airplane as free as possible from any ac-

cumulation of ice or frost. If any ice remains

on the airplane as the landing phase approaches

it must be appreciated that the ice formation

will have reduced CL,., and incurred an increase

in stall speed. Thus, the landing speed will be

greater. When this effect is coupled with the

possibility of poor braking action during the

landing roll, a critical situation can exist. It is

obvious that .great effort must be made to

prevent the accumulation of ice during flight.

In no circumstances should a formation of ice

or frost be allowed to remain on the airplane

wing surfaces prior to takeoff. The undesir-

able effects of ice are obvious but, as previously

mentioned, the effects of frost are more subtle.

If a heavy coat of hard frost exists on the wing

upper surface, a typical reduction in CL,..

would cause a 5 to 10 percent increase in the

airplane stall speed. Because of this magnitude

of effect, the effect of frost on takeoff per-

formance may not be realized until too late.

The takeoff speed of an airplane is generally

some speed 5 to 25 percent greater than the

stall speed, hence the takeoff lift coefficient

will be value from 90 to 65 percent of C1,,..,

Thus, it is possible that the airplane with frost

cannot become airborne at the specified take-

off speed because of premature stalling. Even

if the airplane with frost were to become air-

borne at the specified takeoff speed, the air-

plane could have insufficient margin of air-

speed above stall and turbulence, gusts, turning

flight could produce incipient or con plete

stalling of the airplane.

The increase in drag during takeoff roll due

to frost or ice is not considerable and there

will not be any significant effect on the initial

acceleration during takeoff. Thus, the effect

of frost or ice will be most apparent during the

NAVWEPS DD-8OT-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

later portions of takeoff if the airplane is un-

able to become airborne or if insufficient margin

above stall speed prevents successful initial

climb, In no circumstances should a formation

of ice or frost be allowed to remain on the air-

plane wing surfaces prior to takeoff.

ENGINE FAILURE ON THE MULTIENGINE

AIRPLANE

In the case of the single-engine airplane,

power-plant failure leaves only the alternatives

of effecting a successful power-off landing or

abandoning the airplane. In the case of the

multiengine airplane, the failure of a power-

plant does nor necessarily constitute a disaster

since flight may be continued with the remain-

ing powerplants functioning. However, the

performance of the multiengine airplane with

a powerplant inoperative may be critical for

certain conditions of flight and specific tech-

niques and procedures must be observed to

obtain adequate performance.

The effect of a powerplant failure on the

multiengine turbojet airplane is illustrated by

the first chart of figure 6.8 with the variation

of required and available thrust with velocity.

If half of the airplane powerplants are inoper-

ative, e.g., single-engine operation of a twin-

engine airplane, the maximum thrust available

at each velocity is reduced to half that avail-

able prior to the engine failure. The variation

of thrust required with velocity may be

affected by the failure of a powerplant in that

there may be significant increases in drag if

specific procedures are not followed. The

inoperative powerplant may contribute addi-

tional drag and the pilot must insure that the

additional drag is held to a minimum. In the

case of the propeller powered airplane, the

propeller must be feathered, cowl flaps closed.

etc., as the increased drag will detract con-

siderably from the performance.

The principal effects of the reduced available

thrust are pointed out by the illustration of

figure 6.6. Of course, the lower available

thrust will reduce the maximum level flight

speed but of greater importance is the reduc-

tion in excess thrust. Since the acceleration

and climb performance is a function of the

excess thrust and power, the failure of a power-

plant will be most immediately appreciated in

this area of performance. As illustrated in

figure 6.8, loss of one-half the maximum avail-

able thrust will reduce the excess thrust to less

than half the original value. Since some

thrust is required to sustain flight, the excess

which remains to accelerate and climb the

airplane may be greatly reduced. The most

critical conditions will exist when various

factors combine to produce a minimum of

excess thrust or power when engine failure

occurs. Thus, critical conditions will be com-

mon to high gross weight and high density altitude

(and high temperatures in the case of the

turbine powered airplane) as each of these

factors will reduce the excess thrust at any

specific flight condition.

The asymmetrical power condition which

results when a powerplant fails can provide

critical control requirements. First consid-

eration is due the yawing moment produced

by the asymmetrical power condition. Ade-

quate directional control will be available

only when the airplane speed is greater than

the minimum directional control speed. Thus,

the pilot must insure that the flight speed never

falls below the minimum directional control

speed because the application of maximum

power on the functioning powerplants will

produce an uncontrollable yaw if adequate

directional control is unavailable. A second

consideration which is due the propeller

powered airplane involves the rolling moments

caused by the slipstream velocity. Asym-

metrical power on the propeller airplane will

create a dissymmetry of the slipstream veloc-

ities on the wing and create rolling moments

which must be controlled. These slipstream

induced rolling moments will be greatest at

high power and low velocity and the pilot

must be sure of adequate lateral control,

especially for the crosswind landing.

The effect of an engine failure on the remain-

ing range and endurance is specific to the air-

plane type and configuration. If an engine

fails during optimum cruise of the turbojet

airplane, the airplane must descend and experi-

ence a loss of range. Since the turbojet air-

plane is generally overpowered at (L/D),,,

a loss of a powerplant will not cause a signi-

ficant change in maximum endurance. If an

engine fails during cruise of a reciprocating

powered airplane, there will be a significant

loss of range only if the maximum range condi-

tion cannot be sustained with the remaining

powerplants operating within the cruise power

rating. If a power greater than the maximum

cruise rating is necessary to sustain cruise, the

specific fuel consumption increases and causes

a reduction of range. Essentially the same

relationship exists regarding maximum endur-

ance of the reciprocating powered airplane.

When critical conditions exist due to failure

of a powerplant, the pilot must appreciate the

reduced excess thrust and operate the airplane

within specific limitations. If the engine-out

performance of the airplane is marginal, the

pilot must be aware of the very detrimental

effect of steep turns.. Due to the increased load

factor in a coordinated turn, there will be an

increase in stall speed and-of greater import-

ance to engine-out performance-an increase

in induced drag. The following table illus-

trates the effect of bank angle on stall speed

and induced drag.

TABLE 6.1

Bank mglc, 6, dcgrccs Load factor

0 0

0.2 0.8

0.7 3.1

1.7 7.2

3.2 13.3

5.0 21.7

7.5 33.3

10.5 4% 0

14.3 70.4

IS. 9 loo. 0

41.4 303.0

NAVWEPS OD-BOT-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

The previous table of values illustrates the

fact that coordinated turns with less than 15”

of bank .cause no appreciable effect on stall

speed or induced drag. However, note that 30”

of bank will increase the induced drag by 33.3

percent. Under critical conditions, such an in-

crease in induced drag (and, hence, total drag)

would be prohibitive causing the airplane to

descend rather than climb. The second graph

of figure 6.7 illustrates the case where the steep

turn causes such a large increase in required

thrust that a deficiency of thrust exists. When-

ever engine failure produces critical perform-

ance conditions it is wise to limit all turns to

II0 of bank wherever possible.

Another factor to consider in turning flight

is the effect of sideslip. If the turn is not coor-

dinated to hold sideslip to a minimum, addi-

tional drag will be incurred due to the sideslip.

The use of the flaps and landing gear can

greatly affect the performance of the multi-

engine airplane when a powerplant is inopera-

tive. Since the extension of the landing gear

and flaps increases the parasite drag, maximum

performance of the airplane will be obtained

with airplane in the clean configuration. In

certain critical conditions, the extension of the

landing gear and full flaps may create a defi-

ciency of thrust at any speed and commit the

airplane to descend. This condition is illus-

trated by the second graph of figure 6.8. Thus,

judicious use of the flaps and landing gear is

necessary in the case of an engine failure.

In the case of engine failure immediately

after takeoff, it is important to maintain air-

speed in excess of the minimum directional con-

trol speed and accelerate to the best climb

speed. After the engine failure, it will be fa-

vorable to climb only as necenary to clear obstacles

until the airplane reaches the best climb speed. Of

course, the landing gear should be retracted as

soon as the airplane is airborne to reduce para-

site drag and, in the case of the propeller pow-

ered airplane, it is imperative that the wind

milling propeller be feathered. The flaps should

be retracted only as rapidly as the increase in

NAVWEPS 00-801-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

THRUST

REQ’D

AND

AVAILABLE

LBS.

THRUST AVAJLABLE WJTH ALL

ENGINES OPERATING

THRUST AVAILABLE WITH

NES OPERATING

THRUST

REO’U

AND

AVAILABLE

LB.%

I VELOCITY, KNOTS

THRUST REP’D THRUST REO’D CLEAN

LANDING CONFIGURATION CONFIGURATION

WING LEVEL FLIGHT , BUT TURNING FLIGHT

WING LEVEL FLIGHT

AVAILABLE DUE TO

ENGINE FAILURE

VELOCITY, KNOTS

Figure 6.8. Engine Failure on Multi-engine Aircraft

airspeed will allow. If full flap deflection is

utilized for takeoff it is important to recall that

the last 50 percent of flap deflection creates

more than half the total drag increase but less

than half the total change in CL,-. Thus, for

some configurations of airplanes, a greater re-

duction in drag may be accomplished by partial

retraction of the flaps rather than retraction of

the landing gear. Also, it is important that no

steep turns be attempted because of the unde-

sirable increase in induced drag.

During the landing with an engine inopera-

tive, the same fundamental precautions must

be observed as during takeoff, i.e., minimum

directional control speed must be maintained

(or exceeded), no steep turns should be at-

tempted, and the extension of the flaps and

landing gear must be well planned. In the case

of’a critical power condition it may be neces-

sary to delay the extension of the landing gear

and full flaps until a successful landing is as-

sured. If a waveoff is necessary, maximum per-

formance will be obtained cleaning up the air-

plane and accelerating to the best climb speed

before attempting any gain in altitude.

At all times during flight with an engine

inoperative, the pilot must utilize the proper

techniques for control of airspeed and altitude,

e.g., for the conditions of steady flight, angle

of attack is the primary control of airspeed

and excess power is the primary control of

rate of climb. For example, if during approach

to landing the extension of full flaps and

landing gear creates a deficiency of power at

all speeds, the airplane will be committed to

descend. If the approach is not properly

planned and the airplane sinks below the

desired glide path, an increase in angle of

attack will only allow the airplane to fly more

slowly and descend more rapidly. An attempt

to hold altitude by increased angle of attack

when a power deficiency exists only causes a

continued loss of airspeed. Proper procedures

and technique are an absolute necessity for

safe flight when an engine failure occurs.

NAVWEPS OO-BOT-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

GROUND EFFECT

When an airplane in flight nears the ground

(or water) surface, a change occurs in the

three dimensional flow pattern because the

local airflow cannot have a vertical component

at the ground plane. Thus, the ground plane

will furnish a restriction to the flow and alter

the wing upwash, downwash, and tip vortices.

These general effects due to the presence of

the ground plane are referred to as “ground

effect. ‘*

AERODYNAMIC INFLUENCE OF

GROUND EFFECT. While the aerodynamic

characteristics of the tail and fuselage are

altered by ground effects, the principal effects

due to proximity of the ground plane are the

changes in the aerodynamic characteristics

of the wing. As the wing encounters ground

effect and is maintained at a constant lift

coefficient, there is a reduction in the upwash,

downwash, and the tip vortices. These effects

are illustrated by the sketches of figure 6.9.

As a result of the reduced tip vortices, the wing

in the presence of ground effect will behave as

if it were of a greater aspect ratio. In other

words, the induced velocities due to the tip

(or trailing) vortices will be reduced and the

wing will incur smaller values of induced

drag coefficient, C,<, and induced angle of

attack, OL;, for any specific lift coefhcient, C,.

In order for ground effect to be of a signifi-

cant magnitude, the wing must be quite close

to the ground plane. Figure 6.9 illustrates

one of the direct results of ground effect by

the variation of induced drag coefficient with

wing height above the ground plane for a

representative unswept wing at constant lift

coefficient. Notice that the wing must be

quite close to the ground for a noticeable

reduction in induced drag. When the wing

is at a height equal to the span (h/b=l.O),

the reduction in induced drag is only 1.4

percent. However, when the wing is at a

height equal to one-fourth the span (b/b=

0.25), the reduction in induced drag is 23.5

NAVWEPS 00-802-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYtNG

AIRPLANE OUT OF

GROUND EFFECT TIP VORTEX

/

REDUCED DOWNWASH

AND UPWASH- REDUCED t-- SFkAN’ --I

PERCENT

REDUCTION

IN

INDUCED

DRAG

COEFFICIENT

LIFT

COEFFICIEN’

CL CONSTANT

IO

RATIO OF WING HEIGHT TO SPAN, h/b

AIRPLANE IN

THRUST

REQ’D

LBS.

AIRPLANE OUT OF

GROUND EFFECT

w - w

ANGLE OF ATTACK, 0 VELOCITY, KNOTS

Figure 6.9. Ground Effect

AIRPLANE OUT OF /

(-,’ < AIRPLANE IN

GROUND EFFECT

percent and, when the wing is at a height

equal to one-tenth the span (h/b=O.l), the

reduction in induced drag is 47.6 percent.

Thus, a large reduction in induced drag will

take place only when the wing is very close

to the ground. Because of this variation,

ground effect is most usually recognized during

the liftoff of takeoff or prior to touchdown on

landing.

The reduction of the tip or trailing vortices

due to ground effect alters the spanwise lift

distribution and reduces the induced angle of

attack. In this case, the wing will require

a lower angle of attack in ground effect to

produce the same lift coefficient. This effect

is illustrated by the lift curves of figure 6.9

which show that the airplane in ground effect

will develop a greater slope of the lift curve.

For the wing in ground effect, a lower angle of

attack is necessary to produce the same lift

coefficient or, if a constant angle of attack is

maintained, an increase in lift coefficient will

result.

Figure 6.9 illustrates the manner in which

ground effect will alter the curve of thrust re-

quired versus velocity. Since induced drag

predominates at low speeds, the reduction of

induced drag due to ground effect will cause

the most significant reduction of thrust re-

quired (parasite plus induced drag) only at

low speeds. At high speeds where parasite

drag predominates, the induced drag is but

a small part of the total drag and ground

effect causes no significant change in thrust re-

quired. Because ground effect involves the

induced effects of airplane when in close prox-

imity to the ground, its effects are of greatest

concern during the takeoff and landing. Ordi-

narily, these are the only phases of flight in

which the airplane would be in close proximity

to the ground.

GROUND EFFECT ON SPECIFIC FLIGHT

CONDITIONS. The overall influence of

ground effect is best realized by assuming that

the airplane descends into ground effect while

maintaining a constant lift coefficient and,

NAVWEPS CKLBOT-BO

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

thus, a constant dynamic pressure and equiva-

lent airspeed. As the airplane descends into

ground effect, the following. effects will take

place:

(1) Because of the reduced induced angle

of attack and change in lift distribution, a

smaller wing angle of attack will be required

to produce the same lift coefficient. If a

constant pitch attitude is maintained as

ground effect is encountered, an increase in

lift coefficient will be incurred.

(2) The reduction in induced flow due to

ground effect causes a significant reduction

in induced drag but causes no direct effect on

parasite drag. As a result of the reduction

in induced drag, the thrust required at low

speeds will be reduced.

(3) The reduction in downwash due to

ground effect will produce a change in longi-

tudinal stability and trim. Generally, the

reduction in downwash at the horizontal

tail increases the contribution to static longi-

tudinal stability. In addition, the reduction

of downwash at the tail usually requires

a greater up elevator to trim the airplane at

a specific lift coefficient. For the conven-

tional airplane configuration, encountering

ground effect will produce a nose-down

change in pitching moment. Of course, the

increase in stability and trim change associ-

ated with ground effect provide a critical re-

quirement of adequate longitudinal control

power for landing and takeoff.

(4) Due to the change in upwash, down-

wash, and tip vortices, there will be a change

in position error of the airspeed system, as-

sociated with ground effect. In the majority

of cases, ground effect will cause an increase

in the local pressure at the static source and

produce a lower indication of airspeed and

altitude.

During the landing pha~c of flight, the effect

of proximity to the ground plane must be

understood and appreciated. If the airplane

is brought into ground effect with a constant

angle of attack, the airplane will experience

3&l

NAVWEPS OD-8OT-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYfNG

an increase in lift coeflicient and reduction in

thrust required. Hence, a “floating” sensa-

tion may be experienced. Because of the re-

duced drag and power-off deceleration in

ground effect, any excess speed at the point of

flare may incur a considerable “float” distance.

As the airplane nears the point of touchdown

on the approach, ground effect will be most

realized at altitudes less than the wing span.

An exact appreciation of the ground effect may

be obtained during a PcZd approach with the

mirror landing system furnishing an exact

reference of the flight path. During the final

phases of the field approach as the airplane

nears the ground plane, a reduced power

setting is necessary or the reduced thrust re-

quired would allow the airplane to climb

above the desired glide path. During ship-

board operations, ground effect will be delayed

until the airplane passes the edge of the deck

and the reduction in power setting that is

common to field operations should not be

encountered. Thus, a habit pattern should

not be formed during field landings which

would prove dangerous during carrier oper-

ations.

An additional factor to consider is the aero-

dynamic drag of the airplane during the land-

ing roll. Because of the reduced induced drag

when in ground effect, aerodynamic braking

will be of greatest significance only when

partial stalling of the wing can be accom-

plished. The reduced drag when in ground

effect accounts for the fact that the brakes

are the most effective source of deceleration

for the majority of airplane configurations.

During the takeoff pharc of flight ground

effect produces some important relationships.

Of course, the airplane leaving ground effect

encounters just the reverse of the airplane

entering ground effect, i.e., the airplane leaving

ground effect will (1) require an increase in

angle of attack to maintain the same lift

coefficient, (2) experience an increase in in-

duced drag and thrust required, (3) experience a

decrease in stability and a nose-up change in

moment, and (4) usually a reduction in static

source pressure and increase in indicated air-

speed. These general effects should point out

the possible danger in attempting takeoff

prior to achieving the recommended takeoff

speed. Due to the reduced drag in ground

effect the airplane may seem capable of takeoff

below the recommended speed. However, as

the airplane rises out of ground effect with a

deficiency of speed, the greater induced drag

may produce marginal initial climb perform-

ance. In the extreme conditions such as high

gross weight, high density altitude, and high

temperature, a deficiency of airspeed at takeoff

may permit the airplane to become airborne

but be incapable of flying’out of ground effect.

In this case, the airplane may become airborne

initially with a deficiency of speed, but later

settle back to the runway. It is imperative

that no attempt be made to force the airplane

to become airborne with a deficiency of speed;

the recommended takeoff speed is necessary to

provide adequate initial climb performance.

In fact, ground effect can be used to advantage

if no obstacles exist by using the reduced drag

to improve initial acceleration.

The results of the airplane leaving ground

effect can be most easily realized during the

deck launch of a heavily loaded airplane. As

the airplane moves forward and passes over the

edge of the deck, whatever ground effect exists

will be lost immediately. Thus, proper rota-

tion of the airplane will be necessary to main-

tain the same lift coefficient and the increase

in induced drag must be expected.

The rotor of the helicopter experiences a

similar restraint of induced flow when in prox-

imity to the ground plane. Since the induced

rotor power required will predominate at low

flight speeds, ground effect will produce a con-

siderable effect on the power required at low

speeds. During hovering and flight at low

speeds, the elevation of the rotor above the

ground plane will be an important factor de-

termining the power required for flight.

The range sf the reciprocating powered air-

plane can be augmented by the use of ground

effect. When the airplane is close to the

ground or water surface the reduction of in-

duced drag increases the maximum lift-drag

ratio and causes a corresponding increase in

range. Of course, the airplane must be quite

close to the surface to obtain a noticeable in-

crease in (L/D),., and range. The difficulty in

holding the airplane at the precise altitude

without contacting the ground or water will

preclude the use of ground effect during ordi-

nary flying operations. The use of ground

effect to extend range should be reserved as

a final measure in case of emergency. Because

of the very detrimental effect of low altitude

on the range of the turbojet, ground effect will

not be of a particular advantage in an attempt

to augment range.

The most outstanding examples of the use

of ground effect are shown in the cases of multi-

engine airplanes with some engines inoperative.

When the power loss is quite severe, the air-

plane may not be capable of sustaining altitude

and will descend. As ground effect is en-

countered, the reduced power required may

allow the airplane to sustain flight at extremely

low altitude with the remaining powerplants

functioning. In ground effect, the recipro-

cating powered airplane will encounter a

greater (L/D),, which occurs at a lower air-

speed and power required and the increase in

range may be quite important during emer-

gency conditions.

INTERFERENCE BETWEEN AIRPLANES IN

FLIGHT

During formation flying and inflight refuel-

ing, airplanes in proximity to one another will

produce a mutual interference of the flow pat-

terns and alter the aerodynamic characteristics

of each airplane. The principal effects of this

interference must be appreciated since certain

factors due to the mutual interference may

enhance the possibility of a collision.

NAVWEPS D&ROT-R0

APPLICATION OF AERODYNAMICS

TO SPECIFIC ‘PROBLEMS OF FLYING

One example of interference between air-

planes in flight is shown first in figure 6.10 with

the effect of lateral separation of two airplanes

flying in line abreast. A plane of symmetry

would exist halfway between two identical air-

planes and would furnish a boundary of flow

across which there would be no lateral com-

ponents of flow. As the two airplane wing

tips are in proximity, the effect is to reduce the

strength of the tip or trailing vortices and re-

duce the induced velocities in the vicinity of

wing tip. Thus, each airplane will experience

a local increase in the lift distribution as the

tip vortices are reduced and a rolling moment is

developed which tends to roll each airplane

away from the other. This disturbance may

provide the possibility of collision if other air-

planes are in the vicinity and there is delay in

control correction or overcontrol. If the wing

tips are displaced in a fore-and-aft direction,

the same effect exists but generally it is of a

lower magnitude.

The magnitude of the interference effect due

to lateral separation of the wing tips depends

on the proximity of the wi.ig tips and the ex-

tent of induced Pov;. This implies that the

interference v-r 1 e grealest when the tips

are very close AL-L the airplanes are operating

at high lift coefficients. An interesting ramifi-

cation of this effect is that several airplanes in

line abreast with the wing tips quite close will

experience a reduction in induced drag.

An indirect form of interference can be en-

countered from the vortex system created by a

preceding airplane along the intended flight

path. The vortex sheet rolls up a considerable

distance behind an airplane and creates consid-

erable turbulence for any closely following air-

plane. This wake can prove troublesome if air-

planes taking off and landing are not provided

adequate separation. The rolled-up vortex

sheet will be strongest when the preceding air-

planes is large, high gross weight, and operat-

ing at high lift coefhcients. At times this tur-

bulence may be falsely attributed to propwash

or jetwash.

NAVWBPS OO-BOT-BO

APPLICATION OF AERODYNAMlCS

TO SPECIFIC PROBLEMS OF FLYING

LIFT DISTRIBUTION

LBWFT OF SPAN

TIP VORTEX

PLANE OF

SYMMETRY

REDUCED CHANGE IN

LIFT DISTRIBUTION

-

--

%SH

\’

DOCASH

TRIM CHANGE

figure 6.10. Interference 8etween Airplanes in Flight

Another important form of direct inter-

ference is common when the two airplanes are

in a trail position and stepped down. As shown

in figure 6.10, the single airplane in flight de-

velops upwash ahead of the wing and down-

wash behind and any restriction accorded the

flow can alter the distribution and magnitude of

the upwash and downwash. When the trailing

airplane is in close proximity aft and below the

leading airplane a mutual interference takes

place betweetrthe two airplanes. The leading

airplane above will experience an effect which

would be somewhat similar to encountermg

ground effect, i.e., a reduction in induced drag,

a reduction in downwash at the tail, and a

change in pitching moment nose down. The

trailing airplane below will experience an effect

which is generally the opposite of the airplane

above. In other words, the airplane below

will experience an increase in induced drag, an

increase in downwash at the tail, and a change

in pitching moment nose up. Thus, when

the airplanes are in close proximity, a definite

collision possibility exists because of the trim

change experienced by each airplane. The

magnitude of the trim change is greatest

when the airplanes are operating at high lift

coefficients, e.g., low speed flight, and when

the airplanes are in close proximity.

In formation flying, this sort of interference

must be appreciated and anticipated. In cross-

ing under another airplane, care must be

taken to anticipate the trim change and

adequate clearance must be maintained, other-

wise a collision may result. The pilot of the

leading aircraft will know of the presence of

the trailing airplane by the trim change

experienced. Obviously, some anticipation is

necessary and adequate separation is necessary

to prevent a disturbing magnitude of the

trim change. In a close diamond formation

the leader will be able to “feel” the presence

of the slot man even though the airplane is

not within view. Obviously, the slot man

will have a difficult job during formation

maneuvers because of the unstable trim changes

NAVWEPS OO-ROT-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

and greater power changes required to hold

position.

A common collision problem is the case of

an airplane with a malfunctioning landing

gear. If another”airpIane is called to inspect

the malfunctioning landing gear, great care

must be taken to maintain adequate separation

and preserve orientation. Many instances

such as this have resulted in a collision when

the pilo: of the trailing airplane became dis-

oriented and did not maintain adequate sepa-

ration.

During inflight refueling, essentially the

same problems of interference exist. AS the

receiver approaches the tanker from behind

and below, the receiver will encounter the

downwash from the tanker and require a

slight, gradual increase in power and pitch

attitude to continue approach to the receiving

position. While.‘the .receiver may not be

visible to the pilot ‘of the tanker, he will

anticipate the receiver coming into position

by the slight reduttion in power required and

nose down changein pitching moment. Ade-

quate clearance and, proper position must be

maintained by the pilot of the receiver for a

collision possibility is enhanced by the rela-

tive positions of the airplanes. A hazardous

condition exists if the pilot of the receiver

has excessive speed and runs under the tanker

in close proximity.* ‘The trim change expe-

rienced by both airphines may be large and

unexpected and it may be difficult to avoid a

collision.

In addition to the forms of interference

previously mentioned, there exists the possi-

bility of strong interference between airplanes

in supersonic flight. In this case, the shock

waves from one airplane may strongly affect

the pressure distribution and rolling, yawing,

and pitching moments of an adjacent air-

Pl ane. It is difficult to express general rela-

tionships of the effect except that magnitude

of the effects will be greatest when in close

proximity at low altitude and high 4. General-

ly, the trailing airplane will be most affected.

BRAKING PERFORMANCE

For the majority of airplane configurations

and runways conditions, the airplane brakes

furnish the most powerful means of deceler-

ation. While specific techniques of braking

are required for specific situations, there

are various fundamentals which are common

to all conditions.

Solid ftictim is the resistance to relative

motion of two surfaces in contact. When

relative motion exists between the surfaces,

the resistance to relative motion is termed

“kinetic” or “sliding” friction; when no

relative motion exists between the surfaces,

the resistance to the impending relative mo-

tion is termed “static” friction. The minute

discontinuities of the surfaces in contact are

able to mate quite closely when relative

motion impends rather than exists, so static

friction will generally exceed kinetic friction.

The magnitude of the friction force between

two surfaces will depend in great part on the

types of surfaces in contact and the magnitude

of force pressing the surfaces together. A

convenient method of relating the friction

charactersitics of surfaces in contact is a

proportion of the friction force to the normal

(or perpendicular) force pressing the surfaces

together. This proportion defines the coeffi-

cient of friction, ~1.

,L= F/N

where

p =coefFicient of friction (mu)

F =friction force, Ibs.

N = normal force, lbs.

The coefficient of friction of tires on a runway

surface is a function of many factors. Runway

surface condition, rubber composition, tread,

inflation pressure, surface friction shearing

stress, relative slip speed, etc., all are factors

which affect the coefficient of friction. When

the tire is rolling along the runway without

the use of brakes, the friction force resulting is

simple rolling resistance. The coefficient of

NAVWEPS O&ROT-R0

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

rolling friction is of an approximate magnitude

of 0.015 to 0.030 for dry, hard runway surface.

The application of brakes supplies a torque

to the wheel which tends co retard wheel rota-

tion. However, the initial application of

brakes creates a braking torque but the initial

retarding torque is balanced by the increase in

friction force which produces a driving or

rolling torque. Of course, when the braking

torque is equal to the rolling torque, the wheel

experiences no acceleration in rotation and the

equilibrium of a constant rotational speed is

maintained. Thus, the application of brake

develops a retarding torque and causes an

increase in friction force between the tire and

runway surface. A common problem of brak-

ing technique is application of excessive brake

pressure which creates a braking torque greater

than the maximum possible rolling torque.

In this case, the wheel loses rotational speed

and decelerates until the wheel is stationary

and the result is a locked wheel with the tire

surface subject to a full slip condition.

The relationship of friction force, normal

force, braking torque, and rolling torque is

illustrated in figure 6.11.

The effect of slip velocity on the coefficient

of friction is illustrated by the graph of figure

6.11. The conditions of zero slip corresponds

to the rolling wheel without brake application

while the condition of full, 100 percent slip

corresponds to the locked wheel where the

relative velocity between the tire surface and

the runway equals the actual velocity. With

the application of brakes, the coefficient of

friction increases but incurs a small but meas-

urable apparent slip. Continued increase in

friction coefficient is obtained until some max-

imum is achieved then decreases as the slip

increases and approaching the 100 percent slip

condition. Actually, the peak value of co-

efficient of friction occurs at an incipient skid

condition and the relative slip apparent at this

point consists primarily of elastic shearing

deflection of the tire structure.

NAVWEPS DD-BOl-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

When the runway surface is dry, brush-

finished concrete, the maximum value for the

coefficient of friction for most aircraft tires is

on the order of 0.6 to 0.8. Many factors can

determine small differences in this peak value

of friction coefhcient for dry surface conditions.

For example, a soft gum rubber composition

can develop a very high value of coefficient of

friction but only for low values of surface

shearing stress. At high values of surface

shearing stress, the soft gum rubber will shear

or scrub off before high values of friction co-

efficient are developed. The higher strength

compounds used in the production of aircraft

tires produce greater resistance to surface shear

and scrubbing but the harder rubber has lower

intrinsic friction coeflicient. Since the high

performance airplane cannot afford the luxury

of excessive tire weight or size, the majority

of airplane tires will be of relatively hard

rubber and will operate at or near the rated

load capacities. As a result, there will be

little difference between the peak values of

friction coefficient for the dry, hard surface

runway for the majority of aircraft tires.

If high traction on dry surfaces were the

only consideration in the design of tires, the

result would be a soft rubber tire of extreme

width to create a large footprint and reduce

surface shearing stresses, e.g., driving tires on

a drag racer. However, such a tire has many

other characteristics which are undesirable

such as high rolling friction, large size, poor

side force characteristics, etc.

When the runway has water or ice on the

surface, the maximum value for the coefficient

of friction is reduced greatly below the value

obtained for the dry runway condition. When

water is on the surface, the tread design be-

comes of greater importance to maintain con-

tact between the rubber and the runway and

prevent a film of water from lubricating the

surfaces. When the rainfall is light, the peak

value for friction coefficient is on the order of

0.5. With heavy rainfall it is more likely

that sufficient water will stand to form a liquid

film between the tire and the runway. In this

case, the peak coefficient of friction rarely

exceeds 0.3. In some extreme conditions, the

tire may simply plane along the water without

contact of the runway and the coefficient of

friction is much lower than 0.3. Smooth,

clear ice on the runway will cause extremely

low values for the coefficient of friction. In

such a condition, the peak value for the co-

efhcient of friction may be on the order of 0.2

or 0.15.

Note that immediately past the incipient

skidding condition the coefficient of friction

decreases with increased slip speed, especially

for the wet or icy runway conditions. Thus,

once skid begins, a reduction in friction force

and rolling torque must be met with a reduc-

tion in braking torque, otherwise the wheel

will decelerate and lock. This is an important

factor to consider in braking technique because

the skidding tire surface on the locked wheel

produces considerably less retarding force than

when at the incipient skid condition which

causes the peak coeflicient of friction. If the

wheel locks from excessive braking, the sliding

tire surface produces less than the maximum

retarding force and the tires become relatively

incapable of developing any significant side

force. Stop distance will increase and it may

be difficult-if not impossible-to control the

airplane when full slip is developed. In addi-

tion, at high rolling vel,ocities on the dry sur-

face runway, the immediate problem of a skid-

ding tire is not necessarily the loss of retard-

ing force but the imminence of tire failure. The

pilot must insure that the application of brakes

does not produce some excessive braking torque

which is greater than the maximum rolling

torque and particular care must be taken when

the runway conditions produce low values of

friction coefficient and when the normal force

on the braking surfaces is small. When it is

difficult to perceive or distinguish a skidding

condition, the value of an antiskid or auto-

matic braking system will be appreciated.

NAVWEPS OD4OT-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PRO&EMS OF FLYING

NORMAL FORCE

COEFFICIENT

OF

FRICTION 0.6

F/N 0.4

0.2 -

ROLLING

WHEEL \

DRY CONCRETE

--CONCRETE

\-

\ \ LIGHT RAIN

\

\

HEAVY RAIN

I i- LOCKED

WHEEL

IO 20 30 40 50 60 70 80 90 100

PER CENT SLIP

Figure 6.7 1. Braking Perhnance

NAVWEPS DD-BOT-BO

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

BRAKING TECHNIQUE. It must be

clearly distinguished that the techniques for

minimum stop distance may differ greatly from

the techniques required to minimize wear and

tear on the tires and brakes. For the majority

of airplane configurations, brakes will provide

the most important source of deceleration for

all but the most severe of icy runway condi-

tions. Of course, aerodynamic drag is very

durable and should be utilized to decelerate the

airplane if the runway is long enough and the

drag high enough. Aerodynamic drag will be

of importance only for the initial 20 to 30 per-

cent of speed reduction from the point of touch-

down. At speeds less than 60 to 70 percent of

the landing speed, aerodynamic drag is of little

consequence and brakes will be the principal

source of deceleration regardless of the runway

surface. For the conditions of minimum land-

ing distance, aerodynamic drag will be a prin-

cipal source of deceleration only for the initial

portion of landing roll for very high drag con-

figurations on very poor runway conditions.

These cases are quite limited so considerable

importance must be assigned to proper use of

the brakes to produce maximum effectiveness.

In order to provide the maximum possible

retarding force, effort must be directed to pro-

duce the maximum normal force on the braking

surfaces. (See figure 6.11.) The pilot will be

able to influence the normal force on the brak-

ing surfaces during the initial part of the land-

ing roll when dynamic pressure is large and

aerodynamic forces and moments are of conse-

quence. During this portion of the landing

roll the pilot can control the airplane lift and

the distribution of normal force to the landing

gears.

First to consider is that any positive lift will

support a part of the airplane weight and reduce

the normal force on the landing gear. Of

course, for the purposes of braking friction, it

would be to advantage to create negative lift

but this is not the usual capability of the air-

plane with the tricycle landing gear. Since

the airplane lift may be considerable immedi-

ately after landing, retraction of flaps or ex-

tension of spoilers immediately after touch-

down will reduce the wing lift and increase

the normal force on the landing gear. With

the retraction of flaps, the reduced drag is more

than compensated for by the increased braking

friction force afforded by the increased normal

force on the braking surfaces.

A second possible factor to control braking

effectiveness is the distribution of normal force

to the landing gear surfaces. The nose wheel

of the tricycle landing gear configuration usu-

ally has no brakes and any normal force dis-

tributed to this wheel is useful only for pro-

ducing side force for control of the airplane.

Under conditions of deceleration, the nose-

down pitching moment created by the friction

force and the inertia force tends to transfer

a significant amount of normal force to nose

wheel where it is unavailable to assist in

creating friction force. For the instant after

landing touchdown, the pilot may control

this condition to some extent and regain or

increase the normal force on the main wheels.

After touchdown, the nose is lowered until the

nose wheel contacts the runway then brakes

are applied while the stick is eased back with-

out lifting the nose wheel back off the runway.

The effect is to minimize the normal force on

the nose wheel and increase the normal force

on braking surfaces. While the principal

effect is to transfer normal force to the main

wheels, there may be a significant increase in

normal force due to a reduction in net lift, i.e.,

tail download is noticeable. This reduction

in net lift tends to be particular to tailless or

short coupled airplane configurations.

The combined effect of flap retraction and

aft stickis a significant increase in braking

friction force. Of course, the flaps should not

be retracted while still airborne and aft stick

should be used just enough without lifting

the nosewheel off the runway. These tech-

niques are to no avail if proper use of the

brakes does not produce the maximum coefi-

cient of friction. The incipient skid condi-

tion will produce the maximum coefficient of

friction but this peak is difficult to recognize

and maintain without an antiskid system.

Judicious use of the brakes is necessary to

obtain the peak coefficient of friction but not

develop a skid or locked wheel which could

cause tire failure, loss of control, or consider-

able reduction in the friction coefficient.

The capacity of the brakes must be sufficient

to create adequate braking torque and produce

the high coefficient of friction. In addition,

the brakes must be capable of withstanding

the heat generated without fading or losing

effectiveness. The most critical requirements

of the brakes occur during landing at the

maximum allowable landing weight.

TYPICAL ERRORS OF BRAKING TECH-

NIQUE. Errors in braking technique are usu-

ally coincident with errors of other sorts. For

example, if the pilot lands an airplane with

excessive airspeed, poor braking technique

could accompany the original error to produce

an unsafe situation. One common error of

of braking technique is the application of

braking torque in excess of the maximum

possible rolling torque. The result will be

that the wheel decelerates and locks and the

skid reduces the coefficient of friction, lowers

the capability for side force, and enhances the

possibility of tire failure. If maximum brak-

ing is necessary, caution must be used to

modulate the braking torque to prevent lock-

ing the wheel and causing a skid. On the

other hand, maximum coefficient of friction is

obtained at the incipient skidding condition

so sufficient brake torque must be applied to

produce maximum friction force. Intermittent

braking serves no useful purpose when the

objective is maximum deceleration because

the periods between brake application produce

only slight or negligible cooling. Brake

should be applied smoothly and braking

torque modulated at or near the peak value

to insure that skid does not develop.

NAVWEPS OD-BOT-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

One of the important factors affecting the

landing roll distance is landing touchdown

speed. Any excess velocity at landing causes

a large increase in the minimum stop distance

and it is necessary that the pilot control the

landing precisely so to land at the appropriate

speed. When landing on the dry, hard surface

runway of adequate length, a tendency is to

take advantage of any excess runway and

allow the airplane to touchdown with excess

speed. Of course, such- errors in technique

cannot be tolerated and the pilot must strive

for precision in all landings. Immediately

after touchdown, the airp1ar.e lift may be

considerable and the normal force on the

braking surfaces quite low. Thus, if excessive

braking torque is applied, the wheel may lock

easily at high speeds and tire failure may take

place suddenly.

Landing on a wet or icy runway requires

judicious use of the brakes because of the re-

duction in the maximum coefficient of friction.

Because of reduction in the maximum attain-

able value of the coefficient of friction, the

pilot must anticipate an increase in the mini-

mum landing distance above that applicable

for the dry runway conditions. When there

is considerable water or ice on rhe runway, an

increase in landing distance on the order of 40

to 100 percent must be expected for similar

conditions of gross weight, density altitude,

wind, etc. Unfortunately, the conditions

likely to produce poor braking action also

will cause high idle thrust of the turbojet

engine and the extreme case (smooth, glazed

ice or heavy rain) may dictate shutting down

the engine to effect a reasonable stopping

distance.

REFUSAL SPEEDS, LINE SPEEDS, AND

CRITICAL FIELD LENGTH

During takeoff, it is necessary to monitor

the performance of the airplane and evaluate

the acceleration to insure that the airplane will

NAVWEPS 00401-80

APPLICATION OF AERODYNAlvllCS

TO SPECIFIC PROBLEMS OF FLYING

achieve the takeoff speed in the specified dis-

tance. If it is apparent that the airplane is

not accelerating normally or that the airplane

or powerplant is not functioning properly,

a decision must be made to refuse or continue

takeoff. If the decision to refuse takeoff is

made early in the takeoff roll, no problem

exists because the airplane has not gained

much speed and a large portion of runway

distance is unused. However, at speeds near

the takeoff speed, the airplane has used a large

portion of the takeoff distance and the distance

required to stop is appreciable. The problem

which exists is to define the highest speed

attained during takeoff acceleration from which

the airplane may be decelerated to a stop on

the runway length remaining, i.e., the “refusal

speed. ’ ’

The refusal speed will be a function of take-

off performance, stopping performance, and

the length of available runway. The ideal

situation would be to have a runway length

which exceeds the total distance required to

accelerate to the takeoff speed then decelerate

from the takeoff speed. In this case, the

refusal speed would exceed the takeoff speed

and there would be little concern for the case

of refused takeoff. While this may be the

case for some instances, the usual case is that

the runway length is less than the “accelerate-

stop” distance and the refusal speed is less than

the takeoff speed. A graphical representation

of the refused takeoff condition is illustrated

in figure 6.12 by a plot of velocity versus dis-

tance. At the beginning of the runway, the

airplane starts accelerating and the variation

of velocity and distance is defined by the

takeoff acceleration profile. The deceleration

profile describes the variation of velocity with

distance where the airplane is brought to a

stop at the end of the runway. The inter-

section of the acceleration and deceleration

profiles then defines the refusal speed and the

refusal distance along the runway. Of course,

an allowance must be made for the time spent

at the refusal speed as the power is reduced

and braking action is initiated.

During takeoff, the airplane could be accel-

erated to any speed up to the refusal speed,

then decelerated to a stop on- the runway

remaining. Once past the refusal speed, the

airplane cannot be brought to a stop on the

runway remaining and the airplane is com-

mitted to an unsafe stop. If takeoff is refused

when above the refusal speed, the only hope

is for assistance from the arresting gear, run-

way barrier, or an extensive overrun at the

end of the runway. This fact points to the

need for planning of the takeoff and the require-

ment to monitor the takeoff acceleration.

If the refusal speed data are not available,

the following equations may be used to ap-

proximate the refusal speed and distance:

where

V,= refusal speed

S,= refusal distance

and for the appropriate takeoff configuration,

V,*= takeoff speed

S,,= takeoff distance

V,= landing speed

J,=landing distance

R. = runway length available

These approximate relationships do not ac-

count for the time spent at the refusal point and

must not be used in lieu of accurate handbook

data.

In the case of the single-engine airplane, the

pilot must monitor the takeoff performance to

recognize malfunctions or lack of adequate ac-

celeration prior to reaching the refusal speed.

Obviously, it is to advantage to recognize rhe

3’92

NAVWEPS OO-EOT-80

APP,LlCATlON OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

TAKEOFF SPEED TAKEOFF SPEED

REF”z

/

ACCELERATION

PROFILE

F REFUSAL DISTANCE I P P c c

TAKEOFF DISTANCE TAKEOFF DISTANCE

.DECELERATloN

PROFlLE

RUNWAY AVAILABLE I

VARIATION OF SPEED WITH DISTANCE FOR

UNIFORMLY ACCELERATED MOTION DURING

TAKEOFF ROLL

O~mi-rrmLurauLurauupuLnUFFFPI.vm

0 10 20 30 40 50 60 i-o 60 90 100

PER CENT OF TAKEOFF DISTANCE

Figure 6.12. Refused Take& and Takeof\ Velocity Variafion

NAVWEPS DD4OT-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYI’NG

possibility of a refused takeoff before exceed-

ing the refusal speed. To this end, the pilot

must carefully evaluate airplane and power-

plant performance and judge the acceleration

of the airplane by the use of “line speeds.”

The accelerated motion of the airplane during

takeoff roll will define certain relationships be-

tween velocity and distance when the acceler-

ation of the airplane is normal. By comparison

of predicted and actual speeds at various points

along the runway, the pilot can evaluate the

acceleration and assess the takeoff perfotm-

axe.

An example of an acceleration profile is

shown by the second illustration of figure 6.12,

where the variation of velocity and distance is

defined for the case of uniformly accelerated

motion, i.e., constant acceleration. While the

case of uniformly accelerated motion doesnot

correspond exactly to the takeoff performance

of all airplanes, it is sufficiently applicable to

illustrate the principle of line speeds and ac-

celeration checks. If the takeoff acceleration

of the airplane were constant, the airplane

would develop specific percentages of the take-

off speed at specific percentages of the takeoff

distance. Representative values from figure

6.12 are as follows:

Pmmr 0, ‘&Ofl diJh?%Z Pmmr of r‘iko~

"docit~

PInmr 0, &off

rim

0 0 0

25 so. 0 50.0

SO 70.7 70.7

75 86. 5 86.5

100 100 100

As an example of this uniformly accelerated

motion, the airplane upon reaching the half-

way point of takeoff roll would have spent

70.7 percent of the total takeoff time and ac-

celerated to 70.7 percent of the takeoff speed.

If the airplane has not reached a specific speed

at a specific distance, it is obvious that the ac-

celeration is below the predicted value and the

airplane surely will not achieve the takeoff

speed in the specified takeoff distance. There-

fore, properly computed line speeds at various

points along the runway will allow the pilot

to monitor the takeoff performance and recog-

nize a deficiency of acceleration. Of course,

a deficiency of acceleration must be recognized

prior to reaching some point along the runway

where takeoff cannot be safely achieved or

refused

The fundamental principles of refusal speeds

and line speeds are applicable equally well to

single-engine and multiengine airplanes. How-

ever, in the case of the multiengine airplane

additional consideration must be given to the

decision to continue or refuse takeoff when

engine failure occurs during the takeoff roll.

IF failure of one engine occurs prior to reaching

the-refusal speed, takeoff should be discon-

tinued and the airplane brought to a stop on

the remaining runway. If failure of one engine

c~curs after exceeding the refusal speed, the

airplane is committed to continue takeoff with

the remaining engines operative or an unsafe

refused take&. Sn some cases, the remaining

runway may not be sufficient to allow acceler-

ation to the takeoff speed and the airplane can

neither takeoff or stop on the runway rcmain-

ibg. To facilitate consideration of this prob-

lem, several specific defmitions are necessary.

(1) Takeoff and initial climb speed: A speed,

usually a fixed percentage above the stall speed,

at which the airplane will become airborne and

best clear obstacles immediately after takeoff.

For a particular airplane in the takeoff con-

figuration, this speed (in EAS or CM) is a

function of gross weight but in no circumstances

should it he less than the minimum directional

control speed for the critical asymmetrical

power condition. Generally, the takeoff and

initial climb speed is referred to as the “V,”

speed.

(2) Critical engine jaih~~ speed: A speed

achieved during the takeoff roll at which fail-

ure of one engine will require the same distance

to continue accelerating with the operative en-

gines to accomplish safe takeoff or refuse

takeoff and decelerate to a stop utilizing the

airplane brakes. At critical engine failure

NAVWEPS OD-BOT-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

RUNWAY LENGTH EQUAL TO CRITICAL

FIELD LENGTH

TAKEOFF d:;‘,

CLIMB SP

CRITICAL ENGINE LACCELERATION WITH 1

FAILURE SPEED q ENGINE INOPERATIVE

ACCELERATION

WITH ALL ENGINES

OPERATIVE

\

PROFILE

\

RUNWAY LENGTH

RUNWAY LENGTH LESS THAN CRITICAL

FIELD LENGTH

MINIMUM SPEED NECESSAR

TO CONTINUE TAKEOFF WITH

ONE ENGINE IN

REFUSAL SPEE LERATION WITH

ONE ENGINE INOPERATIVE

ACCELERATION DECELERATION

TH ALL ENGINES

OPERATIVE

Figure 6.13. Critical Field Len&

NAVWEPS OD-ROT-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

speed, the distance necessary to continue take-

off with one engine inoperative is equal to the

stopping distance. The critical engine failure

speed is generally referred to as the “I’,”

speed and it is a function of the same factors

which determine the takeoff performance, e.g.,

density altitude, gross weight, temperature,

humidity, etc.

(3) &t&l jield kngrh: The runway length

necessary to accelerate with all engines opera-

tive to the critical engine failure speed (VJ

then continue accelerating to the takeoff and

initial climb speed (VJ with one engine

inoperative and achieve safe takeoff or refuse

takeoff. By this definition, critical field

length describes the minimum length of run-

way necessary for safe operation of the multi-

engine airplane. Obviously, the critical field

length is a function of the same factors affect-

ing the takeoff distance of the airplane.

The conditions of Vi, V,, and critical field

length are illustrated by figure 6.13. The

first illustration of figure 6.13 depicts the

case where the runway length is equal to the

rritical jield kngth. In this case, the airplane

could accelerate to Vi with all engines opera-

tive then either continue takeoff safely with

one engine inoperative or refuse takeoff and

decelerate to a stop on the remaining runway.

For this condition, an engine failure occurring

at lefs than I’, speed dictates that takeoff must

be refused because inadequate distance remains

to effect a safe takeoff at V, speed. However,

at or below V, speed, adequate distance re-

mains to bring the airplane to a stop. If

engine failure occurs at some speed greater

than Vi speed, takeoff should be continued

because adequate distance remains to accelerate

to V, speed and effect a safe takeoff with one

engine inoperative. If engine failure occurs

beyond Vi speed, inadequate distance remains

to brake the airplane to a stop on the runway,

The second illustration of figure 6.13 depicts

the case where the ranway length is 1~s than

the titical field length. In this case, the term

of “V,” speed is not applicable because of

inadequate distance and the refusal speed is

less than the minimum speed necessary to

continue a safe takeoff with one engine inoper-

ative. If engine failure occurs below refusal

speed, the takeoff must be refused and adequate

distance remains to effect a stop on the runway.

If engine failure occurs above refusal speed

but below the minimum speed necessary to

continue takeoff with one engine inoperative,

an accident is inevitable. Within this range

of speeds, the airplane cannot effect a safe

takeoff at L’s with one engine inoperative or

a safe stop on the remaining runway. For this

reason, the pilot must properly plan the

takeoff and insure that the runway available

is equal to or greater than the critical field

length. If the runway available is less than

the critical field length, there must be sufficient

justification for the particular operation be-

cause of the hazardous consequences of engine

failure between the refusal speed and the

minimum speed necessary to continue takeoff

with one engine inoperative. Otherwise, the

gross weight of the airplane should be reduced

in attempt to decrease the critical field length

to equal the available runway.

SONIC “BOOMS’

From the standpoint of public relations

and the maintaining of friendly public support

for Naval Aviation, great care must be taken

to prevent sonic booms in populated areas.

While the ordinary sonic boom does not carry

any potential of physical damage, the disturb-

ance must be avoided because of the undesirable

annoyance and apprehension. As supersonic

flight becomes more commonplace and an

ordinary consequence of flying operations, the

prevention of sonic booms in populated areas

becomes a difficult and perplexing job.

When the airplane is in supersonic flight,

the local pressure and velocity changes on the

airplane surfaces are coincident with the

formation of shock waves. The pressure jump

through the shock waves in the immediate

vicinity of the airplane surfaces is determined

by the local flow changes at these surfaces.

Of course, the strength of the shock waves

and the pressure jump through the wave

decreases rapidly with distance away from the

airplane. While the pressure jump through

the shock wave decreases with distance away

from the surface, it does not disappear com-

pletely and a measurable-but very small-

pressure will exist at a considerable distance

from the airplane.

Sound is transmitted through the air as a

series of very weak pressure waves. In the

ordinary range of audible frequencies, the

threshold of audibility for intensity of sound

is for pressure waves with an approximate

R.M.S. value of pressure as low as 0.0000002

psf. Within this same range of frequencies,

the threshold of feeling for intensity of sound

is for pressure values with an approximate

R.M.S. value of pressure of 0.2 to 0.5 psf.

Continuous sound at the threshold of feeling

is of the intensity to cause painful hearing.

Thus, the shock waves generated by an air-

plane in supersonic flight are capable of creat-

ing audible sound and, in the extreme case, can

be of a magnitude to cause considerable dis-

turbance. Pressure jumps of 0.02 to 0.3 psf

have been recorded during the passage of an

airplane in supersonic flight. As a result,

the sonic “booms” are the pressure waves

generated by the shock waves formed on the

airplane in supersonic flight.

The source of sonic booms is illustrated by

figure 6.14. When the airplane is in level

supersonic flight, a pattern of shock waves is

developed which is much dependent on the

configuration and flight Mach number of the

airplane. At a considerable distance from the

airplane, these shock waves tend to combine

along two common fronts and extend away

from the airplane in a sort of conical surface.

The waves decrease in strength with distance

away from the airplane but the pressure jump

remains of an audible intensity for a consider-

able distance from the airplane. If the wave

extends to the ground or water surface, it will

NAVWEPS OD-8OT-RO

APP,LICATlON OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

be reflected and attenuated to some extent

depending on the character of the reflecting

surface. Of course, if this attached wave form

is carried,across a populated area at the surface,

th.- population will experience the pressure

waves as a sonic boom.

The intensity of the boom will depend on

many different factors. The characteristics of

the airplane generating the shock waves will

be of some importance since a large, high drag,

high gross weight airplane in flight at high

Mach number will be transferring a greater

energy to the air mass. Flight altitude will

have an important bearing on boom intensity

since at high altitude the pressure jump across

a given wave form is much less. In addition,

at high altitude a greater distance exists be-

tween the generating source of the pressure

disturbance and the ground level and the

strength of the wave will have a greater dis-

tance in which to decay. The ordinary vari-

ation of temperature and density plus the

natural turbulence of atmosphere will tend to

reflect or dissipate the shock wave generated

at high altitude. However, in a stable, quies-

cent atmosphere, the pressure wave from the

airplane in high supersonic flight at high alti-

tude may be of an audible magnitude at lateral

distances as great as 10 to 30 miles. Thus,

supersonic flight over or adjacent to populated

areas will produce a sonic boom.

Actually, it is not necessary for any airplane

to fly supersonic over or adjacent to a popu-

lated area to create a sonic boom. This

possibility is shown by the second illustration

of figure 6.14 where an airplane decelerates to

subsonic from a supersonic dive. As the air-

plane slows to subsonic from supersonic speed,

the airplane will release the leading bow and

tail waves which formed as the airplane accel-

erated from subsonic to supersonic speed. The

release of these shock waves is analogous to

the case where a surface ship slows to below

the wave propagation speed and releases the

bow wave which then travels out ahead of

NAVWEPS oo-8OT-80

APPUCATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYllNG

AIRPLANE IN SUPERSONIC FLIGHT

‘AIL WAVE

FLIGHT

Revised JonuaV 1965

Figure 6.14. Sonic Booms

the ship. When the airplane slows to sub-

sonic, the shock wave travels out ahead of the

airplane in a form which is somewhat spheri-

cal. Because there are density variations

through the shock wave, the shock wave

moving ahead of the airplane can cause aber-

rations in light waves and it may appear.to

the pilot as if a large sheet of clear cellulose

or plastic were in front of the airplane. In

addition, the density variation and initial

shape of the wave leaving the airplane may

cause reflection of sunlight which would

appear as a sudden, brilliant “flash” to the

pilot.

Of course, the wave released by decelerating

to subsonic speed can travel out ahead of the

airplane and traverse a populated area to cause

a sonic boom. The initial direction of the

released wave will be the flight path of the

airplane at the instant it decelerates to sub-

sonic speed. To be sure, the released wave

should not be aimed in the direction of a popu-

lated area, even if a considerable distance

away. There are instances where a released

wave has been of an audible magnitude as far

as 30 to 40 miles ahead of the point of release.

The released pressure wave will be of greatest

intensity when created by a large, high drag

configuration at low altitude. Since the wave

intensity decreases rapidly with distance away

from the source, the boom will be of strongest

audibility near the point of release.

It should become apparent that sonic booms

are a byproduct of supersonic aviation and,

with supersonic flight becoming more common-

place, the problem is more perplexing. The

potential of sonic booms is mostly of the

audible nature and nuisance of the disturbance.

The damage potential of the ordinary sonic

boom is quite small and the principal effects

are confined to structures which are extremely

brittle, low strength, and have characteristic

high residual stresses. In other words, only

the extremes of pressure waves generated by

airplanes in flight could possibly cause cracked

plaster and window glass. Such materials

NAVWEPS OD-ROT-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

are quite prone to sharp dynamic stresses and,

when .superimposed on the high residual

stresses common to the products and building

construction, slight but insignificant damage

may result. Actually, the most objectionable

feature of the sonic boom is the audibility and

the anxiety or apprehension caused by the

sharp, loud noise which resembles a blast.

The pressure jump through the shock waves

in the immediate vicinity of the airplane is

much greater than those common to the

audible “booms” at ground level. Thus,

airplanes in close formation at supersonic

speeds may encounter considerable interference

between airplanes. In addition, to eliminate

even the most remote possibility of structural

damage, a high speed airplane should not

make a supersonic pass close to a large air-

plane which may have low limit load factor

and be prone to be easily disturbed or damaged

by a strong pressure wave.

HELICOPTER PROBLEMS

The main difference between helicopter and

an airplane is the main source of lift. The

airplane derives its lift from a fixed airfoil

surface while the helicopter derives lift from

a rotating airfoil called the rotor. Hence, the

aircraft will be classified as either “fixed-

wing” or “rotating wing.” The word “heli-

copter” is derived from the Greek words

meaning “helical wing” or “rotating wing. ”

Lift generation, by a “rotating wing” enables

the helicopter to accomplish its unique mission

of hovering motionless in the air, taking off

and landing in a confined or restricted area,

and autorotating to a safe landing following

a power failure. Lift generation by “rotating

wing’ ’ is also responsible for some of the

unusual problems the helicopter can encounter.

Since the helicopter problems are due to par-

ticular nature of .the rotor aerodynamics, the

basic flow conditions within the rotor must be

considered in detail. For simplicity, the

initial discussion will consider only the hover-

ing rotor. Although the term hovering

NAVWEPS DO-ROT-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

usually means remaining over a particular

spot on the ground, it shall be considered

here as flight at zero airspeed. This is necessary

because the aerodynamic characteristics of the

rotor depend on its motion with respect to

the air and not the ground. Hovering in a 20

knot wind is aerodynamically equivalent to

flying at an airspeed of 20 knots in a no-wind

condition, and the characteristics will be

identical in the two conditions.

The first point to realize is that the rotor is

subject to the same physical laws of aero-

dynamics and motion that govern flight of

the fixed-wing airplane. The manner in which

the rotor is subject to these laws is much more

complicated due to the complex flow con-

ditions.

Rotor lift can be explained by either of two

methods. The first method, utilizing simple

momentum theory based on Newton’s Laws,

merely states that lift results from the rotor

accelerating a mass of air downward in the

same way that the jet engine develops thrust

by accelerating a mass of air out the tailpipe.

The second method of viewing rotor lift

concerns the pressure forces acting on the

various sections of the blade from root to tip.

The simple momentum theory is useful in

determining only lift characteristics while

the “blade element” theory gives drag as

well as lift characteristics and is useful in

giving a picture of the forces at work on the

rotor. In the “blade element” theory, the

blade is divided up into “blade elements” as

shown in figure 6.15. The forces acting on

each blade element are analyzed. Then the

forces on all elements are summed up to give

the characteristics of the whole rotor. The

relative wind acting on each segment is the

resultant of two velocity components: (1) the

velocity due CO the rotation of the blades

about the hub and (2) the induced velocity,

or downwash velocity caused by the rotor.

the velocity due to rotation at a particular

element is proportional to the rotor speed and

the distance of the element from the rotor hub.

Thus, the velocity due to rotation varies line-

arly from zero at the hub to a maximum at

the tip. A typical blade section with the

forces acting on it is shown in figure 6.15.

A summation of the forces acting perpen-

dicular to the plane of rotation (tip path plane)

will determine the rotor thrust (or lift) char-

acteristics while summation of the moments

resulting from forces acting in the plane of

rotation will determine the rotor torque char-

acteristics. As a result of this analysis, the

rotor thrust (or lift) is found to be propoc-

tional to the air density, a nondimensional

thrust coefficient, and the square of the tip

speed, or linear speed of the tip of the blade.

The thrust coefficient is a function of the aver-

age blade section lift coefficient and the rotor

solidity, which is the proportion of blade area

to disc area. The lift coefficient is identical to

that used in airplane aerodynamics while the

solidity is analagous to the aspect ratio in air-

plane aerodynamics. The rotor torque is

found to be proportional to a nondimensional

torque coefficient, the air density, the disc

area, the square of the tip speed, and the blade

radius. The torque coefficient is dependent

upon the average profile drag coefficient of the

blades, the blade pitch angle, and the average

lift coefficient of the blades. The torque can

be thought to result from components of profile

and induced drag forces acting on the blades,

similar to those on an airplane.

As in the airplane, there is one angle of

attack or blade pitch condition that will result

in the most efficient operation. Unfortu-

nately, the typical helicopter rotor operates

at a near constant RPM and thus a constant

true airspeed and cannot operate at this most

eficient condition over a wide range of altitude

and gross weight as the fixed-wing airplane.

The airplane is able to maintain an efficient

angle of attack at various altitudes, and gross

weights by flying at various airspeeds but the

helicopter will operate with a near constant

rotor velocity and vary blade angle to contend

with variations in altitude and gross weight.

MAVWEPS 00-BOT-80

APPLICATION OF AEBODYNAMICS

TO SPECIFIC PBOBLEMS OF FLYING

ROTOR BLADE ELEMENT

RELATIVE -

ROTATION WIND COMPONENT

DUE TO ROTATION

LOCAL FLOW AT BLADE ELEMENT

VELOCITY DUE

RESULTANT

RELATIVE VELOCITY

--_

TIP PATH PLANE

Figure 6.75. Rotor Blade Flemenf Aerodynamics

NAVWEPS oo-80~-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYl,NG

If the rotor could operate within a wide

range of rotor speed, the efficiency and per-

formance could be improved.

With the previous relationships established

for the rotor in hovering flight, the effect of

forward flight br rotor translation can be con-

sidered. With forward flight, a third velocity

component, that tif the forward velocity of the

helicopter, must be considered in determining

the relative wind acting on each rotor blade

element. Since the entire rotor moves with the

helicopter, the velocity of air passing over

each of the elements on the advancfng blade is

increased by the forward speed of the heli-

copter and the velocity of the air passing over

each element of the retreating blade is de-

creased by the same amount. This is shown in

figure 6.16.

If the blade angles of attack on both advanc-

ing and retreating blades remained the same

as in hovering flight, the higher velocity on

the advancing blade would cause a dissym-

metry of lift and the helicopter would tend to

roll to the left. It was this effect that created

great difficu!ty during many early helicopter

and autogiro projects. Juan De La Cierva was

the first to realize what caused this effect and

he solved the problem by mounting his auto-

giro blades individually on flapping hinges,

thus allowing a flapping action to automati-

cally correct the dissymmetry of lift that re-

sulted from forward flight. This is the method

still used in an articulated rotor system today.

The see-saw, or semi-rigid, rotor corrects the

lift dissymmetry by rocking the entire hub and

blades about a gimbal joint, By rocking the

entire rotor system forward, the angle of at-

tack on the advancing blade is reduced and

the angle of attack on the retreating blade is

increased. The rigid rotor must produce cyclic

variation of the blade pitch mechanically as

the blade rotates to eliminate the lift dissym-

metry. Irrespective of the method used to

correct the dissymmetry of lift, identical aero-

dynamic characteristics result. Thus, what is

said about rotor aerodynamics is equally valid

for all types of rotor systems.

By analyzing the velocity components acting

on the rotor blade sections from the blade

root to the tip on both advancing and retreat-

ing blades, a large variation of blade section

angle of attack is found. Figure 6.16 illus-

trates a typical variation of the local blade

angle of attack for various spanwise positions

along the advancing and retreating blades of

a rotor at high forward speed. There is a

region of positive angles of attack resulting

in positive lift over the entire advancing blade.

Immediately next to the hub of the retreating

blade there is an area of reversed flow where

the velocity due to the forward motion of the

helicopter is greater than the rearward velocity

due to the blade rotation. The next area is a

negative stall region where, although the

flow is in the proper direction relative the

blade, the angle of attack exceeds that for

negative stall. Progressing out the retreating

blade, the blade angle of attack becomes less

negative, resulting in an area of negative lift.

Then the blade angle becomes positive again,

resulting in a positive lift region. The blade

angle continues to increase, until near the tip

of the retreating blade the positive stall angle

of attack is exceeded, resulting in stalling of

the tip section. This wide variation in blade

section angles of attack results in a large

variation in blade section lift and drag coefK-

cients. The overall lift force on the left and

right sides of the rotor disc are equalized by

cyclically varying the blade pitch as explained

previously, but the drag variation is not

eliminated. This drag variation causes a

shaking force on the rotor system and con-

tributes to the vibration of the helicopter.

RETREATING BLADE STALL. Retreat-

ing blade stall results whenever the angle of

attack of the blade exceeds the stall angle of

attack of the blade section. This condition

occurs in high speed flight at the tip of the

retreating blade since, in order to develop the

same lift as the advancing blade, the retreating

NAVWEPS OO-ROT-RO

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

VELOCITY DUE

TO FORWARD

FLIGHT

RETREATING GLADE

VELOCITY DUE

TO ROTATION

REVERSED FLOW

NEGATIVE STALL

NEGATIVE LIFT

VELOCITY DUE

I - POSITIVE STALL ANGLE

LOCAL I/

BLADE

ANGLE OD- nrc7 I

OF HUB

ATTACK

ETRiATING BLADE

-lop I _- - - NEGATIVE STALL ANGLE

,

-ADVANCING

BLADE

Figure 6.16. Rotor Flow Conditions in Forward f/i&

NAVWEPS OD-80140

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

blade must operate at a greater angle of attack.

If the blade pitch is increased or the forward

speed increased the stalled portion of the rotor

disc becomes larger with the stall progressing

in toward the hub from the tip of the retreating

blade. When approximately 15 percent of

the rotor disc is stalled, control of the heli-

copter will be impossible. Flight tests have

determined that control becomes marginal and

the stall is considered severe when the outer

one-quarter of the retreating blade is stalled.

Retreating blade stall can be recognized by

rotor toughness, erratic stick forces, a vibration

and stick shake with a frequency determined

by the number of blades and the rotor speed.

Each of the blades of a three-bladed rotor will

stall as it passes through the stall region and

create a vibration with three beats pet rotor

revolution. Other evidence of retreating blade

stall is partial or complete loss of control or a

pitch-up tendency which can be uncontrollable

if the stall is severe.

Conditions favorable for the occurrence of

retreating blade stall are those conditions that

result in high retreating blade angles of attack.

Each of the following conditions results in a

higher angle of attack on the retreating blade

and may contribute to retreating blade stall:

1. High airspeed

2. Low totor RPM-operation at low

rotor RPM necessitates the use of

higher blade pitch to get a given

thrust from the rotor, thus a higher

angle of attack

3. High gross weight

4. High density altitude

5. Accelerated flight, high load factor

6. Flight through turbulent air or gusts-

sharp updrafts result in temporary

increase in blade angle of attack

7. Excessive ot abrupt control deflections

during maneuvers

Recovery from a stalled condition can be

effected only by decreasing the blade angle of

attack below the stall angle. This can be

accomplished by one or a combination of the

following items depending on severity of the

stall:

1. Decrease collective pitch

2. Decrease airspeed

3. Increase rotor RPM

4. Decrease severity of accelerated ma-

newer or control deflection

If the stall is severe enough to result in pitch-up,

forward cyclic to attempt to control pitch-up

is ineffective and may aggravate the stall since

forward cyclic results in an increase in blade

angle of attack on the retreating blade. The

helicopter will automatically recover from

a severe stall since the airspeed is decreased in

the nose high attitude but recovery can be

assisted by gradual reduction in collective

pitch, increasing RPM, and leveling the heli-

copter with pedal and cyclic stick.

From the previous discussion, it is apparent

that there is some degree of retreating blade

stall even at moderate airspeeds. However,

the helicopter is able to perform satisfactorily

until a sufficiently large area of the rotor disc

is stalled. Adequate warning of the impend-

ing stall is present when the stall condition

is approached slowly. There is inadequate

warni,ng of the stall only when the blade pitch

or blade angle of attack is increased rapidly.

Therefore, unintentional severe stall is most

likely to occur during abrupt control motions

or rapid accelerated maneuvers.

COMPRESSIBILITY EFFECTS. The highest

relative velocities occur at the tip of the ad-

vancing blade since the speed of the helicopter

is added to the speed due to rotation at this

point. When the Mach number of the tip

section of the advancing blade exceeds the

critical Mach number for the rotor blade sec-

tion, compressibility effects result. The criti-

cal Mach number is reduced by thick, highly

cambered airfoils and critical Mach number

decreases with increased lift coefficient. Most

helicopter blades have symmetrical sections

and therefore have relatively high critical

Mach numbers at low lift coefhcients. Since

the principal effects of compressibility are the

large increase in drag and rearward shift of the

airfoil aerodynamic center, compressibility ef-

fects on the helicopter increase the power te-

quired to maintain rotor RPM and cause rotor

roughness, vibration, stick shake, and an un-

desirable structural twisting of the blade.

Since compressibility effects become more

severe at higher lift coefficients (higher blade

angles of attack) and higher Mach numbers,

the following operating conditions represent

the most adverse conditions from the stand-

point of compressibility:

1. High airspeed

2. High rotor RPM

3. High gross weight

4. High density altitude

5. Low temperature-the speed of sound

is proportional to the square root of

the absolute temperature. Therefore,

sonic velocity will be more easily

obtained at low temperatures when

the sonic speed is lower.

6. Turbulent air-sharp gusts momen-

tarily increase the blade angle of

attack and thus lower the critical

Mach number to the point where

compressibility effects may be en-

countered on the blade.

Compressibility effects will vanish by de-

creasing the blade pitch. The similarities in

the critical conditions for retreating blade

stall and compressibility should be noticed

but one basic difference must be appreciated-

compressibility occurs at HIGH RPM while

retreating blade stall occurs at LOW RPM.

Recovery technique is identical for both with

the exception of RPM control.

AUTOROTATION CHARACTERISTICS.

One of the unique characteristics of helicopters

is their ability to take part of the energy of

the airstream to keep the rotor turning and

glide down to a landing with no power.

Consideration of the rotor during a vertical

autorotation will provide an understanding of

why the rotor continues to rotate without

power. During autorotation, the flow of air

NAVWEPS CID-ROT-R0

APP,LlCATlON OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYmING

is upward through the rotor disc and there is

a vertical velocity component equal to the

rate of descent of the helicopter. In addition,

there is a velocity component due to rotation

of the rotor. The vector sum of these two

velocities is the relative wind for the blade

element. The forces resulting from the relative

wind on each particular blade section will

provide the reason why the rotor will continue

to operate without power. First, consider, a

blade element near the tip of the blade as illus-

trated in figure 6.17. At this point there is

a lift force acting perpendicular to the relative

wind and a drag force acting parallel to the

relative wind through the aerodynamic center.

Since the rotation of the rotor is affected only

by forces acting in the plane of rotation, the

important forces are components of the lift

and drag force in the plane of rotation. In

this low angle of attack high speed tip section,

the net in-plane force is a drag force which

would tend to retard the rotor. Next, con-

sider a blade section at about the half-span

position as illustrated in figure 6.17. In this

case, the same forces are present, but the iti-

plane component of lift force is greater than

the drag force and this results in a net thrust

or forward force in the plane of rotation which

tends to drive the rotor.

During a steady autorotation, there is a

balance of torque from the forces along the

blade so that the RPM is maintained in equi-

librium at some particular value. The region

of the rotor disc where there is a net drag force

on the blade is called the “propeller region”

and the region of the rotor disc where there

is a net in-plane thrust force is called the

“autorotation region.” These regions are

shown for vertical autorotation and forward

speed (or normal) autorotation in figure 6.17.

Forces acting on the rotor blades in forward

flight autorotation are similar to those in

vertical autorotation but the difference will

consist mainly of shifts of the autorotation

region to the left and the addition of reverse

NAVWEPS 004oT-80

APPLICATION 0~ AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

LIFT FORCES IN THE

AUTOROTATION REGION

FORCES IN THE

PROPELLER REGION I

LIFT

’ \ DRAG

RESULTANT

VELOCITi DUE TO

ROTe;TION

FLIGHT 1

I DIRECTION

UTOROTATION

VERTICAL AUTOROTATION FORWARD FLIGHT

AUTQRQTa-i\QN

Figure 6.17. Rotor Autorotation Flaw Conditions

flow and negative stall regions similar to the

powered flight condition.

Autorotation is essentially a stable flight

condition. If external disturbances cause the

rotor to slow down, the autorotation region of

the disc automatically expands to restore the

rotor speed to the original equilibrium condi-

tion. On the other hand, if an external

disturbance causes the rotor to speed up, the

propeller region automatically expands and

tends to accelerate the rotor to the original

equilibrium condition. Actually the stable

autorotation condition will exist only when

the autorotational speed is within certain

limits. If the rotor speed is allowed to slow

some excessive amount, then the rotor becomes

unstable and the RPM will decrease even

further unless the pilot immediately corrects

the condition by proper control action.

In case of engine failure, the fixed-wing

airplane will be glided at maximum lift-drag

ratio to produce maximum glide distance. If

minimum rate of descent is desired in power-off

flight rather than maximum glide distance, the

fixed-wing airplane will be flown at some

lower airspeed. Actually, the minimum rate

of descent will occur at minimum power

required. The helicopter exhibits similar char-

acteristics but ordinarily the best autorota~tion

speed may be considered that speed that results

in the minimum rate of descent rather than

maximum glide distance. The aerodynamic

condition of the rotor which produces mini-

mum rate of descent is:

Maximum ratio of

(Mean blade lift coetIicient)3”

Mean blade drag coefficient

It is this ratio which determines the auto-

rotation rate of descent. Figure 6.18 illus-

trates the variation of autorotation rate of

descent with equivalent airspeed for a typical

helicopter. Point A on this curve defines the

point which produces autorotation with mini-

mum rate of descent. Maximum glide distance

NAVWEPS OO-BOT-BO

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYl,NG

during autorotation descent would be obtained

at the flight condition which produces the

greatest proportion between airspeed and rate

of descent. Thus, a straight line from the

origin tangent to the curve will define the

point for maximum autorotative glide dis-

tance. This corresponds to Point B of figure

6.18. If the helicopter is being glided at the

speed for maximum glide distance, a decrease

in airspeed would reduce the rate of descent

but the glide distance would decrease. If the

helicopter is being glided at the speed for

minimum rate of descent, the rate of descent

(steady state) can not be reduced but the glide

distance can be increased by increasing the

glide speed to that for maximum distance.

Weight and wind affect the glide character-

istics of a helicopter the same way an airplane

is affected. Ideally, the helicopter autorotates

at a higher equivalent airspeed at higher gross

weight or when autorotating into a headwind.

In addition to aerodynamic forces which act

on the rotor during autorotation, inertia forces

are also important. These effects are usually

associated with the pilot’s response time be-

cause the rate a pilot reacts to a power failure

is quite critical. The time necessary to reduce

collective pitch and enter autorotation be-

comes critical if the rotor inertia characteristics

are such as to allow the rotor to slow down to

a dangerous level before the pilot can react.

With power on, the blade pitch is relatively

high and the engine supplies enough torque to

overcome the drag of the blades. At the

instant of power failure the blades are at a high

pitch with high drag. If there is no engine

torque to maintain the RPM, the rotor will

decelerate depending on the rotor torque and

rotor inertia. If the rotor has high rotational

energy the rotor will lose RPM less rapidly,

giving the pilot more time to reduce collective

pitch and enter autorotation. If the rotor has

low rotational energy, the rotor will lose RPM

rapidly and the pilot may not be able to react

quickly enough to prevent a serious loss of

rotor RPM. Once the collective pitch is at

PdAVWEPS OD-BOT-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

the low pitch limit, the rotor RPM can be in-

creased only by a sacrifice in altitude or air-

speed. If insufficient altitude is available to

exchange for rotor speed, a hard landing is

inevitable. SufIicient rotor rotational energy

must be available to permit adding collective

pitch to reduce the helicopter’s rate of descent

before final ground contact.

In the case of most small helicopters, at

least 300 feet of altitude is necessary for an

average pilot to set up a steady autorotation

and land the helicopter safely without damage.

This minimum becomes 500 to 600 feet for the

larger helicopters, and will be even greater for

helicopters with increased disc loading. These

characteristics are usually presented in the

flight handbook in the form of a “dead man’s

curve” which shows the combinations of air-

speed and altitude above the terrain where a

successful autorotative landing would be dish-

cult, if not impossible.

A typical “dead man’s curve” is shown in

figure 6.18. The most critical combinations

are due to low altitude and low airspeed illus-

trated by area A of figure 6.18. Less critical

conditions exist at higher airspeeds because of

the greater energy available to set up a steady

autorotation. The lower limit of area A is a

finite altitude because the helicopter can be

landed successfully if collective pitch is held

rather than reduced. In this specific case there

is not sufficient energy to reach a steady state

autorotation. The maximum altitude at which

this is possible is approximately ten feet on

most helicopters.

Area B on the “dead man’s curve” of figure

6.18 is critical because of ground contact flight

speed or rate of descent, which is based on the

strength of the landing gear. The average

pilot may have difhculty in successfully flaring

the helicopter from a high speed flight con-

dition without allowing the tail rotor to strike

the ground or contacting the ground at an ex-

cessive airspeed. A less critical zone is some-

times shown on this curve to indicate that

higher ground contact speeds can be permitted

when the landing surface is smooth. In ad-

dition, various stability and control character-

istics of a helicopter may produce critical con-

ditions in this area. The critical areas of the

“dead man’s curve” should be avoided unless

such operation is a specific mission require-

ment.

POWER SETTLING. The term “power

settling” has been used to describe a variety of

flight conditions of the helicopter. True

“power settling” occurs only when the heli-

copter rotor is operating in a rotary flow

condition called the “vortex ring state.”

The flow through the rotor in the “vortex

ring state” is upward near the center of the

disc and downward in the outer portion,

resulting in a condition of zero net thrust on

the rotor. If the rotor thrust is zero, the

helicopter is effectively free-falling and ex-

tremely high rates of descent can result.

The downwash distribution within the

rotor is shown in figure 6.19 for the conditions

of normal hovering and power settling. Part

A of figure 6.19 illustrates the typical down-

wash distribution for hovering flight. If

sufficient power were not available to hover

at this condition, the helicopter would begin

to settle at some rate of descent depending on

the deficiency of power. This rate of descent

would effectively decrease the downwash

throughout the rotor and result in a redistri-

bution of downwash similar to Part B of

figure 6.19. At the outer portion of the

rotor disc, the local induced downwash veloc-

ity is greater than the rate of descent and

downflow exists. At the center of the rotor

disc, the rate of descent is greater than the

local induced downwash velocity and the

resultant flow is upward. This flow condition

results in the rotary “vortex ring” state. By

reference to the basic momentum theory it is

apparent that the rotor will produce no thrust

in this condition if the net mass flow of air

through the rotor is zero. It is important to

note that the main lifting part of the rotor is

not stalled. The rotor roughness and loss of

NAVWEPS OO-BOT-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

RATE

OF

DESCENT,

FPM

POWER

OFF

MINIMUM

RATE OF

/ DESCENT

I VELOCITY, KNOTS

DEAD MAN’S CURVE

ALTITUDE ~

ABOVE

TERRAIN

SAFE

F T.

VELOCITY, KNOTS

Figure 6.1%. Autorotation Characteristics

NAVWEPS DO-BOT-BO

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

VARIATION OF INDUCED VELOCITY

ALONG THE BLADE SPAN DURING

HOVERING FLIGHT

VARIATION OF INDUCED VELOCITY

ALONG THE BLADE SPAN DURING

VORTEX RING STATE

VORTEX RING STATE

Figure 6.79. Rotor Downwash Distribution

control experienced during “power settling”

results from the turbulent rotational flow on

the blades and the unsteady shifting of the

flow in and out spanwise along the blade.

There is an area of positive thrust in the outer

portion of the rotor as a result of the mass of

air accelerated downward and an area of

negative thrust at the center of the rotor as a

result of the mass of air flowing upward. The

rotor is stalled only near the hub but no

important effect is contributed because of the

low local velocities.

Operation in the “vortex ring” state is a

transient condition and the helicopter will

seek equilibrium by descending. As the heli-

copter descends, a greater upflow through the

disc results until eventually the flow is entirely

up through the rotor and the rotor enters auto-

rotation where lower rates of descent can be

achieved. Unfortunately, considerable alti-

tude will be lost before the autorotative type

of flow is achieved and a positive recovery

technique must be applied to minimize the loss

of altitude. “Power settling” can be recog-

nized by rotor roughness, loss of control due

to the turbulent rotational flow, and a very

high rate of descent (as high as 3,000 fpm).

It is most likely to be encountered inadvert-

ently when attempting to hover when suf-

ficient power is not available because of high

gross weight or high density altitude.

Recovery from “power settling” can be ac-

complished by getting the rotor out of the

“vortex ring state.” If the condition is en-

countered with low power, rapid application

of full power may increase the downwash suf-

ficiently to get .the rotor out of the condition.

If the condition is encountered at high or

maximum power or, if maximum power does

not effect a recovery, increasing airspeed by

diving will result in recovery with minimum

loss of altitude. This type of recovery is most

effective but adequate cyclic control must be

available. If cyclic control has been lost, re-

covery must be effected by reducing power and

collective pitch and entering autorotation.

NAVWEPS OD-EOT-80

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYING

When normal autorotation has been estab-

lished, a normal power recovery from the auto-

rotation can be made. While such a recovery

technique is effective, considerable altitude

may be lost. Hence, diving out of the power

settling condition provides the most favorable

means of recovery.

Actually, real instances of true “power

settling” are quite rare. A condition often

described incorrectly as “power settling” is

merely a high sink rate as a result of insufficient

power to terminate an approach to landing.

This situation frequently occurs during high

gross weight or high density altitude operation.

The flow conditions within the rotor are quite

normal and there is merely insufficient power

to reduce rate of descent and terminate an

approach. Such a situation becomes more

critical with a steep approach since the more

rapid descent will require more power to

terminate the approach.

THE FLIGHT HANDBOOK

For the professional aviator, there are few

documents which are as important as the air-

plane flight handbook. The information and

data contained in the various sections of the

flight handbook provide the basis for safe and

effective operation of the airplane.

Various sections of the flight handbook are

devoted to the following subjects:

(1) Equipment and Systems. With the me-

chanical complexity of the modern airplane,

it is imperative that the pilot be familiar with

every item of the aircraft. Only through exact

knowledge of the equipment can the pilot

properly operate the airplane and contend

with malfunctions.

(2) Operating Procedures. Good procedures

are mandatory to effect safe operation of the

airplane and its equipment. The complexity

of modern equipment dictates the use of special

and exact procedures of operation and any

haphazard or non-standard procedure is an

NAVWEPS O&ROT-SO

APPLICATION OF AERODYNAMICS

TO SPECIFIC PROBLEMS OF FLYl.NG

invitation for trouble of many sorts. The

normal and emergency procedures applicable

to each specific airplane will insure the

proper operation of the equipment.

(3) Operating Limitatiom. The operation of

the airplane and powerplant must be conducted

within the established limitations. Failure

to do so will invite failure or malfunction of

the equipment and increase the operating cost

or possibly cause an accident.

(4) Flight Characteristics. While all aircraft

will have certain minimum requirements for

flying qualities, the actual peculiarities and

special features of specific airplanes will differ.

These particular flight characteristics must be

well known and understood by the pilot.

(5) Operating Data. The performance of

each specific airplane defines its application to

various uses and missions. The handbook

operating data must be available at all times

to properly plan and elnccate the flight of an

aircraft. Constant reference to the operating

data will insure safe and effective operation

of the airplane.

Great time and effort are expended in the 1

preparation of the flight handbook to provide

the most exact information, data, and pro-

cedures. Diligent study and continuous UC

of the flight handbook will ensure that the

greatest effectiveness is achieved from the

airplane while still operating within the

inherent capabilities of the design.

NAVWEPS 00-802-30

SELECTED REFERENCES

SELECTED REFERENCES

1. Dommasch, Sherby, and Connolly

“Airplane Aerodynamics”

Pitman Publishing Co.

2d Edition, 1957

2. Perkins and Hage

“Airplane Performance, Stability, and Control”

John Wiley and Sons

3. E. A. Bonney

“Engineering Supersonic Aerodynamics”

McGraw-Hill Book Co.

4. Hurt, Vernon, and Martin

“Aeronautical Engineering, Section I, Manual of Instruction, Avi-

ation Safety Officer Course”

University of Southern California

5. Fairchild, Magill, and Brye

“Principles of Helicopter Engineering”

University of Southern California

Revised January 1965

NAVWEPS 00-8OT-80

INDEX

INDEX

P.W

accelerated motion. .......................... 182

adverseyaw ................................. 291

aerodynamic center. .......................... 47

Aerodynamics, Basic, Chapter I. ............... 1

Aerodynamics, High Speed, Chapter III. ........ 201

aeroelastic effects. ............................ 330

afterburner. ................................. 129

aileron reversal. .............................. 339

airfoil

drag characteristics. ........................ 33

lift characteristics. ......................... 27

pitching moments. ......................... 47

terminology. .............................. 20

airspeed

calibrated. ................................ 10

equivalent ................................. 11

indicated .................................. 10

mcasurcmcnt ............................... 9

primary control of airspeed. ................ 27,350

fT”C ....................................... 14

altitude

density altitude. ........................... 4

pressure altitude. ........................... 4

primary control of altitude. ............... 154,352

angle of attack. .............................. 22

angle of attack indicator. ..................... 357

angleofbank ............................... 37,176

angle of climb. .............................. 152

Application of Aerodynamics to Specific Prob-

lems of Flying, Chapter VI. ............... 349

approach .................................... 360

aspect ratio. ................................. 61

asymmetrical Power, multi-engine airplane, 294

atmosphere

properties ................................. 1

standard ................................... 4

autorotation characteristics. ................... 405

autorotative rolling. ....................... 309,317

available thrust and power. ................... 104

axis system, airplane reference. ................ 249

Bernoulli equation. ............................ 6

bobweight .................................. 273

boundarylayer ............................... 52

boundary layer control. ....................... 43

brake mean effective pressure, BMEP. .......... 137

*IL*e

brake horsepower, BHP. ...................... 137

braking performance. .................. ..... 387

braking technique. ......... .... ..... ..... 390

calibrated airspeed, CAS ....................... 10

center of gravity limitations. ........... 259,275

center of pressure. ............... ..... ..... 47

circulation. .................................. 16

climb angle. ................................. 152

climb performance. ...... ..... ...... .... 150

climb rate. .. ........................ ...... 154

components of the gas turbine. ................ 109

compressible flow. .......................... 204

compressibility ............................. 201

compressor stall or surge. .. .... ...... .... 125

control force stability. ........................ 264

control of airspeed and altitude. ................ 349

control, Stability and Control, Chapter IV. ...... 243

control systems, longitudinal. ................. 281

creep considerations. ......................... 330

critical altitude. .......... .................. 143

critical field length. ............ ............. 396

critical Mach number. ........................ 215

cumulative damage. ... ..... ...... ..... 328

cycle of operation

gas turbineengine .......................... 106

reciprocating engine. ....................... 135

damping ..................................... 247

density, density ratio. ........................ 2

density altitude. .. .......................... 4

detonation .. .:. ....................... 140, 194

dihedral ..................................... 295

directional control .. .......... ............. 290

directional stability. ......................... 284

divergence ................................ 245, 342

downspring, ................................. 270

downwash ................................... 66

drag

coefficient. ........ ................. 29

equation ................................... 29

induced ................................... 66

parasite. .. .. ..... ... ............. 87

total ...................................... 92

dynamic pressure. .... ... .... ............ : 9

dynamic stability., ... .... .... ... ....... 245

efficiency factor. ..... ... ...... .. ....... 89

endurance Pwe

off-optimum. .............................. 172

performance. ............... .... ......... 170

specific ................................. 158, 170

engine failure

effect on multiengine airplane. ............ 294, 376

power off glide performance. ................ 369

equilibrium conditions. ....................... 150

equivalent airspeed, EAT. .................... 11

equivalent parasite area. ...................... 89

equivalent shaft horsepower, ESHP. ........... 133

expansionwave .............................. 211

factorofsafcty ............................... 326

fatigue considerations. ........................ 328

feathering and governing of propellers. ......... 148

flap

aerodynamic effects. ....................... 37, 43

typCS ...................................... 41

flutter ....................................... 342

force divergence. ............................. 218

friction

braking, ............................. 388

cocfficicnt. ................................ 388

skin friction. .............................. 54

frost ........................................ 373

fuel qualities. ................................ 141

glide performance. ........................... 369

governing apparatus, turbine engines. .......... 121

governing and feathering of propellers. ......... 147

gusts and wind shear. .................... ... 367

gust load factor. ........................... 332

groundeffect ................................. 379

heating, aerodynamic. ........................ 242

helicopter, problems. ......................... 399

helicopter stability and control. ............. 319

high lift

devices .. ...... ............ ... ., ., 39

flight at high lift conditions ................. 35

High Speed Aerodynamics, Chapter III. ........ 201

humidity, effect on power. .................... 144

ice .......................................... 373

indicated airspeed, IAS. ......... ............. 10

induced

angle of attack. ........................... 66

drag. .................................... 66

drag coefficient. ........................... 68

flow. ..................................... 63

inertia coupling. ................... ....... 315

inlets, supersonic powerplant. ................. 238

interference between airplanes in flight. ........ 383

items of airplane performance. ................. 150

landing and ground loads. .................... 343

landing flare and touchdown, ............. 362

NAVWEPS 00-8OT-80

INDEX

Psge

!a”ding gear configuration stability. ........... 305

landing performance. ...... ... .... ... 192

factors affecting performance. .... ........... 196

lateral co”trol, ............................... 300

lateral stability. ....................... .... 294

lift

characteristics. ........................... 24

coefficient .................................. 23

equation ................................... 23

generation .. ............ ............ ... 16, 63

lift-drag ratio. ............................... 32

limit load. ................................. 326

linespeeds ................................... 394

load factor ................................ 37, 331

load spectrum. ............. _ ................. 328

longitudinal

control .................................... 275

dynamic stability. .......................... 279

static stability. ........................... 250

Mach number

definition. .................................. 202

critical Mach “umber. ...................... 2!5

maneuvering load factor ..................... 331

maneuvering performance. ........ ........... 176

maneuvering stability. ...................... 268

mean aerodynamic chord, MAC. ............. 63

mirror landing system ......................... 358

normal shock wave. .......................... 207

obliqueshockwave .......................... 207

operating limitations

propellers, ..................... .... 148

reciproczring c ... .................. 144

turbojet ................................... 124

.. turboprop. ............................... 133

Operating Strength Limitations, Chapter V. .... 325

overstress, effect on service life. ................ 344

parasite area, equivalent. .... .............. 89

parasitedrag ................................. 87

performance, Airplane Performance, Chapter II. 95

pilot induced oscillarion. ..................... 314

pitching moment

airfoil. .................................... 47

longitudinal. .................. ........ 249, 251

pitch-up ..................................... 313

pitot-static system. ............... ........... 9

planform effects. ............................. 61

power effects on stability. ..................... 259

power off stability ... ........................ 259

power required. ................... .......... 96

power settling. ................... ........ 4c3

preignition, ........... .... .... 140

pressure altitude. ......... .... ... ... .. 4

pressure distribution. .. ......... ..... 14

NAVWEPS OO-EOT-80

INDEX

proprllcrs lmd

charactcrlstics. ........... : ............... 14s

efficiency .................................. 145

opcrarmg limitations. ............ : ......... 148

propulsion

etlicicncy .................................. 106

principles. ............. : _ ................. 104

ram tempcraturc rise. ......................... 242

range performance. $ .................... ..... 158

off-optimum conditions. .................... 172

propeller airplanes. ......................... 160

turbojet airplanes ........................... 164

rate of climb. ................................ 154

reciprocating engines

operating characteristics ..................... 13s

operating limitations. ....................... 144

refusal speed, ....... .+: .................... :, .... 392

tetreating blade stall. ......................... 402

reversed command region. ..................... 353

Reynolds number. ............. :. ............. 54

scale effect. .................................. 59

separation, airflow. ............................ 56

service life. ................................ 328

shock induced separation. ..................... 218

shock wave formation. ....................... 218

sideslip angle. ............................... 284

slipstream rotation. .......................... 294

sonic booms. ................................. 396

spanwise lift distribution. ..................... 74

specificendurance ............................. 170

specific fuel consumption

reciprocating engine. ....................... 141

turbojet cngi.ne. ......................... 117

specificrange ................................. 158

speed, maximum and minimum. ............... 150

spin,spinrecovery..........................291, 307

Srability and Control, Chapter IV. ............. 243

stability

directional. ................................ 284

dynamic ................................... 245

helicopter .................................. 319

lateral ..................................... 294

longitudinal. ... : .......................... 250

miscellaneous problems. ..................... 305

static ............................ ......... 243

stallspeeds ................................. 35

Page

seal pattern. ................................ 77

stall rec”very. ............................... 39

standard atmosphere. ......................... 4

static strength. ............................... 326

streamline pattern. ............. ............. 14

supercharging. ............................... 141

supersonic airfoil sections. .................... 223

sweepback ................................... 63

advantages .................................. 226

disadvantages. ............................. 231

takeoff ...................................... 365

takeoff performance. .......................... 184

factors affecting performance. ................ 187

taper, taper ratio. ............................ 63

thrust augmentation. ......................... 129

thrust required. .............................. 96

time limitations, powcrplants. ............... 128, 144

tip stall. .................................... 77

tip vortex. .................................. 63

torque. ............................... ,;, ........ 137

transition of boundary layer. .................. 52 .. transon1c aIrfoIl scctlo”s. ...................... 220

true airspeed, TAS. ........................... 14

turbojetengines .............................. 107

operating characteristics. ................... 116

operating limitations. ...................... 124

turboprop, gas turbine-propeller combination. ... 132

turbulence.................................332, 339

turning performance. ......................... 178

turn rate, turn radius. ........................ 176

unsymmetrical power, see asymmetrical power.

viscosity. ................................... 4

V-n or V-g diagram. ......................... 334

vortex system. ............................... 63

line or bound vortex. ....................... 64

tip or trailing vortex. ...................... 64

w&r injection

reciprocating engine. ....................... 144

turbojetengine ............................. 131

wavedrag................................. , 215

wind, effect on range. ........................ 168

windshear ................................. 367

yaw,adverse ................................ 291

yawangle ................................... 284

YPWm”me”t ................................ 284

t?evised Jcmuarv 1965