Chapter 1 — Part 4

NAVWEPS C&801-80

AIRPLANE PERFORMANCE

TYPICAL PROPELLER AIRCRAFT ALTlTUOE PERFORMANCE

. RATE OF,CL!MB_, _-

.

tiAXlMUM LEVEL FLIGHT SPEED

HIGH BLOWER CRITICAL ALTITUDE

FEE0 FOR MA% R c

LOW BLOWER CRITICAL ALTITUDE

= y$y VELOCITY, KNOTS

-e-*--

TROPOPAUSE

\ MAXIMUM LEVEL

\

\ FLIGHT SPEED

-RATE OF CLIMB

\

\

\

\

I I I I b

-8

VELOCITY, KNOTS

POWER OFF DESCENT PERFORMANCE

POWER

REQUIRED

HP

MINIMUM POWER REP’D

I VELOCITY, KNOTS

Figure UP, Climb ad Desceni Pedormome

lS7

NAVWEPS 00-8OT-80

AIRPLANE PERFORMANCE

with altitude above the tropopause. This is

due in great part to the more rapid decay of

engine thrust in the stratosphere.

During a power off descent the deficiency of

thrust and power define the angle of descent

and rate of descent. TWO particular points

are of interest during a power off descent:

minimum angle of descent and minimum rate

of descent. The minimum angle of descent

would provide maximum glide distance through

the air. Since no thrust is available from the

power plant, minimum angle of descent would

be obtained at (L/D)-. At (L/D),, the

deficiency of thrust is a minimum and, as

shown by figure 2.22, the greatest proportion

between velocity and power required is ob-

tained. The minimum rate of descent in

power off flight is obtained at the angle of

attack and airspeed which produce minimum

power required. For airplanes of moderate

aspect ratio, the speed for minimum rate of

descent is approximately 75 percent of the

speed for minimum angle of descent

RANGE PERFORMANCE

The ability of an airplane to convert fuel

energy into flying distance is one of the most

important items of airplane performance. The

problem of eficient range operation of an air-

plane appears of two general forms in flying

operations: (1) to extract the maximum flying

distance from a given fuel load or (2) to fly a

specified distance with minimum expenditure

of fuel. An obvious common denominator for

each of these operating problems is the “spe-

cific range, ” nautical miles of flying distance

per lb. of fuel. Cruise flight for maximum

range cond.itions should be conducted so that

the airplane obtains maximum specific range

throughout the flight.

GENERAL RANGE PERFORMANCE.

The principal items of range performance can

be visualized by use of the illustrations of figure

2.23. From the characteristics of the aero-

dynamic configuration and the powerplant, the

conditions of steady level flight will define

various rates of fuel flow throughout the range

of flight speed. The first graph of figure 2.23

illustrates a typical variation of fuel flow versus

velocity. The specific range can be defined by

the following relationship:

nautical miles

specific raw= lbs, of fuel

nautical miles/hr.

‘pecific range= lbs. of fuel/hr.

thus,

specific range = velocity, knots

fuel flow, lbs. per hr.

If maximum specific range is desired, the flight

condition must provide a maxinium of velocity

fuel flow. This particular point would be

located by drawing .a straight line from the

origin tangent to the curve of fuel flow versus

velocity.

The general item of range must be clearly

distinguished from the item of endurance. The

item of range involves consideration of flying

distance while endurance involves consideration

of flying time. Thus, it is appropriate to define

a separate term, “specific endurance.”

specific endurance= flight hours

lb. of fuel

specific endurance = flight hours/hr.

lbs. of fuel/hr.

then,

specific endurance= 1

fuel flow, lbs. per hr.

By this definition, the specific endurance is

s&ply the reciprocal of the fuel ~flow. Thus,

.ifl.maximum endurance is desired, the flight

condition ‘must provide a minimum of fuel

flow. This point is readily appreciated as the

lowest point of the curve of fuel flow versus

velocity. Generally, in subsonic performance,

the speed at which maximum endurance is

NAVWEPS 00-501-50

AIRPLANE PERFORMANCE

FUEL

FLOW

I APPLICABLE FOR A

PARTICULAR: WEIGHT

MAXIMUM ALTITUDE

ENDURANCE CONFIGURATION

LINE FROM ORIGIN

TANGENT TO CURVE

VELOCITY, KNOTS

100%

MAXIMUM

-- 99% MAXIMUM RANGE

SPECIFIC

RANGE APPLICABLE FOR A PARTICLAR

-CONFIGURATION

-ALTITUDE

-WEIGHT

VELOCITY, KNOTS

AREA REPRESENTS

Figure 2.23. Geneml Range Performance

NAVWEPS oo-80~~80

AIRPLANE PERFORMANCE

obtained is approximately 75 percent of the

speed for maximum range.

A more exact analysis of range may be ob-

tained by a plot of specific range versus velocity

similar to the second graph of figure 2.23. Of

course, the source of these values of specific

range is derived by the proportion of velocity

and fuel flow from the previous curve of fuel

flow versus velocity. The maximum specific

range of the airplane is at the very peak of the

curve. Maximum endurance point is located

by a straight line from the origin tangent to

the curve of specific range versus velocity.

This tangency point defines a maximum of

(nmi/lb.) per (nmi/hr.) or simply a maximum

of (hrs./lb.).

While the very peak value of specific range

would provide maximum range operation, long

range cruise operation is generally recom-

mended at some slightly higher airspeed.

Most long range cruise operation is conducted

at the flight condition which provides 99 per-

cent of the absolute maximum specific range.

The advantage of such operation is that 1

percent of range is traded for 3 to 5 percent

higher cruise. velocity. Since the higher cruise

speed has a great number of advantages, the

small sacrifice of range is a fair bargain. The

curves of specific range versus velocity are

affected by three principal variables: airplane

gross weight, altitude, and the external aero-

dynamic configuration of the airplane. These

curves are the source of range and endurance

operating data and are included in the per-

formance section of the flight handbook.

“Cruise control” of an airplane implies that

the airplane is operated to maintain the recom-

mended long range cruise condition through-

out the flight. Since fuel is consumed during

cruise, the gross weight of the airplane will

vary and optimum airspeed, altitude, and

power setting can vary, Generally, “cruise

control” means the control of optimum air-

speed, altitude, and power setting to maintain

the 99 percent maximum specific range condi-

tion. At the beginning of cruise, the high

initial weight of the airplane will require spe-

cific values of airspeed, altitude,’ and power

setting to produce the recommended cruise

condition. As fuel is consumed and the air-

plane gross weight decreases, the optimum ai,r-

speed and power setting may decrease or the

optimum altitude may increase. Also, the

optimum specific range will increase. The

pilot must provide the proper cruise control

technique to ensure that the optimum condi-

tions are maintained.

The final graph of figure 2.23 shows a typical

variation of specific range with gross weight

for some particular cruise operation. At the

beginning of cruise the gross weight is high

and the specific range is low. As fuel is con-

sumed, and the gross weight reduces, the

specific range increases. .This’ type of curve

relates the range obtained by the expenditure

of fuel .by the crosshatched area between the

gross weights at beginning and end of cruise.

For example, if the airplane begins cruise at

18,500 Jbs. and ends cruise at 13,000 lbs., 5,500

lbs. of fuel is expended. If the average spe-

cific range were 0.2 nmi/Jb., the total range

would be:

range=(0.2)$ (5,500) lb.

= 1,100 nmi.

Thus, the total range is dependent on both

the fuel available and the specific range. When

range and economy of operation predominate,

the pilot must ensure that the airplane will be

operated at the recommended long range cruise

condition. By this procedure, the airplane

will be capable of its,maximum design operat-

ing radius or flight distances less than the

maximum can be achieved with a maximtim of

fuel reserve at the destination.

RANGE, PROPELLER DRIVEN AIR-

PLANES. The propeller driven airplane com-

bines the propeller with the reciprocating

engine or the gas turbine for propulsive power.

In the case of either the reciprocating engine or

the gas turbine combination, powerplant fuel

NAVWEPS OS80140

AIRPLANE PERFORMANCE

flow is determined mainly by the shaft poluet

put into the propeller rather than thrust. Thus,

the powerplant fuel flow could be related di-

rectly to power required to maintain the air-

plane in steady, level flight. This fact allows

study of the range of the propeller powered

airplane by analysis of the curves of power

required versus velocity.

Figure 2.24 illustrates a typical curve of

power required versus velocity which, for the

propeller powered airplane, would be analo-

gous to the variation of fuel flow versus veloc-

ity. Maximum endurance condition would be

obtained at the point of minimum power re-

quired since this would require the lowest fuel

flow to keep the airplane in steady, level flight.

Maximum range condition would occur where

the proportion between velocity and power re-

quired is greatest and this point is located by

a straight line from the origin tangent to the

curve.

The maximum range condition is obtained

at maximum lift-drag ratio and it is important

to note that (L/D),, for a given airplane

configuration occurs at a particular angle of

attack and li5t coefficient and is unaffected by

weight or altitude (within compressibility

limits). Since approximately 50 percent of

the total dra.g a’t (L/D)* is induced drag, the

propeller powered airplane which is designed

specifically i3r IJong range will have a strong

preference for rbe thigh aspect rario planform.

The effect ,df tihe variation of airplane gross

weight is illustrated by the second graph of

figure 2.24. ‘The flight condition of (L/D),.,

is achieved a’t,one-particular value of lift coefIi-

cient for a given airplane configuration.

Hence, a variation of gross weight will alter

the values of airspeed, power required, and spe-

cific range obtained at (L/D)m.r. If a given

configuration ‘of airplane is operated at con-

stant altitude and the lift coefficient for

WDL the following relationships will

awb :

-4 v*- E VI K

pr* w* s’*

-=H PC WI

where

SRs WI -=-

SRI W,

condition (1) applies to some known condi-

tion of velocity, power required, and

specific range for (L/D),., at some basic

weight, WI

condition (2) applies to some new values of

velocity, power required, and specific

range for (L/D),., at some different

weight, WI

and,

V= velocity, knots

W= gross weight, Jbs.

Pr=power required, h.p.

SK= specific range, nmi/lb.

Thus a 10 percent increase in gross weight

would create:

a 5 percent increase in velocity

a 15 percent increase in power required

a 9 percent decrease in specific range

when flight is maintained at the optimum con-

ditions of (L/D),.,. The variations of veloc-

ity and power required must be monitored by

the pilot as part of the cruise control to main-

tain .(L/D),.+ When the airplane fuel weight

is a small part of the gross-weight and the range

is small, then cruise control procedure can be

simplified to essentially a constant speed and

power setting throughout cruise. However,

the long range airplane has a fuel weight which

is a conside’rable part of the gross weight and

cruise control procedure must employ sched-

uled airspeed and power changes to maintain

optimum range conditions.

The effect of altitude on the range of the

propeller powered airplane may be appreciated

by inspection of the final graph of figure 2.24.

If a given configuration of airplane is operated

at constant gross weight and the lift coefficient

NAVWEPS OO-ROT-RO

AIRPLANE PERFORMANCE

GENER,AL. RANGE CONDITIONS

PROPELLER AIRPLANE

POWER

REO’D

HP

APPLICABLE FOR

A PARTICULAR

MAXIMUM -WEIGHT

ENDURANCE -ALTITUDE

-CONFIGURATION

VELOCITY, KNOTS

POWER

REO’D

EFFECT OF GROSS WEIGHT

HlGHER WT.

CONSTANT

ALTITUDE

VELOCITY, KNOTS

HP HP

A t

EFFECT OF ALTITUDE EFFECT OF ALTITUDE

AT ALTITUDE AT ALTITUDE

SEA LEVEL SEA LEVEL

CONSTANT CONSTANT

WEIGHT WEIGHT

I VELOCITY, KNOTS

Figure 2.24. Range Performance, Propeller Aircraft

for WD)m.z, a change in altitude will produce

the following relationships:

where

condition (I) applies to some known condi-

tion of velocity and power required for

W’),,,,,z at some original, basic altitude

condirion (2) applies to some new values of

velocity and power required for (L/D),,

at some different altitude

and

V= velocity, knots (TAX, of course)

Pr=power required, h.p.

o=altitude density ratio (sigma)

Thus, if flight is conducted at 22,000 ft.

(o=O.498), the airplane will have:

a 42 percent higher velocity

a 42 percent higher power required

than when operating at sea level. Of course,

the greater velocity is a higher TAS since the

airplane at a given weight and lift coefficient

will require the same PAS independent of

altitude. Also, the drag of the airplane at

altitude is the same as the drag at sea level but

the higher TAS causes a proportionately

greater power required. Note chat the same

straight line from the origin tangent to the sea

level power curve also is tangent to the

altitude power curve.

The effect of altitude on specific range can be

appreciated from the previous relationships.

If a change in altitude causes identical changes

in velocity and power required, the proportion

of velocity to power required would be un-

changed. This fact implies that the specific

range of the propeller powered airplane would

be unaffected by altitude. In the actual case,

this is true to the extent that powerplant specif-

ic fuel consumption (c) and propeller efficiency

(qp) are the principal factors which could

cause a variation of specific range with altitude.

NAWEPS oo-EOT-80

AWPLANE PERFORMAhlCE

If compressibility effects are negligible, any

variation of ~peci)c range with altitude is strictly a

function of engine-propeller pcrformanCC.

The airplane equipped with the reciprocating

engine will experience very little, if any,

variation of specific range with altitude at low

altitudes, There is negligible variation of

brake specific fuel consumption for values of

BHP below the maximum cruise power rating

of the powerplant which is the auto-lean or

manual lean range of engine operation. Thus,

an increase in altitude will produce a decrease

in specific range only when the increased power

requirement exceeds the maximum cruise power

rating of the powerplants. One advantage of

supercharging is that the cruise power may be

maintained at high altitude and the airplane

may achieve the range at high altitude with

the corresponding increase in TAS. The prin-

cipal differences in the high altitude cruise and

low altitude cruise are the true airspeeds and

climb fuel requirements.

The airplane equipped with the turboprop

powerplant will exhibit a variation of specific

range with altitude for two reasons. First,

the specific fuel consumption (c) of the turbine

engine improves with the lower inlet tem-

peratures common to high altitudes. Also,

the low power requirements to achieve opti-

mum aerodynamic conditions at low altitude

necessitate engine operation at low, inefficient

output power. The increased power require-

ments at high .altitudes allow the turbine

powerplant to operate in an efficient output

range. Thus, while the airplane has no

particular preference for altitude, the power-

plants prefer the higher altitudes and cause

an increase in specific range with altitude.

Generally, the upper limit of altitude for

efficient cruise operation is defined by airplane

gross weight (and power required) or com-

presslbility effects.

The optimum climb and descent for the

propeller powered airplane is affected by

many different factors and no general, all-

inclusive relationship is applicable. Hand-

book data for the specific airplane and various

NAVWEPS OO-SOT-80

AIRPLANE PERFORMANCE

operational factors will define operating pro-

cedures.

RANGE, TURBOJET AIRPLANES. Many

different factors influence the range of the

turbojet airplane. In order to simplify the

analysis of the overall range problem, it is

convenient to separate airplane factors from

powerplant factors and analyze each item

independently. An analogy would be the

study of “horsecart” performance by separat-

ing “cart” performance from “horse” per-

formance to distinguish the principal factors

which affect the overall performance.

In the case of the turbojet airplane, the

fuel flow is determined mainly by the thrust

rather than power. Thus, the fuel flow could

be most directly related to the thrust required

to maintain the airplane in steady, level flight.

.This fact allows study of the turbojet powered

airplane by analysis of the curves of thrust

required versus velocity. Figure 2.25 illu-

strates a typical curve of thrust required versus

velocity which would be (somewhat) analo-

gous to the variation of fuel flow versus veloc-

ity. Maximum endurance condition would

be obtained at (L/D)- since this would incur

the lowest fuel flow to keep the airplane in

steady, level flight. Maximum range condition

would occur where the proportion between

velocity and thrust required is greatest and

this point is located by a straight line from

the origin tangent to the curve.

The maximum range is obtained at the aero-

dynamic condition which produces a maximum

proportion between the square root of the

lift coefficient (CJ and the drag coe&cient

(CD), or (&/CD)-. In subsonic perform-

ance, (G/C > D - occurs at a particular value

angle of attack and lift coefficient and is un-

affected by weight or altitude (within com-

pressibility limits). At this specific aerody-

namic condition, induced drag is approxi-

mately 25 percent of the total drag so the

turbojet airplane designed for long range does

not have the strong preference for high aspect

ratio planform like the propeller airplane.

On the other hand, since approximately 75

percent of the total drag is parasite drag, the

turbojet airplane designed specifically for long

range has the special requirement for great

aerodynamic cleanness.

The effect of the variation of airplane gross

weight is illustrated by the second graph

of figure 2.25. The flight condition of

(mc 1 D IMI is achieved at one value of lift

coefbcient for a given airplane in subsonic

flight. Hence, a variation of gross weight will

alter the values of airspeed, thrust required,

and specific range obtained at ,(&/CD)-. If

a given configuration is operated at constant

altitude and lift coefficient the following re-~

lationships will apply:

SR2 -=

SRI (constant .altitude)

where

condition (1) applies to some! known condi-

tion of velocity, thrust required, and

specific range for (&/CD)- at some

basic weight, Wi

condition (2) applies to some new values of

velocity, thrust required, and specific

range for (&/CD)- at some different

weight, W,

and

V= velocity, knots

W=gross weight, lbs.

Tr= thrust required, lbs.

.SR= specific range, nmi/lb.

Thus, a 10 percent increase in gross weight

would create:

a 5 percent increase in velocity

a 10 percent increase in thrust required

a 5 percent decrease in specific range

when flight is maintained at the optimum con-

ditions of (&/CD)-. Since most jet airplanes

NAVWEPS 00-8OT-80

AIRPLANE PERFORMANCE

GENERAL RANGE CONDITIONS

TURBOJET

THRUST

REO’D

LBS

THRUST

REO’D

LBS

THRUST

REP’0

LBS

MAXIMUM

ENDURANCE

MAXIMUM

APPLICABLE FOR

A PARTICULAR

-WEIGHT

-ALTITUDE

-CONFIGURATION

VELOCITY, KNOTS

EFFECT OF GROSS WEIGHT

CONSTANT

ALTITUDE

EFFECT OF ALTITUDE

.%A LEVEL SEA LEVEL AT ALTITUDE

/

CONSTANT

WEIGHT

7 VELOCITY. KNOTS

VELOCITY. KNOTS

Ftgure P.25. Rangt Performoncr, Jet Aircraft

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

have a fuel weight which is a large part of the

gross weight, cruise control procedures will be

necessary to account for the changes in opti-

mum airspeeds and power settings as fuel is

consumed.

The effect of altitude on the range of the

turbojet airplane is of great importance be-

cause no other single item can cause such large

variations of specific range. If a given con-

figuration of airplane is operated at constant

gross weight and the lift coefficient for

(JCL/CDL, a change in altitude will produce

the following relationships:

vz - -= 3

J VI .Y*

Tr=constant (neglecting compressibility

effects)

JR.2 - -=

JR1 rJ*

(neglecting factors affecting en-

gine performance)

where

condition (I) applies some known condition

of velocity, thrust required, and specific

range for (&QCD),, at some original,

basic altitude.

condition (2) applies to some new values of

velocity, thrust required, and specific

range for (fi/CD)mm at some different

altitude.

and

V= velocity, knots (TAX, of course)

Tr= thrust required, lbs.

JR= specific range, nmi/lb.

a=altitude density ratio (sigma)

Thus, if flight is conducted at 40,000 ft.

(u=O.246), the airplane will have:

a 102 percent higher velocity

the same thrust required

a 102 percent higher specific range

(even when the beneficial effects of altitude

on engine performance are neglected)

than when operating at sea level. Of course,

the greater velocity is a higher TAJ and the

same thrust required must be obtained with a

greater engine RPM.

At this point it is necessary to consider the

effect of the operating condition on powerplant

performance. An increase in altitude will im-

prove powerplant performance in two respects.

First, an increase in altitude when below the

tropopause will provide lower inlet Gr tem-

peratures which redqce the specific fuel con-

sumption (c~). Of course, above the tropo-

pause the specific fuel consumption tends to

increase. A; low altitude, the engine RPM

necessary to produce the required thrust is low

and, generally, well below the normal rated

value. Thus, a second benefit of altifude on

engine performance is due to the increased

RPM required to furnish cruise thrust. An

increase in engine speed to the normal rated

value will reduce the specific fu,el consumption.

The increase in specific range with altitude

of the turbojet airplane can be attributed to

these three factors:

(1) An increase in altitude will increase the

proportion of (V/Tr) and provide a greater

TAS for the same TY.

(2) An increase in altitude in the tropo-

sphere will produce lower inlet air temperature

which reduces the specific.fuel consumption.

(3) An increase in altitude requires in-

creased engine RPM to provide cruise thrust

and the specific fuel consumption reduces as

normal rated RPM is approached.

The combined effect of these three factors de-

fines altitude as the one most important item

affecting the specific range of the turbojet air-

Pl ane. As an example of this combined’effect,

the typical turbojet airplane obtains a specific

range at 40,ooO ft. which is approximately 150

percent greater than that obtained at sea leirel.

The increased TAS accounts for approxi-

mately two-thirds of this benefit while in-

creased engine performance (reduced cJ ,~ ‘ac-

counts for the other one-third of the benefit.

For example, at sea level the maximum spe-

cific range of a turbojet airplane may be 0.1

nmi/lb. but at 40,000 ft. the maximum specific

range would be approximately 0.25 nmi/lb.

From the previous analysis, it is apparent

that the cruise altitude of the turbojet should

be as high as possible within compressibility

or thrust limits. Generally, the optimum alti-

tude to begin cruise is the highest altitude at

which the maximum continuous thrust can

provide the optimum aerodynamic conditions.

Of course, the optimum altitude is determined

mainly by the gross weight at the begin of

cruise. For the majority of turbojet airplanes

this altitude will be at or above the tropopause

for normal cruise configurations.

Most turbojet airplanes which have rran-

sonic or moderate supersonic performance will

obtain maximum range with a high subsonic

cruise. However, the airplane designed spe-

cifically for high supersonic performance will

obtain maximum range with a supersonic

cruise and subsonic operation will cause low

lift-drag ratios, poor inlet and engine perform-

ance and redute the range capability.

The cruise control of the turbojet airplane

is considerably ~different from that of the pro-

peller driven airplane. Since the specific range

is so greatly affected by altitude, the optimum

altitude for begin of cruise should be attained

as rapidly as is consistent with climb fuel re-

quirements. The range-climb program varies

considerably between airplanes and the per-

formance section of the flight handbook will

specify the appropriate procedure. The de-

scent from cruise altitude will employ essen-

tially the same feature, a rapid descent is

necessary to minimize the time at low altitudes

where specific’ range is low and fuel flow is high

for a given engine speed.

During cruise flight of the turbojet airplane,

the decrease of gross weight from expenditure

of fuel can result in two types of cruise control.

During a constant altitlrdc C&SC, a reduction in

gross weight will require a reduction of air-

speed and engine thrust ‘to maintain the opti-

mum lift coefhcient of subsonic cruise. While

such a cruise may be necessary to conform to

the flow of traffic, it constitutes a certain in-

efficiency of operation. If the airplane were

NAVWEPS OO-BOT-RO

AIRPLANE PERFORMANCE

not restrained to a particular altitude, main-

taining the same lift coeAicient and engine

speed would allow the airplane to climb as the

gross weight decreases. Since altitude gen-

erally produces a beneficial effect on range, the

climbing C&SC implies a more efficient flight

path.

The cruising flight of the turbojet airplane

will begin usually at or above the tropopause

in order to provide optimum range conditions.

If flight is conducted at (a/&)-, optimum

range will be obtained at specific values of lift

coefficient and drag coefficient. When the air-

plane is fixed at these values of CL and C, and

the TAS is held constant, both lift and drag are

directly proportional to the density ratio, (T.

Also, above the tropopause, the thrust is pro-

portional to .J when the TAS and RPM are con-

stant. As a result, a reduction of gross weight

by the expenditure of fuel would allow the

airplane to climb but the airplane would re-

main in equilibrium because lift, drag, and

thrust all vary in the same fashion. This re-

lationship is illustrated by figure 2.26.

The relationship of lift, drag, and thrust is

convenient for, in part, it justifies the condi-

tion of a constant velocity. Above the tropo-

pause, rhe speed of sound is constant hence a

constant velocity during the cruise-climb

would produce a constant Mach number. In

this case, the optimum values of (&,/CD), C,

and C, do not vary during the climb since the

Mach number is constant. The specific fuel

consumption is initially constant above the

tropopause but begins to increase at altitudes

much above the tropopause. If the specific

fuel consumption is assumed to be constant

during the cruise-climb, the following rela-

tionships will apply:

V, M, CL and C, are constant

62 wz

61 w,

FR 02

FFI ~1

JR2-W, (cruise climb above tropopause,

x-W9 constant M, c,)

NAVWEPS oo-801-80

AIRPLANE PERFORMANCE

where

condition (1) applies to some known condi-

tion of weight, fuel flow, and specific

range at some original basic altitude

during cruise climb.

con&&r (2) applies to some new values of

weight, fuel flow, and specific range at

some different altitude along a partic-

ular cruise path.

and

V= velocity, knots

M = Mach number

W= gross weight, lbs.

FF=fuel flow, lbs./hr.

JR= specific range, nmi./lb.

e=altitude density ratio

Thus, during a cruise-climb flight, a 10 percent

decrease in gross weight from the consumption

of fuel would create:

no change in Mach number or ‘TAS

a 5 percent decrease in EAS

a 10 percent decrease in C, i.e., higher

altitude

a 10 percent decrease in fuel flow

an 11 percent increase in specific range

An important comparison can be made between

the constant altitude cruise and the cruise-

climb with respect to the variation of specific

range. From the previous relationships, a

2 percent reduction in gross weight durmg

cruise would create a 1 percent increase in

specific range in a constant altitude cruise but

a 2 percent increase in specific range in a cruise-

climb at constant .Mach number. Thus, a

higher average specific range can.be maintained

during the expenditure of a given increment of

fuel. If an airplane begins a cruise at optimum

conditions at or above the tropopause with a

given weight of fuel, the following data

provide a comparison of the total range avail-

able from a constant altitude or cruise-climb

0.0 Loo0

.I 1.026

.2 1.057

.3 1.92

.4 1.136

.5 1.182

.6 1.248

.7 1.331

For example, if the cruise fuel weight is 50 per-

cent of the gross weight, the climbing cruise

flight path will provide a range 18.2 percent

greater than cruise at constant ,altitude. This

comparison does not include consideration of

any variation of specific fuel consumption dur-

ing cruise or the effects of compressibility in

defining the optimum aerodynamic conditions

for cruising flight. However, the comparison

is generally applicable for aircraft which have

subsonic cruise.

When the airplane has a supersonic cruise for

maximum range, the optimum flight path is

generally one of a constant Mach number.

The optimum flight path is generally-but not

necessarily-a climbing cruise. In this case of

subsonic. or supersonic cruise, a Machmeter is

of principal importance in cruise control of the

jet airplane.

The @ct of wind on nznge is of considerable

importance in flying operations. Of course,

a headwind will always reduce range and a

tailwind will always increase range. The

selection of a cruise altitude with the most

favorable (or least unfa:vorable) winds is a rel-

atively simple matter for the case of the

propeller powered airplane. Since the range of

the.propeller powered airplane is relatively un-

affected by altitude, the altitude with the most

favorable winds is selected for range. However,

the range of the turbojet airplane is greatly

affected by altitude so the selection of an op-

timum altitude will involve considering the

wind profile ‘with the variation of range with

altitude. Since the turbojet range increases

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

TURBOJET CRUISE-CLIMB

IF CL AND TAS ARE CONSTANT,

LIFT IS PROPORTIONAL TOE

IF co AND T/h ARE CONSTANT,

DRAG IS PROPORTIONAL TO a

(SPEEDS FOR MAXIMUM

FUEL GROUNO NAUTICAL ,MlLES

FLOW PER LB. OF FUEL)

LBS/HR I HEADWIND I /

IF RPM AND TAS ARE CONSTANT,

THRUST IS PROPORTIONAL TO”

(APPROXIMATE)

WEIGHT DECREASES AS FUEL IS

CONSUMED

EFFECT OF WIN0 ON RANGE

-I-

VELOCITY, KNOTS

VELOCITY VELOCITY

Figure 2.26. Range Performance

NAVWEPS 00401-60

AIRPLANE PERFORMANCE

greatly with altitude, the turbojet can tolerate

less favorable (or more unfavorable) winds

with increased altitude.

In some cases, large values of wind may

cause a significant change in cruise velocity to

maintain maximum ground nautical miles per

lb. of fuel. As an example of an extreme con-

dition, consider an airplane flying into a head-

wind which equals the cruise velocity. In this

case, ““9 increase in velocity would improve

range.

To appreciate the changes in optimum speeds

with various winds, refer to the illustration of

figure 2.26. When zero wind conditions exist,

a straight line from the origin tangent to the

curve of fuel flow versus velocity will locate

maximum range conditions. When a head-

wind condition exists, the speed for maximum

ground range is located by a line tangent drawn

from a velocity offset equal to the headwind

velocity. This will locate maximum range at

some higher velocity and fuel flow. Of course,

the range will be less than when at zero wind

conditions but the higher velocity and fuel flow

will minimize the range loss due to the head-

wind. In a similar sense, a tailwind will re-

duce the cruise velocity to maximize the

benefit of the tailwind.

The procedure of employing different cruise

velocities to account for the effects of wind is

necessary only at extreme values of wind

velocity. It is necessary to consider the

change in optimum cruise airspeed when the

wind velocities exceed 25 percent of the zero

wind cruise velocity.

ENDURANCE PERFORMANCE

The ability of the airplane to convert fuel

energy into flying time is an important factor

in flying operations. The “specific endurance”

of the airplane is defined as follows:

specific endurance==1

specific endurance= 1

fuel flow, Ibs. per hr.

The specific endurance is simply the reciprocal

of the fuel flow, hence maximum endurance

conditions would be obtained at the lowest

fuel flow required to hold the airplane in steady

level flight. Obviously, minimum fuel flow

will provide the maximum flying time from a

given quantity of fuel. Generally, in subsonic

performance, the speed at which maximum en-

durance is achieved is approximately 75 per-

cent of the speed for maximum range.

While many different factors can affect the

specific endurance, the most important factors

at the control of the pilot are the configuration

and operating altitude. Of course, for maxi-

mum endurance conditions the airplane must

be in the clean configuration and operated at

the proper aerodynamic conditions.

EFFECT OF ALTITUDE ON ENDUR-

ANCE, PROPELLER DRIVEN AIRPLANES.

Since the fuel flow of the propeller driven air-

plane is proportional to power required, the

propeller powered airplane will achieve maxi-

mum specific endurance when operated at mini-

mum power required. The point of minimum

power required is obtained at a specific value

of lift coefficient for a particular airplane con-

figuration and is essentially independent of

weight or altitude. However, an increase in

altitude will increase the value of the minimum

power required as illustrated by figure 2.27.

If the specific fuel consumption were not in-

fluenced by altitude or engine power, the spe-

cific endurance would be directly proportional

to ji, e.g., the specific endurance at 22,000 ft.

(a=O.498) would be approximately 70 percent

of the value at sea level. This example is very

nearly the case of the airplane with the recipro-

cat&g engine since specific fuel consumption and

propeller efficiency are not directly affected by

altitude. The obvious conclusion is that

maximum endurance of the reciprocating en-

gine airplane is obtained at the lowest practical

altitude.

The variation with altitude of the maximum

endurance of the turboprop airplane requires

consideration of powerplant factors in addition

NAV’iiEPS Oo-801-80

AIRPLANE PERFORMANCE

EFFECT OF ALTlTUOE ON MINIMUM

POWER REO’D

AT ALTITUDE

SEA.LEVEL /

/

MINIMUM /

/

/

CONSTANT

WEIGHT 8

CONFIGURATION

VELOCITY, KNOTS

EFFECT OF ALTITUDE ON MINIMUM

THRUST REO’D

SEA LEVEL AT ALTITUDE

T;;;g MINIMUM THRUST REO’D

LBS /’

A’

,’

CONSTANT

-- WEIGHT 8

CONFIGURATION

VELOCITY, KNOTS

Figure 2.27. Endurance Performance

NAVWEPJ OO-ROT-80

AIRPLANE PERFORMANCE

to airplane factors. The turboprop power-

plant prefers operation at low inlet air tem-

peratures and relatively high power setting to

produce low specific fuel consumption. While

an increase in altitude will increase the mini-

mum power required for the airplane, the

powerplant achieves more efficient operation.

As a result of these differences, maximum en-

durance of the multiengine turboprop airplane

at low altitudes may require shutting down

some of the powerplants in order to operate

the remaining powerplants at a higher, more

efficient power setting.

EFFECT OF ALTITUDE ON ENDUR-

ANCE, TURBOJET AIRPLANES. Since the

fuel flow of the turbojet powered airplane is

proportional to thrust required, the turbojet

airplane will achieve maximum specific endur-

ance when operated at minimum thrust re-

quired or (L/D),. In subsonic flight,

(L/D)m~ occurs at a specific value of lift

coefBcient for a given airplane and is essentially

independent of weight or altitude. If a given

weight an~d configuration of airplane is oper-

ated at various altitudes, the value of the

minimum thrust required is unaffected by the

curves of thrust required versus velocity shown

in figure 2.27. Hence, it is apparent that the

aerodynamic configuration has no prefeience

for altitude (within compressibility limits)

and specific endurance is a function only of

engine performance.

The specific fuel consumption of the turbojet

engine is strongly affected by operating RPM

and altitude. Generally, the turbojet engine

prefers the operating range near normal rated

engine speed and the low temperatures of the

stratosphere to produce low specific fuel con-

sumption. Thus, increased altitude provides

the favorable lower inlet air temperature and

requires a greater engine speed to provide the

thrust required at (L/D)-. The typical

turbojet airplane experiences an increase in

specific endurance with altitude with the peak

values occurring at or near the tropopausc.

For example, a typical single-engine turbojet

airplane will have a maximum specific endur-

ance at 35,ooO ft. which is at least 40 percent

greater than the maximum value at sea level.

If the turbojet airplane is at low altitude and

it is necessary to hold for a considerable time,

maximum time in the air will be obtained by

beginning a climb to some optimum altitude

dependent upon the fuel quantity available.

Even though fuel is expended during the climb,

the higher altitude will provide greater total

endurance. Of course, the use of afterburner

for the climb would produce a prohibitive re-

duction in endurance.

OFl4X’TIMUM RANGE AND ENDUR-

ANCE

There are many conditions of flying oper-

ations in which optimum range or endurance

conditions are not possible or practical. In

many instances, the off-optimum conditions

result from certain operational requirements

or simplification of operating procedure. In

addition, off-optimum performance may be the

result of a powerplant malfunction or failure.

The most important conditions are discussed

for various airplanes by powerplant type.

RECIPROCATING POWERED AIR-

PLANE. In the majority of cases, the recipro-

cating powered airplane is operated at’an engine

dictated cruise. Service use will most probably

define some continuous power setting which

will give good service life and trouble-free

operation of the powerplant. When range or

endurance is of no special interest, the simple

expedient is to operate the powerplant at the

recommended power setting and accept what-

ever speed, range, or endurance that results.

While such a procedure greatly simplifies the

matter of cruise control, the practice does not

provide the necessary knowledge required for

operating a high performance, long range

airplane.

The failure of an engine on the multiengine

reciprocating powered airplane has interesting

ramifications. The first problem appearing is

to produce sufficient power from the remaining

engines to keep the airplane airborne. The

problem will be most .critical if the airplane is

at high altitude, high gross weight, and with

gaps and gear extended. Lower altitude,

jettisoning of weight items, and cleaning up

the airplane will reduce the power required for

flight. Of course, the propeller on the in-

operative engine must be feathered or the

power required may exceed that available from

the remaining operating powerplants.

The effect on range is much dependent on

the airplane configuration. When the pro-

peller on the’inoperative engine is feathered,

the added drag is at a minimum, but there is

added the trim drag ,required to balance

the unsymmetrical power. When both these

sources of added drag are accounted for, the

(L/D)- ,is reduced but not by significant

amounts. Generally, if the specific fuel con-

sumption and propeller efficiency do not deteri-

orate, the maximum specific range is not greatly

reduced. On the twin-engine airplane the

power required must .be furnished by the one

remaining engine and this. usually requires

more than the,maximum cruise-rating of the

powerplant.i As a result the powerplant can-

not be operated in the auto-lean or manual

lean, power range and the specific ,fuel con-

sumption increasesgreatly! Thus, noticeable

loss of range must be anticipated when one

engine fails on the twin-engine airplane. The

failure of oneengine on the four (or more)

engine airpla,W may allow the required, power

to be,develo,ped:by.the three remaining power-

plants operating in an economical power range.

If the airplane is clean, at low altitude, and

low gross weight, ,the failure of one engine is

not likely to cause a, loss of range. However,

then loss. of ‘two engines is likely ‘to cause a

considerable loss of range.

When engine failure produces a critical

power or range situation, improved perform-

ance is possible with- theairplane in ;the clean

configuration at low altitude. Also, jetti-

soning of expendable weight items will reduce

the power required and improve the specific

range.

NAVWEPS OO-ROT-RO

AtRPLANE PERFORMANCE

TURBOPROP POWERED AIRPLANE.

The turbine engine has the preference for

relatively high power settings and high alti-

tudes to provide low specific fuel consumption.

Thus, the off-optimum conditions of range or

endurance can be concerned with altitudes

less than the optimum. Altitudes less than

the optimum can reduce the range but the

loss can be minimized on the multiengine

airplane by shutting down some powerplants

and operating the remaining powerplants at a

higher, more efficient output. In this case

the change of range is confined to the variation

of specific fuel consumption with altitude.

Essentially the same situation exists in the

case of engine failure when cruising at optimum

altitude. If the propeller on the inoperative

engine is feathered, the loss of range will be

confined to the change in specific fuel con-

sumption from the reduced cruise altitude. If

a critical power situation exists due to engine

failure, a reduction in altitude provides im-

mediate benefit because of the reduction of

power required and the increase in power

available from the power plants. In addition,

the jettisoning of expendable weight items

will improve performance and, of course, the

clean configuration provides minimum parasite

drag.

Maximum specific endurance of the turbo-

prop airplane does not vary as greatly with

altitude as the turbojet airplane. While each

configuration has its own particular operating

requirements, low altitude endurance of the

turboprop airplane requires special considera-

tion. The single-engine turboprop will gen-

eraBy experience an increase in specific endur-

ance with an increase in altitude from sea level.

However, if the airplane is at low altitude and

must hold or endure for a period of time, the

decision to begin a climb or hold the existing

altitude will depend on the quantity of fuel

available. The decision depends primarily on

the climb fuel,requirements and the variation of

specific endurance with altitude. A somewhat

similar problem exists with the multiengine

turboprop airplane but additional factors are

available to influence the specific endurance at

low altitude. In other words, low altitude

endurance can be improved by shutting down

some powerplants and operating the remaining

powerplants at higher, more efbcient power

setting. Many operational factors could decide

whether such procedure would be a suitable

technique.

TURBOJET POWERED AIRPLANE. In-

creasing altitude has a powerful effect on both

the range and endurance of the turbojet air-

plane. As a result of this powerful effect, the

typical turbojet airplane will achieve maxi-

mum specific endurance at or near the tropo-

pause. Also, the maximum specific range will

be obtained at even higher altitudes since the

peak specific range generally occurs at the

highest altitude at which the normal rating of

the engine can sustain the optimum aero-

dynamic conditions. At low altitude cruise

conditions, the engine speed necessary to sus-

tain optimum aerodynamic conditions is very

low and the specific fuel consumption is rela-

tively poor. Thus, at low altitude, the air-

plane prefers the low speeds to obtain

(&/CD)- but the powerplant prefers the

higher speeds common to higher engine effi-

ciency. The compromise results in maximum

specific range at flight speeds well above the

optimum aerodynamic conditions. In a sense,

low altitude cruise conditions are engine

dictated.

Altitude is the one most important factor

affecting the specific range of the turbojet

airplane. Any operation below the optimum

altitude will have a noticeable effect on the

range capability and proper consideration

must be given to the loss of range. In addi-

tion, turbojet airplanes designed specifically for

long range will have a large percent of the

gross weight as fuel. The large changes in

gross weight during cruise will require partic-

ular methods of cruise control to extract the

maximum flight range. A variation from the

optimum flight path of cruise (constant Mach

NAVWEPS OO-EOT-80

AIRPLANE PERFORMANCE

number, cruise-climb, or whatever the appro-

priate technique) will result in a loss of range

capability.

The failure of an engine during the optimum

cruise of a multiengine turbojet airplane will

cause a noticeable loss of range. Since the

optimum cruise of the turbojet is generally a

thrust-limited cruise, the loss of part of the

total thrust means that the airplane must

descend to a lower altitude. For example, if a

twin-engine jet begins an optimum cruise at

35,000 ft. (e=O.31) and one powerplant fails,

the airplane must descend to a lower altitude

so that the operative engine can provide the

cruise thrust. The resulting altitude would be

approximately 16,030 ft. (~=0.61). Thus, the

airplane will experience a loss of the range

remaining at the point of engine failure and

loss could be accounted for by the reduced

velocity (TM) and the increase in specific fuel

consumption (c~) from the higher ambient air

temperature. In the case of the example air-

plane, engine failure would cause a 30 to 40

percent loss of range from the point of engine

failure. Of course, the jettisoning of expend-

able weight items would allow higher altitude

and would increase the specific range.

Maximum endurance in the turbojet air-

plane varies with altitude but the variation is

due to the changes in ‘fuel flow necessary to

provide the thrust required at (I./D),... The

low inlet air temperature of the tropopause

and the greater engine speed reduce the specific

fuel consumption to a minimum. If the single-

engine turbojet airplane is at low altitude

and must hold or endure for a period of time,

a climb should begin to take advantage of the

higher specific endurance at higher altitude.

The altitude to which to climb will be deter-

mined by the quantity of fuel remaining. In

the case of the multiengine turbojet at low

altitude, some slightly different procedure

may be utilized. If all powerplants are oper-

ating, it is desirable to climb to a higher

altitude which is a function of the remaining

fuel quantity. An alternative at low altitude

17s

NAVWEPS oo-80mo

AIRPLANE PERFORMANCE

would be to provide the endurance thrust with

some engine(s) shut down and the remaining

engine(s) operating at a more efficient power

output. This technique would cause a mmi-

mum loss of endurance if at low altitude. The

feasibility of such a procedure is dependent

on many operational factors.

In all cases, the airplane should be in the

cleanest possible external configuration because

the specific endurance is directly proportional

to the (L/D).

MANEUVERING PERFORMANCE ,...s’ .i :.,cyz’

When the airplane is’in turning flight, the

airplane is not in static equilibrium for there

must be developed the unbalance of force to

produce the acceleration of the turn. During

a steady coordinated turn, the lift is inclined

to produce a horizontal component of force to

equal the centrifugal force of the turn. In

addition, the steady turn is achieved by pro-

ducing a vertical component of lift which is

equal to the weight of the airplane. Figure

2.28 illustrates the forces which act on the

airplane in a steady, coordinated turn.

For the case of the steady, coordinatedturn,

the vertical component oft lift must equal the

weight of the aircraft so that there will be no

acceleration in the vertical direction. This

requirement leads to the following relation-

ship:

L *=- W

where

1 BE-- cos q5

n=sec $6

rz= load factor or “G”

L=lift, lbs.

W= weight, Ibs.

+= bank angle, degrees (phi)

From this relationship it is apparent that the

steady, coordinated turn requires specific values

of load factor, n, at various angles of bank, 6.

For example, a bank angle of 60’ requires a

load factor of 2.0 (cos 60’=0.5 or set 60’=2.0)

to provide the steady, coordinated turn. If

the airplane were at a 60’ bank and lift were

not provided to produce the exact load factor

of 2.0, the aircraft would be accelerating in the

vertical direction as well as the horizontal di-

rection and the turn would not be steady.

Also, any sideforce on the aircraft due to

sideslip, etc., would place the resultant aero-

dynamic force out of the plane of symmetry

perpendicular to the lateral axis and the turn

would not be coordinated.

As a consequence of the increase lift re-

quired to produce the steady turn in a bank,

’ ihe induced drag is increased above that in-

curred by steady, wing level, lift-equal-weight

flight. In a sense, the increased lift required

in a steady turn will increase the total drag or

power required in the same manner as increased

gross weight in level flight. The curves of

figure 2.28 illustrate the general effect of turn-

ing flight on the total thrust and power re-

quired. Of course, the change in thrust re-

quired at any given speed is due to the change

in induced drag and the magnitude of change

depends on the value of induced drag in level

flight and the angle of bank in .turning flight.

Since the induced drag generally varies as the

square of C,, the following data provide an

illustration of the effect of various degrees of

bank :

Load factor, Pcrccnt incrcaw in

n induced drag from

lcvcl flight

Since the, induced drag predominates at low

speeds, steep turns at low speeds can produce

significant increases in thrust or power required

to maintain altitude. Thus, steep turns must

be avoided after takeoff, during approach, and

especially during a critical power situation

from failure or malfunction of a powerplant.

The greatly increased induced drag is just as

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

CENTRIFUGAL FORCE

iRUST

I I TURNING FLIGHT&

\ \

I VELOCITY, KNOTS

LEVEL FLIGHT

VELOCITY, KNOTS

Figure 2.28. Effect of Turning Flight

NAVWEPS 00-8OT-80

AIRPLANE PERFORMANCE

important-if not more important-as the

increased stall speed in turning flight. It is

important also that any turn be well coordi-

nated to prevent the increased drag attendant

to a sideslip.

TURNING PERFORMANCE. The hori-

zontal component of lift will equal the centrif-

ugal force of steady, turning flight. This fact

allows development of the following relation-

ships of turning performance:

turn radius

r= 11.26 tan 6

where

r= turn radius, ft.

I’= velocity, knots (TAX)

ti = bank angle, degrees

ttrrn rate

ROT= 1,091 tan rb

where

ROT=rate of turn, degrees per sec.

$= bank angle, degrees

v=velocity, knots, TAS

These relationships define the turn radius, I,

and rate of turn, ROT, as functions of the two

principal variables: bank angle, +, and velocity,

I’ (TAX). Thus, when the airplane is flown

in the steady, coordinated turn at specific

values of bank angle and velocity, the turn

rate and turn radius are fixed and independent

of the airplane type. As an example, an air-

plane in a steady, coordinated turn at a bank

angle of 45’ and a velocity of 250 knots (TAS)

would have the following turn performance:

= 5,550 ft.

and

ROT=(I,091)(1.000)

-4.37 deg. per sec.

If the airplane were to hold the same angle of

bank at 500 knots (TAS), the turn radius

would quadruple (r=22,200 ft.) and the turn

rate would be one-half the original value

(ROT=2.19 deg. per sec.).

Values of turn radius and turn rate versus

velocity are shown in figure 2.29 for various

angles of bank and the corresponding load

factors. The conditions are for the steady,

coordinated turn at constant altitude but the

results are applicable for climbing or descend-

ing flight when the angle of climb or descent

is relatively small. While the effect of alti-

tude on turning performance is not immediately

apparent from these curves, the principal effect

must be appreciated as an increased true air-

speed (TAX) for a given equivalent airspeed

(EAS).

TACTICAL PERFORMANCE. Many tac-

tical maneuvers require the use of the maxi-

mum turning capability of the airplane. The

maximum turning capability of an airplane will

be defined by three factors:

(1) Maximum lift capability. The combi-

nation of maximum lift coefIicient, C,,=,

and wing loading, W/S, will define the

ability of the airplane to develop aero-

dynamically the load factors of maneuvering

flight.

(2) Optrating ftrcngth limits will define the

upper limits of maneuvering load factors

which will not damage the primary struc-

ture of the airplane. These limits must not

be exceeded in normal operations because of

the possibility of structural damage or

failure.

(3) Thwt or power limits will define the

ability of the airplane to turn at constant

altitude. The limiting condition would al-

low increased load factor and induced drag

until the drag equals the maximum thrust

available from the powerplant. Such a case

would produce the maximum turning capa-

bility for maintaining constant altitude.

The first illustration of figure 2.30 shows

how the aerodynamic and structural limits

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

define the maximum turning performance.

The acrodynomic limir describes the minimum

turn radius available to the airplane when

operated at C,,,,. When the airplane is at the

stall speed in level flight, all the lift is neces-

sary to sustain the aircraft in flight and none

is available to produce a steady turn. Hence,

the turn radius at the stall speed is infinite.

As speed is increased above the stall speed, the

airplane at C,,, is able to develop lift greater

than weight and produce a finite turn radius.

For example, at a speed twice the stall speed,

the airplane at CL,,,,= is able to develop a load

factor of four and utilize a bank angle of 75.5’

(cos 75.~~ = 0.25). Continued increase in

speed increases the load factor and bank angle

which is available aerodynamically but, be-

cause of the increase in velocity and the basic

effect on turn radius, the turn radius approaches

an absolute minimum value. When C,,, is

unaffected by velocity, the aerodynamic mini-

mum turn radius approaches this absolute

value which is a function of C,,,,,,,, W/S, and 6.

Actually, the one common denominator of

aerodynamic turning performance is the wing

level stall speed.

The aerodynamic limit of turn radius requires

that the increased velocity be utilized to pro-

duce increasing load factors and greater angles

of bank. Obviously, very high speeds will

require very high load factors and the absolute

aerodynamic minimum turn radius will require

an infinite load factor. Increasing speed above

the stall speed will eventually produce the

limit load factor and continued increase in

speed above this point will require that load

factor and bank angle be limited to prevent

structural damage. When the load factor and

bank angle are held constant at the structural

limit, the turn radius varies as the square of

the velocity and increases rapidly above the

aerodynamic limit. The intersection of ‘the

aerodynamic limit and structural limit lines

is the ‘*maneuver speed.” The maneuver

speed is the minimum speed necessary to

develop aerodynamically the limit load factor

and it produces the minimum turn radius

within aerodynamic and structural limitations.

At speeds less than the maneuver speed, the

limit load factor is not available aerodynami-

cally and turning performance is aerody-

namically limited. At speeds greater than

the maneuver speed, CL- and maximum

aerodynamic load factor are not available and

turning performance is structurally limited.

When the stall speed and limit load factor

are known for a particular configuration, the

maneuver speed is related by the following

expression:

where

V,=maneuver speed, knots

V.=stall speed, knots

n limit = limit load factor

For example, an airplane with a limit load

factor of 4.0 would have a maneuver speed

which is twice the stall speed.

The aerodynamic limit line of the first

illustration of figure 2.30 is typical of an air-

plane with a CL, which is invariant with

speed. While this is applicable for the ma-

jority of subsonic airplanes, considerable differ-

ence would be typical of the transonic or

supersonic airplane at altitude. Compressi-

bility effects and changes in longitudinal

control power may produce a maximum avail-

able CL which varies with velocity and an

aerodynamic turn radius which is not an

absolute minimum at the maximum of velocity.

The second illustration of figure 2.30 describes

the constant altitude turning performance

of an airplane. When an airplane is at high

,altitude, the turning performance at the high

speed end of the flight speed range is more

usually thrust limited rather than structurally

limited. In flight at constant altitude, the

thrust must equal the drag to maintain equilib-

rium and, thus, the constant altitude turn

radius is infinite at the maximum level flight

speed. Any bank or turn at maximum level

flight speed would incur additional drag and

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

TURN

RADIUS

F:

A-- I t

VELOCITY, KNOTS (TAS)

EFFECT OF AERODYNAMIC AND

STRUCTURAL LIMIT ON TURNING

PERFORMANCE

ABSOLUTE MINIMUM

TURN

RADIUS

F:

CONSTANT ALTITUDE TURNING

PERFORMANCE

,-INCREASING

BANK ANGLE

THRUST OR

VELOCITY, KNOTS (TAS)

figure 2.30. Maneuvering Performance

NAVWEPS OO-EOT-80

AIRPLANE PERFORMANCE

cause the airplane to descend. However, as

speed is reduced below the maximum level

flight speed, parasite drag reduces and allows

increased load factors and bank angles and

reduced radius of turn, i.e., decreased parasite

drag allows increased induced drag to accom-

modate turns within the maximum thrust

available. Thus, the considerations of con-

stant altitude will increase the minimum turn

radius above the aerodynamic limit and define

a particular airspeed for minimum turn radius.

Each of the three limiting factors (aero-

dynamic, structural, and power) may combine

to define the turning performance of an air-

Pl ane. Generally, aerodynamic and structural

limits predominate at low altitude while aero-

dynamic and power limits predominate at high

altitude. The knowledge of this turning per-

formance is particularly necessary for effective

operation of fighter and interceptor types of

airplanes.

TAKEOFF AND LANDING PERFORMANCE

The majority of pilot caused airplane acci-

dents occur during the takeoff and landing

phase of flight. Because of this fact, the

Naval Aviator must be familiar with all the

many variables which influence the takeoff and

landing performance of an airplane and must

strive for exacting, professional techniques of

operation during these phases of flight.

Takeoff and landing performance is a con-

dition of accelerated motion, For instance,

during takeoff the airplane starts at zero veloc-

ity and accelerates to the takeoff velocity to

become airborne. During landing, the air-

plane touches down at the landing speed and

decelerates (or accelerates negatively) to the

zero velocity of the stop. In fact, the landing

performance could be considered as a takeoff

in reverse for purposes of study. In either

case, takeoff or landing, the airplane is ac-

celerated between zero velocity and the takeoff

or landing velocity. The important factors of

takeoff or landing performance are:

(1) The takeoff or landing velocity which

will generally be a function of the stall

speed or minimum flying speed, e.g., 15 per-

cent above the stall speed.

(2) The accclcration during the takeoff or

landing roll. The acceleration experienced

by any object varies directly with the un-

balance of force and inversely as the mass of

the object.

(3) The takeoff or landing roll distance is

a function of both the acceleration and

velocity.

In the actual case, the takeoff and landing dis-

tance is related to velocity and acceleration in

a .very complex fashion. The main source of

the complexity is that the forces acting on the

airplane during the takeoff or landing roll are

“difficult to define wit,h simple relationships.

Since the acceleration is a function of these

forces, the acceleration is difficult to define in

a simple fashion and it is a principal variable

affecting distance. However, some simplifica-

tion can be made to study the basic relatiomhip

of acceleration, velocity, and distance While

the acceleration is not necessarily constant or

uniform throughout the takeoff or landing

roll, the assumption of uniformly acceler-

ated motion will facilitate study of the princi-

pal variables. affecting takeoff and landing

distance.

From basic physics, the relationship of

velocity, acceleration, and distance for uni-

formly accelerated motion is defined by the

following equation:

s=g

where

S= acceleration distance, ft.

V= final velocity, ft. per sec., after accel-

erating uniformly from zero velocity

a= acceleration, ft. per sec.*

This equation ‘could relate the takeoff distance

in terms of the takeoff velocity and acceleration

when the airplane is accelerated uniformly

from zero velocity to the final takeoff velocity.

Also, this expression could relate the landing

distance in terms of the landing velocity and

deceleration when the airplane is accelerated

(negatively) from the landing velocity to a

complete stop. It is important to note that

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

the distance varies directly as the square of the

velocity and inversely as the acceleration.

As an example of this relationship, assume

that during takeoff an airplane is, accelerated

uniformly from zero velocity to a takeoff

velocity of 150 knots (253.5 ft. per sec.) with

an acceleration of 6.434 ft. per sec.* (or, 0.2g,

since g=32.17 ft. per sec.*). The takeoff

distance would be:

= (253.5)*

(2)(6.434)

=5,ooo ft.

If the acceleration during takeoff were reduced

10 percent, the takeoff distance would increase

11.1 percent; if the takeoff velocity were

increased 10 percent, the takeoff distance

would increase 21 percent. These relation-

ships point to the fact that proper accounting

must be made of altitude, temperature, gross

weight, wind, etc. because any item affecting

acceleration or takeoff velocity will have a

definite effect on takeoff distance.

If an airplane were to land at a velocity of

150 knots and be decelerated uniformly to a

stop with the same acceleration of 0.2g, the

landing stop distance would be 5,000 ft.

However, the case is not necessarily that an

aircraft may have identical takeoff and landing

performance but the principle illustrated is that

distance is a function of velocity and accelera-

tion. As before, a 10 percent lower accelera-

tion increases stop distance Il.1 percent, and a

10 percent higher landing speed increases

landing distance 21 percent.

The general relationship of velocity, accel-

eration, and distance for uniformly accelerated

motion is illustrated by figure 2.31. In this

illustration., acceleration distance is shown as

a function of velocity for various values of

acceleration.

TAKEOFF PERFORMANCE. The mini-

mum takeoff distance is of primary interest in

the operation of any aircraft because it defines

the runway requirements. The minimum take-

off distance is obtained by takeoff at some

minimum safe velocity which allows sufficient

margin above stall and provides satisfactory

control and initial rate of climb. Generally,

the takeoff speed is some fixed percentage of

the stall speed or minimum control speed for

the airplane in the takeoff configuration. As

such, the takeoff will be accomplished at some

particular value of lift coefficient and angle of

attack. Depending on the airplane character-

istics, the takeoff speed will be anywhere from

1.05 to 1.25 times the stall speed or minimum

control speed. If the takeoff speed is specified

as 1.10 times the stall speed, the takeoff lift

coefficient is 82.6 percent of CL- and the angle

of attack and lift coeticient for takeoff are

fixed values independent of weight, altitude,

wind, etc. Hence, an angle of attack indicator

can be a valuable aid during takeoff.

To obtain minimum takeoff distance at the

specified takeoff velocity, the forces which act

on the aircraft must provide the maximum

acceleration during the takeoff roll. The

various forces acting on the aircraft may or

may not be at the control of the pilot and

various techniques may be necessary in certain

airplanes to maintain takeoff acceleration at

the highest value.

Figure 2.32 illustrates the various forces

which act on the aircraft during takeoff roll.

The powerplant thrust is the principal force to

provide the acceleration and, for minimum

takeoff ,distance, the output thrust should be

at a maximum. Lift and drag are produced as

soon as the airplane has speed and the values

of lift and drag depend on the angle of attack

and dynamic .pressure. Rolling friction results

when there is a normal force on the wheels

and the friction force is the product of the

normal force and the coefficient of rolling

friction. The normal force pressing the wheels

against the runway surface is the net of weight

and lift while the rolling friction coefficient is

a function of the tire type and runway surface

texture.

The acceleration of the airplane at any

instant during takeoff roll is a function of the

net accelerating force and the airplane mass.

From Newton’s second law of motion:

or

where

a=acceleration,~fr. per set

Fn- net accelerating force,

W=weight, lbs.

g? gravitational accelerat

=32.17 ft. per sec.*

M= mass, slugb

= WE

The riet aicelerating fdrce on ‘the airplane,

F,, is the net of thiust, T, drag, D, and rolling

friction, F. Thus, the acceleration -at any

instant during takeoff roll is:

a=&T-D-F)

Figure 2.32 illustrates the typical variation of

the various fbrces acting on the aircraft

throughout the takeoff roll: If ‘it is assumed

that the aircraft is at essentially constant

angle of attack during takeoff roll, CL and Co

are constant and the forces of lift and drag

vary as the square of the speed. For the case

of uniformly accelerated motion, distance

along the takeoff roll is proportional also to

the square bf the velocity hence velocity

squared and distance can be used almost synon-

omously. Thus, lift and drag will vary lint

arly with dyriamic pressure (4) or P from

the point of beginning takeoff roll. As the

rolling friction coefficient -is esscnti&y un-

affected by velocity, the rolling ftiction will

vary as the normal force on the wheels. At

zero velocity, the normal force on the wheels

is equal to the airplane weight but, at takeoff

velocity, the lift is equal to the weight and

the normal force is zero. Hence, rolling fric-

tion decreases linearly with 4 or Vz from the

beginning of takeoff roll and reaches zero at

the point of takeoff.

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

The total retarding for& on the aircraft is

the sum of drag and rolling friction (D+F)

and, for the majority of configurations, this

sum is nearly Constant or changes only slightly

during the takeoff roll. The net accelerating

force is then the difference between the power-

plant thrust and the total retarding force,

Fn=T-D-F

The variation of the net accelerating force

throughout the takeoff roll is shown in figure

2.32. The typical propeller airplane demon-

strates a net accelerating force which decreases

with velocity and the resulting acceleration is

initially high but decreases throughout the

takeoff roll. The typical jet airplane demon-

strates a net accelerating force which is essen-

tially constant throughout the takeoff roll.

As a result, the takeoff performance of the

typical turbojet airpiane will compare closely

with the case for uniformly accelerated motion.

The pilot technique required to achieve peak

acceleration throughout takeoff roll can vary

considerably between airplane configurations.

In some instances, maximum acceleration will

be obtained by allowing the airplane to remain

in the three-point attitude throughout the roll

until the airplane simply reaches lift-equal-to-

weight and flies off the ground. Other air-

planes may require the three-point attitude

until the takeoff speed is reached then rotation

to the takeoff angle of attack to become air-

borne. Still other configurations may require

partial or complete rotation to the takeoff

angle of attack prior to reaching the takeoff

speed. In this case, the procedure may be

necessary to provide a smaller retarding force

(D+F) to achieve peak acceleration. When-

ever any form of pitch rotation is necessary the

pilot must provide the proper angle of attack

since an excessive angle of attack will cause

excessive drag and hinder (or possibly pre-

clude) a successful takeoff. Also, irisufficient

rotation may provide added rolling resistance

or require that the airplane accelerate to some

excessive speed prior to becoming airborne.

Revised January 1965

NAVWEPS O&601-80

AIRPLANE PERFORMANCE

FORCES ACTING ON THE AIRPLANE DURING

TAKEOFF ROLL

LlFT,L7

/’

,-THRUST (PROPELLER), T ,/

/

THRUST (JETI,T /

/’ ‘\

(T-D-F) / ‘1

NET

ACCELERATING /’

FORCE

(PROPELLER)- , I ’

(T;&F)

CONSTANT

a 1

ACCELERATING

INNING WHICH IS ESSENTIALLY POINT OFF

OF TAKEOFF PROPORTIONAL TO DISTANCE TAKEOFF

ROLL IN UNIFORMLY ACCELERATED

MOTION

Figure 2.32. Forces Acting on the Airplane During Takeoff Roll

In this sense, an angle of attack indicator is

especially useful for night or instrument takeoff

conditions as well as. the ordinary day VFR

takeoff conditions. Acceleration errors of the

attitude gyro usually preclude accurate pitch

rotation under these conditions.

FACTORS AFFECTING TAKEOFF PER-

FORMANCE. In addition to the important

factors of proper technique, many other vari-

ables affect the takeoff performance of an air-

plane. Any item which alters the takeoff

velocity or acceleration during takeoff roll will

affect the takeoff distance. In order to evalu-

ate the effect of the many variables, the prin-

cipal relationships of uniformly accelerated

motion,will be assumed and consideration will

be given to those effects due to any nonuni-

formity of acceleration during the process of

takeoff. Generally, in the case of uniformly

accelerated motion, distance varies directly

with the square of the takeoff velocity and in-

versely as the takeoff acceleration.

where

S= distance

V= velocity,

a= acceleration

;’ con&&‘(I) applies to some known takeoff

distance, Si, which was common to

some original takeoff velocity, Vi, and

acceleration, ai.

condition (2) applies to some new takeoff

distance, Sa, which is the result of some

different value of takeoff velocity, Vs, or

acceleration, aa.

With xhis basic relationship, the effect of the

many variables on takeoff ‘distance can be

approximated.

The effect of gross weight on takeoff distance is

large and proper consideration of this item

must be made in predicting takeoff distance.

Increased gross weight can be considered to

produce a threefold effect on takeoff perform-

ance: (1) increased takeoff velocity, (2) greater

NAVWEPS 00401-80

AIRPLANE PERFORMANCE

mass to accelerate, and (3) increased retarding

force (D+F). If the gross weight increases,

a greater speed is necessary to produce the

greater lift to get the airplane airborne at the

takeoff lift coefficient. The relationship of

takeoff speed and gross weight would be as

follows:

where

VI= takeoff velocity corresponding to

some original weight, Wi

V2= takeoff velocity corresponding to

some different weight, W,

Thus, a given airplane in the takeoff configura-

tion at a given gross weight will have a specific

takeoff speed (EAS or CAS) which is invariant

with altitude, temperature, wind, etc. because

a certain value of 4 is necessary to provide lift

equal to weight at the takeoff CL. As an ex-

ample of the effect of a change in gross weight

a 21 percent increase in takeoff weight will

require a 10 percent increase in takeoff speed to

support the greater weight.

A change in gross weight will change the

net accelerating force, Fn, and change the

mass, M, which is being accelerated. If the

airplane has a relatively high thrust-to-weight

ratio, the change in the net accelerating force

is slight and the principal effect on accelera-

tion is due to the change in mass.

To evaluate the effect of gross weight on

takeoff distance, the following relationship

are used :

the effect of weight on takeoff velocity is

if the change in net accelerating force~is

neglected, the effect of weight on accelera-

tion is

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

the effect of these items on takeoff dis-

tance is

or

g+?)x(Z)

J-2 WY2 a -= - J-1 ( ) WI

(ut 1eaJt this effect because weight will

alter the net accelerating force)

This result approximates the e5ect of gross

weight on takeoff distance for airplanes with

relatively high thrust-to-weight ratios. In

effect, the takeoff distance will vary at least

as the square of the gross weight. For ex-

ample, a 10 percent increase ,in takeoff gross

weight would cause:

a 5 percent increase in takeoff velocity

at least a, 9 percent decrease in acceleration

at least a 21 percent increase in takeoff

distance

For the airplane with a high thrust-to-weight

ratio, the increase in takeoff distance would

be approximately 21 to 22 percent but, for

the airplane with a relatively low thrust-to-

*eight ratio, the increase in takeoff distance

would be approximately 25 to 30 percent.

Such a powerful effect requires proper con-

sideration of gross weight in predicting takeoff

distance.

The effect of wind on takeoff distance is large

and proper consideration also must be provided

when predicting takeoff distance. The effect

of a headwind is to allow the airplane to reach

the takeoff velocity at a lower ground velocity

while the effect of a tailwind is to require the

airplane to achieve a greater ground velocity

to attain the takeoff velocity. The effect of

the wind on acceleration is relatively small

and, for the most part, can be neglected. To

evaluate the effect of wind on takeoff distance,

the following relationships are used:

the effect of a headwind is to reduce the

takeoff ground velocity by the amount of

the headwind velocity, VW

the effect of wind on acceleration is

negligible,

the effect of these items on takeoff distance

is

where

Xi= zero wind takeoff distance

Sa=takeoff distance into the head-

wind

V,= headwind velocity

VI= takeoff ground velocity with zero

wind, or, simply, the take05

airspeed

As a .result of this relationship, a headwind

wh,ich is 10 percent of the takeoff airspeed will

reduce the takeoff distance 19 percent. How-

ever, a tailwind (or negative headwind) which

is 10 percent of the take05 airspeed will in-

crease the takeoff distance 21 percent. In the

case where the headwind velocity is 50 percent

of the takeoff speed, the takeoff distance would

be approximately 25 percent of the zero wind

takeoff distance (75 percent reduction).

The e5ect of wind on landing distance is

identical to the effect on takeoff distance.

Figure 2.33 illustrates the general dfect of

wind by the percent change in takeoff or land-

ing distance as a function of the ratio of wind

velocity to takeoff or landing speed.

NAVWEPS 00-801-80

AIRPLANE PEkFORMANCE

Figure 2.33. Approximate Effect of Wind Velocity on Takeoff or Landing Distance

NAVWEPS 00-8OT-80

AIRPLANE PERFORffANCE

The cffcct of nrnzuay slope on takeoff distance

is due to the component of weight along the

inclined path of the airplane. A runway

slope of 1 percent would provide a force com-

ponent along the path of the airplane which is

1 percent of the gross weight. Of course, an

upslope would contribute a retarding force

component while a downslope would contri-

bute an accelerating force component. For

the case of the upslope, the retarding force

component adds to drag and rolling friction to

reduce the net accelerating force. Ordinarily,

a 1 percent runway slope can cause a 2’tO 4

percent change in takeoff distance depending

on rhe airplane characrerisrics. The airplane

with the high thrust-to-weight ratio is least

affected while the airplane with the low thrust-

to-weight ratio is most affected because the

slope force component causes a relatively

greater change in the net accelerating force.

The effect of runway slope must be consid-

ered when predicting the takeoff distance but

the effect is usually minor for the ordinary run-

way slopes and airplanes with moderate

thrust-to-weight ratios. In fact, runway slope

considerations are of great significance only

when the runway slope is large and the airplane

has an intrinsic low acceleration, i.e., low

thrust-to-weight ratio. In the ordinary case,

the selection of the takeoff runway will favor

the direction with an upslope and headwind

rather than the direction with a downslope

and tailwind.

The effect of proper takeoff t&city is important

when runway lengths and takeoff distances are

critical. The takeoff speeds specified in the

flight handbook are generally the minimum

safe speeds at which the airplane can become

airborne. Any attempt to take 05 below the

recommended speed may mean that the air-

craft may stall, be difficult to control, or have

very low initial rate of climb. In some cases,

an excessive angle of attack may not allow

the airplane to climb out of ground effect. On

the other hand, an excessive airspeed at takeoff

may improve the initial rare of climb and

“feel” of the airplane but will produce an un-

desirable increase in takeoff distance. Assum-

ing that the acceleration is essentially un-

affected, the takeoff distance varies as the

square of the takeoff velocity,

s* vz.2 -= -

0 J-1 v,

Thus, 10 percent excess airspeed would increase

the takeoff distance 21 percent. In most criti-

cal takeoff conditions, such an increase in

takeoff distance would be prohibitive and the

pilot must adhere to the recommended takeoff

speeds.

The effect of prcs~wc altitude and ambient

rcmpcraturc is to define primarily the density

altitude and its effect on takeoff performance.

While subsequent corrections are appropriate

for the effect of temperature on certain items

of powerplant performance, density altitude

defines certain effects on takeoff performance.

An increase in density altitude can produce a

two-fold effect on takeoff performance: (I) in-

creased takeoff velocity and (2) decreased

thrust and reduced net accelerating force. If

a given weight and configuration of airplane is

taken to altitude above standard sea level, the

airplane will still require the same dynamic

pressure to become airborne at the takeoff lift

coefficient. Thus, the airplane at altitude will

take 05 at the same equivalent airspeed (EAS)

as at sea level, but because of the reduced

density, the true airspeed (TAS) will be

greater. From basic aerodynamics, the rela-

tionship between true airspeed and equivalent

airspeed is as follows:

TAS 1

EAS=F

where

TAS= true airspeed

EAS= equivalent airspeed

n=altitude density ratio

0 = Plpo

The effect of density altitude on powerplant

thrust depends much on the type of power-

plant. An increase in altitude above standard

sea level will bring an immediate decrease in

power output for the unsupercharged or ground

boosted reciprocating engine or the turbojet

and turboprop engines. However, an increase

in altitude above standard sea level will not

cause a decrease in power output for the super-

charged reciprocating engine until the altitude

exceeds the critical altitude. For those power-

plants which experience a decay in thrust with

an increase in altitude, the effect on the net

accelerating force and acceleration can be ap-

proximated by assuming a direct variation

with density. Actually, this assumed vari-

ation would closely approximate the effect on

airplanes with high thrust-to-weight ratios.

This relationship would be as follows:

a2 Fm P -=-=-En

al Frill PO

where

ai, Fn, = acceleration and net accelerating

force corresponding to sea level

aa, Fn, = acceleration and net accelerating

force corresponding to altitude

~=altitude density ratio

In order to evaluate the effect of these items on

takeoff distance, the following relationships

are used :

if an increase in altitude does not alter ac-

celeration, the principal effect would be

due to the greater TAS

;=(g,yxe)

where

f2 1 -=-

$1 (T

Si=standard sea level takeoff distance

St= takeoff distance at altitude

o-altitude density ratio

if an increase in altitude reduces accelera-

tion in addition to the increase in TAS, the

NAVWEPS 00-805-80

AIRPLANE PERFORMANCE

combined effects would be approximated

for the case of the airplane with high in-

trinsic acceleration by the following:

g=(gyx(~)

g=(i)x(;)

s2 12 -= -

0 J-1 a

where

S,= standard sea level takeoff distance

Ja= takeoff distance at altitude

o=altitude density ratio

As a result of these relationships, it should.

be appreciated that density altitude will affect

takeoff performance in a fashion depending

much on the powerplant type. The effect of

density altitude on takeoff distance can be

appreciated by the following comparison:

sealevel....

I.cmft.....

Z,cmfC.....

,,mfi.....

4.@JJfc.....

5.Ccnft.....

6.-xafC.....

--

-

..om

.0?.98

..c605

L. wls

L. 126

L. 1605

1.1965

L.cca

L.oa5

1.125

1.191

1.264

1.347

1.431

-

--

-

drirude

--

0 0

2.98 6.05

6.05 12.5

9.28 19.5

12.6 26.4

16.05 34.7

19.65 0.1

9.8

19.9

30.1

40.6

52.3

65.8

-

From the previous table, some approximate

rules of thumb may be derived to illustrated

the differences between the various airplane

types. A 1,ooo-ft. increase in density altitude

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

will cause these approximate increases in

takeoff distance:

3% percent for the supercharged recipro-

cating airplane when below critical

altitude

7 percent for the turbojet with high thtust-

to-weight ratio

10 percent for the turbojet with low

thrust-to-weight ratio

These approximate relationships show the

turbojet airplane to be much more sensitive to

density altitude than the reciprocating powered

airplane, This is an important fact which

must be appreciated by pilots in transition

from propeller type to jet type airplanes.

Proper accounting of pressure altitude (field

elevation is a poor substitute) and temperature

is mandatory for accurate prediction of takeoff

roll distance.

The most critical conditions of takeoff

performance are the result of somecombination

of high gross weight, altitude, temperature

and unfavorable wind. In a11 cases, ir be-

hooves the pilot to make an accurate prcdic-

tion of takeoff’ distance from the performance

data of the Flight Handboo& regardless of the

runway available, and to strive for.2 polished,

professional takeoff technique.

In the prediction of takeoff distance from

the handbook data, the following primary

considerations must be given:

Reciprocating powered airplane

(1) Pressure altitude and temperature-

to define the effect of density altitude on

distance.

(2) Gross weight-a large effect on dis-

tance.

(3) Specific humidity-to correct cake-

off distance for the power loss associated

with water vapor.

(4) Wind-a large effect due to the wind

or wind component along the runway.

Turbine powered airplane

(I) Pressure altitude and temperature-

to define the effect of density altitude.

(2) Gross weight.

(3) Temperature--an additional correc-

tion for nonstandard temperatures to ac-

count for the thrust loss associated with

high compressor inlet air temperature.

For this correction the ambient tempera-

ture at the runway conditions is appro-

priate rather than the ambient temperature

at some distant location.

(4) Wind.

In addition, corrections are necessary to ac-

count for runway slope, engine power defi-

ciencies, etc.

LANDING PERFORMANCE. In many

cases, the landing distance of an airplane will

define the runway requirements for flying

operations. This is particularly the case of

high speed ‘jet airplanes at low altitudes where

landing distance is the problem rather than

takeoff performance. The minimum landing

distance is obtained by landing at some mini-

mum safe velocity which allows sufficient mar-

gin above stall and provides satisfactory, con-

trol and capability for waveoff Generally,

the landing speed is some fixed percentage of

the stall speed or minimum control speed for

the airplane in the landing configuration. As

such, the landing will be accomplished at

some particuIar value of ~lift coefficient and

angle of attack. The exact value of CL and

P for landing will depend on the airplane

characteristics but, once defined, the values are

independent of weight, altitude, wind, etc.

Thus, an angle of attack indicator can be a

valuable aid during approach and landing.

To obtain minimum landing distance at the

specified landing velocity, the forces which

act on the airplane must provide maximum

deceleration (or negative.acceIeration) during

the landing roll. The various forces actin~g.

on the airplane during the landing roll may

require various techniques to maintain landing

deceleration at the peak value.

Figure 2.34 illustrates the forces acting on

the aircraft during landing roll. The power-

plant thnrJt should be a minimum positive

value, or, if reverse thrust is available, a maxi-

mum negative value for minimum landing dis-

tance. Lift and drag are produced as long as

the airplane has speed and the values of lift

and drag depend on dynamic pressure and

angle of attack. Braking friction results when

there is a normal force on the braking wheel

surfaces and the friction force is the product of

the normal force and the coe&cient of braking

friction. The normal force on the braking

surfaces is some part of the net of weight and

lift, i.e., some other part of this net may be

distributed to wheels which have no brakes.

The maximum coefficient of braking friction is

primarily a function of the runway surface con-

dition (dry, wet, icy, etc.) and rather inde-

pendent of the type of tire for ordinary condi-

tions (dry, hard surface runway). However,

the operating coefficient of braking friction is

controlled by the pilot by the use of brakes.

The acceleration of the airplane during the

landing roll is negative (deceleration) and will

be considered to be in that sense. At any in-

stant during the landing roll the acceleration

is a function of the net retarding force and the

airplane mass. From Newton’s second law of

motion:

B = Fr/M

or

where

a=g 0+/W)

a= acceleration, ft. per seca (negative)

Fr=net retarding force, lbs.

g= gravitational acceleration, ft. per sec.’

W=weight, lbs.

M= mass, slugs

= Wig

The net retarding force on the airplane, Fr, is

the net of drag, D, braking friction, F, and

thrust, T. Thus, the acceleration (negative)

at any instant during the landing roll is :

d=$ (Df F--T)

NAVWEPS OO-EOT-RO

AtRPtANE PERFORMANCE

Figure 2.34 illustrates the typical variation

of the various forces acting on the aircraft

throughout the landing roll. If it is assumed

that the aircraft is at essentially constant angle

of attack from the point of touchdown, CL and

CD are constant and the forces of lift and drag

vary as the square of the velocity. Thus, lift

and drag will decrease linearly with 4 or V’

from the point of touchdown. If the braking

coefficient is maintained at the maximum

value, this maximum value of coefficient of

friction is essentially constant with speed and

the braking friction force will vary as the

normal force on the braking surfaces. As the

airplane nears a complete stop, the velocity

and lift approach zero and the normal force on

the wheels approaches the weight of the air-

plane. At this point, the braking friction

force is at a maximum. Immediately after

touchdown, the lift: is quite large and the

normal force on the wheels is small. As a re-

sult, the braking friction force is small. A

common error at this point is to apply exces-

sive brake pressure without sufficient normal

force on the wheels. This may develop a skid

with a locked wheel and cause the tire to blow

out so suddenly that judicious use of the brakes

is necessary.

The coefficient of braking friction can reach

peak values of 0.8 but ordinarily values near

0.5 are typical for the dry hard surface runway.

Of course, a slick, icy runway can reduce the

maximum braking friction coefficient to values

as low as 0.2 or 0.1: If the entire weight of

the airplane were the normal force on the brak-

ing surfaces, a coefficient of braking friction of

0.5 would produce a deceleration of %g, 16.1 ft.

per sec.a Most airplanes in ground effect

rarely produce lift-drag ratios lower than 3 or

4. If the lift of the airplane were equal to the

weight, an L/D = 4 would produce a decelera-

tion of xg, 8 ft. per sec.* By this comparison

it should be apparent that friction braking

offers the possibility of greater deceleration

than airplane aerodynamic braking. To this

end, the majority of airplanes operating from

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

FORCES ACTING ON THE AIRPLANE

DURING LAUDING ROLL

I-- LIFT

DRAG + BRAKING

POINT FINAL

OF LANDING STOP

TOUCHDOWN

Figure 2.34. Forces Acting on Airplane During Landing Roll

dry hard surface runways will require particular

techniques to obtain minimum landing dis-

tance. Generally, the technique involves low-

ering the nose wheel to the runway and retract-

ing the flaps to increase the normal force on

the braking surfaces. While the airplane drag

is reduced, the greater normal force can pro-

vide greater braking friction force to com-

pensate for the reduced drag and the net retard-

ing force is increased.

The technique necessary for minimum land-

ing distance can be altered~ to some extent in

certain situations. For example, low aspect

ratio airplanes with high longitudinal control

power can create very high drag at the high

speeds immediate to landing touchdown. If

the landing gear configuration or flap or

incidence setting precludes a large reduction

of CL, the normal force on the braking surfaces

and braking friction force capability are rela-

tively small. Thus, in the initial high speed

part of the landing roll, maximum deceleration

would be obtained by creating the greatest

possible aerodynamic drag. By the time the

aircraft has slowed to 70 or 80 percent of the

touchdown speed, aerodynamic drag decays

but braking action will then be effective.

Some form of this technique may be necessary

to achieve minimum distance for some con-

figurations when the coefficient of braking

friction is low (wet, icy runway) and the

braking friction force capability is reduced

relative to airplane aerodynamic drag.

A distinction should be made between the

techniques for minimum landing distance and

an ordinary landing roll with considerable

excess runway .available. Minimum landing

distance will be obtained from the landing

speed by creating a continuous peak decelera-

tion of the airplane. This condition usually

requites extensive use of the brakes for maxi-

mum deceleration. On the other hand, an

ordinary landing roll with considerable excess

runway may allow extensive use of aero-

dynamic drag to minimize wear and tear on

the tires and brakes. If aerodynamic drag is

NAVWEPS 00-ROT-80

AIRPLANE PERFORMANCE

sufficient to cause deceleration of the airplane

it can be used in deference to the brakes in the

early stages of the landing roll, i.e., brakes

and tires suffer from continuous, hard use but

airplane aerodynamic drag is free and does not 1

wear out with use. The use of aerodynamic

drag is applicable only for deceleration to 60

ot 70 percent of the touchdown speed. At

speeds less than 60 to 70 percent of the touch-

down speed, aerodynamic drag is so slight as

to be of little use and braking must be utilized

to produce continued deceleration of the

airplane.

Powerplant thrust is not illustrated on

figure 2.34 for there are so many possible

variations. Since the objective during the

landing toll is to decelerate, the powerplant

thrust should be the smallest possible positive

value or largest possible negative value. In

the case of the turbojet aircraft, the idle

thrust of the engine is nearly constant with

speed throughout the landing roll. The idle

thrust is of significant magnitude on cold days 1

because of the low compressor inlet air temper-

ature and low density altitude. Unfortu-

nately, such atmospheric conditions usually

have the corollary of poor braking action be-

cause of ice or water on the runway. The

thrust from a windmilling propeller with the

engine at idle can produce large negative thrust

early in the landing roll but the negative force

decreases with speed. The .large negative

thrust at high speed is valuable in adding to

drag and braking friction to increase the net

retarding force.

Various devices can be utilized to provide

greater deceleration-of the airplane or to mini-

mize the wear and teat on tires and brakes.

‘The drag parachute can provide a large retatd-

ing force at high 4 and greatly increase the de-

celeration during the initial phase of landing

toll. It should be noted that the contribution

of the drag chute is important only during the

high speed portion of the landing roll. For

maximum effectiveness, the drag chute must be

deployed immediately after the airplane is in

contact with the runway. Reverse thrust of

Revised January 1965

NAVWEPS 00-EOT-80

AIRPLANE PERFORMANCE

propellers is obtained by rotating the blade

angle well below the low pitch stop and

applying engine power. The action is to ex-

tract a large amount of momentum from the

airstream and thereby create negative thrust.

The magnitude of the reverse thrust from pro-

pellets is very large, especially in the case of

the turboprop where a very large shaft power

can be fed into the propeller. In the case of

reverse propeller thrust, maximum effective-

ness is achieved by use immediately after the

airplane is in contact with the runway. The

reverse thrust capability is greatest at the

high speed and, obviously, any delay in pro-

ducing deceleration allows runway to pass by

at a rapid rate. Reverse thrust of turbojet

engines will usually employ some form of

vanes, buckets, or clamshells in the exhaust to

turn or direct the exhaust gases forward.

Whenever the exit velocity is less than the in-

let velocity (or negative), a negative momen-

tum change occurs and negative thrust is

produced. The reverse jet thrust is valuable

and effective but it should not be compared

with the reverse thrust capability of a com-

parable propeller powerplant which has the

high intrinsic thrust at low velocities. As

with the propeller reverse thrust, jet reverse

thrust must be applied immediately after

ground contact for maximum effectiveness in

reducing landing distance.

FACTORS AFFECTING LANDING PER-

FORMANCE. In addition to the important

factors of proper technique, many other vari-

ables affect the landing performance of an air-

plane. Any item which alters the landing

velocity or deceleration during landing toll

will affect the landing distance. As with

takeoff performance, the relationships of uni-

formly accelerated motion will be assumed

applicable for studying the principal effects on

landing distance. The case of uniformly ac-

celerated motion defines landing distance as

varying directly as the square of the landing

velocity and inversely as the acceleration dur-

ing landing toll.

where

Si = landing distance resulting from certain

values of landing velocity, Vi, and

acceleration, 6zi

S2=landing distance resulting from some

different values of landing velocity,

V2, or acceleration, a2

With this relationship, the effect of the many

variables on landing distance can be apptoxi-

mated.

The effect of gross wclght on landing distance

is one of the principal items determining the

landing distance of an airplane One effect

of an increased gross weight is that the airplane

will require a greater speed to support the

airplane at the landing angle of attack

and lift coefficient. The relationship of land-

ing speed and gross weight would be as

follows:

where

Vi=landing velocity corresponding to

some original weight, W,

Vs = landing velocity corresponding to

some different weight, W,

Thus, a given airplane in the landing con-

figuration at a given gross weight will have a

specific landing speed (MS ot CAS) which is

invariant with altitude, temperature, wind,

etc., because a certain value of 4 is necessary

to provide lifr equal to weight at the landing

C,. As an example of the effect of a change in

gross weight, a 21 percent increase in landing

weight will require a 10 percent increase in

landing speed to support the greater weight.

When minimum landing distances are con-

sidered, braking friction forces predominate

during the landing toll and, for the majority

of airplane configurations, braking friction is

the main source of deceleration. In this case,

an increase in gross weight provides a greater

NAVWEPS OO-ROT-80

AIRPLANE PERFORMANCE

normal force and increased braking friction

force to cope with the increased mass. Also,

the higher landing speed at the same CL and

CD produce an average drag which increased in

the same proportion as the increased weight.

Thus, increased gross weight causes like in-

creases in the sum of drag plus braking friction

and the acceleration is essentially unaffected.

To evaluate the effect of gross weight on

landing distance, the following relationships

are used:

the effect of weight on landing velocity is

if the net retarding force increases in the

same proportion as the .weight, the accel-

eration is unaffected.

the effect of these items on landing dis-

tance is,

or

$2 w*

s,=w,

In effect, the minimum landing distance will

vary directly as the gross weight. For ex-

ample, a 10 percent increase in gross weight

at landing would cause:

a 5 percent increase in landing velocity

a 10 percent increase in landing distance

A contingency of the previous analysis is the

relationship between weight and braking ftic-

tion force. The maximum coefficient of brak-

ing friction is relatively independent of the

usual range of normal forces and rolling speeds,

e.g., a 10 percent increase in normal force would

create a like 10 percent increase in braking

friction force. Consider the case of two air-

planes of the same type and c.g. position but

of ~diffetent gross weights. If these two air-

planes are rolling along the runway at some

speed at which aerodynamic forces are negli-

gible, the use of the maximum coefficient of

braking friction will bring both airplanes to

a stop in the same distance. The heavier ait-

plane will have the gteater mass to decelerate

but the greater normal force will provide a

greater retarding friction force. As a result,

both airplanes would have identical accelera-

tion and identical stop distances from a given

velocity. However, the heavier airplane

would have a greater kinetic energy to be dis-

sipated by the brakes and the principal differ-

ence between the two airplanes as they reach

a stop would be that the heavier airplane

would have the hotter brakes. Therefore,

one of the factors of braking performance is the

ability of the brakes to dissipate energy with-

out developing excessive temperatures and

losing effectiveness.

To appreciate the effectiveness of modern

brakes, a 30,000-lb. aircraft landing at 175

knots has a kinetic energy of 41 million ft.-lbs.

at the instant of touchdown. In a minimum

distance landing, the brakes must dissipate

most of this kinetic energy and sach brake must

absotb an input power of approximately 1,200

h.p. for 25 seconds. Such requirements for

brakes are extreme but the example serves to

illustrate the ptoblems of brakes for high

performance airplanes.

While a 10 percent increase in landing

weight causes :

a 5 percent higher landing speed

a 10 percent greater landing distance,

it also produces a 21 percent increase in the

kinetic energy of the airplane to be dissipated

during the landing roll. Hence, high landing

weights may approach the energy dissipating

capability of the brakes.

The s&t of wind on landing distance is large

and deserves proper consideration when pre-

dicting landing distance. Since the airplane

will land at a particular airspeed independent

of the wind, the principal effect of wind on

landing distance is due to the change in the

ground velocity at which the airplane touches

down. The effect of wind on acceleration

duting the landing distance is identical to the

NAVWEPS OO-ROLRO

AIRPlANE PERFORMANCE

effect on takeoff distance and is approximated

by the following relationship:

$2 v 2 ..-.= Sl c 1 13

where

Si= zero wind landing distance

Sa=landing distance into a headwind

I’, = headwind velocity

Vi=landing ground velocity with zero

wind or, simply, the landing airspeed

As a result of this relationship, a headwind

which is 10 percent of the landing airspeed will

reduce the landing distance 19 percent but a

tailwind (or ‘negative headwind) which is 10

percent of the landing speed will increase the

landing distance 21 percent. Figure 2.33 illus-

trates this general effect.

The effect of ranway slope on landing distance

is due to the component of weight along the

inclined path of the airplane. The relation-

ship is identical to the case of takeoff per-

formance but the magnitude of the effect is

not as great. While account must be made

for the effect, the ordinary values of runway

slope do not contribute a large effect on landing

distance. For this reason, the selection of the

landing runway will ordinarily favor the direc-

tion with a downslope and’headwind rather

than an upslope and tailwind.

The effect of pressure altitude and ambient tem-

perature is to define density altitude and its effect

on landing performance. An increase in dens-

ity altitude will increase the landing velocity

but will not alter the net retarding force. If

a given weight and configuration of airplane

is taken to altitude above standard sea level,

the airplane will still require the same 4 to

provide lift equal to weight at the landing C,.

Thus, the airplane at altitude will land at the

same equivalent airspeed (EAS) as at sea level

but, because of the reduced density, the true

airspeed (TM) will be greater. The relation-

ship between true airspeed and equivalent air-

speed is as follows:

TAS 1

E-33=5

where

TAS= true airspeed

EAS= equivalent airspeed

a=altitude density ratio

Since the airplane lands at altitude with the

same weight and dynamic pressure, the drag

and braking friction throughout the landing

toll have the same values as at sea level. As

long as the condition is within the capability

of the brakes, the net retarding force is un-

changed and the acceleration is the same as

with the landing at sea level.

To evaluate the effect of density altitude on

landing distance, the following relationships

are used :

since an increase in altitude does not alter

acceleration, the effect would be due to

the greater TAS

where

S1= standard sea level landing dis-

tance

Sa=Ianding distance at altitude

c=altitude density ratio

From this relationship, the minimum land-

ing distance at 5,OCO ft. (u=O.8617) would be

16 percent greater than the minimum landing

distance at sea level. The approximate increase

in landing distance with altitude is approxi-

mately 3% percent for each 1,ooO ft. of altitude.

Proper accounting of density altitude is neces-

sary to accurately predict landing distance.

The effect of proper landing velocity is impor-

tant when runway lengths and landing dis-

tances are critical. The landing speeds specified

in the flight handbook ate generally the mini-

mum safe speeds at which the airplane can be

landed. Any attempt to land at below the

NAVWEPS O&ROT-R0

AIRPLANE PERFORMANCE

specified speed may mean that the airplane may

stall, be difhcult to control, or develop high

rates of descent. On the other hand, an exces-

sive speed at landing may improve the control-

lability (especially in crosswinds) but will

cause an undesirable increase in landing dis-

tance. The principal effect of excess landing

speed is described by:

& v2 * -= - h 0 VI

Thus, a 10 percent excess landing speed would

cause a 21 percent increase in landing distance.

The excess speed places a greater working load

on the brakes because of the additional kinetic

energy to be dissipated. Also, the additional

speed causes increased drag and lift in the nor-

mal ground attitude and the increased lift will

reduce the normal force on the braking sur-

faces. The acceleration during this range of

speed immediately after touchdown may suffer

and it will be more likely that a tire can be

blown out from braking at this point. As a

result, 10 percent excess landing speed will

cause at JUJ; 21 percent greater landing dis-

tance.

The most critical conditions of landing per-

formance are the result of some combination of

high gross weight, density altitude, and un-

favorable wind. These conditions produce the

greatest landing distance and provide critical

levels of energy dissipation required of the

brakes. In all cases, it is necessary to make an

accurate prediction of minimum landing dis-

tance to compare with the available runway.

A polished, professional landing technique is

necessary because the landing phase of flight

accounts for more pilot caused aircraft acci-

dents than any other single phase of flight.

In the prediction of minimum landing dis-

tance from the handbook data, the following

considerations must be given:

(1) Pressure altitude and temperature-to

define the effect of density altitude.

(2)’ Gross weight-which define the CAS

or EAS for landing.

(3) Wind-a large effect due to wind or

wind component along the runway.

(4) Runway slope-a relatively small cor-

rection for ordinary values of runway slope.

IMPORTANCE OF HANDBOOK PER-

FORMANCE DATA. The performance sec-

tion or supplement of the flight handbook con-

tains all the operating data for the airplane.

For example, all data specific to takeoff, climb,

range, endurance, descent and landing are in-

cluded in this section. The ordinary use of

these data in flying operations is mandatory

and great knowledge and familiarity of the air-

plane can be gained through study of this

material. A complete familiarity of an air-

plane’s characteristics can be obtained only

through extensive analysis and study of the

handbook data.

NAVWEPS 00-801-80

HIGH SPEED AERODYNAMICS

Chapter 3

HIGH SPEED AERODYNAMICS

Developments in aircraft and powerplants

have produced high performance airplanes

with capabilities for very high speed flight.

The study of aerodynamics at these very high

flight speeds has many significant differences

from the study of classical low speed aero-

dynamics. Therefore, it is quite necessary

that the Naval Aviator be familiar with the

nature of high speed airflow and the charac-

teristics of high performance airplane

configurations.

GENERAL CONCEPTS AND SUPERSONIC

FLOW PATTERNS

NATURE OF COMPRESSIBILITY

At low flight speeds the study of aero-

dynamics is greatly simplified by the fact

that air may experience relatively small

changes in pressure with only negligible

changes in density. This airflow is termed

incompressible since the air may undergo changes

NAVWEPS 00-601-60

HIGH SPEED AERODYNAMICS

in pressure without apparent changes in den-

sity. Such a condition of airflow is analogous

to the flow of water, hydraulic fluid, or any

other incompressible fluid. However, at high

flight speeds the pressure changes that take

place are quite large and significant changes

in air density occur. The study of airflow at

high speeds must account for these changes

1 in air density and must consider that the

1 air is compressible and that there will be

“compressibility effects.”

A factor of great importance in the study of

high speed airflow is the speed of sound.

The speed of sound is the rate at which small

pressure disturbances will be propagated

through the air and this propagation speed

is solely a function of air temperature. The

accompanying table illustrates the variation

of the speed of sound in the standard

atmosphere.

TABLE 3-I. V.r;afIm <

Altitude in

,I T<

the -

--

-

D F. - c. K?uI,

59.0 15.0 661.7

41.1 5.1 650.3

23.3 -4.8 6%. 6

5.5 -14.7 6X6.7

--12., --24.6 614.6

--30.2 -34.5 602.2

-48.0 -44.4 589.6

-65.8 --w.3 516.6

-69.7 -56.5 573:s

-69.1 -56.5 573.8

-69.7 -56.5 573.8

As an object moves through the air mass,

velocity and pressure changes occur which

create pressure disturbances in the airflow sur-

rounding the object. Of course, these pressure

disturbances are propagated through the air

at the speed of sound. If the object is travel-

ling at low speed the pressure disturbances are

propagated ahead of the object and the airflow

immediately ahead of the object is influenced

by the pressure field on the object. Actually,

these pressure disturbances are transmitted in

all directions and extend indefinitely in all

directions. Evidence of this “pressure warn-

ing’ ’ is seeii in the typical subsonic flow

pattern of figure 3.1 where there is upwash

and flow direction change well ahead of the

leading edge. If the object is travelling at

some ,speed above the speed of sound the air-

flow ahead of the object will not be influenced

by the pressure field on the object since pres-

-sure disturbances cannot. be propagated ahead

of the object. Thus, as the flight speed nears

the speed of sound a compression wave will

form at the leading edge and all changes in

velocity and pressure will take place quite

sharply and suddenly. The airflow, ahead of

the object is not influenced until the air par-

ticles are suddenly forced out .of the way by

the concentrated pressure wave set up by the

object. Evidence of this phenomenon is seen

in the typical supersonic flow pattern of

figure 3.1.

The analogy of surface waves on the water

may help clarify these phenomena. Since a

surface wave is simply the propagation of a

pressure disturbance, a ship moving at a speed

much less than the wave speed will not form

a “bow wave.” As the. ship’s speed nears

the wave pro$agation speed the bow wave

will form and become stronger as speed is

increased beyond the wave speed.

At this point it should become apparent

that all compressibility effects depend upon

the relationship of airspeed to the speed of

sound. The term used to describe this rela-

tionship is the Mach number, M, and this

term is the ratio of the true airspeed to the

speed of sound. ,-I

M=;

where

M=Mach number

V= true airspeed, knots

d= speed of sound, knots

=a&

aO=speed of sound at standard sea level

conditions, 661 knots

e= temperature ratio

= T/T,

Revised January 1965

NAVWEPS OD-8OT-80

HIGH SPEED AERODYNAMICS

TYPICAL SUBSONIC FLOW PATTERN

FLOW DIRECTION CHANGES WELL AHEAD

OF LEADING EDGE

TYPICAL SUPERSONIC FLOW PATTERN

APPARENT AHEAD OF LEADING EDGE

Figure 3.1. Comparison of Subsonic and Supersonic Now Patterns

NAVWEPS OCMOT-60

HIGH SPEED AERODYNAMICS

It is important to note that compressibility

effects are not limited to flight speeds at and

above the speed of sound. Since any aircraft

will have some aerodynamic shape and will

be developing lift there will be local flow

velocities on the surfaces which arc greater

than the flight speed. Thus, an aircraft can

experience compressibility effects at flight

speeds well below the speed of sound. Since

there is the possibility of having both subsonic

and supersonic flows existing on the aircraft

it is convenient to define certain regimes of

flight. These regimes are defined approxi-

mately as follows:

Subsonic-Mach numbers below 0.75

Transonic-Mach numbers from 0.75 to

1.20

Supersonic-Mach numbers from 1.20 to

5.00

Hypersonic-Mach numbers above 5.00

While the flight Mach numbers used to define

these regimes of flight are quite approximate,

it is important to appreciate the types of flow

existing in each area. In the subsonic regime

it is most likely that pure subsonic airflow

exists on all parts of the aircraft. In the

transonic regime it is very probable that flow

on the aircraft components may be partly sub-

sonic and partly supersonic. The supersonic

and hypersonic’ flight regimes will provide

definite supersonic flow velocities on all parts

of the aircraft. Of course, in supersonic flight

there will be some portions of the boundary

layer which are subsonic but the predominating

flow is still supersonic.

The principal differences between subsonic

and supersonic flow are due to the cmprrs-

Jibi& of the supersonic flow. Thus, any

change of velocity or pressure of a supersonic

flow will produce a related change of density

which must be considered and accounted for.

Figure 3.2 provides a comparison of incom-

pressible and compressible flow through a

closed tube. Of course, the condition of con-

tinuity must exist in the flow through the

closed tube; the mass flow at any station along

the tube is constant. This qualification must

exist in both compressible and incompressible

cases.

The example of subsonic incompressible flow

is simplified by the fact that the density of

flow is constant throughout the tube. Thus,

as the flow approaches a constriction and the

streamlines converge, velocity increases and

static pressure decreases. In other words, a

convergence of the tube requires an increasing

velocity to accommodate the continuity of

flow. Also, as the subsonic incompressible

flow enters a diverging section of the tube,

velocity decreases and static pressure increases

but density remains unchanged. The behavior

of subsonic incompressible flow is that a con-

vergence causes expansion (decreasing pressure)

while a divergence causes compression (in-

creasing pressure).

The example of supersonic compressible flow

is complicated by the fact that the variations

of flow density are related to the changes

in velocity and static pressure. The behavior

of supersonic compressible flow is that a con-

vergence causes compression while a divergence

causes expansion. Thus, as the supersonic

compressible flow approaches a constriction

and the streamlines converge, velocity dc-

creases and static pressure increases. Con-

tinuity of mass flow is maintained by the

increase in flow density which accompanies the

decrease in velocity. As the supersonic com-

pressible flow enters a diverging section of the

tube, velocity increases, static pressure de-

creases, and density decreases to accommodate

the condition of continuity.

The previous comparison points out three 1

significant differences between supersonic corn- 1

pressible and subsonic incompressible flow.

(a) Compressible flow includes the addi-

tional variable of flow density.

(b) Convergence of flow causes expansion

of incompressible flow but compression of

compressible flow.

(c) Divergence of flow causes compression

of incompressible flow but expansion of

compressible flow.

Revised January 1965

NAVWEPS OD-8OT-80

HIGH SPEEO AERODYNAMICS

INCOMPRESSIBLE

(SUBSONIC)

//------

--

--- -- ---- --- -- --_-__-- ------

__--__----- -------

---- --- ---_ ---

-- ---_ -----

_---- ---__-

.,,,,,,,,,,l--~-

CONVERGING

INCREASING VELOCITY DECREASING VELOCITY

DECREASING PRESSURE INCREASING PRESSURE

CONSTANT DENSITY CONSTANT DENSITY

COMPRESSIBLE

(SUPERSONIC)

CONVERGING DIVERGING

DECREASING VELOCITY INCREASING VELOCITY

INCREASING PRESSURE DECREASING PRESSURE

JNCI~EASJ~~G DENSITY DECREASING DENSITY

figure 3.2. Comparison of Compressible and lncomprossible Flow Through a Closed Tube

NAVWEPS OD-SOT-80

HIGH SPEED AERODYNAMICS

OBLIQUE SHOCK WAVE-,

SUPERSONIC FLOW INTO A CORNER

SERfES OFOBLIOUE SHOCK WAVES

r\

SUPERSONIC FLOW INTO A ROUNDED CORNER

Figure 3.3. Oblique Shock Wave Formotion

‘I-YPICAL SUPERSONIC FLOW PATTERNS

When supersonic flow is clearly established,

all changes in velocity, pressure, density, flow

direction, etc., take place quite suddenly and

in relatively confined areas. The areas of flows

change are generally distinct and the phenom-

ena are referred to as “wave” formations. All

compression waves occur suddenly and are

wasteful of energy. Hence, the compression

waves are distinguished by the sudden “shock”

type of behavior. All expansion waves are not

so sudden in their occurrence and are not waste-

ful of energy like the compression shock waves.

Various types of waves can occur in supersonic

flow and the nature of the wave formed depends

upon the airstream and the shape of the object

causing the flow change. Essentially, there

are three fundamental types of waves formed

in supersonic flow: (1) the oblip shock wave

(compression), (2) the normal shock wave

(compression), (3) the expansion wave (no

shock).

OBLIQUE SHOCK WAVE. Consider the

case where a supersonic airstream is turned

into the preceding airflow. Such would be

the case of a supersonic flow “into a comer”

as shown in figure 3.3. A supersonic airstream

passing through the oblique shock wave will

experience these changes:

(1) The airstream is slowed down; the

velocity and Mach number behind the wave

are reduced but the flow is still supersonic

(2) The flow direction is changed to flow

along the surface

(3) The static pressure of the airstrea:m

behind the wave is increased

(4) The density of the airstream behind

the wave is increased

(5) Some of the available energy of the

airstream (indicated by the sum of dynamic

and static pressure) is dissipated and turned

into unavailable heat energy. Hence, the

shock wave is wasteful of energy.

A typical case of oblique shock wave forma-

tion is that of a wedge pointed into a super-

sonic airstream. The oblique shock wave

NAVWEPS OD-807-80

HIGH SPEED AERODkNAMlCS

will form on each surface of the wedge and the

inclination of the shock wave will be a func-

tion of the free stream Mach number and the

wedge angle. As the free stream Mach number

increases, the shock wave angle decreases; as

the wedge angle increases the shock wave

angle increases, and, if the wedge angle is in-

creased to some critical amount, the shock

wave will detach from the leading edge of the

wedge. It is important to note that detach-

ment of the shock wave will produce sub$onic

flow immediately after the central portion of

the shock wave. Figure 3.4 illustrates these

typical flow patterns and the effect of Mach

number and wedge angle.

The previous flow across a wedge in a

supersonic airstream would allow flow in ;UU

dimensions. If a cone were placed in a super-

sonic airstream the airflow would occur in

three dimensions and there would be some

noticeable differences in flow characteristics.

Three-dimensional flow for the same Mach

number and flow direction change would pro-

duce a weaker shock wave with less change in

pressure and density. Also, this conical wave

formation allows changes in airflow that con-

tinue to occur past the wave front and the

wave strength varies with distance away from

the surface. Figure 3.5 depicts the typical

three-dimensional flow past a cone.

Oblique shock waves can be reflected like

any pressure wave and this effect is shown in

figure 3.5. This reflection appears logical and

necessary since the original wave changes the

flow direction toward the wall and the reflected

wave creates the subsequent flow change to

cause the flow to remain parallel to the wall

surface. This reflection phenomenon places

definite restrictions on the size of a model in a

wind tunnel since a wave reflected back to the

model would cause a pressure distribution not

typical of free flight.

NORMAL SHOCK WAVE. If a blunt-

nosed object is placed in a supersonic airstream

the shock wave which is formed will be de-

tached from the leading edge. This detached

NAVWEPS 00-8OT-80

HIGH SPEED AERODYNAMICS

DETACHED

M = 3.0

M = 3.0 \

Figure 3.4. Shock Waves Formed by Various Wedge Shapes