Chapter 1 — Part 3

NAVWEPS Oo-ROT-80

AIRPLANE PERFORMANCE

F=mo

F=$(mV)

T, = Q (V,-V,)

Pa= T,, V,

Pw=Q/,(v2-v,)2

2VI 7)p=-

v2 +v,

1.0

.9

.6

.7

.6

7p .5

.4

.3

.2

.I

0 .I .2 .3 .4 .5 .6 .? .6 .9 1.0

%f2

Figure 2.5. Principles of Propulsion

NAWEPS 0040140

AlRPLANE PERFORMANCE

Of course, the development of thrus,t with

some finite mass flow will require some finite

velocity change and there will be the inevita-

ble waste of power in the airstream. In order

to achieve high efficiency of propulsion, the

thrust should be developed with a minimum

of wasted power.

The propulsion efficiency of the jet power-

plant can be evaluated by comparing the

propulsive output power with the input power.

Since the input power is the sum of the output

power and wasted power, an expression for

propulsion efficiency can be derived.

Pa

vp=Pa+Pw

zv,

')p= v*+v1

where

trp = propulsion efficiency

9=“eta”

Pa = propulsive power available

= TCZV~

Pw= power wasted

The resulting expression for propulsion effi-

ciency, v,,, shows a dependency on the flight

velocity, V,, and the jet velocity, VZ. When

the flight velocity is zero, the propulsion

efficiency is zero since all power generated is

wasted in the slipstream and the propulsive

power is zero. The propulsion efliciency would

be I.00 (or 100 percent) only when the flight

velocity, Vi, equals the jet velocity, Vz.

Actually, it would not be possible to produce

thrust under such conditions with a finite mass

flow. While 100 percent efficiency of propul-

sion can not be attained practically, some

insight is furnished to the means of creating

high values of propulsion efficiency. To ob

tain high propulsion efficiency it is necessary

to produce the required thrust with the highest

possible mass flow and lowest possible velocity

change.

The graph of figure 2.5 shows the variation

of propulsion efficiency, qP, with the ratio of

flight speed to jet velocity, VJV,. To achieve

a propulsion efficiency of 0.85 requires that the

flight velocity be approximately 75 percent of

the slipstream speed relative to the airplane.

Such a propulsive efficiency could be typical

of a propeller powered airplane which derives

its thrust by the propeller handling a large

mass flow of air. The typical turbojet power-

plant cannot achieve such high propulsive

ethciency because the thrust is derived with a

relatively smaller mass flow and larger vcloc-

ity change. For example, if the jet velocity is

1,200 ft. per sec. at a flight velocity of 600 ft.

per sec., the propulsion efficiency is 0.67. The

ducted fan, bypass jet, and turboprop are vari-

aCon -which impiove tliC propulsive efIiciency

of a type of powerplant which has very high

power capability.

When the conditions of range, endurance, or

economy of operation are predominant, high

propulsion efhciency is necessary. Thus, the

propeller powered airplane with its inherent

high propulsive efliciency will always find ap

plication. The requirements of very high

speed and high altitude demand very high

propulsive power from relatively small powcr-

plants. When there are practical limits to the

increase of mass flow, high output is obtained

by large velocity changes and low propulsive

efficiency is an inevitable consequence.

TURBOJET ENGINES

The turbojet engine has foundwidespread USC

in aircraft propulsion because of the relatively

high power output per powerplant weight and

size. Very few aircraft powerplants can com-

pare with the high output, flexibility, simplic-

ity, and small size of the aircraft gas turbine.

The coupling of the propeller and recipro-

cating engine is one of the most efficient means

known for converting fuel energy into propul-

sive energy. However, the intermittent action

of the reciprocating engine places practical

limits to the airflow that can be processed and

restricts the development of power. The con-

tinuous, steady flow feature of the gas turbine

allows such a powerplant to process consider-

ably greater airflow and, thus, utilize a greater

expenditure of fuel energy. While the pro-

pulsive efficiency of the turbojet engine is con-

siderably below that of the reciprocating en-

gine-propeller combination, the specific power

output of the turbojet at high speeds is quite

superior.

compressor pressure ratio should be high to

produce a high thermal efliciency in the engine

The area XCDZ represents the work done by

the compressor during the compression of the

unit weight of air. Of course, certain losses

and inefliciencies are incurred during the com-

pression and the power required to operate the

compressor will be greater than that indicated

by the work done on the engine airflow.

The operation of the turbojet engine involves

a relatively large change in velocity being im-

parted to the mass flow through the engine.

Figure 2.6 illustrates the operation of a typical

turbojet engine by considering the processing

given a unit weight of inlet airflow. Consider

a unit weight of ambient air approaching the

inlet to the engine then experiencing the

changes in pressure and volume as it is proc-

essed by’the turbojet. The chart of pressure

versus volume of figure 2.6 shows that the unit

weight of airflow at atmospheric condition A

is delivered to the inlet entrance at condition

B. The purpose of the inlet or diffuser as to

reduce the velocity and increase the pressure

of the flow entering the compressor section.

Thus, the aerodynamic compression produces

an increase in pressure and decrease in volume

of the unit weight of air and delivers air to

the compressor at condition C. The work done

by the aerodynamic compression of the inlet

ot diffuser is represented by the area ABCX.

Generally, most conventional turbojet engines

require that the compressor inlet flow be sub-

sonic and supersonic flight will involve con-

siderable aerodynamic compression in the inlet.

Compressed air is discharged from the com-

pressor to the combustion chamber at condition

D. Fuel is added in the combustion chamber,

and the combustion of fuel liberates consider-

able heat energy. The combustion process in

the gas turbine differs from that of the recipro-

cating engine in that the process is essentially

a constant pressure addition of heat energy.

As a result, the combustion of fuel causes a

large change in temperature and large change

of volume of the unit weight of airflow. The

process in the combustion chamber is repre-

sented by the change from point D to point E of

the pressure-volume diagram of figure 2.6.

Air delivered to the compressor inlet at con-

dition C is then subject to further compression

through the compressor section. As a result

of the function of the compressor, the unit

weight of air is subject to a decrease in volume

and increase in pressure to condition D. The

NAVWEPS 00-801-80

ARPLANE PERFORMANCE

The combustion products are delivered to the

turbine section where sufficient work must be

extracted to power the compressor section.

The combustion chamber discharges high tem-

perature, high pressure gas to the turbine where

a partial expansion is accomplished with a drop

in pressure and increase in volume to point F

on the pressure-volume diagram. The work

extracted from the unit weight of air by the

turbine section is represented by the area

ZEFY. As with the compressor, the actual

shaft work extracted by the turbine will differ

from that indicated by the pressure-volume

diagram because of certain losses incurred

through the turbine section. For steady, sta-

bilized operation of the turbojet engine the

power extracted by the turbine will equal the

power required to operate the compressor. If

the turbine power exceeds the compressor

power required, the engine will accelerate; if

the turbine power is less than the compressor

power required, the engine will decelerate.

NAVWEPS 00-807-80

AIRPLANE PERFORMANCE

INLET OR

DIFFUSER COMPRESSOR

COMBUSTION TAILPIPE

CHAMBER TURBINE NOZZLE

TURBOJET ENGINE CYCLE

iiT! TURBINE WORK .

E Y

it

COMPRESSOR

I 1 c

VOLUME. CU. FT.

Figure 2.6. Turbojet Engines

The partial expansion of the gases through

the turbine will provide the power to operate

the engine. As. the gases are discharged from

the turbine at point F, expansion will continue

through the tailpipe nozzle. until atmospheric

pressure is achieved in the exhaust. Thus,

continued expansion in the jet nozzle will re-

duce the pressure and increase the volume of

the unit weight of air to point G on the pressure

volume diagram. As a result, the final jet

velocity is greater than the inlet velocity and

the momentum change necessary for the .de-

velopment of thrust ha~s’been created. The

area YFGA represents the work remaining to

provide the expansion to jet velocity after the

turbine has extracted the work requited to

operate the compressor.

Of course, the combustion chamber discharge

could be more completely expanded through a

larger turbine section and the net power could

be used to operate a propeller rather than pro-

vide high exhaust gas velocity. For certain

applications, the gas turbine-propeller combi-

nation could utilize the high power capability

of the gas turbine with greater propulsive

efficiency.

FUNCTION OF THE COMPONENTS.

Each of the engine components previously de-

scribed will contribute some function affecting

the efficiency and output of the turbojet engine.

For this reason, each of these components

should be analyzed to determine the requite-

ments for satisfactory operating characteristics.

The i&t or &@er must be matched to the

powerplant to provide the compressor entry

with the required airflow. Generally, the

compressor inlet must receive the required air-

flow at subsonic velocity with uniform dis-

tribution of velocity and direction at the

compressor face. The diffuser must capture

high energy air and deliver it at low Mach

number uniformly to the compressor. When

the inlet is along the sides of the fuselage, the

edges of the inlet must be located such that

the inlet receives only high energy air and

provision must be made to dispose of the

NAVWEPS OO-ROT-RO

AtRPlANE PERFORMANCE

boundary layer along the fuselage surface. At

supersonic flight speeds, the diffuser must slow

the air to subsonic with the least waste of

energy in the inlet air and accomplish the

process with a minimum of aerodynamic drag.

In addition, the inlet must be efIicient and

stable in operation throughout the range of

angles of attack and Mach numbers of which

the airplane is capable.

The operation of the compressor can be af-

fected greatly by the uniformity of flow at the

compressor face. When large variations in

flow velocity and direction exist at the face of

the axial compressor, the efficiency and stall-

surge limits are lowered. Thus, the flight

conditions which involve high angle of attack

and high sideslip can cause deterioration of

inlet performance.

The compreJ.ror s&on is one of the most im-

portant components of the turbojet engine.

The compressor must furnish the combustion

chamber with large quantities of high pressure

air in a most efficient manner. Since the com-

pressor of a jet engine has no direct cooling,

the compression process takes place with a

minimum of heat Ioss of the compressed air.

Any friction loss or inefficiency of the com-

pression process is manifested as an undesirable

additional increase in the temperature of the

compressor discharge air. Hence, compressor

efficiency will determine the compressor power

necessary to create the pressure rise of a given

airflow and will affect the temperature change

which can take place in the combustion

chamber.

The compressor section of a jet engine may

be an axial flow or centrifugal flow compressor.

The centrifugal flow compressor has great util-

ity, simplicity, and flexibility of operation.

The operation of the centrifugal compressor

requires relatively low inlet velocities and a

plenum chamber or expansion space must be

provided for the inlet. The impeller rotating

at high speed receives the inlet air and pto-

vides high acceleration by virtue of centrifugal

force. As a result, the air leaves the impeller

NAVWEPS GOdOT-

AIRPLANE PERFORMANCE

DWGLE ENTRY

CENfRlFuGAL COMPRESSCR

f-~&ARGE

CENTRIFUGAL COMPRESSOR

9A

AXIAL FLOW COMPRESSOR

STA’VM BLADES7

INLET

SHAFT7

COMPRESSOR BLADING

USCHARGE

ROTATING

Rows

Figure 2.7. Compressor Types

at very high velocity and high kinetic energy.

A pressure rise is produced by subsequent ex-

pansion in the diffuser manifold by converting

the kinetic energy into static pressure energy.

The manifold then distributes the high pres-

sure discharge to the combustion chambers.

A double entry impeller allows a given diam-

eter compressor to process a greater airflow.

The major components of the centrifugal com-

pressor are illustrated in figure 2.7.

The centrifugal compressor can provide a

relatively high pressure ratio per stage but the

provision of more than one or two stages is

rarely feasible for aircraft turbine engines.

The single stage centrifugal compressor is

capable of producing pressure ratios of about

three or four with reasonable efficiency. &es-

sure ratios greater than four require such high

impeller tip speed that compressor efficiency

decreases very rapidly. Since high pressure

ratios are necessary to achieve low fuel con-

sumption, the centrifugal compressor finds

greatest application to the smaller engines

where simplicity and flexibility of operation are

the principal requirements rather than high

efficiency.

The axial flow compressor consists of altet-

nate rows of rotating and stationary airfoils.

The major components of the axial flow com-

pressor ate illustrated in figure 2.7. A pressure

rise occurs through the row of rotating blades

since the airfoils cause a decrease in velocity

relative to the blades. Additional pressure

rise takes place through the row of stationary

blades since these airfoils cause a decrease in

the absolute velocity of flow. The decrease

I in velocity, relative or absolute, eEeLts a com-

1 ptession of the flow and causes the increase in

static pressure. While the pressure rise pet

stage of the axial compressor is relatively Jo%-,

the efficiency is very high and high pressure

ratios can be obtained efficiently by successive

axial stages. Of course, the eficient pressure

rise in each stage is limited by excessive gas

velocities. The multistage axial flow com-

pressor is capable of providing pressure ratios

NAWEPS 00-8OT-80

AIRPLANE PERFORMANCE

from five to ten (or greater) with efficiencies

which cannot be approached with a multi-

stage centrifugal compressor.

The axial flow compressor can provide

efficiently the high. pressure ratios necessary

for low fuel consumption. Also, the axial

compressor is capable of providing high air-

flow with a minimum of compressor diameter.

When compared with the centrifugal com-

pressor, the design and construction of the

axial compressor is relatively complex and

costly and the high efficiency is sustained over

a much narrower range of operating conditions.

For these reasons, the axial compressor finds

greatest application where rhe demands of

efficiency and output predominate over con-

siderations. of cost, simplicity, flexibility of

operation, etc. Multispool compressors and

variable statot blades serve to improve the

operating characteristics of the axial com-

pressor and increase the flexibility of operation.

The combustion chamber must convert the fuel

chemical energy into heat energy and cause a

large increase in the total energy of the engine

airflow. The combustion chamber will opet-

ate with one principal limitation: the dis-

charge from the combustion chamber must be

at temperatures which can be tolerated by the

turbine section. The combustion of liquid

hydrocarbon fuels can produce gas temperatures

which are in excess of 1,700 to 1,800° C.

However, the maximum continuous turbine

blade operating temperatures rarely exceed

NO0 to J,OOO” C and considerable excess air

must be used in the combustion chamber to

prevent exceeding these temperature limits.

While the combustion chamber design may

.take various forms and configurations, the

main features of a typical combustion chamber

ate illustrated by figure 2.8. The combustion

chamber receives the high pressure discharge

from the compressor and introduces apptoxi-

mately one half of this air into the immediate

area of the fuel spray. This primary combus-

tion air must be introduced with relatively

high turbulence and quite low velocities to

Revised Januwy 1965

NAVWEPS 00-80T-80

AIRPLANE PERFORMANCE

PRIMARY

COMBUSTION

AIR7

TYPICAL COMBUSTION CHAMBER

SECONDARY Al R

OR COOLING FLOW

FUEL

SPRAY

NOZZLE

DISCHARGE

TO TURBINE

NOZZLES

COMBUsTlON

NUCLEUS

TURBINE SECTION

TUR’BINE NOZZLE VANES

r / 11 TmaiNt BLADES

TURBINE WHEEL SHAFT

TURBIhE BLADING

(STATIONARY)

(ROTATING) TURBINE BLADES

Figure 2.8. Combustion Chamber and Turbine Components

maintain a nucleus of combustion in the com-

bustion chamber. In rhe normal combustion

process, the speed of flame propagation is quite

low and, if the local velocities are too high at

the forward end of the combustion chamber,

poor combustion will result and it is likely

rhar the flame will blow out. The secondary

air-or cooling flow-is introduced downstream

from the combustion nucleus to dilute the com-

bustion products and lower the discharge gas

temperature.

The fuel nozzle must provide a finely

atomized, evenly distributed spray of fuel

through a wide range of flow rates. Very

specialized design is necessary to provide a

nozzle with suitable characteristics. The

spray parrern and circulation in the combustion

chamber must make efficient use of the fuel by

complete combustion. The temperatures in

the combustion nucleus can exceed 1,700” to

1,SW’ C but the secondary air will dilute the

gas and reduce the temperature to some value

which can be tolerated in the turbine section.

A pressure drop will occur through the com-

bustion chamber to accelerate the combustion

gas rearward. In addition, turbulence and

fluid friction will cause a pressure drop but this

loss must be held to the minimum incurred by

providing complete combustion. Heat trans-

ferred through the walls of the combustion

chamber constitutes a loss of thermal energy

and should be held to a minimum. Thus, the

combustion chamber should enclose the com-

bustion space with a minimum of surface area

to minimize heat and friction losses. Hence,

the “annular” typ: combustion chamber offers

certain advantages over the multiple “can”

type combustion chamber.

The tur6inc section is the most critical element

of the turbojet engine. The function of the

turbine is to extract energy from the combus-

tion gases and furnish power to drive the com-

pressor and accessories. In the case of the

turboprop engine, the turbine section must ex-

tract a very large portion of the exhaust gas

NAVWEPS O(L8OT-80

AIRPLANE PERFORMANCE

energy to drive the propeller in addition to the

compressor and accessories.

The combustion chamber delivers high en-

ergy combustion gases to the turbine section at

high pressure and tolerable temperature. The

turbine nozzle vanes are a row of stationary

blades immediately ahead of the rotating tur-

bine. These blades form the nozzles which

discharge the combustion gases as high ve-

locity jets onto the rotating turbine. In this

manner, the high pressure energy of the com-

bustion gases is converted into kinetic energy

and a pressure and temperature drop takes

place. The function of the turbine blades

operating in these jets is to develop a tangen-

tial force along the turbine wheel thus extract-

ing mechanical energy from the combustion

gases. This is illustrated in figure 2.8.

The form of the turbine blades may be a com-

bination of two distinct types. The imp&c

type turbine relies upon the nozzle vanes to

accomplish the conversion of combustion gas

static pressure to high velocity jets. The

impulse turbine blades are shaped to produce

a large deflection of the gas and develop the

tangential force by the flow direction change.

In such a design, negligible velocity and pres-

sure drop occurs with the flow across the tur-

bine rotor blades. The reaction type turbine

differs in that large velocity and pressure

changes occur across the turbine rotor blades.

In the reaction turbine, rhe stationary nozzle

vanes serve only to guide the combustion gas

onto the turbine rotor with negligible changes

in velocity and pressure. The reaction tur-

bine rotor blades are shaped to provide a pres-

sure drop and velocity increase across the

blades and the reaction from this velocity in-

crease provides the tangential force on the

wheel. Generally, the turbine design is a

form utilizing some feature of each of the two

types.

The turbine blade is subjected to high

centrifugal stresses which vary as the square

of the rorative speed. In addition, the blade

Revised January 1965

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

is subjected to the bending and torsion of

the tangential impulse-reaction forces. The

blade must wirhstand these stresses which are

generally of a vibratory and cyclic nature

while at high temperatures. The elevated

temperatures at which the turbine must func-

tion produce extreme conditions for struc-

tural creep and fatigue considerations. Conse-

quently, the engine speed and temperature op-

erating limits demand very careful considera-

tion. Excessive engine temperatures or speeds

may produce damage which is immediately

apparent. However, creep and fatigue damage

is cumulative and even though damage may

not be immediately apparent by visual inspec-

tion, proper inspection methods (other than

visual) must be utilized and proper records

kept regarding the occurrence.

Actually, the development of high tempera-

ture alloys for turbines is a critical factor in the

develop,mcnt of high ei%ciciicy, high output

aircraft gas turbines. The higher the tem-

peratute of gases entering the turbine, the

higher can be the temperature and pressure of

the gases at discharge from the turbine with

greater exhaust jet velocity and thrust.

The function of the t&pipe or exhaust no?&

is to discharge the exhaust gases to the atmos-

phere at the highest possible velocity to pro-

duce the greatest momentum change and thrust.

If a majority of the expansion occurs through

the turbine section, there remains only to con-

duct the exhaust gases rearward with a mini-

mum energy loss. However, if the turbine

operates against a noticeable back pressure, the

nozzle must convert the remaining pressure

energy into exhaust gas velocity. Under ideal

conditions, the nozzle would expand the flow

to the ambient static pressure at the exhaust

and the area distribution in the nozzle must

provide these conditions. When the ratio af

exhaust gas pressure to ambient pressure is

relatively low and incapable of producing sonic

flow, a converging nozzle provides the expan-

sion. The exit area must be of proper size to

bring about proper exit conditions. If the exit

area is too large, incomplete expansion will

take place; if the exit area is too small, an over

expansion tendency results. The exit area can

affect the upstream conditions and must be

properly proportioned for overall performance.

When the ratio of exhaust gas pressure to

ambient pressure is greater than some critical

due, sonic flow can exist and the nozzle will

be choked or limited to some maximum flow.

When supersonic exhaust gas velocities are re-

quired to produce the necessary momentum

change, the expansion process will require the

convergent-divergent nozzle illustrated in fig-

ure 2.9. With sui?icient pressure available the

initial expansion in the converging portion is

subsonic increasing to sonic velocity at the

throat. Subsequent expansion in the divergent

portion of the nozzle is supersonic and the re-

sult is the highest exit velocity for a given

pressure ratio and mass flow. When the pres-

sure ratio is very high the final exit diameter

required to expand to ambient pressure may be

very large but is practically. limited to the

fuselage or nacelle afterbody diameter. If the

exhaust gases exceed sonic velocity, as is porsi-

ble in a ramjet combustion chamber or after-

burner section, only the divergent portion of

the nozzle may be necessary.

Figure 2.9 provides illustration of the func-

tion of the various engine components and the

changes in static pressure, temperature, and

velocity through the engine. The conditions

at the inlet provide the initial properties of the

engine airflow. The compressor section fur-

nishes the compression pressure rise with a

certain unavoidable but undesirable increase in

temperature. High pressure air delivered to

combustion chamber receives heat from the

combustion of fuel and experiences a rise in

temperature. The fuel flow is limited so that

the turbine inlet temperature is within limits

which can be tolerated by the turbine structure.

The combustion takes place at relatively con-

stant pressure and initially low velocity. Heat

addition then causes large increases in gas vol-

ume and flow velocity.

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

NOZZLE TYPES

CONVERGENT NOZZLE CONMRGPIT-DDMRGENT NOZZLE

--3- ~--

ENGINE OPERATING CONOITIONS

COMPRESSOR TURBlElE EXHAUST

NOZZLE

STATIC

PRESSURE

INLET

TEMPERATURE

CHANGE

INLET

VELOCITY

CHANGE

INLEl

Figure 2.9. Exhaust Nozzle Types and Engine Operating Conditions

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

Generally, the overall fuel-air ratio of the

turbojet is quite low because of the limiting

turbine inlet temperature. The overall air-

fuel ratio is usually some value between 80 to

40 during ordinary operating conditions be-

cause of the large amount of secondary air or

cooling flow.

High temperature, high energy combustion

gas is delivered to the turbine section where

power is extracted to operate the compressor

section. Partial or near-complete expansion

can take place through the turbine section with

the accompanying pressure and tempcratute

drop. The exhaust nozzle completes the ex-

pansion by producing the final jet velocity and

momentum change necessary in the develop-

ment of thrust.

TURBOJET OPERATING CHARACTER-

ISTICS. The turbojet engine has many oper-

ating characteristics which are of great im-

portance to the various items of jet airp!ane

performance. Certain of these operating char-

acteristics will provide a strong influence on

the range, endurance, etc., of the jet-powered

airplane. Other operating characteristics will

require operating techniques which differ

greatly from more conventional powerplants.

The turbojet engine is essentially a thrust-

producing powerplant and the propulsive

power produced is a result of the flight speed.

The variation of available thrust with speed is

relatively small and the engine output is very

nearly constant with flight speed. The mo-

mentum change given the engine airflow de-

velops thrust by the following relationship:

where

Ta= thrust available, lbs.

Q=mass flow, slugs per sec.

vi=inlet or flight velocity, ft. per sec.

Va= jet velocity, ft. per see.

Since an increase in flight speed will increase

the magnitude of Vi, a constant thrust will be

obtained only if there is an increase in mass

flow, Q, or jet velocity, Vs, When at low

velocity, an increase in velocity will reduce

the velocity change through the engine with-

out a corresponding increase in mass flow and

the available thrust will decrease. At higher

velocity, the beneficial ram helps to overcome

this effect and the available thrust no longer

decreases, but increases with speed.

The propulsive power available from the

turbojet engine is the roduct of available

thrust and velocity. t T e propulsive horsc-

power available from the turbojet engine’is

related by the following expression:

pyav --

where

Pa=propulsive power available, h.p.

T.-*Le..;- ;--;11.1*~ LC‘--LL,IlLSL ‘t”.uiaOK, ibs.

V= flight velocity, knots

The factor of 321 evolves from the use of the

nautical unit of velocity and implies that

each pound of thrust developed at 325 knots

is the equivalent of one horsepower of propul-

sive power. Since the thrust of the turbojet

engine is essentially constant with speed, tht

power available increases almost linearly with

speed. In this sense, a turbojet with 5000 Ibs.

of thrust available could produce a propulsive

power of 3,ooO h.p. at 325 knots or 10,000

h.p. at 650 knots. The tremendous propulsive

power at high velocities is one of the principal

features of the turbojet engine. When the

engine RPM and operating altitude arc fixed,

the variation with speed of turbolet thrust and

power available is typified by the first graph

of figure 2.10.

The variation of thrust output with engine

speed is a factor of great importance in the

operation of the turbojet engine. By reason-

ing that static pressure changes depend on the

square of the flow velocity, the changer of

pressure throughout the turbojet engine would

be expected to vary as the square of the rota-

tive speed, N. However, since a variation in

rotative speed will alter airflow, fuel flow,

compressor and turbine efficiency, etc., the

thrust variation will be much greater than

just the second power of rotative speed. In-

stead of thrust being proportional to iV2, the

typical fixed geometry engine develops thrust

approximately proportional to N3.6. Of course,

such a variation is particular to constant alti-

tude and speed.

Figure 2.10 illustrates the variation of per-

cent maximum thrust with percent maximum

RPM for a ‘typical fixed geometry engine.

Typical values from this graph are as follows:

P<m#r ma%. RPM Pmwit IMX. tlJrw,r

100 loo (of course)

99 96.5

95 83.6

90 69.2

80 45.8

70 28.7

Note that in the top end of power output, each

1 percent RPM change causes a 3.5-percent

change in thrust output. This illustrates the

power of variation of thrust with rotative

speed which, iii this example, is N3.“. Also

note that the top 20 percent of RPM controls

more than half of the output thrust.

While the fixed geometry engine develops

thrust approximately proportional to Na.“, the

engine with variable geometrywill demonstrate

a much more powerful effect of rotative speed.

When the jet engine is equipped with a vari-

able nozzle, multispool compressor, variable

stator blades, etc., the engine is more likely

to develop thrust proportional to rotative

speed from values of N4.6 to N6.0. For ex-

ample, if a variable geometry engine develops

thrust proportional to Ns.‘, each one per cent

RPM change causes a 5.0-percent thrust change

at the top end of power output. Also, the

top 13 percent of RPM would control the top

50 percent of thrust output.

The powerful variation of thrust with engine

speed has certain ramifications which should

NAVWEPS 00-801-80

AlR,PlANE PERFORMANCE

be appreciated. If the turbojet powerplant

operates at less than the “trimmed” or adjusted

speed for maximum thrust, the deficiency of

thrust for takeoff may cause a considerable

increase in takeoff distance. During approach,

an excessively low RPM may cause very low

thrust and produce a very steep glide path.

In addition, the low RPM range involves the

much greater engine acceleration time to pro-

duce thrust for a waveoff. Another compli-

cation exists when the thrust is proportional

to some large power of rotative speed, e.g.,

Nb.O. The small changes in RPM produce

such large variations in thrust that instruments

other than the tachometer must be furnished

for accurate indication of thrust output.

The “specific fuel consumption, ci’ is an

important factor for evaluating the perform-

ance and efficiency of operation of a turbojet

engine. The specific fuel consumption is the

proportion between the fuel flow (in lbs. per

hr.) and the thrust (in lbs.). For example,

an engine which has a fuel flow of 14,000 lbs.

per hr. and a thrust of 12,500 lbs. has a specific

fuel consumption of:

Fuel flow

“= Thrust

14,000 lbs./hr.

‘I= 12,500 lbs.

c,=1.12 lbs./hr./lb.

Thus, each unit pound of thrust requires 1.12

lbs. per hr. fuel flow. Obviously, high engine

efficiency would be indicated by a low value of

c,. Typical values for turbojet engines with

relatively high pressure ratios range from 0.8

to 1.2 at design operating conditions in sub-

sonic flight. High energy fuels and greater

pressure ratios tend to produce the lower values

of ct. Supersonic flight with the attendant in-

let losses and high compressor inlet air tem-

peratures tend to increase the specific fuel con-

sumption to values of 1.2 to 2.0. Of course,

the use of an afterburner is quite inefficient

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

VARIATION OF THRUST AN0 POWER WITH VELOCITY

/

/STATIC THRUST

.

THRUST

AvA’&?eLE

POWER

AVAILABLE

THRUST

AVAILABLE

/

/ AV!$%EHp’ E

(CONSTANT ALTITUDE 8 RPM)

VELOCITY, KNOTS

i-cl

PERCENT 6o

mmlgTM 50

40 1

IO 1

VARIATION OF THRUST WITH RPM

(CONSTANT ALTITUDE

a VELOCITY)

ThrN3.5

04 I I 1 0 1

0 IO 20 30 40 50 SO 70 80 90 100

PERCENT MAXIMUM RPM

I VARIATION OF SPECIFIC FUEL

CONSUMPTION WITH RPM

3.0

(CONSTANT ALTITUDE

8 VELOCITY)

sEzc 2.0

CONSUMPTION

ct 1.0

.T, * I I I I I I I I.

0 IO 20 30 40 50 60 70 80 90 100

PERCENT MAXIMUM RPM

Figure 2.10. Turbojet Performance

due to thc~ low combustion pressure and values

of c, from 2.0 to 4.0 are typical with aftet-

burner operation.

The turbojet engine usually has a strong

preference fot high RPM to produce low specif-

ic fuel consumption. Since the normal rated

thrust condition is a particular design point

for the engine, the minimum value of c, will

occur at or near this range of RPM. The

illustration of figure 2.10 shows a typical vati-

ation of c, with percent maximum RPM where

values of RPM less than 80 to 85 percent pro-

duce a specific fuel consumption much greater

than the minimum obtainable. This pref-

erence for high.RPM to obtain low values of

C, is very pronounced in the fixed geometry

engine. Turbojet engines with multispool

compressors tend to be less sensitive in this

respect and are more flexible in their operating

characteristics. Whenever low values of cI ate

necessary to obtain range or endurance, the

preference of the turboiet engine for the design

operating RPM can be a factor of great

influence.

Altitude is one factor which strongly affects

the performance of the turbojet engine. An

increase in altitude produces a decrease in

density and pressure and, if below the tropo-

pause, a decrease in temperature. If a typical

nonaftcrbutning turbojet engine is operated at

a constant RPM and true airspeed, the vatia-

tion of thtust and specific fuel consumption

with altitude can be approximated from figure

221. The variation of density in the standard

atmosphere is shown by the values of density

ratio at vatious altitudes. Typical values of

the density ratio at specific altitudes are as

follows:

Altitude, ft.: Dews@ ra#ie

scaleeel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Loo0

5,ooo.. :. . .a617

lO,coo.............................. .7385

.?2#XQ. .4976

35,cao . . . . . . . . . . . . . . . . . . . . . .3099

40,oal.. . . . .2462

~,OUO. . . . .lS32

NAVWEPS 00-8OT-80

AtRPlANE PERFORMANCE

If the fixed geometry engine is operated at a

constant V (TAS) in subsonic flight and con-

stant N (RPM) the inlet velocity, inlet ram,

and compressor pressure ratio are essentially

constant with altitude. An increase in alti-

tude then causes the engine air mass flow to

decrease in a manner very nearly identical to

the altitude density ratio. Of coutsc, this de-

crease in mass flow will produce a significant

e&ct on the output thrust of the engine.

Actually, the variation of thrust with altitude

is not quite as severe as the density variation

because favorable decreases in temperature

occut. The decrease in inlet air temperature

will provide a relatively greater combustion

gas &ergy and allow a greater jet velocity.

The increase in jet velocity somewhat offsets

the decrease in mass flow. Of course, an in-

crease in altitude provides lower temperatures

below the tropopause. Above the tropopause,

no further favorable decrease in temperature

takes place so a more rapid variation of thrust

will take place. The approximate variation

of thrust with altitude is represented by figure

2.11 and some typical values at specific alti-

tudes ate as follows :

RIrio of Tbrvrt at dri14 Altitude, ft. : ( ) Thi ti I,‘ bwl

Scalevel............................. 1.m

5,ooo................................ ,888

lO,ooo............................... .785

2o,ooo............................... ,604

35,Mx)............................... .392

40,Ko. .315

=Jo,ocQ ._._..,...._....._,.,.__.,..... .180

Since the change in density with altitude is

quite rapid at low altitude turbojet takeoff pet-

formance wil1 Abe greatly affected at high alti-

tude. Also note that the thrust at 35,000 ft.

is approximately 39 percent of the sea level

value.

The thrust added by the afterburner of a

turbojet engine is not affected so greatly by

altitude as the basic engine thrust. The use of

afterburner may provide a thrust increase of 50

percent at low altitude or as much as 100 per-

cent at high altitude.

kAVWEPS OO-EOT-80

AIRPLANE PERFORMANCE

50,ooc

45,ooc

40,ooc

35,ooc

30.000

0” 2 25,000

5 a

20,000

SEA

LEVEL’

\ I

\\ !

\ \\

CONSUMPTION

,FIXED GEOMETRY

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.6 0.9 1.0

RATIO OF WANTITY) AT ALTITUDE

(QUANTIT’I) AT SEA LEVEL

Figure 2.7 1. Approximate Eftect of Altitude on Engine Performance

When the inlet ram and compressor pressure

ratio is fixed, the principal factor affecting the

specific fuel consumption is the inlet air temp-

erature. When the inlet air temperature is

lowered, a given heat addition can provide

relatively greater changes in pressure or vol-

ume. As a result, a given thrust output

requires less fuel flow and the specific fuel con-

sumption, c,, is reduced. While the effect of

altitude on specific fuel consumption does not

compare with the effect on thrust output, the

variation is large enough to strongly influence

range and endurance conditions. Figure 2.11

illustrates a typical variation of specific fuel

consumption with altitude. Generally, the

specific fuel consumption decreases steadily

with altitude until the tropopause is reached

and the specific fuel consumption at this point

is approximately 80 percent of the sea level

value.

Above the tropopause the temperature is con-

stant and altitudes slightly above the tropo-

pause cause no further decrease in specific fuel

consumption. Actually, altitudes much above

the tropopause bring about a general deteriora-

tion of overall engine efficiency and the~spkific

fuel consumption begins an increase with

altitude. The extreme altitudes above the

tropopause produce low combustion chamber

pressures, low compressor Reynolds Numbers,

low fuel flow, etc. which are notconduci,ve to

high engine efficiency.

Because of the variation of c, with altitude,

the majority of turbojet engines achieve maxi-

mum efficiency at or above 35,000 ft. For this

reason, the turbojet airplane will find optimum

range and endurance conditions at. or above

35,000 ft. provided the aircraft is not thrust

or compressibility limited at these altitudes.

The governing apparatus of the turbojet engine

consists primarily of the, items which control

the flow of fuel to the engine. In addition,

there may be included certain functions which

operate variable nozzles, variable stator vanes,

variable inlets, etc. Generally, the fuel con-

trol and associated items should regulate fuel

NAVWEPS 00-8OT-80

AIRPLANE PERFORMANCE

flow, nozzle area, etc. to provide engine per-

formance scheduled by the throttle or power

lever. These regulatory functions provided

must account for variations in altitude, tem-

perature, and flight velocity.

One principal governing factor which must

be available is that a selected power setting

(RPM) must be maintained throughout a wide

range of flight conditions. Figure 2.12 illus-

trates the sariation of fuel flow with RPM for

a turbojet operating at a particular set of

flight conditions. Curve 1 depicts the varia-

tion with RPM of the fuel flow required for

stabilized, ste,ady state operation of the engine.

Each point along this curve 1 defines the fuel

flow which is necessary to achieve equilib-

rium at a given RPM. The steady state fuel

flow produces a turbine, power to equal the

compressor power requirement at a particular

RPM. The throttle position primarily com-

mands .a given, engine speed and, as changes

occur in the ambient pressure, temperature,

and flight speed, the .steady state fuel flow will . vary. The governing’ apparatus must account

for these variations in flight conditions and

maintain the power setting scheduled by

throtrle position.

In addition to the maintenance of steady

state operation, the fuel control and associ-

ated engine control itemsmust provide for the

transient conditions of engine acceleration and

deceleration. In order to accelerate the en-

gine, the fuel control must supply a fuel flow

greater than that required for steady state

operation to ,produce a’ turbine power greater

than the compressor power requirement. How-

ever, the additional fuel flow to accelerate the

engine must be controlled and regulated to

prevent any one or combination of the follow-

ing items:

(1) compressor stall or surge

(2) excessive turbine inlet temperature

(3) excessively rich fuel-air ratio which

may not sustain combustion

Generally, the stall-surge and turbine tem-

perature limits predominate to form an ac-

celeration fuel flow boundary typified by curve

NAVWEPS 00-807-80

AIRPLANE PERFORMANCE

ALL CURVES APPROPRIATE

FOR A PARTICULAR:

ALTITUDE

M&N NUMBER

BOUNDARY A&

DECELEFlATlON

BOUNDARY

MAFfGIN

E I (IDLE) N-RPM (MA%)

EXHAUST GAS

TEMPERATURE

RPM c

PRESSURE . _ . _ _ - - -

TEMPERATURE

rAILPIPE TOTAL

PRESSURE

Figure 2.12. Engine Governing and Instrumentation

2 of figure 2.12. Curve 2 of this illustration

defines an upper limit of fuel flow which can

be tolerated within stall-surge and tempera-

ture limits. The governing apparatus of the

engine must limit the acceleration fuel flow

within this boundary.

To appreciate the governing requirements

during the acceleration process, assume the

engine described in figure 2.12 is in steady state

stabilized operation at point A and it is desired

to acceler&the engine to maximum RPM and

stabilize:at point C. As the throttle is placed

at the position for maximum RPM, the fuel

control will increase the fuel flow to point B

to provide acceleration fuel flow. As the

engine accelerates and increases RPM, the fuel

control will continue to increase the fuel flow

within the acceleration boundary until the

engine speed approaches the controlled maxi-

mum RPM at point C. As the engine speed

nears the maximum at point C, the fuel contrcl’

will reduce fuel flow to produce stabilized oper-

ation at this point and prevent the engine

overspeeding the commanded RPM. Of course,

if the throttle is opened very gradually, the

acceleration fuel flow is barely above the steady

state condition and the engine does not ap-

proach the acceleration fuel flow boundary.

While this technique is recommended for

ordinary conditions to achieve trouble free

operation and good service life, the engine must

be capable of good acceleration to produce

rapid thrust changes for satisfactory flight

control.

In order for the powerplant to achieve mini-

mum acceleration times, the fuel control must

provide acceleration fuel flow as close as

practical to the acceleration boundary. Thus,

a maximum controlled acceleration may pro-

duce limiting turbine inlet temperatures or

slight incipient stall-surge of the compressor.

Proper maintenance and adjustment of the

engine governing apparatus is essential to

produce minimum acceleration times without

incurring excessive temperatures or heavy stall-

surge conditions.

NAVWEPS 00-8OT-30

AIRPLANE PERFORMANCE

During deceleration conditions, the mini-

mum allowable fuel flow is defined by the lean

limit to support combustion. If the fuel flow

is reduced below some critical value at each

RPM, lean blowout or flameout will occur.

This condition is illustrated by curve 3 of

figure 2.12 which forms the deceleration fuel

flow boundary. The governing apparatus must

regulate the deceleration fuel flow within this

boundary.

To appreciate the governing requirements

during the deceleration process, assume the

engine described in figure 2.12 is in stabilized,

steady state operation at point C and it is

desired to decelerate to idle conditions and

stabilize at point E. As the throttle is placed

at the position for idle RPM, the fuel control

will decrease the fuel flow to point D to provide

the deceleration fuel flow. As the engine

decelerates and decreases RPM, the fuel gov-

erning will continue to decrease the fuel flow

within the deceleration boundary until the idle

fuel flow is reached and RPM is established at

point E. Of course, if the throttle is closed

very slowly, the deceleration fuel flow is barely

below the steady state condition and the engine

does not approach the deceleration fuel flow

boundary. The fuel control must provide a

deceleration flow close to the boundary to

provide rapid decrease in thrust and satisfactory

flight control.

In most cases, the deceleration fuel flow

boundary is considerably below the steady

state fuel flow and no great problem exists in

obtaining satisfactory deceleration character-

istics. In fact, the greater problem is con-

cerned with obtaining proper acceleration

characteristics. For the majority of centrifu-

gal flow engines, the acceleration boundary is

set usually by temperature limiting conditions

rather than compressor surge conditions. Peak

operating efficiency of the centrifugal com-

pressor is obtained at flow conditions which

are below the surge limit, hence acceleration

fuel flow boundary is determined by turbine

temperature limits. The usual result is that

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

the centrifugal flow engine has relatively large

acceleration margins and good acceleration

characteristics result with the low rotational

inertia. The axial flow compressor must oper-

ate relatively close to the stall-surge limit to

obtain peak efficiency. Thus, the acceleration

fuel flow boundary for the axial flow engine is

set by these stall-surge limits which are more

immediate to steady state conditions than tur-

bine temperature limits. The fixed geometry

axial flow engine encounters relatively small

acceleration margins and, when compared to

the centrifugal flow engine with larger accel-

eration margins and lower rotational inertia,

has inferior acceleration characteristics. Cer-

tain variation of the axial flow engine such as

variable nozzles, variable stator blades, multi-

ple-spool compressors, etc., greatly improve

the acceleration characteristics.

A note of caution is appropriate at this

point. If the main fuel control and govern-

ing apparatus should malfunction or become

inoperative and an unmodulated secondary or

emergency system be substitued, extreme care

must be taken to avoid abrupt changes in

throttle position. In such a case, very gradual

movement of the throttle is necessary to ac-

complish changes in power setting without

excessive turbine temperatures, compressor

stall or surge, or flameout.

There are various instruments to relate irnr

portant items of turbojet engine performance.

Certain combinations of these instruments are

capable of immediately relating the thrust

output of the powerplant in a qualitative man-

ner. It is difficult to provide an instrument or

combination of instruments which immedi-

ately relate the thrust output in a ~arrantitativ~

manner. As a result, the pilot must rely on

a combination of instrument readings and judge

the output performance according to standard

values particular to the powerplant. Some of

the usual engine indicating instruments are as

follows :

(1) The tachometer provides indication of

engine speed, N, by percent of the maximum

RPM. Since the variation of thrust with

RPM is quite powerful, the tachometer in-

dication is a powerful reference.

(2) The exhaust gas temperature gauge

provides an important reference for engine

operating limitations. While the tempera-

ture probe may be located downstream from

the turbine (tailpipe or turbine discharge

temperature) the instrument should provide

an accurate reflection of temperatures up-

stream in the turbine section. The exhaust

gas temperature relates the energy change

accomplished by fuel addition.

(3) The fuel flowmeter can provide a fair

reflection of thrust output. and operating

efficiency. Operation at high density alti-

tude or high inlet air temperatures-reduces

the output thrust and this effect is related by

a reduction of fuel flow.

(4) The’ tailpipe total pressure (p+q in

the tailpipe) can be correlated with the jet

thrust for a given engine geometry and set of

operating conditions. The output thrust

can be related accurately with various com-

binations of compressor inlet total pressure,

tailpipe total pressure, ambient pressure and

temperature. Hence; pressure differential

(Ap), pressure ratio, and ,tailpipe total pres-

sure instruments can provide more accurate

immediate indications of output thrust than

combined indications of RPM and EGT.

This is especially true with variable geom-

etry or multiple spool engines.

Many other specialized instruments furnish

additional information for more detailed items

of engine performance. Various additional

engine information is realized from fuel pres-

sure, nozzle positions, compressor inlet air

temperature, etc.

TURBOJET OPERATING LIMITATIONS.

The operating characteristics of the turbojet

engine provide various operating limitations

which must be given due respect. Operation

of the powerplant within the specified limita-

tions is absolutely necessary in order to obtain

the design service life with trouble-free opera-

tion. The following items describe the critical

areas encountered during the operational use

of the turbojet engine:

(1) The limiting exhaust gag tcmpcra;wcs pro-

vide the most important restrictions to the op-

eration of the turbojet engine. The turbine

components are subject to centrifugal loads of

rotation, impulse and reaction loads on the

blades, and various vibratory loads which may

be inherent with the design. When the turbine

components are subject to this variety of stress

in the presence of high temperature, two types

of structural phenomena must be considered.

when a part is subject to a certain stress at some

high temperature, weep failure will take place

after a period of time. Of course, an increase

in .tcmperature or stress will increase the rate

at which creep damage is accumulated and

reduce the time required to cause failure. An-

other problem results when a part is subjected

to a repeated or cyclic stress. F&&e failure

will occur after a number of cycles of a varying

stress. An increase in temperature or magni-

tude of cyclic stress will increase the rate of

fatigue damage and reduce the number of cycles

necessary to produce failure. It is important

to note that both fatigue and creep damage are

cumulative.

A gross overstress or overtemperature of the

turbine section will produce damage that is

immediately apparent. However, the creep

and fatigue damage accumulated through pe-

riods of less extreme’ overstress or overtem-

perature is more subtle. If the turbine is

sibject to repeated excessive temperatures, the

greatly increased rate of creep and fatigue

damage wiIl produce failure early within the

anticipated service life.

Generally, the operations which produce

the highest exhaust gas temperatures are

starting, acceleration, and maximum thrust

at high altitude. The time spent at these

temperatures must be limited arbitrarily to

prevent excessive accumulation of creep and

fatigue. Any time spent at temperatures in

NAVWEPS OO-SOT-RO

AIR.PLANE PERFORMANCE

excess of the operational limits for these con-

ditions will increase the possibility of early

failure of the turbine components.

While the turbine components are the most

critically stressed high temperature elements

they are not the only items. The combustion

chamber components may be critical at low

altitude where high combustion chamber pres-

sures exist. Also, the airframe structure and

equipment adjacent to the engine may be sub-

ject to quite high temperatures and require

provision to prevent damage by excess time at

high temperature.

(2) The c~mprcs~or Jtall or surge has the pos-

sibility of producing damaging temperatures

in the turbine and combustion chamber or un-

usual transient loads in the compressor. While

the stall-surge phenomenon is possible with

the centrifugal compressor, the more common

.occurrence is with the axial flow compressor.

Figure 2.13 depicts the pressure distribution

that may exist for steady state operation of

the engine. In order to accelerate the engine

to a greater speed, more fuel must be added to

increase the turbine power above that required

to operate the compressor.

Suppose that the fuel flow is increased be-

yond the steady state requirement without a

change in rotative speed. The increased com-

bustion chamber pressure due to the greater

fuel flow requires that the compressor dis-

charge pressure be higher. For the instant

before an engine speed change occurs, an in-

crease in compressor discharge pressure will be

accompanied by a decrease in compressor flow

velocity. The equivalent effect is illustrated

by the flow components onto the rotating com-

pressor blade of figure 2.13. One component

of velocity is due to rotation and this compo-

nent remains unchanged for a given rotative

velocity of the single blade. The axial flow

velocity for steady state operation combines

with rotational component to define a result-

ant velocity and direction. If the axial flow

component is reduced, the resultant velocity

and direction provide an increase in angle of

NAVWEPS 00-BOT-80

AIRPLANE PERFORMANCE

COMPRESSOR STALL

COMPRESSOR

COMBUSTION EXHAUST

CHAMBER T”RB,NE NOZZLE

PRESSURE RISE

LIMITED BY

STATIC

PRESSURE

CHANGE

INLET

INCREASED

BLADE ANGLE

ROTATING

COMPRESSOR

,STEADY STATE

AXIAL FLOW VEL

/ VELOCITY COMPONENT

DUE TO ROTATION

EFFECT OF INLET TEMPERATURE

-REDUCED AXIAL

FLOW VELOCITY

TEMPERATURE EXHAUST

CHANGE TEMPERATURE RISE

THROUGH COMBUSTION

-- CHAMBER

INLET

.OCITY

COMPRESSOR COMBUSTION TURBINE EXHAUST

CHAMBER NOZZLE

Figure 2.13. Effect of Compressor Stall ond Inlet Temperature on Engine Operation

attack for the rotating blade with a subsequent

increase in pressure rise. Of course, if the

change in angle of attack or pressure rise is

beyond some critical value, stall will occur.

While the stall phenomenon of a series of

rotating compressor blades differs from that

of a single airfoil section in a free airstream,

the cause and effect are essentially the same.

If an excessive pressure rise is required

through the compressor, stall may occur with

the attendant breakdown of stable, steady flow

through the compressor. As stall occurs, the

pressure rise drops and the compressor does not

furnish discharge at a pressure equal to the

combustion chamber pressure. As a result, a

flow reversal or backfire takes place. If the

stall is transient and intermittent, the indica-

tion will be the intermittent “bang” as back-

fire and flow reversal take place. If the stall

develops and becomes steady, strong vibration

and a loud (and possibly expensive) roar

develops from the continuous flow reversal.

The increase in compressor power required

tends to reduce RPM and the reduced airflow

and increased fuel flow cause rapid, immediate

rise in exhaust gas temperature. The pos-

sibility of damage is immediate with the steady

stall and recovery must be accomplished

quickly by reducing throttle setting, lowering

the airplane angle of attack, and increasing

airspeed. Generally, the compressor stall is

caused by one or a combination of the fol-

lowing items:

(ti) A malfunctioning fuel control or gov-

erning apparatus is a common cause. Proper

maintenance and adjustment is a necessity for

stall-free operation. The malfunctioning is

most usually apparent during engine

acceleration.

(6) Poor inlet conditions are typical at

high angles of attack and sideslip. These

conditions reduce inlet airflow and create

nonuniform flow conditions at the com-

pressor face. Of course, these conditions are

at the immediate control of the pilot.

NAVWEPS 00-801-80

AIRMANE Pl?RFORMANCE

(c) Very high altitude flight produces low

compressor Reynolds numbers and an effect

similar to that of airfoil sections. As a

decrease to low Reynolds numbers reduces

the section c&, very high altitudes reduce

the maximum pressure ratio of the com-

pressor. The reduced stall margins increase

the likelihood of compressor stall.

Thus, the recovery from a compressor stall

must entail reduction of throttle setting to

reduce fuel flow, lowering angle of attack and

sideslip and increasing airspeed to improve

inlet condition, and reducing altitude if high

altitude is a contributing factor.

(3) While the j7ameout is a rare occurrence

with modern engines, various malfunctions

and operating conditions allow the flameout to

remain a possibility. A uniform mixture of

fuel and air will sustain combustion within a

relatively wide range of fuel-air ratios. Com-

bustion can be sustained with a fuel-air ratio

as rich as one to five or as lean as one to twenty-

five. Fuel air ratios outside these limits will

not support combustion due to the deficiency

of air or deficiency of fuel. The characteristics

of the fuel nozzle and spray pattern as well as

the governing apoaratus must insure that the

nucleus of combt .,on is maintained through-

out the range of engine operation.

If the rich limit of fuel-air ratio is exceeded

in the combustion chamber, the flame will

blow out. While this condition is a pos-

sibility the more usual cause of a flameout is

exceeding the lean blowout limit. Any con-

dition which produces some fuel-air ratio

leaner than the lean limit of combustion will

produce a flameout. Any interruption of the

fuel supply could bring on this condition.

Fuel system failure, fuel system icing, or pro-

longed unusual attitudes could starve the flows

of fuel to the engine. It should be noted the

majority of aviation fuels are capable of

holding in solution a certain small amount of

water. If the aircraft is refueled with rela-

tively w&m fuel then flown to high altitude,

NAVWEPS OO-BOT-80

AIRPLANE PERFORMANCE

the lower temperatures can precipitate this

water out of solution in liquid or ice crystal

form.

High altitude flight produces relatively small

air mass flow through the engine and the rela-

tively low fuel flow rate. At these conditions

a malfunction of the fuel control and governing

apparatus could cause flameout. If the fuel

control allows excessively low fuel flow during

controlled deceleration, the lean blow out limit

may be exceeded. Also, if the governed idle

condition allows any deceleration below the

idle condition the engine will usually continue

to lose speed and flameout.

Restarting the engine in flight requires sufli-

cient RPM and airflow to allow stabilized op-

eration. Generally, the extremes of altitude

are most critical for attempted airstart.

(4) An increased compressor inlet air tcmpcra-

tare can have a profound effect on the output

tbLrust of 2 rnrhniet m&n,= ---“-,-- --o---. As shown in

figure 2.13, an increase in compressor inlet

temperature produces an even greater increase

in the compressor discharge temperature. Since

the turbine inlet temperature is limited to

some maximum value, any increase in com-

pressor discharge temperature will reduce the

temperature change which can take place in

the combustion chamber. Hence, the fuel flow

will be limited and a reduction in thrust is

incurred.

The effect of inlet air temperature on thrust

output has two special ramifications. At rakc-

off, a high ambient air temperature at a given

pressure altitude relates a high density altitude.

Thus, the takeoff thrust is reduced because of

low density and low mass flow. In addition

to the loss of thrust due to reduced mass flow,

thrust and fuel flow are reduced further be-

cause of the high compressor inlet temperature.

In flight at Sigh Mach number, the aerodynamic

heating will provide an increase in compressor

inlet temperature. Since the compressor inlet

temperature will reflect the compressor dis-

charge temperature and the allowable fuel

flow, the compressor inlet air temperature may

provide a convenient limit to sustained high

speed flight.

(5) The effect of engine overspeed or critical vi-

bration speed ranger is important in the service

life of an engine. One of the principal sources

of turbine loads is the centrifugal loads due to

rotation. Since the centrifugal loads vary as

the square of the rotative speed, a 5 percent

overspeed would produce 10.25 percent over-

stress (1.05*= 1.1025). The large increase in

stress with rorative speed could produce very

rapid accumulation of creep and fatigue dam-

age at high temperature. Repeated overspeed

and, hence, overstress can cause failure early

in the anticipated service life.

Since the turbojet engine is composed of

many different distributed masses and elastic

structure, there are certain vibra~tory modes

and frequencies for the shaft, blades, etc.

While it is necessary to prevent any resonant

conditions from existing within the normal

operating range, there may be certain vibra-

tory modes encountered in the low power range

common to ground operation, low altitude

endurance, acceleration or deceleration. If

certain operating RPM range restrictions are

specified due to vibratory conditions, opera-

tions must be conducted with a minimum of

time in this area. The greatly increased

stresses common to vibratory conditions are

quite likely to cause fatigue failures of the

offending components.

The operating limitations of the engine are

usually specified by various combinations of

RPM, exhaust gas temperature, and allowable

time. The conditions of high power output

and acceleration have relatively short times

allowable to prevent abuse of the powerplant

and obtain good service life. While the al-

lowable times at various high power and

acceleration condition appear arbitrary, the

purpose is to reduce the spectrum of loading

which contributes the most rapid accumulation

of creep and fatigue damage. In fact, in some

instances, the arbitrary time standards can be

set to suit the particular requirements of a

certain type of operation. Of course, the

effect on service life of any particular load

spectrum must be anticipated.

One exception to the arbitrary time standard

for operation at high temperatures or sus-

tained high powers is the case of the after-

burner operation. When the cooling flow is

only that necessary to prevent excessive tem-

peratures for adjacent structure and equipment,

sustained operation past a time limit may cause

damage to these items.

THRUST AUGMENTATION. Many op-

erating performance conditions may require

that additional thrust be provided for short

periods of time. Any means of augmenting

the thrust of the turbojet engine must be ac-

complished without an increase in engine speed

or maximum turbine section temperature. The

various forms of afterburning or water injection

allow the use of additional fuel to provide

thrust augmentation without increase in engine

speed or turbine temperature.

The aftsrbumer is a relatively simple means

of thrust augmentation and the principal fea-

tures are light weight and large thrust increase.

A typical afterburner installation may add only

10 to 20 percent of the basic engine wei,ght but

can provide a 40- to 60-percent increase in the

static sea level thrust. The afterburner con-

sists of an additional combustion area aft of

the turbine section with an arrangement of

fuel nozzles and flameholders. Because the

local flow velocities in the afterburner are

quite high, the flameholders are necessary to

provide the turbulence to maintain combustion

within the afterburner section. The turbojet

engine operates with airflows greatly in excess

of that chemically required to support combus-

tion of engine fuel. This is necessary because

of cooling requirements and turbine tempera-

ture limitations. Since only 15 to 30 percent

of the engine airflow is used in the combustion

chamber, the large excess air in the turbine

discharge can support combustion of large

amounts of additional fuel. Also, there are

no highly stressed, rotating members in the

NAVWEPS OO-EOT-80

AIRPLANE PERFORMANCE

afterburner and very high temperatures can be

tolerated. The combustion of fuel in the after-

burner brings additional increase in tempera-

ture and volume and\ adds considerable energy

to the exhaust. gases producing increased jet

velocity. The major components of the after-

burner are illustrated in figure 2.14.

One necessary feature of the turbojet engine

equipped with afterburner is a variable nozzle

area. As the afterburner begins functioning,

the exit nozzle area must increase to accom-

modate the increased combustion products.

If the afterburner were to begin functioning

without an increase in exit area, the mass flow

through the engine would drop and the tem-

peratures would increase rapidly. The nozzle

area must be controlled to increase as after-

burner combustion, begins. As a result, the

engine mass flow is given a large increase in

jet velocity with the corresponding increase in

thrust. .,

The combustion of fuel in the afterburner

takes place at low pressures and is relatively

inefficient. This basic inefficiency of the low

pressure combustion is given evidence by the

large increase in specific fuel combustion.

Generally, the use of afterburner at least will

double the specihtfuel consumption. As an

example, consider a turbojet engine capable

of producing 10,000 lbs. of thrust which can

develop 15,ooO lbs.. of thrust with the use of

afterburner. Typical values for specific fuel

consumption would. be c,= 1.05 for the basic

engine or t,= 2.1 when the afterburner is in

use. The fuel flow during operation would be

as follows:

fuel flow = (thrust) (specific fuel consump-

tion)

without afterburner,

fuel flow=(10,000) (1.05)

= 10,500 lbs./hr.

with afterburner,

fuel flow=(15,COO) (2.1)

=31,500 lbs./hr.

The low efficiency of the afterburner is illus-

trated by the additional 21,CCO lbs./hr. of fuel

flow to create the additional 5,ooO lbs. of

NAVWEPS 0040T-80

AIRPLANE PERFORMANCE

AFTERBURNER COMPONENTS

AFTt$lRNRNER

HOLDERS

PRE -COMPRESSOR

WATER INJECTION

WATER INJECTION

NOZZLES

CHAMBER NOZZLE

INJECTION

TURBINE-PROPELLER COMBINATION

REDUCTION

TURBINES

CHAMBER NOZZLE

Figure 2.14. Thrust Augmentation and the Gas Turbine-Propeller Combination

thrust. Because of the high fuel consumption

during afterburner operation and the adverse

effect on endurance, the use of the afterburner

should be limited to short periods of time.

In addition, there may be limited time for the

use of the afterburner due to critical heating

of supporting or adjacent structure in the vicin-

ity of the afterburner.

The specific fuel consumption of the basic

engine will increase with the addition of the

afterburner apparatus. The losses incurred by

the greater fluid friction, nozzle and flame-

holder pressure drop, etc. increase the specific

fuel consumption of the basic engine approxi-

mately 5 to 10 percent.

The principal advantage of afterburner is the

ability to add large amounts of thrust with

relatively small weight penalty. The applica-

tion of the afterburner is most common to the

interceptor, fighter, and high speed type

aircraft.

The use of wafer injection in the turbojet en-

gine is another means of thrust augmentation

which allows the combustion of additional fuel

within engine speed and temperature limits.

The most usual addition of water injection de-

vices is to supplement takeoff and climbout

performance, especially at high ambient tem-

peratures and high altitudes. The typical

water injection device can produce a 25 to 35

percent increase in thrust.

The most usual means of water injection is

direct flow of the fluid into the combustion

chamber. This is illustrated in figure 2.14.

The addition of the fluid directly into the com-

bustion chamber increases the mass flow and

reduces the turbine inlet temperature. The

drop in temperature reduces the turbine power

and a greater fuel flow is required to maintain

engine speed. Thus, the mass flow is increased,

more fuel flow is allowed within turbine limits,

and greater, energy is imparted to the exhaust

gases.

The fluid injected into the combustion cham-

bers is generally a mixture of water and alco-

hol. The water-alcohol solution has one

NAVWEPS 00-30T-30

AIRPLANE PERFORMAPJCE

immediate advantage in that it prevents fouling

of the plumbing from the freezing of residual

fluid at low temperatures. In addition, a large

concentration of alcohol in the mixture can

provide part of the additional chemical energy

required to maintain engine speed. In fact,

the large concentration of alcohol in the in-

jection mixture is a preferred means of adding

additional fuel energy. If the added chemical

energy is included with the water flow, no

abrupt changes in governed fuel flow are

necessary and there is less chance of underspeed

with fluid injection and overspeed or over-

temperature when fluid flow is exhausted. Of

course, strict proportions of the mixture are

necessary. Since most water injection devices

are essentially an unmodulated flow, the use

of this device is limited to high engine speed

and low altitude to prevent the water flow

from quenching combustion.

THE GAS TURBINE-PROPELLER COM-

BINATION. The turbojet engine utilizes the

turbine to extract suflicient power to operate

the compressor. The remaining exhaust gas

energy is utilized to provide the high exhaust

gas velocity and jet thrust. The propulsive

efficiency of the turbojet engine is relatively

low because thrust is produced by creating a

large velocity change with a relatively small

mass flow. The gas turbine-propeller combin-

ation is capable of producing higher propulsive

efficiency in subsonic flight by having the pro-

peller operate on a much greater mass flow.

The turboprop or propjet powerplant re-

quires additional turbine stages to continue

expansion in the turbine section and extract

a very large percent of the exhaust gas energy

as shaft power. In this sense, the turboprop

is primarily a power producing machine and

the jet thrust is a small amount of the output

propulsive power. Ordinarily, the jet thrust

of the turboprop accounts for 15 to 25 percent

of the total thrust output. Since the turbo-

prop is primarily a power producing machine,

3~PWbWtlOdWd 3NVldUlV

08-108-00 SdSMAVN

the turboprop powerplant is rated by an

“equivalent shaft horsepower.”

T,y ESHP= BHP+325vp

where

ESHP=equivalent shaft horsepower

EHP= brake horsepower, or shaft horse-

power applied to the propeller

T,= jet thrust, lbs.

V=flight velocity, knots, TAS

‘1s = propeller efficiency

The gas turbine engine is capable of processing

large quantities of air and can produce high

output power for a given engine size. Thus,

the principal advantage of the turboprop

powerplant is the high specific power output,

high power per engine weight and high power

per engine size.

The gas turbine engine must operate at quite

high rotative speed to process large airflows

and produce high power. However, high

rotative speeds are not conducive to high

propeller efficiency because of compressibility

effects. A large reduction of shaft speed must

be provided in order to match the powerplant

and the propeller. The reduction gearing must

provide a propeller shaft speed which can be

utilized effectively by the propeller and, be-

cause of the high rotative speeds of the turbine,

gearing ratios of 6 to 15 may be typical. The

transmission of large shaft horsepower with

such high gearing involves considerable desi,gn

problems to provide good service life. The

problems of such gearing were one of the

greatest difficulties in the development of

turboprop powerplants.

The governing apparatus for the turboprop

powerplant must account for one additional

variable, the propeller blade angle. If the

propeller is governed separately from the tur-

bine, an interaction can exist between the

engine and propeller governers and various

“hunting,” overspeed, and overtemperature

conditions are possible. For this reason, the

NAVWEPS Oo-ROT-30

AIRPLANE PERFORMANCE

engine-propeller combination is operated at a

constant RPM throughout the major range of

output power and the principal variables ofcon-

trol are fuel flow and propeller blade angle.

In the major range of power output, the

throttle commands a certain fuel flow and the

propeller blade angle adjusts to increase the

propeller load and remain at the governed

speed.

The operating limitations of the turboprop

powerplant are quite similar in nature to the

operating limitations of the turbojet engine.

Generally, the turbine temperature limnations

are the most critical items. In addition, over-

speed conditions can produce overstress of the

gearing and propeller as well as overstress of

the turbine section.

The performance of the turboprop illustrates

the typical advantages of the propeller-engine

combination. Higher propulsive efficiency

and high thrust and low speeds provide the

characteristic of range, endurance, and takeoff

performance superior to the turbojet. As is

typical of all propeller equipped powerplants,

the power available is nearly constant with

speed. Because the power from the jet thrust

depends on velocity, the power available in-

creases slightly with speed. However, the

thrust available decreases with speed. The

equivalent shaft horsepower, ESHP, of the

turboprop is affected by mass ,flow and inlet

temperature in fashion similar to that of the

turbojet. Thus, the ESHP will vary with

altitude much like the thrust output of the

turbojet because the higher altitude produces

much lower density and engine mass flow.

The gas turbine-propeller combination utilizes

a number of turbine stages to extract shaft

power from the exhaust gases and, as high

compressor inlet temperatures reduce the fuel

flow allowable within turbine temperature

limits, hot days will cause a noticeable loss of

output power. Generally, the turboprop is

just as sensitive, if not more sensitive, to com-

pressor inlet air temperature as the turbojet

engine.

The specific fuel consumption of the turbo-

prop powerplant is defined as follows :

specific fuel consumption=

engine fuel flow

equivalent shaft horsepower

c=lbs. per hr.

ESHP

Typical values for specific fuel consumption, c,

range from 0.5 to 0.8 lbs. per hr. per ESHP.

The variation of specific fuel consumption with

operating conditions is similar to that of the

turbojet engine. The minimum specific fuel

consumption is obtained at relatively high

power setting and high altitudes. The low

inlet air temperature reduces the specific fuel

consumption and the lowest values of c are ob-

tained near altitudes of 25,ooO to 3900 ft.

Thus; the turboprop as well as the turbojet has

a preference for high altitude operation.

THE RECRIPROCATING ENGINE

The reciprocating engine is one of the most

efficient powerplants used for aircraft power.

The combination of the reciprocating engine

and propeller is one of the most efficient means

of converting the chemical energy of fuel into

flying time or distance. Because of the in-

herent high efficiency, the reciprocating engine

is an important type of aircraft powerplant.

OPERATING CHARACTERISTICS. The

function of the typical reciprocating engine in-

volves four strokes of the piston to complete

one operating cycle. This principal operating

cycle is illustrated in figure 2.15 by the varia-

tion of pressure and volume within the cylin-

der. The first stroke of the operating cycle is

the downstroke of the piston with the intake

valve open. This stroke draws in a charge of

fuel-air mixture along AB of the pressure-

volume diagram. The second stroke accom-

plishes compression of the fuel-air mixture

along line EC. Combustion is initiated by a

spark ignition apparatus and combustion takes

place in essentially a constant volume. The

combustion of the fuel-air mixture liberates

NAVWEPS 00-8OT-80

AlR,Pl.ANE PERFORMANCE

heat and causes the rise of pressure along line

CD. The power stroke utilizes the increased

pressure through the expansion along line DE.

Then the exhaust begins by the initial rejection

along line EB and is completed by the upstroke

along line BA.

The net work produced by the cycle of opera-

tion is idealized by the area BCDE on the

pressure-volume diagram of figure 2.15. Dur-

ing the actual rather than ideal cycle of op-

eration, the intake pressure is lower than the

exhaust pressure and the negative work repre-

sents a pumping loss. The incomplete expan-

sion during the power stroke represents a basic

loss in the operating cycle because of the re-

jection of combustion products along line EB.

The area EFB represents a basic loss in the

operating cycle because of the rejection of

combustion products along line EB. The area

EFB represents a certain amount of energy of

the exhaust gases, a part of which can be ex-

tracted by exhaust turbines as additional shaft

power to be coupled to the crankshaft (turbo-

compound engine) or to be used in operating a

supercharger (turbosupercharger). In addi-

tion, the exhaust gas energy may be utilized to

augment engine cooling flow (ejector exhaust)

and reduce cowl drag.

Since the net work produced during the op-

erating cycle is represented by the enclosed area

of pressure-volume diagram, the output of the

engine is affected by any factor which influences

this area. The weight of fuel-air mixture will

determine the energy released by combustion

and the weight of charge can be altered by

altitude,supercharging,etc. Mixturestrength,

preignition, spark timing, etc., can affect the

energy release of a given airflow and alter the

work produced during the operating cycle.

The mechanical work accomplished during

the power stroke is the result of the gas pres-

sure sustained on the piston. The linkage of

the piston to a crankshaft by the connecting

rod applies torque to the output shaft. During

this conversion of pressure energy to mechani-

cal energy, certain losses are inevitable because

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

INTAKE COMPRESSION COMBUSTION POWER EXHAUST

RECIPROCATING ENGINE

OPERATING CYCLE

\ \

‘. -. -\

B ------==.f=

EXHAUST

VOLUME

Figure 2.15. Reciprocating Engines

of friction and the mechanical output is less

than the available pressure energy. The power

output from the engine will be determined by

the magnitude and rate of the power impulses.

In order to determine the power output of the

reciprocating engine, a brake or load device is

attached to the output shaft and the operating

characteristics are determined. Hence, the

term “brake” horsepower, BHP, is used to

denote the output power of the powerplant.

From the physical definition of “power” and

the particular unit of “horsepower” (1 h.p. =

33,ooO ft.-lbs. per min.), the brake horsepower

can be expressed in the following form.

BHP=G

or

TN

BHP= 5255

where

BHP= brake horsepower

T=output torque, ft.-lbs.

N=output shaft speed, RPM

In this relationship, the output power is ap-

preciated as some direct variable of torque, T,

and RPM. Of course, the output torque is

some function of the combustion gas pressure

during the power stroke. Thus, it is helpful

to consider the mean effective gas pressure

during the power stroke, the “brake mean

effective pressure” or BMEP. With use of

this term, the BHP can be expressed in the

following form.

BHP=@MEP)(D)(N) 792,m

where

BHP= brake horsepower

BMEP= brake mean effective pressure, psi

D=engine displacement, cu. in.

N= engine speed, RPM

The BMEP is not actual pressure within the

cylinder, but an effective pressure representing

the mean gas load acting on the piston during

NAVWEPS 00401-30

AlRPlANE PERFORMANCE

the power stroke. As such, BMEP is a con-

venient index for a majority of items of recip-

rocating engine output, efficiency, and operat-

ing limitations.

The actual power output of any reciptocat-

ing engine is a direct function of the combina-

tion of engine torque and rotative speed.

Thus, output brake horsepower can be related

by the combination of BMEP and RPM or

torque prc~surc and RPM. No other engine

instruments can provide this immediate indi-

cation of output power.

If all other factors are constant, the engine

power output is directly related to the engine

airflow. Evidence of this fact could be appre-

ciated from the equation for BHP in terms of

BMEP.

BHP = @M.W(DXN)

792,000

This equation relates that, for a given BMEP,

the BHP is determined by the product of en-

gine RPM, N, and displacement, D. In a

sense, the reciprocating engine could be con-

sidered primarily as an air pump with the

pump capacity directly affecting the power

output. Thus, any engine instrumems which

relate factors affecting airflow can provide some

indirect reflection of engine power. The pres-

sure and temperature of the fuel-air mixture

decide the density of the mixture entering the

cylinder. The carburetor air temperature will

provide the temperature of the inlet air at the

carburetor. While this carburetor inlet air

is not the same temperature as the air in the

cylinder inlet manifold, the carburetor inlet

temperature provides a stable indication inde-

pendent of fuel flow and can be used as a stand-

ard of performance. Cylinder inlet manifold

temperature is difficult to determine with the

same degree of accuracy because of the normal

variation of fuel-air mixture strength. The

inlet manifold pressure provides an additional

indication of the density of airflow entering the

combustion chamber. The manifold absolute

pressure, MAP, is affected by the carburetor

NAVWEPS 00-801-80

AIRPLANE PRRFORMANCE

inlet pressure, throttle position, and super-

charger or impeller pressure ratio. Of course,

the throttle is the principal control of mani-

fold pressure and the throttling action controls

the pressure of the fuel-air mixture delivered

to the supercharger inlet. The pressure re-

ceived by the supercharger is magnified by

the supercharger in some proportion depend-

ing on impeller speed. Then the high pressure

mixture is delivered to the manifold.

Of course, the engine airflow is a function of

RPM for two reasons. A higher engine speed

increases the pumping rate and the volume flow

through the engine. Also, with the engine

driven supercharger or impeller, an increase in

engine speed increases the supercharger pres-

sure ratio. With the exception of near closed

throttle position, an increase in engine speed

will produce an increase in manifold pressure.

The many variables affecting the character

,.F the romL.,*r;nn :...^---” “1 L..,, c YYU”Cl”Y process a:e an I.n~“Lrant

subject of reciprocating engine operation.

Uniform mixtures of fuel and air will support

combustion between fuel-air ratios of approxi-

mately 0.04 and 0.20. The chemically correct

proportions of air and hydrocarbon fuel would

be 15 lbs. of air for each lb. of fuel, or a fuel-

air ratio of 0.067. This chemically correct, or

“stoichiometric,” fuel-air ratio would provide

the proportions of fuel and air to produce

maximum release of heat during combustion of

a grven weight of mixture. If the fuel-air

ratio were leaner than stoichiometric, the ex-

cess of air and deficiency of fuel would produce

lower combustion temperatures and reduced

heat release for a given weight of charge. If

the fuel-air ratio were richer than stoichio-

metric, the excess of fuel and deficiency of air

would produce lower combustion temperatures

and reduced heat release for a given weight of

charge.

The stoichiometric conditions would pro-

duce maximum heat release for ideal conditions

of combustion and may apply quite closely for

the individual cylinders of the low speed re-

ciprocating engine. Because of the effects of

flame propagation speed, fuel distribution,

temperature variation, etc., the maximum

power obtained with a fixed airflow occurs at

fuel-air ratios of approximately 0.07 to 0.08.

The first graph of figure 2.16 shows the varia-

tion of output power with fuel-air ratio for a

a constant engine airflow, i.e., constant RPM,

MAP, and CAT (carburetor air temperature);

Combustion can be supported by fuel-air ratios

just greater than .0.04 but the energy released

is insufficient to overcome pumping losses and

engine mechanical friction. Essentially, the

same result is obtained for the rich fuel-air

ratios just below 0.20. Fuel-air ratios be-

tween these limits produce varying amounts of

output power and the maximum power output

generally occurs at fuel-air ratios of approxi-

mately 0.07 to 0.08. Thus, this range of fuel-

air ratios which produces maximum power for

a given airflow is termed ,the “best power”

range. At jo,me lower range of f-ue;-air rariop,

a maximum of power per fuel-air ratio is ob-

tained and this the “best economy” range.

The best economy range generally occurs be-

tween fuel-air ratios of 0.05 and 0.07. When

maximum engine power is required for take-

off, fuel-air ratios greater than 0.08 are neces-

sary to suppress detonation. Hence, fuel-air

ratios of 0.09 to 0.11 are typical during this

operation.

The pattern of combustion in the cylinder is

best illustrated by the second graph of figure

2.16. The normal combustion process begins

by spark ignition toward the end of the com-

pression stroke. The electric spark provides

the beginning of combustion and a flame front

is propagated smoothly through the com-

pressed mixture. Such normal combustion is

shown by the plot of cylinder pressure versus

piston travel. Spark ignition begins a smooth

rise of cylinder pressure to some peak value

with subsequent expansion through the power

stroke. The variation of pressure with piston

travel must be controlled to achieve the great-

est net work during the cycle of operation.

PERCENT

POWEFI

CONSTANT

AIRFLOW

BEST

OVERLEAN WER-RICH

NAVWEPS 00-307-80

AIRPLANE PERFORMANCE

I FUEL-AIR RATIO

NORMAL COMBUSTION

SPARK

PLUG

DETONATION

FLAME PROPAGATION

BURNJNG IGNITION

FROM HOT SFfYT

NORMAL CCMBUSTION

COMPRESSION STROKE POWER STROKE

TOP CENTER :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::~:::::::::::::::::::::::::::~:::::::::::::::::::::::::::::::::::::::::::::::::::::::::~.:::::::~::::::::::::::~~~~~~~~~~~~~~~~~~~~~~ ::::::::::::::::::::::::::::::::::::::::::~::::~:::::::::::::::::::::::::::::::::::::::::::::::::::~::::::::::::::::::::::::::::~:::::::::::::::::::::::::::::::::::::::::::::::::::...~.............., . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ~ .._..______._.,,.,.,,...................,......................,,...............,..... . . . . . . . . . . . . . . .

MAXIMUM

1 RATED TAKEOFF

CRUISE POWER 1 1 POWER

DETONATION

ENGINE AIRFLOW, LBS. PER HR.

Figure 2.16. Reciprocating Engine Operation

NAVWEPS 00-8OT-RO

AIRPLANE PERFORMANCE

Obviously, spark ignition timing is an impor-

tant factor controlling the initial rise of pres-

sure in the combustion chamber. The ignition

of the fuel mixture must begin at the proper

time to allow flame front propagation and the

release of heat to build up peak pressure for the

power stroke .

The speed of flame front propagation is a

major factor affecting the power output of the

reciprocating engine since this factor controls

the rate of heat release and rate of pressure rise

in the combustion chamber. For this reason,

dual ignition is necessary for powerplants of

high specific power output. Obviously, nor-

mal combustion can be accomplished more

rapidly with the propagation of two flame

fronts rather than one. The two sources of

ignition are able to accomplish the combus-

tion heat release and pressure rise in a shorter

period of time. Fuel-air ratio is another factor

affecting the flame propagation speed in the

combustion chamber. The maximum flame

propagation speed occurs near a fuel-air ratio

of 0.08 and, thus, maximum power output for

a given airflow will tend to occur at this value

rather than the stoichiometric value.

Two aberrations of the combustion process

are preignition and detonation. Preignition

is simply a premature ignition and flame f&t

propagation due to hot spots in the combustion

chamber. Various lead and carbon deposits

and feathered edges on metal surfaces can sup-

ply a glow ignition spot and begin a flame

propagation prior to normal spark ignition.

As shown on the graph of figure 2.16, pre-

ignition causes a premature rise of

pressure during the piston travel. As a result,

preignition combustion pressures and tempera-

tures will exceed normal combustion values and

are very likely to cause engine damage. Be-

cause of the premature rise of pressure toward

the end of the compression stroke, the net work

of the operating cycle is reduced. Preignition

is evidenced by a rise in cylinder head tempera-

ture and drop in BMEP or torque pressure.

Denotation offers the possibility of immedi-

ate destruction of the powerplant. The nor-

mal combustion process is initiated by the

spark and beginning of flame front propaga-

tion As the flame front is propagated, the

combustion chamber pressure and temperature

begin to rise. Under certain conditions of

high combustion pressure and temperature,

the mixture ahead of the advancing flame front

may suddenly explode with considerable vi-

olence and send strong detonation waves

through the combustion chamber. The result

is depicted by the graph of figure 2.16, whete:a

sharp, explosive increase in pressure takes place

with a subsequent reduction of the mean pres;

sure during the power stroke. Detonation

produces sharp explosive pressure peaks many

times greater than normal combustion1 Also,

the exploding gases radiate considerable heat

and cause excessive temperatures for many local

parts of the engine. The effects of heavy

detonation are so severe that structural damage

is the immediate result. Rapid rise of cylinder

head temperature, rapid drop in BMEP, and

loud, expensive noises are evidence of detona-

tion.

Detonation is not necessarily confined to. a

period after the beginning of normal flame front

propagation. With extremely low grades of

fuel, detonation can occur before normal igni-

tion. In addition, the high temperatures and

pressure caused by preignition will mean that

detonation is usually a corollary of preigniticn.

Detonation results from a sudden, unstable de-

composition of fuel at some critical combina-

tion of high temperature and pressure. Thus,

detonation is most likely to occur at any op

erating condition which produces high com-

bustion pressures and temperatures. Gener-

ally, high engine airflow and fuel-air ratios for

maximum heat release will produce the critical

conditions. High engine airflow is common

to high MAP and RPM and the engine is most

sensitive to CAT and fuel-air ratio in this

region.

NAVWEPS 00-8OT-80

AIRPLANE PERFORMANCE

cruise power is the upper limit of power that

can be utilized for this operation. Higher air-

flows and higher power wirhout a change in

fuel-air ratio will intersect the knee of the

detonation envelope.

The primary factor relating the efficiency of

operation of the reciprocating engine is the

brake specific fuel consumption, iWE%, or

simply c.

Brake suecific fuel consumution

The detonation properties of a fuel are de-

termined by the basic molecular structure of

the fuel and the various additives. The fuel

detonation properties are generally specified

by the antidetonation or antiknock qualities of

an octane rating. Since the antiknock proper-

ties of a high quality fuel may depend on the

mixture strength, provision must be made

in. the rating of fuels. Thus, a fuel grade of

IIS/ would relate a lean mixture antiknock

rating of 115 and a rich mixture antiknock

rating of 145. One of the most common opera-

tional causes of detonation is fuel contamina-

tion. An extremely small contamination of

high octane fuel with jet fuel can cause a serious

,decrease in the antiknock rating. Also, the

contamination of a high grade fuel with the

next lower grade will cause a noticeable loss of

antiknock quality.

The fuel metering requirements for an engine

are illustrated by the third graph of figure 2.16

which is a plot of fuel-air ratio versus engine

airflow. The carburetor must provide specific

fuel-air ratios throughout the range of engine

airflow to accommodate certain output power.

Most modern engines equipped with auto-

matic mixture control provide a scheduling of

fuel-air ratio for automatic rich or automatic

lean operation. The auto-rich scheduling usu-

ally provides a fuel-air ratio at or near the

maximum heat release value for the middle

range of airflows. However, at high airflows

a power enrichment must be provided to sup-

press detonation. The auto-rich schedule gen-

erally will provide an approximate fuel-air

ratio of 0.08 which increases to 0.10 or 0.11 at

the airflow for takeoff power. In addition,

the low airflow and mixture dilution that oc-

curs in the idle power range requires enrich-

ment for satisfactory operation.

The schedule of fuel-air ratios with an auto-

matic lean fuel-air ratio will automatically

provide maximum usable economy. If manual

leaning procedures are applicable a lower fuel-

air ratio may be necessary for maximum possi-

ble efficiency. The maximum continuous

engine fuel flow

= brake horsepower

C= lbs. per hr.

BHP

Typical minimum values for c range from 0.4

to 0.6 lbs. per hr. per BHP and most aircraft

powerplaots average 0.5. The turbocompound

engine is generally the most efficient because

of the power recovery turbines and can ap-

proach values of c=O.38 to 0.42. It should be

noted that the minimum values of specific fuel

consumption will be obtained only within the

range of cruise power operation, 30 to 60 per-

cent of the maximum power output. Gen-

erally, the conditions of minimum specific fuel

consumption are achieved with auto-lean or

manual lean scheduling of fuel-air ratios and

high BMEP and low RPM. The low RPM is

the usual requirement to minimize friction

horsepower and improve output efficiency.

The effect of &it&c is to reduce the engine

airflow and power output and supercharging

is necessary to maintain high power output

at high altitude. Since the basic engine is

able to process air only by the basic volume

displacement, the function of the supercharger

is to compress the inlet air and provide a

greater weight of air for the engine to process.

Of course, shaft power is necessary to operate

the engine driven supercharger and a tempera-

ture rise occurs through the supercharger com-

pression. The effect of various forms of super-

charging on altitude performance is illustrated

in figure 2.17.

The unsupercharged-or naturally aspi-

rated-engine has no means of providing a

NAVWEPS OO-ROT-RO

AIRPLANE PERFORMANCE

EFFECT OF SUPERCHARGING ON ALTITUDE

PERFORMANCE

UNAVAILABLE

\

LOW SLOWER

\ LIMIT MAP

_c U&Q f-

HIGH SLOWER

LIMIT MAf

\ b CONSTANT

N,D

Figure 2.17. Fffect of Supercharging on Altitude Performonce

manifold pressure any greater than the induc-

tion system inlet pressure. As altitude is

increased with full throttle and a governed

RPM, the airflow through the engine is

reduced and BHP decreases. The first forms of

supercharging were of relatively low pressure

ratio and the added airflow and power could

be handled at full throttle within detonation

limits. Such a “ground boosted” engine

would achieve higher output power at all

altitudes but an increase in altitude would

produce a decrease in manifold pressure, air-

flow, and power output.

More advanced forms of supercharging with

higher pressure ratios can produce very large

engine airflow. In fact, the typical case of

altitude supercharging will produce such high

airflow at low altitude operation that full

throttle operation cannot be utilized within

detonation limits. Figure 2.17 illustrates this

case for a typical two-speed engine driven

altitude supercharging installation. At sea

level, the limiting manifold pressure produces

a certain amount of BHP. Full throttle oper-

ation could produce a higher MAP and BHP

if detonation were not the problem. In this

case full throttle operation is unavailable

because of detonation limits. As altitude is

increased with the supercharger or “blower”

at low speed, the constant MAP is maintained

by opening the throttle and the BHP increases

above the sea level value because of the re-

duced exhaust back pressure. Opening the

throttle allows the supercharger inlet to re-

ceive the same inlet pressure and produce the

same MAP. Finally, the increase of altitude

will require full throttle to produce the con-

stant MAP with low blower and this point is

termed the “critical altitude” or “full throttle

height.” If altitude is increased beyond the

critical altitude, the engine MAP, airflow, and

BHP decrease.

The critical altitude with a particular super-

charger installation is specific to a given com-

bination of MAP and RPM. Obviously, a

lower MAP could be maintained to some

NAVWEPS OO-ROT-RO

AWIANE PERFORMANCE

higher altitude or a lower engine speed would

produce less supercharging and a given MAP

would require a greater throttle opening.

Generally, the most important critical alti-

tudes will be specified for maximum, rated,

and maximum cruise power conditions.

A change of the blower to a high speed will

provide greater supercharging but will require

more shaft power and incur a greater tempera-

ture rise. Thus, the high blower speed can

produce an increase in altitude performance

within the detonation limitations. The vari-

ation of BHP with altitude for the blower at

high speed shows an increase in critical alti-

tude and greater BHP than is obtainable in low

blower. Operation below the high blower

critical altitude requires some limiting mani-

fold pressure to remain within detonation

limits. It is apparent that the shift to high

blower is not required just past low blower

critical altitude but at the point where the

transition from low blower, full throttle to

high blower, limit hiAP will produce greater

BHP. Of course, if the blower speed is

increased without reducing the throttle

opening, an “overboost” can occur.

Since the exhaust gases have considerable

energy, exhaust turbines provide a source of

supercharger power. The turbosupercharger

(TB.S) allows control of the supercharger

speed and output to very high altitudes with

a variable discharge exhaust turbine (PDT).

The turbosupercharger is capable of providing

the engine airflow with increasing altitude by

increasing turbine and supercharger speed.

Critical altitude for the turbosupercharger is

usually defined by the altitude which produces

the limiting exhaust turbine speed.

The minimum specific fuel consumption of

the supercharged engine is not greatly affected

by altitudes less than the critical altitude. At

the maximum cruise power condition, specific

fuel consumption will decrease slightly with

an increase in altitude up to the critical

altitude. Above critical altitude, maximum

,cruise power cannot be maintained but the

NAVWEPS O&ROT-SO

AIRPLANE PERFORMANCE

specific fuel consumption is not adversely

affected as long as auto-lean or manual lean

power can be used at the cruise power setting.

One operating characteristic of the recipro-

cating engine is distinctly different from that

of the turbojet. Water vapor in the air will

cause a significant reduction in output power of

the reciprocating engine but a negligible loss

of thrust for the turbojet engine. This basic

difference exists because the reciprocating

engine operates with a fixed displacement and

all air processed is directly associated with the

combustion process. If water vapor enters the

induction system of the reciprocating engine,

the amount of air available for combustion is

reduced and, since most carburetors do not

distinguish water vapor from air, an enrich-

ment of the fuel-air ratio takes place. The

maximum power output at takeoff requires

fuel-air ratios richer than that for maximum

-haezt re1m.e rn ,, C,I+P- nnr:rLmm.c . . ..I1 *-IF- --A-“-\- “W . A....A c. b.IIA.cIIIIICIIL “1111 La&C

place with subsequent loss of power. The

turbojet operates with such great excess of air

that the combustion process essentially is

unaffected and the reduction of air mass flow

is the principal consideration. As an example,

extreme conditions which would produce high

specific humidity may cause a 3 percent thrust

loss for a turbojet but a 12 percent loss of BHP

for a reciprocating engine. Proper accounting

of the loss due to humidity is essential in the

operation of the reciprocating engine.

OPERATING LIMITATIONS. Recipro-

cating engines have achieved a great degree of

refinement and development and are one of the

most reliable of all types of aircraft power-

plants. However, reliable operation of the re-

ciprocating engine is obtained only by strict

adherence to the specific operating limitations.

The most important operating limitations of

the reciprocating engine are those provided to

ensure that detonation and preignition do not

take place. The pilot must ensure that proper

fuel grades are used that limit MAP, BMEP,

RPM, CAT, etc., are not exceeded. Since

Revised January 1965

heavy detonation or preignition is common to

the high airflow at maximum power, the most

likely chance of detonation or preignition is at

takeoff. In order to suppress detonation or

allow greater power for takeoff, water injec-

tion is often used in the reciprocating engine.

At high power’settings, the injection of the

water-alcohol mixture can replace the excess

fuel required to suppress detonation, and de-

richment provisions can reduce the fuel-air

ratio toward the value for maximum heat re-

lease. Thus, an increase in power will be ob-

tained by the better fuel-air ratio. In some

instances, a higher manifold pressure can be 1

utilized to produce additional power. The in-

jection fluid will require proportions of alcohol

and water quite different from the injection

fluid for jet engine thrust augmentation.

Since derichment of the fuel-air ratio is de-

sired, the anti-detonant injection (AOZ) will

rr\n+l;n ,Ir,.Le, :.. -.....^*;*:- r-^--..-.*--.:J..-l b”IICLIALI PlC”ll”l111 yu‘a”c’l’L~ L” pC”LuL Ic>luual

fluid from fouling the plumbing.

When the fuel grades are altered during oper-

ation and the engine must be’operated on a

next lower fuel grade, proper account must be

made for the change in the operating limita-

tions. This accounting must be made for the

maximum power for takeoff and the maximum

cruise power since both of these operating con-

ditions are near the detonation envelope. In

addition, when the higher grade of fuel again

becomes available, the higher operating,limits

cannot be used until it is sure chat no contamina-

tion exists from the lower grade fuel remaining

in the tanks.

Spark plug fouling can provide certain high

as well as low limits of operating temperatures.

When excessively low operating temperatures

are encountered, rapid carbon fouling of the

plugs will take place. On the other hand,

excessively high operating temperatures will

produce plug fouling from lead bromide de-

posits from the fuel additives.

Generally, the limited periods of time at

various high power settings are set to mini-

mize the accumulation of high rates of wear

and fatigue damage. By minimizing the

amount of total time spent at high power

setting, greater overhaul life of the powerplant

can be achieved. This should not imply that

the-takeoff rating of the engine should not be

used. Actually, the use of the full maximum

power at takeoff will accumulate less total

engine wear than a reduced power setting at

the same RPM because of less time required to

climb to a given altitude or to accelerate to a

given speed.

The most severe rate of wear and fatigue

damage occurs at high RPM and low MAP.

High RPM produces high centrifugal loads

and reciprocating iuertia loads. When the

large reciprocating inertia loads are not cush-

ioned by high compression pressures, critical

resultant loads can be produced. Thus, op-

erating time at maximum RPM and MAP must

be held to a minimum and operation at mari-

mum RPM and low MAP must be avoided.

AIRCRAFT PROPELLERS

.The aircraft propeller functions to convert

the powerplant shaft horsepower into propul-

sive horsepower. The basic principles of pro-

pulsion apply to the propeller in that thrust is

produced by providing the airstream a mo-

mentum change. The propeller achieves high

propulsive ef?iciency by processing a relatively

large mass flow of air and imparting a rela-

tively small velocity change. The momentum

change created by propeller is shown by the

illustration of figure 2.18.

The action of the propeller can be idealized

by the assumption that the rotating propeller

is simply an actuating disc. As shown in fig-

ure 2.18, the inflow approaching the propeller

disc indicates converging streamlines with an

increase in velocity and drop in pressure. The

converging streamlines leaving the propeller

disc indicate a drop in pressure and increase in

velocity behind the propeller. The pressure

change through the disc results from the distri-

bution of thrust over the area of the propeller

NAVWEPS OO-EOT-80

AIRPLANE PERFORMANCE

disc. In this idealized propeller disc, the pres-

sure difference is uniformly distributed over the

disc area but the actual case is rather different

from this.

The final velocity of the propeller slipstream,

V,, is achieved some distance behind the pro-

peller. Because of the nature of the flow pat-

tern produced by the propeller, one half of the

total velocity change is produced as the flow

reaches the propeller disc. If the complete

velocity increase amounts to Za, the flow veloc-

ity has increased by the amount II at the pro-

peller disc. The propulsive e$icien~, vp, of the

ideal propeller could be expressed by the fol-

lowing relationship:

output power ?%I= . mput power

TV

‘I’= T(V+a)

where

v,=propulsive efficiency

T=thrust, lbs.

V=fligkt velocity, knots

IJ = velocity increment at the

propeller disc, knots

Since the final velocity, Vs, is the sum of total

velocity change 2a and the initial velocity,

V,, the propulsive efliciency rearranges to a

form identical to that for the turbojet.

2 VP’

1+ k 0

So, the same relationship exists as with the

turbojet engine in that high efficiency is de-

veloped by producing thrust with the highest

possible mass flow and smallest necessary

velocity change.

The actual propeller must be evaluated in a

more exact sense to appreciate the effect of

nonuniform disc loading, propeller blade drag

forces, interference flow between blades, etc.

With these differences from the ideal Propeller,

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

-- r PROPELLER DISC

--

---

“1 *-

~3

_ =“,.?*a

--- -

-- --

PRESSURE CHANGE

P;;;lW;;E THROUGH DISC

1 ,

DISTRIBUTION OF

ROTATIONAL FLOW COMPONENT

mDAT TIP

VORTEX

ii- 2.18. Rhuiples of Ropellerr

it is more appropriate to define propeller effi-

ciency in the following manner:

‘)~= output propulsive power

mput shaft horsepower

where

vP= propeller efficiency

T= propeller thrust

V= flight velocity, knots

BHP= brake horsepower applied to the

propeller

Many di,fferent factors govern the efficiency of

a propeller. Generally, a large diameter pro-

peller favors a high propeller efficiency from

the standpoint of large mass flow. However,

a powerful adverse effect on propeller efficiency

is produced by high tip speeds and conipressi-

bility effects. Of course, small diameter pro-

pellers favor low tip speeds. In addition, the

propeller and powerplant must be matched for

compatibility of output and efficiency.

In order to appreciate some of the principal

factors controlling the efficiency of a given

propeller, figure 2.18 Uustrates the distribu-

tion of rotative velocity along the rotating

propeller blade. These rotative velocities add

to the local inflow velocities to produce a

variation of resultant velocity and direction

along the blade. The typical distribution of

thrust along the propeller blade is shown with

the predominating thrust being located on the

outer portions of the blade. Note that the

propeller producing thrust develops a tip

vortex similar to the wing producing lift.

Evidence of this vortex can be seen by the con-

densation phenomenon occurring at this Ioca-

tion under certain atmospheric conditions.

The component velocities at a given propeller

blade section are shown by the diagram of

figure 2.18. The inflow velocity adds vec-

torially to the velocity due to rotation to pro-

duce an inclination of the resultant wind with

respect to the planes of rotation. This incli-

nation is termed + (phi), the effective pitch

NAVWEPS 00-8OL80

AiRPlANE PERFORMANCE

angle, and is a function of some proportion of

the flight velocity, V, and the velocity due to

rotation which is mD at the tip. The pro-

portions of these terms describe the propeller

“advance ratio”, J.

where

J=propeller advance ratio

V=flight velocity, ft. per sec.

n=propeller rotative speed, revolutions

per sec.

D = propeller diameter, ft.

The propeller blade angle, fi (beta), varies

throughout the length of the blade but a

representative value is measured at 75 percent

of the blade length from the hub.

Note that the difference between the effec-

tive pitch angle, 4, and the blade angle, 8,

determines an effective angle of attack for the

propeller blade section. Since the angle of

attack is the principal factor affecting the

efficiency of an airfoil section, it is reasonable

to make the analogy that the advance ratio, J,

and blade angle, 8, are the principal factors

affecting .propeller efficiency. The perform-

ance of a propelleris typified by the chart of

figure 2.19 which- illustrates the variation of

propeller efficiency, ~a, with advance ratio, J,

for various values of blade angle, 8. The

value of vP for each fl increases with J

until a peak is reached, then decreases. It is

apparent that a fixed pitch propeller may be

selected to provide suitable performance in a

narrow range of advance ratio but efficiency

would suffer considerably outside this range.

In order to provide high propeller efficiency

through a wide range of operation, the pro-

peller blade angle must be controllable. The

most convenient means of controlling the

propeller is the provision of a constant speed

governing apparatus. The constant speed gov-

erning feature is favorable from the standpoint

of engine operation in that engine output and

efficiency is positively controlled and governed.

NAVWEPS OO-ROT-RO

AIRPLANE PERFORMANCE

The governing of the engine-propeller combi-

nation will allow operation throughout a wide

range of power and speed while maintaining

efficient operation.

If the envelope of maximum propeller dfi-

ciency is available, the propulsive horsepower

available will appear as shown in the second

chart of figure 2.19. The propulsive power

available, Pa, is the product of the propeller

efficiency and applied shaft horsepower.

The propellers used on most large reciprocating

engines derive peak propeller efficiencies on the

order of s,=O.85 to 0.88. Of course, the peak

values are designed to occur at some specific

design condition. For example, the selection

of a propel!er for a !ong rasge transport wsuld

require matching of the engine-propeller com-

bination for peak efhciency at cruise condjtion.

On the other hand, selection of a propeller for

a utility or liaison type airplane would require

matching of the engine-propeller combination

to achieve high propulsive power at low speed

and high power for good takeoff and climb

performance.

Several special considerations must be made

for the application of aircraft propellers. In

the event of a powerplant malfunction or

failure, provision must be made to streamline

the propeller blades and reduce drag so that

flight may be continued on the remaining op-

erating engines. This is accomplished by

feathering the propeller blades which .stops

rotation and incurs a minimum of drag for the

inoperative engine. The necessity for feather-

ing is illustrated in figure 2.19 by the change

in equivalent parasite area, Af, with propeller

blade angle, 8, of a typical instaliation. When

the propeller blade angle is in the feathered

position, the change in parasite drag is at a

minimum and, in the case of a typical multi-

engine aircraft, the added parasite drag from

a single feathered propeller is a relatively small

contribution to the airpfane total drag.

At smaller blade angles near the Rat pitch

position, the drag added by the propeller is

very large. AC these small blade angles, the

propeller windmilling at high RPM can create

such a tremendous amount of drag that the

airplane may be uncontrollable. The propel-

ler windmilling at high speed in the low range

of blade angles can produce an increase in para-

site drag which may be as great as the parasite

drag of the basic airplane. An indication of

this powerful drag is seen by the hclieopter in

autorotation. The windmilling rotor is ca-

pable of producing autorotation rates ofdcscent

which approach that of a parachute canopy

with the identical disc area laading. THUS,

the propeller windmilling at high speed and

small blade angle can produce an cffccti+e

drag coefficient of the disc area which compares

with tha~t of a parachute canopy. The drag

and yawing moment caused by loss of power

at high engine-propeller speed is considerable

and the transient yawing displaccmcnt of the

aircraft’ may produce critical loads for the

vertical tail. For this reason, automatic

feathering may be a necessity rather than a

luxury.

The large drag which can be produced by

the rotating propeller can be utilized to im-

prove the stopping performance of the air-

plane. Rotation of the propekr blade to

small positive values or negative values with

applied power can produce large drag or re-

verse thrust. Since the thrust capability of the

propeller is quite high at low speeds, very

high deceleration can be provided by reverse

thrust alone,

The qs&zg limitatiar of the pmpcllcr are

closely associated with those of the Rower-

plant. Overspeed conditions are critical be-

cause of the large centrifugal loads and blade

twisting moments produced by an excessive

rotative speed. In addition, the propeller

blades will have various vibratory modes and

certain operating limitations may hc necessary

to prevent exciting resonant conditions.

PRO~‘ELLER EFFICIENCY

ENVELOPE OF MAXIMUM EFFICIENCY

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

PROPELLER

EFFICIENCY

-lP

-I PROPELLER ADVANCE RATIO, J . . . . . . . . . . . . . . . . . . . . . ...... . . -.-................::::::::: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..~.~~.................................... . . . . . .._.........._................ ::::::::::::::::::::::::::::::::::::::::::::~~:~~~~~~~~~~~~~~~~~~~~::::::::~::::::: liiiiiii!lililliiiiiiiliiiii8iiliili::::::::::::::::::::::::::::~~~~~~~~~~~ ::::::::::: ::::::::::::::~~::::::::::::: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .,............._............................................. I..

--.

POWER AVAILABLE

\ \ BHP

---

POWER

AVAILABLE

HP

VELOCITY, KNOTS :::::::::::::::::::::::::::::::::::::::~:::::::::::::::::::::::::::::~::::::::::::::::::::::::::::::::.::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::~~~~~~~~~~.~: ::::::::::::::::::::::::::::::::::::::::::::::::::::::~::::::::::::::::::::::::::::::::::::::::::::::l::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::............~...,..~..~

PROPELLER DRAG CONTRIBUTION

CHANGE IN

EQUIVALENT

PARASITE

AREA

Af

-

FEATHEREO

POSITION

0 I5 30 45 60 90

PROPELLER BLADE ANGLE,P

Figure 2.79. Propeller Operation

MAWEPS 00-801-80

AIRPLANE PERFORMANCE

The various items of airplane performance

result from the combination of airplane and

powerplant characteristics. The aerodynamic

characteristics of the airplane generally define

the power and thrust requirements at various

conditions of flight while the powerplant

characteristics generally define the power and

thrust available at various conditions of flight.

The matching of the aerodynamic configura-

tion with the powerplant will be accomplished

to provide maximum performance at the speci-

fic design condition, e.g., range, endurance,

climb, etc.

STRAIGHT AND LEVEL FLlGHT

When the airyJane is in steady, level flight,

the condition of equilibrium must prevail.

The unaccelerated condition of flight is

achieved with the airplane trimmed for lift

equal to weight and the powerplant set for a

thrust to equal the airplane drag. In certain

conditions of airplane performance it is con-

venient to consider the airplane requirements

by the thnr$t required (or drag) while in other

cases it is more applicable to consider the

power re@red. Generally, the jet airplane will

require consideration of the thrust required

and the propeller airplane will require consid-

eration of the power required. Hence, the

airplane in steady level flight will require lift

equal to weight and thrust available equal to

thrust required (drag) or power available equal

to power required.

The variation of power required and thrust

required with velocity is illustrated in figure

2.20. Each specific curve of power or thrust

required is valid for a particular aerodynamic

configuration at a given weight and altitude.

These curves define the power or thrust re-

quired to achieve equilibrium, Jift-equal-

weight, constant altitude flight at various

airspeeds. As shown by the curves of figure

2.20, ifit is desired to operate the airplane at

the airspeed corresponding to point A, the

power or thrust required curves define a par-

ticular value of thrust or power that must be

made available from the powerplant ~to achieve

equilibrium. Some different airspeed such as

that corresponding to point B changes the

value of thrust or power required to achieve

equilibrium. Of course, the change of air-

speed to point B also would require a change

in angle of attack to maintain a constant lift

equal to the airplane weight. Similarly, to

establish airspeed and achieve equilibrium at

point C will require a particular angle of attack

and powerplant thrust or power. In this case,

flight at point C would be in the vicinity of

the minimum flying speed and a major portion

of the ,thrust or power required would be due

to induced drag.

The maximum level flight speed for the air-

plane will be obtained when the power :or

thrust required equals the maximum power or

thrust available from the powerplant. The

minimum level flight airspeed is not usually

defined by thrust or power requirement since

conditions of, stall or stability and control

problems generally predominate.

CLIMB PERFOLWANCE

During climbing flight, the airplane gains

potential energy by virtue of elevation. This

increase in potential energy during a climb is

provided by one, or a combination, of two

means: (1) expenditure of propulsive energy

above that required to maintain level flight or

(2) expenditure of airplane kinetic energy, i.e.,

loss of velocity by a zoom. Zooming for alti-

tude is a transient process of trading kinetic

energy for potential energy and is of considera-

ble importance for airplane configurations

which can operate at very high levels of kinetic

energy. However, the major portions of climb

performance for most airplanes is a near steady

process in which additional propulsive energy

is converted into potential energy. The funda-

mental parts of airplane climb performance in-

volve a flight condition where the airplane is

in equilibrium but not at constant altitude.

NAVWEPS OO-ROT-80

AIRPLANE PERFORMANCE

THRUST

1 WEIGHT

THRUST

REQUIRED

-MAXIMUM LEVEL

FLIGHT SPEED

VELOCITY

POWER

REQUIRED

- MAXIMUM LEVEL

FLIGHT SPEED

VELOCITY

Figure 2.20. Level Right Pedormancc

NAVWEPS OO-SOT-80

AIRPLANE PERFORMANCE

The forces acting on the airplane during a

climb are shown by the illustration of figure

2.21. When the airplane is in steady flight

with moderate angle of climb, the vertical

component of lift is very nearly the same as the

actual lift. Such climbing flight would exist

with the lift very nearly equal to the weight.

The net thrust of the powerplant may be in-

clined relative to the flight path but this effect

will be neglectec! for the sake of simplicity.

Note that the weight of the aircraft is vertical

but a component of weight will act aft along

the flight path.

If it is assumed that the aircraft is in a steady

climb with essentially small inclination of the

flight path, the summation of forces along the

flight path resolves to the following:

Forces forward= Forces aft

where

T= thrust available, lbs.

D= drag, lbs.

W= weight, lbs.

v=flight path inclination or angle ,of

climb, degrees (“gamma”)

This basic relationship neglects some of the

factors which may be of importance for air-

planes of very high climb performance. For

example, a more detailed consideration would

account for the inclination of thrust from the

flight path, lift not equal to weight, subse-

quent change of induced drag, etc. However,

this basic relationship will define the principal

factors affecting climb performance. With

this relationship established by the condition

of equilibrium, the following relationship

exists to express the trigonometric sine of the

climb angle, y:

T-D sin y=- W

This relationship simply states that, for a

given weight airplane, the angle of climb (7)

depends on the difference between thrust and

drag (T-D), or excess thrust. Of course,

when the excess thrust is zero (T-D=0 or

T=D), the inclination of, the flight path is

zero-and the airplane is in steady, level flight.

When the thrust is greater than the drag, the

excess thrust will allow a climb angle depend-

ing on the value of excess thrust. Also, when

the thrust is less than the drag. the deficiency

of thrust will allow an angle ~of descent.

The most immediate interest in the climb

angle performance involves obstacle clearance.

The maximum angle of climb would occur

where there exists the greatest difference be-

tweenthrust available and thrust required, i.e.,

maximum (T-D). Figure 2.21 illustrates the

climb angle performance with the curves of

thrust available and thrust required versus

velocity. The thrust required, or drag, curve

is nss,~pued to be ppw=n*~r;.rP nc CnmP +-+a! y.“- ..I‘..&. c “I ““IILL ‘, y

airplane configuration which could be powered

by either a turbojet or propeller type power-

plant. The thrust available curves included

are for a characteristic propeller powerplant

and jet powerplant operating at maximum

output.

The thrust curves for the representative pro-

peller aircraft show the typical propeller thrust

which is high at low velocities and decreases

with an. increase in velocity. For the pro-

peiler powered airplane, the maximum excess

thrust and angle of climb will occur at some

speed just above the stall speed. Thus, if it

is necessary to clear an obstacle after takeoff,

the propeller powered airplane will attain

maximum angle of climb at an airspeed con-

veniently close to-if not at-the takeoff

speed.

The thrust curves for the representative jet

aircraft show the typ~ical turbojet thrust which

is very nearly constant ~with speed. If the

thrust available is essentially constant with

speed, the maximum excess thrust and angle

of climb will occur where the thrust required

NAVWEPS OD-80T-80

AIRPLANE PERFORMANCE

w SIN ,-- COMPONENT OF WEIGHT

ALONG FLIGHT PATH

THRUST - - -- __---- AVAILABLE AVAILABLE

AND JET ACFT

THRUST

REOUIRED

LBS.

POWER

AVAILABLE

AND

POWER

REolYLRED

VELOCITY, KNOTS

l=‘a JET

Pr, POWER REOUIRED

POWER AVAILABLE

PROP ACFT

SPEED FOR MAX R.C., JET

SPEED FOR MAX R.C., PROP

I VELOCITY, KNOTS

Figure 2.21. Climb Performance

NAVWEPS 00-801-80

AIRPLANE PERFORMANCE

is at a minimum, (LID),. Thus, for maxi-

mum steady-state angle of climb, the turbojet

aircraft would be operated at the speed ,for

(L/D),. This poses somewhat of a problem

in determining the proper procedure for ob-

stacle clearance after takeoff. If the obstacle

is a considerable distance from the takeoff

point, the problem is essentially that of a long

term gain and steady state conditions will pre-

dominate. That is, acceleration from the take-

off speed to (L/D), speed will be favorable

because the maximum steady climb angle can

be attained. However, if the obstacle is a rela-

tively short distance from the takeoff point,

the additional distance required to accelerate

to (L/D),, speed may be detrimental and the

resulting situation may prove to be a short

term gain problem. In this case, it may prove

necessary to begin climb out at or near the take-

off speed or hold the aircraft on the runway

for extra speed and a subsequent zoom. The

problem is su&ciently varied that no general

conclusion can be applied to all jer aircraft and

particular procedures are specified for each air-

craft in the Flight Handbook.

Of greater general interest in climb per-

formance are the factors which affect the rate of

climb. The vertical velocity of an airplane

depends on the flight speed and the inclination

of the flight path. In fact, the rate of climb

is the vertical component of the flight path

velocity. By the diagram of figure 2.21, the

following relationship is developed:

since

RC- 101.3 V sin y

then

RC=101.3 V

a&

2-v with Pa=%

and Pr=&

where

RC=rate of climb, f.p.-.

P11=power available, h.p.

Pr=power re

W=weight, 1 %

uired, h.p.

and

V=true airspeed, knots

33,000 is the factor converting horsepower

to ft-lbs/min

101.3isthefactorconvertingknocstof.p.m.

The above relationship states that, for a given

weight airplane, the rate af climb (RC) depends

on the difference between the power available

and the power required (Pd- Pr), or excess

power. Of course, when the excess power is

zero (Pa-Pr=O or Pa== PI), the rate of climb

is zero and the airplane is in steady level flight.

When the power available is greater than the

power required, the excess power will, allow a

rate of climb specific to the magnitude of excess

power. Also, when the power available is

less than the power required, the deficiency of

power produces a rate of descent. This rela-

tionship provides the basis for an important

axiom of flight technique: “For the conditions

of steady flight, the power setting is the pri-

mary control of rate of climb or descent”.

One of the most important items of climb

performance is the maximum rate of climb.

By the previous equation for rate of climb,

maximum rate of climb would occur where

there exists the greatest difference between

power available and power required, i.e.,

maximum (Pa- Pr). Figure 2.21 illustrates

the climb rate performance with the curves of

power available and power required versus

velocity. The power required curve is again a

representative airplane which could be powered

by either a turbojet or propeller type power-

plant. The power available curves included

are for a characteristic propeller powerplant

and jet powerplant operating at maximum

output.

The power curves for the representative pro-

peller aircraft show a variation of propulsive

power typical of a reciprocating engine-pro-

peller combination. The maximum rate of

climb for this aircraft will occur at some speed

RevId J4mwy 1ws

NAVWEPS 06801-80

AIRPLANE PERFORMANCE

near the speed for (L/D&-. There is no direct

relationship which establishes this situation

since the variation of propeller efficiency is the

principal factor accounting for the variation

of power available with velocity. In an ideal

sense, if the propeller efficiency were constant,

maximum rate of climb would occur at the

speed for minimum power required. How-

ever, in the actual case, the propeller efficiency

of the ordinary airplane will produce lower

power available at low velocity and cause the

maximum rate of climb to occur at a speed

greater than that for minimum power required.

The power curves for the representative. jet

aircraft show the near linear variation of power

available with velocity. The maximum rate

of climb for the typical jet airplane will occur

at some speed much higher than that for max-

imum rate of climb of the equivalent propeller

powered airplane. In part, this is accounted

for by the continued increase in power avail-

able with speed. Note that a 50 percent in-

increase in thrust by use of an afterburner may

cause an increase in rate of climb of approxi-

mately 100 percent.

The climb performance of an airplane is

affected by many various factors. The con-

ditions of maximum climb angle or climb rate

occur at specific speeds and variations in speed

will produce variations in climb performance.

Generally, there is sufficient latitude that small

variations in speed from the optimum do not

produce large changes in climb performance

and certain operational items may require

speeds slightly different from the optimum.

Of course, climb performance would be most

critical at high weight, high altitude, or dur-

ing malfunction of a powerplant. Then, opti-

mum climb speeds are necessary. A change

in airplane weight produces a twofold effect

on climb performance. First, the weight, W,

appears directly in denominator of the equa-

tions for ,both climb angle and climb rate.

In addition, a change in weight will alter the

drag and power required. Generally, an in-

crease in weight will reduce the maximum rate

of climb but the airplane must be operated at

some increase of speed to achieve the ,smaller

peak climb rate (unless the airplane is compres-

sibility limited).

The effect of altitude on climb performance

is illustrated by the composite graphs of figure

2.22. Generally, an increase in altitude will

increase the power required and decrease the

power available. Hence, the climb perform-

ance of an airplane is expected to be greatly

affected by altitude. The composite chart of

climb performance depicts the variation with

altitude of the speeds for maximum rate of

climb, maximum angle of climb, and maximum

and minimum level flight airspeeds. As alti-

tude is increased, these various speeds finally

converge at the absolute ceiling of the airplane.

At the absolute ceiling, there is no excess of

power or thrust and only one speed will allow

steady level flight. The variation of rate of

climb and maximum level flight’ speed’ with

altitude for the typical propeller powered air-

plane give evidence of the effect of supercharg-

ing. Distinct aberrations in these curves take

place at the supercharger critical altitudes and

~blower shift points. The curve of time to

climb is the result of summing.up the incre-

ments of time spent climbing through incre-

ments of altitude. Note that approach to the

absolute ceiling produces tremendous increase

in the time curve.

Specific reference points are established by

these composite curves of climb performance.

Of course, the absolute ceiling of the airplane

produces zero rate of climb. The service ceiling

is specified as the altitude which produces a

rate of climb of 100 fpm. The altitude which

produces a rate of climb of 500 fpm is termed

the combat ceiling. Usually, these specific refer-

ence points are provided for the airplane at

the combat configuration or a specific design

configuration.

The composite curves of climb performance

for the typical turbojet airplane are shown in

figure 2.22. One particular point to note is

the more rapid decay of climb performance