Category AVIATORS

TURBOJET ENGINES

The turbojet engine has found widespread use in aircraft propulsion because of the relatively high power output per powerplant weight and size. Very few aircraft powerplants can com­pare with the high output, flexibility, simplic­ity, and small size of the aircraft gas turbine. The coupling of the propeller and recipro­cating engine is one of the most efficient means

known for converting fuel energy into propul­sive 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 con­tinuous, steady flow feature of the gas turbine allows such a powerplant to process consider­ably greater airflow and, thus, utilize a greater expenditure of fuel energy. While the pro­pulsive efficiency of the turbojet engine is con­siderably below that of the reciprocating en­gine-propeller combination, the specific power output of the turbojet at high speeds is quite superior.

The operation of the turbojet engine involves a relatively large change in velocity being im­parted 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 proc­essed 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 j^s 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 cond ition C. The work done by the aerodynamic compression of the inlet or diffuser is represented by the area ABCX. Generally, most conventional turbojet engines require that the compressor inlet flow be sub­sonic and supersonic flight will involve con­siderable aerodynamic compression in the inlet.

Air delivered to the compressor inlet at con­dition 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 compressor pressure ratio should be high to produce a high thermal efficiency 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 inefficiencies are incurred during the com­pression and the power required to operate the compressor will be greater than that indicated by the work done on the engine airflow.

Compressed air is discharged from the com­pressor to the combustion chamber at condition D. Fuel is added in the combustion chamber and the combustion of fuel liberates consider­able heat energy. The combustion process in the gas turbine differs from that of the recipro­cating 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 repre­sented by the change from point D to point E of the pressure-volume diagram of figure 2.6.

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 tem­perature, 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, sta­bilized 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.

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 re­duce 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 de­velopment of thrust has4 been created. The area YFGA represents the work remaining to provide the expansion to jet velocity after the turbine has extracted the work required 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 pro­vide high exhaust gas velocity. For certain applications, the gas turbine-propeller combi­nation could utilize the high power capability of the gas turbine with greater propulsive efficiency.

FUNCTION OF THE COMPONENTS. Each of the engine components previously de­scribed 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 require­ments for satisfactory operating characteristics.

The inlet or diffuser must be matched to the powerplant to provide the compressor entry with the required airflow. Generally, the compressor inlet must receive the required air­flow at subsonic velocity with uniform dis­tribution 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 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 efficient 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 af­fected 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 compressor section is one of the most im­portant 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 com­pressor of a jet engine has no direct cooling, the compression process takes place with a minimum of heat loss of the compressed air. Any friction loss or inefficiency of the com­pression 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 util­ity, 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 pro­vides high acceleration by virtue of centrifugal force. As a result, the air leaves the impeller

at very high velocity and high kinetic energy. A pressure rise is produced by subsequent ex­pansion in the diffuser manifold by converting the kinetic energy into static pressure energy. The manifold then distributes the high pres­sure discharge to the combustion chambers. A double entry impeller allows a given diam­eter compressor to process a greater airflow. The major components of the centrifugal com­pressor 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. Pres­sure 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 con­sumption, 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 alter­nate rows of rotating and stationary airfoils. The major components of the axial flow com­pressor are 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, effects a com – | pression of the flow and causes the increase in static pressure. While the pressure rise per stage of the axial compressor is relatively low, the efficiency is very high and high pressure ratios can be obtained efficiently by successive axial stages. Of course, the efficient pressure rise in each stage is limited by excessive gas velocities. The multistage axial flow com­pressor is capable of providing pressure ratios from five to ten (or greater) with efficiencies which cannot be approached with a multi­stage 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 air­flow with a minimum of compressor diameter. When compared with the centrifugal com­pressor, 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 the demands of efficiency and output predominate over con­siderations’ of cost, simplicity, flexibility of operation, etc. Multi spool compressors and variable stator blades serve to improve the operating characteristics of the axial com­pressor 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 oper­ate with one principal limitation: the dis­charge 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 800° to 1,000° 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 are illustrated by figure 2.8. The combustion chamber receives the high pressure discharge from the compressor and introduces approxi­mately one half of this air into the immediate area of the fuel spray. This primary combus­tion air must be introduced with relatively high turbulence and quite low velocities to

NAVWEPS 00-80T-80

airplane performance

maintain, a nucleus of combustion in the com­bustion chamber. In the 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 that the flame will blow out. The secondary air—or cooling flow—is introduced downstream from the combustion nucleus to dilute the com­bustion products and lower the discharge gas temperature.

The fuel nozzie 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 pattern 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 1,800° 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 com­bustion 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 trans­ferred 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 com­bustion 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 turbine section is the most critical element of the turbojet engine. The function of the turbine is to extract energy from the combus­tion gases and furnish power to drive the com­pressor and accessories. In the case of the turboprop engine, the turbine section must ex­tract a very large portion of the exhaust gas energy to drive the propeller in addition to the compressor and accessories.

The combustion chamber delivers high en­ergy 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 tur­bine. These blades form the nozzles which discharge the combustion gases as high ve­locity jets onto the rotating turbine. In this manner, the high pressure energy of the com­bustion 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 tangen­tial force along the turbine wheel thus extract­ing mechanical energy from the combustion gases. This is illustrated in figure 2.8.

The form of the turbine blades may be a com­bination of two distinct types. The impulse 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 pres­sure drop occurs with the flow across the tur­bine rotor blades. The reaction type turbine differs in that large velocity and pressure changes occur across the turbine rotor blades. In the reaction turbine, the stationary nozzle vanes serve only to guide the combustion gas onto the turbine rotor with negligible changes in velocity and pressure. The reaction tur­bine rotor blades are shaped to provide a pres­sure drop and velocity increase across the blades and the reaction from this velocity in­crease 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 rotative speed. In addition, the blade is subjected to the bending and torsion of the tangential impulse-reaction forces. The blade must withstand these stresses which are generally of a vibratory and cyclic nature while at high temperatures. The elevated temperatures at which the turbine must func­tion produce extreme conditions for struc­tural creep and fatigue considerations. Conse­quently, the engine speed and temperature op­erating limits demand very careful considera­tion. 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 inspec­tion, proper inspection methods (other than visual) must be utilized and proper records kept regarding the occurrence.

Actually, the development of high tempera­ture alloys for turbines is a critical factor in the development of high efficiency, high output aircraft gas turbines. The higher the tem­perature 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 tailpipe or exhaust notice is to discharge the exhaust gases to the atmos­phere at the highest possible velocity to pro­duce the greatest momentum change and thrust. If a majority of the expansion occurs through the turbine section, there remains only to con­duct the exhaust gases rearward with a mini­mum. 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 of exhaust gas pressure to ambient pressure is relatively low and incapable of producing sonic flow, a converging nozzle provides the expan­sion. 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 value, sonic flow can exist and the nozzle will be choked or limited to some maximum flow. When supersonic exhaust gas velocities are re­quired to produce the necessary momentum change, the expansion process will require the convergent-divergent nozzle illustrated in fig­ure 2.9. With sufficient 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 re­sult is the highest exit velocity for a given pressure ratio and mass flow. When the pres­sure 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 possi­ble in a ramjet combustion chamber or after­burner section, only the divergent portion of the nozzle may be necessary.

Figure 2.9 provides illustration of the func­tion 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 fur­nishes 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 con­stant pressure and initially low velocity. Heat addition then causes large increases in gas vol­ume and flow velocity.

NOZZLE TYPES

CONVERGENT NOZZLE CONVERGENT-DIVERGENT NOZZLE

ENGINE OPERATING CONDITIONS

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 be­cause 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 temperature drop. The exhaust nozzle completes the ex­pansion by producing the final jet velocity and momentum change necessary in the develop­ment of thrust.

TURBOJET OPERATING CHARACTER­ISTICS. The turbojet engine has many oper­ating characteristics wh’ich are of great im­portance to the various items of jet airplane performance. Certain of these operating char­acteristics 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 mo­mentum change given the engine airflow de­velops thrust by the following relationship:

Ta=Q(Va-Vd

where

Та — thrust available, lbs. ig=mass flow, slugs per sec.

F^inlet or flight velocity, ft. per sec.

Fa=jet velocity, ft. per see.

Since an increase in flight speed will increase the magnitude of Vu a constant thrust will be obtained only if there is an increase in mass flow, jQ, or jet velocity, V2, When at low velocity, an increase in velocity will reduce the velocity change through the engine with­out 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 product of available thrust and velocity. The propulsive horse­power available from the turbojet engine is related by the following expression: where

Pa=propulsive power available, h. p.

*T* .L – ____ ‘ 1 _ 1 1 11

i#=uuusi av ana Die, ids.

V = flight velocity, knots

The factor of 325 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 propul­sive power. Since the thrust of the turbojet engine is essentially constant with speed, the power available increases almost linearly with speed. In this sense, a turbojet with 5000 lbs. of thrust available could produce a propulsive power of 5,000 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 turbojet 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 reason­ing that static pressure changes depend on the square of the flow velocity, the changes of pressure throughout the turbojet engine would

be expected to vary as the square of the rota­tive 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. In­stead of thrust being proportional to N2, the typical fixed geometry engine develops thrust approximately proportional to N3-6. Of course, such a variation is particular to constant alti­tude and speed.

Figure 2.10 illustrates the variation of per­cent maximum thrust with percent maximum RPM for a typical fixed geometry engine. Typical values from this graph are as follows:

Percent max. thrust

100 (of course)

96.5

83.6

69.2 45-8

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, in this example, is N3‘6. 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 N33, the engine with variable geometry will demonstrate a much more powerful effect of rotative speed. When the jet engine is equipped with a vari­able nozzle, multispool compressor, variable stator blades, etc., the engine is more likely to develop thrust proportional to rotative speed from values of N4"5 to N60. For ex­ample, if a variable geometry engine develops thrust proportional to N50, 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
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. Du-ring 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 pro­duce thrust for a waveoff. Another compli­cation exists when the thrust is proportional to some large power of rotative speed, e. g., N®°. 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, c” is an important factor for evaluating the perform­ance 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

c‘~ Thrust

14,0 lbs./hr.

Ct~ 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 et. Typical values for turbojet engines with relatively high pressure ratios range from 0.8 to 1.2 at design operating conditions in sub­sonic flight. High energy fuels and greater pressure ratios tend to produce the lower values of ct. Supersonic flight with the attendant in­let losses and high compressor inlet air tem­peratures tend to increase the specific fuel con­sumption to values of 1.2 to 2.0. Of course, the use of an afterburner is quite inefficient

О 10 20 30 40 50 60 70 80 90 100
PERCENT MAXIMUM RPM

due to the low combustion pressure and values of c, from 2.0 to 4.0 are typical with after­burner operation.

The turbojet engine usually has a strong preference for high RPM to produce low specif­ic 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 vari­ation of c, with percent maximum RPM where values of RPM less than 80 to 85 percent pro­duce a specific fuel consumption much greater than the minimum obtainable. This pref­erence 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 c, are necessary to obtain range or endurance, the preference of the turbojet 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 nonafterburning turbojet engine is operated at a constant RPM and true airspeed, the varia­tion of thrust and specific fuel consumption with altitude can be approximated from figure 2.11. The variation of density in the standard atmosphere is shown by the values of density ratio at various altitudes. Typical values of the density ratio at specific altitudes are as follows:

Altitude, ft.: Sea level

5,000.

10,000

22,000

55.000

40.000

50,000

If the fixed geometry engine is operated at a constant V (TAS) in subsonic flight and con­stant N (RPM) the inlet velocity, inlet ram, and compressor pressure ratio are essentially constant with altitude. An increase in alti­tude then causes the engine air mass flow to decrease in a manner very nearly identical to the altitude density ratio. Of course, this de­crease in mass flow will produce a significant effect 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 occur. The decrease in inlet air temperature will provide a relatively greater combustion gas energy and allow a greater jet velocity. The increase in jet velocity somewhat offsets the decrease in mass flow. Of course, an in­crease 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 alti­tudes are as follows :

Thrust at altit]uU ,Tkrust at sta tml}

……….. 1.000

……………….. 888

…………………. 785

…………………. 604

…………………. 392

…………………. 315

……………….. 180

Since the change in density with altitude is quite rapid at low altitude turbojet takeoff per­formance will be greatly affected at high alti­tude. 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 per­cent at high altitude.

(QUANTITY) AT SEA LEVEL Figure 2.11. Approximate Effect 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 temp­erature, When the inlet air temperature is lowered, a given heat addition can provide relatively greater changes in pressure or vol­ume. As a result, a given thrust output requires less fuel flow and the specific fuel con­sumption, 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 con­stant and altitudes slightly above the tropo­pause cause no further decrease in specific fuel consumption. Actually, altitudes much above the tropopause bring about a general deteriora­tion of overall engine efficiency and the specific 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 not conducive to high engine efficiency.

Because of the variation of c, with altitude, the majority of turbojet engines achieve maxi­mum 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 Con­trol and associated items should regulate fuel flow, nozzle area, etc. to provide engine per­formance scheduled by the throttle or power lever. These regulatory functions provided must account for variations in altitude, tem­perature, 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 illus­trates the variation of fuel flow with RPM for a turbojet operating at a particular set of flight conditions. Curve 1 depicts the varia­tion with RPM of the fuel flow required for stabilized, steady state operation of the engine. Each point along this curve 1 defines the fuel flow which is necessary to achieve equilib­rium 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 com­mands 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 throttle position.

In addition to the maintenance of steady state operation, the fuel control and associ­ated engine control items must provide for the transient conditions of engine acceleration and deceleration, In order to accelerate the en­gine, 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. How­ever, the additional fuel flow to accelerate the engine must be controlled and regulated to prevent any one or combination of the follow­ing 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 tem­perature limits predominate to form an ac­celeration fuel flow boundary typified by curve

ALL CURVES APPROPRIATE FOR A PARTICULAR:

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 tempera­ture 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 accelerate 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 В 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 maxi­mum RPM at point C. As the engine speed nears the maximum at point C, the fuel control will reduce fuel flow to produce stabilized oper­ation 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 ap­proach 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 mini­mum acceleration times, the fuel control must provide acceleration fuel flow as close as practical to the acceleration boundary. Thus, a maximum controlled acceleration may pro­duce 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.

During deceleration conditions, the mini­mum 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 gov­erning 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 character­istics. In fact, the greater problem is con­cerned with obtaining proper acceleration characteristics. For the majority of centrifu­gal flow engines, the acceleration boundary is set usually by temperature limiting conditions rather than compressor surge conditions. Pea к operating efficiency of the centrifugal com­pressor 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

the centrifugal flow engine has relatively large acceleration margins and good acceleration characteristics result with the low rotational inertia. The axial flow compressor must oper­ate 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 tur­bine temperature limits. The fixed geometry axial flow engine encounters relatively small acceleration margins and, when compared to the centrifugal flow engine with larger accel­eration margins and lower rotational inertia, has inferior acceleration characteristics. Cer­tain variation of the axial flow engine such as variable nozzles, variable stator blades, multi­ple-spool compressors, etc., greatly improve the acceleration characteristics.

A note of caution is appropriate at this point. If the main fuel control and govern­ing 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 ac­complish changes in power setting without excessive turbine temperatures, compressor stall or surge, or flameout.

There are various instruments to relate ІШт 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 man­ner. It is difficult to provide an instrument or combination of instruments which immedi­ately relate the thrust output in a quantitative 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 in­dication is a powerful reference.

(2) The exhaust gas temperature gauge provides an important reference for engine operating limitations. While the tempera­ture probe may be located downstream from the turbine (tailpipe or turbine discharge temperature) the instrument should provide an accurate reflection of temperatures up­stream 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 alti­tude 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 (jp’+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 com­binations of compressor inlet total pressure, tailpipe total pressure, ambient pressure and temperature. Hence, pressure differential (Af), pressure ratio, and tailpipe total pres­sure instruments can provide more accurate immediate indications of output thrust than combined indications of RPM and EGT. This is especially true with variable geom­etry 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 pres­sure, 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 limita­tions is absolutely necessary in order to obtain the design service life with trouble-free opera­tion. The following items describe the critical areas encountered during the operational use of the turbojet engine:

(1) The limiting exhaust gas temperatures pro­vide the most important restrictions to the op­eration 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, creep failure will take place after a period of time. Of course, an increase in temperature or stress will increase the rate at which creep damage is accumulated and reduce the time required to cause failure. An­other problem results when a part is subjected to a repeated or cyclic stress. Fatigue failure will occur after a number of cycles of a varying stress. An increase in temperature or magni­tude 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 pe­riods of less extreme’ overstress or overtem­perature is more subtle. If the turbine is subject to repeated excessive temperatures, the greatly increased rate of creep and fatigue damage will 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 excess of the operational limits for these con­ditions 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 pres­sures exist. Also, the airframe structure and equipment adjacent to the engine may be sub­ject to quite high temperatures and require provision to prevent damage by excess time at high temperature.

(2) The compressor stall or surge has the pos­sibility of producing damaging temperatures in the turbine and combustion chamber or un­usual 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 be­yond the steady state requirement without a change in rotative speed. The increased com­bustion chamber pressure due to the greater fuel flow requires that the compressor dis­charge pressure be higher. For the instant before an engine speed change occurs, an in­crease 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 com­pressor blade of figure 2.13. One component of velocity is due to rotation and this compo­nent 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 result­ant velocity and direction. If the axial flow component is reduced, the resultant velocity and direction provide an increase in angle of

COMPRESSOR STALL

COMPRESSOR COMBUSTION TURBINE EXHAUST

CHAMBER NOZZLE

Figure 2,13. Effect of Compressor Stall and 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 indica­tion will be the intermittent "bang” as back­fire 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 pos­sibility 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 fol­lowing items:

(a) A malfunctioning fuel control or gov­erning 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.

(b) Poor inlet conditions are typical at high angles of attack and sideslip. These conditions reduce inlet airflow and create nonuniform flow conditions at the com­pressor face. Of course, these conditions are at the immediate control of the pilot.

(r) 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 clmai very high altitudes reduce the maximum pressure ratio of the com­pressor. 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 flameout 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. Com­bustion 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 combi, .ion is maintained through­out 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 pos­sibility the more usual cause of a flameout is exceeding the lean blowout limit. Any con­dition 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 pro­longed unusual attitudes could starve the flow 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 rela­tively warm fuel then flown to high altitude,

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 rela­tively 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 suffi­cient RPM and airflow to allow stabilized op­eration. Generally, the extremes of altitude are most critical for attempted airstart.

(43 An increased compressor inlet air tempera­ture can have a profound effect on the output thrust of я turbojet engine. 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 com­pressor 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 take­off, 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 be­cause of the high compressor inlet temperature. In flight at high Mach number, the aerodynamic heating will provide an increase in compressor inlet temperature. Since the compressor inlet temperature will reflect the compressor dis­charge 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 vi­bration speed ranges 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 over­stress (1.05* = 1-10253- The large increase in stress with rotative speed could produce very rapid accumulation of creep and fatigue dam­age 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 vibratory 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 vibra­tory 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, opera­tions 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 al­lowable 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 sus­tained high powers is the case of the after­burner operation. When the cooling flow is only that necessary to prevent excessive tem­peratures for adjacent structure and equipment, sustained operation past a time limit may cause damage to these items.

THRUST AUGMENTATION. Many op­erating 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 ac­complished 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 afterburner is a relatively simple means of thrust augmentation and the principal fea­tures are light weight and large thrust increase. A typical afterburner installation may add only 10 to 20 percent of the basic engine weight but can provide a 40- to 60-percent increase in the static sea level thrust. The afterburner con­sists 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 combus­tion of engine fuel. This is necessary because of cooling requirements and turbine tempera­ture 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 afterburner and very high temperatures can be tolerated. The combustion of fuel in the after­burner brings additional increase in tempera­ture and volume and’ adds considerable energy to the exhaust-gases producing increased jet velocity. The majoT components of the after­burner 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 accom­modate 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- peratnres would increase rapidly. The nozzle area must be controlled to increase as after­burner 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 specific fuel consumption. As an example, consider a turbojet engine capable of producing 10,000 lbs. of thrust which can develop 15,000 lbs.-of thrust with the use of afterburner. Typical values for specific fuel consumption would-be r< = 1.05 for the basic engine or r( = 2.1 when the afterburner is in use. The fuel flow during operation would be as follows:

fuel flow = (thrust) (specific fuel consump­tion)

without afterburner,

fuel flow = (10,000) (1.05)

= 10,500 lbs./hr.

with afterburner,

fuel flow = (15,000) (2.1)

= 31,500 lbs./hr.

The low efficiency of the afterburner is illus­trated by the additional 21,000 lbs./hr. of fuel flow to create the additional 5,000 lbs. of

AFTERBURNER COMPONENTS

WATER INJECTION

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 vicin­ity 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 approxi­mately 5 to 10 percent.

The principal advantage of afterburner is the ability to add large amounts of thrust with relatively small weight penalty. The applica­tion of the afterburner is most common to the interceptor, fighter, and high speed type aircraft. .

The use of water injection in the turbojet en­gine 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 de­vices is to supplement takeoff and climbout performance, especially at high ambient tem­peratures 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 com­bustion 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 cham­bers is generally a mixture of water and alco­hol. The water-alcohol solution has one 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 in­jection 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 over­temperature 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 COM­BINATION. The turbojet engine utilizes the turbine to extract sufficient 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 combin­ation is capable of producing higher propulsive efficiency in subsonic flight by having the pro­peller operate on a much greater mass flow.

The turboprop or prop jet powerplant re­quires 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 turbo­prop is primarily a power producing machine,

the turboprop powerplant is rated by an ‘‘equivalent shaft horsepower.”

eshp^bhpa-Щ-

325i?„

where

ESHP=equivalent shaft horsepower BHP= brake horsepower, or shaft horse­power applied to the propeller Ту = jet thrust, lbs.

V=flight velocity, knots, TAS Up = 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, be­cause 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 design 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 tur­bine, an interaction can exist between the engine and propeller governers and various “hunting,” overspeed, and overtemperature conditions are possible. For this reason, the engine-propeller combination is operated at a constant RPM throughout the major range of output power and the principal variables of con­trol 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 limitations are the most critical items. In addition, over­speed 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 in­creases 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 com­pressor inlet air temperature as the turbojet engine.

The specific fuel consumption of the turbo­prop powerplant is defined as follows:

specific fuel consumption =

_____ engine fuel flow

equivalent shaft horsepower

__ 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 ob­tained near altitudes of 25,000 to 35,000 ft. Thus, the turboprop as well as the turbojet has a preference for high altitude operation.

AVAILABLE THRUST AND POWER

PRINCIPLES OF PROPULSION

All powerplants have in common certain general principles. Regardless of the type of propulsion device, the development of thrust is related by Newton’s laws of motion.

F~ma

or

F_ d(mV) dt

where

jF=force or thrust, lbs.

m=mass, slugs

a=acceleration, ft, per sec.2

^_derivative with respect to time, e. g., dt rate of change with time

mV= momentum, lb.-sec., product of mass and velocity

The force of thrust results from the accelera­tion provided the mass of working fluid. The magnitude of thrust is accounted for by the rate of change of momentum produced by the powerplant, A rocket powerplant creates thrust by creating a very large change in veloc­ity of a relatively small mass of propellants. A propeller produces thrust by creating a com­paratively small change in velocity of a rela­tively large mass of air.

The development of thrust by a turbojet or ramjet powerplant is illustrated by figure 2.5- Air approaches at a velocity, V, depending on the flight speed and the powerplant operates on a certain mass flow of air, Q, which passes through the engine. Within the powerplant the air is compressed, energy is added by the burning of fuel, and the mass flow is expelled from the nozzle finally reaching a velocity, W The momentum change accomplished bv this action produces the thrust,

Ta = Q(V2-V0

where

Ta = thrust, lbs.

X) = mass flow, slugs per sec.

Vі= inlet (or flight) velocity, ft, per sec.

V2— jet velocity, ft. per sec.

The typical ramjet or turbojet powerplant de­rives its thrust by working with a mass flow relatively smaller than that of a propeller but a relatively greater change of velocity. From the previous equation it should be appreciated that the jet thrust varies directly with the mass flow Q, and velocity change, V2—Vx. This fact is useful in accounting for many of the performance characteristics of the jet power – plant.

In the process of creating thrust by mo­mentum change of the airstream, a relative velocity, Vs—Vi, is imparted to the airstream. Thus, some of the available energy is essen­tially wasted by this addition of kinetic energy to the airstream. The change of kinetic energy per time can account for the power wasted in the airstream.

Pw=KE/t

-§ (v,-v, y


Ta = Q (V2-V,)

Pq*T0V,

Pw=Q/2(v2-V|) 2

Of course, the development of thrust with some finite mass flow will require some finite velocity change and there will be the inevita­ble 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 V2+Vi

where

r/p = propulsion efficiency r) = “ eta’ ’

Pa = propulsive power available = TaV,

Pw = power wasted

The resulting expression for propulsion effi­ciency, vP, shows a dependency on the flight velocity, Vi, and the jet velocity, V2. 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 efficiency would be 1.00 (or 100 percent) only when the flight velocity, V1} equals the jet velocity, V2. Actually, it would not be possible to produce thrust under such conditions with a finite mass flow. While 100 percent efficiency of propul­sion can not be attained practically, some insight is furnished to the means of creating high values of propulsion efficiency. To ob­tain 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, ifp, with the ratio of flight speed to jet velocity, VijV2. 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 efficiency because the thrust is derived with a relatively smaller mass flow and larger veloc­ity 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 arc vari­ations which improve the propulsive efficiency 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 efficiency is necessary. Thus, the propeller powered airplane with its inherent high propulsive efficiency will always find ap­plication. The requirements of very high speed and high altitude demand very high propulsive power from relatively small power – 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.

VARIATIONS OF THRUST REQUIRED AND POWER REQUIRED

The curves of thrust required and power required versus velocity provide the basis for comprehensive analysis of all the major items of airplane performance. The changes in the drag and power curves with variations of air­plane gross weight, configuration, and altitude furnish insight for the variation of range, endurance, climb performance, etc., with these same items.

The effect of a change in weight on the thrust and power required is illustrated by figure 2.2.

I The primary effect of a weight change is a change in the induced drag and induced power required at any given speed. Thus, the great­est changes in the curves of thrust and power required will take place in the range of low speed flight where the induced effects pre­dominate. The changes in thrust and power required in the range of high speed flight are relatively slight because parasite effects pre­dominate at high speed. The induced effects at high speed are relatively small and changes in these items produce a small effect on the total thrust or power required.

In addition to the general effect on the in­duced drag and power required at particular speeds, a change in weight will require that the airplane operate at different airspeeds to main­tain conditions of a specific lift coefficient and angle of attack. If the airplane is in steady flight at a particular CL, the airpseed required for this CL will vary with weight in the fol­lowing manner:


vrVWt

where

Vi — speed corresponding to a specific CL and weight, Wx

V2= speed corresponding to the same CL
but a different weight, W%

For the example airplane of figure 2.2, a change of gross weight from 15,000 to 22,500 lbs. re­quires that the airplane operate at speeds which are 22.5 percent greater to maintain a specific lift coefficient. For example, if the 15,000-lb. airplane operates at 160 knots for QL/D’)mai, the speed for (_L/D’)maI at 22,500 lbs. is:
—196 knots

The same situation exists with respect to the curves of power required where a change in weight requires a change of speed to maintain flight at a particular CL. For example, if the 15,000-lb. airplane achieves minimum power required at 122 knots, an increase in weight to 22,500 lbs. increases the speed for minimum power required to 149 knots.

Qf course, the thrust and power required at specific lift coefficients are altered by changes in weight. At a specific CL, any change in weight causes a like change in thrust required, e. g., a 50-percent increase in weight causes a 50-per­cent increase in thrust required at the same CL. The effect of a weight change on the power re­quired at a specific CL is a bit more complex be­cause a change in speed accompanies the change

THRUST

REQUIRED

(LBS)

POWER

REQUIRED

in drag and there is a two-fold effect. A 50- percent increase in weight produces an increase of 83.8 percent in the power required to main­tain a specific CL. This is the result of a 50- percent increase in thrust required coupled with a 22.5-percent increase in speed. The effect of a weight change on thrust required, power re­quired, and airspeed at specific angles of attack and lift coefficients provides an important basis for various techniques of cruise and endurance conditions of flight.

I Figure 2.3 illustrates the effect on the curves of thrust and power required of a change in the equivalent parasite area,/, of the configuration. Since parasite drag predominates in the region of high flight speed, a change in /will produce the greatest change in thrust and power re­quired at high speed. Since parasite drag is relatively small in the region of low speed flight, a change in / will produce relatively small changes in thrust and power required at low speeds. The principal effect of a change in equivalent parasite area of the configuration is to change the parasite drag at any given air­speed.

The curves of figure 2.3 depict the changes in the curves of thrust and power required due to a 50 percent increase in equivalent parasite area of the configuration. The minimum total drag is increased by an increase in / and the (L(D)mox is reduced. Also, the increase in / will increase the CL for (L/D)^ and require a reduction in speed at the new, but decreased, (LjD^ma. The point of minimum power re­quired occurs at a lower airspeed and the value of the minimum power required is increased slightly. Generally, the effect on the mini­mum power required is slight because the para­site drag is only 25 percent of the total at this specific condition of flight.

An increase in the equivalent parasite area of an airplane may be brought about by the deflection of flaps, extension of landing gear, extension of speed brakes, addition of external stores, etc. In such instances a decrease in the airplane efficiency factor, e, may accompany

an increase in / to account for the additional changes in parasite drag which may vary with

CL.

A change in altitude can produce signifi­cant changes in the curves of thrust and power required. The effects of altitude on these curves provide a great part of the explanation of the effect of altitude on range and endurance. Figure 2.4 illustrates the effect of a change in altitude on the curves of thrust and power re­quired for a specific airplane configuration and gross weight. As long as compressibility effects are negligible, the principal effect of increased altitude on the curve of thrust re­quired is that specific aerodynamic conditions occur at higher true airspeeds. For example, the subject airplane at sea level has a minimum drag of 1,250 lbs. at 160 knots. The same airplane would incur the same drag at altitude if operated at the same equivalent airspeed of 160 knots. However, the equivalent airspeed of 160 knots at 22,000 ft. altitude would produce a true airspeed of 227 knots. Thus, an in­crease in altitude will cause the curve of thrust required to flatten out and move to the direc­tion of higher velocity. Note that altitude alone will not alter the value of minimum drag.

The effect of altitude on the curve of power required can best be considered from the effect on true airspeed to achieve a specific aero­dynamic condition. The sea level power re­quired curve of figure 2.4 indicates that occurs at 160 knots and requires 615 h. p. If this same airplane is operated at (L/D^wa at an altitude of 22,000 ft., the same drag is incurred at a higher velocity and re­quires a higher power. The increase in ve­locity to 227 knots accounts for the increase in power required to 872 h. p. Actually, the various points on the curve of power required can be considered affected in this same fashion. At specific lift coefficients and angles of attack, a change in altitude will alter the true airspeed particular to these points and cause a change in power required because of the change in true airspeed. An increase in altitude will

POWER

REQUIRED

(HP)

THRUST

REQUIRED

(LBS)

POWER

REQUIRED

(HP.)

cause the power required curve to flatten out and move to higher velocities and powers required.

The curves of thrust and power required and their variation with weight, altitude, and con­figuration are the basis of all phases of airplane performance. These curves define the require­ments of the airplane and must be considered with the power and thrust available from the powerplants to provide detailed study of the various items of airplane performance.

AIRPLANE PERFORMANCE

The performance of an aircraft is. the most important feature which defines its suitability for specific missions. The principal items of airplane performance deserve detailed consid­eration in order to better understand and appreciate the capabilities of each airplane. Knowledge of the various items of airplane performance will provide the Naval Aviator with a more complete appreciation of the
operating limitations and insight to obtain the design performance of his aircraft. The performance section of the flight handbook provides the specific information regarding the capabilities and limitations of each airplane. Every Naval Aviator must rely upon these handbook data as the guide to safe and effec­tive operation of his aircraft.

REQUIRED THRUST AND POWER

DEFINITIONS

All of the principal items of flight perform­ance involve steady state flight conditions and equilibrium of the airplane. For the airplane to remain in steady level flight, equilibrium must be obtained by a lift equal to the air­plane weight and a powerplant thrust equal to the airplane drag. Thus, the airplane drag defines the thrust required to maintain steady level flight.

The total drag of the airplane is the sum of the parasite and induced drags. Parasite drag is the sum of pressure and friction drag which is due to the basic configuration and, as de­fined, is independent of lift. Induced drag is the undesirable but unavoidable consequence of the development of lift. In the process of creating lift by the deflection of an airstream, the actual lift is inclined and a component of lift is incurred parallel to the flight path direc­tion. This component of lift combines with any change in pressure and friction drag due to change in lift to form the induced drag. While the parasite drag predominates at high speed, induced drag predominates at low speed. Figure 2.1 illustrates the variation with speed of the induced, parasite, and total drag for a specific airplane configuration in steady level flight.

The power required for flight depends on the thrust required and the flight velocity. By definition, the propulsive horsepower required is related to thrust required and flight velocity by the following equation:

TrV

325

knots requires one horsepower of propulsive power. However, each pound of drag at 650 knots requires two horsepower while each pound of drag at 162.5 knots requires one-half horsepower. The term “power” implies work rate and, as such, will be a function of the speed at which a particular force is developed.

Distinction between thrust required and power required is necessary for several reasons. For the items of performance such as range and endurance, it is necessary to relate powerplant fuel flow with the propulsive requirement for steady level flight. Some powerpiants incur fuel flow rate according to output thrust while other powerpiants incur fuel flow rate depend­ing on output power. For example, the turbo­jet engine is principally, a thrust producing machine and fuel flow is most directly related to thrust output. The reciprocating engine is principally a power producing machine and fuel flow is most directiv related to power output. For these reasons the variation of thrust required will be of greatest interest in the performance of the turbojet powered air­plane while the variation of power required will be of greatest interest in the performance of the propeller powered airplane. Also, dis­tinction between power and thrust required is necessary in the study of climb performance. During a steady climb, the rate of climb will depend on excess power while the angle of climb is a function of excess thrust.

The total power required for flight can be considered as the sum of induced and parasite effects similar to the total drag of the airplane. The induced power required is a function of the induced drag and velocity.

Thus, induced power required will vary with lift, aspect ratio, altitude, etc., in the same manner as the induced drag. The only differ­ence will be the variation with speed. If all other factors remain constant, the induced power required varies inversely with velocity while induced drag varies inversely with the square of the velocity.

^h = Vi Prh V2

where

Ргіх = induced power required corresponding to some original speed, Vx Pfi2= induced power required corresponding to some different speed, V2

For example, if an airplane in steady level flight is operated at twice as great a speed, the in­duced drag is one-fourth the original value but the induced power required is one-half the original value.

The parasite power required is a function of the parasite drag and velocity.

where

Prv = parasite power required, h. p.

Dp = parafcitfe drag, lbs.

K=true airspeed, knots

Thus, parasite power required will vary with altitude and equivalent parasite area ( /) in the same manner as the parasite drag. However, the variation with speed will be different. If all other factors are constant, the parasite drag varies as the square of velocity but parasite power varies as the cube of velocity.

PrP2_(V2 V PrPl VJ

where

Pfpi = parasite power required corresponding to some original speed, Vx

Pfp2— parasite power required corresponding to some different speed, V2

For example, if an airplane in steady flight is operated at twice as great a speed, the parasite drag is four times as great but the parasite power required is eight times the original value.

Figure 2.1 presents the thrust required and power required for a specific airplane configu­ration and altitude. The curves of figure 2.1 are applicable for the following airplane data: gross weight, 15,000 lbs. span, b = 40 ft.

equivalent parasite area, f—1.1 sq. ft. airplane efficiency factor, e— .827 sea level altitude, <r= 1.000 compressibility corrections neglected

The curve of drag or thrust required versus velocity shows the variation of induced, para­site, and total drag. Induced drag predomi­nates at low speeds. When the airplane is operated at maximum lift-drag ratio, the total drag is at a minimum and the induced and parasite drags are equal. For the specific airplane of figure 2.1, (L/D)moi and minimum total drag are obtained at a speed of 160 knots.

The curve of power required versus velocity shows the variation of induced, parasite, and total power required. As before, induced power required predominates at low speeds and parasite power required predominates at high speeds and the induced and parasite power are equal at (L/D)mai. However, the condition of (L/D)m<u. defines only the point of minimum drag and does not define the point of minimum ■power required. Ordinarily, the point of mini­mum power required will occur at a speed which is 76 percent of the speed for minimum drag and, in the case of the airplane configura­tion of figure 2.1, the speed for minimum power required would be 122 knots. The total drag at the speed for minimum power required is 15 percent higher than the drag at (L/D’)max but the minimum power required is 12 percent lower than the power required at (,L/D’)mex.

Induced drag predominates at speeds below the point of minimum total drag. When the airplane is operated at the condition of mini­mum power required, the total drag is 75 percent induced drag and 25 percent parasite drag. Thus, the induced drag is three times as great as the parasite drag when at minimum power required.

AIRPLANE TOTAL DRAG

TV. ^ tofi 1 on 1П fli rrV. t’ 1 c t’h я»

V_/A till **ll.^luus. ill 111^114. 1.11V

sum of the induced and parasite drag. Figure 1.35 illustrates the variation of total drag with speed for a given airplane in level flight at a particular weight, configuration, and alti­tude. The parasite drag increases with speed varying as the square of the velocity while the induced drag decreases with speed varying in­versely as the square of the velocity. The total drag of the airplane shows the predomi­nance of induced drag at low speed and parasite drag at high speed. Specific points of interest on the drag curve are as follows;

(A) Stall of this particular airplane occurs at 100 knots and is indicated by a sharp rise in the actual drag. Since the generalized equa­tions for induced and parasite do not account for conditions at stall, the actual drag of the airplane is depicted by the “hook” of the dotted line.

(B) At a speed of 124 knots, the airplane would incur a minimum rate of descent in power-off flight. Note that at this speed the induced drag comprises 75 percent of the total drag. If this airplane were powered with a reciprocating-propeller type powerplant, maxi­mum endurance would occur at this airspeed.

Figure 1.35. Typical Airplane Drag Curves


(C) The point of minimum total drag occurs at a speed of 163 knots. Since this speed in­curs the least total drag for lift-equal-weight flight, the airplane is operating at (L/D)mei. Because of the particular manner in which parasite and induced drags vary with speed (parasite drag directly as the speed squared; induced drag inversely as the speed squared) the minimum total drag occurs when the in­duced and parasite drags are equal. The speed for minimum drag is an important reference for many items of airplane performance. One item previously presented related glide per­formance and lift-drag ratio. At the speed of 163 knots this airplane incurs a total drag of 778 lbs. while producing 12,000 lbs. of lift. These figures indicate a maximum lift-drag ratio of 15.4’and relate a glide ratio of 15-4. In addition, if this airplane were jet powered, the airplane would achieve maximum en­durance at this airspeed for the specified alti­tude. If this airplane were propeller powered, the airplane would achieve maximum range at this airspeed for the specified altitude.

(D) Point (D) is at an airspeed approxi­mately 32 percent greater than the speed for (LjD’)maI. Note that the parasite drag com­prises 75 percent of the total drag at a speed of 215 knots. This point on the drag curve pro­duces the highest proportion between velocity and drag and would be the point for maximum range if the airplane were jet powered. Be­cause of the high proportion of parasite drag at this point the long range jet airplane has great preference for great aerodynamic clean­ness and less demand for a high aspect ratio than the long range propeller powered airplane.

(E) At a speed of 400 knots, the induced drag is an extremely small part of the total drag and parasite drag predominates.

(F) As the airplane reaches very high flight speeds, the drag rises in a very rapid fashion due to compressibility. Since the generalized equation for parasite drag does not account for compressibility effects, the actual drag rise is typified by the dashed line.

The airplane drag curve shown in figure 1.34 is particular to one weight, configuration, and altitude in level flight. Any change in one of these variables will affect the specific drags at specific velocities.

The airplane drag curve is a major factor in many items of airplane performance. Range, endurance, climb, maneuver, landing, takeoff, etc., performance are based on some relation­ship involving the airplane drag curve.

PARASITE DRAG

In addition to the drag caused by the de­velopment of lift (induced drag) there is the obvious drag which is not due to the develop­ment of lift. A wing surface even at zero lift will have “profile” drag due to skin friction and form. The other components of the air­plane such as the fuselage, tail, nacelles, etc., contribute to drag because of their own form and skin friction. Any loss of momentum of the airstream due to powerplant cooling, air conditioning, or leakage through construction or access gaps is, in effect, an additional drag. When the various components of the airplane are put together the total drag will be greater than the sum of the individual components because of “interference” of one surface on the other.

The most usual interference of importance occurs at the wing-body intersection where the growth of boundary layer on the fuselage re­duces the boundary layer velocities on the wing root surface. This reduction in energy allows the wing root boundary layer to be more easily separated in the presence of an adverse pressure gradient. Since the upper wing surface has the more critical pressure gradients, a low wing position on a circular fuselage would create greater interference drag than a high wing position. Adequate filleting and control of local pressure gradients is necessary to mini­mize such additional drag due to interference.

The sum of all the drags due to form, fric­tion, leakage and momentum losses, and inter­ference drag is termed “parasite” drag since it is not directly associated with the develop­ment of lift. While this parasite drag is not directly associated with the production of lift it is a variable with lift. The variation of parasite drag coefficient, CDpt with lift coef­ficient, CL, is shown for a typical airplane in figure 1.34. The minimum parasite drag co­efficient, CDn, usually occurs at or near zero

■nwn J

lift and parasite drag coefficient increases above this point in a smooth curve. The in­duced drag coefficient is shown on the same graph for purposes of comparison since the total drag of the airplane is a sum of the parasite and induced drag.

In many parts of airplane performance it is necessary to completely distinguish between drag due to lift and drag not due to lift. The total drag of an airplane is the sum of the para­site and induced drags.

С© = (jDp~h^D і

where

CD=airplane drag coefficient CDp=parasite drag coefficient CDf= induced drag coefficient

C *

=°-318s

From inspection of figure 1.34 it is seen that both CDp and CD( vary with lift coefficient. However, the usual variation of parasite drag allows a simple correlation with the induced drag term. In effect, the part of parasite drag above the minimum at zero lift can be ‘ Tumped”

1.2

0 1.0

1 °e

ё 0.6

О

I-

u.

□ 0.4

0.2

in with the induced drag coefficient by a con­stant factor which is defined as the “airplane efficiency factor", e. By this method of ac­counting the airplane drag coefficient is ex­pressed as:

C

l I

D = ‘-‘Dp. "t

C

с»=с"-.,+°-318(ж«)

where

_ minimum parasite drag Coefficient

CDi= induced drag coefficient

e = airplane efficiency factor

In this form, the airplane drag coefficient is expressed as the sum of drag not due to lift

(CDp ( ) and drag due to lift (—0- The air­plane efficiency factor is some constant (usually less than unity) which includes parasite drag due to lift with the drag induced by lift. CDts is invariant with lift and represents the

■*min t

parasite drag at zero lift. A typical value of CB„ would be 0.020, of which the wing may account for 50 percent, the fuselage and nacelles 40 percent, and the tail 10 percent. The term

(

Q 2 <

0.318 accounts for all drag due’ to

lift—the drag induced by lift and the extra parasite drag due to lift. Typical values of the airplane efficiency factor range from 0.6 to 0.9 depending on the airplane configuration and its characteristics. While the term of drag due to lift does include some parasite drag, it is still generally referred to as induced drag.

The second graph of figure 1.34 shows that C ■

the sum of Cn„ and can approximate the

гmin g L A

actual airplane CD through a large range of lift coefficients. For airplanes of moderate aspect ratio, this representation of the airplane total drag is quite accurate in the ordinary range of lift coefficients up to near 70 percent of CLmax. At high lift coefficients near CLmax, the proced­
ure is not too accurate because of the sharper variation of parasite drag at high angles of attack. In a sense, the airplane efficiency fac­tor would change from the constant value and decrease. The deviation of the actual airplane drag from the approximating curve is quite noticeable for airplanes with low aspect ratio and sweepback. Another factor to consider is the effect of compressibility. Since compressi­bility effects would destroy this relationship, the greatest application is for subsonic perform­ance analysis.

The total airplane drag is the sum of the parasite and induced drags.

D=DP+Di Di= induced drag

=(°-318lf>

Dp = parasite drag
CDp qS

^mn

When expressed in this form the induced drag, Diy includes all drags due to lift and is solely a function of lift. The parasite drag, Dp, is the parasite drag and is completely independent of lift—it could be called the “barn door” drag of the airplane.

An alternate expression for the parasite drag is:

DP=fq

where

/= equivalent parasite area, sq. ft.

f=CDp. S

mm

q= dynamic pressure, psf

<rV2

or

293

faV2

295

In this form, the equivalent parasite area, /, is the product of CD and S and relates an

1 Pmin

impression of the “bam door” size. Hence, parasite drag can be appreciated as the result of the dynamic pressure, q, acting on the equivalent parasite area, /. The “equivalent” parasite area is defined by this relationship as a hypothetical surface with a CD= 1.0 which produces the same parasite drag as the air­plane. An analogy would be a barn door in the airstream which is equivalent to the air­plane. Typical values for the equivalent para­site area range from 4 sq. ft. for a clean fighter type airplane to 40 sq. ft. for a large transport type airplane. Of course, when any airplane is changed from the clean configuration to the landing configuration, the equivalent parasite area increases.

EFFECT OF CONFIGURATION. The par­asite drag, Dp, is unaffected by lift, but is variable with dynamic pressure and equivalent parasite area. This principle furnishes the basis for illustrating the variation of parasite drag with the various conditions of flight. If all other factors are held constant, the para­site drag varies directly with the equivalent parasite area.

■^P2_ //Л

DP1 KfJ

where

DPl = parasite drag corresponding to some orig­inal parasite area, fi

DP2=parasite drag corresponding to some new parasite area, Д

(V and a are constant)

As an example, the lowering of the landing gear and flaps may increase the parasite area 80 percent. At any given speed and altitude this airplane would experience an 80 percent increase in parasite drag.

EFFECT OF ALTITUDE. In a similar man­ner the effect of altitude on parasite drag may be appreciated. The general effect of altitude is expressed by: where

DPl = parasite drag corresponding to some orig­inal altitude density ratio, oi

Dpj=parasite drag corresponding to some new altitude density ratio, c2

(and /, V are constant)

This relationship implies that parasite drag would decrease at altitude, e. g., a given air­plane in flight at a given TAS at 40,000 ft. (a=0.25) would have one-fourth the parasite drag when at sea level (<r= 1.00). This effect results when the lower air density produces less dynamic pressure. However, if the air­plane is flown at a constant EAS, the dynamic pressure and, thus, parasite drag do not vary. In this case, the TAS would be higher at altitude to provide the same EAS.

EFFECT OF SPEED. The effect of speed alone on parasite drag is the most important. If all other factors are held constant, the effect of velocity on parasite drag is expressed as:

о*, /рл2

DPl VJ

where

Dpparasite drag corresponding to some orig­inal speed, Vt

DPi=parasite drag corresponding to some new speed, Vs

(J and a are constant)

This relationship expresses a powerful effect of speed on parasite drag. As an example, a given airplane in flight at some altitude would have four times as much parasite drag at twice as great a speed or one-fourth as much parasite drag at half the original speed. This fact may­be appreciated by the relationship of dynamic pressure with speed—twice as much V, four times as much q, and four times as much Dp. This expressed variation of parasite drag with speed points out that parasite drag will be of greatest importance at high speeds and prac­tically insignificant in flight at low dynamic pressures. To illustrate this fact, an airplane in flight just above the stall speed could have a parasite drag which is only 25 percent of the total drag. However, this same airplane at maximum level flight speed at low altitude would have a parasite drag which’ is very nearly 100 percent of the total drag. The predominance of parasite drag at high flight speeds emphasizes the necessity for great aero­dynamic cleanness (low /) to obtain high speed performance.

In the subsonic regime of flight, the ordinary configuration of airplane has a very large por­tion of the equivalent parasite area determined by skin friction drag. As the wing contrib­utes nearly half of the total parasite drag, the profile drag of the wing can be minimized by the use of the airfoil sections which produce extensive laminar flow. A subtle effect on parasite drag occurs from the influence of the wing area. Since the wing area (T) appears directly in the parasite drag equation, a reduc­tion in wing area would reduce the parasite drag if all other factors were unchanged. While the exact relationship involves con­sideration of many factors, most optimum airplane configurations have a strong preference for the highest practical wing loading and minimum wing surface area.

As the flight speeds of aircraft approach the speed of sound, great care must be taken to delay and alleviate compressibility effects. In order to delay and reduce the drag rise associated with compressibility effects, the components of the airplanes must be arranged to reduce the early formation of shock waves on the airplane. This will generally require fuselage and nacelles of high fineness ratio, well faired canopies, and thin wing sections which have very smooth uniform pressure dis­tributions. Low aspect ratios and sweepback are favorable in delaying and reducing the compressibility drag rise. In addition, inter­ference effects are quite important in transonic and supersonic flight and the airplane cross section area distribution must be controlled to minimize local velocity peaks which could create premature strong shock wave formation.

The modern configuration of airplane will illustrate the features required to effect very high speed performance—’low aspect ratio, sweepback, thin low drag sections, etc. These same features produce flight characteristics at low airspeeds which necessitate proper flying technique.

STALL PATTERNS

An additional effect of the planform area distribution is on stall pattern of wing. The desirable stall pattern of any wing is a stall which begins on the root sections first. The advantages of root stall first are that ailerons remain effective at high angles of attack, favorable stall warning results from the buffet on the empennage and aft portion of the fuse­lage, and the loss of downwash behind the root usually provides a stable nose down moment to the airplane. Such a stall pattern is favored but may be difficult to obtain with certain wing configurations. The types of stall patterns in­herent with various pianforms are illustrated in figure 1.33. The various planform effects are separated as follows:

(A) The elliptical planform has constant local lift coefficients throughout the span from root to tip. Such a lift distribution means that all sections will reach stall at essentially the same wing angle of attack and stall will begin and progress uniformly throughout the span. While the elliptical wing would reach high lift coefficients before incipient stall, there would be little advance warning of complete stall. Also, the ailerons may lack effectiveness when the wing operates near the stall and lat­eral control may be difficult.

(B) The lift distribution of the rectangular wing exhibits low local lift coefficients at the tip and high local lift coefficients at the root. Since the wing will initiate stall in the area of highest local lift coefficients, the rectangular wing is characterized by a strong root stall tendency. Of course, this stall pattern is fav­orable since there is adequate stall warning buffet, adequate aileron effectiveness, and usu­ally strong stable moment changes on the air­plane. Because of the great aerodynamic and structural inefficiency of this planform, the rectangular wing finds limited application only to low cost, low speed light planes. The sim­plicity of construction and favorable stall characteristics are predominating requirements of such an airplane. The stall sequence for a rectangular wing is shown by the tuft-grid pictures. The progressive flow separation il­lustrates the strong root stall tendency.

(C) The wing of moderate taper (taper ratio = 0.5) has a lift distribution which closely

(0) TUFT GRID 6 INCHES FROM (b) TUFT GRID 24 INCHES FROM

TRAILING EDGE TRAILING EDGE

FROM NACA TN 2674

30° OF FLOW ANGULARITY

FROM NACA TN 2674

SURFACE TUFT PHOTOGRAPHS
FOR A SWEPT, TAPERED WING
45° DELTA, AR=4.0, X=0

FROM NACA TN 2674
Figure 1.33. Stall Patterns (sheet 5 o! 8)


(a) TUFT GRID 6 INCHES FROM
TRAILING EDGE
(b) TUFT GRID 24 INCHES FROM
TRAILING EDGE

FROM NACA TN 2674

а = 8 DEGREES

FROM NACA TN 2674

approximates that of the elliptical wing. Hence, the stall pattern is much the same as the elliptical wing.

(D) The highly tapered wing of taper ratio=0.25 shows the stall tendency inherent with high taper. The lift distribution of such a wing has distinct peaks just inboard from the tip. Since the wing stall is started in the vicinity of the highest local lift coefficient, this planform has a strong “tip stall” tendency. The initial stall is not started at the exact tip but at the station inboard from the tip where highest local lift coefficients prevail. If an actual wing were allowed to stall in this fashion the occurrence of stall would be typi­fied by aileron buffet and wing drop. There would be no buffet of the empennage or aft fuselage, no strong nose down moment, and very little—if any—aileron effectiveness. In order to prevent such Undesirable happenings, the wing must be tailored to favor the stall pattern. The wing may be given a geometric twist or “washout” to decrease the local angles of attack at the tip. In addition, the airfoil section may be varied throughout the span such that sections with greater thickness and camber are located in the areas of highest local lift coefficients. The higher ciof such sections can then develop the higher local ci’s and be less likely to stall. The addition of leading edge slots or slats toward the tip increase ihe local c> and stall angle of attack and are useful in allaying tip stall and loss of aileron effectiveness. Another device for im­proving the stall pattern would be the forcing of stall in the desired location by decreasing the section cimax in this vicinity. The use of sharp leading edges or “stall strips” is a powerful device to control the stall pattern.

(E) The pointed tip wing of taper ratio equal to zero develops extremely high local lift coefficients at the tip. For all practical purposes, the pointed tip will be stalled at any condition of lift unless extensive tailoring is applied to the wing. Such a planform has no practical application to an airplane which is definitely subsonic in performance.

(F) Sweepback applied to a wing planform alters the lift distribution similar to decreasing taper ratio. Also, a predominating influence of the swept planform is the tendency for a strong crossflow of the boundary layer at high lift coefficients. Since the outboard sections of the wing trail the inboard sections, the out­board suction pressures tend to draw the boundary layer toward the tip. The result is a thickened low energy boundary layer at the tips which is easily separated. The develop­ment of the spanwise flow in the boundary layer is illustrated by the photographs of figure 1.33. Note that the dye streamers on the upper surface of the swept wing develop a strong spanwise crossflow at high angles of attack. Slots, slats, and flow fences help to allay the strong tendency for spanwise flow.

When sweepback and taper are combined in a planform, the inherent tip stall tendency is considerable. If tip stall of any significance is allowed to occur on the swept wing, an addi­tional complication results: the forward shift in the wing center of pressure creates an un­stable nose up pitching moment. The stall sequence of a swept, tapered wing is indicated by the tuft-grid photographs of figure 1.33.

An additional effect on sweepback is the re­duction in the slope of the lift curve and maxi­mum lift coefficient. When the sweepback is large and combined with low aspect ratio the lift curve is very shallow and maximum lift coefficient can occur at tremendous angles of attack. The lift curve of one typical low aspect ratio, highly tapered, swept wing air­plane depicts a maximum lift coefficient at approximately 45° angle of attack. Such dras­tic angles of attack are impractical in many respects. If the airplane is operated at such high angles of attack an extreme landing gear configuration is required, induced drag is ex­tremely high, and the stability of the airplane may seriously deteriorate. Thus, the modern configuration of airplane may have ‘ ‘minimum control speeds’ ‘ set by these factors rather than simple stall speeds based on CLna.

When a wing of a given planform has various high lift devices added, the lift distribution and stall pattern can be greatly affected. Deflcc* tion of trailing edge flaps increases the local lift coefficients in the flapped areas and since the stall angle of the flapped section is de­creased, initial stall usually begins in the flapped area. The extension of slats simply allows the slatted areas to go to higher lift coefficients and angles of attack and generally delays stall in that vicinity. Also, power effects may adversely affect the stall pattern of the propeller powered airplane. When the propeller powered airplane is at high power and low speed, the flow induced at the wing root by the slipstream may cause considerable delay in the stall of the root sections. Hence, the propeller powered airplane may have its most undesirable stall characteristics during the power-on stall rather than the power-off stall.

EFFECT OF TAPER AND SWEEPBACK

The aspect ratio of a wing is the primary factor in determining the three-dimensional characteristics of the ordinary wing and its drag due to lift. However, certain local effects take place throughout the span of the wing and these effects are due to the distribution of area throughout the span. The distribution of lift along the span of a wing cannot have sharp discontinuities. (Nature just doesn’t arrange natural forces with sharp discontinuities.) The typical lift distribution is arranged in some elliptical fashion. A representative dis­tribution of the lift per foot of span along the span of a wing is shown in figure 1.32.

The natural distribution of lift along the span of a wing provides a basis for appreciating the effect of area distribution and taper along the span. If the elliptical lift distribution is

matched with a planform whose chord is dis­tributed in an elliptical fashion (the elliptical wing), each square foot of area along the span produces exactly the same lift pressure. The elliptical wing planform then has each section of the wing working at exactly the same local Lift coefficient and the induced downflow at the wing is uniform throughout the span. In the aerodynamic sense, the elliptical wing is the most efficient planform because the uni­formity of lift coefficient and downwash incurs the least induced drag for a given aspect ratio. The merit of any wing planform is then meas­ured by the closeness with which the distribu­tion of lift coefficient and downwash approach that of the elliptical planform.

The effect of the elliptical planform is illus­trated in figure 1.32 by the plot of local lift

coefficient to wing lift coefficient, 4r, versus

Oz,

semispan distance. The elliptical wing pro­duces a constant value of4r = 1.0 throughout

the span from root to tip. Thus, the local section angle of attack, a0, and local induced angle of attack, are constant throughout the span. If the planform area distribution is anything other than elliptical, it may be ex­pected that the local section and induced angles of attack will not be constant along the span.

A planform previously considered is the simple rectangular wing which has a taper ratio of 1.0. A characteristic of the rectangular wing is a strong vortex at the tip with local downwash behind the wing which is high at the tip and low at the root. This large non­uniformity in downwash causes similar varia­tion in the local induced angles of attack along the span. At the tip. where high downwash exists, the local induced angle of attack is greater than the average for the wing. Since the wing angle of attack is composed of the sum of cr( and a0, a large local a, reduces the local ao creating low local lift coefficients at the tip. The reverse is true at the root of the rectangular wing where low local downwash exists. This situation creates an induced angle of attack at the root which is less than the average for the wing and a local section angle of attack higher than the average for the wing. The result is shown by the graph of figure 1.32 which depicts a local lift coefficient at the root almost 20 percent greater than the wing lift coefficient.

The effect of the rectangular planform may be appreciated by matching a near elliptical lift distribution with a planform with a constant chord. The chords near the tip develop less lift pressure than the root and consequently have lower section lift coeffi­cients. The great nonuniformity of local lift coefficient along the span implies that some sections carry more than their share of the load while others carry less than their share of the load. Hence, for a given aspect ratio, the rectangular planform will be less efficient than the elliptical wing. For example, a rectangular wing of AR=6 would have 16 percent higher induced angle of attack for the wing and 5 percent higher induced drag than an elliptical wing of the same aspect ratio.

At the other extreme of taper is the pointed wing which has a taper ratio of zero. The extremely small parcel of area at the pointed tip is not capable of holding the main tip vortex at the tip and a drastic change in down – wash distribution results. The pointed wing has greatest downwash at the root and this downwash decreases toward the tip. In the immediate vicinity of the pointed tip, an upwash is encountered which indicates that negative induced angles of attack exist in this area. The resulting variation of local lift coefficient shows low a at the root and very high ct at the tip. This effect may be appre­ciated by realizing that the wide chords at the root produce low lift pressures while the very narrow chords toward the tip are sub­ject to very high lift pressures. The varia­tion of U – throughout the span of the wing of taper ratio=0 is shown on the graph of figure

1.32. As with the rectangular wing, the non­uniformity of downwash and lift distribution result in inefficiency of this planform. For example, a pointed wing of AR=6 would have 17 percent higher induced angle of attack for the wing and 13 percent higher induced drag than an elliptical wing of the same aspect ratio.

Between the two extremes of taper will exist pianforms of more tolerable efficiency.

The variations of p for a wing of taper ratio

=0.5 closely approximates the lift distribution of the elliptical wing and the drag due to lift characteristics are nearly identical. A wing of AR=6 and taper ratio = 0.5 has only 3 percent higher а і and 1 percent greater CDi than an elliptical wing of the same aspect ratio.

A separate effect on the spanwise lift dis­tribution is contributed by wing sweepback. Sweepback of the planform tends to alter the lift distribution similar to decreasing the taper ratio. Also, large sweepback tends to increase induced drag.

The elliptical wing is the ideal of the sub­sonic aerodynamic planform since it provides a minimum of induced drag for a given aspect ratio. However, the major objection to the elliptical planform is the extreme difficulty of mechanical layout and construction. A highly tapered planform is desirable from the stand­point of structural weight and stiffness and the usual wing planform may have a taper ratio from 0.45 to 0.20. Since structural con­siderations are quite important in the develop­ment of an airplane configuration, the tapered planform is a necessity for an efficient configu­ration. In order to preserve the aerodynamic efficiency, the resulting planform is tailored by wing twist and section variation to obtain as near as possible the elliptic lift distribution.

INDUCED DRAG

Another important influence of the induced flow is the orientation of the actual lift on a wing. Figure 1.30 illustrates the fact that the lift produced by the wing sections is perpen­dicular to the average relative wind. Since the average relative wind is inclined down­ward, the section lift is inclined aft by the same amount—the induced angle of attack, The lift and drag of a wing must continue to be referred perpendicular and parallel to the remote free stream ahead of the wing. In this respect, the lift on the wing has a component of force parallel to the remote free stream. This component of lift in the drag direction is the undesirable—but unavoidable—conse-

BOUND OR LINE VORTEX

qucncc of developing lift with a finite wing and is termed INDUCED DRAG, D,. In­duced drag is separate from the drag due to form and friction and is due simply to the de­velopment of lift.

By inspection of the force diagram of figure

1.30, a relationship between induced drag, lift, and induced angle of attack is apparent. The induced drag coefficient, CDi, will vary directly with the wing lift coefficient, CL, and the in­duced angle of attack, The effective lift is the vertical component of the actual lift and, if the induced angle of attack is small, will be essentially the same as the actual lift. The J horizontal and vertical component of drag is insignificant under the same conditions. By a detailed study of the factors involved, the fol­lowing relationships can be derived for a wing with an elliptical lift distribution:

(1) The induced drag equation follows the same form as atmlied to anv other aerodv-

А А Ф *

namic force.

Di—CDiqS

where

D{— induced drag, lbs. q=dynamic pressures, psf trV1

295

CD.=induced drag coefficient S= wing area, sq. ft.

(2) The induced drag coefficient can be derived as: or where

CL—lih coefficient

sin a,=natural sine of the induced angle of attack, degrees и-=3.141б, constant ЛИ=wing aspect ratio

(3) The induced angle of attack can be derived as:

<*i= 18.24 (degrees)

(Note: the derivation of these relationships may be found in any of the standard engi­neering aerodynamics textbooks.)

These relationships facilitate an understanding and appreciation of induced drag.

The induced angle of attack

depends on the lift coefficient and aspect ratio. Flight at high lift conditions such as low speed or maneuvering flight will create high induced angles of attack while high speed, low lift flight will create very small induced angles of attack. The inference is that high lift coeffi­cients require large downwash and result in large induced angles of attack. The effect of aspect ratio is significant since a very high aspect ratio would produce a negligible induced angle of attack. If the aspect ratio were in­finite, the induced angle of attack would be zero and the aerodynamic characteristics of the wing would be identical with the airfoil sec­tion properties. On the other hand, if the wing aspect ratio is low, the induced angle of attack will be large and the low aspect ratio airplane must operate at high angles of attack at maximum lift. Essentially, the low aspect ratio wing affects a relatively small mass of air and consequently must provide a large de­flection (downwash) to produce lift.

EFFECT OF LIFT. The induced drag co­

efficient

ilar effects of lift coefficient and aspect ratio. Because of thepower of variation of induced drag coefficient with lift coefficient, high lift coeffi­cients provide very high induced drag and low lift coefficients very low induced drag. The di­rect effect of CL can be best appreciated by assum­ing an airplane is flying at a given weight, alti­tude, and airspeed. If the airplane is maneuvered from steady level flight to a load factor of two,

favliMf January 1965

the lift coefficient is doubled and the induced drag is four times as great. If the flight load factor is changed from one to five, the induced drag is twenty-five times as great. If all other factors are held constant to single out this effect, it could be stated that “induced drag varies as the square of the lift”

where

Dix = induced drag corresponding to some original lift, Li Z),4= induced drag corresponding to some new lift, La

(and q (or EAS~), S, AR are constant)

This expression defines the effect of gross weight, maneuvers, and steep turns on the induced drag, e. g., 10 percent higher gross weight increases induced drag 21 percent, 4G maneuvers cause 16 times as much induced drag, a turn with 45° bank requires a load factor of 1.41 and this doubles the induced drag.

EFFECT OF ALTITUDE. The effect of altitude on induced drag can be appreciated by holding all other factors constant. The gen­eral effect of altitude is expressed by:

Dij_ /ffA

Dii <г2/

where

Dii=induced drag corresponding to some orig­inal altitude density ratio, <n

Di2= induced drag corresponding to some new altitude density ratio, <r2

(and L, S, AR, V are constant)

This relationship implies that induced drag would increase with altitude, e. g., a given airplane flying in level flight at a given TAS at 40,000 ft. (ir=0.25) would have four times as much induced drag than when at sea level (<r=1.00). This effect results when the lower air density requires a greater deflection of the airstream to produce the same lift. However, if the airplane is flown at the same EAS, the dynamic pressure will be the same and induced drag will not vary. In this case, the TAS would be higher at altitude to provide the same EAS.

EFFECT OF SPEED. The general effect of speed on induced drag is unusual since low air­speeds are associated with high lift coefficients and high lift coefficients create high induced drag coefficients. The immediate implication is that induced drag increases with decreasing air­speed. If all other factors are held constant to single out the effect of airspeed, a rearrange­ment of the previous equations would predict that “induced drag varies inversely as the square of the airspeed.’’

DhjVA*

Dh Vj

where

Dii=induced drag corresponding to some orig­inal speed, Vі

Dt2 = induced drag corresponding to some new speed, V2

(and L, S, AR, в are constant)

Such an effect would imply that a given air­plane in steady flight would incur one-fourth as great an induced drag at twice as great a speed or four times as great an induced drag at half the original speed. This variation may be illustrated by assuming that an airplane in steady level flight is slowed from 300 to 150 knots. The dynamic pressure at 150 knots is one-fourth the dynamic pressure at 300 knots and the wing must deflect the airstream four times as greatly to create the same lift. The same lift force is then slanted aft four times as greatly and the induced drag is four times as great.

The expressed variation of induced drag with speed points out that induced drag will be of

greatest importance at low speeds and prac­tically insignificant in flight at high dynamic pressures. For example, a typical single en­gine jet airplane at low altitude and maximum level flight airspeed has an induced drag which is less than 1 percent of the total drag. How­ever, this same airplane in steady flight just above the stall speed could have an induced drag which is approximately 75 percent of the total drag.

EFFECT OF ASPECT RATIO, The effect of aspect ratio on the induced drag

^=0.318^0

is the principal effect of the wing planform. The relationship for induced drag coefficient emphasizes the need of a high aspect ratio for the airplane which is continually operated at high lift coefficients. In other words, airplane configurations designed to operate at high lift coefficients during the major portion of their flight (sailplanes, cargo, transport, patrol, and antisubmarine types) demand a high aspect ratio wing to minimize the induced drag. While the high aspect ratio wing will minimize induced drag, long, thin wings increase structural weight and have relatively poor stiffness characteristics. This fact will temper the preference for a very high aspect ratio. Airplane configurations which are developed for very high speed flight (es- specially supersonic flight) operate at relatively low lift coefficients and demand great aero­dynamic cleanness. These configurations of airplanes do not have the same preference for high aspect ratio as the airplanes which op­erate continually at high lift coefficients. This usually results in the development of low aspect ratio planforms for these airplane con­figurations.

The effect of aspect ratio on the lift and drag characteristics is shown in figure 1.31 for wings of a basic 9 percent symmetrical section. The basic airfoil section properties are shown on these curves and these properties would be
typical only of a wing planform of extremely high (infinite) aspect ratio. When a wing of some finite aspect ratio is constructed of this basic section, the principal differences will be in the lift and drag characteristics—the mo­ment characteristics remain essentially the same. The effect of decreasing aspect ratio on the lift curve is to increase the wing angle of attack necessary to produce a given lift co­efficient. The difference between the wing angle of attack and the section angle of attack

Q

is the induced angle of attack, ai—18.24

ЛД

which increases with decreasing aspect ratio. The wing with the lower aspect ratio is less sensitive to changes in angle of attack and re­quires higher angles of attack for maximum lift. When the aspect ratio is very low (below 5 or 6) the induced angles of attack are not accurately predicted by the elementary equa­tion for а і and the graph of CL versus a develops distinct curvature. This effect is especially true at high lift coefficients where the lift curve for the very low aspect ratio wing is very shallow and CLmgx and stall angle of attack are less sharply defined.

The effect of aspect ratio on wing drag char­acteristics may be appreciated from inspection of figure 1.31. The basic section properties are shown as the drag characteristics of an infinite aspect ratio wing. When a planform of some finite aspect ratio is constructed, the wing drag coefficient is the sum of the induced drag coeffi­, and the section drag со efficient. Decreasing aspect ratio increases the wing drag coefficient at any lift coefficient since the induced drag coefficient varies inversely with aspect ratio. When the aspect ratio is very low, the induced drag varies greatly with lift and at high lift coefficients, the induced drag is very high and increases very rapidly with lift coefficient.

While the effect of aspect ratio on lift curve slope and drag due to lift is an important re­lationship, it must be realized that design for

WING LIFT COEFFICIENT, CL WING LIFT COEFFICIENT, CL

very high speed flight does not favor the use of high aspect ratio planforms. Low aspect ratio planforms have structural advantages and allow the use of thin, low drag sections for high speed flight. The aerodynamics of transonic and supersonic flight also favor short span, low aspect ratio surfaces. Thus, the modern con­figuration of airplane designed for high speed flight will have a low aspect ratio planform with characteristic aspect ratios of two to four. The most important impression that should result is that the typical modem configuration will have high angles of attack for maximum lift and very prodigious drag due to lift at low flight speeds. This fact is of importance to the Naval Aviator because the majority of pilot – caused accidents occur during this regime of flight—during takeoff, approach, and landing. Induced drag predominates in these regimes of flight.

The modern configuration of high speed air­plane usually has a low aspect ratio planform with high wing loading. When wing sweep – back is coupled with low aspect ratio, the wing lift curve has distinct curvature and is very flat at high angles of attack, i. e., at high CL, CL in­creases very slowly with an increase in a. In addition, the drag curve shows extremely rapid rise at high lift coefficients since the drag due to lift is so very large. These effects produce flying qualities which are distinctly different from a more "conventional” high aspect ratio airplane configuration.

Some of the most important ramifications of the modern high speed configuration are:

(1) During takeoff where the airplane must not be over-rotated to an excessive angle of attack. Any given airplane will have some fixed angle of attack (and Cff) which produces the best takeoff performance and this angle of attack will not vary with weight, density altitude, or temperature. An excessive angle of attack produces additional induced drag and may have an undesirable effect on takeoff performance. Takeoff acceleration may be seriously reduced and a large increase in

takeoff distance may occur. Also, the initial climb performance may be marginal at an excessively low airspeed. There are modern configurations of airplanes of very low aspect ratio (plus sweepback) which—if over­rotated during a high altitude, high gross weight takeoff—cannot fly out of ground effect. With the more conventional airplane configuration, an excess angle of attack pro­duces a well defined stall. However, the modern airplane configuration at an excessive angle of attack has no sharply defined stall but developes an excessive amount of induced drag. To be sure that it will not go unsaid, an excessively low angle of attack on takeoff creates its own problems—excess takeoff speed and distance and critical tire loads.

(2) During approach where the pilot must exercise proper technique to control the flight path. “Attitude plus power equals performance. ” The modern high speed con­figuration at low speeds will have low lift – drag ratios due to the high induced drag | and can require relatively high power set­tings during the power approach. If the pilot interprets that his airplane is below the desired glide path, his first reaction must not be to just ease the nose up. An increase in angle of attack without an increase in power will lower the airspeed and greatly increase the induced drag. Such a reaction could create a high rate of descent and lead to very undesirable consequences. The an­gle of attack indicator coupled with the mirror landing system provides reference to the pilot and emphasizes that during the steady approach “angle of attack is the primary control of airspeed and power is the primary control of rate of climb or descent.” Steep turns during approach at low airspeed are always undesirable in any type of air­plane because of the increased stall speed and induced drag. Steep turns at low airspeeds in a low aspect ratio airplane can create extremely high induced drag and can incur dangerous sink rates.

(3) During the landing phase where an excessive angle of attack (or excessively low airspeed) would create high induced drag and a high power setting to control rate of descent. A common error in the technique of landing modern configurations is a steep, low power approach to landing. The steep flight path requires considerable maneuver to flare the airplane for touchdown and necessitates a definite increase in angle of attack. Since the maneuver of the flare is a transient condition, the variation of both lift and drag with angle of attack must be considered. The lift and drag curves for a high aspect ratio wing (fig. 1.31) show con­tinued strong increase in CL with a up to stall and large changes in CD only at the point of stall. These characteristics imply that the high aspect ratio airplane is usually capable of flare without unusual results. The in­crease in angle of attack at flare provides the increase in lift to change the flight path direction without large changes in drag to decelerate the airplane.

The lift and drag curves for a low aspect ratio wing (fig. 1.31) show that at high angles of attack the lift curve is shallow, i. e., small changes in Cl with increased a. This implies a large rotation needed to provide the lift to flare the airplane from a steep approach. The drag curve for the low aspect ratio wing shows large, powerful increases in CD with Cl well below the stall. These lift and drag charac­teristics of the low aspect ratio wing create a distinct change in the flare characteristics. If a flare is attempted from a steep approach at low airspeed, the increased angle of attack may provide such increased induced drag and rapid loss of airspeed that the airplane does not actually flare. A possible result is that an even higher sink rate may be incurred. This is one factor favoring the use of the ‘‘no-flare” or “minimum flare” type landing technique for certain modern configurations. These same aerodynamic properties set the best glide speeds of low aspect ratio airplanes above the speed for (L/D)^. The additional speed pro­vides a more favorable margin of flare capabil­ity for flameout landing from a steep glide path (low aspect ratio, low (L/D)^, low glide ratio).

The landing technique must emphasize proper control of angle of attack and rate of descent to prevent high sink rates and hard landings. As before, to be sure that it will not go unsaid, excessive airspeed at landing creates its own problems—excessive wear and tear on tires and brakes, excessive landing distance, etc.

The effect of the low aspect ratio planform of modern airplanes emphasizes the need for proper flying techniques at low airspeeds. Excessive angles of attack create enormous induced drag which can hinder takeoff per­formance and incur high sink rates at landing. Since such aircraft have intrinsic high mini­mum flying speeds, an excessively low angle of attack at takeoff or landing creates its own problems. These facts underscore the im­portance of a “thread-the-needle,” professional flying technique.

PLANFORM EFFECTS AND. AIRPLANE DRAG

EFFECT OF WING PLANFORM

The previous discussion of aerodynamic forces concerned the properties of airfoil sec­tions in two-dimensional flow with no consid­eration given to the influence of the planform. When the effects of wing planform are intro­duced, attention must be directed to the ex­istence of flow components in the spanwise direction. In other words, airfoil section properties, deal with flow in two dimensions while planform properties consider flow in three dimensions.

In order to fully describe the planform of a wing, several terms are required. The terms having the greatest influence on the aerody­namic characteristics are illustrated in figure

1.28.

(1) The wing area, T, is simply the plan surface area of the wing. Although a por­tion of the area may be covered by fuselage or nacelles, the pressure carryover on these surfaces allows legitimate consideration of the entire plan area.

(2) The wing span, b, is measured tip to tip.

(3) The average chord, c, is the geometric average. The product of the span and the average chord is the wing area (bXc=S’).

(4) The aspect ratio, AR, is the proportion of the span and the average chord.

AR=bjc


If the planform has curvature and the aver­age chord is not easily determined, an alternate expression is:

AK~b2jS

The aspect ratio is a fineness ratio of the wing and this quantity is very powerful in determing the aerodynamic characteristics and structural weight. Typical aspect ratios vary from 35 for a high performance sail­plane to 3.5 for a jet fighter to 1.28 for a flying saucer.

(5) The root chord, cT, is the chord at the wing centerline and the tip chord, ct, is measured at the tip.

(6) Considering the wing planform to have straight lines for the leading and trail­ing edges, the taper ratio, X (lambda), is the ratio of the tip chord to the root chord.

= Ctlcr

The taper ratio affects the lift distribution and the structural weight of the wing. A rectangular wing has a taper ratio of 1.0 while the pointed tip delta wing has a taper ratio of 0.0.

(7) The sweep angle, A (cap lambda), is usually measured as the angle between the line of 25 percent chords and a perpendicular to the root chord. The sweep of a wing causes definite changes in compressibility, maximum lift, and stall characteristics-

(8) The mean aerodynamic chord, MAC, is the chord drawn through the centroid (geographical center) of plan area. A rec­tangular wing of this chord and the same span would have identical pitching moment characteristics. The MAC is located on the reference axis of the airplane and is a primary reference for longitudinal stability considera­tions. Note that the MAC is not the average chord but is the chord through the centroid of area. As an example, the pointed-tip delta wing with a taper ratio of zero would have an average chord equal to one-half the

root chord but an MAC equal to two-thirds

of the root chord.

The aspect ratio, taper ratio, and sweepback of a planform are the principal factors which determine the aerodynamic characteristics of a wing. These same quantities also have a defi­nite influence on the structural weight and stiff­ness of a wing.

DEVELOPMENT OF LIFT BY A WING. In order to appreciate the effect of the planform on the aerodynamic characteristics, it is neces­sary to study the manner in which a wing produces lift. Figure 1.29 illustrates the three­dimensional flow pattern which results when the rectangular wing creates lift.

If a wing is producing lift, a pressure differ­ential will exist between the upper and lower surfaces, i. e., for positive lift, the static pres­sure on the upper surface will be less than on the lower surface. At the tips of the wing, the existence of this pressure differential creates the spanwise flow components shown in figure

1.27. For the rectangular wing, the lateral flow developed at the tip is quite strong and a strong vortex is created at the tip. The lateral flow—and consequent vortex strength—reduces inboard from the tip until it is zero at the centerline.

The existence of the tip vortex is described by the drawings of figure 1.29. The rotational pressure flow combines with the local airstream flow to produce the resultant flow of the trailing vortex. Also, the downwash flow field behind a delta wing is illustrated by the photographs of figure 1.29. A tuft-grid is mounted aft of the wing to visualize the local flow direction by deflection of the tuft ele­ments. This tuft-grid illustrates the existence of the tip vortices and the deflected airstream aft of the wing. Note that an increase in angle of attack increases lift and increases the flow deflection and strength of the tip vortices.

Figure 1.30 illustrates the principal effect of the wing vortex system. The wing pro­ducing lift can be represented by a series of

DOWNWASH FLOW FIELD BEHIND A DELTA WING ILLUSTRATED BY TUFT-GRID PHOTOGRAPHS AT

VARIOUS ANGLES OF ATTACK

FROM NACA TN 2674

Figure 7.29. Wing Three Dimensional Flow (sheet 2 of 2)


vortex filaments which consist of the tip or trailing vortices coupled with the bound or line vortex. The tip vortices are coupled with the bound vortex when circulation is induced with lift. The effect of this vortex system is to create certain vertical velocity components in the vicinity of the wing. The illustration of these vertical velocities shows that ahead of the wing the bound vortex induces an up – wash. Behind the wing, the coupled action of the bound vortex and the tip vortices in­duces a downwash. With the action of tip and bound vortices coupled, a final vertical velocity O-tv) is imparted to the airstream by the wing producing lift. This result is an inevitable consequence of a finite wing pro­ducing lift. The wing producing lift applies the equal and opposite force to the airstream and deflects it downward. One of the impor­tant factors in this system is that a downward velocity is created at the aerodynamic center (w) which is one half the final downward velocity imparted to the airstream (2w).

The effect of the vertical velocities in the vicinity of the wing is best appreciated when they are added vectorially to the airstream velocity. The remote free stream well ahead of the wing is unaffected and its direction is opposite the flight path of the airplane. Aft of the wing, the vertical velocity (2tv) adds to the airstream velocity to produce the down – wash angle « (epsilon). At the aerodynamic center of the wing, the vertical velocity (tv) adds to the airstream velocity to produce a downward deflection of the airstream one-half that of the downwash angle. In other words, the wing producing lift by the deflection of an airstream incurs a downward slant to the wind in the immediate vicinity of the wing. Hence, the sections of the wing operate in an average rela­tive wind which is inclined downward one-half the final downwash angle. This is one important feature which distinguishes the aerodynamic properties of a wing from the aerodynamic properties of an airfoil section.

The induced velocities existing at the aero­dynamic center of a finite wing create an aver­age relative wind which is different from the remote free stream wind. Since the aerody­namic forces created by the airfoil sections of a wing depend upon the immediate airstream in which they operate, consideration must be given to the effect of the inclined average rela­tive wind.

To create a certain lift coefficient with the airfoil section, a certain angle must exist be­tween the airfoil chord line and the average relative wind. This angle of attack is a0, the section angle of attack. However, as this lift is developed on the wing, downwash is in­curred and the average relative wind is in­clined. Thus, the wing must be given some angle attack greater than the required section angle of attack to account for the inclination of the average relative wind. Since the wing must be given this additional angle of attack because of the induced flow, the angle between the average relative wind and the remote free stream is termed the induced angle of attack, a*. From this influence, the wing angle of attack is the sum of the section and induced angles of attack.

a=ao+«t

where a—wing angle of attack

«0=section angle of attack induced angle of attack