ENDURANCE PERFORMANCE

The ability of the airplane to convert fuel energy into flying time is an important factor in flying operati on s. The ‘ ‘ specific end urance ’ ’ of the airplane is defined as follows:

specific endurance—тг^-7-r—j lb. of fuel

_________ 1________

fuel flow, lbs. per hr.

The specific endurance is simply the reciprocal of the fuel flow, hence maximum endurance conditions would be obtained at the lowest fuel flow required to hold the airplane in steady level flight. Obviously, minimum fuel flow will provide the maximum flying time from a given quantity of fuel. Generally, in subsonic performance, the speed at which maximum en­durance is achieved is approximately 75 per­cent of the speed for maximum range.

While many different factors can affect the specific endurance, the most important factors at the control of the pilot are the configuration and operating altitude. Of course, for maxi­mum endurance conditions the airplane must be in the clean configuration and operated at the proper aerodynamic conditions.

EFFECT OF ALTITUDE ON ENDUR­ANCE, PROPELLER DRIVEN AIRPLANES. Since the fuel flow of the propeller driven air­plane is proportional to power required, the propeller powered airplane will achieve maxi­mum specific endurance when operated at mini­mum power required. The point of minimum power required is obtained at a specific value of lift coefficient for a particular airplane con­figuration and is essentially independent of weight or altitude. However, an increase in altitude will increase the value of the minimum power required as illustrated by figure 2.27. If the specific fuel consumption were not in­fluenced by altitude or engine power, the spe­cific endurance would be directly proportional to v’ff, e. g., the specific endurance at 22,000 ft. (jt=0.498) would be approximately 70 percent of the value at sea level. This example is very nearly the case of the airplane with the recipro­cating engine since specific fuel consumption and propeller efficiency are not directly affected by altitude. The obvious conclusion is that maximum endurance of the reciprocating en­gine airplane is obtained at the lowest practical altitude.

The variation with altitude of the maximum endurance of the turboprop airplane requires consideration of powerplant factors in addition

to airplane factors. The turboprop power – plant prefers operation at low inlet air tem­peratures and relatively high power setting to produce low specific fuel consumption. While an increase in altitude will increase the mini­mum power required for the airplane, the powerplant achieves more efficient operation. As a result of these differences, maximum en­durance of the multiengine turboprop airplane at low altitudes may require shutting down some of the powerplants in order to operate the remaining powerplants at a higher, more efficient power setting.

EFFECT OF ALTITUDE ON ENDUR­ANCE, TURBOJET AIRPLANES. Since the fuel flow of the turbojet powered airplane is proportional to thrust required, the turbojet airplane will achieve maximum specific endur­ance when operated at minimum thrust re­quired or (L/D)™*. In subsonic flight, (L/D)m« occurs at a specific value of lift coefficient for a given airplane and is essentially independent of weight or altitude. If a given weight arid configuration of airplane is oper­ated at various altitudes, the value of the minimum thrust required is unaffected by the curves of thrust required versus velocity shown in figure 2.27. Hence, it is apparent that the aerodynamic configuration has no preference for altitude (within compressibility limits) and specific endurance is a function only of engine performance.

The specific fuel consumption of the turbojet engine is strongly affected by operating RPM and altitude. Generally, the turbojet engine prefers the operating range near normal rated engine speed and the low temperatures of the stratosphere to produce low specific fuel con­sumption. Thus, increased altitude provides the favorable lower inlet air temperature and requires a greater engine speed to provide the thrust required at (X/D)™*. The typical turbojet airplane experiences an increase in specific endurance with altitude with the peak values occurring at or near the tropopause. For example, a typical single-engine turbojet airplane will have a maximum specific endur­ance at 35,000 ft. which is at least 40 percent greater than the maximum value at sea level. If the turbojet airplane is at low altitude and it is necessary to hold for a considerable time, maximum time in the air will be obtained by beginning a climb to some optimum altitude dependent upon the fuel quantity available. Even though fuel is expended during the climb, the higher altitude will provide greater total endurance. Of course, the use of afterburner for the climb would produce a prohibitive re­duction in endurance.

OFF-OPTIMUM RANGE AND ENDUR­ANCE

There are many conditions of flying oper­ations in which optimum range or endurance conditions are not possible or practical. In many instances, the off-optimum conditions result from certain operational requirements or simplification of operating procedure. In addition, off-optimum performance may be the result of a powerplant malfunction or failure. The most important conditions are discussed for various airplanes by powerplant type.

RECIPROCATING POWERED AIR­PLANE. In the majority of cases, the recipro­cating powered airplane is operated at an engine dictated cruise. Service use will most probably define some continuous power setting which will give good service life and trouble-free operation of the powerplant. When range or endurance is of no special interest, the simple expedient is to operate the powerplant at the recommended power setting and accept what­ever speed, range, or endurance that results. While such a procedure greatly simplifies the matter of cruise control, the practice does not provide the necessary knowledge required for operating a high performance, long range airplane.

The failure of an engine on the multiengine reciprocating powered airplane has interesting ramifications. The first problem appearing is to produce sufficient powtr from the remaining engines to keep the airplane airborne. The

problem will be most. critical if the airplane is at high altitude, high gross weight, and with flaps and gear extended. Lower altitude, jettisoning of weight items, and cleaning up the airplane will reduce the power required for flight. Of course, the propeller on the in­operative engine must be feathered or the power required may exceed that available from the remaining operating powerplants.

The effect on range is much dependent on the airplane configuration. When the pro­peller on the’inoperative engine is feathered, the added drag is at a minimum, but there is added the trim drag required to balance the unsymmetrical power. When both these sources of added drag are accounted for, the (LjD’)ma is reduced but not by significant amounts. Generally, if the specific fuel con­sumption and propeller efficiency do not deteri­orate, the maximum specific range is not greatly reduced. On the twin-engine airplane the power required1 must be furnished by the one remaining engine and this, usually requires more than the maximum cruise-rating of the powerplants As a result the powerplant can­not be operated in the auto-lean or manual lean power range and the specific fuel con­sumption increases. greatly1. Thus, noticeable loss of range must be anticipated when one engine fails on the twin-engine airplane. The failure of one engine on the four (or more) engine airplartir may allow the required power to be developed і by the three remaining power – plants operating in an economical power range. If the airplane is clean, at low altitude, and low gross weight, the failure of one engine is not likely to cause a loss of range. However, the loss – of two engines is likely to cause a considerable loss of range.

When engine failure produces a critical power or range situation, improved perform­ance is possible with the"airplane in the clean configuration at low altitude. Also, jetti­soning of expendable weight items will reduce the power required and improve the specific range.

TURBOPROP POWERED AIRPLANE. The turbine engine has the preference for relatively high power settings and high alti­tudes to provide low specific fuel consumption. Thus, the off-optimum conditions of range or endurance can be concerned with altitudes less than the optimum. Altitudes less than the optimum can reduce the range but the loss can be minimized on the multiengine airplane by shutting down some powerplants and operating the remaining powerplants at a higher, more efficient output. In this case the change of range is confined to the variation of specific fuel consumption with altitude.

Essentially the same situation exists in the case of engine failure when cruising at optimum altitude. If the propeller on the inoperative engine is feathered, the loss of range will be confined to the change in specific fuel con­sumption from the reduced cruise altitude. If a critical power situation exists due to engine failure, a reduction in altitude provides im­mediate benefit because of the reduction of power required and the increase in power available from the power plants. In addition, the jettisoning of expendable weight items will improve performance and, of course, the clean configuration provides minimum parasite drag.

Maximum specific endurance of the turbo­prop airplane does not vary as greatly with altitude as the turbojet airplane. While each configuration has its own particular operating requirements, low altitude endurance of the turboprop airplane requires special considera­tion. The single-engine turboprop will gen­erally experience an increase in specific endur­ance with an increase in altitude from sea level. However, if the airplane is at low altitude and must hold or endure for a period of time, the decision to begin a climb or hold the existing altitude will depend on the quantity of fuel available. The decision depends primarily on the climb fuel requirements and the variation of specific endurance with altitude. A somewhat similar problem exists with the multiengine

turboprop airplane but additional factors are available to influence the specific endurance at low altitude. In other words, low altitude endurance can be improved by shutting down some powerplants and operating the remaining powerplants at higher, more efficient power setting. Many operati onal fact ors could dec ide whether such procedure would be a suitable technique.

TURBOJET TOWERED AIRPLANE. In­creasing altitude has a powerful effect on both the range and endurance of the turbojet air­plane. As a result of this powerful effect, the typical turbojet airplane will achieve maxi­mum specific endurance at or near the tropo – pause. Also, the maximum specific range will be obtained at even higher altitudes since the peak specific range generally occurs at the highest altitude at which the normal rating of the engine can sustain the optimum aero­dynamic conditions. At low altitude cruise conditions, the engine speed necessary to sus­tain optimum aerodynamic conditions is very low and the specific fuel consumption is rela­tively poor. Thus, at low altitude, the air­plane prefers the low speeds to obtain (VC/CtDffloa: but the powerplant prefers the higher speeds common to higher engine effi­ciency. The compromise results in maximum specific range at flight speeds well above the optimum aerodynamic conditions. In a sense, low altitude cruise conditions are engine dictated.

Altitude is the one most important factor affecting the specific range of the turbojet airplane. Any operation below the optimum altitude will have a noticeable effect on the range capability and proper consideration must be given to the loss of range. In addi­tion, turbojet airplanes designed specifically for long range will have a large percent of the gross weight as fuel. The large changes in gross weight during cruise will require partic­ular methods of cruise control to extract the maximum flight range. A variation from the optimum flight path of cruise (constant Mach number, cruise-climb, or whatever the appro­priate technique) will result in a loss of range capability.

The failure of an engine during the optimum cruise of a multiengine turbojet airplane will cause a noticeable loss of range. Since the optimum cruise of the turbojet is generally a thrust-limited cruise, the loss of part of the total thrust means that the airplane must descend to a lower altitude. For example, if a twin-engine jet begins an optimum cruise at

35,0 ft. (<r=0.31) and one powerplant fails, the airplane must descend to a lower altitude so that the operative engine can provide the cruise thrust. The resulting altitude would be approximately 16,000 ft. («г=0.61). Thus, the airplane will experience a loss of the range remaining at the point of engine failure and loss could be accounted for by the reduced velocity (TAS) and the increase in specific fuel consumption OO ftom the higher ambient air temperature. In the case of the example air­plane, engine failure would cause a 30 to 40 percent loss of range from the point of engine failure. Of course, the jettisoning of expend­able weight items would allow higher altitude and would increase the specific range.

Maximum endurance in the turbojet air­plane varies with altitude but the variation is due to the changes in fuel flow necessary to provide the thrust required at (L/D)mai. The low inlet air temperature of the tropopause and the greater engine speed reduce the specific fuel consumption to a minimum. If the single­engine turbojet airplane is at low altitude and must hold or endure for a period of time, a climb should begin to take advantage of the higher specific endurance at higher altitude. The altitude to which to climb will be deter­mined by the quantity of fuel remaining. In the case of the multiengine turbojet at low altitude, some slightly different procedure may be utilized. If all powerplants are oper­ating, it is desirable to climb to a higher altitude which is a function of the remaining fuel quantity. An alternative at low altitude

would, be to provide the endurance thrust with some engineCO shut down and the remaining engine(s) operating at a more efficient power output. This technique would cause a mini­mum loss of endurance if at low altitude. The feasibility of such a procedure is dependent on many operational factors.

In all cases, the airplane should be in the cleanest possible external configuration because the specific endurance is directly proportional to the (LjD).

MANEUVERING PERFORMANCE y,.

When the airplane is in turning flight, the airplane is not in static equilibrium for there must be developed the unbalance of force to produce the acceleration of the turn. During a steady coordinated turn, the lift is inclined to produce a horizontal component of force to equal the centrifugal force of the turn. In addition, the steady turn is achieved by pro­ducing a vertical component of lift which is equal to the weight of the airplane. Figure 2.28 illustrates the forces which act on the airplane in a steady, coordinated tufn.

For the case of the steady, coordinated turn, the vertical component of lift musr <=qual the weight of the aircraft so that there will be no acceleration in the vertical direction. This requirement leads to the following relation­ship:

From this relationship it is apparent that the steady, coordinated turn requires specific values of load factor, n, at various angles of bank, ф. For example, a bank angle of 60° requires a load factor of 2.0 (cos 60° = 0.5 or sec 60° = 2.0) to provide the steady, coordinated turn. If the airplane were at a 60° bank and lift were not provided to produce the exact load factor of 2.0, the aircraft would be accelerating in the vertical direction as well as the horizontal di­rection and the turn would not be steady. Also, any sideforce on the aircraft due to sideslip, etc., would place the resultant aero­dynamic force out of the plane of symmetry perpendicular to the lateral axis and the turn would not be coordinated.

As a consequence of the increase lift re­quired to produce the steady turn in a bank, the induced drag is increased above that in­curred by steady, wing level, lift-equal-weight flight. In a sense, the increased lift required in a steady turn will increase the total drag or power required in the same manner as increased gross weight in level flight. The curves of figure 2.28 illustrate the general effect of turn­ing flight on the total thrust and power re­quired. Of course, the change in thrust re­quired at any given speed is due to the change in induced drag and the magnitude of change depends on the value of induced drag in level flight and the angle of bank in turning flight. Since the induced drag generally varies as the square of CL, the following data provide an illustration of the effect of various degrees of bank:

Bank angle, ф	Load factor, n	Percent increase in induced drag from level flight
0°……………………………………………	1.000	0 (of course)
15°…………………………………………	1.036	7.2
30°………………………………………….	1.154	33.3
45°……………………………………… :.	1.414	100.0
60°………………………………………….	2.000	300.0

Since the. induced drag predominates at low speeds, steep turns at low speeds can produce significant increases in thrust or power required to maintain altitude. Thus, steep turns must be avoided after takeoff, during approach, and especially during a critical power situation from failure or malfunction of a powerplant. The greatly increased induced drag is just as

important—if not more important—as the increased stall speed in turning flight. It is important also that any turn be well coordi­nated to prevent the increased drag attendant to a sideslip.

TURNING PERFORMANCE. The hori­zontal component of Lift will equal the centrif­ugal force of steady, turning flight. This fact allows development of the following relation­ships of turning performance:

turn radius

_ Vі Г 11.26 tan ф

where

return radius, ft.

V= velocity, knots (TAS)

0 = bank angle, degrees

turn rate

R0T= 1-°9уаП ф

where

ROT= rate of turn, degrees per sec. tf>=bank angle, degrees V— velocity, knots, TAS

These relationships define the turn radius, r, and rate of turn, ROT, as functions of the two principal variables; bank angle, Ф, and velocity, V (TAS’). Thus, when the airplane is flown in the steady, coordinated turn at specific values of bank angle and velocity, the turn rate and turn radius are fixed and independent of the airplane type. As an example, an air­plane in a steady, coordinated turn at a bank angle of 45° and a velocity of 250 knots (TAS) would have the following turn performance:

_ (250)2

Г (U.26)(l.000)

= 5,550 ft.

and (1,091)0.000)

250

= 4.37 deg. per sec.

If the airplane were to hold the same angle of bank at 500 knots (TAS), the turn radius would quadruple (r= 22,200 ft.) and the turn rate would be one-half the original value (R0T= 2.19 deg. per sec.).

Values of turn radius and turn rate versus velocity are shown in figure 2.29 for various angles of bank and the corresponding load factors. The conditions are for the steady, coordinated turn at constant altitude but the results are applicable for climbing or descend­ing flight when the angle of climb or descent is relatively small. While the effect of alti­tude on turning performance is not immediately apparent from these curves, the principal effect must be appreciated as an increased true air­speed (TAS) for a given equivalent airspeed (EAS).

TACTICAL PERFORMANCE. Many tac­tical maneuvers require the use of the maxi­mum turning capability of the airplane. The maximum turning capability of an airplane will be defined by three factors:

(1) Maximum lift capability. The combi­nation of maximum lift coefficient,

and wing loading, WjS, will define the ability of the airplane to develop aero­dynamically the load factors of maneuvering flight.

(2) Operating strength limits will define the upper limits of maneuvering load factors which will not damage the primary struc­ture of the airplane. These limits must not be exceeded in normal operations because of the possibility of structural damage or failure.

(3) Thrust or power limits will define the ability of the airplane to turn at constant altitude. The limiting condition would al­low increased load factor and induced drag until the drag equals the maximum thrust available from the powerplant. Such a case would produce the maximum turning capa­bility for maintaining constant altitude.

The first illustration of figure 2.30 shows

how the aerodynamic and structural limits

define the maximum turning performance. The aerodynamic limit describes the minimum turn radius available to the airplane when operated at Cbmax – When the airplane is at the stall speed in level flight, all the lift is neces­sary to sustain the aircraft in flight and none is available to produce a steady turn. Hence, the turn radius at the stall speed is infinite. As speed is increased above the stall speed, the airplane at Сі^ая is able to develop lift greater than weight and produce a finite turn radius. For example, at a speed twice the stall speed, the airplane at CLmax is able to develop a load factor of four and utilize a bank angle of 75-5° Ceos 75-5° = 0.25). Continued increase in speed increases the load factor and bank angle which is available aerodynamically but, be­cause of the increase in velocity and the basic effect on turn radius, the turn radius approaches an absolute minimum value. When Ct^ax is unaffected by velocity, the aerodynamic mini­mum turn radius approaches this absolute value which is a function of CLpiaxt WjS, and <r. Actually, the one common denominator of aerodynamic turning performance is the wing level stall speed.

The aerodynamic limit of turn radius requires that the increased velocity be utilized to pro­duce increasing load factors and greater angles of bank. Obviously, very high speeds will require very high load factors and the absolute aerodynamic minimum turn radius will require an infinite load factor. Increasing speed above the stall speed will eventually produce the limit load factor and continued increase in speed above this point will require that load factor and bank angle be limited to prevent structural damage. When the load factor and bank angle are held constant at the structural limit, the turn radius varies as the square of the velocity and increases rapidly above the aerodynamic limit. The intersection of the aerodynamic limit and structural limit lines is the “maneuver speed.” The maneuver speed is the minimum speed necessary to develop aerodynamically the limit load factor

and it produces the minimum turn radius within aerodynamic and structural limitations. At speeds less than the maneuver speed, the limit load factor is not available aerodynami­cally and turning performance is aerody­namically limited. At speeds greater than the maneuver speed, Cl^ and maximum aerodynamic load factor are not available and turning performance is structurally limited. When the stall speed and limit load factor are known for a particular configuration, the maneuver speed is related by the following expression:

Vp = V,^n limit

where

Vp = maneuver speed, knots

V„ = stall speed, knots

n limit = limit load factor

For example, an airplane with a limit load factor of 4.0 would have a maneuver speed which is twice the stall speed.

The aerodynamic limit line of the first illustration of figure 2.30 is typical of an air­plane with a CLmax which is invariant with speed. While this is applicable for the ma­jority of subsonic airplanes, considerable differ­ence would be typical of the transonic or supersonic airplane at altitude. Compressi­bility effects and changes in longitudinal control power may produce a maximum avail­able CL which varies with velocity and an aerodynamic turn radius which is not an absolute minimum at the maximum of velocity.

The second illustration of figure 2.30 describes the constant altitude turning performance of an airplane. When an airplane is at high altitude, the turning performance at the high speed end of the flight speed range is more usually thrust limited rather than structurally limited. In flight at constant altitude, the thrust must equal the drag to maintain equilib­rium and, thus, the constant altitude turn radius is infinite at the maximum level flight speed. Any bank or turn at maximum level flight speed would incut additional drag and

TURN

RADIUS

Г

FT

VELOCITY, KNOTS (TAS)

cause the airplane to descend. However, as speed is reduced below the maximum level flight speed, parasite drag reduces and allows increased load factors and bank angles and reduced radius of turn, i. e., decreased parasite drag allows increased induced drag to accom­modate turns within the maximum thrust available. Thus, the considerations of con­stant altitude will increase the minimum turn radius above the aerodynamic limit and define a particular airspeed for minimum turn radius.

Each of the three limiting factors (aero­dynamic, structural, and power) may combine to define the turning performance of an air­plane. Generally, aerodynamic and structural limits predominate at low altitude while aero­dynamic and power limits predominate at high altitude. The knowledge of this turning per­formance is particularly necessary for effective operation of fighter and interceptor types of airplanes.