RANGE PERFORMANCE

The ability of an airplane to convert fuel energy into flying distance is one of the most important items of airplane performance. The problem of efficient range operation of an air­plane appears of two general forms in flying operations: (T) to extract the maximum flying distance from a given fuel load or (2) to fly a specified distance with minimum expenditure of fuel. An obvious common denominator for each of these operating problems is the “spe­cific range," nautical miles of flying distance per lb. of fuel. Cruise flight for maximum range conditions should be conducted so that the airplane obtains maximum specific range throughout the flight.

GENERAL RANGE PERFORMANCE. The principal items of range performance can be visualized by use of the illustrations of figure

2.23. From the characteristics of the aero­dynamic configuration and the powerplant, the
conditions of steady level flight will define various rates of fuel flow throughout the range of flight speed. The first graph of figure 2.23 illustrates a typical variation of fuel flow versus velocity. The specific range can be defined by the following relationship:

nautical miles lbs. of fuel

or,

.r nautical miles/hr.

specific range – lbs.„ffadTht.

thus,

.ґ velocity, knots

specific range-^д^^^-

If maximum specific range is desired, the flight condition must provide a maximum of velocity fuel flow. This particular point would be located by drawing a straight line from the origin tangent to the curve of fuel flow versus velocity.

The general item of range must be clearly distinguished from the item of endurance. The item of range involves consideration of flying distance while endurance involves consideration of flying time. Thus, it is appropriate to define a separate term, “specific endurance.”

flight hours lb. of fuel

or,

flight hours/hr. lbs. of fuel/hr.

________ 1________

fuel flow, lbs. per hr.

By this definition, the specific endurance is simply the reciprocal of the fuel flow. Thus, if maximum endurance is desired, the flight condition must provide a minimum of fuel flow. This point is readily appreciated as the lowest point of the curve of fuel flow versus velocity. Generally, in subsonic performance, the speed at which maximum endurance is

GROSS WEIGHT LBS.

Figure 2.23. GeneraI Range Performance

obtained is approximately 75 percent of the speed for maximum range.

A more exact analysis of range may be ob­tained by a plot of specific range versus velocity similar to the second graph of figure 2.23. Of course, the source of these values of specific range is derived by the proportion of velocity and fuel flow from the previous curve of fuel flow versus velocity. The maximum specific range of the airplane is at the very peak of the curve. Maximum endurance point is located by a straight line from the origin tangent to the curve of specific range versus velocity. This tangency point defines a maximum of (nmi/lb-) per (nmi/hr.) or simply a maximum of (hrs./lb.).

While the very peak value of specific range would provide maximum range operation, long range cruise operation is generally recom­mended at some slightly higher airspeed. Most long range cruise operation is conducted at the flight condition which provides 99 per­cent of the absolute maximum specific range. The advantage of such operation is that 1 percent of range is traded for 3 to 5 percent higher cruise velocity. Since the higher cruise speed has a great number of advantages, the small sacrifice of range is a fair bargain. The curves of specific range versus velocity are affected by three principal variables: airplane gross weight, altitude, and the external aero­dynamic configuration of the airplane. These curves are the source of range and endurance operating data and are included in the per­formance section of the flight handbook.

"Cruise control” of an airplane implies that the airplane is operated to maintain the recom­mended long range cruise condition through­out the flight. Since fuel is consumed during cruise, the gross weight of the airplane will vary and optimum airspeed, altitude, and power setting can vary, Generally, "cruise control" means the control of optimum air­speed, altitude, and power setting to maintain the 99 percent maximum specific range condi­tion. At the beginning of cruise, the high initial weight of the airplane will require spe­cific values of airspeed, altitude, and power setting to produce the recommended cruise condition. As fuel is consumed and the air­plane gross weight decreases, the optimum air­speed and power setting may decrease or the optimum altitude may increase. Also, the optimum specific range will increase. The pilot must provide the proper cruise control technique to ensure that the optimum condi­tions are maintained.

The final graph of figure 2.23 shows a typical variation of specific range with gross weight for some particular cruise operation. At the beginning of cruise the gross weight is high and the specific range is low. As fuel is con­sumed, and the gross weight reduces, the specific range increases. This type of curve relates the range obtained by the expenditure of fuel by the crosshatched area between the gross weights at beginning and end of cruise. For example, if the airplane begins cruise at 18,500 lbs. and ends cruise at 13,000 lbs., 5,500 lbs. of fuel is expended. If the average spe­cific range were 0.2 nmi/lb., the total range would be:

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

= 1,100 nmi.

Thus, the total range is dependent on both the fuel available and the specific range. When range and economy of operation predominate, the pilot must ensure that the airplane will be operated at the recommended long range cruise condition. By this procedure, the airplane will be capable of its maximum design operat­ing radius or flight distances less than the maximum can be achieved with a maximum of fuel reserve at the destination.

RANGE, PROPELLER DRIVEN AIR­PLANES. The propeller driven airplane com­bines the propeller with the reciprocating engine or the gas turbine for propulsive power. In the case of either the reciprocating engine or the gas turbine combination, powerplant fuel

flow is determined mainly by the shaft power put into the propeller rather than thrust. Thus, the powerplant fuel flow could be related di­rectly to power required to maintain the air­plane in steady, level flight. This fact allows study of the range of the propeller powered airplane by analysis of the curves of power required versus velocity.

Figure 2.24 illustrates a typical curve of power required versus velocity which, for the propeller powered airplane, would be analo­gous to the variation of fuel flow versus veloc­ity. Maximum endurance condition would be obtained at the point of minimum power re­quired since this would require the lowest fuel flow to keep the airplane in steady, level flight. Maximum range condition would occur where the proportion between velocity and power re­quired is greatest and this point is located by a straight line from the origin tangent to the curve.

The maximum range condition is obtained at maximum lift-drag ratio and it is important to note that (L! D’)max for a given airplane configuration occurs at a particular angle of attack and lift coefficient and is unaffected by weight or altitude (within compressibility limits). Since approximately 50 percent of the total drag at (L/jD)7MJ. is induced drag, the propeller powered airplane which is designed specifically fo’r long range will have a strong preference for the high aspect ratio planform.

The effect of the variation of airplane gross weight is illustrated by the second graph of figure 2.24. The flight condition of (L/D)mai is achieved at one particular value of lift coeffi­cient for a given airplane configuration. Hence, a variation of gross weight will alter the values of airspeed, power required, and spe­cific range obtained at (L/D)MBI. If a given configuration of airplane is operated at con­stant altitude and the lift coefficient for (L/D)raor, the following relationships will apply:

where

condition (2) applies to some known condi­tion of velocity, power required, and specific range for (L/D)m« at some basic weight, W

condition (2) applies to some new values of velocity, power required, and specific range for (L/D)mar at some different weight, W2

and,

V— velocity, knots W= gross weight, Ibs – Pr — power required, h. p.

SR— specific range, nmi/lb.

Thus a 10 percent increase in gross weight would create:

a 5 percent increase in velocity a 15 percent increase in power required a 9 percent decrease in specific range when flight is maintained at the optimum con­ditions of (L/D)mar. The variations of veloc­ity and power required must be monitored by the pilot as part of the cruise control to main­tain (L/D)„aj. When the airplane fuel weight is a small part of the gross weight and the range is small, the cruise control procedure can be simplified to essentially a constant speed and power setting throughout cruise. However, the long range airplane has a fuel weight which is a considerable part of the gross weight and cruise control procedure must employ sched­uled airspeed and power changes to maintain optimum range conditions.

The effect of altitude on the range of the propeller powered airplane may be appreciated by inspection of the final graph of figure 2.24. If a given configuration of airplane is operated at constant gross weight and the lift coefficient

for (LjD’)max, a change in altitude will produce the following relationships:

where

condition (2) applies to some known condi­tion of velocity and power required for (L/D)^ at some original, basic altitude condition (2) applies to some new values of velocity and power required for (L/D)^ at some different altitude and

V = velocity, knots ( TAS, of course)

Pr=power required, h. p. tr=altitude density ratio (sigma)

Thus, if flight is conducted at 22,000 ft. (<r=0.498), the airplane will have: a 42 percent higher velocity a 42 percent higher power required

than when operating at sea level. Of course, the greater velocity is a higher TAS since the airplane at a given weight and lift coefficient will require the same EAS independent of altitude. Also, the drag of the airplane at altitude is the same as the drag at sea level but the higher TAS causes a proportionately greater power required. Note that the same straight line from the origin tangent to the sea level power curve also is tangent to the altitude power curve.

The effect of altitude on specific range can be appreciated from the previous relationships. If a change in altitude causes identical changes in velocity and power required, the proportion of velocity to power required would be un­changed. This fact implies that the specific range of the propeller powered airplane would be unaffected by altitude. In the actual case, this is true to the extent that powerplant specif­ic fuel consumption (r) and propeller efficiency (fjp) are the principal factors which could cause a variation of specific range with altitude.

If compressibility effects are negligible, any variation of specific range with altitude is strictly a function of engine-propeller performance.

The airplane equipped with the reciprocating engine will experience very little, if any, variation of specific range with altitude at low altitudes. There is negligible variation of brake specific fuel consumption for values of ВНР below the maximum cruise power rating of the powerplant which is the auto-lean or manual lean range of engine operation. Thus, an increase in altitude will produce a decrease in specific range only when the increased power requirement exceeds the maximum cruise power rating of the powerplants. One advantage of supercharging is that the cruise power may be maintained at high altitude and the airplane may achieve the range at high altitude with the corresponding increase in TAS. The prin­cipal differences in the high altitude cruise and low altitude cruise are the true airspeeds and climb fuel requirements.

The airplane equipped with, the turboprop powerplant will exhibit a variation of specific range with altitude for two reasons. First, the specific fuel consumption (/) of the turbine engine improves with the lower inlet tem­peratures common to high altitudes. Also, the low power requirements to achieve opti­mum aerodynamic conditions at low altitude necessitate engine operation at low, inefficient output power. The increased power require­ments at high altitudes allow the turbine powerplant to operate in an efficient output range. Thus, while the airplane has no particular preference for altitude, the power – plants prefer the higher altitudes and cause an increase in specific range with altitude. Generally, the upper limit of altitude for efficient cruise operation is defined by airplane gross weight (and power required) or com­pressibility effects.

The optimum climb and descent for the propeller powered airplane is affected by many different factors and no general, all­inclusive relationship is applicable. Hand­book data for the specific airplane and various

operational factors will define operating pro­cedures.

RANGE, TURBOJET AIRPLANES. Many different factors influence the range of the turbojet airplane. In order to simplify the analysis of the overall range problem, it is convenient to separate airplane factors from powerplant factors and analyze each item independently. An analogy would be the study of “horsecart” performance by separat­ing “cart” performance from “horse” per­formance to distinguish the principal factors which affect the overall performance.

In the case of the turbojet airplane, the fuel flow is determined mainly by the thrust rather than power. Thus, the fuel flow could be most directly related to the thrust required to maintain the airplane in steady, level flight. This fact allows study of the turbojet powered airplane by analysis of the curves of thrust required versus velocity. Figure 2.25 illu­strates a typical curve of thrust required versus velocity which would be (somewhat) analo­gous to the variation of fuel flow versus veloc­ity. Maximum endurance condition would be obtained at (L/D)^ since this would incur the lowest fuel flow to keep the airplane in stead у, level flight. Maximum range condition would occur where the proportion between velocity and thrust required is greatest and this point is located by a straight line from the origin tangent to the curve.

The maximum range is obtained at the aero­dynamic condition which produces a maximum proportion between the square root of the lift coefficient^ (CL) and the drag coefficient (Cd), or_C^CL/CD’)max. In subsonic perform­ance, occurs at a particular value

angle of attack and lift coefficient and is un­affected by weight or altitude (within com­pressibility limits). At this specific aerody­namic condition, induced drag is approxi­mately 25 percent of the total drag so the turbojet airplane designed for long range does not have the strong preference for high aspect ratio planform like the propeller airplane.

On the other hand, since approximately 75 percent of the total drag is parasite drag, the turbojet airplane designed specifically for long range has the special requirement for great aerodynamic cleanness.

The effect of the variation of airplane gross weight is illustrated by the second graph of figure 2.25. The flight condition of (jIqjcbx« is achieved at one value of lift coefficient for a given airplane in subsonic flight. Hence, a variation of gross weight will alter the values of airspeed, thrust required, and specific range obtained at (_^СьіС^)тят. If a given configuration is operated at constant altitude and lift coefficient the following re­lationships will apply:

Thus, a 10 percent increase in gross weight would create:

a 5 percent increase in velocity a 10 percent increase in thrust required a 5 percent decrease in specific range when flight is maintained at the optimum con­ditions of (VC/Cd)™^ Since most jet airplanes

have a fuel weight which is a large part of the gross weight, cruise control procedures will be necessary to account for the changes in opti­mum airspeeds and power settings as fuel is consumed.

The effect of altitude on the range of the turbojet airplane is of great importance be­cause no other single item can cause such large variations of specific range. If a given con­figuration of airplane is operated at constant gross weight and the lift coefficient for a change in altitude will produce the following relationships:

Tr= constant (neglecting compressibility effects)

SR-i_ fir, (neglecting factors affecting en – TjRi у с2 gine performance)

where

condition (i) applies some known condition of velocity, thrust required, and specific range for (■}JCL! CD’)ma at some original, basic altitude.

condition (2) applies to some new values of velocity, thrust required, and specific range for (VcyCzOUz at some different altitude.

and

V— velocity, knots (TAS, of course)

Tr= thrust required, lbs.

SR= specific range, nmi/lb.

<r=altitude density ratio (sigma)

Thus, if flight is conducted at 40,000 ft. (<r = 0.246), the airplane will have: a 102 percent higher velocity the same thrust required a 102 percent higher specific range (even when the beneficial effects of altitude on engine performance are neglected)

than when operating at sea level. Of course, the greater velocity is a higher TAS and the same thrust required must be obtained with a greater engine RPM.

At this point it is necessary to consider the effect of the operating condition on pojverplant performance. An increase in altitude will im­prove powerplant performance in two respects. First, an increase in altitude when below the tropopause will provide lower inlet air tem­peratures which reduce the specific fuel con­sumption (c(). Of course, above the tropo­pause the specific fuel consumption tends to increase. At low altitude, the engine RPM necessary to produce the required thrust is low and, generally, well below the normal rated value. Thus, a second benefit of altitude on engine performance is due to the increased RPM required to furnish cruise thrust. An increase in engine speed to the normal rated value will reduce the specific fuel consumption.

The increase in specific range with altitude of the turbojet airplane can be attributed to these three factors:

(1) An increase in altitude will increase the proportion of (V/Tr) and provide a greater TAS for the same Tr.

(2) An increase in altitude in the tropo­sphere will produce lower inlet air temperature which reduces the specific fuel consumption.

(3) An increase in altitude requires in­creased engine RPM. to provide cruise thrust and the specific fuel consumption reduces as normal rated RPM is approached.

The combined effect of these three factors de­fines altitude as the one most important item affecting the specific range of the turbojet air­plane. As an example of this combined’effect, the typical turbojet airplane obtains a specific range at 40,000 ft. which is approximately 130 percent greater than that obtained at sea level. The increased TAS accounts for approxi­mately two-thirds of this benefit while in­creased engine performance (reduced q) ac­counts for the other one-third of the benefit. For example, at sea level the maximum spe­cific range of a turbojet airplane may be 0.1 nmi/lb. but at 40,000 ft. the maximum specific range would be approximately 0.25 nmi/lb.

From the previous analysis, it is apparent that the cruise altitude of the turbojet should be as high as possible within compressibility or thrust limits. Generally, the optimum alti­tude to begin cruise is the highest altitude at which the maximum continuous thrust can provide the optimum aerodynamic conditions. Of course, the optimum altitude is determined mainly by the gross weight at the begin of cruise. For the majority of turbojet airplanes this altitude will be at or above the tropopause for normal cruise configurations.

Most turbojet airplanes which have tran­sonic or moderate supersonic performance will obtain maximum range with a high subsonic cruise. However, the airplane designed spe­cifically for high supersonic performance will obtain maximum range with a supersonic cruise and subsonic operation will cause low lift-drag ratios, poor inlet and engine perform­ance and reduce the range capability.

The cruise control of the turbojet airplane is considerably different from that of the pro­peller driven airplane. Since the specific range is so greatly affected by altitude, the optimum altitude for begin of cruise should be attained as rapidly as is consistent with climb fuel re­quirements. The range-climb program varies considerably between airplanes and the per­formance section of the flight handbook will specify the appropriate procedure. The de­scent from cruise altitude will employ essen­tially the same feature, a rapid descent is necessary to minimize the time at low altitudes where specific range is low and fuel flow is high for a given engine speed.

During cruise flight of the turbojet airplane, the decrease of gross weight from expenditure of fuel can result in two types of cruise control. During a constant altitude cruise, a reduction in gross weight will require a reduction of air­speed and engine thrust to maintain the opti­mum lift coefficient of subsonic cruise. While such a cruise may be necessary to conform to the flow of traffic, it constitutes a certain in­efficiency of operation. If the airplane were not restrained to a particular altitude, main­taining the same lift coefficient and engine speed would allow the airplane to climb as the gross weight decreases. Since altitude gen­erally produces a beneficial effect on range, the climbing cruise implies a more efficient flight path.

The cruising flight of the turbojet airplane will begin usually at or above the tropopause in order to provide optimum range conditions. If flight is conducted at QjcL/CD’)max, optimum range will be obtained at specific values of lift coefficient and drag coefficient. When the air­plane is fixed at these values of CL and CD and the TAS is held constant, both lift and drag are directly proportional to the density ratio, a. Also, above the tropopause, the thrust is pro­portional to a when the TAS and RPM are con­stant. As a result, a reduction of gross weight by the expenditure of fuel would allow the airplane to climb but the airplane would re­main in equilibrium because lift, drag, and thrust all vary in the same fashion. This re­lationship is illustrated by figure 2.26.

The relationship of lift, drag, and thrust is convenient for, in part, it justifies the condi­tion of a constant velocity. Above the tropo­pause, the speed of sound is constant hence a constant velocity during the cruise-climb would produce a constant Mach number. In this case, the optimum values of Q^CJC^), CL and CD do not vary during the climb since the Mach number is constant. The specific fuel consumption is initially constant above the tropopause but begins to increase at altitudes much above the tropopause. If the specific fuel consumption is assumed to be constant during the cruise-climb, the following rela­tionships will apply:

V, M, CL and CD arc constant <H_W2 a, Wx

FF2_ <r2

FFi <гі

SRi_JWi (cruise climb above tropopause,

SR і W2 constant M, ci)

where

condition (X) applies to some known condi­tion of weight, fuel flow, and specific range at some original basic altitude during cruise climb.

condition (2) applies to some new values of weight, fuel flow, and specific range at some different altitude along a partic­ular cruise path.

and

V= velocity, knots

M=Mach number

W= gross weight, lbs.

RF=fuel flow, lbs./hr.

SR— specific range, nmi./lb.

<r= altitude density ratio

Thus, during a cruise-climb flight, a 10 percent decrease in gross weight from the consumption of fuel would create:

no change in Mach number or TAS a 5 percent decrease in EAS a 10 percent decrease in <r, i. e., higher altitude

a 10 percent decrease in fuel flow an 11 percent increase in specific range

An important comparison can be made between the constant altitude cruise and the cruise – climb with respect to the variation of specific range. From the previous relationships, a 2 percent reduction in gross weight during

SR,= IWi SRi W2

SR2_ Wi.

SRi W2

cruise would create a 1 percent increase in specific range in a constant altitude cruise but a 2 percent increase in specific range in a cruise – climb at constant Mach number. Thus, a higher average specific range cari. be maintained during the expenditure of a given increment of fuel. If an airplane begins a cruise at optimum conditions at or above the tropopause with a given weight of fuel, the following data

provide a comparison of the total range avail­able from a constant altitude or cruise-climb

flight path.

Hath of cruise fuel weight to airplane grots weight at beginning of cruise

0. 0

.1

.2

• 3 .4

• 5 .6 .7

For example, if the cruise fuel weight is 50 per­cent of the gross weight, the climbing cruise flight path will provide a range 18.2 percent greater than cruise at constant altitude. This comparison does not include consideration of any variation of specific fuel consumption dur­ing cruise or the effects of compressibility in defining the optimum aerodynamic conditions for cruising flight. However, the comparison is generally applicable for aircraft which have Subsonic cruise.

When the airplane has a supersonic cruise for maximum range, the optimum flight path is generally one of a constant Mach number. The optimum flight path is generally—but not necessarily—a climbing cruise. In this case of subsonic or supersonic cruise, a Machmeter is of principal importance in cruise control of the jet airplane.

The effect of wind on range is of considerable importance in flying operations. Of course, a headwind will always reduce range and a tailwind will always increase range. The selection of a cruise altitude with the most favorable (or least unfavorable) winds is a rel­atively simple matter for the case of the propeller powered airplane. Since the range of the. propeller powered airplane is relatively un­affected by altitude, the altitude with the most favorable winds is selected for range. However, the range of the turbojet airplane is greatly affected by altitude so the selection of an op­timum altitude will involve considering the wind profile with the variation of range with altitude. Since the turbojet range increases

TURBOJET CRUISE-CLIMB

greatly with altitude, the turbojet can tolerate less favorable (or more unfavorable) winds with increased altitude.

In some cases, large values of wind may cause a significant change in cruise velocity to maintain maximum ground nautical miles per lb. of fuel. As an example of an extreme con­dition, consider an airplane flying into a head­wind which equals the cruise velocity. In this case, any increase in velocity would improve range.

To appreciate the changes in optimum speeds with various winds, refer to the illustration of figure 2.26. When zero wind conditions exist, a straight line from the origin tangent to the curve of fuel flow versus velocity will locate maximum range conditions. When a head­wind condition exists, the speed for maximum ground range is located by a line tangent drawn from a velocity offset equal to the headwind velocity. This will locate maximum range at some higher velocity and fuel flow. Of course, the range will be less than when at zero wind conditions but the higher velocity and fuel flow will minimize the range loss due to the head­wind. In a similar sense, a tailwind will re­duce the cruise velocity to maximize the benefit of the tailwind.

The procedure of employing different cruise velocities to account for the effects of wind is necessary only at extreme values of wind velocity. It is necessary to consider the change in optimum cruise airspeed when the wind velocities exceed 25 percent of the zero wind cruise velocity.