Fighter Aircraft

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NASA TP 1837 NASA TechnicalPaper 1837 c. 1

A Computer Technique for Detailed Analysis of MissionRadius and ManeuverabilityCharacteristics of Fighter Aircraft

Willard E. FOSS, Jr.

MARCH 198 1 TECH LIBRARY KAFB, NM

00b788Z NASA Technical Paper 1837

A ComputerTechnique for Detailed Analysis of Mission Radiusand ManeuverabilityCharacteristics of FighterAircraft

Willard E. FOSS, Jr. La ugley Resea rcb Ceu ter Harnpton, Virginia

National Aeronautics and Space Administration Scientific and Technical Information Branch

1981 SUMMARY

A computer technique to determine the mission radius and maneuverability characteristics ofcombat aircraft has been developed. The technique has been used at the Langley ResearchCenter to determine critical operational requirements and theareas in which research programs would be expected to yield the most beneficialresults. In turn,the results of researchefforts havebeen evaluated in terms of aircraft performance on selected mission segments and for complete mission profiles. The aircraftcharacteristics and flight constraints arerepresented in sufficient detail to permit realistic sensitivity studies in terms of eitherconfiguration modifications or changes in operational procedures. Sample calculationsare provided to illustrate the wide variety of military mission profilesthat maybe represented.Extensive use of thetechnique in evaluationstudies indicates that the calculated performance is essentially the same asthat obtained by theproprietary programs in use throughout the aircraft industry.

INTRODUCTION

A computer technique to determinethe mission radius and maneuverability characteristics ofcombat aircraft for a variety of military profiles hasbeen developed. The technique has beenused at the Langley Research Center todeter- mine critical operational requirements and theareas in which research programs wouldbe expected toyield the most beneficialresults. In turn, the results of research efforts havebeen evaluated in terms of aircraft performance on selected mission segments and for complete mission profiles. The aircraft characteristics and flight constraints are represented in sufficient detail to permit realistic sensitivity studies of configurationmodifications and changes in operational procedures. The technique has also been utilized in cooperative efforts with the Department of Defense to evaluate the performance capabilities of a proposed military aircraft andof configurationconcepts developed at Langley Research Center. In a preliminary phase of the former effort, the performance for several mission profiles was determined by using thepresent tech- - " nique, and theresults werecompared with similarcalculations by thecontractor forthe purpose of calibrating any differences in calculation technique. The results were in excellent agreement both in terms of overall mission capability and detailed mission segment performance.

Themain text of this paper is a description of thefeatures andassump- tions of the technique andof theassociated numerical computerprogram. The mission profiles are described, and thenthe representation of each mission segment is discussed in detail. As each item is described, examples are included to illustrate aircraft performance. Appendix A contains a description of the input data required to define the aircraft as well as the input data concerned with profileselection and flight-pathcontrol. Appendix B contains descriptions of theoutput data. Options to control both the amountand form of theoutput resultsare described, and sample output listings are included to illustrate the effect of theseoptions. The outputparameters are also defined in appendix B.

The program requires 105 0008 words of central core memory to run on the Control Data CYBER 175 computer system operating under NOS 1 .3 at the Langley computercomplex. The run time for a single mission profile is aboutfour seconds; about 12 seconds arerequired for a series of five different profiles.

SYMBOLS

The units used forthe physical quantities in thefigures and discussion in this paper are given in theInternational Systemof Units (SI) and parentheti- cally in the U.S. Customary Units. The tabulatedoutput data are in SI units. Calculations weremade in U.S. Customary Units. Conversion factorsrelating the two systems arepresented in reference 1.

D aircraft drag

Dr engine ram drag

ESF engine s izing factor

ES aircraft specific energy

9 gravitational acceleration h altitude

L aircraft lift

L/D aircraftlift-drag ratio

M Machnumber n load factor

OWE aircraft operating weight empty

PS aircraft specific power R range

SEC engine specific fuel consumption

SLS sea-level-static conditions

enginegross thrust T9 Tom aircraft take-offgross weight

T/w aircraft thrust-weight ratio(thrust loading), installed SLS

2 V velocitytrue

W we ight

Wf engine-fuelweight w/s wing loading,gross weight over wing reference area

X horizontaldistance c1 ofangle attack

Y flight-pathangle 6 thrustinclination angle, positive nozzle down

A dot over a symbol denotes its time derivative.

RESULTS AND DISCUSSION

GENERAL DESCRIPTION OF PROGRAM

Inthe development of the program a modularconcept was selected as the most logicalapproach to a multimissionprogram. The presentprogram is a combination of five mission modules which represent mission profiles currently of interest. The missionmodules are listed by number identificationin table 1 withbrief descriptions to indicatethe profile variety that is available. Each mission module is designed to determinethe combat radius or rangecapability for a specificmilitary mission with its associatedground rules and profile definitions.Several of these mission modules contain optional profile segments which may bedeleted to representalternate missions. The module conceptper- mits theaddition of new modules, or themodification of existing modules, to represent new or unusualmission profile specifications.

Althoughthe mission modules havebeen used in vehicle sizing studies, the program is notdesigned to internallysynthesize configurations or to generate aerodynamic,propulsion, or structural characteristics. The characteristicsof thesevehicles are predetermined by specialists in each discipline, andthey are input to theprogram as a database for all calculations. The representa- tionof the aircraft data (appendix A) is extensive and includes realistic limits on engine and aircraft operational boundaries andon maximum attainable lift coefficients.

Each missionmodule controls the calculation of themission-segment data (take-off, climb, cruise, combat, etc.) required by theprofile definition and utilizesappropriate segment modules. The profile logic withinthe mission module is thenused to calculate theoverall range or radiuscapability with balancedoutbound and inbound radii and with the required combat fuelallowance. If a low-levelpenetration, or dash, is includedin the profile definition, the outboundand inbound dash radii may also bebalanced. Performance for missions withalternate radii and combat fuelallowances are also calculatedfor use in

3 trade-offstudies. For each mission profile, an iterative procedure is used to balancethe radii.Initially, the outbound performance is calculatedto a desired mission radius. Then the fuel allowances at the combat stationare determined. Finally,the remaining fuel is consumed to determine the inbound (return)radius. Basedon thedifference in outbound and inbound radii, an estimate of the outbound radius is made,and thecalculations are repeated until the radiiare equal. During each iteration some outbound segments, and all inbound segments, must be recalculated because of the sensitivity of segment performance tovehicle weight. Although most mission profilesare balanced in severaliterations, this processcould involve a large numberof calculations, particularly if the inbound profileincludes a climb to a return cruisecondition.

MISSION SEGMENT MODULES

The present program was developed with the assumption that great emphasis wouldbe placed on balanced-radius profiles, and that alternate radius missions wouldbe of interestas trade-off information. A technique was therefore developed that would produce accurate performance results for all mission segments andwould minimize the repetitive calculations normally requiredto bal- ance radii and develop radiustrades. When a segmentmodule is first utilized to compute performance for a particular modeof flight (for example, climb to cruisealtitude) which is known to be sensitiveto vehicle weight, the segment performance is automatically computed for a series of four initial weights. The results, in terms of quantitiesappropriate to the particular segment, are retained in dataarrays as functions of thefour initial weights. These data arraysare referred to as mission-segment data. The four initial weights are selected(internally) to cover the range of actual weights that wouldbe expected to occurthroughout the mission. Specificdetails of the segment data arepresented as each segmentmodule is described in a subsequent section.

Afterthe mission-segment data has been calculatedfor all segments in the mission definition, the mission-module logic can determinethe balanced radii and alternate radii missionsvery efficiently by interpolatingthe segment data forrequired parameters at theappropriate segment weight.

I Afterthe performance hasbeen determined for a given aircraft take-off i gross weight (TOGW) and associatedoperating weight empty (OWE), additional missions maybe calculatedfor four other combinations of TOGW and OWE. The results of theseoptional missions indicate the performance sensitivity to vari- 1 ations in fuel loador to overall aircraft weight, depending on therelationship of the two inputweights. More specifically, an increase in TOGW with no 1 increase in OWE would represent an increase in fuelload; an equalincrease in LI! both inputweights would represent an increase in the vehicle OWE with the same k fuel load; andan increase in OWE with no increase in TOW would represent an increase in thevehicle OWE with an equalreduction in thefuel load. These sensitivities are of great interest in the early development stage ofan aircraft concept. They areavailable for all mission modules as an optionaloutput and require very little computer effort because they utilize the mission-segment data that was calculated for the original aircraft TOGW.

i APPLICATION TO VEHICLE SIZING

Theprogram may beoperated in a preliminarysizing mode, that is, to pro- vide an indicationof which combinations of TOGW, wing-loading W/S, andthrust- loading T/W would providethe best performance for a givenmission requirement. For this mode ofoperation, the OWE should be input as a functionof TOGW, W/S, and T/W to represent realistic weight variations with the size of the aircraft, the wing area, andthe engines. The segmentdata for each input TOGW is recomputed for eachcombination of W/S and T/W that results in a new wing area, or enginesizing factor (ESF), so thatthe segment performance reflects these changes. The propulsiondata are scaled to correspond to thedesired engine size, andthe aerodynamic lift anddrag are scaled to thedesired wing area, but the basic aerodynamic characteristics are not internally modified to reflect the actual wing or engineconfiguration changes. Caution must be used if T/W and W/S are variedfar from the original input concept. The results ofsuch a sizingstudy serve as usefulguidelines for resizing the aircraft by configuration specialists. Theaerodynamic characteristics of the resized configuration are thenestimated and are resubmitted to theprogram to evaluatethe results in terms of missionperformance. This process hasbeen used successfullyfor several aircraft concepts studied at theLangley Research Center.

DESCRIPTION OF SEGMENT MODULES

The subsequentsections describe (in chronological order for a typical missionprofile) how eachmission segment is calculated. The descriptionsinclude thetechniques and assumptions employed and present sample results. Thesample cases representan aircraft concept developed at theLangley Research Center. It is representativeof anadvanced fighter-type aircraft with supersonic cruise capability. The concept is poweredby two advancedturbofan engines. For the purposes of thepresent paper, the aircraft is sized with a basic TOGW of 196 kN (44 000 lbf), a W/S of2.93 kPa (61.2lb/ft2), and a T/W of1.04. For missionprofiles which specifyexternal fuel tanks, the aircraft carries an additionalweight of 23.5(5290 lbf), with a resulting TOGW of 21 9 kN (49 290 lbf) .

Take-of f Segment .. The take-offsegment of the mission is consideredonly to theextent that it affectsthe mission performance. No estimate oftake-off distance is made, butincrements of range and time to the initial climb point may be determined externallyand input to theprogram. The primary output of this module is a fuelallowance to simulate thetake-off. There are two inputoptions available forthe fuel allowance. The first is either a fixedweight of fuel or a fixed percentageof the aircraft TOGW. The secondoption is thefuel required for thecombination of a number ofminutes of engine operation at normalrated thrust plus a number ofminutes at maximum thrust.For this option, the total fuelallowance is calculated at sea-level-static (SLS) conditionsfor the appropriate number and sizeof engines. For the sample aircraft,one minute at normal ratedthrust plus one-half minute at maximum power consumes498 kg (1097 lbm) of fuel.

5 Climb and Acceleration~~ . Segment

Climb Profile

In the climb and acceleration segment, the performanceis computed along any desired climb profile described in termsof Mach number and altitude. Either of two engine power settings may be selectedat each point along the profile.- The climb - profileand engine power setting may beselected by- the user in an effortto maximize the performance within any operational constraints peculiar to the vehicle, the flight envelope restrictions, or the missionprofile ground rules. Accessory programs that determine minimum-time-to-climb or minimum-fuel profiles basedon specific energy techniques may be used to select the climb profile. An excellent discussionof the energy approach to aircraft performance problems can be found in reference2. An alternate approach is toselect a nominal climb profile and then compute a series of missions, each with the nominal profile perturbed slightly.The climb profile used for the sample aircraft is shown in figure1.

Method of Calculations

The performance along the climb profile is determinedby a numerical inte- gration of the following equations of motion:

-g y = - [T~sin + 6) + L - w cos y] vw (a

x = v cos y

w = -wf

The first input Mach number and altitude of the profile are assumedto be the conditions that exist after the take-off segment and are the initial conditions for the climb. An iterative procedure is utilized to determine the fuel, range, and time increments from point to point along the climb profile. For each step, a weight change is assumed, and the equations of motion are utilized to determine the instantaneous rates of climb, acceleration, and fuel atflow the end point. The initial and end-point rates for eachstep are averaged and then used to compute the time interval and actual fuel usage for the step. This process

6 is continueduntil the assumedweight change for the step equals thecalculated fuelconsumption. The steprange is thencomputed, and the initial point values of all variables(weight, range, time, etc. ) are incremented by the computed step changes.This procedure is repeatedfrom point to pointalong the climb profileuntil the desired cruise Mach number is reached.In the event a speci- fiedrate-of-climb limit is reachedduring the climb and acceleration before the cruise Mach number is reached, an estimate is made ofthe climb ceiling for theaircraft and the mission calculations are terminated. When thecruise Mach number is reached,the same stepwise technique is used to climb at the cruise Mach number, butadditional calculations describedin the next section are made afterthe climb performance to eachaltitude has been determined.

Termination ofClimb

The climb at cruise Mach number continuesuntil one of the following conditions is met: (1) Ifthe last inputprofile altitude is reached,the cruise segment is begun at thataltitude. (2) Ifthe rate ofclimb at any altitude falls belowthe specified level, an iterative technique is utilized to determine thealtitude ceiling (to within 15 m (50 ft)) at which the minimum rate ofclimb canbe met, and thecruise segment is begun at thataltitude. (3) Ifneither of theseevents occurs, the climb continuesuntil the altitude for most efficient cruise is located.

Determination of Start of Cruise

The rangeduring cruise is determined by usingthe Breguet range equation. The equation, which is developedin reference 3, is as follows:

When the first term inparentheses (referred to as theBreguet factor) is maximized,the range for a given cruise weight ratio is also maximized. The values .. of L/D and SFC are determined,for a given Mach number and altitude, by the solutionof the equations of motion for the lift coefficient and the engine thrustsetting required to sustainsteady level flight. The start-of-cruise altitude is selected, noton the basis of thebest Breguet factor at the initial cruise condition,but on thebasis ofthe lowest total fuel consumed fromthe start ofclimb to endof a cruise to a desiredrange. The selection is made by computing, at eachclimb altitude, a single-stepBreguet cruise segment to thedesired outbound cruise range,and then choosing the altitude resulting in theheaviest aircraft weight at theend of cruise. Forlong-range missions, wherethe cruise segment consumes a major portion of themission fuel, the alti- tudeselected for the beginning of the cruise by thisprocedure is also the altitude whichdevelops the best cruise Breguetfactor. For short-range missions, typical o€ fighteraircraft, using the present procedure results in a cruise segment at altitudes lower than wouldbe indicated by the initial Breguet

p factor.Short-range missions do not expend the additional climb fuelthat would be required to reachhigher altitudes in order to attain the best cruise efficiency. The initialclimb steps at thecruise Mach number are normallyin intervals of 610 m (2000 ft), andan iteration procedure in the search-forcruise-altitudelogic determines the start-of-cruise altitude to within 15 m (50 ft) ofthe optimum.

Sample Initial Climb Calculation

The climb performance to the start of cruise, calculatedalong the profile offigure 1 andutilizing maximum enginethrust, is presentedin figure 2 forthe sample aircraft with an initial climb weightof 214 kN (48 193 lbf). Thisweight corresponds to a take-offweight with external tanks of 219 kN (49 290 lbf) less thetake-off fuel allowance. Climb to thestart-of-cruise altitude consumes 1.70 Mg (3747 lbm) offuel and attains a rangeof 78.5 km (42.4 n. mi.) inonly 3.5 minutes. As would beexpected with the high T/W (0.93), no rate-of-climb limits are encountered,and the cruise altitudeof 15.4 km (50 650 ft) is determinedon the basis ofoptimum cruise performance. The cruise Breguetfactor is 72.7 km-N/g (4005 n. mi.) forthe aircraft with theexternal fuel tanksand weapons aboard. The cruise efficiencyfor other store combinations is discussedin a subsequentsection.

Effect of Initial Climb Weight

The variationof the final values of the major climb performance parameters withinitial climb weight is presentedin figure 3. These are the climb- segmentparameters used by themission modules to determinethe start-of-cruise weight,range, and altitude forany initial climb weight. The values at the heaviestinitial weight are the same performancedata shown infigure 2. All thedata shown infigure 3 are for the same aircraft size (that is, the wing area andthe engine size are fixed); therefore, the data representperformance variations as weight is reduced(fuel is expended). As mentionedpreviously, theinitial weights are selected to coverthe range of weights that are likely to occur throughoutthe mission profile.

Inbound Climb

Ifthe inbound (return) climb of a particularmission profile does not begin at the same Mach and altitudeconditions as theoutbound climb, thesegment data forthe outbound climb cannot be used directly to representthe return-climbperformance. As the climb calculations are made foreach initial aircraftweight, increments in the weight, range, and time required to climb to anenergy level representing the return start-of-climb conditions are retained as part of thesegment data. By subtractingthese increments from the appropriate initial-climb-segmentquantity, a second set of climb data is developed, whichrepresents the performance from the return start-of-climb conditions to thereturn start-of-cruise conditions.

8 Assumptions

There are two assumptions inherent in the useof the climb-segment data. The first assumption is that the climb Mach-number-altitude profile and the cruise Machnumber must be the same for the outbound andinbound mission segments. This is not considered to be a significant assumption, because most militaryprofiles are defined in this manner.The second assumption is that the aircraft external configuration is the same forthe outbound and inbound climbs. This is notthe case for many mission definitions in which external fuel tanksare dropped when empty, or in which large external weapons are dropped at the combat (or radius)station. The effect of the second assump tion on overall mission performance is described in detail in the discussion of the airsuperiority mission profile. Sample calculations show theeffect to be small, and a procedure to evaluate this assumption is built into the program.

Cruise Segment

The aircraft weight and altitude and theassociated Breguet cruise factor are determined duringthe climb calculationspreviously discussed. The cruise- segment data represent the variation of the Breguet factor with aircraft weight. The cruise segments of all mission profiles are calculated as single-step Breguet cruises. For profiles whichhave relatively short-rangecruise requirements, the Breguet factor at thestart-of-cruise weight is used to compute the performance. For the long-range cruise ofmodule 5, an average of theinitial and final Breguet factors is used to calculate the range.

Loiter Segment

The loiter orholding operation is a steady(nonaccelerating) flight condi- tionat a fixedaltitude for a given period of time. The performance parameter of primary interest is thefuel flow rate. For a given Machnumber and altitude, an iterative procedure is used tosolve the equations of motion for the lift coefficient and engine throttle setting required to sustain steady level flight. The fuel flow rateassociated with the throttle setting is the required loiter fuel flow. These calculationsare made atthree Mach numbers, and thelowest fuel flow is used. Figure 4 presentsthe results of theloiter calculations for fourvalues of aircraft weight. Note thatthe loiter fuel flow is sensitiveto aircraft weight. When the mission-module logicinterpolates these data, the average of the actual missionweights before and after loiter is used to determine the mission loiter fuel flow.

DashSegment

The dash or low-level penetration is essentially a cruise at a constant altitude. The mission specificationsusually define both the flight altitude

9 and the Machnumber. For this modeof flight, theperformance parameter of interest is thespecific-range factor, which is defined as the aircraft velocity divided by thefuel-flow rate. The specific-rangefactor is an instantaneous cruiseefficiency, as it is a measure of the distance that canbe traveledfor agiven amountof fuel. An iterativesolution of theequations of motion is employed toobtain the required fuel-flow rate. The results of the dash-segment calculationsare presented in figure 5 forfour values of aircraft weight. Per- formance is shown forthe aircraft with and without external weapons. As was thecase with theloiter-segment data, the specific-range factor is a strong function of aircraft weight. When thesedata are interpolated by the mission module, an average dash-segment weight is used forthe independent variable.

CombatSegment

CombatWeight Specifications

This segment calculatesthe fuel allowance requiredto perform the combat operationsspecified in each mission definition. Because of the wide variety ofcombat definitions, this segment module contains a numberof optional calculations that maybe selected to represent many fuel-allowancespecifications. The referenceaircraft weight (combat weight) at which the combat fuel allowances areto be calculated is an importantconsideration. Some missionspeci- fications identify the combat weight in terms of a percent of the fuel capacity of the aircraft(e.g., weight with 50 percent of internalfuel). Other missions specify that the combat weight be the actual weight of the aircraft when it reachesthe combat station(overall mission radius). The former specification results in combat fuel allowances that are independent of theother segments of themission definition (i.e., the calculated combat fuel allowance is the same for all mission radiustrade-offs). The later combat weight definition results in a variable combat fuel allowance with changes in missionradius.

The options available within the program for the reference combat weight are the aircraft OWE with a fraction of the internal fuel remaining,the aircraft TOGW with a fraction of the total fuel (internal plus external) removed, orthe actual weight of the aircraftat the combat radius. The third combat weight option is a calculation of the combat fuel allowance for a series of four weights. Thus, the combat fuelfor the actual aircraft weight canbe interpolated during the mission-balancing logic.

Combat Fuel-Allowance Options

At thepresent time thereare four combat fuel-allowancespecifications available in the combat-segmentmodule. Additionalrequirements maybe inserted as desired to represent new specifications.

Specific power.-The first combat fuel-allowanceoption is specified as the fuelrequired to increase the specific-energy level of theaircraft. The spe- cif ic energy E, is the total energy of the aircraft per unit of aircraft weight. The time requiredto accomplish theincrease in E, is determined by the energy rate, or specific power at agiven flight condition. The fuel allow-

IO ance is theproduct of the fuel flow at the flight condition and theresulting time interval.Specific power Ps is theinstantaneous excess power per unit of aircraft weight and is expressed in m/s (ft/sec) as

Ps = [ Tg cos (a + 6) - Dr - D]V/W

Specific power is calculatedfor a specified Machnumber, altitude, load factor, and throttlesetting. The aircraft drag D in thepreceding equation is associated with the lift and angle of attack that are obtained from an iterative solution of theexpression for load factor, which is

n = [L + Tg sin (a + 6)l/W

Figure 6 presents,as a function of aircraft weight, the specific powerand combat fuel allowance based on a specific energy increase of 43.9 km (144 000 ft) and typical combat specifications.

Specified Mach number, altitude, and throttle setting.- The second combat fuel-allowanceoption is calculated as the fuel required to fight for a given time intervalat a specified Machnumber, altitude, and throttlesetting. The fuel required is independent of aircraft weight and aerodynamic characteristics. It is calculatedas the product of the time interval and theengine fuel flow forthe given flight conditions. For the sample aircraft, combat for 2 minutes at M = 1.2 and h = 9144 m (30 000 ft) at maximum augmented throttle would require 973 kg (2144 lbm) of fuel.

Acceleration~~ to combat.- The third combat fuel-allowance option is similar to the previous option except that it requires a constant altitude acceleration before combat begins. The acceleration is calculated in a stepwisefashion similarto that described for the climb segment. The fuel expended duringthe acceleration is a function of both the weight and the aerodynamic characteristics of the aircraft, so thesecalculations are repeated for four representative combat weights. The individualfuel requirements foracceleration andcombat are shown in figure 7 for a typical set ofcombat specifications.

Accelerate and maneuver.- The fourth combat fuel-allowanceoption is speci- f iedas the sum of three fuel requirements. The first requirement is an acceleration at constant altitude, which is calculatedas described in the third option.After the acceleration, two sets of sustainedturn maneuvers are required. Eachmaneuver is calculatedat a given Mach number, altitude, and throttle setting for a given numberof turns, and at the maximum loadfactor for sustainedflight. This loadfactor is found by a technique which involvescal- culation of thevariation of Ps with loadfactor to determinethe load factor for which Ps is zero. The variation of Ps with loadfactor is shown in figure 8 for a typical set ofcombat specifications and a combat weight of 160 k~ (36 000 lbf). Themaximum sustainedload factor is 3.09 at M = 0.90 and 4.47 at M = 1.20. Turns at load factorsless than the maximum sustainedload factor

11 (withpositive Ps) would gainaltitude or speed;turns at higher load factors (withnegative Ps) would lose altitude or speed.

The fuelrequired for each turn maneuver is theproduct of the number of turnsspecified, the time required foreach turn, and the fuel-flow rate. The relationshipof turn rate (indegrees per second) to theload factor is given by

180g \F1 TURN RAW = V

The individualfuel requirements for the acceleration and the two sets of sus- taineaturns are presentedin figure 9 as a functionof aircraft weight. The fuel required forthe turn maneuvers is for a single 360° turnand is based on theinstantaneous turn rate calculatedfor the weight at thebeginning of the turn. When this combat-segment data is utilizedin the mission module to calculate the total fuelallowance for the acceleration and the specified number ofturns, two optional summing techniques are available. All theindividual combat componentscan be determined on the basis of a single fixed (i.e., the combat weight), or the component fuelscan be assembled onthe basis of the actual chronologicalweight that exists at the start ofeach maneuver. For the latter option,an iterative procedure is used to accountfor the weight of fuelburned during each set ofturn maneuvers.

All calculationsof combat fuelallowances assume thatthe external tanks, if carriedduring the outbound segments of the mission profile, have been dropped;thus, the tank drag-coefficient increments are notincluded in the aircraftdrag. In addition, with the exception of the sustained turn maneuvers ofthe last combat option,calculations of Ps donot include the drag- coefficientincrements for the external weapons.The valuesof P, represent theenergy-maneuverability characteristics of a "clean"aircraft configuration. If anymission-profile specification requires thatthe store-drag increments be includedin the Ps calculations,this can be accomplishedeasily for selected profiles.

Descent Segment

The descentand deceleration segments of most military profiles are specified as "non-segments"with no creditfor range gained or fuelexpended. The presentprogram represents the final descent with increments in range, time, and fuelburned. The increments must be estimated externally. The fuel-burned increment may be input as a percentageof the weight at theend of the descent, so that it increasesproportionally with increases in the landing weight of the aircraft.In the mission modules, anydescents other than the final descent are non-segmentswith no range, time, or fuel credits. An exception is thepre- targetdescent in mission module 4. The outbounddescent increments of fuel and range are scaledfrom the final descent increments, based on a ratio ofthe aircraft weights.

12 ReserveSegment

Thereserve fuel allowance for a military mission is generally specified in terms of a percentageof fuel capacity; or a given number ofminutes of engineoperation at sea-level-staticfuel flow, or some combinationof these or similar modes. Because ofthe variety of reserve fuel definitions among the militaryservices and the missions, the reserve-segment module containssix optional calculations which may be selected to represent many fuel specifications. The options may beselected individually or incombination in any sequence. The operationalreserve modes are listedin table 2. They varyin complexityfrom a simple fuel-weightincrement to the calculation of the fuel required to hold or loiter for a given period of time. The reservedescrip- tionsof table 2 are selfexplanatory with the exception of mode 5. Ifdesired, the hold calculations of mode 5 may beperformed at five Mach numbers,and the Mach number withthe lowest fuelflow wouldbe selected.The fuel flow is determinedfrom the engine throttle setting required to maintain a steady level flightcondition at each particular Mach number at a givenaltitude. The weight basisfor these calculations is thelanding weight of the aircraft for the particular mission. The aircraftdrag is calculatedfor the existing external store configuration at theend of the mission. For the sample aircraft,with a weightof 107 kN (24 000 lbf) , a lo-minutehold at an altitudeof 1.52 km (5000 ft), conducted at a Mach number of 0.40, requires 401 kg (883 lbm)of reservefuel. Since the reserve fuel allowance is notaffected by themission- radiustrades, the reserves are calculatedonly once for each mission. If addi- tionalcalculations are desired,either €or a changein aircraft OWE or for a change insizing (T/W or W/S) ofthe aircraft, the reserve fuel is recalculated as required cor eachmission.

Confi2uration- - Changes

Typesof Changes

Configurationchanges occur when any externally mounted store is expended during the mission.Each mission definition specifies the stores (fuel tanks andweapons) to be carriedand whether they are to be retained or dropped duringthe mission. Each external store is represented as anincremental weight andan incremental drag coefficinet as a functionof Mach number. Internal . weapons may berepresented by a weightincrement and a dragcoefficient of zero. If the user wishes to retainthe external tanks for a missionmodule that is designed to dropthe tanks, there is sufficient input flexibility to represent retentionof the tanks. In general, all missionprofiles have the capability to retain or to dropthe external weapons at thecombat (or radius)station. As indicatedin table 1, three ofthe five profiles have external-tank capability, but the logic for retaining or droppingthese stores varieswith each profile. Thesedetails are presentedin the subsequent discussions of the individual missions modules.

13 Acceleration and Climb

In the acceleration-and-climb-segment module, the performance is calculated on theassumption that the external stores are to be retained until the end-of-climb (start-of-cruise) point is reached. This is a reasonableassump tion becausethe external fuel load is usually selected to accomplish both the climb and a portion (sometimes all) of the outbound cruise segment. For profiles which specifythat the stores be dropped duringthe mission, the inbound (return) climbperformance is conservative because it is interpolated from the climb-segment data, which includethe effect of thestore-drag increments. The amountof conservatism depends onmany factors, such as the aircraft sizing (excessthrust capability), theclimb profile, and, of course,the magnitude of the combined store-dragincrements with respect to the drag of theclean aircraft. The overalleffect in terms of mission radius is discussedfor the sample aircraft in asubsequent section.

Cruise

The search for the best start-of-cruise altitude is also based on theaircraft with thestore-drag increments included. If the profiledefinition specifiesthat either the fuel tanks orthe weapons areto be dropped, thecal- culationsfor the cruise Breguet factorare repeated for the appropriate aircraft-storeconfigurations. The Breguet factorsfor these alternate config- urationsare retained as part of the segment datafor use in determiningthe cruise performance afterthe stores are expended. The variation of the Breguet factor with aircraft weight forthe sample aircraft, with and without external stores, is presented in figure 10 for a cruise Machnumber of 1.60. The lower curve of figure 10, forthe aircraft with external tanks andweapons, would be used in the mission module forthe outbound cruise. Mission definitions which permitthe tanks to be dropped when they are emptywould usethe middle curve (which excludes the tank-dragincrement) to continuethe outbound cruise after thetanks are dropped. The upper curve, which represents theclean aircraft, wouldbe used forthe return (inbound) cruiseif the weapons are expended at the combat station.

It should be noted thatthe twoupper curves are calculated at the altitudes whichwere selectedfor cruise with theexternal stores. As an indication of theeffect of this assumption, thecruise Breguet factorsfor a cleanaircraft havebeen calculated, and theresults are shown as symbols in figure 10. These latter calculations weremade at the altitudesfor the best cruise perfor- manceof the aircraft with no externalstores. Theupper curve is in good agreement with theactual clean-aircraft efficiency. The present procedure is about 2 percentconservative at lower aircraft weights, which arerepresentative of thereturn cruise conditions.

Loiter j The loiter fuel-flowcalculations are made for the aircraft with theexter- 'I nal weapons aboard. At thepresent time, no otheraircraft configurations are

14 I included in the calculations, because no mission definitions with other store specifications havebeen encountered.

Dash

The dash specific range factors are calculated on the assumption that the externalfuel tanks are dropped beforethe dash segment begins; therefore, the external tank-dragincrements are not considered. Ifthe mission specifiesthat the weapons are to be expended, the dash calculations are made with and without the weapon-drag increments. Both sets of range factorsare retained as segment data for use in determiningthe outbound andinbound dash performance.

Reserves

As mentioned previously,the reserve fuel allowance forholding is calculated for the external-store configuration that exists at the endof the mission.

MISSION-PROFILE MODULES

Gener-a1Considerations

As discussed briefly in preceding sections of this paper, thereare five mission modules in the program (table 1). Eachof these modules is designed to determinethe performance for a specific military mission with its associated ground rules and profiledefinitions. The mission module controls thecalcu- lation of the required mission-segment performance with appropriate store configurations. The segment data is then utilizedto calculate the overall mission performance with balanced outbound andinbound radii and with the specified combat fuel allowance. Alternate mission profiles, with differentradii andcombat fuel allowances,are also calculated using the segment data. Subse- quent sections of this paper describe each mission profile and present examples of performance resultsappropriate to each. For the sample cases,the aircraft sizing and store combinations, as wellas the choice of flight conditions forcruise, dash, and holding operations,are not intended torepresent best or optimum conditions. They areselected solely to illustrate the available features of each module. Specialfeatures or optionspeculiar to eachmission prc- file are described and, in most cases, illustrated with typical results.

Mission Profile 1 - Air-Superiority

Mission Description

The first mission module represents an air-superiority profile with a low- levelpenetration to the combat.The Hi-Lo-Lo-Hi profile is shown schematically in table 3 with a generaldescription of eachmission segment. The items listedas inputs for eachsegment arethe major inputs which are used todefine

15 themission in greater detail. The word "options" appears for mission segments whichhave two or more optionalcalculations, and represents the segment with a fuel allowance. Thesesegments are the take-off, combat, andreserve fuel allowances.The inputs for each option are described inthe individual segment discussions. The climb Mach-number-altitudeschedule and the cruise Mach number definethe climb and the outbound cruise segments which are intially calculated for the desired cruiseradius. The dash segments are defined by a dash Mach number, a dash altitude, and a desireddash radius. Theinbound dash is assumed to be equal to theoutbound dash radius, unless the inbound dash radius is specificallyinput as a zerodistance. For such a case, thereturn climb to profile point 13would begin immediately after the combat with no returndash, andthe result would be a Hi-Lo-Hi profile.The weapon is retained to theend ofthe mission if the weapon weight is inputwith a positivesign. A negative signcauses the weapon weight to drop beforethe combat.

Externaltanks

Ifexternal tanks are carried, they are dropped when empty duringthe outbound cruise, as indicatedin table 3. Two restrictions are imposedon this logic;first, if the tanks are emptiedduring the climb to the start of cruise, they are dropped at profilepoint 3; secondly,tanks are not carried beyond profile point6. Even if theycontain fuel, thetanks and any remaining external fuel are dropped when theaircraft reaches the cruise radius (point 6). In an earlydefinition of the air-superiority mission, the tanks were alwaysretained to profilepoint 6 andthen dropped just as thedescent began. This tank logic is still available,and when it is selected it overrides all othertank-drop logic.

Sample Calculations

Resultsof calculations for mission profile 1 are presented in figure 11 for the aircraft withexternal tanks and a TOGW of 219 kN (49290 lbf). The resultingtake-off T/W is 0.93 and W/S is 3.28 kPa (68.5lb/ft2). The aircraftweight and flight altitude are shown as functionsof the mission radius. Straight lines are used to connectthe actual profile-point data. Thefollow- ingspecific ground rules were used to definethe mission: The takeoff fuel allowance selected is theoption which involves engine operation. This option consumes498 kg (1097lbm) of fuel. The climb is calculatedalong the schedule shown in figure 1 using maximum power. Forthis mission option, the externalfuel is burnedduring the take-off and climb segments, and thetanks are dropped at theend of the climb. The high-altitudecruise is at a Mach number of 1.60 with a desired cruise range of 1111 h (600 n. mi.). The low- levelpenetration is conducted at a Mach number of 0.80 at analtitude of 61 0 m (2000 ft), with a desired radiusof 185 )an (1 00 n. mi. ) . The combat fuel allowance selected is theoption requiring an increase in the specific-energy I E, level of the aircraft. The available specific power P, is calculated, for a fixedreference weight, at a Mach number of 1.20and an altitude of 1524 m 'Ij (5000 ft).For E, = 43.9 km (144 000 ft), thefuel allowance required for com- 1 bat is 1571 kg (3463lbm) . The reservefuel allowance is calculated as thefuel i required to loiter at an altitude of 1524 m (5000 ft) for 10minutes. The E \ 16

I! loiter is conducted at a Machnumber of 0.40 and requires 401 kg (883 lbm) of fuel. The primary mission results shown in figure 11 indicatethat with the desiredcruise radius of 1111 km (600 n. mi.) and with thespecified combat allowance, the dash-radius capability is 298 km (1 61 n. mi. 1.

Sample Alternate Mission Calculations

Two additionalmission options are calculated for this profile, with alter- nateradii. With one option, a desired 1111 km (600 n. mi.) cruiseradius anda 185 )an (100 n. mi. ) dash radius is assumed,and the fuel available for combat is calculated to be 72 percentgreater than the specified allowance. With theother option, the desired-radius and the specified combat allowance are assumed,and a cruiseradius of 1496 km (808 n. mi.) is calculated. These threesets of mis- sionresults are calculated’each time this mission module is selected. A sample of the summary outputlisting for this module is presented in table 4. (Defini- tions of theoutput parameters are given in appendix B). These threemissions arereferred to as options 1, 2, and 3, respectively. The weight, range and altitudeare listed for each profilepoint. Note that the combat fuel allowance is the same foroptions 1 and 3 because theselected combat option is independent of theactual combat weight.

Additional Performance Quantities

Two additional performance quantities are computed using this mission module. The first is a levelacceleration for a given Machnumber schedule. The second is concerned with theenergy-maneuverability characteristics of the aircraft. The calculationsare independent of themission-profile results, except that theyare basedon the initial combat weight of the option-1mission. For the sample aircraft, an acceleration from Mach = 0.80 to Mach = 1.30 at an altitude of 10.7 km (35 000 ft) requires 35 seconds. The accelerationperfor- mance is computed withoutthe external tanks. The second calculation determines the instantaneous specific powerand turn-rate capability for 12 .preselected flight conditions. The specifiedconditions are Mach number, altitude, load factor, and engine power setting.Results of thesecalculations maybe compared with results previously determinedfor alternate aircraft sizes or with a set of energy-maneuverabilityrequirements which might represent anenemy aircraft. The performance is computed forthe clean-aircraft configuration with no externalstores. These calculationsare performed without themission-profile calculations if the outbound cruise radius is inputas zero.

Effect of Stor e-Dr ag Assumptions

This mission profile is used to indicate the effect of the assumption that, even though theexternal tanks andweapons are dropped before the return climb begins,the external store-drag increments may be included in the return climb performance. Two stepsare required to determine theeffect of thestore drag on thereturn climb. The first step is a separate run,without the store-drag increments, togenerate the climb-segment datafor the clean aircraft. The second step is to recalculate the mission with the external stores, but with the

17 new clean-segment data superimposed inthe mission-module logic forthe return- climb and cruise segments.The results of thesecond step representthe exactmission performance, and the profile points that are affected are plotted with square symbols infigure 11.The overallmission radius is 1420 km (767 n. mi.), with a dashradius of 309 km (167 n. mi.). The effect ofthe store-dragassumption on dash radius in the original calculations is short (conservative) by 11 km ( 6n. mi.). The rangedecrement is believed to be typical for a missionof this type and could be considered as a toleranceon supersonic cruise missionsemploying relatively large external stores which are dropped duringthe mission. The decrementwould be less for a missionwith a subsonic cruise segment,and is, of course, dependenton aircraft configuration, the rel- ativemagnitude of the store drag,and the specific mission profile. The radius incrementsthat might be calculated for variations in aircraft TOGW or OWE would be realistic sensitivities,even though the absolute radii would beslightly underestimated. For missionprofiles which do notinvolve store configuration changes, or whichdo not have a return-climb-segment,the performance results are notaffected by thepresent assumption.

As an aid to theuser who wishes to determinethe exact performance capability of a particular aircraft and mission-profilecombination (which would be affected by thereturn-climb decrement), an optional mode ofcalculation is available. It would be used to determinethe exact range capability for a missionprofile with a return climb andinvolving a configurationchange. The optional mode logiccorrectly accounts for theconfiguration change in the calculation of thereturn-climb performance: thus, the mission results are exact. As oomputed usingthe two-step procedure,the optional mode forthe example aircraft andmission profile mentioned previously results in a dash radius of 309 km (167 n. mi.). The optional mode can be usedfor only one combination of TQGW and OWE at a time. The sensitivity of radius to variationsof these two weights wouldhave to be calculated with a series ofinput cases. The option would not be used (or required) ininitial exploratory runs to size a new configuration or to determine,for example, the best cruise anddash Mach numbers.

Second Sample Calculation

As an indicationof the flexibility of this module in the representation of otherprofiles, a secondexample is presentedfor the same aircraftconfig- uration. The mission is a Hi-LeHi profilewith a penetration to the combat station, but without a returndash. The followingspecific ground rules definethe mission. The take-offand reserve fuel allowances are the same as in the first sample calculations. Theoutbound cruise is conducted at a Mach number of1.60, as inthe previous example, with a desiredrange of 1111 km (600 n. mi. ) . The penetration is at a Mach number of0.90 and an altitude of 91 44 m (30 000 ft). The combat fuelallowance is theoption which requires an acceleration and two sets of sustainedturn maneuvers. The acceleration is from Mach 0.90 to 1.20,and is followed by threesustained turns at Mach 0.90 andone turn at Mach 1.20. All combat maneuvers are calculated at an altitude of 91 44 m (30 000 ft) and are basedon a fixed combatweight. The total combat fuelallowance is the sum of theindividual components at theactual mission combat weight. The inbounddash-radius requirement is input as zero, so thereturn climb beginsimmediately after combat.

18 The primarymission results shown in figure 12 indicatethat, with the desired cruise radiusof 1111 km (600 n. mi.) andthe specified combat allow ance,the dash capability is 912 km (493 n. mi.) for a total missionradius of 2024 km (1093 n. mi. ) . The total combat fuelallowance is 1552 kg (3422 lbm) and is thedirect sum ofthe components shown in figure 9 for a combatweight of 153 kN (34304 lbf). The outputlisting for this mission profile is presentedin table 5. Two additionalmissions are calculatedfor this profile. For the first additional mission (option 2 in table 5 (b) ) , the desired cruise anddash radii are assumed,and it is calculatedthat the fuel available for combatwould be 142-percentgreater than the specified allowance. For the see ondadditional mission (option 3 intable 5(b)) the desired dash radius and thespecified combat are assumed,and it is calcualtedthat the outbound cruise radius is 2045 km (1104 n. mi. ) . Note that the combat fuelallowance for option 3 is greaterthan that of option 1. This is becausethe allowance is basedon the actual weight at the start ofthe combat, which is greaterin option 3.

Mission Profile 2 - Fighter Escort

Mission Description

The secondmission module represents a fighter-escortprofile. The Hi-Lo- Hi profile is shown schematicallyin table 6 along with a generaldescription of each missionsegment. The climband cruise segmentsof the profile are definedwith the same inputs as formission profile 1. There are no lowlevel dashsegments in this mission. The descent is made to thealtitude specified inthe particular combat optionselected. As with all profiles,the weapon is retained to theend of themission if the weapon weight is inputwith a positivesign. A negativesign causes the weapon to be droppedbefore the combat. The missionlogic contains no provision for droppingthe tanks. If tanks are installed at takeoff, they are retainedthroughout the mission.

Sample Calculations

Results of calculations for missionprofile 2 are presentedin figure 13 forthe sample aircraft with and without externaltanks. The circular symbols representthe aircraft without external tanks with TOGW = 196 kN (44 000 lbf). The square symbolsrepresent the aircraft with tanks and TOGW = 219 kN (49290 lbf). The followingspecific ground rules were used to definethe mission. The take-offfuel allowance selected is theoption involving engine operation andconsumes 498 kg (1097 lbm)of fuel. The cruise is at a Machnum- ber of 0.85 andthe climb schedule of figure 1 is useduntil the cruise speed is reached. The desired cruise radius is 1111 km (600 n. mi.) withoutexternal tanksand is 1296 km (700 n. mi.) withthe external fuel. Thecombat fuel allowanceselected is the option requiring 2 minutesof combat at full power at a Mach number of 1.0 andan altitude of 3048 m (10 000 f t). This option is independent of theaircraft weight and aerodynamic efficiency and requires 1662 kg (3664 lbm) of fuel. The reservefuel allawance selected is the same as forthe previous mission with a fuelrequirement of 393 kg (866 lbm) for the cleanaircraft and 402 kg (887 lbm) forthe aircraft with the external tanks.

19 The mission results indicate that with the full specified combat allowance, theradius without tanks is 1165 km (629 n. mi.), and it can be increased to 1406 km (759 n. mi.) when tanksare carried. The alternate mission for this profile is to cruise to the desired radius and calculate the available combat allowance. With a designradius of 11 11 km (600 n. mi. ) , the basic aircraft withouttanks can fight for 2.3 minutes or 11 4 .percent of the specification COP bat time. At a radius of 1296 km (700 n. mi.), the aircraft with tanks can combat for 2.7 minutesor 133 percent of therequired combat time.

This mission module also determinesthe time and fuel required for an acceleration from Mach = 0.80 to Mach 1.00 at an altitude of 3048 (10 000 ft). The acceleration is independent of themission profile and is calculated with the tankdrag excluded, even ifthe mission specifiesexternal tanks. For a weight of 160 kN (36 000 lbf ) , theacceleration is completed in 7 seconds and consumes 86 kg (1 90 lbm) of fuel. A sample of the summary output listing for this mission is presented in table 7 forthe mission with external tanks.

Mission Profile 3 - Combat Air Patrol

Mission Description

The third mission module represents a Combat-Air-Patrol profile. The Hi- Hi profile is shown schematically in table 8 along with the segment descriptions. The distinquishing segmentof this mission is theloiter at the combat station.Typically, a loiter time is required and the Machnumber and altitude aredefined. This profilespecifies that the external tanks, if carried,are dropped at the endof cruise, even if the externalfuel is completely burned at a shorterradius. A specialfeature regarding the tankdrop is that, if any externalfuel is in thetanks at the end of cruise, it is retained. In this event,the mission summary indicates that this has occurred by listing the amountof externalfuel that is retained.

Sample Calculations

Results of calculated performance formission profile 3 arepresented in figure 14 forthe sample aircraft with and without externaltanks. The aircraft is the same asthat described in theprevious mission profiles. Thesame mission specifications were also used for this profile, but with thefollowing modifications: The desiredcruise radius is 556 km (300 n. mi.) forthe clean aircraft and 741 km (400 n. mi.) forthe aircraft with externaltanks. The required loiter time at the combat radius station is 2 hours at a Mach number of 0.70 and an altitude of 9144 m (30 000 ft). Thecombat fuel allowance selected is the option requiring a level acceleration at 91 44 m (30 000 f t) altitude from the loiter Machnumber to a Machnumber of 1.0. Two minutes of combat at full power at the final Machnumber and altitude are also required. The acceleration portion of this combat option is dependent on the aircraft weight and the aerodynamic efficiency, but the final combat for 2 minutes is only a function of thefuel-flow rate at the specified conditions. When calculated on thebasis of a fixed combat weight of 133 kN (30 000 lbf), the requiredacceleration fuel is 106 kg (233 lbm) withouttanks and 124 kg

20 (273 lbm) , withtanks. Thetwo-minute combat allowance is the same forboth configurationsand requires 798 kg (1759 lbm) offuel.

The missionperformance shown in figure 14 indicatesthat, with the full two-hour loiter at the combat station,the radius achieved without tanks is 468 km (253 n. mi.). Thisradius can be increased to 796 km (430 n. mi.) when externalfuel is carried. The alternatemission for this profile is to cruise to the desired radiusand determine the loiter time with the full combat fuel allowance.With no external fuel the aircraft can loiter for 1.8 hours at a radius of 556 km (300 n. mi.). The aircraftwith external fuel can loiter at a radiusof 741 km (400 n. mi.) for 2.1 hours. A sample of the summary output listing for this module is presented in table 9 for themission with external tanks. Note thatthe retained external fuel is listed as zero,which indicate that notank fuel remained aboard when the tanks were dropped.

Mission Profile 4 - Lons-Ranse Penetration

Mission Description

The fourthmission module represents a long-range-penetrationprofile. The Hi-Lo-Lo-Hi profile is shown schematicallyin table 10 alongwith the segment descriptions.Although a radius-typemission can be represented by this module, the profile is depicted as a long-rangemission composed offour range increments (A to D), eachof which may have a specifiedvalue. Theoutbound (pre- target)penetration and the inbound (post-target) dash may beconducted at differentspeeds and altitudes. The outbounddescent increments of fuel and range are scaledfrom the final descent increments based on a ratio ofthe air- craftweights. The module doesnot contain the logic to dropexternal fuel tanks;therefore, if they are carried, they are retainedthroughout the profile. Theweapon is dropped at theend of theoutbound penetration if given a negative sign.

Air-to-Air Refueling

The aircraft canbe refueled during the outbound cruise if thecruise speed is compatible with thetanker capability. Theoptimum fuel-transferrange is determined by internal logic, so thatthe receiver aircraft can be"topped off" to a specifiedgross weight at the maximum possiblerange. This technique is illustratedin figure 15 for a refueling Mach number of 0.75. The tanker capability is represented by thechange, with range, of theweight of fuel available for transfer. The availablefuel is dependent upon theground rules that may be specified for thetanker, such as thepoint of origin of thetanker and whether it mustreturn to the same or an alternate base after the refueling operation. Thiscurve must be developedexternally, for thespecific tanker rules, and it is input to thepresent program. For convenience, the range scale is referenced to thereceiver aircraft, and it is in terms of the range at theconclusion of therefueling operation. The curvefor the receiver aircraft representsthe weight of fuel to top off to a givengross weight as a function of range at the end of refueling.This curve is calculatedinternally and considers the climb- and-cruisefuel plus the fuel burned during "hook-up'' andrefueling operations.

21 The fuel flow for thereceiver aircraft duringrefueling is basedon cruise at theappropriate Mach number andaltitude and the average refueling weight. No consideration is given to possibleinterference due to the proximity of the tanker (or other aircraft in the case of a multiaircraftrefueling).

The intersection of the two curves in figure15 represents the point where, at theend of refueling,the receiver aircraft is at the desired grossweight. The tanker musthave sufficient fuel remaining to return to its specifiedbase. Therange of the receiver at this point is the maximum thatcan be attained withthe specified tanker rules.

Sample Calculations

Resultsof calculations for mission profile 4 are presented in figure16 forthe sample aircraftwith a TOGW of 198 kN (44600 lbf). Thefollowing specific rules were used to definethe mission. The take-offfuel allowance, the descentincrements, and the reserve allowance are the same as for mission profile 3. Cruise is at aMach number of 0.75 andthe climb schedule of figure 1 is useduntil the cruise speed is reached.Pre-target penetration is conducted at a Mach number of 0.80 and analtitude of 152 m (500 ft) for a range of 370 m (200 n. mi.). Theweapon weightof 4.5 kN (1000 lbf) is dropped at thetarget station. The post-target dash is for 185 km (100 n. mi.) at a Mach number of 0.55and an altitude of 152 m (500 ft). The desiredrange for the return climb, cruise, and thedescent is 926 km (500 n. mi.). Figure16 indicates that the outbound cruise radius is 1.99 Mm (1076 n. mi.) withan overall mission range of 3.53 Mm (1907 n. mi.). The aircraft was refueled to theoriginal TOGW at a range of 1.16 Mm (625 n. mi. ) . A sample summary output listing of this mission is presentedin table 11.The refueling details forthis mission are those indicated in figure15, which describe the refueling logic. No optional missions are calculatedfor this profile.

Themission performance without refueling is also shown infigure 16. The overall range is 2.04 Mm (1102 n. mi.), andthe effect of refueling is to increase the range by 1.49 Mm (805 n. mi. ) .

Mission Profile" 5 - Long-Range Cruise

Mission Description

The fifth mission module represents thelong-range-cruise (ferry-mission) profile. The profile is shown schematicallyin table 12 along with a general description of each mission segment. The segments are the same as in previous missions. Ifexternal tanks are carried,they are dropped during cruise when they are empty.

Sample Calculations

Results of calculations for mission profile 5 are presented in figure17 for the sample aircraft withexternal tanks and a TOW of 219 kN (49290 lbf) .

22 The fuel-allowancespecifications for the take-off, descent, and reserves are the same as formission profile 4. The cruise Mach number is 0.85, and the range is 3.87 Mm (2089 n. mi.). The flight time for a long-rangemission is important frmthe standpoint of crew fatigue.For this profile, the total mission time is 4.4 hours.

Optional Calculations

An optional calculation for this modulecan be used to determinethe radius capability with a given number ofsustained turns at themidrange station. The turns are calculated at cruise conditions (Mach number, altitude, andweight) that exist at theradius (midrange) station. Theweapon may be expendedbefore the turns are initiated,and, if this occurs, theturn-rate calculations are basedon the clean configuration. For the present example, the weapon is retained, so thatthe turn performance includes the effect of theexternal-store drag. The sustained turn rate is calculated to be 4.9 deg/secand a half-turn (180O) requires 171 kg (377 lbm)of fuel. The missionradius, which does not include the radius of theturn maneuver, is 1.9 Mm (1025 n. mi.). Thesummary output listingfor this mission is presented in table 13.

The climbperformance for this mission was calculated by usingthe maximum thrust of theengines, which is thestandard operating procedure for most militaryprofiles. On theother hand, the ferry mission is notconcerned primarily withrapid climb times; thus,the performance has also beendetermined by using a reducedlevel of thrust. The resultingrange is 4.0 Mm (2169 n. mi.) with anoverall time of 4.6 hours. At thereduced thrust level, the climb to start of cruise takes more time anddistance, but the reduced fuel-flow rates result in a reduction in the total fuelrequired for climb. The fuelsaved during theclimb is availablefor a more efficientcruise, thus increasing range. An additionalfuel savings is possiblein that, since it is not employed during thismodified mission, the take-off allowance(which also simulates theengine warm-up) wouldnot have to include operation at full power.

SUMMARYOF SAMPLE MISSION PERFORMANCE

Theprimary performance for the five mission profiles is summarizied in table 14. Specific details forthese, and the alternate missions, may befound inthe tables for each profile. As discussedin previous sections, the missions varyin complexity from a long-range cruise mission to a multisegmentedcombat- radiusmission. The specific cruise anddash Mach numbersand the combat fuel allowances selected forthe sample cases illustrate theflexibility of the program in the representation of a wide variety of military mission profiles.

CONCLUDING REMARKS

A computer technique to determinethe mission radius and maneuverability character istics of combat aircrafthas beendeveloped. The aircraft characteristics and flight constraints are represented in sufficient detail to permit

23 ...... __ ......

realistic sensitivity studies in terms of either configuration modificationsor changes in operational procedures. Sample performance results are provided to illustrate the wide varietyof military mission profiles that may be represented. Extensive use of the technique in evaluation studies indicates that the calculated performance is essentially the sameas that obtained by the proprietary programs in use throughout the aircraft industry.

Langley Research Center National Aeronautics and Space Administration Hampton, VA 23665 February 6, 1981

24 APPENDIX A

DESCRIPTION OF PROGRAM INPUTS

This appendix contains descriptions theof input data required to define the aircraft configuration and the mission requirements. The aircraft descriptions are presentedto give the reader afeel for the degree of detail available to define a specific aircraft design.The inputs related to mission specifications illustrate that a wide varietyof mission profiles and combatfuel requirements maybe represented.

AIRCRAFT INPUTS

The description of the aircraft inputs is divided into three major sets. The first and largest set deals with the characteristics of the propulsion system. The second set defines the aerodynamic characteristics of the aircraft and of any external stores that may be carried. The third set deals primarily with the weight and size of the vehicle and its components.

The propulsion characteristics are precomputed, usually from data supplied by an engine manufacturer. All engine characteristics are given for a single, full-size engine. These values are multiplied within the program by the number of engines on the aircraft and are scaled (sized) to the proper thrust levelas required by the vehicle inputs. The propulsion data are considered to be installed in that they include the effects of inlet pressure recovery, horse- power and bleed-air extraction, and nozzle velocity coefficient. The data also include all engine-related drags (inlet bleed, bypass, spillage, and boattail) except the nacelle external skin-friction drag. The latter drag is included in the aerodynamic data, and the change in external nacelle drag with engine size is represented by an incremental drag input. The engine characteristics required for performance calculations are the gross thrust, ram drag, and fuel flow. These data are input in two groups. The first group isfor climb operations at either of two fixed throttle settings. For each throttle setting, the data are input as a functionof flight Mach number and altitude. The program can accept data foras many as 15 altitudes at each of15 Mach numbers. The second group is for cruise and loiter operations at reduced engine throttle settings. The ram-drag and fuel-flow parameters are inputas functions of the thrust level for up to ten selected Mach-number-altitude combinations. The program can accept data foras many as 15 throttle settings at each flight condition. These two data groups can be interpolated to determine the engine characteristics at any Mach number, altitude, and throttle-setting combination. Independent multipliersfor each parameter are available which can be used to simulate another engine typeor to represent, for example, an improvement in specific fuel consumptionfor a sensitivity study.

The aerodynamic characteristics aof given configuration are represented in terms of liftand drag coefficients as functionsof aircraft angle of attack and flight Mach number. The data areinput for full-scale trimmed conditions for a clean configuration (retracted gear, no external stores).The data are based on a given reference wingarea. The program can acceptas many as 15 angles of

25 APPENDIX A

attack of each of 15 Mach numbers. At each Mach number, the friction drag contribution to the total aircraft drag is basedon a reference flight altitude. The reference altitude is usually coincident with the nominal climb schedule, but can be any altitude. When calculations are made for the aircraft atdrag other altitudes, the change in the friction drag contribution (dueto Reynolds number effects) can be accounted for. If this option is used, the rate of change of the friction drag coefficient with altitude must be predetermined at each Mach number and input along with the basic aerodynamic characteristics.

Three separate arrays of drag-coefficient increments are available to mod- ify the basic drag dataat any Mach number. The first isa general-purpose increment that may be used to represent any drag increments not in the basic drag data. This increment is useful for drag sensitivity studiesor to represent store racks that are retained when the stores are dropped.The other two arrays are utilized specifically to define the drag-coefficient increments of external weapons and external fuel tanks. The application of these two increments is controlled by individual mission-modulelogic so that they are not included in calculations of performance in mission segments occurring after the individual stores have been dropped.

The size ofthe aircraft is defined in terms of the wing area, the size and number of engines, and the take-off gross weight.The wing area and engine size may be defined alternately in terms of wing loading and thrust loading. Addi- tional weight items are required to define the aircraft. They are the operating weight empty OWE and the weight of external stores. If external fuel is to be carried, the weight of both the fuel and the tanks must be defined.The OWE can be input in several ways. For preliminary performance studies, theOWE is input either as a constant or as a tabular function of the aircraft TOGW.It may be expressed in absolute unitsor as a percentageof the TOW. In more detailed studies, particularly those involving size changes of the aircraft wing and engines, OWE can be considered as the sum of three items.The first item is the weight of the aircraft minus the wing and propulsion-system weights.The other two items would be the wing and engine weights with appropriate scaling factors applied. This method does not recognize the interface between the components. For example, it could not represent the possible reduction in wing weight as the engines (if wing mounted) were reduced in size.A third method of representing OWE is to input the variationof OWE as a three-dimensional function of three major components; TOGW, wing area, and engine size.Data in this form, which would be calculated externally, would include the integrated effects on all components as each individual component was changed. The effort required to calculate the required matrix of data for this methodof representing OWE is considered excessive, but in principle, the resultingOWE would correctly reflect the configuration changes. A moredirect approach would be to incorpo- rate theweight equations in the program as a module.A compromise would be to calculate the OWE for selected combinations of the three components toand input the results using the first option described in this paragraph.

A caution previously noted is repeated here. In aircraft sizing studies, the weight and propulsion characteristics can be appropriately modified internally as changes in both wing area and enginesize occur, but the basic aerodynamic characteristics are not altered by the program to reflectsuch configuration modifications. Therefore, caution must be used if T/Wthe and

26 APPENDIX A

W/S are varied far from the original input concept. The repetitive technique described in the section entitled "Application to Vehicle Sizing" is recom- mended as a practical approach to large excursions from the original aircraft concept.

MISS ION INPUTS

The major mission inputs are described in detail in the main text and are briefly reviewed in this section. The desired mission profile is selectedby the mission module from table1. The schedule of climb altitude versus Mach number must be developed with considerationof all operational constraints of the vehicle and the specific mission ground rules.The desired ranges for the mission segments must be input along with the definitionof the required Mach number and altitude for any dashor loiter segment. The fuel allowance options for the take-off, combat maneuvers, and the reserve segments are selectedby input controls, and the associated Mach number, altitude, and time specifications required by each selected option must be input. For a given set of input data the program can be used to calculate the mission results along with the optional radius trade-off data for each value TOGW of that is input upto five values. As described in themain text, these results would indicate the performance sensitivity to the variations input for the TOGW andOWE. the

The additional results described in some of the mission modules,as such the accelerating performance and energy-maneuverability characteristics, may be calculated without the mission-profile performance by inputting the desired cruise range as a zero.

The following optional features are available and can be incorporated in the performance calculations with control inputs.They are briefly described in order of their significance to the mission performance results. The atmospheric model utilized was the U.S. Standard Atmosphere of 1962. (See ref. 4.) An atmospheric model with a nonstandard temperature can be representedby inputing the desired temperature increment (which is the same for all altitudes). The propulsion data must be basedon the same atmospheric modelfor a proper representation of the hot-day effects on mission performance.The thrust-inclination terms in the equations of motion can be eliminated; however, these terms result in beneficial effectson performance, particularly at the high angles of attack encountered during combat maneuvers. The engine nozzle may be inclined to increase the benefit, and the input angle can be usedto simulate thrust vector- ing. It should also be noted that it is the gross thrust that is being inclined, not the net thrust. This is significant because the magnitude of the gross thrust is twoor more times that of the net thrust. Gravitational acceleration can be held constant (usually at the sea level value)or, more realisti- cally, can be allowed to vary with altitude usingthe inverse-square variation. The effects of centrifugal force due to flight-path curvatureof the and contribution of the Earth's rotational velocity are also available but are insignifi- cant for the missions being considered. Indeed, the latter effect is canceled on a radius-type mission.

.. . APPENDIX B

DESCRIPTION OF PROGRAM OUTPUTS

Thisappendix contains descriptions of theoutput options and the specific output parameters. Sampletabulations are presentedwhich illustrate both the minimum summary outputand the extensive detail of thepoint-by-point output.

OUTPUTOPTIONS

Theamount oftabulated output resulting from a given set ofcalculations is controlled by inputs.The minimum output from thecalculations for a partic- ularprofile is illustratedfor each profile. A typicalexample is shown in table 4 forprofile 1. (Definitionsof output parameters are given at theend of thisappendix.) The tabulatedoutput for a given profile can be progres- sivelyincreased until each calculated flight point during the climb is represented. A sample ofsuch a flight-pointtabulation is presentedin table 15. Thisflight point is at the endof the climb for theaircraft used to describe mission1. The tabulationincludes 18 state variablesand acceleration rates. An additionaloption is availablewhich controls the printout of interimresults duringthe iterations required to balancethe equations of motion at eachpoint alongthe climb profile. Such a listing is usefulin the analysis of problems that may develop in some extreme cases.

The performancefor many individual aircraft or mission-profile combinations may be calculatedin series (upper limit of 50) . For thistype of produc- tionrunning, it is convenient to request the minimum mission-profileprintout and to havethe results summarized as indicatedin table 16.The calculations of a particular profile are represented by a singleline containing selected parameters which identifythe mission and the aircraft and showkey results. Thisform of output can be used to scan the results of many calculations in order to observesignificant trends. The eleven cases shown in table 16 are for the sample missions described in this report and are in the same order as theresults of table 14,with the exception of the second case. The dash radius ofthe second case is theexact performance capability for missionprofile 1 as referred to in the main text and illustrated in figure 11.

DEFINITIONS OF OUTPUT PARAMETERS

Thefollowing is a list of theabbreviations, and their definitions, for the parameters usedin the tabular outputs. The parameters as indicatedon the tables, may bein either the SI or foot-pound-secondsystem of units.

PARAMETER DEFINITION

ACC FUEL Accelerationfuelweight

ALPHA Aircraftangleof attack

28 APPENDIX B

PARAMETER DEFINITION

AVCRH Average cruise altitude

AVGAM Average flight-pathangle

AVG COMBAT PS Averagecombat specific power

AVG TR Average turnrate

AVG TRAD Average turnradius

AV STTRl Average sustainedturn rate, first requirement

AV STTR2 Average sustainedturn rate, second requirement

BF Breguet cruisefactor

CD Aircraft drag coefficient

CL Aircraft lift coefficient

COMFUELI Combat fuel-allowance weight

CRM Flight cruise Machnumber

CR RD Cruiseradius

DASH RD Dash radius

DW1 Take-off fuel weight

ES Aircraft specific energy

ESF Engine sizingfactor

FEXT External fuel weight

FFML Fuel flow at military power

FFMX Fuel flow at maximumpower

FINT Internal fuel weight

H Flight altitude

H1-H16 Altitude at profile points 1-16

LOD Aircraft lift-drag ratio

M Flight Machnumber

29 APPENDIX B

PARAMF,TER DEFINITION

MID CR WT Aircraft weight at midrange

MI ss Mission-profile identification number

OWE Aircraft operating weight empty

PER COMBAT Percentof specified combat fuelweight

PER LOITER Percentof specified loiter time

Q Flight dynamic pressure

RES Reserve-f uel weight mTFEXT Retainedexternal fuel weight

RNG/KG Range loss per unit fuel mass

ROC Rate ofclimb

R1 -R16 Radiusfor profile points 1-16

S Aircraft wing area

T Aircraft thrust

TFF Total fuelflow, all engines

TMD Thrustminus drag

TM1 -TM16 Time at profile points 1-16

TOGW Aircrafttake-off gross weight

TOW Aircraftthrust-weight ratio

TTNET Totalengine net thrust, all engines

TURN FUEL Turn fuelweight

V Flightvelocity

W Weight wos Wing loading,weight per area

WTANKS Weightof external tanks

WT1 -WT16 Weight at profile points 1-16

30 REFERENCES

1. Standardfor Metric Practice. E 380-79, American Soc. Testing & Mater., c. 1980.

2. Rutowski, Edward S.: EnergyApproach to the GeneralAircraft Performance Problem. J. Aeronaut. Sci., vol. 21, no. 3, Mar. 1954, pp. 187-195.

3. Perkins,Courtland D.; and Hage, Robert E.: AirplanePerformance Stability andControl. John Wiley & Sons,Inc., c.1949, pp. 185-186.

31 TABLE 1 .- MISSION MODULES

-. ~ Module Type Profile description Tank-drop logic

" . .. - - .. " ...... ~~ - Rad ius Hi-Lo-Lo-Hi: Air superiority Yes Radius Hi-Lo-Hi: Fighterescort No Radius Hi-Hi; Combat air patrol Yes Range Hi-Lo-Lo-Hi: Long-range penetration No Range Hi: Long-range cruise Yes ~- _____c. " " . 1____" - .. - . -

TABLE 2.- RESERVE-FUEL MODES

"" . "" ". ~ Description

~. . -~- .. . - . ." ~ .. ~"-~ Fixed fuel weight

" ". .. ". ~" Fraction of internal fuel

. ~" Fraction of total fuel .. " -~~____~ " - .- - - Fraction of take-offgross weight

." . ~ "" . ." . - ~- Loiter at a given altitude for time interval ___. .. "" ~ .. "_ Time interval at military-power fuel flow plus I time interval at maximum-power fuel flow I

" - . .. " ______. .J

32 TABLE 3.- MISSIONPROFILE 1: AIR SUPERIORITY;HI-LO-LO-HI

." Profile points Description Inputs

1-2 rake-off f ue 1 allowance 3ptions

2-3 kcelerate and climb to start of cruise Climb schedule

3-4 3utbound cruise(with tanks, if carried) Cruise Mach number

4-5 Drop tanks(if carried) Tank weight

5-6 Outbound cruise(without tanks) Cruiseradius

6-7 Descend,no range or fuel """""""""""

7-8 Outbound dash Mach numberl altitude, radius

8 - 10 Weapon expended Weapon weight

10 - 11 Combat fuelallowance Options

11 - 12 Inbound dash Dash radius

12 - 13 Accelerate and climb to cruise altitude """"""""""~ 13 - 14 Inbound cruise """"""""""- 14 - 15 Descend Increment weight, range time

15 - 16 Reserve-fuelallowance Options ~.." . . . ~~..- ~ ~" 'Optional tank drop logic described in main text.

I TABLE 4 .- MISS ION DETAILS FOR PROFILE 1 (a) Primary mission

+**+* FOR TOGW= 219.25 T/w= .930 w/S= 3.?b *+*e+

++* TAKEOF6 FUEL‘ 4.8q ***

*** TOTAL RESEQVES’ 3.93 ***

OPTION 1 CdUISE RADIUS=llll.Z AT MACH=1.60 04SY RADIUS=298.9 AT MACH= .WO COM9AT FUEL W1.r 15.40 AVG COMr3AT 553.95PS=

UT1 = 21’3.25UT2= 214.37 YT3= 197.71 WT4= 197.71 YT5= 19S.57 uTb= 177.00 UT7 = 177.00 YTY= 161.93 UT’)= 161.93 WT10= 160.15 WT11= 144.75UT12= 130.7b wT13=121.94 YT14= 111.13 WTlS= 11O.bR WT16= 106.76

R1 = 0.00 RZ = 18.52 R3 = 79.59 R4 = 79.59 95 = 7H.59 P6=11]1.15 R7 =llll.lH RH =1410.03 R9 =14ln.O:3 R10=1410.03Rll=1410.03 R12=11]1.19 ~13=1071.08 RI*= 37.04 Rls= 0.00 ~16= 0.00

H1 = 0. H2 = 15. H3 = 15453. H4 = 15453. Y5 = 15453.H6 = 16153. H7 = 610.H8 = 610. H9 = 1524.H10=1524. till= 610,H12=610. H13= lU5ll. H14=19022.H15= 15. H16= 0.

34 TABLE 4.- Concluded

(b) Alternatemissions

OPTION P CPUISERADIUS=llll.P DASH R4UlUS=185.2 COYdAT FUE.L= 26.43 PE? C3MbAT=171.59

UT1 = 219.25 dT2= 214.37 UT3= 197.71 WT4= 197.71 uT5= 195.57 WTb= 177.00 UT7 = 177.00 UTd= 167.65 UT9= 167.65 wTlo= 155.87 WTll= 139.44 WTl?= 130.78 WT13= 121.94UT14= 111.13 UT15= 110.68 UT16= 106.76

R1 = 0.00 R2 = 1R.52 R3 = 78.59 R4 = 79.5Y RS = 7A.59 R6 =1111.19 R7 =1111.18 R8 =1296.38 R9 =1296.3A R10=1?Yh.jB Rll=1?95.38 R12=1111.18 R13=1071.04R14=37.04 R15= 0.00 Rl6= 0.00

H1 = 0. H2 = 15. H3 = 15453.H4 = 15453. H5 = 15453. Hb = 16153. H7 = 610. HB = 610. H9 = -1524.H10=1524. Hll= 610. Hli= 610. H13=18511. Hl4= 19022.H15= 15. Hl6= 0.

OPTION 3 OASH RADIUS=185.2 CRUISEHAOIUS=1497.0 COHHAT FUEL= 15.40

I TABLE 5 .- MISSIONDETAILS MIR PROFILE 1 WITH NO RETURN DASH

(a) Primary mission

36 TABLE 5 .- Concluded

(b) Alternatemissions

37 TABLE 6.- MISSION PROFILE 2: FIGHTERESCORT; HI-LO-HI

~ .~ Profile points Description Inputs - .. - 1-2 Ta ke-of f fuel allowance Options

2-3 Accelerate and climb to start of cruise Climb schedule

3-6 Outboundcruise1 Cruise Mach number andradius

""""""""" i 6-7 Descend,no range or fuel I 7 - 10 Weapon expended Weapon weight

10 - 12 Combat fuelallowance Options

12 - 13 Accelerate andclimb to cru.ise altitude """""""""

13 - 14 Inboundcruise """""""""

14 - 15 Descend Increment weight, range, time 15 - 16 1 Reserve-fuelallowance Options

" . . . ~ " - . . - - L' 'Tanks, if carried, are retainedthroughout mission.

38 TABm 7.- MISSIONDETAILS FOR PROFILE 2

**** UNITS FOR OUTPUT DATA ****

SYSTEM ALTITUDEDISTANCE FORCE TIME ANGLE PRESSURE VELOCITY FUEL FLOW SI M KM KN MIVKP OEG M/ S KG IS FP S N FT MI HINLQF DEGFpS PSF Lewn

**IN TOFUELISLSFFMLZ 0.0000 SLSFFHXz 0.0000 DU1=4.A8

**e TOTALRESESVESf 3.95 ***

39 TABLE 8.- MISSIONPROFILE 3: COMBAT AIR PATROL; HI-HI

" " ~- . . - - -. . -~... - ~ ~ . . .~ - .. -- ." -- . . Profile points Description Inputs

" ~" " ". .". ~ .-_ - ~ "- - - 1-2 Take-of f fuel allowance Options

2-3 Accelerate andclimb to start of cruise Climbschedule

3-4 Outbound cruise(with tanks, if carried) Cruise Mach number andradius

4-6 Drop tanks(if carried)l Tank weight

6-9 Loiterfor given time Mach number, altitude

9 - 10 Weapon expended Weapon weight

10 - 13 Combat fuelallowance """""""""

13 - 14 Inboundcruise """""""""

14 - 15 Descend Increment weight, range , time

15 - 16 Reserve-fuel allowance Options

. .. . -- - - " 'Tanksdropped at end of cruise.

40 TABLE 9.- MISSION DETAILS FOR PROFILE 3

+++ CASES7.00 2003MISSION SUMMARY TOGU= 219.25 OYEZ 106076 S= 66.81 €SF= 1.0000 PAYLOADS 21.40FEXT=87.19FINTI -1.78 UTANKSZ 2-14

++++ UNITS FOR OUTPUTDATA ++++

SYSTEM ALTITUDEDISTANCE FORCE TIME ANGLEPRESSURE VELOCITY FUEL FLO* SI M KM KN WIN DEG KPA MIS KGIS FP S FT N MI LBF MIY DEG PSF FPS LPYIH

++IN TOFUEL9 SLSFFMLs 0.0000 SLSFFYX= 0.0000 OUl= 4.88

+++ TOTAL RESERVES= 3.93 ++4

+ OPTION 1 MISSIONRADIUS= 796.5 AT MACH= .85 LOITERFUEL UT= 43.47 LOITER !+?= 2.00

UT1 = 210.25YTE= 214.37 uT3= 205.89 UT4= 180.86 UT5= 178.72 WT6= 176.72 uT7 = 135.25YT8f 134.05 UT9= 126.22 YT10= 124.45 wTll= 124.45UT12= 124.45 UT132124.45 UT14r 111.13 WTlS= 110.68 UTl6= 106.76

R1 = 0.00 R2 x 18.52 R3 2 33.59 R4 = 796.45 R5 = 796.45R6 = 796.45 R7 2 796.45 R8 796.45 R9 = 796.45 R10= 796.08 Rll= 796.06R12= 796.08 R13' 796.08 R14~37.04 R15= 0.00 R16= 0.00

Hl 0. H2 15. H3 = 7163. H4 8792. H5 = 8792. H6 = R792. H7 = 9144. H8 = 9144. H9 = 9144. H10= 9144. H11=9144. H12=9144. H13- 11948. H14= 12854. H15Z 15. H16= 0.

ACC. FUEL= 1.20 COMBATTOT. FUEL= 9.03 RE TF EX T= 0 .oo

+ OPTION2 MISSION RADIUS'740.8LOITER FUEL= 46.20 LOITER HR' 2.12

UT1219.25 UT2x 214.37 UT3 205.89UT4= 182.58 UT%1A0.44 YT6' 1P0.44 UT7 = 134.24 UT8= 133.03 uT9= 125.21 wTlO= 123.43 UT11' 123.43UTlZ= 123.43 UT13= 123.43 UTl4= 111.13 WTlSs 110.68 W116= 106.76

R1 = 0.00 R2 = 18.52 R3 = 33.59R4 = 740.79 95 = 740.79R6 = 740.79 R7 740.79 R8 f 740.79 R9 740.79R10= 740.79 Rll= 740.79R12z 740.79 R13=740.79 R14= 37.04 Rl5= 0.00 R16= 0.00

nl = 0. H2 = 15. H3 = 7163.H4 = 8792. HS = 8792. H6 = 8792. H7 = 9144. H8 = 9144. H9 = 9144.H10= 9144. H11" 9144. H12= 4144. H13=12917.H14312854. H15=15. H16" 0.

PER LO1 TERr106.06 RE TF EX T= 0 .o 0

I TABLE 10.- MISSIONPROFILE 4: LONGRANGE PENETRATION; HI-LO-LO-HI

Profile points Description Inputs

" 1-2 Ta ke-of f fuel allowance Options

2-3 Accelerate andclimb to start of cruise Climb schedule

3-4 Outbound cruise1 Cruise Mach number

4-5 Refuel Tankerdata

5-6 Outbound cruise Cruiserange2

6-7 Descend Scaledincrements

7-8 3utbounddash Mach number, a1ti tude, range

8 - 11 Meapon expended Weapon weight

11 - 12 Cnbound dash !4ach number, altitude, range

12 - 13 lccelerate and climb to cruise """""""""""

13 - 14 Cnbound cruise 3ange

14 - 15 Iescend Cncrements

15 - 16 teser ve-f uel allowance Iptions

" ~~~ -. .. - -" .. - . .. loutboundrefers to pre-targetevents, inbound refers to post-target events. 2A, B,C, and D aredesired range increments.

42 TABLE 11 .- MISSIONDETAILS FOR PROFILE 4

**I* UNITS FOROUTPUT DATA *o**

SYSTEMALTITUUE OISTANCE FOQCE TIME ANGLE,PRESSU'?E VtLOCITY SI M KM Khl MIY OEG KPA MI5 FPS FT r4 MI LRF WIN DEG PS F FD S

*** TAKEOFFFUEL= 4.RA ***

*** TOTALRESERVES= 3.93 **a

43 TABLE 12.- MISSIONPROFILE 5: LONG-RANGE CRUISE

r ." Profile points Description Inputs - 1-2 Take-off fuel allowance Options

2-3 Accelerate and climb to start of cruise Climbschedul e

3-4 Outbound cruise (withtanks, if carried: Cruise Mach number

4-5 Drop tanks (if carried) Tank weight

5-7 Outbound cruise(without tanks) """""""""

7 - 13 Midrangestation """""""""

13 - 14 Continuedcruise Cruise range

14 - 15 Descend Incrementweight, range, time

15 - 16 Reserve-fuelallowance 3p t ions

Tanks dropped when empty.

44 TABLE 13.- MISSION DETAILS FOR PROFILE 5

WISSION RADIUS= 1997.54

45 TABLE 14.- SUMMARY OF MISSION PROFILE RESULTS

Seetables 1 to 13 foralternate profiles and details

Mission ' Cruise Externalfuel weight, hnbat fuel weight, Mission distance1 TOGW Table profile Mach number kN (lbf) kN (lbf) kN (lbf) km (n. mi.)

1 - Airsuperiority I 1.60 219(49 290) 21.40 (4810) 15.40(3463) 1410(761) 4 15.24(3422) 22023(1093) 5

. -- ". ~ ". 2 - Fighter esmrt 0.85 196(44 000) 0 16.30(3664) 1165(629) _" 219(49 290) 21.40(4810) 16.31(3664) 1406(759) 7

. - .. " 3 - Combat air 0.85 196(44 000) 0 8.86(1991) 468(253) patrol 219(49 290) 21.40(4810) 9.03(2029) 796(430) -9- 1 ~. " 4 - Long-range 198(44 600) 0 0 2041(1 102) penetration 33532 (1 907) ---11 I ___. .. . 5 - Long-range 1 0.85 219(49 290) 21.40(4810) 0 3837(2088) cruise 44017(2169)

lRadius or range,see profile. 2No returndash. 3With refuel. 4Climb at reducedpower.

46 TABLE: 15.- SAMPLE OF TABULATED RESULTS FOREACH FLIGHTPOINT

CASE VTSS FEXTFINT ?ES CR OD OATH 30 CnMFlJEL %U r(N Kty K"1 KH KI( K'J

1.00 2001. 2lY.3 3. ?8 .93 10 6.76 -1.73 a7.1Y 21-40 3.93 1111.2 299.9 15.40

2.00 2001. 219.3 3.2a .q3 10 6.76 -1.7p 97.1Y 21.40 3.93 111 1.2 30 3.5 15. 40

3.00 2001. ?13.3 3.28 .93 10 6. 76 -1.7X 97.1321.40 3.93 1111.2 91 2. n 19. zk

4.00 7002. 1Y3.7 2.93 1.04 10 5. 74 -1.7P 0.00L(7.19 3 .WS 1164.6 0.0 16.3U

5.00 2002. 2 19.3 3. ,?8 .93 10 6.76 - 1.7n 87.1921.40 3.95 140 6. 0 0.0 I 6. 30 0.00 2003. 1 Y5.7 2. 93 1. 04 16 6. 7b - 1.7R 87 -1 3 0. fJ0 3.85 467.8 0. 0 9. Yh 2 19.3 7.00 2003. 3. 28 .93 10 6. 76 - 1.7k 67.1921.40 3.93 796.5 0.0 Q. 03

'3.00 2004. 1YY .4 2.97 1. 03 10 6. 7b -4.45 b3.6 5 21. 40 3.937046.Y 370.4 0. no

9.00 2004. 198.4 2.97 1.03 106.74 -4.45 43.65 21.40 3.93 3532.0 370.4 n. 00

10.00 2005. 219.3 3.28 .93 106.76 1.7a 87.19 21.40 4.01 3F367.3 0.0 0. no

11 -00 2005. 219.3 3.28 .93 10 6.76 1.7n 87.19 21.40 4.01 4017.4 0.0 n. on

1 TOTAL RANGL FOR MISSION PQOFILE 4 AND 5.

47 Ill I I I I, . .. I

- . . . - . .. . 0 .5 1.o 1.5 2.0 Mach number

Figure 1.- Climb Mach-number-altitude profile for sample mission performance.

48 Range, n.mi. 10 20 10 30 40 I I I I 2.0

0 lo

50 220 48 33- 210 5 46 B 200 B 4.4 i 90 20 30 40 50 60 70 80 Range, km

Figure 2.- Climbperformance to start ofcruise. Initial weight = 21 4 kN (48193 lbf) .

49 Ipitial weight X lbf 30 40 60 I I i 20 - 60

I 18 60 16

14 40

80 A

f 60

200 la46

I D4

120 120 160 200 240 Initial rei@& kN

Figure 3.- Climb-segment data.Variation of start-of-cruiseconditions with initial climbweight.

50 Aircraft weight X IO-’, lbf 20 30 40 50

3200 7000

2800 6000

2400 5000 2000 4000 C / 1600 3000 1200 100 1 LO 180 220 Aircraft weight, kN

Figure 4.- Loiter-segment data. M = 0.70; Altitude = 9144 m (30 000 ft).

51 External weapons v Off “-0”- On

Aircraft weight X lo-’, lbf 20 30 40 50 I I I 1

.I2 ! .11

.IO

B .38 L +2 d .09 n L

.08

.30 I “L80 120 160 200 240 Aircraft weight, kN

Figure 5.- Dash-segmentdata. M = 0.90; Altitude = 9144 m (30 000 ft).

52 Combat weight X lo-', lbf 20 30 40 50 I I I 1

2500 0 a, 2000 < 1500 - a" 1000

5000 R 4000 $ .PIM rv 3000 P d

2000

100 140 180 220 Combat weight, kN

Figure 6.- Combat segment data, option 1. A change inspecific energy of 43.9 km (144 x 103 ft),at M = 1.2 andAltitude = 1524 m (5000 ft).

53 tp L Aircraft weight X lo-', lbf 20 30 40 50 I I I 1 I 2000 t 1500

Maneuver Acceleration - Combat 3 I 1000 .r( t 500

0 100 140 180 220 Aircraft weight, kN Figure 7 .- Combat segment data, option 3. An acceleration from M = 0.75 to 1.00 and a 2-minutecombat at M = 1.0, both at an altitude of 9144 m (30 000 ft).

54 Mach number v 0.90 “-0“- 1.20

250 800 c 200 600

150 ( 400 100

200 50

0 0

-50 -200

-100 1 2 3 4 5 6 Maneuver load factor

Figure 8.- Determination of sustained maneuver loadfactors for two Mach numbers at an altitude of 91 44 m (30 000 ft). Aircraftweight is 160 kN (36 000 lbf) .

? ?, Maneuver 0 Acceleration Sustainedturn, M=0-90 0 Sustained turn, M=1.20

Combat weight X lo-', lbf 20 30 40 50 ~ " ~ ." . - ~ .- - I I I 1 6

0 100180 140 220 Combat weight, kN

56 External storor Weaponsandtanka """_ weapons Oprr "- Chap, approximate 0 Clean, exact

Aircref't weight X lo-, Ib! 26 30 36 40 46 I I I I 3

120 140 160 180 200 Aircraft wefeht, kN

Figure 10.- Variation of cruise Breguet factor and altitude with aircraft weight for aircraft with and without external stores. M = 1.60.

57 Radius, mmi. 0 200 800

-7 I

--- " -I--- I"~ T-I- I t. b 1 I I Normal results Special option

0 400 800 1600 Radius, km

Figure 11.- Results for mission profile 1 with externaltanks. Cruise at M = 1.60: dash at M = 0.80; specialoption calculates exact radius.

58 Radius, n.mi. 0 200 400 600 am 1200 1000 I 1 I I 1 I I I I 11' ' I/

240

200 k 3 I $, 160 I .r( I.

120 I

ao I 0 400 800 1600 2000 2400 Radius, km

Figure 12.- Resultsfor mission profile 1 withno return dash. Aircraft withexternal tanks; cruise at M = 1.60;dash at M = 0.90 at Altitude = 91 44 m (30 000 ft).

59 Radius, n.mi. 0 200 400 600 800 -i 1 I

r 240 r External tanks

- v No "-+J."- Yes

80 I 0 400 800 1200 1600 Radius, km

Figure 13.- Results for missionprofile 2 withand without external tanks. Cruise at M = 0.85.

60 Radius, n.mi. 0 100 200 300 400 500 I I I I I I

" i

.. i 1 .cc -I-

~ 200 400 600 800 1000 Radius, km

Figure 14.- Results for mission profile 3 withand without external tanks. Cruise at M = 0.85; 2-hour loiter at combat station.

61 hrel n U - Tanker "- e-" Receiver

Range at end of refuel, n.mi. 0 400 800 1200 1600 r 1 I I I I I -1

u ff I-12 4, -a

-4

-0 0 1 2 3 Range at end of refuel, Mm

Figure 15.- Determination ofoptimum fuel-transfer range.Refuel at M = 0.75 at an altitude of 7620 m (25 000 ft).

62 Range, n.mi. 0 500 1000 1500 2000 i- I 1 I 1

240 r Refueled " -"e"- 200

53 r 3 160 I w -d dl

L Q b '. 120

0 1 2 3 4 Range, Mm

Figure 16.- Resultsfor mission profile 4 withand without refueling. Cruise and refuel at M = 0.75.

63 Range, n.mi. 0 500 1000 1500 2000 1

T[ I

240 I I I I Climb power V Maximum "- 8 "- Reduced 200 !

120 I 9 80 I I I 0 1 2 3 4 Range, Mm

Figure 17.- Results for mission profile 5 with externaltanks. Cruise at M = 0.85.

64 " - . . -. -. . 1. Report No. 2. Government Accession No. 3. Recipient's Catalog No. NASA TP-1837 ~. .. " - - - .. .. - . 4. Title andSubtitle 5. Report Date A COMPUTER TECHNIQUE FOR DETAILED ANALYSIS OF MISSION RADIUS AND MANEUVERABILITY CHARACTERISTICS OF FIGHTER AIRCRAFT - 7. Author(s1 Performing Organization Report 1 8. Willard E. FOSS, Jr. 10. Work UnitNo. 9. PerformlngOrganization Name andAddress NASA Langley Research Center 11. Contractor Grant Hampton, VA 23665 t"----No. 13. Type of Report andPeriod Co\ Sponsoring Agency Name and Address and Name Agency12. Sponsoring Technical Paper NationalAeronautics and Space Administration Washington, DC 20546 Code Agency 14. Sponsoring

~~ 15. SupplementaryNotes

16. Abstract A computer technique to determinethe mission radius and maneuverabilitycharacteristics ofcombat aircraft has been developed. The technique has beenused at the Langley Research Center to determine critical operational requirements and tl areas in which research programs wouldbe expected to yield the most beneficial results. In turn,the results of research efforts havebeen evaluated in terms of aircraft performance on selected mission segments and for complete mission prc files. Extensive use of thetechnique in evaluationstudies indicates that the calculated performance is essentially the same asthat obtained by theproprietal programs in use throughoutthe aircraft industry.

~~ - - 17. KeyWords (Suggested by Author(s) ) 1 18. Distribution Statement Aerodynamics Unclassified - Unlimited Mission performance I Aircraft combat Maneuverability Subject Category 0 ~ 19. Security Classif. (of thisreport1 PTSGurityClassif. (of this page) I Unclassified 64 - ". . For sale by the National Technical Information Servlce. Springfield, Vlrglnla 22161

NASA-Langley, 1981 4 National Aeronauticsand THIRD-CLASSBULK RATE Postage and Fees Paid National Aeronautics and Space Administration Space Administration NASA451 Washington, D.C. 20546

Official Business Penalty for Private Use, $300

3 f ~UIA~ 039981 SO09030S DkPT OF THE AIR FORCE AF WEAPUNS LAGORATORY ATTN : TECHNICAL 1 IBKARY 1 SUL ) KIRTLANDAFS NH 87217

TER: If Undeliverable(Section 158 .. Postal Manual) Do Not Return