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payload range diagrams

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Payload Range Diagrams Explanation of the payload range diagram: The payload range diagram illustrates the tradeoff relationship between the payload and the range of one single aircraft. The payload refers to all the mass that is taken by an airplane, excluding fuel. The structure of an aircraft is designed in order to be sustain a certain amount of loads. These loads depends on the amount of weight which is carried by the aircraft. Hence there is a value for the aircraft maximum take off weight, which can never be exceeded or the frame would collapse. Once the aircraft is loaded with the maximum amount of payload, the amount of fuel that can be embarked to fly a certain range is then limited by the maximum take off weight. Once arrived at such point, any further range is achieved only by reducing the payload, which follows a nearly linear relationship. Still, the amount of fuel that an airplane can carry is also limited. That is the reason that at one sudden point, the linear relationship changes drastically.

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Payload Range Diagrams

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  • Payload Range Diagrams

    Explanation of the payload range diagram: Thepayloadrangediagramillustratesthetradeoffrelationshipbetweenthepayloadandtherangeofonesingleaircraft.Thepayloadreferstoallthemassthatistakenbyanairplane,excludingfuel.Thestructureofanaircraftisdesignedinordertobesustainacertainamountofloads.Theseloadsdependsontheamountofweightwhichiscarriedbytheaircraft.Hencethereisavaluefortheaircraftmaximumtakeoffweight,whichcanneverbeexceededortheframewouldcollapse.Oncetheaircraftisloadedwiththemaximumamountofpayload,theamountoffuelthatcanbeembarkedtoflyacertainrangeisthenlimitedbythemaximumtakeoffweight.Oncearrivedatsuchpoint,anyfurtherrangeisachievedonlybyreducingthepayload,whichfollowsanearlylinearrelationship.Still,theamountoffuelthatanairplanecancarryisalsolimited.Thatisthereasonthatatonesuddenpoint,thelinearrelationshipchangesdrastically.

  • How to build up a payload range diagram:

    1 - Collect all important data Inordertostartbuildingupapayloadrangediagramitisnecessarytoalreadyhavecompletedtheweightestimationcalculations.Youshouldknowaboutthefollowing:WtoWoeWpl

    Point A: ThispointissimplyW(pl,max),atR=0

    Point B: ThispointisW(pl,max),atR=maxformaxpayload

    Point C: ThispointisW(pl)andR(max)whencarryingthemaximumamountoffuel.sincethefueltankshaveamaximumamounttheycancarry,thereisstillspaceforpayload.therefor,W(pl)isnotzeroherewhileW(f)ismaximum.

    Point D: Here,W(pl)=0andW(f)=max.TherangeishigherthanatpointChere,becauseyouflyfurtherwithlessweightaboard.calculations:

  • Point B: ForpointByouwillneedtofocusonBrequetsformula.Really,theonlythingyouhavetodoisfindoutthemaxrangetheairplanecanfly@maxpayload:

    Asyoucansee,mostofthevariablesinthisformulaincludeconstants.Forajetaircraftweshouldbeprovidedwithinformationsimilartothis:

    OuronlychallengeistofindoutwhatW4/W5is,sowecanuseitintheformula.Forthiswemuststartoffusingthisformula:

    Wto(max)=Woe+Wpl(max)+WfStartoffbyfindingoutwhattheamountoffuelistheairplanecantakeonboard@maximumtakeoffweightandmaxpayload.(Note:Woe=We+Wtfo+WcrewandWe=a*Wto+b)Onceyouknowthat,youcanfindoutthefuelfractionWf/Wtofortheaircraft.Youshouldthenbegivenatablecontaininginformationoffuelfractionatdifferentphasessimilartotheoneshownbelow.Yourtaskistofindoutthefuelfractionforcruise(Note:Youmightneedtoincludeloiteranddiversionphases!)

  • Recallthat:

    SowehavealreadyWf/Wto,wecanfindoutMff:M f f = 1

    WFWTO

    OnceweknowMff,wecanfindoutW5/W4.Thentaketheinverseofit,andyoufinallyhaveW4/W5,whichyouneededinordertouseBrequetsformulasandfindpointB.

    Point C ForPointCyoumustbegivenhowmuchfuelyouraircraftcantake@maxWto.Withityoucanthencalculatehowmuchpayloadcanbecarriedbyagainusing:

    Wto(max)=Woe+Wpl+Wf(max)Andthen,therest,yes,youguessedit,isjustthesameprocedureastofindtherangeforpointB:justfollowthis:findfuelfractionfindMfffindW5/W4calculateRange

  • Point D: Inthiscase,allpayloadistakenoutandyouflyatmaxWfinordertoachievemaximumrange.Thereforeourformulaforweightsreducesto:

    Wto=Woe+Wpl+Wf(max)andagainwemustfindWto.Oncedonethat,just,yesyes,repeatwhatyoudidforpointBandC.


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