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.