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Specific Range & Specific Endurance

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  • Specific Range & Specific Endurance

    Hi all!

    Could someone please help with a small stumbling block? I can't get how the Range = Distance/Fuel is adjusted to become Specific Range = TAS/Fuel Flow. Same obviously for the Endurace.
    I've tried to rearrange the formula to the best of my ability but just amn't getting it. I know this isn't vital to know and I could just memorise the SR= TAS/Fuel Flow but it's still just bothering me.

    Any help would be greatly appreciated.

  • #2
    SAR = TAS (kts/hr)/FF(kgs/hr)


    • #3
      Agh! I see. The times simple. Thanks Colin


      • #4
        I knew there was something else that was confusing me. Where does the time(hr) come into Fuel Flow? I realise it's obvious that fuel flow would be in Kg/h but the formula for fuel flow in the books is Fuel Flow = Amount of Fuel per Unit of Thrust (Presumably Kg/N)* Total Thrust (N). I assumed that from this Fuel Flow is in Kg only. I realise I must be missing something.


        • #5
          I cover this at the brush up. For now I'll just deal with the jet.
          I should have said for range it's nm/kg and for endurance it's kg/hr
          There are two elements to consider for range flying, the airframe and the engine so we need to look at two formula and then combine them.
          SAR = TAS/FF
          SFC = FF/TH (SFC is the mass of fuel burnt to develop x amount of thrust)
          Let's transpose the latter and we get
          SFC x TH = FF
          In the cruise in level non accelerating flight the thrust is balanced by the drag so it's equally correct to say
          SFC x Drag = FF
          Now substitute this value of FF into the first formula and we get:
          SAR = TAS/Drag x 1/SFC
          The TAS/Drag is the airframe consideration and the 1/SFC is the engine consideration.
          Down at SL under ISA conditions TAS = EAS so we can plot this on the drag curve and we get the best ratio of EAS to drag at 1.32VMD (the tangent to the drag curve)
          So on a jet we fly at 1.32VMD for range and that satisfies the airframe consideration.
          Next we must operate the engine at it's best SFC, typically around 90% of maximum thrust, the SI units are KGS/NEWTONS of TH/HR
          So we can say our best range, nm/kg, is dependent on the best TAS/Drag ratio and the thrust (and therefore FF) that just opposes the drag at that ratio.
          Endurance is kg/hr.
          We're just going around in circles keeping the FF at a minimum where the thrust just opposes the drag at VMD.
          For both conditions we need to consider the optimum altitude but let's leave that for now.