Endurance Vs Range
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Endurance Vs Range
Hi, Have this confusion about the Endurance and Range for any given drag curve. Is it necessary that on any drag curve, the point of maximum L/D ratio and the Minimum drag speed (Vimd) coincide ? If yes then how will the point of Maximum endurance and the Maximum range differ on this drag curve, and if no then where will these points lie ?
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That is one big question!
In teaching about range and endurance you are trying to get over a complex subject in a simple and easily understood way, and to do this you make several simplifying assumptions about aerodynamics, drag, engines and fuel consumption. With those caveats in place, let's see how it goes, for jets at least.
If you assume that profile drag is proportional to Vsquared and induced drag proportional to 1/Vsquared and add them together you finish up with the well known total drag curve. Next assumption is that fuel flow is directly proportional to thrust and therefore to drag in level flight. If this is so, then flying at your mimimum drag speed will get you minimum thrust, minimum fuel flow and longest endurance. As you are in level flight and lift is fixed at equal to weight as drag is at a minimum this speed, by definition, gives the best lift/drag ratio.
Range is at its greatest when air miles flown over fuel used is at a maximum. This speed is found at the tangent from the origin to the total drag curve. The slope of the tangent is drag over V, so at its minumum V/drag is a maximum, and so is V/thrust and V/fuel used.
If your drag curves were mathematically exact this point would be at exactly1.32 times the minimum drag speed, but it is more realistic to say "approximately 1.32".
As the effects of transonic flow begin to distort the drag curves at higher Mach number you would still get max endurance at the minimum drag speed and best range at the tangent to the now modified drag curve, but these speeds will change.
How far do you want to go?
Dick
In teaching about range and endurance you are trying to get over a complex subject in a simple and easily understood way, and to do this you make several simplifying assumptions about aerodynamics, drag, engines and fuel consumption. With those caveats in place, let's see how it goes, for jets at least.
If you assume that profile drag is proportional to Vsquared and induced drag proportional to 1/Vsquared and add them together you finish up with the well known total drag curve. Next assumption is that fuel flow is directly proportional to thrust and therefore to drag in level flight. If this is so, then flying at your mimimum drag speed will get you minimum thrust, minimum fuel flow and longest endurance. As you are in level flight and lift is fixed at equal to weight as drag is at a minimum this speed, by definition, gives the best lift/drag ratio.
Range is at its greatest when air miles flown over fuel used is at a maximum. This speed is found at the tangent from the origin to the total drag curve. The slope of the tangent is drag over V, so at its minumum V/drag is a maximum, and so is V/thrust and V/fuel used.
If your drag curves were mathematically exact this point would be at exactly1.32 times the minimum drag speed, but it is more realistic to say "approximately 1.32".
As the effects of transonic flow begin to distort the drag curves at higher Mach number you would still get max endurance at the minimum drag speed and best range at the tangent to the now modified drag curve, but these speeds will change.
How far do you want to go?
Dick
