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Old 3rd Jun 2011, 09:22
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bookworm
 
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2°)Can someone explain me why the speed for max range is equal to 1,32 Vmd for a jet?
Here comes the calculus... (^ is to-the-power-of)

If the drag curve has the shape D = V^2 + 1/V^2 (parasite drag + induced drag), then its minimum can be found by differentiating and finding the zero. So the minimum is at 2*V - 2/V^3 = 0, in other words V = 1. So for that curve, minimum drag occurs at V = 1. Assuming constant thrust-specific fuel consumption, that gives you best endurance.

The curve D/V represents the drag per unit distance travelled, and if you want to maximise range you minimise drag per unit distance travelled. D/V = V + 1/V^3 so the minimum is where 1 - 3/V^4 = 0, or V = 3^(1/4) = 1.32. Assuming constant thrust-specific fuel consumption, that gives you best range.

You can stick prefactors in front of the terms in the drag curve, but they cancel out and don't change the ratio between the minima of the two curves.

So the 1.32 ratio applies when:

* the drag curve has the shape V^2 + 1/V^2 (usually a pretty good approximation)
and
* thrust specific fuel consumption is constant (a truly lousy approximation for modern engines, but loved by text books).

Last edited by bookworm; 3rd Jun 2011 at 11:58.
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