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Old 30th January 2008 | 09:17
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BEagle
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Joined: May 1999
: ATP+Mil
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From: Quite near 'An aerodrome somewhere in England'
Ah, good old 1.32 (or, to be precise, 1.316074)!

When I went through CFS, the grounskool bod couldn't explain it and just said " 'cos it is!".

So I did a bit of basic mechanics and calculus:

Total drag = Zero Lift Drag + Lift Dependent Drag

i.e. D = AV**2 + BV**-2

To find the minimum drag speed, differentiate with respect to V and equate to zero:

dD/dV = 2AV – 2BV**-3 = 0

Hence VMD =(B/A)**-4


Power is the ‘rate of doing work’, i.e. Work/time or (Force x dist)/time

Hence Power = Force (in this case Drag) x velocity

P = DV

Thus P = AV**3 + BV**-1

Again, to find the minimum power speed, differentiate with respect to V and equate to zero:

dP/dV = 3AV**2 - BV**-2 = 0

Hence VMP = (B/3A)**-4

The relation between VMD and VMP is thusVMD = VMP x 3**-4

and therefore VMD = 1.32 VMP

Sorry if this isn't easy to read - this basic forum doesn't support subscript or superscript notation, hence I've had to use ** as 'to the power of', so **-4 means 'the fourth root of'.

A similar argument will give you the 0.76 answer - it's the reciprocal of the fourth root of 3, i.e. 0.7598357.
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