OK Buster – since you asked!
1. First the 1.32 mystery. Remember that Total Drag is the sum of zero lift drag which increases with the square of speed and lift dependant drag which decreases with the square of speed – or algebraically D=AV²+B/V². To find the value of minimum drag speed, differentiate this expression and equate to zero and you get the result that at minimum drag speed dD/dV=0=2AV-2B/V³. In other words V at min drag = (fourth root) (B/A).
However, for minimum power speed, we are looking for the minimum value of work rate, i.e. the minimum rate of (Force x Distance)/Time - the force in this case being Total Drag. This is the obviously the same as Total Dragx(Distance/Time), i.e. Total Drag x Speed (or rather more correctly, the product of Total Drag and Velocity). Go back to our first equation and you get P=DV=AV³+B/V. Do the same differentiation as before and this time you get the result dP/dV=0=3AV²-B/V², or in other words V at min power = (fourth root)(B/3A). Divide the 2 results algebraically and you find that Vmin drag =V min power x (fourth root) 3. And the fourth root of 3 is 1.316074 – or 1.32!!
2. For endurance, you are interested in the minimum value of fuel burn with respect to time, for range you are interested in the minimum fuel burn with respect to distance. But since fuel burn/distance is the same as fuel burn/time x time/distance, for range you fly at the speed which is the best value of Endurance/Speed. By their very nature, jet and propeller engined aircraft produce thrust and power differently; max endurance in a piston engined aircraft occurs at the lowest practical BHP, IE at the minimum power speed – and hence max range is obtained at the speed equating to the minimum value of BHP/speed – but since BHP is proportional to Total Drag x Speed, then max range is fairly obviously obtained (in theory) at the speed equating to the minimum value of (Total Drag x Speed)/Speed – i.e. at minimum drag speed which is 1.32 x minimum power speed. For a jet engined aircraft which produces thrust pretty well irrespective of speed, similar number crunching and algebra will show that maximum endurance is obtained at minimum drag speed and maximum range at the speed which gives best TAS/Drag ratio – and this equals 1.32 x minimum drag speed.
[ 20 January 2002: Message edited by: BEagle ]</p>