“Increase the power, reduce the drag and the limit is raised but it is in no way linear past 200 knots . It is very exponential.”

 

Not linear at all, in fact.  At these speeds in the thick air we customarily fly in with aspirated airplanes and with the weight and aspect ratio of the wings, the total drag is almost entirely parasitic drag.   Only a vanishingly small amount of induced drag (drag arising from lift) occurs at the speeds discussed. 

 

This means that to a very good approximation, with a propeller airplane, power (shaft horsepower) goes as the cube of speed.

 

So it is cubic curve.

 

However…. One can linearize the curve for small deviations without incurring much of an error (mathematically throw away the third order and higher terms) to arrive at a simplification for constant conditions (same drag coefficient, same flight conditions) –

 

Which is:

 

For a 1% increase in speed, you need 3% more power.

For a 2% increase in speed, you need 6% more power

For n% more speed, you need 3n% more power for small n (say less than 10%)

 

Test - for 10% more speed, the simplification yields 30% more power.  Compare this to 1.1 cubed which is 1.331, or 33.1% more power.  So the simple approximation is not bad.

 

It is MUCH BETTER to reduce drag than increase power.  Unfortunately, for constant power, to get a 1% speed increase requires a 3% drag coefficient decrease, and 2% speed increase requires 6% drag coefficient decrease etc. etc.  (another linear simplification for small changes).

 

No free lunch.

 

Fred Moreno

AKA Captain Tuna, Chicken of the Skies