Speed for maximum range

[Keith.Williams.]

ALEX,

My use of the term "narrow and deep or shallow and wide" was deliberate, but you do not appear to understand its significance.

Let's imagine an aircraft for which CDP is zero and CDI is more than zero (impossible I know, but let's just consider it) If we set aside shock induced drag, then VMD will be at infinity. Now draw a tangent to that curve and it will not touch at 1.32 VMD.

Now let's consider one with CDI zero and CDP more than zero. In this case VMD is zero and the tangent will touch very close to zero. Neither of these cases give a tangent touching at 1.32 VMD.

Now let's look at something more realistic.

Sketch a typical situation with DI and DP crossing below the minimum drag value, and a tangent touching the total drag curve at 1.32 VMD.

Now imagine that we have reduced both CDI and CDP such that VMD remains constant. The whole of the total drag curve will be lower, shallower and and wider. But a tangent will no longer touch the curve at 1.32 VMD. It will touch closer to VMD.

Do the same again and the curve again becomes lower, shallower and wider. The tangent is now even closer to VMD.

Now let's do the opposite. Increase both CDI and CDP such that VMD remains constant. The curve will move upwards and be deeper and narrower. But now the tangent touches at more than 1.32 VMD.

If we now add shock induced drag, the main effect will be to make the right hand side of the curves steeper. This will limit the maximum value of the best range speed. As Old Smokey has pointed out, this could well mean that best range is at a speed lower than the VMD predicted by the x squared + 1/x squared curve.

As I said earlier, 1.32 VMD is simply conventional wisdom. It is not absolutely accurate for all aircraft and it is not set in stone.