[mliben]

Yes, the range-optimal speed is where the parasitic drag is equal to the lift-induced drag.

If you go through the analysis, the air density drops out of the range equation if you assume are operating at the range-optimal speed (which is higher at lower air densities).

[gnramires]

> the range-optimal speed is where the parasitic drag is equal to the lift-induced drag

Not quite true -- range-optimal speed is where the sum of those terms is minimal. With some assumptions, this is where the derivative is 0, dDrag/dv = 0, and since derivative is linear, this means: the range-optimal speed is where the (infinitesimal) increase of parasitic drag (with speed) is equal to the decrease of lift-induced drag (in other words, opposite derivatives).

[mliben]

Using the simple drag polar approach,

D = A*v^2 + B/v^2 (D is total drag, first term is parasitic drag, second term is lift-induced drag)

dD/dv = 0 where v = (B/A)^(1/4)

Plug in v = (B/A)^(1/4)

D = sqrt(AB) + sqrt(AB), aka dD/dv = 0 exactly when parasitic drag is equal to the lift-induced drag

[gnramires]

I stand happily corrected :)

[Retric]

That’s only relevant up until you approach the speed of sound. Passenger aircraft are designed to stay subsonic for a host of very good reasons.

[mliben]

Definitely, for sure. Like I said in the other thread, supersonic is a whole other thing, and I don't think anyone is trying to electrify anything supersonic any time soon :)