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Re:Launch HN: H3X (YC W21) – High power density electric air... by mliben on Monday February 22, 2021 @09:54PM (#26233363)
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).

Re:Launch HN: H3X (YC W21) – High power density electric air... by gnramires on Tuesday February 23, 2021 @04:14AM (#26235281)
> 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).

Re:Launch HN: H3X (YC W21) – High power density electric air... by mliben on Tuesday February 23, 2021 @12:15PM (#26239868)
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

Re:Launch HN: H3X (YC W21) – High power density electric air... by gnramires on Tuesday February 23, 2021 @05:00PM (#26243472)
I stand happily corrected :)
Re:Launch HN: H3X (YC W21) – High power density electric air... by Retric on Monday February 22, 2021 @10:03PM (#26233427)
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.
Re:Launch HN: H3X (YC W21) – High power density electric air... by mliben on Monday February 22, 2021 @10:31PM (#26233550)
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 :)