Endurance & maximum range speeds

[NTW]

Hello all...

I know that it can be derived, from first principles, that maximum endurance and maximum range speeds are related by the factor 3^0,25.

But I haven't been able to find a derivation. Could anyone here help...?

Thanks in advance...

 

[SteamKing]

How about this article:

http://web.mit.edu/16.unified/www/FALL/thermodynamics/notes/node99.html

 

[Aero_UoP]

I think it's different for power-producing and thrust-producing powerplants.

 

[AlephZero]

I think it's different for power-producing and thrust-producing powerplants.

The link answers the OP's question about where the "magic number" came from.

But nothing about aircraft is that simple in real life.