Endurance & maximum range speeds

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Maximum endurance and maximum range speeds are related by the factor 3^0.25, but a clear derivation is sought. A provided MIT article addresses the origin of this relationship. However, the discussion highlights that the dynamics can vary between power-producing and thrust-producing powerplants. Additionally, real-world applications of these principles are more complex than theoretical models suggest. Understanding these nuances is essential for accurate analysis in aviation contexts.
NTW
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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...
 
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I think it's different for power-producing and thrust-producing powerplants.
 
Aero_UoP said:
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.
 

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