A Challenging Endurance Problem

[hawk37]

Andrewgr2.

When I said max endurance will not be at minimum drag speed, I was primarily meaning that the minimum drag would be at low altitude, at the speed for L/D max. If one believes that thrust vs fuel flow is flat in at this speed, then minimum drag will be max endurance speed. However, the thrust to fuel flow curve depends on the engine, and for those I've seen, at low altitude, at higher speeds the fuel flow for the same thrust is higher. Hence, in this case, the max endurance speed will be slightly lower than the minimum drag speed.
Now let's add some altitude to the flying aircraft. With that comes extra drag due to compressibility. Hence, the minimum drag at that higher altitude is more than the minimum drag at the lower altitudes. A natural conclusion could be that the fuel flow would thus be lower at low altitude than at high altitude, for max endurance. This conclusion is normally wrong. If you look at holding charts for aircraft with jet engines, you will see that the fuel flow usually decreases with altitude. Now I know that holding speed is not necessarily max endurance speed, but it is normally close enough to demonstrate that higher is slightly better for max endurance.
What is the reason for that you ask? The reason is that when holding at low altitudes the jet engine is at a relatively low power setting, at low fuel efficiency, and this means less pounds of thrust produced for a given fuel flow than at the higher power settings, and higher fuel efficiency available when at the higher altitudes for a high level hold. So, although minimum drag is higher at higher altitudes, the lower specific fuel consumption of a jet engine at higher rotational speeds has a more profound effect on the fuel flow, and hence the fuel flow is slightly lower at higher altitudes.

Now shut down an engine and compare the fuel efficiencies and endurance.....that's would need further analysis...

I agree with FE Hoppy, of course maximum range increases with altitude.

Hope that helps.