Maximum endurance at higher altitude

[alexat]

As a first year aerospace engineer student I had a problem today.

The question was :

Does the altitude effect the endurance of an aircraft (provided that the aircraft engines can generate enough trust at this higher altitude).

Maximum endurance is minimum fuel flow [N/s] F = Ct T

in a steady, horizontal, symmetric flight F = Ct D

D = Cd (1/2) rho V² S

D: Drag
T: Thrust
Cd: Drag coefficient
Cl: lift coefficient
Rho: air denisty
V: velocity
S: wing area

So higher altitude = lower density = lower drag = lower fuel flow = higher endurance.

But also true is that F = Ct (Cd/Cl) W and none of these parameters are effected by the altitude.

Which one is correct and why? And why is the other one wrong?

Kind regards,
Alex

Edit:
D = Cd (1/2) rho V² S
but V is sqrt (W*2*1/(S*rho*Cl))
so the rhos cancel each other out.

Is there a delete button somewhere?

 

[jbsteele]

The correct answer is that higher altitude will result in higher endurance because of the decrease in air density. This is because at higher altitudes, the air density becomes lower, resulting in less drag and therefore less fuel consumption. The other equation does not take into account the effects of air density on drag, so it is incorrect.