|Thermodynamics and Propulsion
We can determine the aerodynamic configuration which provides the minimum energy expenditure:
So the minimum power required (maximum endurance) occurs when is a maximum. With a little algebra we can arrive at an expression for the maximum endurance. Setting
we find that
Thus the minimum power (maximum endurance) condition occurs at a speed which is of the minimum drag (maximum range) condition. The corresponding lift-to-drag ratio is 86.6% of the maximum lift-to-drag ratio, shown in Figure 13.5.
which can be substituted into
Such that, for maximum endurance,
which can be integrated (assuming constant Isp) to yield