|Thermodynamics and Propulsion|
, defined as the propulsive power
over the fuel
power, is constant, maximum endurance can be obtained by minimizing
the required propulsive power or rate of energy expenditure,
shown in Figure 13.3.
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