 Maximum lift-to-drag ratio

The maximum lift-to-drag ratio is the largest attainable ratio of positive lift to drag within stated operating conditions. It depends on both the drag polar and the range of lift coefficients the vehicle can actually attain.

For the positive parabolic drag polar $C_D=C_{D0}+k{C}_L^2$, a short proof uses the arithmetic-geometric mean inequality:Consequently
provided that coefficient is attainable. Equality requires equal modeled zero-lift and lift-dependent drag contributions. This bound supplies a global argument, rather than merely locating a stationary point by differentiation.

A lift-constrained maximum lift-to-drag ratio can be lower. With $C_{D0}=0.020$, $k=0.050$ and allowed $0<C_L\le 0.50$, the unconstrained optimum $C_L^{\ast }\simeq 0.6325$ is excluded. Since the ratio increases up to that point, the constrained optimum is at $C_L=0.50$, giving $L/D=15.3846$, below the unconstrained $15.8114$. A stall-limited interval should therefore be applied before claiming the fitted optimum is reachable.

Parameter bounds on maximum lift-to-drag ratio follow from monotonicity. If $C_{D0}\in [c_{-},c_{+}]$ and $k\in [k_{-},k_{+}]$ are positive intervals, then the unconstrained maximum lies in
This interval arithmetic bound is conservative when the fitted parameters are correlated and not all interval combinations are jointly possible. It quantifies uncertainty in the assumed polar; it does not include failure of the polar model itself.