Oswald efficiency number

The Oswald efficiency is defined for the cases where the overall coefficient of drag of the wing or airplane has a constant+quadratic dependence on the aircraft lift coefficient :C_D = C_{D_0} + \frac{(C_L)^2}{\pi e_0 AR} where : For conventional fixed-wing aircraft with moderate aspect ratio and sweep, Oswald efficiency number with wing flaps retracted is typically between 0.7 and 0.85. At supersonic speeds, Oswald efficiency number decreases substantially. For example, at Mach 1.2 Oswald efficiency number is likely to be between 0.3 and 0.5. ==Comparison with span efficiency factor==

It is frequently assumed that Oswald efficiency number is the same as the span efficiency factor which appears in lifting-line theory, and in fact the same symbol e is typically used for both. But this assumes that the profile drag coefficient is independent of C_L, which is certainly not true in general. Assuming that the profile drag itself has a constant+quadratic dependence on C_L, an alternative drag coefficient breakdown can be given by :C_D = c_{d_0} + c_{d_2} (C_L)^2 + \frac{(C_L)^2}{\pi e AR} where : Equating the two C_D expressions gives the relation between the Oswald efficiency number e0 and the lifting-line span efficiency e. : C_{D_0} = c_{d_0} :\frac{1}{e_0} = \frac{1}{e} + \pi AR c_{d_2} For the typical situation c_{d_2}>0 , we have e_0 . == See also ==