The Oswald efficiency, similar to the span efficiency, is a correction factor that represents the change in drag with lift of a three dimensional wing or airplane, as compared with an ideal wing having the same aspect ratio

Aspect ratio (wing)

In aerodynamics, the aspect ratio of a wing is essentially the ratio of its length to its breadth . A high aspect ratio indicates long, narrow wings, whereas a low aspect ratio indicates short, stubby wings....

 and an elliptical lift distribution.

Definition

The Oswald efficiency is defined for the cases where the overall coefficient of drag

Drag coefficient

In fluid dynamics, the drag coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment such as air or water. It is used in the drag equation, where a lower drag coefficient indicates the object will have less aerodynamic or...

 of the wing or airplane has a constant+quadratic dependence on the aircraft lift coefficient


where

	is the overall drag coefficient Drag coefficient In fluid dynamics, the drag coefficient is a dimensionless quantity that is used to quantify the drag or resistance of an object in a fluid environment such as air or water. It is used in the drag equation, where a lower drag coefficient indicates the object will have less aerodynamic or... ,
	is the zero-lift drag coefficient,
	is the aircraft lift coefficient,
	is the circumference-to-diameter ratio of a circle,
	is the Oswald efficiency number
	is the aspect ratio Aspect ratio (wing) In aerodynamics, the aspect ratio of a wing is essentially the ratio of its length to its breadth . A high aspect ratio indicates long, narrow wings, whereas a low aspect ratio indicates short, stubby wings....

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

Lifting-line theory

Lifting-line theory or Lanchester-Prandtl wing theory was published by Ludwig Prandtl in 1918–1919 after working with Albert Betz and Max Munk on the problem of a useful mathematical tool for examining lift from "real world" wings....

, and in fact the same symbol e is typically used for both. But this assumes that the profile drag coefficient is independent of , which is certainly not true in general. Assuming that the profile drag itself has a constant+quadratic dependence on ,
an alternative drag coefficient breakdown can be given by


where

	is the constant part of the profile drag coefficient,
	is the quadratic part of the profile drag coefficient,
	is the wing span efficiency factor from inviscid theory, such as Lifting-line theory Lifting-line theory Lifting-line theory or Lanchester-Prandtl wing theory was published by Ludwig Prandtl in 1918–1919 after working with Albert Betz and Max Munk on the problem of a useful mathematical tool for examining lift from "real world" wings....

Equating the two expressions gives the relation between the Oswald efficiency number e₀ and the lifting-line span efficiency e.


For the typical situation , we have .