# What is wing inductance?

I am currently trying to understand the ground roll and climbing stage of normal aircraft. I came across this formula which is an expression of the airplanes drag:

$X_a = c_{{x}_a} S \frac{\rho V^2}{2}$

where: $c_{{x}_a} = c_{x0} + A c^2_{x_{a}}$

• S: wing area

• $\rho$: air density

• V: velocity

• $c_{x0}$: drag coefficient when the lifting force = 0

• $c_{x}$: drag coefficient

A is said to be the wing inductance. Could somebody explain what is meant by wing inductance?

• Are there typos in your formulae? Should the second one not be $c_{x_a}=c_{x_0}+A c_{z_a}^2$ where $c_{z_a}$ is the lift coefficient? – Christo Mar 3 '17 at 13:26
• @Christo nope, no mistakes this is the formula that I was provided. Unless there is a mistake in the docs I was given... – traducerad Mar 4 '17 at 21:07

$$A = \frac{1}{\pi \cdot e \cdot AR}$$ where $\pi = 3.14159....$, $e$ is the Oswald efficiency factor, and $AR$ is aspect ratio of the wing.
The drag of a conventional aircraft is $$D = \frac{1}{2}\rho V^2 S C_D$$ where $\rho$ is the air density, $V$ is the true airspeed, $S$ is the wing reference area, and $C_D$ is the drag coefficient.
The drag coeffcient can be approximated by $$C_D = C_{D_0} + \frac{C_L^2}{\pi eA\!R}$$ where $C_{D_0}$ is the zero-lift drag coefficient, $C_L$ is the lift coefficient, $\pi=3.1416\ldots$, $e$ is the span efficiency factor (also called Oswald's efficiency factor), and $A\!R$ is the aspect ratio of the wing. The term $$\frac{C_L^2}{\pi eA\!R}$$ is called the induced drag coefficient.
I suspect that there is a typo in the document where you obtained your formulae. The second formula should be $c_{x_a} = c_{x_o}+Ac_{z_a}^2$ corresponding to $C_D = C_{D_0} + C_L^2/(\pi e A\!R)$. In that case, the $A$ in your second formula corresponds to $1/(\pi e A\!R)$ as @Jared pointed out. The term "wing inductance" that your source uses is probably some variation of the term "induced drag" due to the wing.