# How to calculate the induced drag coefficient?

In an exercice of Flight mechanic, I have to compute the drag coefficient at zero lift: $$C_{D0}$$.We saw in class two ways to find it :

$$C_{D0} = \frac{\pi AR e}{4E_{max}^2}$$

With $$AR$$ the aspect ratio, $$e$$ the Oswald number and $$E_{max}$$ the maximal Lift-to-drag ratio. I don't have the value for the two last ones in my exercice so I can't use this formula.

We saw another way, by using the polar definiton: $$C_D = C_{D0} + kC_L^2$$ with $$C_D$$ the drag coefficient, $$C_L$$ the lift coefficient and $$k$$ the induced drag coefficient. In order to use it I just need to find the value of $$k$$ but the only formula that I have is:

$$k = \frac{1}{\pi e AR}$$

And I still need the value of $$e$$ the Oswald number. Is there a way to compute $$e$$ ? I didn't found any on Internet. If not, is there another way to compute $$k$$ without $$e$$ ?

Thanks for your help and sorry if I don't have the proper english vocabulary.

• Is it only a wing or you have other surfaces or fuselage? If it is only a wing, then there are estimates for the Oswald factor and you don't need CFD. Of-course, these are estimates, but people designed airplanes before CFD also... – ares Nov 2 '18 at 6:20
• Even in the presence of other lifting surfaces and fuselages you can still find estimates. There are formulas for interference drag in classical aerodynamics texts. – ares Nov 2 '18 at 6:23

There's no way to calculate $$e$$ without using computational fluid dynamics (CFD) since it involves the calculation of complex three-dimensional flow interactions with the wing geometry (lift loss due to wingtip vortices).
For most aircraft, 0.8 is a pretty good estimate, so this is probably the value you're expected to use. If you need a more accurate number for your particular problem, you'll either have to know the specific aircraft model (in which case you would likely have to calculate $$e$$ given $$AR$$ and $${C_D}_0$$, $$C_D$$, and $$C_L$$ for a certain state) or be given a number to use for the problem.
• Thanks! In class we studied an airplane close to the one in the exercice, and $e$ was equal to $0.85$ so I'll take this value. – Louis Etienne Oct 31 '18 at 18:10