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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.

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  • $\begingroup$ 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... $\endgroup$ – ares Nov 2 '18 at 6:20
  • $\begingroup$ 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. $\endgroup$ – ares Nov 2 '18 at 6:23
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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.

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  • $\begingroup$ 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. $\endgroup$ – Wizix Oct 31 '18 at 18:10

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