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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, 2018 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, 2018 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. $\endgroup$ Oct 31, 2018 at 18:10
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In the course of looking for other aero data I stumbled across this rather old question. For any future searcher like myself I thought to add a bit more info in case it could be useful.

  1. e - Oswald efficiency factor is a way to categorize any deviation from the ideal elliptical lift distribution.
  2. Idealized lift can be achieved in an untwisted wing by having an elliptical chord distribution (think about the Spitfire planform)

You can often infer by visual inspection the shape of the wing and other characteristics possibly twist, dihedral, taper etc and make an educated guess. Anywhere in the 0.75-0.95 range is probably safe.

For a technical reference on how to calculate this refer to Estimating the Oswald Factor From Basic Aircraft Geometrical Parameters

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