# Oswalds efficiency factor for trapezoidal wing

For a part of my university project we have to approximate 2d to 3d data ideally using oswalds efficiency factor, the equations given to us are for either rectangular or swept wings however the wing I am using is a trapeizoidal wing as seen below and so I am unsure of which approximation to use. Any help would be greatly appreciated  • I'd use the average value from the first two equations, it's anyway just a very rough estimation. Apr 11 at 13:54
• It looks like the wing of the Fokker 27, you should be able to find the Oswald factor for that one. May 13 at 6:46

what not present calculations for all three?

First, some background:

$$C_{drag}$$ = $$Cd_0 + \frac{(Clift)^2}{\pi\varepsilon AR}$$

A smaller $$\varepsilon$$ means a larger coefficient of drag, and, right there, is the AR (aspect ratio) contribution to the formula.

Also, one can notice the (Clift)$$^2$$ term, explaining the shape of the drag vs AoA curve.

OK, AR is around 7.5. 3rd calculation first:

$$\varepsilon$$ = 1. The famous Spitfire wing, beautifully tapered leading and trailing edges, harder to build

Treated as a rectangular wing using the first calculation:

$$\varepsilon$$ = 1.78 × (1-0.045(7.5)$$^{0.68}$$) - 0.64 = 0.825

Treated as a swept wing with 0 sweep using the second calculation:

$$\varepsilon$$ = 2/(2-7.5 + $$\sqrt{(4+7.5^2}$$) = 0.885

What did the Wright Brothers find with their wind tunnel?

Rounding the trailing edge wing tips reduces drag

Half a Spitfire wing.

Without going any further, as we do have a policy regarding homework, one may lean toward the second equation ... BUT

why not get wind tunnel data for your wing for comparison?

This may elevate your work above and beyond an ordinary "assignment" to one worthy of "post graduate"$$^1$$ work. Good luck!

$$^1$$ something an aerospace company may be interested in