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example:

wind tunnel meassure wing lift=5000N

frontal area is 2m2

planform area is 15m2

air 1,2kg/m3

airspeed 50m/sec

Find Cl?

if we use frontal area Cl = 1.66

if we use planform area Cl=0.22

So choosing different reference area we have different results.That mena Cl and Cd are dependent of reference area.. So ARIBITRARY area does not make sense to me ,because than Cl and Cd can be any number.

So wich lift coefficient is corret,also if arbitray area change Cl and Cd value is it impossible to compare it with other type of wings?

So my conlusion is that we cant compare coefficients if reference areas are different,for example one is frontal area and one is planform area (car vs airplane).

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  • $\begingroup$ See here and here for an answer. $\endgroup$ – Peter Kämpf Jul 27 at 16:54
  • $\begingroup$ @PeterKämpf,I am edit my post,see my example. $\endgroup$ – Noah Prandtl Jul 27 at 18:48
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    $\begingroup$ It is “arbitrary” in the sense there is no inherent reason to use the wing area in particular as a reference. Any dimension would do. But of course you need to use wing area as a reference consistently for the coefficients to be of use (they don't have direct physical meaning either way). $\endgroup$ – Jan Hudec Jul 27 at 20:18
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If you want, you can use the area of your favorite stamp in your stamp collection as the reference area. The only condition is that you are consistent, then all is well.

However, difficulties will arise when you try to compare different airplanes. Or test results from the windtunnel with data for the real airplane. For a meaningful comparison, your reference should have some relation with the forces. Now you need to pick a reference area which is unique for each airplane and which has a linear relationship with the forces acting on it. Wing area is the best candidate here because lift grows in proportion with wing area (but not frontal area). Same for drag: Drag is the sum of the backward component of all pressures acting on the airplane body and the friction drag resulting from shear as air flows over the airplane's surfaces. Again, the frontal area has much less of a direct influence and selecting the wing area makes much more sense.

This is different with cars: Lift is not important (except for fast sports and race cars) but drag is the dominant force. Now the major reason for drag is a big separation area at the car's back which grows in proportion with frontal area. Therefore, frontal area makes more sense as a reference area for cars while wing surface area is the better choice for airplanes.

Only be consistent and use the same area for all force coefficients!

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  • $\begingroup$ 1)Car use frontal area for both Cl and Cd? 2) Example:if Audi use frontal area and BMW use planform area,than comparation between their coeffiecents does not make sense at all.Do you agree with me? $\endgroup$ – Noah Prandtl Jul 27 at 20:52
  • $\begingroup$ @NoahPrandtl Yes, I do. $\endgroup$ – Peter Kämpf Jul 27 at 20:54
  • $\begingroup$ ,Ok that is all I want to say with my topic.Thanks for your explanation.. $\endgroup$ – Noah Prandtl Jul 27 at 21:04
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choosing different reference area we have different results

Yes. And it's perfectly fine as long as we all agree on a convention/standard and are consistent. As was pin-pointed by Peter, it makes sense to select a factor with best (linear) relationship. For airplanes (or I should say specifically - AIRFOILS) it is the wing planform. If you are an aerodynamic researcher and want your results to be useful to aircraft designers - you just follow convention & calculate coefficients from established reference.

ARIBITRARY area does not make sense.

It can and often does - as long as you agree on convention. If you were working on researching golf balls, or projectiles like shells/missiles, or naval submersibles (essentially any cylindrical objects) - you would take frontal area. After all, coefficients are essentially "fudge factors" to fit the arbitrary reference area (and normalize it for use by others), as opposed to first principles CFD calculation of actual pressure distribution.

Note that in applied sciences you may not necessarily be interested in absolute fundamental model, but a useable, practical, scaleable representation. I notice it to be particularly true in the field of fluid dynamics because phenomena are just too complex to model.

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  • $\begingroup$ As an aside to your point about different reference areas, you can imagine how much fun designers of blended wing bodies and circular wing aircraft have. Their R&D work would be pretty much limited to their own niche application. $\endgroup$ – sf_711 Jul 31 at 15:34

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