I don't understand how to calculate the drag coefficient

[vinceguar24]

TL;DR Summary

I'm confused since you need lift to calculate the coefficient and its just a loop.

I'm confused about how to solve for the Cl. I know that the equation for lift is L = Cl * r * .5 * V^2 * A, and you need the Cl to find lift. However the equation for lift coefficient that I found is (2L)/(1/2*p*u^2*S) and you need L which is lift to solve for Cl. So i don't understand how in supposed to solve it. Every website I find doesn't explain it well. it is also the same way for the drag coefficient. If someone would help that would be great. Thanks!!

 

[Baluncore]

Welcome to PF.

You have not specified the object that has lift or drag.

It is possible to compute the lift and drag coefficients of some simple shapes, but airfoils involve particularly difficult numerical solutions.
https://en.wikipedia.org/wiki/Joukowsky_transform

 

[Arjan82]

The lift coefficient makes the lift non-dimensional. It by itself does not compute the lift. If you want the lift coefficient, you need to measure or compute the lift (in absolute terms, so in Newtons) and then make it non-dimensional with a velocity, density and surface area as you've shown.

The nice thing about lift coefficients however is that they remain more or less equal when you change the density, velocity or size of your object. So now you can say something about a large wing when doing measurements on a small wing, i.e. you can scale the results.

So there is a third alternative: look up the CL for the case at hand in some reference text, if that exist. Same for the drag coefficient.

 

[Arjan82]

[...] If you want the lift coefficient, you need to [...] compute the lift

Just to be clear: the computation I mean does not involve the lift coefficient, since that would indeed be circular. It would involve some analytical solution like the Kutta-Joukowski theorem that @Baluncore mentioned, or a Boundary Element Method, RANS-method, or whatever.

 

[FactChecker]

It is common to actually measure the lift force in a wind tunnel with a small model. Using those numbers, you can apply your equation to calculate lift in other situations. Without wind tunnel measurements, there are a variety of ways to estimate the lift theoretically. Simple calculations will be rough estimates and even calculations using super-computers and Computational Fluid Dynamics (CFD) need to be used with caution.

 

[FactChecker]

There are some reference books with a lot of wing section data.

 

[boneh3ad]

TL;DR Answer:

You don't.

Longer answer:
In general, you can't just find an equation for lift coefficient, as the lift on an arbitrary object is remarkably complex based on its shape and the flow conditions. There are some shapes where you may be able to calculate it, but not many. In some (many) instances you could calculate lift using a computer simulation (less true for drag), but the gold standard for anchoring computer codes and proving out aircraft designs remains (for the most part) the measurement of lift experimentally. Others have already covered that aspect a bit.