# References for lift and drag coeficient formula/values

I'm looking for references for values/formula for lift and drag coenficients. In this paper https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=6244461 it is said that

$$C_L(α)$$ and $$C_D(α)$$ are the lift and drag coefficients

I recall seen a formula with $$\cos(\alpha)$$ and $$\sin(\alpha)$$ but I'm not been able to find again. Since I have to run some simulations to this dynamics it would be nice to have some formula for these coefficients if someone could give me a direction.

• If you give us more information about your simulations we can for sure give a better answer Commented Jul 8 at 21:46
• Hi, so, I want to run a optimal control simulation to do some test (let say the controls to make minimize the descent from two points. For this I would need the dynamical equations, which are already present on the reference, and the coefficients of drag, lift and wing surface area. Commented Jul 9 at 18:22
• Select an aircraft of interest; we do not know what aircraft that is. There are excellent answers such as by quiet flyer, here or this question by Robt DiGiovanni here. Methods are usually presented as an abstract from which aspects of interest may be determined. Maybe this will help. Commented Jul 9 at 21:45
• Acctually have to check the method and I thought it would be a nice model to test it on. So I don´t have any particular aircraft in mind, just one that I could find the data availabe to Commented Jul 9 at 22:04
• Not wanting to make your task even harder, but the full equation is a Taylor series. Commented Jul 10 at 21:24

I'm looking for references for values/formula for lift and drag coefficients

The USAF STABILITY AND CONTROL DATCOM is freely available and contains plenty of coefficients.

In particular, chapter 4.1.3. contains methods to evaluate the $$C_L$$ of the whole wing (chapter 4.2.1 evaluates the contribution to $$C_L$$ due to the body/fuselage but this contribution can be disregarded as a first approximation). "Method 1" at page 503 of the PDF should give you the needed value based on the actual planform of your wing.

Conversely, chapters 4.1.5 and 4.2.3 evaluate $$C_D$$ of wing and body respectively. For the wing you have two terms, one independent of the lift and one dependent on it. The first term can be evaluated with the method starting at page 722 while the latter with the method starting at page 758.

Also for the body/fuselage you have two terms that you'll find at page 939 and 1008 respectively.

Do not be scared by the page count! You won't find any complicated equations in the DATCOM, only simple empirical/statistical equations mainly based on graphs. At the end of each method you'll also find an example that you can reuse simply changing the parameters with the ones of your airplane.

Check out Flight Mechanics Theory of Flight Paths by Miele chapter 6 diagrams show $$C_D$$ vs. $$C_L$$. $$C_L$$ is proportional to $$\alpha$$ (wing alone the slope is about $$\frac 1{2\pi}$$ per radian. (Hint: view at archive dot org.)