Hello dear Saeb, check out the next link: Thanks

https://www.comsol.com/blogs/how-do-i-compute-lift-and-drag/

@Ahmed S. Mansour, thank you. The source you provided, is not analytical calculation of lift and drag, but it is experimental.

@Anastas Ivanov Ivanov, thanks. Do you mean cylinder (rotating) or sphere? As I know, sphere is symmetric body and probably would have no pure lift in a fluid flow. If this is not correct, then could you please possibly give a reference for analytical calculation of lift force for sphere?.

The lift coefficient associated with the force acting on an airfoil can be estimated analytically using the thin airfoil theory (in 2D) or the lifting line theory (in 3D). See for instance: Anderson, John, D (2007). Fundamentals of Aerodynamics. McGraw-Hill.

Hi, for computing the lift and drag coefficients, apart from CFD, you could use panel method, which is more computationally efficient. Please refer to the Low speed aerodynamics book by Joseph Katz and Allen Plotkin.

Please also see http://web.mit.edu/drela/Public/web/xfoil/ or you may also want to refer to this article https://www.ecn.nl/publications/PdfFetch.aspx?nr=ECN-M--17-003

Just a couple of minor comments about the lift force formulation:

a. the velocity you would use is the relative velocity instead of the free stream velocity

b. And it is recommended to use Vr*modulus(Vr) (where Vr is the relative velocity) in order to preserve the direction.

Hope it helps

Interesting.

By Kutta Zhokovosky theorem lift is equal to density into velocity into circulation intensity. So analytically if you can estimate circulation around an airfoil using Prandtl lifting line theory then lift can be found.

Yes, Lift force acting on an airfoil is calculated as L=1/2 CL ρ V∞2 , where ρ is the air density and V∞ the free upstream flow velocity.

But this is calculated using Lift coefficient CL, which itself seems to be found experimentally (through wind-tunnel).

As per my knowledge the lift coefficient is to be calculated experimentally only.

@Mohsen Jahanmiri. Thank you for the answer.

First you've misspelled Joukowski.

And then, what do you mean by analytically estimate?! If it is analytical, then no estimation is to be required. If it is to be estimated, then it is not analytic. As Mahesh told, lift coefficient is to be estimated experimentally only.

There is no real purely analytical solution to aerodynamics, as Anastas Ivanov Ivanov told: "That is why Fluid Mechanics is semi empirical science".

Regards, AmirAhmadi.

Hi

there are some analytic method for calculating lift of airfoils but they have limitation and don;t applied to all conditions.

some methods are:

1. conformal mapping

2. thin airfoil theory

3. lumped element vortex

However, there is panel method or CFD which they are computationally.

Additional historical elements are available on my website http://genese.imft.fr

Sorry, in french !