# How to calculate lift coefficient using pressure distribution? [duplicate]

Above is the image of the question I want to ask. Please clarify on how the pressure coefficients of the upper and lower surfaces of an airfoil can be used, also if there is a set equation to calculate this lift coefficient.

• The exact way to calculate was not provided. Just wanted to know how it would be calculated. @Bianfable Dec 2, 2021 at 11:44
• Maybe the discussion in this Q&A helps: How are Cd and Cl calculated from Cp data? Dec 2, 2021 at 11:52
• I have looked through that discussion, but I can't seem to use the Xfoil software @Bianfable Dec 2, 2021 at 11:58

Pressure is defined as the force applied perpendicular to a surface divided by the surface's area.

In order to go from the pressure coefficient to the (aerodynamic) force coefficient, one simply have to multiply the former by the surface.

In this particular case this can even be done manually, taking into account that:

• an airfoil is considered in the text; that means that we are dealing with a pure 2D body and therefore a wing area cannot be really defined; instead, we consider as our area only the length along the chord (i.e. we suppose that the wing possesses a unitary span);
• the shape of the airfoil is not know; that means that also the direction perpendicular to it is not know; anyway as a first approximation we can consider that the surface of an generic airfoil is practically horizontal everywhere except close to the leading edge; therefore the relevant aerodynamic force is basically vertical everywhere and then it goes in the development of lift (except close to the leading edge, where it mostly goes in the development of drag; anyway we focus here only on lift).

With those two points in minds, the value of the lift coefficient becomes:

$$C_l=\text{ sum of }(C^i_{p,low}-C^i_{p,upp})c^i$$

where "$$^i$$" means the local i-th station along the chord, from 0 to 14 as given in the text. $$c^i$$ is the local "surface" (piece of chord) and can be approximated with the distance between two stations, that is 0.02 for the firsts 6 stations and 0.1 afterwards. As said, the value at chord=0 is not considered in the calculation of the lift since it contributes almost exclusively to the drag and therefore we start from 1:

$$C_l=(0.54--1.35)\cdot0.02+(0.54--1.512)\cdot0.02+ ... +(0.1404--0.27)\cdot0.1=1.3$$

For a standard NACA 2412 this corresponds to an $$\alpha$$ of some 10°.