# What is the relation between the Lift Coefficient and the Angle of Attack?

I'm trying to understand the relation between the Lift Coefficient and the Angle of Attack using PEP software for the A320 IAE. However, I notice that often for a given Angle of Attack, there could be more than one Lift Coefficient ("slightly different" but different).

Is it an error or a real issue? If yes, what are the standard conditions assumed for the Cl vs AOA graph?

• The airfoil of most aircraft is not identical along the wing, so naturally there would be a difference in Lift coefficient at different points along the wing. – Taher Elhouderi Nov 3 '15 at 8:01
• What do you mean by 'slightly different'? Like a 0.001 difference, or a difference of 0.1? – ROIMaison Nov 3 '15 at 8:21
• 0.1/0.2 of difference – Afe Nov 3 '15 at 17:45

## 1 Answer

Normally the relation is linear within the practical range of angles of attack used in flight. However, the Mach number and the Reynolds number will cause shifts. For the Mach effect, use the Prandtl-Glauert rule in subsonic flow up to Mach 0.7: $$(\alpha - \alpha_0)_{Mach} = (\alpha - \alpha_0)_{incompressible}\cdot\sqrt{1-Mach^2}$$

A higher Reynolds number means a relatively thinner boundary layer, and since the boundary layer on the suction side of the airfoil grows in thickness with increasing angle of attack, the same airfoil will have less boundary layer growth at a higher Reynolds number. This translates into a higher effective angle of attack at the same geometrical angle, so the lift curve slope becomes steeper and will reach stall at a higher angle.

There are no standard conditions, but a proper lift curve graph should note both the Mach and Reynolds number for which it is valid.

• And what happens in a plot where I have to show the full range of Angle of Attacks where there is the stall: the speed changes for sure, thus the graph will be inconsistent, isn't it? – Afe Nov 3 '15 at 17:45
• @jd943bd: For a real aircraft plot you're right. Normally, the polar plot is done for one Mach and Re, and you would need several of them to cover the flight regime. If you plot the actual lift coefficient at the actual Mach and Re, the biggest changes are at small angles of attack. Around stall the change is negligible. – Peter Kämpf Nov 3 '15 at 22:50