# What is the mathematical relation between CLmax and Reynolds number?

I know that Reynolds number influences CLmax, but I am not able to find any formula with which I could plot a graph!

## 1 Answer

The Reynolds number is the ratio of inertial to viscous forces, so viscous effects become smaller with a growing Reynolds number. Viscous effects cause flow separation, so a higher Reynolds number helps to delay stall.

Details depend on the particular airfoil shape, so a general formula does not exist. However, there are many plots of how maximum lift varies over their Reynolds number for groups of similar airfoils.

Below you see Figure 18 from chapter 4 of S. Hoerner's "Fluid Dynamic Lift", giving the maximum lift coefficients of some airfoils of 12% thickness. Besides the Reynolds number, nose shape and camber also influence the maximum lift coefficient, so no simple formula is possible.

Note that the Reynolds number has a logarithmic scale and shows a linear dependency with lift coefficient above Re = 10⁷. So for large Reynolds numbers you might approximate the maximum lift as something like $$c_{L_{max}} = 0.3\cdot log(Re) - 0.5$$ but there is rather little experimental data to support or refine this approximation.

• Can you also give me a relation between CLmax and mach number? – Anirudh Prabhu Feb 28 '18 at 2:53
• Yes. With the same caveats. – Peter Kämpf Feb 28 '18 at 7:53