I Surface roughness and Magnus force of a cylinder

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1. Nov 22, 2016

devansh rathi

I know that the surface roughness plays an role in the Magnus force exerted of a rotating cylinder. But, i cannot find an equation that includes the surface roughness in the equation of the Magnus force. If someone could state the formula (and preferably a source to read up more on it) it would be very helpful.

2. Nov 22, 2016

anlon

$$L = \rho_\infty V_\infty \Gamma$$
Where $\rho_\infty$ and $V_\infty$ are the freestream density and velocity, respectively, and $\Gamma$ is the vortex strength over the cylinder: $$\Gamma = -\oint_C \textbf{V} \cdot \textbf{ds}$$See Anderson, Fundamentals of Aerodynamics, Sixth Edition, p. 269. Surface roughness does not have any influence on the Magnus effect.
Now, surface roughness does affect the drag coefficient; turbulent flow separates from a surface later compared to laminar flow, which is aerodynamically more desirable than a laminar boundary layer that separates more quickly.

3. Nov 24, 2016