Undergrad Surface roughness and Magnus force of a cylinder

[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.

 

[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.
For further reading, read up on the Kutta-Joukowsky theorem.

 

[boneh3ad]

Surface roughness absolutely does affect the lift due to the Magnus effect. It affects boundary-layer transition which affects separation location which affects lift. There isn't a simple equation to take that into account, though. I'm afraid you're out of luck there.

 

[anlon]

Boneh3ad is correct. The explanation I gave is actually only applicable for inviscid, incompressible flows, a fact that I overlooked when replying. When viscous effects are accounted for, surface roughness does indeed have an effect.