I Surface roughness and Magnus force of a cylinder

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Surface roughness influences the Magnus force on a rotating cylinder, but no specific equation incorporating it exists. The Magnus force is primarily described by the equation L = ρ∞V∞Γ, where Γ represents vortex strength. While surface roughness does not directly affect the Magnus effect, it significantly impacts the drag coefficient and boundary-layer transition, which can influence lift. Turbulent flow, associated with rough surfaces, separates later than laminar flow, enhancing aerodynamic performance. For a deeper understanding, the Kutta-Joukowsky theorem provides additional context on these dynamics.
devansh rathi
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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.
 
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$$L = \rho_\infty V_\infty \Gamma$$
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.
 
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.
 
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.
 
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