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I Surface roughness and Magnus force of a cylinder

  1. Nov 22, 2016 #1
    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. jcsd
  3. Nov 22, 2016 #2
    $$L = \rho_\infty V_\infty \Gamma$$
    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.
     
  4. Nov 24, 2016 #3

    boneh3ad

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    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.
     
  5. Nov 24, 2016 #4
    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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