1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Science Advisor
    Gold Member

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted