Relationship Between Magnus Effect and Potential Flow Around a Sphere with Circulation: Post 66

As you may have guessed, this one is pretty nerdy.

Confession: I am not a real aerodynamicist. I’m a mechanical engineer who specializes in fluid dynamics. Aerospace Engineering also concerns itself with fluid dynamics, mostly with the brach we call aerodynamics. Until my interest in baseball aerodynamics, I had never worked in aerodynamics at all. And I am realizing that may have been a good thing.

There is a theory of aerodynamics called Potential Flow Theory. It shows is how flow would behave if air (or any fluid) didn’t have any viscosity (which it does). More specifically, it’s flow without vorticity (the colors in our PIV plots). I’ve always secretly suspected that it is simply a means to torture graduate students.

One of the first flows a student of potential flow theory examines is flow over a cylinder, as shown below left. An important thing to note is that this cylinder has no wake (you may be starting to guess why I am not a fan).

Figure 1: Potential flow solution for a) flow over a cylinder and b) flow over a spinning cylinder.

If that cylinder were to rotate, potential flow theory predicts that the cylinder generates lift. In real life, a spinning cylinder generates lift due to the Magnus effect. What I am here to tell you is that these two phenomena have nothing whatever to do with each other. Nada. Zip. This will be a bit controversial in a tiny segment of the population, but I hope those folks are reading.

I have explained both Seam Shifted Wake (SSW) and Magnus Effect the same way. When the wake forms earlier on one side of the ball than the other, the pressure on the two sides of the ball becomes different resulting in a force. The image below is a SSW case, but it would look very similar if that ball were spinning counter clockwise.

Figure 2: Particle Image Velocimetry measurement of a 90 mph baseball and a seam on top causing an early separation and a SSW effect.

My former boss saw this picture and told me my explanation was wrong since lift (the force) is due to circulation, as in the potential flow theory. He is a real aerodynamicist and much smarter than I am, so this concerned me. I responded with this image of streamlines around a spinning baseball. These are in the inertial reference frame (meaning I subtracted the ball speed from the entire flow field to make it appear that the ball is in a wind tunnel).

Streamlines over a 90 mph baseball spinning at 2000 RPM

Two things are immediately clear: 1) the wake is tilted down meaning there is lift on the ball and 2) The stagnation point, or the streamline that divides the streamlines going over the ball from the ones going under (marked with a blue dot) is smack in the center of the ball. Contrast that picture with Figure 1b. They look nothing alike.

Aerodynamicists make no bones about potential flow being useless in the wake of an object, but they usually figure it can be helpful on the front. I don’t even think that is true.

Okay, let me have it. I have 6 fingers and am ready for you.

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2 thoughts on “Relationship Between Magnus Effect and Potential Flow Around a Sphere with Circulation: Post 66

  1. I am not an aerodynamicist and I’m not gonna throw any punches. But I do have a question that maybe other lay people following this might wonder, as well.

    How are the streamlines drawn given that the object is a sphere rather than a cylinder? It seems the streamlines would be different (and crossing the baseball) at different “depths” into the picture.

    Is there a summary of how that works? Can that mechanism safely be ruled out as a potential source for discrepancy?

  2. For a sphere on a plane slicing through the center (as our PIV system does), the streamlines on a sphere look similar to a cylinder.

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