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This post is strategic. I have an answer to the Mythbusters dimpled car question which was asked elsewhere on SE, but since I have a 1 reputation score at the moment and cannot post its answer, questions gain rep until I can post.

Considering dimpled golf balls and dimpled Mythbusters cars, how does one describe the path that air molecules take as it courses across the surfaces? In motocross, there are whoop-de-doos, the multiple mounds of dirt.

Whoop-de-doos

Given a line (or a flexible piece of thread, really) laid down across a straight line of dimples which are themselves in a straight line, that line or thread which is then, uh, extruded sideways, will carve out a nice set of whoop-de-doos.

Next, fudge the drawing of the line, or the placement of the thread, into and onto the surface of a curved surface… like a golf ball, and, well, there's another micro version of yet another set of whoops, as they're sometimes called.

As air molecules course across a dimpled surface, they'll be far enough away that they go straight across—think laminar—or they'll be close enough to the surface that they'll go up and down, or back and forth. Think turbulent.

Interestingly, the "up and down" is relative to the observer's frame of reference. Talking motocross, since there's gravity, we talk "up and down." However, in the air molecule, dimpled car surface, golf ball realm, it's a different frame, and it's a frame of reference that has to be generalized to accommodate discussions in any context.

How would an engineer describe the paths these air molecules take?


Addendum


More insightfully, as you read through the question above, did you find yourself putting yourself in the frame of reference of a tiny O2 molecule gliding near the surface of the car or golf ball, or did you stay in your chair looking at your monitor?

Where was your observer positioned, to what location or to which frame of reference was your observer moved? Were you aware of your adjustment of your attention? Was it consciously moved, or unconsciously moved? Some will say this line of questioning is rubbish, or invasive, or interesting, or thought-provoking, or any other number of possible responses, but they're all valid, as they answer questions I have which are getting answered through the process of your sharing of your answers—it's complicated…

Those answers—seemingly unrelated to engineering—ARE related to engineering, because they're answering questions on your insides, which only you have access to, but the clarity of your answers and your ability to explain what it was that happened while you were engaged in thinking about it helps others learn how engineers' brains work. It broaches the chasm between engineering and psychology. Those answers will be parlayed into a separate, interesting post.

Incidental note: there is no tag for “laminar.”

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  • $\begingroup$ I have a 1 reputation score at the moment and cannot post its answer ... you can post an answer ... you cannot post a comment ... a comment is not an answer ... this is a comment ... an answer would be added below in the your answer section $\endgroup$
    – jsotola
    Commented Dec 13, 2023 at 18:45
  • $\begingroup$ Ooo… thank you! Now that I've got THAT straightened out… ;-) (See engineering.stackexchange.com/questions/55251/…) $\endgroup$ Commented Dec 13, 2023 at 19:43

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This is a very complex issue. Unlike most things we think of with regard to lifting bodies, lift generated or fiddled with due to rotation does not scale with Reynolds Number or anything else. It is extremely scale sensitive. So the golf ball and the Mythbuster car have to be looked at as totally separate cases. There isn't one single thing that you can generalize across the two.

The way spinners work, Flettner rotors or dimpled golf balls, is that they create an asymmetric flow field outside the boundary layer by creating an asymmetric trapped boundary layer that is attached to the ball or rotor. There is a stagnation zone behind the ball or rotor. If it isn't spinning, it tends to wobble back and forth creating the von Karman vortex street. But if there is rotation, the boundary layer picks up some momentum and pushes the stagnation zones to one side a little, and also stabilizes it somewhat. So no more vortex street; just one starting vortex and a lifting body since the far field flow is now bent around the asymmetry. This is why things don't scale. The boundary layer momentum acts like a flexible wing. It can't support increased pressure as speed rises, and it doesn't grow in proportion to the size of the solid object. So it doesn't make any sense to talk about a coefficient of lift, or coefficient of drag for these devises. You have to test each one over the range you are interested in. There simply isn't any real design metrics for these items.

Nearly everything you read about these devices is completely wrong, and you can't use any formulae or tests from different devises at different scales or speeds. Here's a rather sad and well known example from NASA - Lift of a Rotating Cylinder It is 100% nonsense. And Mark Drela's comment on the NASA webpage.


The golfball car is a different matter. Dimples are a silly way to try to do that in a car. Simple trip strips to trip the boundary layer would do as well. Some vehicles already use turbulators to try to stabilize the rear stagnation zone. You see them on the underside of some spoilers.

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  • $\begingroup$ I overlapped with Mark Drela when I was an MIT student and worked together on man powered airplanes. Mark is a brilliant aerodynamicist. He is not head of the Aero/Astro department at MIT. That would be Steven Barrett. aeroastro.mit.edu/people/steven-barrett $\endgroup$
    – Eric S
    Commented Jan 14 at 1:44
  • $\begingroup$ @EricS Thanks for the correction. I deleted that sentence. $\endgroup$
    – Phil Sweet
    Commented Jan 14 at 12:24

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