I have written a paper that explains why a spiral pass aligns itself with its velocity vector as the orientation of the vector changes by 60 degrees or more. There have been a number of papers published that address the problem, but they either get the assumptions wrong or the mathematics wrong. None of them acknowledge that this is an example of a problem (external ballistics) that is really well understood. A recent paper assumes a solution that doesn't even satisfy the differential equation that the paper says describes the motion. Anyway, our paper shows how the aerodynamic torque causes the ball to stay aligned with the velocity vector by converting the four first-order differential equations into a single complex second-order equation and then interprets the physical meaning of the solution of that equation.

The paper does not present significant new results, simply because the explanation would be familiar to anybody familiar with ballistics, but it is the first (in my opinion) to provide a correct explanation for why the nose of the football aligns with the velocity vector. In my opinion, the value is that this is a great mathematical problem to teach dynamics from, and there truly is no correct explanation of the phenomenon out there. The question is, can somebody recommend a journal for for trying to publish this in (understanding that there may be none)? I have written a more general paper, but think there would be benefit, maybe not necessarily technical merit, to publishing the simpler paper.

One of the things I learned writing the paper is that a terrestrial gyroscope does not rotate around the vertical. The axis will tilt slightly toward the north or south (depending on direction of the spin) due to the rotation of the Earth. The mathematical model of the gyroscope and the football are essentially the same, the only difference is in the physical cause of the torque. The mathematics that explain why an ideal gyroscope will tilt away from the vertical is the same as the mathematics that explain why the football's axis stays near the velocity vector. The lesson also teaches something about how rotating reference frames can subtly change the physics. I am sure others may know this, and think me a knucklehead, but I found it interesting.

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Brian Winkel@ onHi John,

Great issuies you raise and fun stuff as well. Frankly, I am not sure how active our community will be in addressing these issues.

However, I would think something like Physics Teacher or PRIMUS (the latter journal I founded over 30 years ago) - each for different reasons, but both pedagogical, would be appropriate.

I am not sure what your statement, "nose of the football aligns with the velocity vector" being that the nose is a point and the velocity is a vector, though.

The sentence "The mathematics that explain why an ideal gyroscope will tilt away from the vertical is the same as the mathematics that explain why the football's axis stays near the velocity vector." is VERY intriguing and could be worth the price of a dmission for this paper when reviewed. Of course, a journal in Dynamics or Mechanical Systems might be a good host in that regard as well.

Ini SIMIODE we would love a teaching module, we call Modeling Scenarios, which would come from a published paper and walk students through the mathematics from fundamental principals. Of course, some data - could be hard to collect, might help or certainly suggestions on how student reader could collect data and what equipment might be needed, say from physics department storeroom. It has been long time since I handled a gyroscope, but is the angle of inclination directly rellated to its speed of rotation - this could be show by capturing speed of rotation for various angles of inclination.

I suggest you firm the paper up (get the flow smooth, all inner pointers and equation numbers lined up properly, all physics correctly spoken, and all units right), get some colleagues to read it who are knowledgeable of the area, and then submit it for publication and wait on referee reports which will give you your best feedback. Thank you for asking. Take care and be safe.

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