My son had mixed emotions a few Saturday nights ago.

He was annoyed that the University of Michigan made the pecuniary decision to bring football back to campus.  And, were going to play their first game.  But, he also wanted to watch the Wolverines cavort on the field.

But, I’m pretty sure my son had no interest in the physics of that perfect spiral touchdown pass.  Just how does that happen?

Now, I remember my first college physics class more than five decades ago.  Where we had to describe projectile motion.   It’s  a relatively easy (yet relatively compound) problem.  We have vertical motion- the force of gravity on the ball, forcing it to hit the ground (or be caught in someone’s arms).  Every second, the vertical velocity is accelerated downward at 9.8 m/s² (the force of gravity).  Which means the velocity is (v_initial)(t) + (g)(t).  The vertical distance traveled is (v_initial)(t) – ½ (g)(t)².  (The minus is because gravity is working downward.)  What about the horizontal motion?  That’s simply (v)(t).   (I promise- no more math!)

But, that does not describe the spiral motion of the pass, with its angular momentum, and symmetrical motion.  After all, one would expect this ball to wobble, tumble, and fall.  The action conflicts with the conservation of angular momentum (the axis of a spinning object- like the spiraling football- won’t change orientation without a force acting on the ball to force the nose down. Gravity doesn’t provide that energy to keep the spiral motion going, either.

It turns out this was a really tough problem.  One worthy of an academic paper- “The Paradox of the Tight Spiral Pass in American Football:  A Simple Resolution”.  And, the authors- Richard Price (MIT), William Moss (Lawrence Livermore National Laboratory), and T.J. Gay (University of Nebraska).  Obviously, this simple resolution required some pretty high powered thought.  One that might have interested my cousin, Percy (Pete) Halpert.  You see, Pete was Sperry Rand’s go-to gyroscope guy- and their Vice-President.  (Pete died at the very early age of 54 from a heart attack- and we both had a tremendous affinity for model railroads.)

So, by now, you guessed that the spiral involves gyroscopic precession and angular momentum.  (Yeah- I will remind you that you do know what gyroscopic precession means right now.  You remember these experiments- a wheel on an axle [gyroscope] rapidly spinning about the horizontal axle. It’s then placed on the loop of a suspended string and it seems to defy gravity, remaining horizontal while the unsupported end of the string moves in a circular fashion [a precession].)

Now, back to the football.  When it is released, it is spinning like a gyroscope- but  one would expect the ball to continue at the same angle until it falls- end over end.  Instead, the torque (from the air molecules around the spinning football) creates the gyroscopic precession that affords the spiraling pass to complete the trajectory in spiral motion.  While gravity makes the ball fall back towards the earth.  Oh, and let’s not forget the wind force that also affects the ball.  Which means that “perfect spiral” is just an optical illusion- every pass has a detectable wobble.

So much for perfection.

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