By: Eric Yin
Published 2020/09/09 at 1:30 pm
SEATTLE – A few years ago back when I was a High School Senior, my AP Physics teacher once posed a question to the class, “What is the Physics behind a football pass?” Now honestly when I first heard it, it seemed simple enough: we throw the ball in a tight spiral and it goes up into the air, before gravity pulls the nose back down back towards earth. As such it follows this type of trajectory.
This makes common sense and is probably what most people assume is the physics behind a pass. We throw the ball at a certain angle, and because of gravity the tip of the ball will get pulled down and ultimately result in a parabola-like path that our football travels. What this doesn’t consider, however, is the actual physics behind how such a pass could even occur. This explanation is purely results orientated: we know the tip of the ball heads downward as ball moves through the air, therefore we create a seemingly sound justification for why it occurs. Instead, lets approach it from the very beginning. Based purely on the mechanics of how quarterbacks throw a ball, lets determine how the ball would theoretically move throughout the air if we did NOT know that the tip points downwards at the end.
To consider the state of a ball through the air, we must first go over something called angular momentum. Angular momentum can best be illustrated through a ice skater. When the skater spins with her arms out, she moves slowly, yet when she brings her arms in she speeds up and begins to move faster. This is called conservation of angular momentum. The skater in figure a, has a certain angular momentum that is determined by the length of her arm away from the torqueing point (her foot), and the speed she is moving at. Because we know angular momentum is conserved, when one variable increases the other must decrease in order for the momentum to stay constant. Therefore, when the arms go in, the speed must increase and vice versa. When the arms go out, the speed must decrease. This is all due to angular momentum.
In the scenario of a football, we can also apply conservation of angular momentum. When we throw a football, it begins spinning on an axis, much like how a skater spins on her foot. As such, once the ball leaves the quarterbacks hands, unless another force begins acting on it, the footballs angular momentum will be conserved. There is no way for a football to change the distance from it’s torqueing point (i.e it has no hands to pull in, or legs to curl up), meaning that the initial angle and speed at which the football is spinning will be conserved. As such, the footballs angle should not change throughout the air, and should actually look something like this.
As I said above, the football will only maintain this position if there is no external forces. Going back to our initial belief, this is where I imagine most people would assume gravity comes into play. Gravity will be acting on the football and that is why the tip of the football dips downwards as the pass progresses. What I and many other people were forgetting, however, was a fundamental law of gravity: it acts equally. What this means is that gravity is not disproportionally affecting the tip of the football, it will effect every single part of the football in the exact same manner. The center of the football will fall towards earth as quickly as the front nose of the football as quickly as the back nose of the football. As such gravity cannot be the reason why the nose of the football dips.
The last force that we should plausibly consider at this point in time is air resistance. Any object moving through the air will experience some form of air resistance. This is why a piece of paper falls much slower than a crumbled up piece of paper, despite the fact they weigh the same and in theory have the same properties: the first paper has a larger surface area meaning it experiences greater air drag. As such this is what we would expect from an air resistance force diagram of the football moving through the air.
Once again, however, we are left wondering how it is possible for a football to have it’s nose tip downward based purely on air drag. In the scenario that air drag was truly effecting a footballs pass angle, it’s actually more likely the air resistance will tip the ball upwards rather than have the nose tip downward. After doing calculations with my physics professor, the air drag against a ball thrown by a professional athlete would be so negligible anyways, meaning that even when factoring in air resistance the balls angle would not change drastically.
At this point you’re probably lost and I am just as lost as you are. Football is my favorite sport so I’ve spent the past week scouring the internet trying to see if there’s any actual work done on this phenomenon, because thus far the only sources I’ve found online do not show any math and typically just say that the nose tips down because of gravity. If I ever find anything that states the contrary, I will get back to this piece, but until then the physics of a football pass still appears to be a mystery to us.
Edit October 29, 2020: Just a few weeks ago the New York Times posted an article covering why a football pass does not break the laws of physics and I’ll link it down below. Essentially, the issue with my calculations and theoretical force diagrams was that I was assuming quarterbacks threw perfect wobble-free passes. As any fan of the game knows, even Patrick Mahomes and Aaron Rodgers throw visibly wobbly passes. and no one can ever throw a pass that never experiences any wobbling. This wobbling proves to be critical in the calculations as the wobbling causes footballs to undergo a phenomenon called gyroscopic precession which on average pushes the nose of the football downwards. Overall, a great article by the NYT, just wish they used a quarterback who actually throws deep balls for the intro as opposed to Lamar Jackson who any fan knows is more so a runner than a passer.