Step aside Angelina Jolie, there's a new bullet bender and his name is Ben Reeves. In Minneapolis, Ben Reeves pulled off a "Wanted"-esque shot that appeared to curve upon hitting the turf. Reeves may be studying to become a medical doctor, but in my recap article of PLL Week 5, I mentioned this shot should be a problem that appears in physics textbooks. In this article, I will treat it as that and discuss what exactly (read: approximately) happened. Let's take a look at the shot in the video below.
Now if you take a look at Reeves's stick at the beginning and end of his shot, the face of his head rotates roughly 90 degrees as you can see below.
Figure 1: Demonstrating the rotation Ben Reeves applies to the ball by turning the face of his stick during his shot.
The friction between the mesh and the ball apply torque (a "force" that causes something to rotate) to the ball. So, after the ball leaves Reeves's stick, the ball is rotating clockwise (from Reeves's perspective) towards the net as it travels. Once the ball hits the ground, we see the ball deviate from its original trajectory. That's because when the rotating ball hits the ground, the turf applies friction to the ball and now the ball behaves like a car tire. If you press your car's accelerator and there was no friction, your tires would spin and your car would not move. The friction between the bottom of your tire and the road propel the center of your tire forward, thus your car moves forward. Therefore, the ball rotating clockwise suddenly experiences a brief frictional force between itself and the turf propelling the ball toward the net (in the "direction" of the rotation). This is roughly laid out in the schematic below.
We can make many assumptions to roughly estimate things like how much the shot trajectory was changed by the rotation of the ball, how fast the ball has to rotate to achieve this and how much torque Reeves had to apply to the ball to get this effect.
To keep this short and sweet, I'll just report the results and attached some notes for those that are interested. Beware: they are handwritten notes. Here are the results of my calculations:
- The rotation of the ball changed the direction of the shot by almost 14 degrees! The shot should have crossed GLE 2/3 of a yard outside the post. But that's more geometry than physics.
- Assuming no change to the velocity of the ball in the original direction of the trajectory, the rotation added roughly 3% of the original speed to the shot after the bounce.
- Maintaining the previous assumption and adding the assumption that the ball stops rotating in the clockwise direction as a result of the friction from the turf, then the ball is estimated to be rotating in the range of 1320.8-1688.5 rotations per minute (rpm) for an original shot speed range of 70-90 mph. For reference, a drill bit rotates at approximately 1500 rpm. The extra assumption here is a fairly serious simplification, but adding complexity to the calculation did not change much in terms of the results.
- The shot takes about a quarter of a second before it hits the ground. The ball then has to rotate between approximately 5.5 to 7 times before it hits the ground for the direction to change that drastically.
- Reeves had to apply approximately 0.013-0.015 lb ft of torque to the ball which is < 0.01% of the amount of torque applied by a small car to move. So, only a small force needs to be applied to rotate a small ball to change the direction of a shot this much. This is much more of a display of finesse and control than a show of force.
This calculation is likely an overestimation as the analysis did not consider a loss/gain in velocity along the original direction of the shot and the assumption that friction stops the rotation caused by Reeves is a major simplification.
Some other approximations used include: negligible effects of gravity due to short flight time and no contribution from magnus effect as is frequently discussed for soccer kicks due to short flight time, high translational velocity and the short radius of a lacrosse ball. To be more accurate, the ball would have to be marked somehow to track the rotations of the ball and have multiple camera angles more accurately track the balls trajectory. Additionally, it would likely be more appropriate to do a simulation of a shot using physical principles and maybe I’ll pursue that in the future!
But in the meantime, let's just take one more look in super slow-mo and marvel at it's beauty...
This shot was incredible to catch live and an awesome thing to examine more closely. If you want some other play examined, I welcome suggestions for future analysis!