01 September 2013

RGIII Runs Through 1st Week of Sports Physics

Now just over a week into my first offering of Physics of Sports at Lynchburg College, I am finding that the course is more enjoyable than I had imagined (and I initially thought it was going to be loads of fun!).  At the end of the first class, I gave my students a brief survey to complete.  One of the questions asked them to list their three favorite athletes, who could be active, retired, or deceased.  One of the most popular choices was Robert Griffin III, known to most sports fans simply as RGIII (or RG3).  The dynamic young quarterback for the Washington Redskins took the NFL by storm after his Heisman-winning season at Baylor in 2011.

After an overview of dimensions and units conversions, we moved to one-dimensional motion.  London golds earned by Missy Franklin in the 200-m backstroke and Usain Bolt in the 100-m sprint made for good examples of approximately one-dimensional motion.  When it came time to analyze motion more carefully, however, I knew I had to use RGIII.  His 40-yard dash at the 2012 NFL Scouting Combine fit perfectly with what I wanted to do (click here for video of his sprint):  essentially one-dimensional motion using an athlete my students wanted to see.

The video I used was taken at 24 frames per second.  I went frame by frame and recorded RGIII's time at each yard marker.  The graph below is the result of that effort (click on the image for a larger view).
Each red data point is my best estimate of when RGIII's torso passed each yard marker (I converted yards to feet for the plot).  The blue curve is a best-fit function that helps smooth the way for time derivatives, such as RGIII's velocity, which I show below (click on the image for a larger view).
The video claims that RGIII completed the sprint in 4.38 s with a top speed of 24.6 mph (39.6 kph).  Given my admittedly rough estimations of where RGIII's torso was at each yard marker, all of which were angled from the camera view, I found that he completed the sprint in just over 4.37 s with a top speed of 23.2 mph (37.3 kph).  The NFL was certainly using more accurate timing devices, but I'm happy with how close I got.  RGIII's time and top speed are incredible!  Check out his acceleration below (click on the image for a larger view).

I have scaled his acceleration by the acceleration due to gravity.  Note that he explodes off the starting line with more than two g's!

When I began Physics of Sports, I was not planning to look at RGIII in the first week.  Letting students help decide what to cover in a sports physics course means that I get to learn things I wasn't expecting to learn.  RGIII certainly made for a fun first sporting example to analyze in detail.

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