I saw this tweet from my friend Jobe:
Although I don't know too much about tennis, this seems interesting. My first thought was to somehow model a tennis serve. But wait! What if I just look at the records. Fortunately, wikipedia has this data - Fastest recorded tennis serves.
The only thing missing is player height. That shouldn't be too difficult to find since they usually list athlete-type data like this somewhere. So, here is what I found. This is a plot of serve speed vs. player height. I excluded any serves that were challenged for technical reasons. Also, I went through the current ATP Rankings to include some players that didn't have severing speed records. You know, just to see.
Notice that it seems even the non-record setters fit this linear-ish model. Oh, here is a link to the data in a google doc. If it were a linear model, it would be:
Clearly the model isn't really linear. Otherwise someone that is 0 meters tall could still serve the ball at 68 km/hr.
Now that I think about it, there are probably two important factors that influence the serve speed. First, there is player ability (skill, strength, experience level - whatever). Then there is the height. So, there could be a very tall player that just doesn't have the ability. He (or she - I didn't look at female players because there wasn't as much data on Wikipedia) might not be able to set a record. But, this is why included other great players that don't have records. Look at those orange data points in the graph. Those are all top players and they do not have record setting serving speeds. Maybe they have maxed out on speed for their particular size.
Overall, I think Jobe is right. And why shouldn't he be? He basically has a degree in physics, right Jobe?
One more thing. I wonder what the next record will be? How much taller could you get if you are a tennis player? According to the linear model I fit to the data, a player model-fitting player would have to be 2.17 meters tall (like 7 ft 1 inch) to get a faster serve speed. I, for one, await our fast serving tall tennis player overlords.
