## Do More Home Runs Happen When It’s Hot Outside?

Posted in recreational physics with tags , on November 2, 2009 by Grad Student

I was watching the world series the other day when an announcer mentioned that the ball carries farther when it’s hot outside. My wife asked me about this and here’s the explanation/equation that immediately popped into my head:

$density \propto \frac{P}{T}$

I’m guessing that the air pressure change isn’t as important as the temperature change in this context. So, if we say that P is a constant, then the higher the temperature is the lower the air density. This is important, as the drag force on a hit baseball is:
$F_{drag}\propto density \propto \frac{1}{T}$
Thus, the drag force is inversely proportional to the air temperature if we can assume the air pressure is constant. In conclusion, yes, more home runs are hit when it’s hot outside because the drag force on the hit baseball is lower.