Sunday, February 3, 2013

The Physics of Phootball

If you live in the US you probably know that the Super Bowl was today. A great side effect of the big game was the Twitter hashtag #SciBowl2013, where science great Phil Plait (and others) tweeted science related posts about the Super Bowl. Here are a few:

This is why science is awesome: it applies to everything! Any question about anything in the world around us can be answered with science. As an example, here's an equation you'll see in most freshman physics classes:

This equation can be used to calculate the distance that an object travels. d is the distance traveled, V is the velocity it was thrown at, ϴ is the angle it was thrown at, and g is the gravitational constant (9.8 meters/second on earth, but we'll get back to that in a second). This equation is actually pretty simple - you calculate it without even thinking every time you catch a ball. So let's see some of the things we can learn from it.

A typical pro football player can throw a football at about 55 mph. Compared to baseball and hockey this is pretty slow (a typical speed on both is more than 100 mph). This means that the best angle to throw a ball - at least for maximum distance - is when sin(2ϴ) equals 1, which is 45 degrees. An object thrown at 55.9 mph at an angle of 45.0 degrees will travel 69.7 yards.1 Getting a good "world record" for distance thrown is difficult, since NFL records include the distance run after the pass is caught. A pass thrown at about 75 mph would span the distance of the 100 yard football field. On other planets, though, this distance would be very different. Here a few planets, and the distance that a pro football player could throw on those planets:

Earth: 69.7 yards
Mercury: 189.3 yards
Mars: 182.2 yards
Pluto: 1,120 yards
Saturn: 61.0 yards
Jupiter: 26.3 yards
The Sun: 24.46
The Moon: 421.4 yards

So the big things we learn from this is:
  1. You don't want to play football on the sun. Not only would you have to rely on the running game (you can only throw it 25 yards at the most), but you would also die. Because it's the sun. 
  2. When we colonize the moon, the standard football field should be extended to about 600 yards to retain the same game flow.
  3. The Mars rover really should have brought a football. 

[1] I chose 55.9 mph because that's an even 25 meters per second - let's deal in real units here.