Optimum Punting Angle: Applying Physics to Football

By Christopher Moore

NFL teams are currently battling it out in pre-season games, and college teams are gearing up for the beginning of the season. The NFL Regular Season starts 9/7/2006 and ends with Super Bowl on 2/4/2007. That makes this the perfect time to ask football coaches for a job. That’s right. Every football team needs a physicist on staff. If John Fox of the Carolina Panthers or Frank Beamer of the Virginia Tech Hokies are reading this, then sirs, I am ready. Put me in coach.

I know Frank Beamer puts special emphasis on special teams, so I thought I’d help out by providing his punters a little physics lesson:

Rob Gross sent me an interesting article he wrote where he examines the optimum punting angle to maximize net yardage. Here is the introduction:

Using elementary physics, one can easily show that the optimum angle to launch a projectile in order to maximize its range is 45 degrees when air resistance is ignored. Thus when applied to a punt, the kick will travel the most distance when it is kicked at an angle of 45 degrees. However, the analysis is not the same when trying to fnd the optimum angle to maximize the net yardage of a punt. For instance, if the punt is kicked at a greater angle the punt will be in the air longer and will allow the kicking team to get closer to the punter and thus limit his return. However, kicking at this greater angle will also shorten the kick. I will analytically examine this compromise.

Click here to download the entire article.

In the article, Rob develops an equation for optimal punt angle as a function of the speed of both the defense and offense. By using some rough estimates of average player and punt velocity, he comes to the following conclusion:

The optimum angle to maximize the net yardage does depend weakly on the average speed of the punt returner and the speed of the football. However, for realistic speeds, the dependence is so weak that it is very close to 45 degrees and a punter does not have tolerance when kicking to distinguish these angles. Not only is the angle extremely close to 45 degrees, if one could actually kick at that angle, the angle has almost negligible affect on the net return. Thus, to maximize net yardage, the analysis is practically the same as the maximal range angle and the punter should punt at an angle close to 45 degrees.

Rob simplifies the real problem quite a bit. You also have to consider field position. You want to land the ball somewhere between the 20 yard line and the goal line, ideally right on the 1 yard line, to avoid a touchback. (See Frank Beamer, I know a thing or two about football. I’m available if you need me.) But overall, getting your guys to the other end of the field before the ball is caught will usually result in a “fair catch” call, and this is rarely good for the opposing team.
(more…)