# Punted Football

1. Jul 14, 2009

### Golddredger

Yesterday I took a tour of the new Dallas Cowboy stadium and it is an engineering marvel. Above the field is a mammoth 4 sided scoreboard/screen, the bottom of which is 90 feet off the playing field. (Its length extends from 20 yard line to 20 yard line)

There is debate as to whether that is too low and may be hit by punts. I’ve read that the average hang time for an NFL punt is 4.6 seconds. To calculate the height I used the following reasoning, does this seem sound?

Discounting aerodynamics, a punted football will follow a parabolic arc, with exactly half it’s time traveling upwards, and the other half downward. That’s 2.3 seconds going up and 2.3 seconds going down.

Using the formula y= (0.5)(32.2 ft/s sq)(time squared). I calculate the average height based on average hang time is 85.2 feet. A hang time of 4.73 seconds and above translates to 90 feet and higher height.

Does this seem correct? I am ignoring velocity/trajectory in the x direction, and only working in the vertical (y) based on time of flight.

2. Jul 14, 2009

### maverick_starstrider

Yes your analysis is correct (assuming g is 32.2 ft/s, i'm not american so I don't know what it is in empirical and I'm too lazy to check). Although to actually hit the jumbotron the apex of the kick would have to coincide with right underneath it. Also you shouldn't consider the average punt. You're interested in the pathological case (the worst possible scenario) so basically given the heighest known kick done from the perfect position.

3. Jul 14, 2009

### diazona

It is 32.2 ft/s^2 (I'm American and I had to look that up :rofl:)

If the height of an average punt is 85 feet, I think the chances are pretty good that punts will clear 90 feet regularly. You'd need some data on the distribution of hang times to be able to tell for sure, though. I can't imagine that they would actually build a scoreboard which probably costs several million dollars low enough that punts would hit it on a regular basis.

4. Jul 14, 2009

### maverick_starstrider

5. Aug 25, 2009