October 22, 2004


-EXCERPT from Football Physics: The Science of the Game by Timothy Gay

How Helmets Work

After the football, the next most important piece of equipment on the field is the helmet. Unlike some of their predecessors, which were little more than leather skullcaps, today's technological marvels are remarkably successful in preventing serious head injuries. Basically, the modern helmet is a molded plastic shell that fits over the head, with a face mask and an interior lining of compressible material. The advent of face masks, and the replacement of leather with plastic, were both developments of the early 1940s.

Consider the hit that Buffalo Bills defensive back Mark Kelso put on Houston Oilers receiver Curtis Duncan in the incredible 1992 AFC Wild Card game. Duncan is in the end zone drawing a bead on what would be Warren Moon's third touchdown pass. Duncan himself, meanwhile, is being targeted by Kelso, who has built up a considerable head of steam. The ball arrives, and a split second later Kelso bashes his helmet into Duncan's, causing Duncan's head to fly back like a limp doll's. Fortunately, Duncan is able to pick himself up following the hit and celebrate the touchdown, his head still attached. (Unfortunately for the Oilers, they were about to blow the game in unforgettable fashion. Trailing by 32 points in the third quarter, the never-say-die Bills, again led by backup quarterback Frank Reich, put on a dazzling display of offensive fireworks to not only get back in the game but ultimately pull out the victory in overtime, 41-38, on a Steve Christie field goal. It would go into the books as the greatest comeback in NFL history -- although the Oilers and their fans surely can be excused if they don't see it that way.)

Nothing could protect Duncan from the emotional whiplash he would soon suffer, but how did his helmet manage to protect him from physical injury? We can answer this question by considering two physical quantities associated with a hit: pressure and impulse. We've talked briefly about impulse before, and we'll return to it in detail in a moment, but let's first consider pressure.

Pressure is caused when a force is applied to a given area. The actual value of the pressure is the force divided by that area: P = F/A. That's why we talk about pressure in units of pounds per square inch (psi). Remember that in chapter 5 we blew up a football to a regulation pressure of 13 psi. Things can get tricky here, though, because usually when we talk about pressure in this context, we really mean pounds per square inch as read by the gauge (psig), as opposed to an absolute pressure (psia). Absolute pressure is the pressure of the ambient atmosphere plus whatever the gauge reads. Atmospheric pressure, in turn, is what we feel as a result of the force of all the molecules in the air hitting our body. This pressure at sea level is roughly 15 psi. As the altitude increases, there are fewer molecules to hit a given area of our skin within a given time. The force per unit area is less, so the pressure decreases. If a football is blown up to 13 pounds, there are 28 (13 + 15) pounds of force pushing outward on every square inch of the inner surface of the ball.

When Kelso slams Duncan's head with his helmet, we can calculate the force of the hit by again using Newton's Second Law. In this case, Duncan's head and helmet, with a mass of roughly 20 pounds, accelerates to a speed of about 25 feet per second. The collision that causes this takes place in something like a tenth of a second. This corresponds to an average force during the hit of about of 160 pounds, but the instantaneous force can be much higher than the average value.

Now think about what would have happened if Kelso had kept his helmet on but Duncan had removed his.

Bad game, good book.

Posted by Orrin Judd at October 22, 2004 8:02 AM

Wonderful, wonderful game. Chess with violence. I love it. God help me, I do love it so.

Posted by: Brandon at October 22, 2004 9:53 AM

I shoulda been an engineer.

Posted by: Twn at October 22, 2004 9:54 AM

In the days of leather helmets, you could spot
the football players because they had much
longer hair than the other students.

Posted by: Bob Hawkins at October 22, 2004 12:04 PM


Chess punctuated by violence -- best game ever invented.

Also, a game that has a place in it for big fat guys. Being a big fat guy myself, that makes me happy.

Posted by: AML at October 22, 2004 12:23 PM


Bad in what sense?

Posted by: Bartman at October 22, 2004 1:32 PM

boring, skill less, over commercial...etc.

It's the only game where a strike failed--because the replacement player games were indistinguishable from the pros.

Posted by: oj at October 22, 2004 1:37 PM

Fair enough. I don't find it boring (use to). One day my brother and some friends had this old Madden nintendo game where all 5 of us could play on the same team against the computer. I was the odd man out and took control of an offensive lineman. I was hooked from that point on. Blocking left or right. Pulling off and running with the halfback, etc. I found a finesse to football I had never seen before. Been a fan ever since.

Go Pack Go!

Posted by: Bartman at October 22, 2004 2:33 PM


Didn't the WFL have something to do with the strike's failure? The level of skill at the professional level is extreme. Speed, size, strength and guts is football. If you've never played the game I suppose it looks a little boring along the line of scrimmage but there is a quiet war going on along that line which is won by the guy who calls up the strength and energy he no longer thought he had. Believe it or not, football is a game of character as well as charcters.

Posted by: Tom C, Stamford,Ct. at October 22, 2004 2:50 PM


If you'd like to understand what the game can mean to the kids who play it watch "Friday Night Lights". The game and practice scenes will bring back a lot of emotional memories for those who played high school footabll. Good flick.

Posted by: Tom C, Stamford,Ct. at October 22, 2004 3:05 PM

I'd like someone to explain to me why rugby(the greatest sport ever invented) has so few head and neck injuries when compared with football.

Posted by: Bart at October 22, 2004 4:23 PM


No. The point was that the fans started coming back. The level of play was the same and so were the uniforms.

Posted by: oj at October 22, 2004 4:40 PM

College football is the greatest game ever invented.

Posted by: Matt Murphy at October 22, 2004 11:41 PM


Except for a few teams like Purdue and Texas Tech, and wherever Steve Spurrier is coaching, college football looks like bad pro football. However, in its favor, it is easier to bet on.

I guess my frustration comes from being a Rutgers alum and former faculty where the expansion of the athletic department in a mad dash to go to Division I caused our library and other facilities to atrophy. (for more info go to the Rutgers 1000 website where inter alia our most famous alum, Milton Friedman, complains about this disturbing development).

Posted by: Bart at October 23, 2004 7:35 AM


And my alma mater had the greeatest team ever, but it's a function of colleges, not football.

Posted by: oj at October 23, 2004 9:02 AM
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