Superbowl science 2012

By Phil Plait | February 5, 2012 4:14 pm

Today in America is our most revered holiday: the Superbowl. I am not particularly invested in either team — I had to look up who’s playing, to be honest — but there is something about the game I like: science! Yes, science, of which there is plenty to be had during any sporting event. You just have to look for it.

Last year, during the big game, I tweeted a series of science facts relating to football, and, when the game was over, collected them into a blog post.

I thought it would be fun do it again — this time, I’ll use the hashtag #Sciperbowl — but this year, instead of waiting to collect them, I’ll simply update this post as I add them. That way you don’t have to wait until the end of the game to see them all.

So sit back on your recliner, keep one hand in a bag of chips and another on the refresh button. Let’s see how to really enjoy this game! I’ll start the tweets and start updating this post at the start of the game.


First Quarter

1) Realistically, a football is not a ball. It’s more of a prolate spheroid.

2) Football pads work by absorbing impact as well as spreading it out over a larger area.

3) Pads lower the force of impact by lengthening the time of the collision.

4) Pressure = Force/Area, so increasing the area of the impact reduces pressure and therefore injury.

5) Every time a football is thrown, it’s briefly in orbit… but the Earth gets in the way.


Second Quarter

NOTE: The following info uses air (not ground) speed and neglects air resistance. [Note: the math on these next ones can be found online, for example at the CSU San Bernadino website.]

6) To be thrown 100 yards, a football should leave the quarterback’s hand at a 45 degree angle at 70 mph.

7) The ground speed of that throw is about 50 mph.

8) A ball thrown like that will reach a max height of about 80 feet.

9) A 100 yard throw like that will take about 4.5 seconds to go up and come back down.


Halftime

10) Halftime for the Universe was 6.86 billion years ago (+/- .12 billion).


Third Quarter

11) Because the Moon has 1/6 the Earth’s gravity, lunar football would be pretty different.

12) On the Moon, a football thrown at 70 mph would go 600 yards, take 27 seconds, and reach 500 feet high.

13) Throw a lunar football at 28 mph to get it 100 yards downfield. It’ll take 11 seconds & get 80 feet high.

14) All those throws assumed a 45 degree angle. At higher and lower angles, the ball must be thrown faster.

15) Want the ball to go into Earth orbit? You’ll have to throw it at 5 miles per second.

16) In a black hole, it doesn’t matter how hard you throw the ball. It’s not getting out.


Fourth Quarter

17) During a 4 hour game, the Earth rotates 60 degrees.

18) During a 4 hour game, the Earth spins a total of 3200 miles at the latitude of Indianapolis.

19) During a 4 hour game, the Moon travels over 9000 miles around the Earth.

20) During a 4 hour game, the New Horizons Pluto probe travels 130,000 miles farther from the Sun.

21) Since the starting whistle, the Sun’s moved 2 million miles in its orbit around the center of the galaxy.


That’s it! And congrats to whichever team won!

Football picture from Elvert Barnes’ Flick photostream.

CATEGORIZED UNDER: Cool stuff, Science, Top Post
MORE ABOUT: football, Superbowl

Comments (32)

Links to this Post

  1. Super Bowl Science « | February 6, 2012
  1. Yay Sciency Goodness :)

  2. Noel

    Thanks :D . Now I can add prolate spheroid to my mental list of types of spheroids, which up to this point had only included the oblate spheroid, such as the Earth, which is also realistically not a ball, or a sphere.

  3. Does this count as a scientific fact: Rugby players are tougher than (American) football players ‘cos rugby players don’t wear pillows padding?

  4. Chew

    A football thrown at 30 m/s (67 mph) will travel one football yield (not including the endzones and neglecting drag, 45° launch angle).

  5. scot

    Andrew. As you are obviously a troll I’ll bite. I watched the Eng/Scott rugby game yesterday on BBCA. Those players are very tough indeed but the games are entirely different. Rugby players never take a shot like a receiver coming over the middle in american football does. In rugby nobody is allowed to hit above the shoulders either. And it seemed the speed of the game was much slower.
    So I’d say both games are full of guys that are incredibly tough but the rules/speed of the game dictate differences in equipment.
    Maybe just watch the games and enjoy them for what they are (as I do with rugby and aussie rules football) and not try to make short-sighted, rugby guys are more macho arguments?

  6. First of all. GO PATS! (And stop giving your fans hear trouble with that first half performance!)

    And I played both American football and Rugby, and I gotta agree with Andrew W. rugby is indeed the more physical sport. If anyone wants some great entertainment that beats Madonna at halftime, go to youtube and look up New Zealand All Blacks and their Haka.

  7. Bart

    Shouldn’t halftime be 50% of the way to the *end* of time?

  8. Tara Li

    I thought if you threw that football at 7 miles/sec, it would probably end up in *solar* orbit, not terran orbit, as it exceeds the Earth’s escape velocity. (All simplifying assumptions applied).

  9. Tara Li – Yeah, I caught that and corrected it. :) Thanks!

  10. Noel

    You can’t throw stuff into orbit, you’d need an extra burn at apogee or the ball would come right back to where you threw it, and hit you in the back of the head… well, further back because of air resistance.

  11. Steve D

    No, you can’t throw things into orbit. But the “parabola” traveled by a football is actually the end of an elongated ellipse with the center of the earth as its focus. So anything traveling a ballistic path is in an elliptical orbit until the earth interferes with it.

  12. David Masten

    The football trajectory equations neglect aerodynamic effects? Lift and drag play a huge roll in throwing a football.

  13. Mick

    So, howsabout that team eh? Yeah.

  14. Nigel Depledge

    Also, the ball is not a football ‘cos it spends more time getting carried or thrown than kicked.

    Football is a game in which ten out of the eleven players on each team are not allowed to use their hands at all. For some weird reason, you USAians call that game soccer, and your version of rugby you call football.

  15. Gunnar

    Fun article, but of course you know that David Masten is right that aerodynamic effects on a thrown football are not as trivial as you seemed to imply (unless you actually could play the game in a virtual vacuum as on the Moon’s surface). I’m sure that to achieve maximum horizontal throwing distance, the optimum throwing angle is somewhat less than 45 degrees from the horizontal and probably also depends, in part, on the initial throwing speed. An experienced and successful quarterback has obviously learned to automatically optimize both his throwing angle and throwing speed to hit his target at any given distance. It’s really quite remarkable when you realize that the minds of both thrower and receiver are subconsciously and nearly instantaneously performing the equivalent of fairly advanced calculus to enable them to anticipate where the “prolate spheroid” is going and how to intercept it!

  16. David H.

    Nigel, don’t blame Americans for calling football “soccer”–the Brits came up with the name first as an abbreviation of “association football.” The US kept the name while the Brits went back to “football” as the main name.

    So “some weird reason” – blame the British.

  17. 2crudedudes

    @David

    That still doesn’t explain why Americans call a game that’s not played with your feet “football”

  18. john

    2crudedudes: You score field goals with your feet. You play the game “on foot” instead of on horseback.

    The fact is that soccer is the only “football” game you play with your feet. Rugby football, aussie rules football, Canadian football aren’t played “with your feet”.

  19. Oh well. Seems that the Pats can get to the Super Bowl, they just have a hard time winning them…

    By the way, did anyone catch today’s SMBC? Made me smile. :)

  20. Ciaran

    @scot

    Don’t judge rugby on that Scotland v England game, it was one of the worst games I’ve seen in years.

  21. One Eyed Jack

    I have to take issue with you on the “half time comment”, Phil.

    We are not at the end of the Universe, so we don’t know when half time is. From the little astronomy that this chemist knows, I don’t think we’re even out of the first quarter.

    Wait, are you assuming the 2012 doomsdayers are correct? ;)

  22. Dragonchild

    “6) To be thrown 100 yards, a football should leave the quarterback’s hand at a 45 degree angle at 70 mph.
    7) The ground speed of that throw is about 50 mph.”

    A bit more involved than that; that’s assuming maximum efficiency where the ball basically hits the ground at x=100 yards.

    I do like football, and it’s largely because of the physics. NFL defenders have good 360-degree quickness, so sometimes the ball has to be thrown IN ANTICIPATION of an opening, and deliberately thrown at much higher speed (up to and over 90mph) at a high release point (to prevent deflection) and low angle (for minimum time to target) to give the defense no time to act. It’s classic ballistics. On a long pass, the quarterback has to adjust the speed and angle so it drops right in front of the receiver as the receiver runs down the field at full speed. The equation is more complex. There’s little margin for error (underthrow it and the defender can steal it; overthrow it and you’ve basically wasted a chance) and it takes many repetitions to get that sort of precision. But that a human can lob the football with such location and timing just by touch is amazing.

    Receiver routes (the paths guys run to catch passes) themselves involve a lot of physics. One way to spread a defense thin is to have receivers run various distances, but it’s not that simple. If you have a guy just run a few yards forward and then wait for the “long” guy to run 40 yards down the field, he’ll have to stop for several seconds, which is basically several seconds too long for an NFL defender to figure it out and jump in front of him in anticipation of a pass. So you have to do various things to trick the defense and not just stand there waiting for your teammates to do their thing. Inclement weather can make the air unstable and/or ground slippery, making certain routes impractical and thus execution more difficult.

    Even tackling involves a lot of physics. The actual tackle is wicked complex (a good one will involve a lot of angular momentum — you rotate your target’s frame around center of gravity, not just try to knock him backwards), but there’s plenty to be appreciated in just pursuit angles. That’s where the defender knows when and how to run. Too passive and the defender can’t accelerate in time to catch a quick ball carrier; too aggressive and the defender can’t adjust in time and basically “runs himself out of the play”.

  23. TR

    @Nigel Depledge Say, “the ball is not a football ‘cos it spends more time getting carried or thrown than kicked.”
    Perhaps, but more points are scored by kicking the ball in an average NFL game than in an average professional soccer game. In last year’s NFL regular season, football players (across both conferences) kicked the ball through the uprights about a thousand times for extra points and nearly the same number of times for field goals. In fact, NFL match-ups average about 14 points scored by kicking a ball in each game. Even setting aside the fact that field goals are worth more than one point, the average NFL team kicks the ball into the goal over 7 times per game. By comparison, a review of the same season of English Premier League soccer shows those teams average just under 1.4 balls kicked into the goal each game.
    Moreover, in 2011, about 12% of all NFL games were decided by 3 points or less, meaning, as the very least, a field goal would have changed the outcome. It would take a pint-by-point analysis of each game to determine home many were literally decided by a field goal or extra point kick (and, given that points are fungible, such an analysis may not even be possible). Nevertheless, it is clear that many American football games are won or lost because of a kicked ball. However, in 2011, about 40% of all MLS games ended in a tie, which means those games were NOT won by a team kicking a ball.
    So, if you go by number of players allowed to kick the ball, perhaps the name “football” should be used for the game Americans call “soccer.” However, if you go by percentage of games won by kicking a ball, it’s a little less clear which sport has a right to the name. If you go by the number of points scored by a kicked ball, or even the number of times per game a ball is kicked into the goal, there is no doubt that the name “football” clearly belongs to the sport played by the NFL.

  24. Todd

    I’d call this a “Nerd’s Eye View” of the Superbowl. Many thanks!

  25. Phil, thank you for an eye-opening read, and I also appreciate the head-scratchingly good comments!

    I’ve tried to do the maths, but I need some help understanding why a perfectly thrown spheroid (of any -lateness) wouldn’t end up in some kind of orbit.

    I guess I got my confusion from thinking that ANY engine firing on an orbital vehicle was only needed as an error-correcting mechanism, but apparently it’s not that simple.

    Any help clarifying would be much appreciated!

  26. #26.
    Even if you threw the ball gently, if the Earth wasn’t in the way, the ball would in theory enter an orbit about the center of the Earth with the apogee (highest point in the orbit) at the highest altitude of your throw, most of the rest of its theoretical orbit would be deep inside the Earth, with the perigee (lowest point in the orbit) quite close to the center of the Earth, on the completion of one orbit it would be back at its starting point (where you threw it).
    If you threw it hard enough so that your throw was at the perigee (lowest point) of its orbit, and it rose into space after the throw, it would be in an orbit and still return to its perigee, hitting you in the back of the head an hour and a half or more later after completing one orbit.

    That’s the theory, in practice 1. because you’re standing on the Earth and moving with the Earths rotation, you will have moved a thousand or so km as the ball does one orbit and so escape being whacked in the back of the head. 2. obviously the ball isn’t going to stay in orbit if, at the lowest part of its orbit, it’s traveling through the atmosphere.

  27. Nigel Depledge

    TR (23) said:

    Perhaps, but more points are scored by kicking the ball in an average NFL game than in an average professional soccer game. In last year’s NFL regular season, football players (across both conferences) kicked the ball through the uprights about a thousand times for extra points and nearly the same number of times for field goals. In fact, NFL match-ups average about 14 points scored by kicking a ball in each game. Even setting aside the fact that field goals are worth more than one point, the average NFL team kicks the ball into the goal over 7 times per game. By comparison, a review of the same season of English Premier League soccer shows those teams average just under 1.4 balls kicked into the goal each game.

    Hey, I never said football (soccer) was worth watching.

  28. Nigel Depledge

    John (18) said:

    The fact is that soccer is the only “football” game you play with your feet. Rugby football, aussie rules football, Canadian football aren’t played “with your feet”.

    This is true.

    In Europe, “football” refers pretty much only to soccer.

    Rugby football is almost exclusively called just Rugby.

    Aussie rules “football” seems to be a cross between Rugby and a bar-room brawl – does it count as a sport? I don’t know. I know too little of Canadian “football” to make any comment about it.

    I think the point worth remembering here is that there are many versions of “football”, but in only one version is the juxtaposition of foot and ball the default mode of play. This is the only one that – in Europe at least – needs no prefix to distinguish it from other forms.

  29. Nigel Depledge

    John (18) said:

    You play the game “on foot” instead of on horseback.

    This does not wash. Otherwise, why are games such as cricket, rounders (baseball), lacrosse, hockey, basketball, netball and so on not also called “football”?

    After considering the comments here, it seems to me that the variants of football (AFAICT without looking into the matter in any depth) are those team sports in which every player is permitted to kick the ball.

  30. I find bowling and (now) minigolf more interesting as physics lessons because they are more accessible to more people. At a local Koz’s Minibowl, I scored mostly spares and a few strikes last two games. http://www.kozsminibowl.com/

  31. Aidan

    Ew football. I spent my time during our household superbowl party reading up on science. I like being a nerd!

    “Because the Moon has 1/6 the Earth’s gravity, lunar football would be [pretty different].”

    That’s a good clue to the fact that there is VERY little science in Foot ball. x’D

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