Sport Science: Human vs. Bow

By Sean Carroll | February 4, 2010 9:02 am

Super Bowl Sunday is, of course, the great American holiday. Past years have seen inspirational performances by Joe Namath, Joe Montana, and Janet Jackson. This year pits the New Orleans Saints against the Indianapolis Colts. New Orleans, of course, is known as a city of saintly behavior, while Indianapolis’s claim to fame involves horsepower in some tangential way.

When faced with contests of ritualized violence, we like to look for the science. So check out this video of Saints quarterback Drew Brees participating in a rigorous laboratory experiment by throwing the ol’ pigskin at an archery target. Joking aside, that is some pretty sick accuracy there.

Impressive that a human arm beats a bow and arrow for accuracy (although it’s not completely clear that the distances and conditions were perfectly analogous). All in the wobble, apparently. But if I were defending my castle from the barbarian hordes or something, I’d still prefer archers over some guys throwing footballs.

  • Mike

    And I’d like to see a comparison with four 325 pound men trying to flatten you and the target moving :)

  • Justin S

    You’d be right – the conditions aren’t even close to being analogous. Modern Olympian archers shoot from 70 yards, or almost 4 times as far away as the video’s beloved quarterback. I think this is a case of examiner’s bias – they wanted the quarterback to be more accurate (probably because that’s what their viewers want, too), so they just neglected to mention the dissimilar conditions.

  • Per

    What a crappy show. Background techno music and hiding the details of what the distances etc were!

  • Charles Evo

    But what about guys throwing exploding footballs?

  • Mike

    Actually archers shoot from 70 meters — even a little further than 70 yards. But some QBs can throw that far, so I still think it would be an interesting comparison: 70 meters, with the target moving, the shooter/thrower being chased and some amount of pain the likely outcome if caught. Who do you think would come nearest? :)

  • rec

    The archer could always pick off the pass rushers first, being hit by a football doesn’t slow them down at all.

  • Bjørn Østman

    Totally agree about the non-mention of the distances, but still, the man is obviously insane.

  • JonMcSkeptic

    I’m thrown by the observation that a slight off-axis wobble adds to the dynamic stability.

  • Claire C Smith

    JonMcSkeptic, says, “I’m thrown by the observation that a slight off-axis wobble adds to the dynamic stability.”

    That’s what I was thinking.

    Would like to to work out the wobble into the formula. Could be using a cover up technique for this film shot, th e distance isn’t explained.


    Superb topic.


  • weichi

    My favorite football physics question: why is the rotation axis always parallel to the velocity vector? That is, why does it “turn over” in flight on a long bomb, rather than always point in the same direction?

  • fr


    Half-remembered classical mechanics (and my copy of Fetter and Walecka is at the office, nuts!) but for a symmetrical top, the fact that two of the moments of inertia mean that there is no change in the rotation rate around the third axis, so no tumbling end over end. The coupled equations led to something like the projection of the angular momentum vector on the symmetry axis being constant, so it precesses around in the classic football spiral.

    Or maybe not. Anyone?

  • Claire C Smith

    Taking into account the size and weight of football, we already know how the shape acts with the forces available in this vid. It could be that given the distance oit travels to target, its relationship to the rate at which its velocity, angle and rotation axis etc are available, creats a perfect formula for a correct target. If however getting the shot at a longer or shorter distance, does he then change his spin or throw formula accordingly, taking into account different distances per throw, that could then change the rate at which the, inertia, torque rotation axis turns. Another way, the guy already worked out optimal distance for correct shot, from info of ball size, shape, distance to shot, rotation axis speed and velocity, so he must have worked out the optimal wobble formula for that particular distance. Or not.

    Claire I’ll get my coat..

  • Claire C Smith

    At any given distance, certain variables will change. Why didn’t i just say that the first time?


  • Spiv

    Pretty lousy show. I mean no doubt the guy is amazingly accurate, but comparing to an archer who shoots 70 or 90 meters (230-300 feet) is not even remotely plausible. The camera shot makes it appear as though he’s actually throwing from 60 feet out. Even without taking wind, decelleration, etc into account, it’s an easy math problem to do.

    If you’re off by 2.4″ at 60 feet (the edge of the bullseye), you’ll be off by a full foot at 90 meters. This is about halfway out on the target. Consistently scoring at that level makes you a reasonable amateur, but it’s still not analogous until you have the guy throw endzone to endzone and suffer the issues of being outdoors, with variable air temperature, human eyesight issues, etc etc.

  • The Chemist

    I think we’re being too hard on the show for the distance issue. Certainly they should have mentioned it and there’s definitely a heavy bias, but I think it’s an acceptable, even if non-ideal comparison. Olympic archers aren’t being compared on their ability to hit at the very edges of the range, and doing a comparison that way would be equally dishonest. A median range for a football player is compared against the median range for an archer. I think that’s a fair comparison. If we were comparing the relative accuracy of a piece of heavy artillery against an AK-47, we wouldn’t do it across the same distances- that would be stupid.

    Also, arrows wobble too! There’s considerable elastic deformation on release since the nocked arrow is compressed against the string and this is usually manifested as a slight bend along the central axis. Why didn’t they mention that?

    Now what I wanna see is the aerodynamics of those suction cup arrows that never worked for me as a kid. 😛

  • Spiv

    The Chemist: If I had one of those arrows I’d toss it in front of a schlieren optical setup. Maybe I can find one over the weekend. Short answer: thinking Karmen vortices, and depending on the size of the cup and mass of the arrow, the center of pressure being well in front of the center of mass that will result in tumbling.

    If nothing else there are suction cup darts littered around my house. Could just prop one of those up.

    It would also be interesting to see some boundary layer interactions on regular arrows.

  • Hudson Dawes

    Wow the whining by all the nerds on here is sad, pathetic and funny. You so want to believe that archers are cerabral atheletes and good at something and here you get to see Drew Brees eat your lunch.

    Is your crying over science or the fact that you got to watch qb’s beat you up and get the girls they lusted for in high school?

    The best part is quarterbacks dont even train at this exercise after like 8th grade. They instead only work with real receivers and defenders under pressure. So this whole test is an anathema to Brees and he still aces it.

    Suck it geeks

  • The Chemist

    @Hudson Dawes,

    I had to blink a couple of times. Did you not get the memo? The whole point of this is prelude to the Superbowl, because unlike in bad 80’s movies, sometimes people who can read above a sixth grade level can also enjoy sports. Hell some people here might have been quarterbacks.

    But if you’re going to talk about the science of sports, or science in general, it has to be right. That’s kind of the point of science. With a sport as esoter- um, rarely enjoyed, as archery I really doubt most of the people here actually prefer it over football. The issue is whether or not it is a meaningful comparison. It’s like asking whether a kicker scores more than a quarterback considering time spent on the field. It all depends on whether you think it’s fair to compare them that way and whether making that kind of comparison means anything significant anyway.


    Oh I know from experience they result in tumbling. I just wish there was some way to make that not happen- since reliable suction cup weapons could be a lot of fun. Maybe a contraption that opens up at the last second, but I’m a fan of less constrained design. (I own a recalled Toyota :-( ) Maybe the rubber material can be flat against the shaft (tee-hee) and then if elastic enough, spring forward with the force of the arrow’s impulse upon deceleration. (Oh how I wish I lived in the country, apartments in the city are not conducive to experiments with projectiles.)

  • Spiv

    Mr. Dawes seems to be uncomfortable with his status much.

    <– loves football. Mostly a college guy though.

    PS: I stole the linebacker's girl in HS.

  • paulbk

    Any good archer should consistently better a QB in a fair contest. In my teens I use to shoot rats at the dump, on the run, 10-50 feet, at night, in the snow. They would slide down the arrow and bite my leather finger guards. (For folks under 50, in those days a ‘city dump’ was 10 acres of open smelly garbage and almost anything else you can imagine. It was wonderful. I collected speaker magnets and learned electronics by playing with tubes.)

  • Archer

    Sorry Sean, this is a dumb comparison. Olympic archers shoot at 70m, not 20 yards.

    At 20 yards a top archer would expect 100% in the 10 ring (‘bullseye’) even on a target half that size.

  • cope

    Did they say the ball is revolving at 600 RPM at release? That can’t be right.

  • Trevor

    @paulbk: “Any good archer should consistently better a QB in a fair contest.” Well, that wouldn’t be a fair contest then, by definition!

    @Archer: How the heck is your definition of a fair comparison the same distance?

    What if you wanted to know who was more accurate: a winning archer or a spitting contest winner? Would you have the spitter spit 70 meters? Or the archer shoot at 5 meters?

    To make up for the obvious advantage in accuracy having a bow and arrow compared to either the spitter or the quarterback, you need to calibrate them. The show attempted to do that by noting that archers at 70m hit the the target 50% of the time, and a reasonable quarterback hit the moving target dummies 50% of the time at 20 yards.

    Whether that calibration is spot on or not, it is certainly at least *trying* to equalize the abilities, rather than the insane idea of a fair comparison being the same distance for both.

  • Archer

    Trevor, the show was clearly implying that the quarterback can throw more accurately than a top archer can shoot, which is simply false. They made no mention of the different distances involved.

    Your calibration would be reasonable if you wanted to set up a fun competition between people from different sports, but since there was no competing archer in the video it makes no sense here. All you can deduce is that Bree is more accurate than other quarterbacks.

    Hugely impressive skills though, no doubt about that!

  • paulbk

    Tevor — I’ll give Drew Brees credit for being an excellent QB. But there is no fair comparison. That’s why spear throwing cultures lost to archers. End of story. It is a stupid demonstration aimed at the ill informed.

    fyi.. I define a “good archer” as anyone who has released as many arrows as Drew Brees threw footballs. Includes practice and competition.

  • Brian137

    I thought the video was a lot of fun to watch. I was stunned by Brees’ accuracy.

    Hell some people here might have been quarterbacks.

    The Cleveland Browns once had a quarterback, Frank Ryan, with a Ph.D. in math. He was a pretty good player, although not outstanding by NFL standards.

  • Pingback: The Physics of a Quarterback’s Pass | Open Culture()

  • rp

    Not to belabor the point, but archers shooting at 20 meter shoot at a 40cm target, (1/3 the size of the one shown, and using the type of bow shown (compound – a type not allowed in Olympic competition), need to hit the inner 10-ring for a 10 (the smaller circle).

    Good archers can hit 25 out of 30 regularly, with all 30 being 10’s an 9’s … again with a gold spot 1/3 the size they are showing.

    Olympic archers shoot exclusively at 70 meters, and the full size target you see in the video (120 cm) with a type of bow (recurve) that is inherently more difficult to shoot with the same accuracy as a compound bow.

  • jack

    Actually back in the day Redskin QB Sammy Baugh did knock out a pass rusher by hitting in the face with FB.


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About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] .


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