Sunday, April 20, 2008

Bullet vs Puck

Inspired by Rock Deputy's advocation of military-style groin protection for NHL players, I thought I'd take a look at exactly how hard the puck would hit an NHL player when compared to an actual, no shit bullet.

Now, this comes with the caveat that my ability to perform basic physics calculations has diminished greatly since I was the valedictorian of Ardrossan High School's 2002 graduating class (yeah, that's right, valedictorian; deal with it) but between what I remember and scouring the web for confirmation, I think I've more or less got this figured out (assuming, of course, that the puck/bullet moves with constant acceleration in a constant direction, and if anyone has a problem with that you're more than welcome to do the calculations your damn self).

Now, assuming that the puck (weight=170 grams) was shot at about 90mph [*fixed, see comments] (a reasonable speed, I think, but damned if I could find any information on the average speed of an in-game slap shot), and that Thor was about 20 feet from the point of contact with the stick, the puck would take about .152 seconds to reach him, and would hit with an impact of about 45 Newtons (the standard measure of force, in case any of you remember less of Physics 20 than I do), or, as a hasty Google search reveals, roughly the amount of force used by a circular saw to cut through brick. Just in case that means nothing to you, assuming these figures are about right, Patrick Thoresen basically got a 10 pound weight dropped directly onto the Electric Norsemen.

Now, because it was the most readily available information—I assume there are only so many times you can Google phrases like "bullet speed" and "bullet weight" before CSIS people come crashing through your window—for the bullet, I used a standard cartridge from a .22 rifle by means of comparison. Now, any of you who know anything about guns/grew up in rural areas will know that a .22 is basically the firearms equivalent of tickling something to death—as a former valedictorian, I personally use blasts from a .22 rifle for brushing my teeth—but nevertheless, on the off chance a pissed-off farmer wandered into the Verizon Center and mistook Thoresen's groin for a gopher, these numbers reflect how it would feel.

Assuming a bullet weight of 3.26 grams, and assuming an average bullet speed of about 3060km/h, from 20 feet away, Thor would have been felled with about 388 Newtons of pure blunt force (ignoring other bullet properties, like, say, piercing), which would arrived roughly .007 seconds after the shot was taken (two blinks of an eye, more or less). In this scenario, the equivalent of 87 pounds of iridescent, blistering pain would have been dropped on the pride of Norway or, again thanks to a hasty Google search, almost the amount of force the main thrust of a rocket designed to go to Venus provides.

To get the equivalent force from a .22 rifle, our assumed pissed-off farmer would need to be standing about 170 feet away, or about 20 feet closer than you need to be to beat Vesa Toskala. Again, ignoring the other things a bullet is capable of doing, slap shot from the blue line is roughly equivalent to low-calibre rifle from the other team's hash marks. Probably best you don't let that sink in.

The point of all this? None, really, other than to justify a few procrastinated hours dinking around on Google. And, also, perhaps, to remind people of the toughness of a fellow who basically got shot in the testes from 60 yards away and was convinced that ice and happy thoughts would be enough to get him back in the series.

UPDATE: The award for proving my physics ain't worth shit (henceforth referred to as the Alberta Physics Prize) goes to Colby Cosh, who uses something called the law of conversation of energy, or whatever, to show that the energy transferred by the bullet is always greater, or something.


cartooncolin said...

Sweet - I'm Ardrossan Grad '94. S.U. president.

Go Bisons.


andy grabia said...

That may be the best thing I've read all year. Bravo, Dave.

mike w said...


Colby Cosh said...

Yeah, look, the energy transferred from a moving body into your juicemakers varies with the mass and the SQUARE of the impact velocity (distance from the original source is irrelevant), energy being the thing that Is Conserved. Using your figures, the puck is 52 times heavier than the bullet, but the bullet is travelling 34 times as fast, meaning that its kinetic energy is greater by a factor of about (34²/52) = ~20.

I wasn't the valedictorian my grad year. Too busy winning the Alberta Physics Prize.

Art Vandelay said...

You don't need to be The Science Guy to know that a puck to the nuts f***in' hurts. Bad. Everything else is details.

Mr. Plank said...

Robot Chicken needs to update their "Ode To The Nutshot" episode.

Brilliant post.

James Mirtle said...

Now I wanna read Cosh's nutshot post.

... and was convinced that ice and happy thoughts would be enough to get him back in the series.

It's not?

MikeP said...

Everybody knows Real Men use something like a .308/7.62mm, not a .22.

There's several different sizes, so let's go with the middle one listed by Wikipedia: 10.9g, moving at 810m/s.

Using my handy calculator, 810m/s works out to about 2916km/h. So my .308 is going marginally slower than your .22, but weighs more than 3 times as much.

Using Cosh's handy maths, we get a bullet going 0.952 times as fast, with 3 times the weight - multiply by 56, carry the two, divide by my weight at the age of six, and I think we get 0.952^2 * 3 ~= 2.72.

I'll let you work out how many Newtons that is, but good thing it was a farmer mistaking Thor for a gopher, and not a particularly cruel sniper.

I'm going to go with Cosh as well - I'm not sure that a bullet loses speed appreciably at ranges that short. I can say from experience and training that the trajectory of a 5.56mm is virtually flat out to 200-300m. So it's almost irrelevant whether Thor's taking it in the harblz from ranges of 20 or 170 feet (divide by 32.4, add 6, dance a jig, that's 6.1 or 51.8m). I think you'd have to get out into the parking lot before that bullet's losing appreciable velocity.

Speaking of 5.56mm... 4.0g, 940m/s = 3384km/h. Things aren't looking good for Thor's crotch, just like in those movies where the abused woman learns to shoot at a range and tries out her miraculous accuracy with a pistol on the target's groinal region. Poor bastard. Hm, pistol, 9mm 8.0g @ 1260km/h. This is fun, and I've now lost about 20 minutes googling and finding my calculator - same one I used while finishing middle third of my class in high school, about 10,000 years ago. Don't make 'em like they used to.

Oilman said...
This comment has been removed by the author.
Oilman said...

Anyone else find it ironic that Thors injury has generated a ballistics debate?

ba dump ching!

Rob Huck said...

I'm no physics prize winner, just a lowly geophysical engineer. Speed and momentum are all well and good, but the size of the puck relative to a .22 round does make a difference upon impact.

Namely, if you do disregard the effect of a large puck not being affected by wind resistance, there is still the matter of force distribution on the nutsack. I'm not about to get out my trusty ol' HP48G, but there would be considerably more distribution of the impact with a puck -- with it's relatively wide, round face -- with respect to the the focused point of the .22 round.

It would be the difference between getting a nut to swell like a baseball (which happened to a former goalie teammate of mine) and having it obliterated completely.

Good post, though. Made me shift in my seat.

Anonymous said...

Now, assuming that the puck (weight=170 grams) was shot at about 90km/h (a reasonable speed, I think, but damned if I could find any information on the average speed of an in-game slap shot)...

While you nerds were playing with your slide rules, I was actually playing hockey. 90 km/h strikes me as awfully low for the average speed of an in-game NHL slap shot. I would be willing to wager that I can crank it up over that without much difficulty and I'm far from an NHL player. According to the wikipedia FoxTrax article, their puck switched from blue to red whenever the puck's speed exceeded 70 mph; I seem to recall that happening on virtually every shot. I distinctly remember Gretzky getting made fun of when he scored a blue goal.

I'd think that 130 km/h or so is a more reasonable estimate.

This post is, otherwise, awesome. I think we've reached the end of the utility of the convention of referring to something as x times the force of the blast Hiroshima; henceforth, all forces should be expressed in terms of the force applied to Patrick Thoresen's testicles.

doritogrande said...

That made my day. Thanks for the heads up on BoA.

The shot was taken by Mike Green, so you know it's doing probably more than the 130K MC suggests. I think he's closer to dropping bombs at about 100Mph, or 160K if my calculus isn't failing me. Also, are we taking into consideration the angle of which the puck struck dice? Surely said puck could have an impact somewhat the size of a .22 if it caught one of the edges (yes there are edges on a puck) instead of coming on the topside.

I'm not prepared to do the math, so I can only try and guess at how much that would hurt. By comparison, I was hit in the nuts by a kiddie soccer ball travelling 2.7Kph back when I was 5. It dropped me like a stone for a couple minutes. Makes me wonder how much more of a man the Electric Norsehammer is than I.

Black Dog said...

I don't know if I'm reading this correctly but are you suggesting there was a second shooter?

Behind the icy knoll?

Steal Thunder said...

I actually agree with Tyler on something (which amazes me at least), in that when you add in the momentum to an in game slapshot (whether its from the skater moving forward or the puck reversing direction quickly in a whipping action), the speed would be much greater than what you get at a skills competition where the puck is just sitting still on the ice and where the friction of the ice would be much more relevant to a puck than if it were already gliding over it...

DMFB said...

Two things:

First, I messed up with the km/h: I actually used 90 mph, which I assume is a decent guess on the speed of an in-game slap shot. It will be fixed shortly.

Second, with regards to Cosh: I was using distance to figure out the acceleration of the bullet at the time of impact (F=ma and a=v/t being about the only equations I remember, though obviously the latter is only instantaneous acceleration at the moment of impact). The units seem to work, but my physics went out the window the day I decided to take an Arts degree; if you'd care to explain in detail where I went wrong, I know at least I'd appreciate it.

Rock Deputy said...

This post is awesome! And it can be held up as evidence that Oilers fans are, by far, the smartest fans in the league.

If this were on a Leafs blog the responses would be

"damn Valedictorians... go back to your own country!!!"

andy grabia said...

Okay, so what's the current line of thinking then? Bullet, or puck?

Canuckfan said...

In related news, today the Vancouver Canucks ownership group announced that it had fired Patrick Thoresen's left testicle.

"What that scrotum needed was leadership, not a swollen purple throbbing mass that pretty much made all of us watching want to puke."

Canuckfan said...

p.s. Valedictorian? Alberta Physics Prize?

Hah! I blow my nose at you!

I got 100% on the Gauss math contest.

Turns out that even saying the words "math contest" to a girl is like WOW the world's greatest aphrodisiac.

Colby Cosh said...

The issue is that we're talking about a transfer of energy, not force as such, from the puck to the, um, surface it is striking. Your equation is used to derive the acceleration of a body that results from the application of a particular force. We're talking about a transfer of the energy stored in the puck by means of the force originally applied to it.

Simply put, something doesn't have to be accelerating to impart energy in a collision, does it? A flying puck (or a car or a billiard ball) moving at a constant velocity has the energy 1/2mv², and to bring it to rest that's the quantity that has to be absorbed by something else. It's the joules, not the newtons, that are conserved. Insert "family joules" joke here.

You don't need to know the whole history of the puck's acceleration to figure out how much kinetic energy it has, just the impact speed and the mass. (If you want to talk about pressure, you do need to know how fast the puck has decelerated when it hits poor Thoresen, plug THAT into the f=ma equation, and divide by the surface area.)

Anonymous said...

...and divide by the surface area.)

Of the puck or his testicle? If the latter, from before it was struck with a puck or afterwards?

DMFB said...

Ohhhhhhhhhhhhhhhhhhhh. That makes way more sense. Thanks, teach.

Colby Cosh said...

Of the puck or his testicle? If the latter, from before it was struck with a puck or afterwards?

It's the area of contact between puck and testicles.

James Mirtle said...

Somehow, I don't see MacLean referencing this one on HNIC.

DMFB said...

Somehow, I don't see MacLean referencing this one on HNIC.

Godammit! What do I have to do?!?!

andy grabia said...

Godammit! What do I have to do?!?!

Mythbusters-like experiment, obviously. I'd be happy to help, as long as I don't have any projectiles shot at me. We could film it and post it. Maybe we could even get Mike Green to take the slapper. Where's Leonis when we need him? TED!!!! TED!!!!!

mike w said...

Although this seems to be right up Deadspin's alley...

Vic Ferrari said...

I think you were right in the first place, DMFB, if the question was "Hey, how much would that hurt?" ... then impulse-momentum applies, no? So m*v is conserved.

Surely there are a whack of science types lurking around here, hopefully they chime in.

In any case, I've taken direct blows to the can a bunch of times, and once the shock of it and the nausea washes over, I was usually okay pretty quickly. I'm sure most here would say the same, no?

I think you made the relevant point in the last post ... his jock must have shifted when he slid, transforming his cup into a nut cutter.

I've never played organized football, but I read somewhere that the vast majority of NFLers and CFLers do not where a cup for fear of this. They'd rather take the occasional direct blow to the nards than risk getting Thoresen'd.

Again, that's just by memory.

Vic Ferrari said...

A preemptive strike at the grammar Nazis: That should read wear a cup.

MikeP said...

Vic, after Lapointe took a shot to the nards from Fleury, he said that he knew of at least one NHL player who didn't wear a cup (presumably for that reason). Lapointe declined to name him though.

I think as an NHLer, I'd rather wear a cup than not. Thor's misfortune aside, I've seen a lot more guys take a shot to the harbles from a pissed off goalie's stick than I have take a slapshot -- Mike Green's rocket or Ryan Smyth's muffin, take your pick -- there. For that matter, I've seen a lot more skate blades in the vicinity of the babymaker than pucks.

Hm, what's worse, getting a puck there, or a skate blade? I volunteer Avery to find out.

DMFB said...

Surely there are a whack of science types lurking around here, hopefully they chime in.

Yeah, I would really like that, if only to save me from having to call my high school physics teacher about this.

alan said...

A preemptive strike at the grammar Nazis: That should read wear a cup.

If only one sentence follows the colon, do not capitalize the first word of the new sentence.

Ender said...

IIRC, there are three different ways you could look at this: force (how hard it hits), energy (how much damage is done), and momentum (I have nothing to put inside these brackets).

Given that the original question was how hard it would hit, I think the original equation answers the question.

That said, the other 2 equations are relevant as well. I mean, who doesn't want to do the math with regards to how far back Thor fell and what that means with regards to how much momentum carried his junk into his body cavity?

Doogie said...

Incoming maths from a first-year biomechanics student and former electronics major.

On the subject of "how much would that fucking hurt", then you could look at:
--momentum, m*v, the easiest measure based on a few assumptions about relative puck speed
--kinetic energy, 0.5*m*v^2, see above
--the force imparted, which would be the change in momentum (assume the puck comes to rest for simplicity) divided by the time it takes for the force to be imparted (i.e. the time between first contact with the cup and beginning to fall -- probably not something anyone's going to volunteer to measure based on the film or anything).

Based on any of these measures, using Cosh and Dorito's numbers, bullet wins. Consider the first example, the .22. Mass of 3.26 grams, velocity of 3,060 kph, or 850m/s.
--Momentum (p) = m * v = 0.00326 kg * 850 m/s = 2.771 Ns
--Kinetic Energy (E) = 0.5 * m * v ^ 2 = 1177.675 J
--Force imparted (F). I have no idea how long it would take for a bullet to impart a force on a scrotum. Let's go with 5 ms. 2.771 / 0.005 = 554.2 N, or the equivalent of a 126 lb weight.

Compare with the puck (m = 170g; 90mph = 40 m/s)
--p = 0.170 * 40 = 6.8 Ns
--E = 0.5 * 0.170 * 40 ^ 2 = 136 J
--Assume the puck stayed against the cup for four video frames, or 125 ms. F = 6.8 / 0.125 = 54.4 N or 12.3 lb (basically, my numbers roughly agree with Dave's -- If you use his 0.152s number for time of impact rather than time to arrive at the target, you get 44.7 N or 10.2 lb, which agrees with him exactly)

So what we get here is that while the puck has more raw momentum, the bullet has far more kinetic energy and imparts a far greater force based on how long it spends against the area of impact. (I ran the numbers for Dorito's other examples: for the .308, p = 8.829 Ns, E = 3,575.745 J, F = 1,765.8 N or 401.4 lb; for the 5.56 mm, p = 3.76 Ns, E = 1,767.2 J, F = 752 N or 170.9 lb; for the 9 mm, p = 2.8 Ns; E = 490 J; F = 560 N or 127.3 lb)

If you wanted to look at the relative damage done, kinetic energy is one clue, the other being the surface area impacted. The impact surface of a puck, unless you caught the very edge, is going to be a lot larger than a bullet's by default, which means the bullet almost assuredly wins before even considering anything else. And no, I'm not doing that math. Someone else can figure out the relative area of nutsack that would be impacted by the puck or cup.

Doogie said...

That first sentence in the last paragraph should include both kinetic energy and force as indicators of damage done, as well as surface area impacted. Whoops.

Oilman said...

If nothing else, this post has expalined why you don't hear of many "drive by puckings"

doritogrande said...

Can't be givin credit to me, those numbers were mikep's. I'm the kid that went into a 60% final in calculus with an A+, and left the course with a C+.

I can however, dissect anything in the animal kingdom. And coming from a biological standpoint, Thor shouldn't be back at the proverbial plate until the end of the Flyers playoff run. And it'll probably hang a little lower after all the abuse.

DMFB said...

My lifelong dream of bringing rigorous scientific analysis to taking a shot in the pills has finally been realized.

For that, I thank you.

Ryan Budney said...

Military types do quite a lot of ballistics studies on how much damage various projectiles do. And generally speaking, the amount of damage done does not corollate to the energy carried by the projectile -- so E=1/2 mv^2 isn't the whole story. The reason is that a high velocity bullet has the tendancy to go straight through a body. Lower velocity bullets deflect off bones and get several chances to puncture major organs.

Think about the puck that Pronger took to the chest a few years ago. It stopped his heart temporarily or something like that, no? If Pronger had the option of that or a .22 to his heart, I'm pretty sure he'd choose the puck every time. Even if the .22 didn't have a immediate direct impact with the heart, it has a decent likelyhood of hitting a shoulder blade or something and bouncing around his chest cavity, doing real damage. On the other hand a high velocity bullet has a reasonable likelyhood of going straight through the body, not damaging any major organs (unless it's made of something designed to explode on impact but that's another story).

I didn't win any major prizes in highschool, just a heritage scholarship...

Vic Ferrari said...

alan said:

If only one sentence follows the colon, do not capitalize the first word of the new sentence.

That's funny, and thanks for the pointer, I should have known that.

When bitches come out of the woodwork to snark on somebody's inappropriate use of an apostrophe, typos, overuse of ellipses and emoticons, or the wrong there/their being used ... that gets on my tit. :)

Vic Ferrari said...

This is all good stuff, but I'm still not convinced that pure theory is enough, how much of the energy is being dissipated by the bullet disintegrating, the puck rebounding, the player's whole body being jarred back, etc?

I think we need an empirical solution. My MS Paint entry is the nutcracker.

So that heavy steel plate with the L-shaped cross section hangs from the brick wall by a chain. Then you pull it forward and put a walnut behind the business edge of the plate and the wall.

Then, shoot the target on the steel plate with a .22 rifle from different distances, and fire slapshots at it as well.

Then observe the relative damage to the walnuts (or sheep testicles, brusselsprouts, hard boiled eggs ... I'm willing to be flexible here).

As for my high school qualifications, which have never more important than now: I was voted 'most likely to succeed' AND 'partier of the year' by my graduating class. The rare double.

LittleFury said...

But do "shots directed at junk" show up in the Corsi numbers?

teebeeplayer said...

Fantastic thread. Surprised though at the lack of a good Norwegian Wood joke...

andy grabia said...

Isn't that good?

garnet said...

Ducks out; well worth updating blog for!

Lord Bob said...

The CinO guys are probably busy huddled around an altar directing their combined psychic energy to the total defeat of the Flames in game seven.

Granted, the combined psychic energy of the CinO guys probably couldn't coax Joe Thornton to actually shoot the puck when he's alone in the slot, never mind win a hockey game. But still. Dare to dream.

MikeP said...

Vic, would you call somebody who used incorrect maths or poor logic in their posts? If so, why not call out bad grammar? "You knew what I meant" isn't good enough, love your tools and your tools will love you. Abuse your tools, and tools will abuse you. (take that how you like.)

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