Momentum or kinetic energy: Which one pierces a T Rex’s chain mail on a glancing blow?

Here’s a collection of online bric-a-brac with connections to this site’s gaming material:

Dinosaurs and their tails

Having written about both dinosaur design and tail design, I can’t help but comment on the Smithsonian blog’s report that dinosaurs may have had thicker, beefier tails than often depicted. Sounds fine to me, at least until we get that cloning process working to verify things.

What does that mean for critter design? Well, nothing, really. About all I can note is that, using the above tail rules, your dinos really should go for the heavy tail option instead of the slim version – although that always sounded right for dinos anyway. Hmm, the article also suggests that the extra tail muscle may have aided running speed, so that’s another argument for fast dinos – though, as noted in my dino piece above, it’s always been sensible to just make up whatever speed the game action calls for.

All right, so I have no purpose in noting this bit of news. But hey, it’s about dinosaurs.

Tyrannosaurus Had Extra Junk in the Trunk

Swords are good crushing weapons

As are axes, and spears, and any edged weapon, when they whack an armored target into pudding beneath his stout, un-penetrated metal. That’s the premise of my Edge Protection rules, and the gist of findings from test cuttings and battle reports. As compiled in the article linked below, many writings tell of medieval knights left roundly bruised, stunned, and fractured by edged blows that failed to break the armor but still delivered massive crushing wallops to flesh and bone.

The EP rules neatly inject that outcome into GURPS, with interesting related effects like boosting the appeal of maces – the other knightly weapon – when facing armor-clad foes. Give it a try!

Edge vs. Armor 

Glancing blows do glance off

Who’da thunk. The general fact is obvious, but it’s interesting to see research on the additional kinetic energy needed to pierce armor with arrows when striking at specific oblique angles. It fits right in with my DR-enhancing rules for grazes – though seeing as how it apparently takes a pretty severe angle to double the KE requirement, perhaps my use of doubled (and greater) DR is a stronger multiplier than reality calls for?

Glancing Blows and Armor Penetration

What causes damage?

Speaking of KE, I have a geeky interest in that old chestnut of RPG simulation fetish: What sort of physics actually create the “damage” from a sword, club, or bullet? Is it all about momentum? Kinetic energy? Impulse? What?

I’ve been poking into that heavily of late (and in fact have been doing so on and off for years…), and am finally coming to see the big picture. After sifting through academic papers, testing reports, physics treatises, enthusiast forums, and much more, I’m ready to reveal what I’ve learned from countless helpful sources. Get ready; here’s The Answer! In helpful bullet-point form:

  • Damage from an impacting weapon is essentially a matter of kinetic energy.
  • No, it’s not about kinetic energy per se, it’s about energy transfer.
  • Wrong, it’s all about momentum.
  • Kinetic energy. The momentum factor is a myth.
  • It’s momentum. Kinetic energy? Myth.
  • No, it’s [impulse / “stopping power” / work / fill in the blank]. Other stuff is myth.
  • It’s a mixture of [insert two or more factors from the above] and can be neatly simulated as such.
  • It’s a mixture of [insert two or more factors from the above] but is really complex and can’t be reasonably simulated at all.
  • It works this way for low-velocity stuff, and that way for bullets.
  • No, it’s that way for low-velocity stuff, and this way for bullets.
  • Swords, bullets… it’s all the same.
  • Cutting tests on deer prove it’s [pick one of the above].
  • So? My uncle’s friend was a cop, and that proves [pick another of the above].
  • We can find an answer from this guy’s tests with arrows and armor.
  • What? That [guy / armor / arrow design / material under armor / measurement method] is totally bogus.
  • All i know dood is its lethal power thats force times impact and velocity is a square so its like double but ya theres serface area to thats psi or something hey i saw it on discovery chanel LOL OMG THX BAI
  • I don’t know what I’m talking about, but these imagined anecdotes should settle the case for someone who can tell me what my stories mean.
  • No, try these thought exercises instead, none of which recognize the need to reduce the number of variables to few (let alone the desired one).
  • Here’s some big game hunter’s obscure formula for kill power!
  • He was a pansy! Use this game hunter’s formula!
  • Wound channel!
  • No! Depth of penetration!
  • Both! With penetration based on KE! Think of bullets and armor!
  • No! Penetration is based on momentum! Think of arrows and sandbags!
  • But flesh damage is different from penetration!
  • Flesh damage is penetration, of flesh!
  • Won’t someone think of the coefficient of restitution?
  • Sure! Now consider that with loss of kinetic energy, and…
  • (GOTO 1)

Really, do a little digging, and you’ll be amazed at the amount of debate and science and conjecture that comes to nothing concrete. Observe the rampant non-agreement over the respective roles of energy and momentum! Thrill to academic papers that compute punch impact from the mass of a hand vs those that use the mass of a whole arm vs those that use the mass of the whole body! Gaze upon “Physics and the Martial Arts” treatises that say nothing useful at all!

Of course, there are also some really good research and resources out there. And if there’s a lack of a grand Big Answer, perhaps it’s because this genuinely is a complex matter, with no easy, simu-riffic master formula that plugs into a game engine.

The bright side for the armchair game designer is this: With no known “correct” answer to exactly what a thrust sword’s mass and velocity mean for penetration and wounding, simulationists have a lot of leeway in turning those inputs into whatever outputs feel right and play well. There’s even a bit of such “nobody really knows, so I went with this method” to be found in Interior and Terminal Ballistics for GURPS, one of the best pieces of work you’ll find on such topics (and whose author has been very helpful in explaining aspects of his methods to me). If you want nifty universal simulation of bullet effects, you won’t find better!

So with nifty examples like that leading the way, I trundle along toward my own ideal system that’s always lurking just out of sight – but which, I’m happy to say, is lately becoming much, much clearer. Simulationist geeks, stay tuned!


  • The Ryujin

    I’ve never really gotten this it’s got to be one or the other mind set that people have, I’ve always figured that it was both momentum and KE working together (along with how quickly the attack impacts, relative hardness, material strength and so on) that determined penetration. In fact in a home brew that I’m working (that uses a spread sheet to let me do all sorts of crunchy goodness) an attacks penetration power is the square root of it’s KE and momentum divided by it’s surface area in square inches and then divided by 20 to get how many inches of meat the attack can lance through on a normal hit (I got that 20 from looking up the penetration results of several types of firearms and dividing the inches of penetration they did in balistic gel by the sum of the bullets KE and momentum then averaging the results). But anywho, very good article as usual and I really do hope to see you do a follow up soon on this topic.

    • tbone

      Indeed, it is both KE and momentum, plus the other bits of goodness you mention. The trick is how to combine all those…

      Curiosity time: When you say “square root of its KE and momentum”, what do you mean exactly? Square root of (kinetic energy x momentum)? Which, if so, boils down to basing penetration power (or other measure of “damage”) on, among other inputs, (velocity^1.5 x mass) – which is not a bad approach. I’ve seen used in some very respectable works of simulation geekery!

      • Esteemed Visitor

        Oh, sorry for the late reply. I posted this just before my computer at the time kicked the bucket and needless to say I kinda forgot about the fact that I commented here. To answer your question I use (SQRT(KE+momentum)/SA*in^2)/20 for penetration, damage is based on the square root of KE with a multiplier based on how deep an attack penetrated and how wide of a wound channel it makes. My current version also takes in account the fact that velocity a round hits at seems to increase it’s penetrating power. I model this by dividing the rounds velocity to the materials speed of sound and reducing the materials “toughness” (i.e. How resilient it is to damage, an attacks penetration power and damage is divided by this) by that ratio. My next task is to try to model round deformation. As it stands, a typical 9mm round will pierce 0.12 inches of RHA @ 30ft and 16in of meat which is pretty close to reality.

        Oh, and in case your wondering why I use a materials speed of sound to figure how much velocity effects penetration, it’s more or less a hunch. There’s not a lot of free available information on how high velocity impacts effect a materials resilience so I just ran a few thought experiments through my head and that came to me and so far it seems to work pretty well.

        • tbone

          Hmm, the use of SQRT(KE+momentum) is interesting. I don’t believe I’ve played with this sort of SQRT (A+B) for damage purposes, but have for other purposes. It’s somewhat similar to, but more interesting than, a simpler alternative: SQRT (larger of A or B). That is, SQRT (A+B) approaches SQRT (larger of A or B) when one of A or B is many times larger than the other, but never exceeds SQRT (2 * larger of A or B), which happens when A and B are equal.

          Sorry, just a side thought. I note it because I’m already puttering about with a damage scheme for which I didn’t explicitly consider your (KE + momentum)^X, yet for which I perhaps should, as my scheme already has some resemblance to the similar (larger of KE or momentum)^X. Slightly more specifically, it’s a scheme that has momentum-based effects begin transitioning to KE-based effects as velocity exceeds a certain threshold – with said threshold being, just as in your approach, very much a matter of the the materials involved.

          How to set that threshold for any material was an upcoming matter of guesswork for me. Try the speed of sound in the material as a starting point, you say? Hey, that could be a nifty idea! You should confirm your handle here – The Ryujin, right? – so I know who to credit if I oh-so-steal that. (My apologies if ability to leave a name was turned off; it was a temporary measure in battling waves of spam attacks. A name field should now be re-enabled.)

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