# The effect of a 20 kilojoule punch on a person that is wearing a plate armor

I have always been in love of hand to hand combat but I realize the concept of efficiency and why that is not an ideal choice for combat so I decided to write a story in which characters who are powerful martial artists will use hand to hand combat in a medieval setting in which I settled on a gorilla strength for the main characters which I looked up to be around 20000 joules(the power of a 50 cal BMG) so the issue is what would the damage/effect (Will they get launched into the air?) of a punch on armored foes(unarmoured if you could) be?

Assume :

• It is one singular punch
• It is a body blow directly to the chest, it is not aimed to knock out.
• The one doing the punch is durable enough
• The one getting punched is all-around normal
• Mass of the puncher is 100 kg( you may change the weight as you see fit for the character to remain stationary)
• The puncher is 2 meters tall
• To clarify, both parties are human

I trust you to choose to fill in everything else that I missed and if you have a formula or actual examples of such effect that would be great.

• Joules? Newtons are the unit of force. Is this some usage I don’t know? – SRM Nov 27 '19 at 1:29
• Joule can be used in the kinetic energy formula for easy calculations and can be converted into "Lbs" directly which is most commonly how people calculate punching power which can be converted to Psi also you can not convert joule to newton(J to N) but you can if you make it N.m at least this is what I know feel free to correct I am new to this. – Thander Nov 27 '19 at 1:42
• The person will die, unless you've punched somewhere non-lethal. This isn't an answer, because I haven't run the calculations, but plate mail isn't going to help. Punching with the force of a .50 cal round is horrifying. Even the force of a .22 would be effective, if not instantly lethal. – Halfthawed Nov 27 '19 at 1:50
• The assumption is that it is a body blow and with armor and the weapon is the human hand plus the pressure is not the same it is over a 100 times the surface area I am not sure that one hit is lethal unless it is on the head then it would be about accelerating the brain than brute damage by the way 20000 joule is 4 to 6 times a strong boxer it is not that extreme. Considering this unless it is a knockout or a liver shot you could be punching over 100 times I am not sure it is lethal. – Thander Nov 27 '19 at 2:00
• @Halfthawed The kinetic energy of a .22 is negligible when spread over a fist-sized area. If it weren't, then it wouldn't be possible for someone to fire a .22 pistol held in a fist-sized hand. Bullets are dangerous because they're small and concentrate their energy in a small area, not because that energy is particularly high. – manveti Nov 27 '19 at 2:20

You are effectively spreading the energy of a .50 caliber bullet over the area of a human fist, so let's do some math. The diameter of a .50 caliber bullet is (unsurprisingly) half an inch, giving it a frontal area of 1.27 square cm (we're disregarding the fact that the bullet isn't just a cylinder, but it'll do for a first approximation).

Now onto the area of a human fist. We'll assume that the puncher knows how to throw a punch, and is hitting solely with the knuckles. Here, I'll have to rely on my own fist and hope that it's roughly representative of the general population. According to my ruler, my knuckles, when I close my hand into a fist, are about 8 cm wide, and about 1cm high, for an area of 8 square cm.

So, you're hitting with a surface that is almost 7 times the area of a bullet with equivalent energy. According to the Wikipedia article on the .50 BMG, it is capable of penetrating 22.2 mm of steel at 100 yards. Dividing this thickness by a bit less than 7 due to our increase in surface area, we get a rough estimate of being capable of punching through about 3.25 mm of steel. We'll bump this to 4mm, to account for the fact that the kinetic energy of a shot will drop somewhat by the time it makes it 100 yards.

Medieval plate armor thickness varied wildly, depending on who made it, when it was made, where it was made, and what it was for. Jousting armor was typically extremely heavy, and a jousting breastplate was typically about 5mm thick, so that would probably stop a punch. The guy inside is going to start having a significantly worse day, and you'll knock him over (he'll probably slide for a bit, too), but the armor will probably stop at least a single punch without completely failing. Typical armor for actual warfare was generally much thinner, however, as one actually had to be able to do more than ride a horse in a straight line at a single opponent during a battle, so the most likely scenario is that the puncher's knuckles end up somewhere inside the chest cavity of the punchee. On an unarmored punchee or one who simply has the light cloth or leather armor usually worn by the vast majority of medieval soldiers, the likely result is that the punchee ends up impaled on the arm of the puncher.

Note that this is all assuming that the person doing the punching is in possession of an indestructible hand, arm, and shoulder. If you were to somehow try this with an actual person, the result would be a dented piece of armor, a hand that suddenly has an exponentially larger surface area and a lot of screaming.

• I feel that the length of the first fingerbone should perhaps be included in the fist area. If mine are close enough to yours, that would be 6 cm, which will make for a painful but likely non-lethal blow even without armor. Especially since you go into penetration depth, and those fist parts are going to be closer than your penetration depth is deep. – Gloweye Nov 27 '19 at 12:50
• @Gloweye I'm not sure if I punch like a normal human or not, but having run a few tests involving me punching things, the first joint of my fingers is generally at least an inch behind my knuckles in terms of distance from what I hit. So although the fact that one's fist grows in area rapidly will have an impact on the punch, if your knuckles are over an inch into someone's chest, that person is going to be having a very bad day. – Gryphon Nov 27 '19 at 12:56
• I'll fully admit that my fight-experience ranges somewhere between "very rare" and "never", but if I try angle it so that the first joint is an inch away, Then I almost make a 30 degree angle. But of course, I could just be punching wrong. It's not like I'm good at it. And yes, at that force you'll be having a very bad day. On both ends of the fist. – Gloweye Nov 27 '19 at 13:01
• @Gloweye I did put in a paragraph at the end explaining that I'm assuming the puncher is indestructible. Because if any actual human somehow punched steel with that amount of force, their hand would end up splattered over a decent radius. And yeah, I do tilt my fist down a bit when I punch, and it's entirely possible that I'm doing it wrong, not you. My fighting experience is also very much on the "never" end of the spectrum. – Gryphon Nov 27 '19 at 13:04
• I feel like disregarding the fact that a bullet is not a cylinder makes the approximation very inaccurate. Concentrating the force of impact on a very small (far smaller than the .5 inches of the bullet) area is what makes or breaks penetration capabilities of projectiles. – RancidCrab Nov 27 '19 at 14:19

Apparently, Rocky Marciano (the model for Rocky Balboa) had a punch measured at approximately 1000ft-lbs, or 1355 joules in less weird units. He weighed a mere 85kg, so he's a bit lighter than your target 100kg, but it seems close enough.

Lets assume that all else being equal, the energy of a punch scales linearly with the weight of the puncher. A 100kg Rocky would generate 1600J in a punch, and your target is 12.5x that. Assuming you can model a punch using the good old $$E_k = \frac{1}{2}mv^2$$ equiation, to reach 20kJ he'd need to punch about 3.54x faster (because velocity scales in proportion to the square root of the kinetic energy). A fast human punch is about 15m/s (Ricky Hatton was clocked at 32mph, about 14.3m/s, and similar speeds have been observed in other boxers and karateka). Your super-punch therefore needs to be travelling a little over 53m/s. For reference, that's about 119mph.

A black powder musket, by the way, develops a muzzle velocity of over 120m/s, and a medieval crossbow would manage a little over 90m/s. A roman sling bullet on the other hand only managed 45m/s, and they're know to be pretty hazardous things.

So, your peeps can punch 3.5x faster than regular humans, delivering about 12.5x more energy. Force is defined as $$F={\Delta p \over \Delta t}$$, the change of linear momentum over time. Momentum, $$p=mv$$ is proportional to velocity. Lets assume that the time over which momentum is changed is the same for your peeps as it is for regular modern-day human boxers (which is a slightly dubious assumption, but it'll do), so the force of a super punch will be 3.5x stronger than for a regular human.

I found a few more sources for the force a boxer's punch than for the energy of the punch. From this short article, we get a punching force of 1300lbs, eg. 5783N. This mentions a 400kg punching force, eg. 3923N. This suggests that Wladimir Klitschko could develop 5000N of force. He's a bit heavier than your target weight at 109kg. but lets use him as our model.

Using these assumptions, your super-punches develop a force of 17.7kN, which is motor-vehicle-accident level. Exactly how this translates into damage effects though, is hard to say. As Adrian observed above, this amount of force will be extremely bad for the puncher, who risks destroying their own hand and arm unless they have the required secondary superpowers of having really tough bones and flesh. They'll need to work on punching technique to avoid pushing themselves away, or otherwise being unbalanced. A good uppercut would let them push against the ground (which hopefully isn't too soft!) and the energy involved will be enough to lift a 100kg victim off their feet and into the air, streetfighter-style.

Obviously, punching an armoured opponent in the chest would be a silly idea, because if they're decently protected (and a medieval knight certainly would be) you're not going to do much more than knock them over. They're clearly strong enough to lift an armoured knight off the gound and slam him into the ground, probably with enough force to kill if the surface is hard enough and certainly with sufficient force to give them some nasty concussion that will take them right out of the fight. Why risk your hands punching? Punching is a terrible way to fight, and only done by people who can't use weapons!

That said though, if all that force was concentrated on an area of just 1cm2 (say, a knuckle or two) you'd generate an impact pressure of 177MPa. That's quite a lot, and perilously close to the yield strengths of medieval steel. I can't be certain than your super-punchers could dent a breastplate just be punching it, but they're not far off. Even with the simplest of weapons (such as some simple spiked knuckles) they could probably breach armour.

As to the effect on unarmoured foes... well. A punch to the head will be fatal, more or less immediately, through traumatic brain injury and probably a fractured neck into the bargain. A punch to the chest could eaisly break bones, which may in turn cause a punctured lung (especially with a followup punch), an almost certainly fatal injury in medieval times or simple inability to breath due to flail chest. There are a whole load of other chest injuries, most of which are likely to be debilitating and later fatal in the absense of modern medical care. Blows to the abdomen will probably rupture internal organs. Blows to the liver or spleen will be immediately debilitating, and death can follow fairly swiftly from internal bleeding. There will be crush damage to overlying tissue, though under the circumstances this probably won't be a big concern to the victim.

Basically, it'll be like using a mace on an unarmoured target.

There's some more investigation to work out just how tough your super-punchers would have to be to withstand the forces of their own attacks, but they're likely to be formidable combatants. The most sensible thing of course would be for them to don armour and carry weapons, to increase their power and resilience yet further...

Assuming the punch does not penetrate, then the effect in terms of momentum transfer would be the same as someone firing a .50 cal rifle, like a Barrett Fifty.

In other words, very little.

Bean bag rounds which the police fire from 12-gauge shotguns, hit with around 100 joules of energy, kinetic rounds like plastic/rubber bullets, 40mm sponge grenades, etc. up to about 200 joules. These are not effective against anyone wearing armor and essentially rely on pain for their effects as they are designed not to penetrate or do permanent damage. (Exceptions occur with eye sockets and other 'accidental' effects).

Obviously you are talking about higher energy levels....but note that gorillas do not kill each other in fights, nor are they especially dangerous to large predators. A gorilla punch is not a superweapon, and if you punched a solid target you would break many of the bones in your hand.

• "In other words, very little." er, up to a point, lord copper. I wouldn't recommend bracing the butt of a 50 cal against your sternum, or abdomen, and then firing it. Or firing it whilst the butt wasn't actually in contact with you, but a distance away. Don't assume that a well-braced rifle with a proper stock is the same as a random impact to the torso with similar energies. – Starfish Prime Nov 27 '19 at 13:41
• Starfish Prime - certainly, but I would hope the armor does a reasonable hon of spreading the impact. And the Waugh made me smile :) – David Hambling Nov 28 '19 at 15:25

The human arm is 6.5% of total mass therefore 6.5 kg. So your 20 kJ punching-arm is travelling at 78 m/s. Assuming an inelastic collision and a 5kg chest plate, the combined mass of (puncher's arm plus victim plus chest plate) is now moving at 18.9 m/s (42 miles per hour). That's equivalent to being hit by a car and would knock you back some distance. The UK authorities are fond of a statistic that if you're hit by a car at 30 mph there's an 80% chance you'll live, whereas at 40 mph there's an 80% chance you'll die, however, I believe the killing factor tends to be the secondary impact of head-on windshield rather than the initial blow to the torso.

Now set the kinetic energy equal to work done to calculate the impact force. The equation is KE = F x d so we need to know the distance over which the force is exerted. Assume an arm swing of about 60cm, then 20000 = F x d = F X 0.6 therefore the impact force = 33.3 kN. However the victim is wearing plate armour so that 33.3 kN force exerts pressure over the entire chest, let's estimate 600 x 300 mm or 0.18 m^2. So the pressure = force / area is 185 kPa (or 27 psi / 1.9 bar). That might smart but it's definitely not going to kill, although if the victim hits his head when knocked back he may still die - some head protection would be a great help.

The situation is much worse for the strong attacker though: he is spreading the same impact force over a much smaller area, optimistically a fist measuring approx. 100 x 50 mm but potentially just a knuckle measuring 1 x 1 cm. That's an impact pressure of between 6.9 MPa and 344 MPa, which is going to be pretty devastating for his hand. (Bone has a compressive strength of around 170MPa so if the puncher makes contact with only 1 or 2 knuckles rather than a perfectly flat fist then he's going to break bones and is fairly close to the limit of compressive strength of his arm bones. The shear strength of bone is even worse at 51.6MPa, so any bad contact at all is likely to break the proximal phalanges (finger bones nearest the palm of the hand).

20 m/s is a speed of a target (if it will not fall apart) after a punch. This would definitly rise what left of him into the air for about 0.5-1 second (depends on punch vertical angle) and flight distance 10-20 meters

Asuming armor would prolong the acceleration time - it would give about 200-100g of acceleration. Crush dummies bearly survive this (thershold is about 150g). Trained person expecting punch would survive. But surviving - doesn't mean no damage, or even no permanent dammage. Person would die without immediate modern medical help and would die for certan in medieval times. And even if he would be saved for some mirracle - he would be broken for the rest of his life.

Also some secondary superpowers requiered for puncher - he need strong bones (see Gryphon answer) and even more than that - superstrong joints (they are weeker than bones) and supergrip with earth. Last one is very important - third Newton law is plaing against the puncher. There are three possibilites:

• puncher flyes in the opposite directon of target with same or (if puncher has no armor) times greater speed (and target recieves same times less powerfull punch)
• puncher dumps the impulse with its superlegs and supergrip (or by pushing itself from the wall) and stay in place - most powerfull punch
• (most funny one) puncher was already flying to target when he was delivering the punch with the speed 20-40 m/s (depending on it weight) and then he just stops (dumpung impulse in his superarms, superlegs and superspine) and target flyes away.

(I do not consider case when puncher and target fly to sunset together - it wouldn't be punch, but push)

• That does rather assume that a punch is a perfectly elastic collision, and there will be a nice neat transfer of momentum to the punchee. This probably won't be the case, though the victim will in all likelihood leave the ground and fly some short distance. I was careful not to put any numbers of it myself ;-) – Starfish Prime Nov 27 '19 at 14:18
• @StarfishPrime, I doubt that superfighter can deliver punch of exactly 20 +-2 KJ. All numbers are first-order approximations, obviously. So heat losses can be neglected - and this gives us perfectly elastic or inelastic collusions. – ksbes Nov 28 '19 at 6:49