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Comics are full of superheros with super strength. These heroes punch through walls, lift and throw tanks, and wrestle with buildings.

But that's superhero physics. The fact is that without leverage, you'll likely knock yourself back from a significantly strong wall before you break it - it weighs more than you. You may punch hard, but you're not going to send people flying like meteors, because your arms just aren't that fast. And trying to lift a building is a good way to bury yourself in the ground.

Now for this question, I'm mostly concerned about how hard you punch/hit. So:

If some humans are a million times stronger, but not any faster:

* What factors would be most important for how hard they punch? Is it still strength, or do speed or mass become more important?

Bonus questions:

  • How hard would they actually be able to hit? Is there a formula you can use to determine this?
  • How much of a difference does it make if they're braced and can apply full force, vs not being braced?

Assumptions:

  • They're tough enough to take out the damage they would do to their bodies. So these humans aren't going to rip apart their bones and cartilage just by moving around.
  • Define the strength of a punch as the amount of force impacted to the target.
  • Obviously these humans would have incredible lift and grapple capabilities - I'm just concerned here about how much force they can put into a single impact.
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    $\begingroup$ The measure of the strength of a punch may not be ideal. The power (energy/time) of the punch also matters. Consider that a gentle acceleration on a highway onramp puts order of magnitude more energy into you than Bruce Lee's most powerful punch. $\endgroup$ – Cort Ammon - Reinstate Monica Oct 20 '15 at 20:16
  • $\begingroup$ @CortAmmon: Wouldn't that be covered by the kinetic energy imparted by the punch? I was a bit unsure of how to define this, so I tried to go with broad physics terms like energy transfer. $\endgroup$ – Dan Smolinske Oct 20 '15 at 20:22
  • $\begingroup$ I'm not sure what the best measure is. However, if we replace punching with tackling, we can compare a NFL tackle and the car on the onramp. If you are in a car, comfortably buckled in, accelerating to 75mph from a standstill, the car and carseat impart 20x as much energy as Baltimore Ravens starting lineman Haloti Ngata tackling you at full speed. $\endgroup$ – Cort Ammon - Reinstate Monica Oct 20 '15 at 20:45
  • $\begingroup$ Doing a little research, it looks like boxers tend to like to measure in terms of force, not energy. This also leads to interesting answers because you can do a lot of neat tricks with force that you cannot do with energy, because energy is conserved and force is not. $\endgroup$ – Cort Ammon - Reinstate Monica Oct 20 '15 at 20:49
  • $\begingroup$ (The NFL uses force as well. While the car may impart 20x more energy than Ngata's tackle, if you look at force instead of energy, Ngata literally hits like a ton of bricks) $\endgroup$ – Cort Ammon - Reinstate Monica Oct 20 '15 at 20:52
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In comments, I suggested that we should use force instead of energy as a measure of punch strength. I'm not entirely sure it is the most useful measure, but its what boxers use when we measure the strength of their punches. It also yields really nifty results, which is always a bonus in worldbuilding exercises.

You made the assumption that they can keep their body together when using this super strength to punch. However, nothing says the world around them can keep together, so we're going to have to model the forces holding together objects like people and safes. There are molecular forces which try to hold together an object. If you strike an object, the object "responds," typically at the speed of sound for that medium, distributing the force across the bonds. Ideally, it would distribute the force evenly across the object, but in a real world, sometimes that doesn't work. If superman punches a safe with enough force, he can force the object to deform enough that it cannot distribute quickly enough. In that case, some of the molecular bonds fail, and we see the end result of superman punching a hole right through the safe.

So we can model everything in the world besides our superhero as a bunch of small bits (molecules or larger) rigged together with springs which can rip apart if put under too much strain. It doesn't perfectly model physics, but it does describe the world well enough to give us hilarious slow motion videos.

So the question is what can they do without bracing. Because our superhero is being modeled as "tough" enough to not rip apart, we can treat them as one lump body, with a mass and a corresponding center of mass. If the superhero only uses his superhero strength in a way which does not move his center of mass (meaning his fist goes one way, and his body moves slightly the other way to keep his CM still), he can actually accelerate to any speed he pleases (and speed at impact * mass of flying object = force). So super strength actually does help!

However, if you punch at ungodly speeds (speed of sound, relativistic speeds, etc.) the world around you may not withstand the impact. If you try to maximize your force, by maximizing speed, you don't necessarily maximize damage. If you punch Lex Luthor in the gut, you really don't want the damages to be limited to a fist-sized hole. I'm sure he'd find a way to work around that impediment. You really want to do more damage than that. Somehow you want to hit in a way that hurts his entire body!

This is harder because we've hit the limits of what you can do with just the invincible parts of your body. To do more damage, we need to start using all the resources available to us, like the soft squishy body of flesh right in front of our invincible fists. This is going to sound a bit strange, but we're going to hit softer to hit harder!

Visuals time! We need something on a human scale to capture what we're trying to do. Let's say our opponent is something soft, like a nice moist cake standing upright (maybe the cake is in the shape of a punching dummy). We want to use one of our fingers to strike the cake and do as much damage as we can. Sure, we can just ram our finger through it as hard as we can, but that only makes a 1cm wide hole in the cake. However, what if we had something soft and squishy, but bigger to help us out. Soft... squishy... tomato! For our visual, let's pretend we have a tomato in front of our finger, in front of the cake. I have no idea how this got so strange so quickly, but the visual works out. If we unleash full force, we squish a hole through the tomato, into the cake, but we can only make a finger-sized hole. However, if we can unleash softer, we can give the tomato to accelerate into the cake. Now we can make a tomato-sized hole! All we have to do is hold back just enough to avoid breaking the tomato's skin with our strike.

Okay, normal-human scale imagery aside, our superhero needs to punch with just enough force to accelerate the region they hit to use those molecular bonds to accelerate the nearby region. Then this region needs to accelerate just fast enough to accelerate a bigger region, and so forth. By hitting softer, we hit harder!

This means the effect of super strength is also dependent on your ability to strike wisely, not just hard. If you can strike in a direction which takes advantage of the strong directions of a bone, you can affect a much larger region. You're literally using their strength against them.

To strike harder than that, we need to work with our opponent. Yes, first we hit softer, then we work with our opponent. A lot of things in the body, like non-innervated muscle tissue, is really bad at transmitting forces for us. We'd do a lot better if we could convince our opponent to tense their muscles at just the right time. This is not easy. The easiest way to do this is to make them flinch before you punch them. Then they tense up, and the muscle transmits your punch better.

There is a school of thought which suggests that the most powerful punches are not the big ones, but the small ones. The smaller the punch, the more you can feel what your opponent is doing, and adapt to them. If they tense in one way, you adjust yourself to take advantage of that particular way they tensed up. This could hypothetically lead to punches which begin to use the opponent's mind against them. If you can figure out how they're thinking about the punch, and adapt what you are doing to encourage them to give up a mental high ground in return for a physical high ground, you can strike them right in their core, destroying their will to fight, rather than just their ability to.

So super strength is useful because you can generate as much force as you want. However, while a force of four tons may crush bodies, a force of four ounces, applied properly, may crush a soul.

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  • $\begingroup$ he can actually accelerate to any speed he pleases - is this actually true? I'd assumed that there was a limit on how fast muscles could contract or expand that has nothing to do with strength. I mean, to some extent strength seems to be defined by how fast muscles contract: en.wikipedia.org/wiki/Muscle_tissue#Comparison_of_types Which makes this question a bit weird, but I would assume there's some sort of hard physical limit as well. $\endgroup$ – Dan Smolinske Oct 20 '15 at 21:36
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    $\begingroup$ I ran on the assumption that superstrength was best handled in a handwavey manner. Otherwise we have discuss how we modify the behavior of the body to generate super strength, because the implementation of that superpower would suddenly matter greatly, and get bogged down in details. I mean, super strength is right up there with spinning the world backwards to go back in time; -) $\endgroup$ – Cort Ammon - Reinstate Monica Oct 20 '15 at 21:56
  • $\begingroup$ True enough, but usually I assume most super strength to be subject to these limits. So after a certain limit you would need fist weights to increase punch damage. The weight could easily be supplied by the heavily armored gauntlet that is included in your bullet proof plate armor... But really the bottom line is that there are different types of super strength with different assumptions and they, not surprisingly, work differently. $\endgroup$ – Ville Niemi Oct 20 '15 at 22:18
  • $\begingroup$ And for that matter there are different types of punches that work differently, asically you can apply either force (ma / braced) or impact (mv / unbraced). You can also apply power, but that is really more like wrestling. $\endgroup$ – Ville Niemi Oct 20 '15 at 22:21
  • $\begingroup$ "There is a school of thought which suggests that the most powerful punches are not the big ones, but the small ones." Interesting. This works well also for something I'm working on. Would you be willing to expand ever so slightly on this? Any references, links, etc. for those who want to know a bit more? $\endgroup$ – a CVn Oct 21 '15 at 8:32
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I agree with OP's assertion that strength and speed are essentially two different things. And there is rigidity, which is another factor in punching. Here I explain 3 levels of strength and speed.

1- A Punch That Shatters Bones!

This is the first order of strength and speed. People like that exist in hundreds in our world. One punch from a non-gloved heavyweight boxer and goodbye to a few ribs of the opponent. The only thing that matters here is power delivery.

2- A Punch That Sends People Flying!

This is the next level of strength and speed. Here you not only require much more strength, but also quite a faster transfer of energy too. Think about a person hitting another with a baseball bat. We know it shatters bones (like a boxer's punch). Now think about a baseball hit that sends the person flying 5 feet away in the air. The bones are STILL shattered but the swiftness of impact also sends the target flying back. It is sort of like a a shotgun hit. It is blunt impact, but very energetic and very quick. Surprisingly, you do not expect such a punch from boxers (enough energy, but too slow delivery) but from kungfu masters. There are some styles with open palm fighting (ba gwa and ni zhong etc) where the impact is so swift that it really sends the opponent flying 3-4 feet backwards. However, since a palm has a much larger area and is not as hard as knuckles of a punch, the bones are not broken.

With strength alone (and not speed) you can send your opponents sliding on the floor (if it is smooth and lubricated) but not flying in the air.

3- A Punch That Goes Through The Person!

Now this is the epic end of speed. Imagine a person getting hit with a M16 bullet versus a person getting hit with a shotgun shell. The person hit with shotgun pellets would go flying but the person getting hit with the rifle bullet would stay standing and have a hole through him. That is speed!

To punch through a person (or wall) you would need extremely fast energy transfer. You would also require really high levels of energy AND a truly rigid surface. There is a Filipino master who pokes through coconuts with his index finger, but there is no master who could pass his open palm through the opponent. That is too much area and the palm is too soft to crack open a gash in the opponent's skin.

Lifting Buildings

Now that is interesting. Here we are not only talking about extremes of weight lifting (power) abilities, but also the ultimate strength of skeleton too! Weight lifters often have short, stocky physiques to compensate for carrying 200-300 kg weights. To pick up a whole building ...

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  • $\begingroup$ the shotgun shell doesn't go through because it's a lot bigger than an M16 buller, kind of like why bullets don't go through you when you wear a bullet proof jacket. and the speed you're talking about isn't the muscular speed which I think the OP is referring to, which is how fast a muscle can generate movement $\endgroup$ – Aequitas Oct 21 '15 at 21:11
  • $\begingroup$ Shotgun pellets don't go through a person either. And pellets are far smaller than a bullet. $\endgroup$ – Youstay Igo Oct 22 '15 at 16:25
  • $\begingroup$ but there's a lot more of them, in total they're a lot bigger and the energy from the gun is spread out over all of them $\endgroup$ – Aequitas Oct 22 '15 at 21:42
  • $\begingroup$ ... which is the point I already stated in my answer. To punch through a person (or wall) you would need extremely fast energy transfer. You would also require really high levels of energy AND a truly rigid surface. $\endgroup$ – Youstay Igo Oct 23 '15 at 1:00
  • $\begingroup$ yes, but your first paragraph you're saying that the only difference between the shotgun and the rifle is speed, which is simply not true. If a scrunched up piece of paper were travelling at that speed it would not go through a person because it's a lot lighter and thus has less energy $\endgroup$ – Aequitas Oct 23 '15 at 1:25
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One thing the other answers didn't touch on is bracing, and it will definitely help. If you have a solid object to back against then you can apply that much extra force in the direction of your punch. For example a super strong human against a tank is not going to be able to do much, they may just about be able to dent the armour if they take a run up but even that's unlikely.

However if they get their hands in gaps in the tanks armour or get something like a wall to give them a brace then at that point they can actually apply their strength. A super-strong person against a tank with real-world physics is not going to punch their way through, even with a wall to brace against they are more likely to move themselves backwards than damage the tank.

Instead they are going to rip it apart.

Something else to keep in mind is that materials in large scale behave differently, for example think of a film where someone grabs a fire truck and hits another target with it. Is a fire truck really going to act like a solid club in that case or is it going to bend and deform with every impact?

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Slow but unstoppable punches

(Normal) punching power is determined by about 5 factors: footwork, weight shifting, stepping in during a punch, pivoting the arm, and lack of arm punching. This mean that when impacting the arm should already be straight, as it needs to transfer the energy of the impact through the rest of the body. The stronger a person is the better they can do this. If you're not defying physics, this means that a person's punch is always somewhat limited by their mass, and their ability to launch themselves towards their opponents using their surrounds. If the superheroes are flying, the difference in speed between the hero and it's target also equates into the impact of the punches.

If you prefer quick punches, where the punching power comes only from the speed and impact of the arm, the power is determined by the speed and arm mass on impact. Since an arm does not contain a lot of mass, the impact will be less, unless the speed is increased so much, that the mass of the arm becomes irrelevant. You could also rule that your heroes are so good at punching they can set their body's mass behind each quick punch. You might be breaking the physics a bit if you want this.

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Force is always Mass times Acceleration. For a given amount of mechanical power in the arm propelling the fist there is an upper limit on the force exerted .. the mass of the fist.

Oh .. Err; You also have to account for friction against the medium the fist is moving in. If the punches length of travel is long enough heating effects could play a role.

Strong muscles mean high acceleration is possible, as is immense pressure. Throwing a punch means propelling the fist at hundreds or even thousands of metres per second so that our hero can smash walls, pierce metal, and detonate bodies.

a point of information for Youstay Igo about punching holes in things. High level energy transfer is not needed. I can punch a hole in sheet metal by pressing a cutter head thru the sheet at low speed using only about 100 foot-pounds of pressure (my arm + a short lever) because I am creating a localised shearing action at the edge(s) of the cutter head. The "trick” is that there has to be a matching hole in a well anchored backing plate on the other side of the sheet of metal that acts to concentrate the force applied in a very narrow region of the sheet, breaking the crytalline structure of the metal and severing the plug from the surrounding metal, while resisting the pressure being applied.

To punch a hole in something that is not braced against moving you must apply the shearing force against the inertia of the rest of the object's mass .. and that means applying it at a speed to fast for the mass to respond by moving away. Consider the movie effect of punching through a plasterboard wall to surprise our hero sneaking down a hallway .. a fast punch gets through the wall, but a massive weight may be leant against the same wall, at low speed, without even dimpling the surface.

so .. the answer is complete. To calculate the force applied determine the pressure applied to the bones of the arm by the contracting muscles, and the time it takes to move the fist on the end of the arm from rest to contact with the target. If that force is greater than the shear resistance of the material impacted then the fist punches a hole in the target, if not the target moves. If the target cannot move the pressure in the material builds up and you have to think about bursting, crystaline deformations or potentially, fusion as atoms are crushed into one another.

I have revised my answer to make it better apply to the question asked.

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    $\begingroup$ Hello Vulcan. This talks about the central issues of the OP's question, but doesn't actually answer it. In fact, the OP specifically said increased strength but not increased speed. (Also, Larry Niven's article is published on the linked site with permission. Scroll to the bottom, read the red line of text.) $\endgroup$ – JBH Jul 12 '18 at 19:54

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