# You're superstrong but you still weigh the same. What happens when you hit things?

In movies and especially Japanese anime, you can see characters punching through walls, breaking columns by kicking etc. Similar effect is seen in computer games, which is something I'm interested in at the moment.

It seems to me that many of these destructive effects require more energy than how much energy is needed to throw you flying. In other words, if you have nothing to brace against, you maybe just push yourself away from the target object very fast, without harming it much.

And the question is quite simple:

• Given you're strong enough (and your tissues are tough enough, magically) to break a marble column or punch through car roof, are you able to do that at normal weight (say, 80kg)?

If answer is no, then what exactly happens? Do you push yourself meters in the air? What happens after two super-persons lock their swords (magical, indestructible) with that force in a typical anime sword-fight? Do they fly apart at supersonic speeds?

It would be nice to have some basic math leads to the results. Pointers are enough, as this is not Physics.SE question.

This is also not duplicate of the question mentioned in comments, because the other question asks about effects on target human body, while this one considers all humans involved indestructible.

• Depending on your punch angle and body position, you'll get different push backs. Nobody seemss to be taking this into consideration... – msb Mar 31 '16 at 18:24
• Not sure if you're going to appreciate the simplicity of this but it sounds comparable to asking what would happen if I threw a 50-calibur bullet at the wall versus I shot a 50-calibur bullet at the wall using a gun. Since you do not specify a multiplier for "superstrong" I am just going to go ahead and say that your punch is going to generate enough psi through your knuckle to penetrate your target and hopefully the muscles in your shoulder can handle the recoil or else your are simply going to be dislocating your shoulder every time. – MonkeyZeus Mar 31 '16 at 20:24
• Possible duplicate of What would be the physical effects of a fistpunch with greatly magnified strength? – JohnEye Mar 31 '16 at 20:50
• @JohnEye It's not duplicate, the other question asks about effects on human body. – Tomáš Zato Mar 31 '16 at 21:21
• @TomášZato Oops, sorry, I only meant to link it as potentially interesting. Enough flagging for today, I guess :-) – JohnEye Mar 31 '16 at 22:13

The strength of a punch really comes down to two things:

• weight behind the punch,
• and speed of the punch

As you posit the weight to be identical, you need to ramp up your speed in order to achieve super-punches. The problem this will lead to is acceleration and impulse:

Say you, 80 kg super human, want to make an 80 kg column fly through the room:

1. This means that your fist/punch must be fast enough, i.e. have high enough kinetic energy.
2. This kinetic energy will be built up while you accelerate your punch - and while doing this it will exert a force on your body which is identical to the force you eventually deliver to the punched 80 kg column.
3. While some of this force is countered by traction of your feet on the ground, it is not reasonable to expect that all of it will. After all, the column will have some strong traction as well, which you need to overcome to send it flying.
4. Meaning your punch will accelerate your body backwards approx. the same as the column is propelled forwards.

--> You'll end up with rather silly results: your super humans of normal weight will mostly just send themselves flying here and there while trying to deliver super-fast punches or kicks.

• You might be able to pull it off if you spring off of a wall toward the column/enemy at high speeds, though you might damage the wall in the process. – IndigoFenix Mar 31 '16 at 12:08
• Never underestimate high quality cleats! – Lacklub Mar 31 '16 at 12:23
• You could also change how you punch things. Suppose you needed to punch through a wall. If you stand next to a wall and can make your fist go through, you'll be sent backwards. But if your fist is on the other side of the wall, it can now pull you forwards again so that you end up not moving. Some wall may be ejected in various directions. – Lacklub Mar 31 '16 at 12:30
• "…exert a force on your body which is identical to the force…" Ummm, no. Force = mass × acceleration. The acceleration of the build-up a lot less than the acceleration of the slow-down (i.e., when you hit). For the simple reason that it's the same magnitude velocity change in a much shorter period of time. Momentum (= force × time) is conserved, but in order to start slipping you need to exceed the static friction (force). – derobert Mar 31 '16 at 17:40
• This answer uses "kinetic energy" where it should use "momentum." If you want to send an object flying, you need to transfer momentum to it. If you just transfer kinetic energy to it (e.g. by clapping it between your hands as hard as you can), it will heat up and make lots of sound, but it won't go anywhere (and neither will you). – Milo Brandt Apr 1 '16 at 0:41

Maths

Lets see what the maths says. First lets understand the mechanics of a super-punch. Super person starts with their arm extended behind them and uses their super strength to move their fist forwards (see diagram)

Next we'll make some assumptions;

1. a person's whole arm represents on average 5.3% of their body weight.
2. from what I see on TV most super people seem to be American. The average North American weighs 80kg.
3. the arm is accelerated by the maximum force possible for the whole distance of the punch (blue arrow) which is the same as a person's armspan
4. a good armspan for a super person who was good at punching might be 2.1m.
5. the super person exerts the maximum force on their fist while remaining stood in place (they do not recoil and send themselves flying off their feet)

We have simplified to put the entire arm weight at the fist, but this will make the punch stronger and is fitting to a super person.

The maximum force exerted on the fist is determined by the frictional force on the super person's shoes. A good shoe will give a coefficient of friction of around 0.6. That means the maximum force is;

$$F_{max} = \text{coefficient of friction} \times \text{mass of super person} \times \text{gravity}$$

The acceleration of the fist is given by Newton's second law;

$$F = ma$$

so acceleration is;

$$a = \frac{\text{coefficient of friction} \times \text{mass of super person} \times \text{gravity}}{0.053 \times \text{mass of super person}}$$

Next we find out how fast the fist is moving when it hits. For this we need the equations of motion, specifically the velocity/displacement equation;

$$v = \sqrt{2 \times a \times \text{distance}}$$

which gives us;

$$v = \sqrt{\frac{2 \times \text{armspan} \times \text{coefficient of friction} \times \text{mass of super person} \times \text{gravity}}{0.053 \times \text{mass of super person}}}$$

which is around 21 m/s or 47mph. After I did the calculation I did a quick google of "fastest punch" and came across Keith Liddell. He is the current world record holder of the fastest punch, registered at 45mph.

• You had everything to be the best answer: all scientific and such. But you don't answer what was asked! :( what's more, you create an assumption (the person won't recoil) which goes against the exact question, that was "what will happen, will they recoil?" I was so eager to upvote this... :/ – msb Mar 31 '16 at 18:19
• Neat drawing. :-) I fixed up your post with proper formatting of the formulae. – a CVn Mar 31 '16 at 18:23
• There are a lot of good answers here. One assumption that comes up is that only the weight of the arm needs to be taken into account. A properly formed fully extended punch is primarily powered from the legs. The body posture is such that the rear leg takes much of the force of the recoil. If such a punch is fully committed, the puncher's momentum can carry them forward a couple of steps when they miss their target. This means that instead of 5.7% of the body's mass being under consideration, a much larger percentage comes into play (thumbnail guess 30%' based on gut feel trig). – pojo-guy Apr 1 '16 at 2:00
• It also changes how the coefficient of friction affects the overall motion, because at a certain point it would be like throwing a good punch while standing on wet ice. It can be done, but it takes practice. – pojo-guy Apr 1 '16 at 2:00
• I agree with @msb, the math is useful but the first assumption already breaks it. – Tomáš Zato Apr 1 '16 at 9:15

It seems to me that many of these destructive effects require more energy than how much energy is needed to throw you flying.

Herein lies your confusion, I think. The recoil you experience when punching a thing is not in linear proportion to the energy of the punch: it proportional to the change of momentum effected in the thing being punched.

Here's a simple experiment to illustrate: get a sheet of paper. Put a bullet on it. Lift the paper. With the force of gravity, that bullet isn't going to break through the paper. It would need something to brace against, right?

Now shoot the paper with the bullet. Obviously a much higher-energy impact. Is the bullet sent flying? Hardly.

You can get a little intuition into how physics works for heros with absurd strength (and also somehow indestructible fists) from Newton's approximation of impact depth.

The reason normal people can't punch into a brick wall to the depth suggested by Newton's approximation is they can't accelerate their fists sufficiently to make the cohesion of the brick wall insignificant. That, and the cohesion of their fist is significantly less than a brick wall, but I suppose that's not a problem for your super-strong character.

When you hand-wave all those problems away (unlimited strength, bones made of adamantium, whatever) but not mass, what you are left with is just the conservation of momentum as a problem. Real simply, momentum is the mass of a thing, multiplied by it's velocity. If the super-strong character is going to fly away, that means he's going to need to transfer more than his momentum into something else (he'll need to stop his forward momentum, then pick up even more backwards momentum).

But if you punch anything with a fist at high enough velocity, you don't need to transfer momentum into the whole thing, but instead into just a fist-size puck of it which will be torn away by the tremendous kinetic energy of the fist (remember than velocity-squared thing). Since fist-sized pucks of most things are much less massive than even normal weight humans, this doesn't present much of a problem.

• A good illustration of this: humans can break walls with a sledgehammer, yet neither they nor the hammer recoil back at an extreme speed. – user16107 Apr 1 '16 at 14:13
• @dan1111 actually sledgehammer recoils at a high speed(acceleration; a bit lower then the one you hit wall with), but you use muscles and optionally gravity to counter it. And when you break through the wall you just don't lose your whole momentum, meaning that recoil was too weak to stop you. – MatthewRock Apr 1 '16 at 17:03
• @MatthewRock I don't think that's how it works. Humans can break walls by throwing sledgehammers, too. No muscles or gravity required at time of impact. – Phil Frost Apr 1 '16 at 18:48
• @PhilFrost but then again sledgehammer would either recoil a bit, or go through the wall. – MatthewRock Apr 2 '16 at 13:05
• @dan1111: But you can't make a human-weighed object fly through the room using a sledgehammer (the way we constantly see it in anime). Just as you won't send anybody flying backwards movie-style while shooting them with a gun. – fgysin Apr 5 '16 at 15:01

No funny aerial stuff.

You'll need high traction soles on your shoes and very careful use of weight and balance.

Standing on a car roof trying to punch through: You'll put a good dent in it, equivalent to someone falling from twice the height you fire yourself up to.

Inside a car punching up: this one could work as long as you don't hit a reinforced point, but you're going to bend the chassis underneath as well.

Locking swords: This is going to be about balance of power. You've defined the swords as unbreakable, I'm assuming the fighters are too. There are two options: 1) They meet and bounce off like two snooker balls. 2) They meet and stop with the most incredible noise. The energy has to be dispersed, in either case momentum is conserved, so the energy is either returned to the fighters or dispersed in another form.

Breaking pillars In theory yes, it's just a matter of hitting the pillar with more energy in the movement than is required to break the stone. Under normal circumstances the person would break rather than the pillar.

Imagine a catepult strong enough to throw a 200lb object hard enough into a wall or column to break it in the indicated manner.

If you rode the catepult, it would also do so. If you, by your own strength, hit the target with this same energy from a standing pose, you would go flying back by the same amount too: picture the catapolted impact, but in reverse.

Superperson can accelerate his fist (which is connected to his arm) to any arbitrary speed, until the arm is completely extended. It has been said that the mass of the arm is supposed to be 5.3% of the total body mass. If the fist is accelerated to a speed of v, then the arm is on average accelerated to v/2. The rest of the body must move backwards at a speed x. To preserve momentum, v/2 * 0.053 = x * 0.947, or x = v / 35.7.

The fist hits the wall and is stopped instantly, completely transforming its energy into destruction of the wall. Depending on the material, the wall may crumble, or there may be a fist sized hole in the wall. The body of superperson will be moving (possibly flying) backwards at speed v / 35.7.

Superperson cannot send an 80kg statue flying faster than he is flying backward himself, but can definitely destroy it with one hit.

• A well formed punch is a whole body movement, powered from the legs. The secret to developing maximum force is that the rear leg and the punching arm reach maximum extension at the same instant. The traction becomes critical , and I can see a punch like this feeling like you're standing on wet ice. – pojo-guy Apr 1 '16 at 2:10
• If the force in your fist is more than is required to break the wall, the fist will be slowed; but won't stop instantly. – cst1992 Apr 1 '16 at 6:00

# You might not fly away as you might think...

As gooey water balloons, we are not that bouncy, let's say your tissues are indestructible (Magical), but you body's ability to deform is intact, you will absorb most of the energy you apply to, let's say, a wall, just like a lead bullet, it's really rare for a lead bullet to ricochet due to its malleability.

So, let's say you are dropped from a helicopter onto the top of a building with your fist pointing downwards for coolness, and as you hit the building you will first feel the force of the object you hit pushing you upwards but due to your (speed+mass)=energy the concrete will break, and by breaking, it will be absorbing the energy you applied to it, if it doesn't break, you'll bounce, but not a lot, due to your body's ability to deform, therefore, absorbing most of the impact, the rest of the energy will make you bounce a little.

Make sure to be at a fast speed before trying to hit something, and practice before you do that so you're going to have an idea of how fast you need to be to break certain objects, if you want to break a wall without running at it, you could just break it with a hammer or your fist, it's going to take a while though

The punch to a wall has been answered perfectly by Phil Frost.

However if you are going to punch another super-person, you won't be able to punch out a fist-sized piece as you did with the wall. The super-person is too unbreakable. A direct punch will send you both flying backwards.

The tactic with your super-enemy is to use an uppercut either to the jaw or to the sternum, or an upwards kick to the groin. This means that any reaction will be transmitted into the ground. What damage this does to the ground depends purely on the strength of the substrate, the mass of the baddie, and the impulse provided by your fist. If you hit them hard enough they will sail into orbit and you will sink several feet into the ground. You are super so digging yourself out will be easy.

It is actually possible to send things flying, provided that you have enough force behind your punch. And no, you don't go flying backwards after the punch. The shockwave is absorbed by your arm.

You might be interested to know this about Bruce Lee's infamous One Inch Punch:

In the television show Stan Lee's Superhumans, the Shaolin monk Shi Yan Ming demonstrated his one-inch punch on a crash test dummy. The testing showed it was 1.7 times more injurious than a 30mph (48.3 kmh) car crash with modern safety features. ~ One Inch Punch - Wikipedia

And no, that monk did not go flying backwards or whatever after punching his target. The target would certainly go flying across the room, considering that the shock was more than 1.5 times than getting hit by car travelling at 50 km/h.

Also, try watching this real Bruce Lee demonstration video. You will see the target getting pushed back several feet and even then the chair goes back on the floor a foot or so!