How much force/energy is required to punch someone so hard that the person is sent flying at the speed of sound?

Also, what can you compare the force/energy to? For example, is it comparable to a TNT explosion or something?

Edit: Hypothetically assume these beings were superhuman that can survive such attacks.

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    $\begingroup$ If you are punching a human being that hard, whatever you're hitting them with will go through them, not send them flying. $\endgroup$ – Jorgomli Mar 4 '19 at 17:30
  • $\begingroup$ I think you need to provide some more details. As already pointed out, a punch would smash through a person. $\endgroup$ – L.Dutch - Reinstate Monica Mar 4 '19 at 17:31
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    $\begingroup$ E = (mv^2)/2. Do the math. $\endgroup$ – Renan Mar 4 '19 at 17:37
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    $\begingroup$ I'm pretty sure at those energies a human body would not so much "fly" as "splash". $\endgroup$ – plasticinsect Mar 4 '19 at 18:14
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    $\begingroup$ @user45266 - That's a push not a punch! It also require very long arms! $\endgroup$ – chasly - reinstate Monica Mar 5 '19 at 9:44

Suposing speed of sound of 340m/s (sea height normal pressure) a 100kg man (because a 153cm tall superhuman doesn't really cut it), which is a good suposition for a strong, tall man, you'll need about 6 Megajoules of energy (I've rounded up to account for that hard mistress, 2nd law of thermodynamics, and because you need to surpass the speed of sound, even if just by a little bit).

How to deliver this energy without destroying parts of the body of both the puncher and the punched, and without loosing any more energy in heat, spin or other possible non-intended consequences is left as an exercise to the OP.

Also, if you want to compare it to an explosive, that's like a little over a kilogram of TNT.

| improve this answer | |

First of all, we need some metrics first.

The average adult human being is between 60 kg and 80 kg. For this question we will average this as 70 kg.

Let's also assume that the attacker's fist is in contact with the enemy for 0.5 seconds. The less time the fist is in contact with the enemy, the more force will need to be exerted in order to accelerate the enemy to the desired speed.

As a variant on Newton's second law, the required force is given by the following equation: $$F = m \times \frac { v_{f}-v_{i}}{t}$$ where:

  • $m=$ the mass of the object $=70\space kg$
  • $v_i=$ the initial velocity $=0\space m/s$
  • $v_f=$ the final velocity $=343\space m/s =$ speed of sound
  • $t=$ the time it took to change the velocity $=0.5 \space s$
  • $F=$ the force required, measured in Newtons

Now let's plug the data into the equation: $$F = 70 \times \frac { 343-0}{0.5}= 70 \times \frac { 343}{0.5}$$

$$F = 70 \times { 686} = 48020‬ N$$

So we arrive at our answer.

It takes 48020 N, or around 10,795 pounds of force.

The force applied by the engine of a small car during peak acceleration

If you want a quicker punch, I have assembled the following table for consultation:

$$ \begin{array}{c|c} Time \space (s) & Force \space (N) & Force \space (lbs)\\ 0.5 & 48,020 & 10,795.3‬ \\ 0.25 & 96,040 & 21,590.6‬ \\ 0.1 & 240,100 & 53,976.6‬ \\ \end{array} $$

Or, if you prefer to choose the amount time for the fist to be in contact with the enemy, you may use the following formulas: $F= \frac {24010}{t} $ for Newtons and $F= \frac {5397.66272}{t} $ for pounds of force.

| improve this answer | |

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