It might be theoretically possible for a punch to travel faster than the speed of sound* for a very short distance. (*about 355m/s or 1130 ft/s or 1230 km/h or 770 mph) But this would only be possible if one could conserve the momentum of the whole body and transfer it efficiently to the fist.
In classical mechanics momentum is equal to mass times velocity. P=mv
The velocity of a punch depends on the ability to efficiently transfer the maximum momentum of the body to the arm and fist. The momentum is increased by have a well trained connection from the ground through the properly aligned physical structure of the body to the hand. You are essentially converting the downward and backward force of the legs back up through the body and into the hand.
The neat thing about this is that you can, without bending your arm to wind up, make the fist go much faster than the combined speed of your body and arm could go using your own muscular force.
The punch can go faster than your muscles can make it go.
In Tai Chi we say “The power is like a whip.” This doesn’t refer to the quality of the movement, but to the way momentum is transferred.
The whip is the oldest supersonic machine known to man. The cracking sound of the whip is actually a sonic boom caused the the end of the whip breaking the sound barrier.
The tip of the whip is so light that the mass of whipper’s arm translates into velocity at the end of the whip (because the tip of the whip maintains the momentum but can’t increase its mass. (P=mv)
Doing this to your body can have some unfortunate consequences. That is why taijiquan stylists who practice the kind of conservation of momentum necessary to do this prefer instead to keep the body connected and let the momentum go some small part of the other person’s body.
If I can punch at 50 km/h but keep my body connected and properly aligned and stabilised, the momentum in my fist might approach 50 km/h X 90 kg, if I weighed 90 kg. Therefore p= 4500 kg•km/h
If I could efficiently transfer the momentum of my fist to a head that weighs about 3.6 kg then the head will accelerate to 1250 km/h (just a little faster than the speed of sound.)
Of course, even if such an efficient elastic collision could happen, neither of us would likely hear the sonic boom. I would be too distracted by the pain in my fist, and my “target” would be too distracted by the brain bouncing around inside the skull. So, even if I could hit that hard, I don’t think I would ever want to.
Some of fastest visible punching I’ve seen is done by a martial artist named Tommy Carruthers. You can see his videos on youtube.
Mantis Shrimp can “punch” about 80 km/h
In reality a good boxer can punch effectively at about 30 – 60 km/h. If the hand goes faster than that the boxer loses control and risks injury.
The force generated by a properly aligned 40 km/h punch is amazing. I’ve heard of punches with 400 kg of instantaneous force! That person could punch a field goal!
– Ian Sinclair