Optimal power of a boxing punch - how important is mass? I am intrigued by the physics of boxing, and why some people with fast hands do not have good punching power, ie, can not knock other boxers out.
I feel there are three major components of a punch The equations involved, I think,  are: $$F= ma$$
$$KE= \frac 12 mv^2$$

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*Velocity of the fist:  As velocity goes up, the force or energy of the punch goes up exponentially. So, fast hands are optimal.


*Elasticity of the punch: You want the impact to be fully elastic, that is, all the energy gets transferred to the other boxer's chin. Energy gets lost by bad technique - the fist and/or wrist and/or elbow and/or shoulder deflect, crumple, get compacted, get knocked off on a vector. (I think this is why most boxers do not have maximal power - they make have poor impact technique).


*Mass:  This is where I have difficulty. At first I thought this was easy, because the only part of the body that is moving on a vector straight at the chin is the boxer's arm. So, mass, I thought , would simply be the mass of the boxers arm. BUT, boxers are trained to move their whole bodies forward as they punch. If so, and if at the moment of impact they lock all their muscles and make their whole moving body rigid, does this mean that effectively their entire body mass influences the kinetic energy of the punch? IOW, is the apparent mass of the arm increased?  Or is just the arm the proper measure?  If you get clipped by the side mirror of a moving car, you do not experience the mass of the entire car, right?
 A: The important thing for knocking someone out is what kind of acceleration can boxer produce in opponents head for certain amount of time.
The force he exerts is basically immaterial. If his opponent would be quick enough to accelerate his own head to dodge the punch, the exerted force would be zero. But doing so, the opponents head acceleration can become so high, he would basically knock himself out, without the first boxer even exerting any force on him.
If the opponent gets very relaxed, even modest punch power can knock him out. That is because the whole force that boxer exerts on him is used to accelerate only head. If the opponent gets fully rigid, then the boxers punch will accelerate his whole body, not only his head and because $F=ma$, the acceleration would become proportionally smaller and this time, the boxer might fail to knock his opponent out.
The next thing to knock someone out is to keep this acceleration high for longer time. Imagine having very high acceleration for very short amount of time. Say, the whole punch will be done on the length of 0.1mm. If the acceleration is high enaugh, such punch would break the tissues in the impact area, but the broken tissues would not transfer gained momentum further to the brain and the opponent would not be knocked down. He might have hole in his face, but he would remain standing. The acceleration thus needs to be low enaugh so that tissues will hold and thus could transfer the momentum further into the body (that is the reason for wearing boxing gloves). But this transfer process takes time and if you stop the acceleration too soon, before the effect of the punch influences the brain, the punch is already over. 
The higher the speed of the punch, the higher the initial acceleration produced by the punch. But because of the punch recoil (which is enhanced by boxing gloves) the punch might get decelerated too quickly to produce enough effect on the head. The boxer needs to keep the punch steady for as long as is needed and for this, he needs to back up the punch by enough force/inertia. That is why boxer needs to make himself as rigid as possible  and stand in a good position - because this will back up the punch by whole bodies inertia and strength and the effect of recoil gets smaller. And that is why boxers are told that peak of the punch should not happen at the impact, but few centimeters behind it. 
The impact force is not as important as keeping the arm in steady movement after the impact - and this is where power of the punch has advantage over speed.
