# Physics of a punch

So I have odd question revolved around karate and would love to know if my physics assumptions are correct.

Basically I would like to know what equation to use to calculate the force of a punch when two things happen: when one arm punches out and the other pulls in to the hip while pivoting around the torso, this creates a circular type motion when you punch. The second when you just throw a punch and do more of a linear punch with the second hand staying out. A bonus would be if I can also calculate a radius difference, for example if the second hand pulling back actually comes in closer to the body and increases the force since the radius decreases going from a position of the punch being fully extended to a position where it comes back to the hip.

Someone uploaded this image and I'm no physics major but he talks a lot about linear equations, which seems wrong. I see linear all over it, but also see a note mentioning pivot, so I'm a little confused what its actually showing. I thought this would actually be more of a parabolic (might be the wrong word) or centrifugal equation like so:

F= mv2/r

So it's clear from this one that if you have more mass spinning like the second hand, the force would also increase. Seems simple but I wanted to see if my assumption are right it if they are actually using the correct equations.

Just as a background I'm a third degree black belt in karate and I'm trying to have a physics based approach to training, so this would greatly help in dispelling some common myths.

• Could you add some diagrams of the martial art maneuvers you are talking about? I’m having a hard time visualizing the motion involved in the described punch. – cms Jan 10 '19 at 6:00
• I suspect that getting a really accurate answer would require doing some sort of finite-element analysis or simulation involving a 3D model. – pjc50 Jan 10 '19 at 13:05
• youtu.be/y1q6oShJtjs here is a detailed video about the technique, which is called hikite – lukasz Jan 21 '19 at 23:14

I applaud your desire to find an equation to explain the physics of a karate punch, but to be frank I must say that an equation has limited relevance if you don't have numbers to plug into it. The lengths of the upper arm and forearm, their masses, etc., all enter into the equation.

If you deliver your punch by rotating your body so that the punching arm's shoulder moves forward while the other shoulder moves backward, the forward velocity of the punching shoulder adds to the hand-shoulder velocity of the punch. The other shoulder's backward momentum balances that of the punching shoulder, just as pulling the left hand back balances the momentum of the punching hand.

If your feet are not parallel to your body but are placed one forward and one back, your back foot can press backward against the floor while you punch. In that case, you're no longer an inverted pyramid and the above argument does not apply. The entire Earth absorbs the backward momentum so your punch will not lose velocity.

Finally, if you lunge forward while delivering the punch, and keep your rear foot in contact with the ground while punching, and meanwhile turn your body while you punch, the punch will have maximum velocity.

The energy delivered by a punch -- e.g., its ability to cause damage where it lands -- increases as the square of the velocity, so every little bit of extra velocity can make a big difference if your intention is to break bones or cause internal injuries.

• Additionally, if he plunges his body forward the momentum will include the mass of all his body. Of course, a) the parts of the body other than his arms will have the momentum related to the speed of the body, not to the speed of the arms and b) the puncher will not get to transfer all of that momentum through the punch to the punched person. – SJuan76 Jan 10 '19 at 10:13
• This is a great description, thank you. Unfortunately these are all things I already know innately just by doing them, unfortunately I was looking for a more scientific answer via equations, even if the biomechanics are more complex a bit. I'm curious how I could even go about trying to set up the science behind this. So I need an expert in physiology as well as physics? Or is it just a more complex physics problem then I am proposing? Maybe both? Hah. Would love to get to the scientific bottom of it. – lukasz Jan 21 '19 at 23:21
• And just to be clear: I'm looking for more of a binary output. I.e. rotation of the hips causes centrifugal force therefore it's always more powerful even if we input these fake numbers in. The aren't goes that pulling the hand back doesn't actually increase force, which seems counterintuitive to me. – lukasz Jan 21 '19 at 23:24
• Pulling the left hand back actually does increase the force exerted by the right hand. I think you might be able to get a clearer idea of the physics if you did some practice in a swimming pool, in water too deep for your feet to be on the bottom. – S. McGrew Jan 22 '19 at 3:46

There are some aspects of what I teach that are similar. Superimposing rotational forces will be difficult to model as everyone is different in terms of flexibility strength, etc. My experience is that if strength and flexibility are good, this will certainly be effective for power and efficiency. I term efficiency with effort as the flexible person expends less energy.