As martial artists, we often seek to get the maximum bang for our striking buck. This quest results in extensive discussions around the body mechanics of muscle alignment, balance, weight transfer and the like, but on occasion an instructor will suddenly bring in Newtonian physics. The usual way this come in is that they say something along the lines of “force equals mass times acceleration, so to generate maximum force on your target is to accelerate the mass of your fist as hard as you can.”

Actually, no.

Before I continue, time for the caveat: I haven’t touched Newtonian physics since finishing my A-levels in 1990 so I’m quite rusty. If someone more knowledgeable than I is in a position to rebut what I’m spouting and correct me I’d be very happy to fix this post or issue an update - just get in touch via the Facebook group.

Back to the plot. It is true you can calculate the force on an object if you know its mass and acceleration, but force is not a conserved or transferable property - knowing the mass and acceleration of your fist merely tells us how much force is acting

*on the fist*, which may have little bearing on the scale of impact when the fist lands.

So, what

*is*important? What can we transfer to our opponent that they will feel as pain, injury, disruption of balance or whatever? From a striking perspective there are two answers.

- Momentum
- Kinetic energy.

Momentum is calculated as mass times velocity and is conserved when two things interact. It can most clearly be seen in action playing pool - when one ball hits another, the combined momentum is the same after the collision. If one ball stops, the other ends up travelling at the same velocity as it was struck, if both balls are still moving after the collision, their combined velocity is still the same.

For example, if 100kg person leaps forward at 5 meters per second (about 11mph) they will have gained 500 Ns (Newton seconds) of momentum. Because momentum is conserved, and they pushed off from the Earth, the Earth’s momentum will also be altered by 500Ns in the opposite direction but as it weighs about six septillion kg the change in velocity will be negligible.

If our leaping person tackles someone else (who is also conveniently 100kg) and grabs them, taking them off their feet, the 500Ns is conserved. Now it’s distributed between the two people at 200kg, so their velocity will halve to 2.5 m/s until they hit the ground and come to a halt, which will transfer the momentum again - this time back to the Earth.

So, momentum at a basic level is useful to the martial artist because if you can transfer some of yours to your target through a strike you can push them back and make space. Of course, you have to be standing/braced correctly so that the momentum in the other direction is grounded out rather than pushing you back in the opposite direction.

Kinetic energy is perhaps more interesting. Energy is also conserved in this kind of interaction, and the transfer of energy and how it is dissipated through the target can give us a rough measure of the damage done. Kinetic energy is ½mv squared - so the variables are again based on mass and velocity albeit in different proportions. You can’t create or destroy energy, it’s always conserved, so collecting energy and delivering it to your opponent is key, and the most effective way to transfer energy in this case is to use kinetic energy.

- Where does it come from? The contraction of your muscles is a conversion of chemical energy to kinetic - there are additional sources you can use to contribute but these are outside the scope of this post.
- Where does it go? Well, as soon as you hit your opponent your fist (and the body weight you have behind it) start to decelerate transferring momentum and kinetic energy to your opponent. If your fist or foot is travelling slowly, the kinetic energy is transferred pretty much directly as more kinetic energy and the target moves back with the impact absorbing the strike.

If your striking limb is travelling fast enough, the opponent cannot absorb the hit by moving back, even involuntarily under the force of the blow. The inertia of their body effectively holds them in place whilst the transferred momentum accelerates them slowly, but not as fast as needed to avoid damaging energy transfer. Bodily structures start to deform, bruise and break. Kinetic energy is converted to sound, heat and potential energy in the more elastic tissues (which may over-saturate and break up themselves).

This is why we aim to strike

*through*a target rather than at the end of our limb’s range - comments along the lines “at this point you are still accelerating and acceleration yields force” are incorrect. In fact, not only do we need distance for the strike to decelerate into the opponent and transfer energy as it does, but also at the far reach of any hit we are already slowing to protect our own joints and physical structure and therefore losing velocity.

Notice that both of the factors we’ve discussed, momentum and kinetic energy, are derived from mass and speed - force and acceleration are tangential to the discussion. What’s important is the effective mass you can put into the strike, not just your fist but the whole working mass of the body, and the overall speed you can apply regardless of how long it takes you to achieve that speed. This does bring us to acceleration having one point of relevance, because the faster you can accelerate the mass behind your strike the faster it will be travelling on impact and the more momentum and kinetic energy will be available.

Long story short: “Force” is irrelevant and acceleration tangential - to maximise the effectiveness of your strikes, at least at the basic Gekisai levels of fighting, look to making the most of your whole body mass and ensuring you land at maximum speed.

*Matt Savigear, Shodan*