Force

Force is one of the most fundamental principles a martial artist needs to know. Every technique can be represented by the forces involved. Martial artists use their fists, feet, elbows, knees, shins, foreheads, forearms, and just about anything else as battering rams and treat our opponents as a thing to be hit, redirected, or incapacitated by lockouts, chocks, pressure points, or other brutal techniques. All of these techniques involve applying force to the opponent.

Despite the wide variety of strikes, there really are only a few actual principles at work. Newton formulated a set of "rules" that govern the motion of objects. These are called Netwon's Laws, and they are as follows.

Newton's First Law:
An object will remain at rest or in motion until an external force is acted upon it.

Newton's Second Law:
Acceleration is proportional to the force exerted on an object, and inversely proportional to the mass.

Newton's Third Law:
For every action there is an equal and opposite reaction.

I won't go into too much of the details, but they are very powerful statements. Entire books can be written on any one of them. Before we get into the math, we have to understand what force actually is. Most people have a general idea what it is (and no, that doesn't mean the stuff those martial artists with lightsabers use). It is easier to define what a force does. Force causes objects to change velocity (ie. directions and speed). Thus, anything that makes an object slow down, change direction, or speed up is a force. However, forces can be felt by objects that don't move as well. If you try to push a huge boulder, you are exerting a force on it, but it is doesn't move because you would have to overcome the friction between the ground and boulder. Also, gravity is a force that is acting all the time, and you feel its affect because you are always "pushed" toward the ground.

Every strike requires force, because that is what moves the mass of your fist or feet toward the punch bag. As Newton's First Law states, our feet will not tend to move if at rest unless we use force, or muscle power, to accelerate them.

The most basic equation for force is

Equation 1:

Equation of Force

or

Equation of Force


f = force, m = mass, a = acceleration

This is Newton's Second Law. Force is a product of mass and acceleration. This is the force required to accelerate your fist toward the target.

What is acceleration? Acceleration is the change in velocity over time:

Equation 2:

Equation of acceleration over time


a = average acceleration, Δv = change in velocity, Δt = change in time, vf = final velocity, vi = initial velocity, tf = final time, ti = initial time

In both numerator and denominator of Equation 2, the parameters correspond to changes. Acceleration is the change in velocity from an initial velocity, like 0 m/s, which is at rest, to some other speed, such as 2 m/s, divided by how long it took the velocity to change. Acceleration can also be negative, such as going from 2 m/s to 0 m/s. As an example, a punch that starts at rest and accelerates to 10 m/s in 0.04 seconds clearly has a higher acceleration than if it takes 0.4 seconds to do so.

Acceleration for short change in time

Acceleration for short change in time

Acceleration for long change in time

Acceleration for long change in time

How does increasing acceleration increase force? For instance, a martial artist can bring 3 kilograms of mass into play in a straight punch. If her acceleration for a punch is 25 m/s2, then she will require 75 N (Newtons, a measure of force, or kg*m/s2) to perform the punch.

Example of force vs. acceleration

If she does not use any additional equipment (i.e. gloves), but increases her acceleration to 250 m/s2, she will require 10 times the force to do the punch.

Example of force vs. acceleration

Thus, we have to use our muscles more, or more efficiently, to punch faster. However, there is a linear connection between acceleration and force, which means, as most martial artists know, that we get exactly what put into it. In order to punch faster, we have to have more force to do it. The faster our punch is, the more damage it will do. The power of the punch is the result of momentum. All objects in motion relative to another object have kinetic energy, and this is what is used to damage a target.

Before we get to momentum, it will be handy to know how to get velocity from acceleration. An object that is accelerating is in the process of getting faster, or slower, and its velocity is changing with time. The equation for velocity is:

Equation 3:

Equation for Velocity


v = velocity, v0 = initial velocity, a = acceleration, t = time

At any time in the punch, we can obtain velocity if we know the acceleration. The initial velocity, v0, can be 0, such as if a punch is starting from rest, but we can also obtain the velocity if the martial artist is already moving, such as a jumping kick, by filling in the velocity of the martial artist when she started it.

References

  • Serway, R. Physics for Scientists and Engineers. Philadelphia, PA: Saunders College Publishing, Fourth Edition, 1996
  • Giancoli, D. Physics Principles with Applications. Upper Saddle River, NJ: Prentice Hall, Fifth Edition, 1998