# The science of punching harder: why is speed more important than mass?

**“You need to hit faster to generate more power! F = MA!”**

Wait… what? These are the exact words the assistant trainer told his batch of students, which included a much younger version of myself. Back then, I was in high school but already knew something was wrong with what he just said: He told us to hit faster yet the equation used doesn’t use speed but rather, acceleration. Granted, acceleration is related to speed, so hitting faster would translate into bigger acceleration, but then, what about the Mass. Why didn’t he just tell us to augment our mass so that we could generate more power.

*Power!*

As it (often) turned out, the assistant was right about the first part, where greater speed did equate with greater power, the latter part, the one with the equation was wrong.

Every martial artist instinctively knows how to generate power. The goal of this article is to remind martial artists and put words (and science) to the principles they have been using.

**Isaac Newton had it all along**

*Newton doesn't look like much of an martial artist...*

**First law of Newton**: Any body remains in a state of rest or uniform motion unless some external force acts upon it.

**Second law of Newton**: Force = Mass * Acceleration

Although this is the simplest and most cited equation, it is also the hardest to understand and concretely apply. We seldom use acceleration as a unit of measure, in fact, most people only know acceleration as a measure when referring to specifications of cars.

*Speedometer incates speed...*

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*Photograph taken from powerbooktrance@flickr / Wikimedia commons*

**Third law of Newton**: The mutual forces of action and reaction between two bodies are equal, opposite and collinear. (We won’t be using this law for now, but it shall be visited in another article)

**So what do these Newton laws mean?**

It means that if your fist is not moving, then it shall remain motionless until you (or some external force) generate the necessary force to move it.

*From the guard position, the boxer needs to generate necessary force to propel his fist*

The bigger the mass, may it be the arms, the legs or a weapon, the more force it will take to move it towards its target. Similarly, the faster you need an object to move (for a same distance), the bigger the acceleration will need to be, thus the bigger the force required.

Though it may be true that augmenting force makes the hit more powerful, it is also true that it takes the attacker more energy to launch such an attack.

**How to use the Newton's knowledge to improve our punches?**

Neither force, as used in physics equation anyways, nor acceleration are concepts that are intuitive or easily understood. Most people confuse acceleration with speed, power with force, which leads to inexact conclusions.

Even if a fighter understood Force and acceleration, it still wouldn’t explain why the increase of speed (and acceleration) is more beneficial than the increase of mass. Instead, we should be looking out for Kinetic Energy.

**So what is Kinetic Energy? How is kinetic energy pertinent to martial arts?**

**Kinetic energy:** Energy that an object - hands, fists feet or weapons - possess due to its motion.

It is worth mentioning that kinetic energy is linked to force and is not a separate concept.

*Kinetic Energy in real life has little to do with the kinetic energy mastery that x-men member Gambit possesses...*

*Image taken from http://marvel.com/universe/Gambit*

**Useful equations (mathematic definitions)**

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**What is Work?**

By definition, the work done on an object by a net force equals the change in kinetic energy of the object.

In other words:

To simplify the equations, we will assume the fist is motionless, prior to the launching of the punch, which means the fist initially had no kinetic energy.

So if Work equals Kinetic Energy (at least, in our simplified example where the initial energy of the fist is zero), we can say that:

See, that was easy!

**Let’s get rid of acceleration!**

Because we don’t like the concept of acceleration, we shall translate it to its equivalent in terms of speed. By definition, acceleration is the difference of speed per unit of time.

Assuming that prior to its launch, the fist (and the whole body) is motionless, we can safely deduct its *initial* speed was zero.

**On to the force!**

Now that we established the equation of acceleration, using speed as a variable, we can substitute it in the mathematical definition of the force.

*Not that kind of force!*

**Newton's second law**

By replacing acceleration with its equivalent previously calculated, we get:

On its own, this substitution is not very helpful but it will be… keep reading.

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**Let’s take care of the Distance variable:**

The distance, in this case, represents the distance that the fist must travel, from its initial resting point to the point of contact. It would be tempting to write this off as a constant, as the distance – which is the length of the arm – remains relatively unchanged for each individual.

*...unless you can stretch the length of your arms, like Dhalsim from the Street Fighter series*

*image taken from Capcom*

Equation for distance:

Again, distance is expressed in terms of acceleration, which we shall convert in terms of the more familiar “speed”. The fist, initially motionless, has an initial speed of zero.

Earlier, we determined that:

So if we substitute acceleration in the equation, we get:

**Okay, I am totally lost, just quickly conclude before my head explodes!**

Now that everyone is lost in a jungle of mathematics, we shall get to the point and isolate the required equations. First, a little reminder on the mathematical definition of Work:

Now, let’s put in place the equations for the force and distance, in terms of speed.

The resulting multiplication eliminates the time variable, increasing the power of the speed (v), thus we have:

So there you have it, the equation that should be used to describe the “power” of a punch.

The equation and the graphic shows that in order to increase Kinetic Energy, or the energy contained in an object in movement, one could either increase the mass of the object or increase its velocity (speed). Because the velocity has a power of 2, the increase of speed leads to an exponential increase of energy, whereas an increment of mass is linear.

In other words, an increase of one unit of speed will result in greater kinetic energy than an the same increase in mass.

**So how do we interpret this equation for martial arts?**

If your goal is to increase the power of your strikes, then it is much more beneficial to increase the speed (v) of your strikes than it is to increase the mass of your limbs or weapon.

Not only will it give your punches more kinetic energy, thus more potential of damage, more speed will also make your punches harder to react to.

*A good jab, although seldom leading to knockouts , is an important technique in a fighter's arsenal*

**You're wrong! If speed equated power, then jabs would be the most devastating punch in a boxer's arsenal, which obviously is not the case!**

Though speed does indeed increase potential damage to the target, it is not a magic attribute that will guarantee victory.

Being able to generate huge amount of kinetic energy is only as important as being able to transfer that energy onto the target. If your punch doesn't connect properly to the target, then all that energy will be dissipated in your muscles, so it is very important to be able to maximize energy transfer, but that shall be the subject of the next edition of **the Science of punching harder**