Introduction

Most martial artists share the goal of “hitting harder”. This is usually expressed in colloquial terms as hitting with “more force” or “more power”. But even a basic knowledge of physics will tell you that “force” and “power” are not the same thing. Which is it that makes you hit “harder” – force, power or both? And is it more helpful to talk in terms of something else such as momentum?

Understanding force

Many people think of “force” in very nebulous terms (perhaps explaining such misappropriations as “The Force” in Star Wars). So what is “force” as understood in physics?

Force is something that enables you to cause an object with mass to accelerate.

In other words, it is Newton’s famous formula: f = m x a.

Using this formula people commonly argue that in order to hit “harder” they need to –

1. maximise their mass; and
2. maximise the acceleration of their attack.

For the most part this is true: if you have a big mass and accelerate that mass well, you will maximise your chance of applying a greater force to a target. But it is important to note that this argument refers to force you are applying to your own body. It does not refer to the force you are applying to the target.

Put another way, in this argument the equation f = m x a assumes that m = your body mass, not the mass of your target (as it should for the purposes of calculating the force on that target!).

So instead of looking at the force applied to your body, let’s examine the force applied by your body to a target.

For example, consider a stationary object weighing 1 kg. For simplicity’s sake, let’s say you hit/push it, causing it to move a whole metre in one second. You’ve accelerated the 1 kg mass from 0 m/s to 1 m/s; ie. you’ve caused the object to accelerate at 1 m/s². By reference to the formula f = m x a you’ve applied a net force of 1 N or kg/m².

Clearly the more force you apply, the further you will move it in the same time (by accelerating it to a higher velocity). So imagine you have managed to force the 1 kg object 2 m in one second (ie. you’ve managed to accelerate the object from 0 m/s to 2 m/s). In that case you’ve applied a force of 2 N.

So far so good. At this point you might be forgiven for thinking: “If I can knock my opponent across the room with my punch, surely I must be hitting very hard?”

Well yes and no. Let me explain by asking a question: Does “hitting harder” really mean moving something farther? If it does, a strong push or shove arguably constitutes the “hardest hit”, because a strong push is likely to move something farther than a punch or kick. I’m sure you’ll agree that this is an extraordinary proposition (for more on this topic see my article "Visible force vs. applied force"). The former is designed to move, the latter to hurt (with or without moving).

It seems that “movement”, and hence the acceleration of your target, might not be the most significant indicator of “how hard you have hit” after all.

Furthermore, you might hit a brick wall with your fist as hard as you can. You’d be unlikely to move the wall at all. Does this mean you haven’t hit it “hard” (you have) or with any force (you have, except that the wall has exerted an equal force on your fist as per Newton’s Third Law)?

Theoretically if you were heavy enough you could push the brick wall over (ie. move it) – but we’re back to “pushing”. Theoretically if you punched fast enough your peak force¹ would be sufficiently high to break through the brick wall without “moving” it (eg. a high velocity bullet can pass through objects without displacing them).²

So what distinguishes a strike from a push? It is your deceleration before hitting the wall. The more you decelerate before you reach your target, the slower the velocity at impact. If your velocity at the point of impact is low, you’ll effect more of a push. If your velocity at the point of impact is high, you’ll effect a blow.

By now you should be starting to see the limitations of using f = m x a as a means of determining “how hard you hit”. The equation might tell me how to increase the force applied to my body (which is necessary in order for me to apply force to someone/something else), but it doesn’t tell me how to apply my force.

Rather than talk about the acceleration of your mass or the mass of the target, it seems to be more useful to consider the velocity of your mass at the moment of impact.

This is momentum.

The importance of momentum and its transfer

In physics momentum is defined by the following equation:

Momentum (p) = mass (m) x velocity (v)

Obviously a one tonne (m) car travelling at 60 km/h (v) will do some damage if it hits you. A fist, while not so destructive, obeys the same physics.

It appears that a well-thrown fist reaches its maximum velocity when the arm is about 80% extended. Accordingly if your punch covers say, 60 cm from a fully chambered position to full extension, then your punch reaches its maximum velocity at 48 cm.

This speed is generated by moving a number of body parts toward the target; eg. the whole body (by stepping or lunging), hips, leg, shoulder, upper arm and lower arm. If the full range of movement is used, and the body parts act in a staged way to transfer momentum in a whip-like sequence from larger to smaller body parts, then the fist will be accelerated to the fastest possible speed. A reverse punch is biomechanically better suited to transfer momentum than in this way than a leading arm punch.

So far so good. But doesn’t this come to more or less the same thing as previously argued – in other words to hit “hard” you want a mass travelling at a high velocity? Again, close. But there is more. You not only want your body to have momentum; you want to transfer it effectively.

Now, momentum transferred is called "impulse". The equation for impulse is as follows:

Impulse = force x time

In other words force = impulse / time

With impulse a fixed quantity, force and time are necessarily inversely proportional. In other words, one can deliver a given amount of momentum by:

1. transferring a large force for a short time; or
2. by transferring a smaller force over a longer time.

So, the longer your fist is in contact with the target, the less force it applies. That is, the momentum transferred will be the same but there will be less impact force and instead the target will feel more of a push.

When you throw a right cross (see my article “Chambering punches”), the punch travels a longer distance than a straight punch – particularly if (as is inevitably the case) the punch of the right cross follows a curved path to some extent. The further the punch travels from the chambered position to the target, the more time it has to accelerate and the faster its maximum speed will be (at 80% extension). This is why the right cross carries more momentum than any other punch. However, as a result of its (inevitably) curved path, such a punch, like a golf or tennis swing, will usually have to end with a follow-through. Accordingly it must have a longer contact time. This is why such a punch can knock someone across a room. But it's impact force will necessarily be more diffuse than a straighter, more focussed punch.

“But,” I hear you ask, “if this is so, why does a boxer’s punch seem so much more powerful?”

The role of power

That a competitive boxer can apply a staggering amount of force with a right cross compared to, say, a suburban karateka performing a reverse punch, does not detract from the fundamental observation I have made above: the right cross has more “push” and less “hit” than a karate reverse punch. The boxer is big enough, and is moving fast enough, to compensate for any “diffusion” of his/her force. He or she will knock you across the room – and hurt you at the same time.

But were the boxer to learn how to throw an effective reverse punch (ie. a straight punch in which the impulse is maximised) he/she would be applying force far more efficiently. What do I mean by that? The boxer would be transferring the same momentum in less time.

Put another way, the boxer wouldn’t have to work as hard to get the same result.

By “work” I mean, of course, the concept in physics defined by the following equation:

Work (w) = force (f) x displacement (d)

In other words, work is done when a force acts upon an object to cause a displacement. The boxer’s right cross causes more displacement with the same force, meaning that he/she has necessarily done more “work”.

Work can also be described as the amount of energy transferred by a force. In this case the boxer’s right cross, using the same force, transfers less energy. The boxer will need more force (in other words more accelerating mass) to transfer the same energy as the karateka doing the reverse punch.

As I have said above, the boxer will usually more than compensate. He or she will do so by adding more “power”.

In physics the equation for power is as follows:

Power = work / time

To compensate for the diffusion of his/her force using a right cross, the boxer has to work more in a shorter time. This means he/she needs more power.

Don’t all martial artists need power? Of course they do. Everyone will be subject to the same laws of physics. However, remember the purpose of this article: to determine how one can “hit harder”. Power and displacement are directly proportional. Yet “hitting harder” doesn’t require greater displacement...

[For more on the issue of displacement, see my article "Visible force vs. applied force".]

Conclusion

If you want to “hit harder” you should look to maximising your momentum by increasing your velocity and/or your mass. But you also need to look closely at how you transfer that momentum.

Transferring momentum effectively is a question of maximising your impulse; ie. applying a large force over a short time. The alternative (a small force for a longer time) produces a push – not a “hard hit”.

The smaller your impulse (ie. the longer you take to apply a force), the more power you will need to compensate.

A martial discipline or art that is “external” will focus on maximising power where an “internal” art will focus on impulse – see my articles “Internal vs. external martial arts” and “Understanding the internal arts”. As I have noted in that article, no art is purely external or internal – just as no strike can be effected without some impulse and no technique can be effected without power.

A good “civilian defence system” will attempt to find a pragmatic mix of both – or ideally adopt a sequential system of teaching progressively more “impulse-oriented” techniques and less “power-oriented” techniques – something I call “sequential relativism” in martial arts training (see my article “My quest for the martial ‘holy grail’”).

Footnotes

1. It is important to note that when I refer to maximising “force” I am of course referring to the peak force – force is never applied evenly but is applied in a curve. It is the peak force that is in issue when it comes to “hitting hard” – not the average or median force etc.

2. In this article I have not attempted to address factors such as stress and pressure. In the case of the former we are all familiar with the idea that we can increase damage by targeting softer areas. In the case of the latter we also know that we can increase damage by applying force over a smaller surface area – ie. increasing pressure. These are topics unto themselves which I hope to address at another time.

Copyright © 2008 Dejan Djurdjevic

Tags: Hitting Harder Physics Force Momentum Impulse Work Power Time Internal Exte

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