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The Focus on Force in Karate

by on September 24, 2008

People often reference Force as being the best metric to measure a karate technique. While useful to some extent, I argue that we focus on the wrong formulation of it. Force is a measure of how much effort is needed to accelerate a mass. Force is measured in Newtons (kg x m/s^2), which for most people is meaningless.

Student A: … nice technique. How many Newtons of Force does that take?

Student B: well, approximating my mass to be 78 kg, and the proportionate mass of my arm to be 8 kg, about 320 Newtons.

Student A: nice. I hope I’m able to convert enough energy into muscular tension to exert a similar amount of force some day.

See, useless. I want to dig a little deeper into the meaning of force, what contributes to its generation, and what we need to improve to get the most out of it. I want to state what I will not do in this article:

  1. make any conclusions about the utility or practicality of using Force to measure karate techniques
  2. claim to be a physics expert

A More Usable Formula

First off, use of F=ma doesn’t really say much for the above reason. I’m not going to throw out the Force equation, but put it into a format that’s a little more practical. We don’t really want to maximize Force, per se, we want to maximize acceleration through the maximization of force. If we’re going to generate enough energy to transfer into another object to exceed its structural capacity, we need to put a lot of energy into it…

… er, what?Ok, so I’ll get to why we might want to focus our attention on energy a little later. Just bear with me for now.

We want to accelerate fast. So we want to minimize the mass being moved without making it weightless (since the mass will contribute to the energy transferred in the end… again, described below), but maximize the force. If we divide each side of the traditional Force equation by mass, we get

a = F / m

We can assume our mass is constant for the duration of a karate technique, so the only variable is Force. We want to get our limbs moving as fast as possible as quickly as possible. Notice we need to reduce the time to do this since we wouldn’t want our opponent to see it coming. Since acceleration is a function of time, minimizing time increases our acceleration. We now need to look at the general profile of a karate techniques velocity over the duration of its execution. We need to answer: how fast does it accelerate at the start? at what point does it stop accelerating? how quickly does it begin slowing down (negative acceleration)?

Profiling Acceleration

From reading The Physics of Karate Strikes, I drew up this simple velocity profile. The x-axis gives an indication of the velocity at various points of extension of a technique. The y-axis plots the changing velocity. The underlying information here is the acceleration at each point in the technique. We don’t need to get into differentiation here in order to gain some insight into acceleration and velocity.

Velocity profile during execution of a technique

Velocity profile during execution of a technique

The acceleration is greatest at the beginning, even though the velocity is greatest about 75% into a technique (I’ll use a punch as an example). After this point, the arm begins losing velocity as we begin to contract our muscles in order to avoid blowing out an elbow and make the punch look stable. In this regard, contracting the muscles on impact reduces the energy transferred since there is an oppostive force working against the force of the muscles propelling the fist forward. The net force is still in the direction the fist is travelling, but has a lower magnitude. I’ve chosen 4 m/s as the top velocity for example purposes only.

Back on track here… from the profile above, the acceleration is greatest shortly out-of-the-gate. From a fist at rest at our hip, we must quickly get it moving and to do so we must provide the largest amount of force as soon as possible to get the acceleration up. As our arm extends, we exert less force, so the acceleration reduces, but the velocity continues to increase.

Now, why do we want it to accelerate so much? We apply force to the striking limb to increase its acceleration. What will acceleration contribute to?

From Momentum to Deformation Energy

We want to hit something real, real hard. We want to break a board, a face or other vital organ. Doing this is more complicated than “hitting it hard”. What does hard mean in this sense? Very ambiguous indeed.

Acceleration over a short time internal gets our fist traveling at a higher velocity quicker. This velocity, as we’ll see below, is a key point in momentum. Momentum is a conserved quantity meaning it is never destroyed or created. It moves from one object to another. Therefore, generating force increases acceleration; acceleration helps achieve top velocity quickly; finally, transferring energy from one object to another is best achieved by maximizing velocity!

So now you know where I’m going with this. Force, mass, and acceleration all contribute to momentum which is transferred from one object with mass (a fist) to another object with mass (a board/face/stomach/etc.). This transfer can be better described using deformation damage.

Deformation damage computes the amount of energy required to push an object beyond its breaking point. More elastic things (skin) require more energy to break because they can contort to a greater degree before breaking. Less elastic things (a board) only need to bend a little before they break but require more energy in order to make that initial bend. To achieve this energy, we need to know four things:

  • e, the coefficient of restitution: this is a measure of how elastic the collision is. Skin is more elastic than a board. Rock is less elastic than skin. That’s why breaking a board with a rock of the same mass as your fist moving at the same speed as your first would require less energy.
  • v, velocity of the striking object
  • m1, the mass of the object being struck
  • m2, the mass of the striking object

The function is:

Since this function is proportional to the square of velocity of the striking object, the faster its moving, the more energy will be transferred into the struck object. e can be better optimized (that is, the energy created is increased) when you are hitting with hard fists. The mass of the striking object is improved when the fist is heavier—but not so heavy that it cannot be accelerated to reach a high enough velocity to create as much energy as a lighter object.

Thus we have the golden ratio of karate: strength to mass. We want to find the equilibrium between the mass of an object and the force it takes to accelerate it. Too much mass and we can’t get the fist up to the same velocity. Too little, and the strike has less damage.


What have we hoped to learn today? We’ve gained some insight into why we try to generate so much force in our karate techniques. Increased force leads to increased acceleration. Rapidly accelerating gets our fist up to its top speed in preparation for delivery of a technique. A mass moving with as much velocity as we can muster has a better chance of transferring all the energy needed to deform a target beyond its limits, breaking a board or disabling an opponent.

But we need to keep a mind on fitness. From what I can tell, hard fists, connected muscles that utilize as many forces as possible, and a balanced weight (more accurately, mass) will result in increased damage.

I hope I haven’t made any incorrect statements here. Please let me know if there are things that are wrong or if we can extend it without causing our brains to explode from the complexity of it all.


From → karate, research

  1. No I think you’ve made a valid point and theres nothing wrong with your physics… The one thing i might say is that it is actually Energy that is neither created nor destroyed, merely changed from one form to another, so the transfer in this case would be Ep -> Ek -> Ep (of the object struck) and the Ek absorbed by the target and “converted to Ep” is actually not all absorbed by the object, some of it is used in the actual damaging of the target, ie breaking it. It is similar to an electric burn, the body doesn’t absorb all of the electrical energy, some is “wasted” in the resulting burn marks on your skin.

    Now, as P = mv I don’t know if the same “creation/distruction” concept applies directly to momentum, though it could be argued that a “potential momentum” (Inertia) exists due to your mass, and that this “potential momentum” is converted into linear momentum through the application of Force, though in truth if you boil it down it is really the Energy that remains in balance through the process not the P or F. The chemical potential energy within your muscles fire up, converting into kinetic energy of your fist moving. This Ek fuels the “Force” that creates the motion and thus creates the Momentum.

    However, as I said, your physics is still pretty much sound from what I can see / what I remember. I agree with your strength to mass ratio (worth noting for the layman that weight is not the same as mass…). Our strength and mass will both increase through physical activity, but it is also how effective we are at applying our total bodymass to each strike, through our technique and the ever-mentioned use of the hips. “Strength” itself begs for a definition… and I think (and I stand for correction) that a good analogy for it would be the chemical potential energy in the body. We increase our Strength by building not just bigger but also tighter muscle tissue, which we break down and our bodies build up by using the protein in our diet. This process, chemical in nature, converts the energy in the food into stored chemical potential energy in the muscle tissue (a similar process is used for the creation of the fat tissues, our long term energy storage centres, muscle being short term). Our “strength” and fitness level is therefore defined directly by how much Ep we have stored up in our musculature, as the body will use these reserves in applying a Force to an object to move it, including the body itself in carrying out our daily activities. The body uses these fuel cells in much the same way as any engine, more fuel (per “piston fire”) equals more force, so less muscle equals less strength. Perhaps some people are going “duh”, but it is worth explaining as Strength itself is not a term that has a set definition when we say one person is stronger than another… but it definately sounds a lot better than “Wow… his (or her…) chemical potential energy storage cells appear to have quite a large capacity!”

    In fact… I may begin to use that phrase in my daily life….

  2. philipobrien permalink

    Well I don’t want to get into a physics debate, but only to start gaining some insight into the forces.

    Energy conservation is only true in a perfectly elastic collision. Striking a board with a fist is not perfectly elastic. Even striking a face with a fist (or foot) is not perfectly elastic. Much of the kinetic energy of the system is lost in other forms such as thermal energy.

    But in either system, the momentum is conserved completely. Newton was talking about the Law of Conservation of Momentum. Energy is something else.

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