Breaking

How much can a martial artist break? To find out how fast a punch can be, I'll use an example of a filmed break that I performed with a reverse punch. These numbers are all rough estimates. The punch took 1 frame to start (at about the shoulder) and go through the board. It took much longer to begin the technique, but we are only interested in the time it took to travel about a half meter.

Figure 3: Reverse Punch

The equation for speed is:

Equation 1:

v = velocity, d = distance, t = time

In this case, we can estimate the time (1 frame will be 1/30 s or 0.033 s, if there are 30 frames per second). The biggest source of error is the distance, because we can be fairly confident that the digital video is 30 frames per second. My arm is about 50 cm in length from the front of the shoulder to the fully extended reverse punch. Because the video is blurred, I will add + 10 cm. The calculation is then:

Thus, the punch was traveling at 54 kph, or about 33.4 mph. With error, the range is between 36 kph and 54 kph. At this speed, my fist has quite a bit of momentum. The equation for momentum is:

Equation 2:

p = momentum, m = mass, v = velocity

The momentum of the punch is thus:

I used a weight of 3kg as an estimate for the mass of my arm. In practice, there are ways to get more of your mass into play in a strike, but I'll assume I was stationary and only the arm's weight is relevant. In order to see how much force this generates, however, we'll have to do some more physics. The force exerted on the board is the change in momentum divided by the change in time.

Equation 3:

F = force, Δp = change in momentum, Δt = change in time

This is intuitive to anyone that has spent a lot of time hitting stuff. A large change in momentum will increase the force. But the time is also important. If your hand is traveling at 50 kph and it hits a pillow, it won't cause that much pain. That's because the change in time is large. The pillow yields and the contact between the fist and the pillow is lengthened as your fist squishes into the soft stuffing. If you hit a concrete wall, the change in speed is a lot faster. As Δt gets smaller, the force gets bigger. This is also why it hurts when something doesn't break. Wood will flex a little, but if you fail to break concrete, your hand or foot is stopped very quickly, and Newton's third law screams back at you.

To determine the change in momentum, we will assume that the hand went from full speed, 15 m/s or so, to 0 m/s when it broke the board. In order to calculate the time, we'll need to estimate how long it took to do that. If the entire process took 1/30 of a second, then the break itself took less than that. It would be a difficult problem to estimate the exact time. The fist was probably already moving when it crossed the start position just in front of the shoulder. The contact between the fist and the board was not instant, and the fist took some time to get to the board. If at least two thirds of the time was spent traveling to the board, then our contact time, to go from 15 m/s to 0, is 0.0133 of a second. Using this time, we can estimate the force.

How much does it take to break a board? Most of the time, this is sufficient. However, there are some important factors that can determine how much force a board can take. Its density, sap content, moisture, elasticity, and the type of wood all determine how strong it is. Most of the time, it requires far less than 3375 N to break. I would estimate that most boards require less than half that force to break, but it would not be possible to say that that for any board in particular.