The Art and Physics of Martial Arts and breaking.
Martial Arts have been around for many years and its main purpose is mainly for self defense. There are many techniques used in various styles of martial arts. One of the techniques I will be focusing on is Breaking. Breaking is a technique in martial arts that is used in competitions, demonstrations and testing for belt and level promotion. Breaking is an action where a martial artist uses a striking surface to break one or more objects using the skills honed in their art form. The striking surface is usually a hand or foot, but a fingertip, toe, head, elbow, knuckle or knee can be used too. The most common object is a piece of wood, though it is also common to break bricks or cinder blocks. Breaking can be often seen in karate, taekwondo, and pencak silar although not all styles of martial arts place equal emphasis on breaking. In styles where striking and kicking is less important and there is an emphasis on grappling or weaponry, breaking is less prominent.
While breaking is used for various things in different styles of martial arts, it is also based on physics and selection of materials—the most commonly seen breaking involves spaced softwood boards. It is difficult to even break a soft pine wood hitting against (perpendicular to) the grain, so breaking is usually done by a strike with (parallel to) the grain.

In this video, you’ll see me kicking a wooden board. I have a background in Taekwondo and I have been practicing this art for over 9 years. Growing up, I did not fully understand the physics behind board breaking. I was thought how to kick correctly and how much force my body or foot exerts on the board only depends on how hard I try to kick or punch it. I will later on explain and go in depth about the physics of board breaking although use hand/punches instead of foot/kicks as my examples so that it is less complicated

According to Les Burton who has a PhD in Martial arts and Physics, a well- A well-executed taekwondo strike delivers to its target several kilowatts (thousands of watts) of power over several milliseconds (one thousands of a second), quite enough to break blocks of wood and concrete. For a linear punch, the hand of the practitioner of taekwondo can develop a peak velocity of 6 m/s to 10 m/s ((18.7 ft/s and 32.15 ft/s)) and has a mass of 0.65% (0.56%) of the male (female) body mass.

For a faster strike, the overhand strike, the hand can have a speed of 10 m/s to 14 m/s.
For a 70 kg (155 lb.) male, the hand would have a mass of 0.46 kg and the forearm would have 1.14 kg of mass.

For the hand alone, at 10 m/s, the
KE = 0.5 • m • v • v
KE = 0.5 • 0.46 kg • 10 m/s • 10 m/s
KE = 23 Joules.

And at a speed of 14 m/s, the hand would deliver 45 Joules of energy.
The force needed to break the ribs of a person corresponds to the energy needed to break a one inch thick pine board one foot by one foot square. The energy needed is about 30 Joules. It would seem that an overhand strike can break the board, but that a linear punch can not.
The average forearm has a mass of 1.63% (1.38%) of the male (female) body mass. Using proper bone alignment of fist and forearm, a part of the mass of the foreman can be considered added to the fist. This enables more energy to be delivered in the linear punch. (This analysis is much more difficult for the hammer strike, since the fist is moving in an arc, the forearm is not moving as fast as the end point of the arc, the fist. Also the forearm is not in line behind the fist when it hits.) For our 70 kg male, At 10m/s, the energy from the forearm alone will be 57 Joules, adding this value to the fist and we get a total of 80 Joules of energy. Since the total mass of the forearm may not contribute, the total energy will be less, say about 40 or 50 Joules. However, this is well over the 30 Joules needed to break the board.
It should be noted that the energy needed to break the hand is considerably more than that needed to break the pine board (or a rib). Therefore, when done with proper technique, we do not need to worry about the hand. However, I have seen cases where improper technique such as wrong bone alignment can cause a sprained or broken wrist.
Another thing that can happen is that the person, trying to break the board gets cold feet and does not follow through with the punch allowing the board to stop the hand, without breaking the board. This will deliver a large change in momentum to the hand, the hand going from high speed to zero in a fraction of a second. I have seen this case a number of times. If the person is going slow enough, it will only hurt or bruise, but it can and has resulted in a broken knuckle. Newton’s 3rd Law says that if you exert a force on the board by your hand, then the reaction to that would be the force the board exerts on the hand.

We can use the concept of Impulse to calculate the force on the hand by the board.

Force • time interval = mass • change in velocity

Solving for the force we get
Force = (mass • change in velocity) / time interval

Assume the mass of the fist for a male of 70 kg, and the change in speed to be from 10 m/s to 9.8 m/s, and the time interval to be one hundredth of a second.
Force = (0.46 kg) (0.2 m/s) / 0.01 s
Force = 9.2 Newtons

This value of force is not enough to cause damage to the hand. However, if the board does not break, then the change in speed will be from 10 m/s to zero.

Force = (0.46 kg) (10 m/s) / 0.01 s
Force = 460 Newtons

This is a factor of 50 times, a tremendous increase. Even if these numbers are not completely accurate for a given case, they show relative results that should be in the ballpark.