Pressure

Most people have heard of the infamous bed of nails. The notion seems quite uncomfortable, but it's really not so bad after a little investigation. The principles of pressure explain this feat rather well. The equation for pressure is

Equation 1:

p = pressure, F = force, a = area

Pressure is inversely proportional to the area where force is being applied. This generally means that the smaller the area of the item of contact, such as a fist, the more pressure generated. To expand this principle to the bed of nails, the area of the point of one nail is fairly small (0.001 m2). The force on this nail for a 70 kg physics professor is the force of gravity:

And the pressure is:

This produces significant pressure, about 99.5 psi, which is why you won't see anyone (especially physics professors) lying on one nail! If the area is increased by an additional 500 nails, the pressure on each nail is:

Thus, the pressure for each nail is only 0.20 psi, since the force of the physics professor is distributed to each nail. This is simplifying things a little, though, since the physics professor can't distribute his weight equally over all the nails. Also, any variations in the nails, even a millimeter or so, can allow significant pressure for those nails. Even knowing the physics that make it work, it is still dangerous. It requires skill to make sure that pressure is distributed over enough area so that no nails have enough pressure to penetrate. The physics in this case demystify it somewhat, but also shows you why this isn't something you want to do yourself.

Pressure can also be used in every strike made by a martial artist. In order for a martial artist to increase pressure against a target, he can minimize the area of contact. For instance, instead of hitting a target with the top of the foot (area ~ 0.05 m²), he can use the ball of the foot (area ~ 0.01 m²). For a 1000 N force kick, the increase in pressure is:

Top of foot:
Ball of foot:

Just by decreasing the area, the martial artist has increased the pressure. However, decreasing area may not always be practical. Striking with a single finger would increase the pressure, but a finger is not a particularly strong striking point for many people. Density and strength is also important in the "stopping power" of a strike.

Figure 4 - Pressure vs. Area

Figure 4 shows a representation of area versus pressure given a constant force. As the area decreases (A, B, C to the left), the pressure increases. Area A, the large circle on the left, will feel a smaller pressure, while C will feel a higher pressure. When breaking wood, a martial artist wants to minimize the striking surface to get more pressure on the target. This is independent of force, because the graph above assumes that the force is constant. If the martial artist hits the board with his entire palm, the pressure on the board is far less and the force is distributed over a wider area. Thus, she will want to strike with the heel of the palm or the first two knuckles. These are just two examples of striking areas that generally minimize area and are reasonably strong, so that they can take the additional pressure. To prove that we are generating more force on the target, reordering Equation 3 for force will be:

Equation 4:

p = pressure, F = force, a = area

Equation 4 says that force is a product of pressure times the area. Greater pressures mean greater forces. Increasing area will also produce more force, because, as area increases, more force is required to maintain a constant pressure.

Pressure is just as relevant for a punch as it is for a knife. The extremely small area means that high pressure can be created with a small force. This principle can be applied to all strikes. Although it may not be practical to minimize the striking surface for every punch or kick, you can use a basic understanding of pressure to increase the effectiveness of your strikes.

To find out how much pressure is generated for a punch, lets assume that a punch generated 2819 N. We can estimate the area. I usually hit with the first two knuckles. As a rough estimate, each knuckle has approximately 1 square centimeter of area. Our total area is 0.02 m². To calculate pressure, we use equation 3, which is:

This is assuming that, when the board flexed, only those knuckles remained in contact until it broke. This actually probably didn't happen, and 140950 Pa is a maximum bound. Still, it is about 20 psi at the point of contact.

Figure 5 - Using Pressure on a Pressure Point

Figure 5 shows a self-defense technique using pressure. The striking area, right below the ear, is a pressure point. In order to maximize force, the martial artist is minimizing the striking area (two fingers). Although this increases pressure, it also increases stress on the fingers. The minimized striking area increases pressure on the target and on the striking surface.