Physics of punching

In the late 1970s, when Feld was earning a brown belt in karate, his instructor, Ronald McNair, also happened to be his physics student. (McNair later died tragically while working as a scientist-astronaut aboard Space Shuttle Challenger.) The secret to karate, both men agreed, lies in the speed and exceptional focus of the strike. But just how fast does a karate punch move? To find out, they joined with undergraduate Stephen Wilk and set up a strobe light that flashed either 60 or 120 times per second. Then they photographed McNair and others throwing various kicks and punches. Once the film was developed, they could calculate the speed of a punch by counting how many times the strobe flashed until the fist hit its target.

Feld and McNair found that beginning students can throw a karate chop at about 20 feet per second–just enough to break a one-inch board. But a black belt like McNair could chop at 46 feet per second. At that speed, a 1 1/2-pound hand can deliver a wallop of up to 2,800 newtons (one newton is roughly equal to the force exerted by the weight of an apple). Splitting a typical concrete slab 1 1/2 inches thick takes on average only 1,900 newtons.

Of course, the best boxers can punch as quickly and powerfully as any black belt. Why can’t they break concrete blocks too? The answer lies in the nature of their punches. When a boxer throws his fist, he usually ends the movement with follow-through. This gives the punch maximum momentum (golf and tennis players follow through for the same reason), and it can help knock an opponent down. But the impact itself is diffuse: It’s meant to jar an opponent’s brain, not crack his skull.

A karate chop, on the other hand, has no follow-through at all: It lashes out like a cobra and then withdraws instantly When a black belt hits a slab of concrete, for instance, his fist touches the block for fewer than five milliseconds, and yet the block breaks with a resounding crack.

To understand how this works, Jearl Walker, a former tae kwon do student who now teaches physics at Cleveland State University, set up a study much like Feld’s and McNair’s. A well-thrown fist, he found, reaches its maximum velocity when the arm is about 80 percent extended. “That’s exactly what my tae kwon do master had taught me,” Walker says. “You learn to focus your punch in your imagination so that it terminates inside your opponent’s body, rather than on the surface. To deliver the maximum power, you want to make contact before the slowdown begins.”

The purpose of all that focused power is brutally obvious: to break bones and rupture tissue. But success also depends on more subtle forces. Solid as they seem, all materials are at least slightly elastic. Whack them in the right spot and they will start to oscillate. A punch with a follow-through would dampen such oscillations, but a karate chop, by pulling away at the last moment, lets them move freely “If you tweak a rubber band it goes up and down, and the same is true if you tweak a board or a brick with a much greater force,” Feld says. “When they reach their elastic limits, they start to yield. In other words, they break.”

Fortunately for most of us, reaching that limit in bones is no easy matter. Feld says bone can withstand 40 times more force than concrete, and a cylinder of bone less than an inch in diameter and 2 1/3 inches long can withstand a force of more than 25,000 newtons. Hands and feet can withstand even more than that, because their skin, muscles, ligaments, tendons, and cartilage absorb a great deal of impact. As a result, a well-kicked foot can absorb about 2,000 times as much force as concrete before breaking.