Few things in life offer more visceral proof of the power of physics than a karate chop. Punch a brick with your bare hand, and if you are untutored in the martial arts, you may break a finger. Punch it with the proper force, momentum, and positioning, and you’ll break the brick instead. “Amazingly, there are no tricks involved,” says Michael Feld, a physicist at MIT. “What you have here is one of the most efficient human movements ever conceived.”
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 died in 1986 while working as a scientist-astronaut aboard the space shuttle Challenger.) The secret to karate, both men agreed, lies in the speed and 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 kicks and punches and counted how many times the strobe flashed until the foot or 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. Hitting a piece of wood at that speed, a 11/2-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 11/2 inches thick actually takes less, about 1,900 newtons. Of course, brute strength is not the only requirement for breaking concrete blocks — the nature of the chop is also important. Karate students must learn that for a strike to have maximum momentum, it must have a follow-through; golf and tennis players follow through with their swings for the same reason.
To understand how follow-through 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 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.”
What happens after contact is also very important. All materials are at least slightly elastic: Whack them in the right spot and they will start to oscillate. “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 us, reaching the equivalent limit in the body’s bones is no easy matter. Feld says bone can withstand 40 times as much force as concrete, and a cylinder of bone less than an inch in diameter and 21/3 inches long can withstand a force of 25,000 newtons. Hands and feet can take even more abuse, because skin, muscles, ligaments, tendons, and cartilage absorb a great deal of impact. A well-kicked foot can absorb about 2,000 times as much force as concrete before breaking. Feld has never fractured a finger in karate, even though he once broke eight one-inch-thick boards at a time.
If students want to break boards, they have to not only increase their speed and improve their aim but also toughen up their hands and feet by striking them against a post wrapped in foam and canvas. “In the beginning, your skin is so soft you may end up cutting it. And then comes the blood,” says Sihak Henry Cho, a tae kwon do grandmaster. “This is not recommended.” Over time, the shuto, or knife-edge of the hand, develops a callus that acts exactly like a car bumper, absorbing and diffusing the force of a collision.
The important lesson for would-be black belts is that physics needs a little help from perseverance. “Tiger Woods didn’t just wake up one morning and start hitting a ball 320 yards, and we don’t just walk in and shatter a cinder block,” Cho says. “Everybody has to work at it.”