Karate Hits Physics of Sports!

My Physics of Sports students were treated to something special this morning.  Third-degree black belt Clifton Abercrombie and second-degree black belt Cody Davis visited my class and showed us some karate moves.  Mr Abercrombie has been one of my family's lead karate instructors for about a year-and-a-half now.  He is incredibly good at what he does.  The slow-motion video below shows one of his board-breaking feats.  He executes a perfect hammer punch, which uses the knife edge of the palm opposite the thumb.  Using the edge of one's hand allows for more force per area, i.e pressure, at the strike point.  Click on the video for a larger image.

There is a great deal of physics here!  At the start of Mr Abercrombie's motion, you will see his torso beginning to rotate.  His right arm goes back so that as his torso moves forward, he will store a great deal of potential energy in his upper arm.  Once his strong thigh, abdominal, and back muscles get his torso rotating counterclockwise (as seen from above), his right arm is like a whip.  Now cocked full of potential energy, his arm moves forward, thus turning potential energy into kinetic energy.  The red path in the above video clearly shows that after accelerating linearly in the early part of the motion, Mr Abercrombie's hand undergoes mostly centripetal acceleration as his arm follows through and breaks the board.  Note, too, Mr Abercrombie's eyes and how they are focused on his target.  As he follows through with the hammer throw, you will see his mouth open.  He yells, "Kiai!"  His exhale during the blow demonstrates proper breathing technique.

Let's now get more quantitative.  The graph below shows the speed of Mr Abercrombie's hand.  Click on the image for a larger view.

His hand's maximum speed is just over 12 m/s (43.2 kph or 26.8 mph).  That is speeding in a school zone!  To understand what accelerations are involved in making one's hand follow the path you see in the video, check out the plot below.  Click on the image for a larger view.

His hand's maximum acceleration is just over 325 m/s², which is over 33 times the acceleration due to gravity!  A grown man's arm is nearly 6% of his body weight.  I estimate the mass of Mr Abercrombie's right arm to be 5 kg, which corresponds to a weight of about 11 lbs.  He needed about 1641 N (369 lbs) of force on his right arm to execute the hammer punch.  What's great is that he most likely used more force because my camera films at just 60 frames per second, meaning my data points are separated by 0.0167 s.  With a high-speed camera, I could get many more data points, and, I suspect, get instantaneous forces approaching twice the size of what's seen above.

What to learn to break a board like Mr Abercrombie?  Visit Super Kicks Karate in Forest, Virginia.  Click here for their Facebook page.  It's a great place to see physics in action!