The Punch By Joel Goodson

The History of It People have been punching and fighting each other since the beginning of existence. People of all ages, races, and cultures are affected by fighting. Almost everyone I have met has been punched, or been in a fight, at least one time, some more than others.

A very effective punching technique is a basic Taekwondo Punch. “focused” punches rather than “follow through” punches Why a focused punch? In wide swinging punches, a torque may be produced, which can throw the puncher off balance. Next, if the punch occurred in the “follow-through,” then energy is transferred to the opponent by pushing rather than by “deformation.”

What is a Taekwondo punch? “In a standard Taekwondo punch, the fist begins at the hip and terminates with the arm fully extended and the fist at shoulder height.” Studies show that maximum velocity in the punch is attained at about 75% of the stopping point distance. This is why a Taekwondo punch involves focusing on punching several centimeters into their target.

How do you calculate how hard a punch is? Many sources show that a basic formula for force (Force = Mass*Acceleration) is sufficient enough to calculate how hard a punch is… This is a good way to show that the more mass the puncher has and the faster the punch, the harder the punch is… But I figured there had to be more to it than that…

(cont.) You have to take into account the mass of the opponent and the change in velocity of the punch… You need to take into account… the amount of energy transferred!!!

How do you calculate the energy transferred in a punch? The maximum energy transferred to the opponent is the difference in the total kinetic energy before the collision, and after. This is all calculated with a simple formula, of course.

The Math of It All… If we assume that the impact of the puncher’s fist and the internal organs of the opponent are totally inelastic, then M 1 V 1 = (M 1 + M 2 )V’ This is when M1 is the mass of the punching arm, V1 is the speed of the puncher’s fist on contact, M2 is the opponent’s mass, and V’ is the speed of the fist and the opponent right after impact… so…V’ = M 1 V 1 /(M 1 + M 2 )

What about the difference in energy? “ The difference is: DE = ½M 1 V 1 2 – ½(M 1 +M 2 )V’ 2 ” And after filling in M 1 V 1 /(M 1 + M 2 ) for V’… The expression simplifies to: DE = ½M 1 M 2 V 1 2 /(M 1 +M 2 )

How about an example… Generally, the mass of a person’s arm is 10% of their total body mass, which we will assume. (So M 1 equals about 0.1M 2 ) This information fits into the previous equation…DE = ½M 1 M 2 V 1 2 /(M 1 + M 2 ) Simplifying it to…DE = 1/22 M 2 V 1 2

(example continued) Next we assume an average 70 kg. (155 lb.) person is punching a person of the same mass at an average black belt rate of 7 meters per second, then… DE = 156 Joules !!!!!

By definition, a joule “is the SI unit of energy, or work with base units of kg·m 2 /s 2.” 156 Joules is the same as 115 foot-pounds of energy…. So since Work = (Force)*(Distance), 115 ft*lbs = (50lbs)(2.3ft) Therefore a punch that transfers 156 Joules of energy transfers the same amount of energy it would take to lift a 50 pound weight 2.3 feet. What is a Joule? What is 156 Joules equivalent to?

Could that break a bone? The amount of energy that a leg bone can absorb before breaking is… E max = 1/(2Y) Al  b 2 …which is about 350 Joules… But an arm bone is about half the diameter of a leg bone, which proportionally reduces the breaking point to about ¼ of the energy, or 88 Joules. So, yes, a bone could be broken by a punch that delivers 156 Joules in many cases, especially much smaller bones, such as the ribs.

The End Stay tuned for a short video clip.

Works Cited Calculus with Analytic Geometry (8 th Ed.) Houghton Mifflin Co. Boston, NY MacMillan Encyclopedia of Physics (Vol.2) Simon&Schuster Macmillan, NY World of Physics (Vol.1) A-L The Gale Group Farmington Hills, MI Media Cited