# How can I determine the pound-force behind a punch?

I am a martial arts instructor always looking for the next best way to enhance the performance of my students. However, I'm having difficulty understanding how to determine the pound-force (ibf) of a punch delivered to a heavy bag. I understand the formula which is F=m*a is Force = Mass times acceleration. First of all mass is measured in Kg which I get but in the formula which mass is being used, the weight of the student or the weight of the bag? I understand the results of Force is measured in Newtons which I know can be converted in pound-force. I know the acceleration is measured in m/s/s but how can I determine their acceleration ? I've been told that I could use Kinetic energy which is KE= 0.5mv2 but I would get a result in joules which is also kg m/s/s. Please help me determine the right way to determine pound-force as well as to how I can go about performing for my students. Thank you all in advance for your participation.

The answer is, you'll have to be more specific.

When a fist hits a bag, the force varies a lot in terms of time. If you imagine trying to punch a bag as slowly as possible, there is a slow onset as your fingers just graze the leather, followed by something more "meaty" as your bones start to press against your skin which is pressing against the actual padding in the bag. Speeding that process up, all of these nuances continue to be there.

## Improving peak force

You might want to improve, say, the peak force. This is hard to measure; you'll need some sort of "force plate." To give you a sense of what a force plate does, imagine a plate attached to a rail, so that it can move towards you or away from you relatively freely. Now put a spring on it so that it takes more effort to compress. Now the distance that the plate moves correlates with the force on the plate--so that's how that works. In practice, real force plates are very thin so it's not a distance that you can "see".

You can find force plates sort of easily in the form of bathroom scales, but those will not be as configurable as, say, piezoelectric transducers paired with a microcontroller. In particular, getting a bathroom scale to "stop" at the maximum weight it registers may be prohibitively difficult. For that matter, if you can attach the ball to an air piston and then attach the piston to a pressure gauge, you can figure out the peak pressure in the piston. The formula is the peak change in PSI times the square-inch area of the round inside cross-section of the piston.

Probably the easiest way to do this is ultimately a peak-force calculation: you can buy "shock pads" which burst visibly if they register a force greater than some pad-specific threshold. These are used on crash-test dummies etc. to figure out whether they've experienced, say, G-forces which would be lethal to a human. Put some of those on the ball and see which ones burst to get a crude idea.

## Time-averaged force

You might want to measure the speed of the ball instead, if, say, it's connected to a rope hung from the ceiling. This is a very easy calculation, done often on Mythbusters, which requires a high-speed camera with known frames-per-second. Have the student punch in front of a "ruler" (often alternating black-and-white stripes work best) and count the number of frames that the ball requires to travel a certain known distance. This has a great bonus for your students: you can show them the tape, which shows them their form in slow motion.

If the ball has mass $m$ then the momentum imparted is $m v$. Count also the time $T$ that the fist is in contact with the ball, to find the time-averaged force as $m v / T$.

## Transferred kinetic energy

You might want to measure the kinetic energy of the fist. In theory this is as simple as asking someone to punch a ball which is hanging from a fixed pivot by a stiff bar. The bar can also be weighted down to make the "punch" as realistic as you need (I imagine the above solution with the ball hanging from a rope on the ceiling might "feel wrong" when you're punching it.) By allowing the bar to rotate freely, the maximum height attained should give you the energy that was transferred to the ball+bar ensemble.

As for measuring its peak rotation, you'll want to think about how the normal "pen"-style air pressure gauge (for car tires) works: the air pushes out the gauge a certain distance, but then friction prevents it from returning. You can do this for the angle of the bar, too: on the same pivot, have a plate which can rotate independently of the bar. Put a little friction on that plate. Stick out a strut from the edge of the plate, so that the bar runs into the strut on its way up. Then when the ball is going "up" it pushes the strut which rotates the plate; but at its peak, the bar and the strut detach, so the plate stays rotated to the maximum rotation $\theta$. (Safety precaution: install another strut on the other side of the bar with some padding, at a fixed rotation relative to the ground, so that the returning ball does not accidentally whack someone.)

If gravity is the only factor slowing down the machine, then the kinetic energy of the punch was $E = E_0 (1 - \cos(\theta))$ for some constant $E_0$ which depends on the masses of things involved, which you'd have to determine experimentally. Once you've determined that constant, you can use this formula to simply label the plate and you won't need to do any complicated cosines in front of your class. Notice that this will be an energy, so you'll have to use e.g. foot-pounds instead of pounds. There is no good way to turn this energy back into a force. Roughly speaking, this is because you can expend the same energy travelling forwards on a bicycle (low force) or climbing upwards on a rock wall (high force), so we need to know the time-scale and distance of your overall exertion. For bicycles and climbing those parameters aren't too hard to figure out, but microscopic measurements of a ball as it's being punched will be difficult without the aforementioned high-speed camera.

• Alot of interesting information but to be more specific ultimate I want to determine a student's acceleration which I know 1.0 m/s = 2.2 pmh and their pound force then help increase their acceleration. So I could I capture their acceleration without using a accelerometer and which mass is being used the weight of the student or the weight of the bag? – Senpai Roy Mar 10 '15 at 19:42
• Again, if you want to capture their acceleration without using an accelerometer, use a force-plate or high-speed camera. For the high-speed camera, measure the velocity of the fist with a background ruler, then measure the contact interval, and measure the speed afterwards (which ideally should be 0 but if people punch "through" the bags maybe it's not). – CR Drost Mar 11 '15 at 17:14

I was just thinking how this could be done accurately, which lead me to this website. I came up with a good idea.

First attach a block of clay to a wall, then punch the clay on the wall and measure the depth of the indention. Next, set a block of the same type of clay shaped to the same dimensions on the ground, then drop a fist sized hard heavy ball on the clay block. A hard mold of your fist would be ideal but a shot put ball would be good. Then measure the indention of the ball in the clay. If you want the indention to look the same on both clay blocks (without casting a mold of your fist) wear a thin piece of leather over your knuckles.

The goal is to find the distance you have to drop the ball to create a depth in the clay equal to the depth your fist caused in the clay. Then measure the distance the ball traveled to get the velocity of the ball at impact, and get the weight of the ball. With this information you can get figure the kinetic energy the ball had at impact, which will be the same as what your fist had.

The force of an object is a product of that object's acceleration and mass. English physicist Isaac Newton introduced this fundamental identity of classical mechanics with his second law of motion, F = ma. F represents force; m represents mass; and the variable a represents acceleration. A fighter's fist or a boxer's glove when it reaches a punching bag will have a force dependent on how fast the fist or glove is speeding up and the mass of the fist or glove and arm. The unit of force is typically the Newton (N), which is one kilogram meter per second squared.

STEP 1

Weigh the boxer or fighter on a bathroom scale. For example, the boxer weighs 147.7 pounds. STEP 2

Multiply the boxer or fighter's weight by 0.0345 using a calculator, to determine the mass of the boxer's arm. For example, 0.0345 x 147 = 5.0715. The estimated mass of this boxer's arm is 5.1 kilograms.

STEP 3

Station the boxer in front of a punching bag. Place two assistants to the right and left of the boxer. The assistants should be facing each other with a line of vision perpendicular to the direction in which the boxer will punch. Equip one assistant with a digital stopwatch and the other with a velocimeter.

STEP 4

Instruct the assistant holding the velocimeter to hold the device immediately to the left of the surface of the punching bag, opposite the boxer. Instruct the assistant holding the stopwatch to time the boxer's punch, starting the stopwatch when the boxer begins his punching movement and stopping the stopwatch when the boxer's fist strikes the punching bag. STEP 5

Instruct the boxer to punch the bag, allowing the two assistants to take their measurements. For example, the assistant holding the stopwatch measures a punch time of 0.1 seconds; the assistant holding the velocimeter measures a velocity of 19.0 mph. STEP 6

Multiply the punch velocity by 1.61 to convert the velocity to kilometers per hour, using a calculator. For example, 19 x 1.61 = 30.59. Multiply your answer by 0.277 to convert the punch velocity to meters per second. For example, 30.59 x 0.2778 = 8.49. The boxer's punch velocity was approximately 8.49 meters per second (m/s). STEP 7

Divide your answer by the measured time of the punch. For example, the measured time of the punch was 0.1 seconds: 8.49 divided by 0.1 = 84.9. The acceleration of the boxer's fist and arm was approximately 84.9 meters per second squared (m/s^2). STEP 8

Multiply your answer by the calculated mass of the boxer's arm in kilograms. For example, 84.9 x 5.1 = 432.99. The force of this boxer's punch when it reaches the punching bag is approximately 433 kilogram meters per second squared, or 433 Newtons (N). THINGS YOU'LL NEED

Bathroom scale Assistants Velocimeter Stopwatch Calculator