Punching Bag Physics: Solving for Impact Force and Acceleration

[jpcoelho]

Dear forum,

I have the following phisics problem. I want to be able to measure the impact of a punch in a regular punching bag. I'm able to measure the acceleration in all the three axis. Besides that I know the punching bag dimensions and weight. The colision between the fist and the bag is not ellastic. Substacial energy is absorbed by the bag. Below I present some pictures of the setup.

I'm looking for the physical differential equations that relates the acceleration and the impact force on the bag. Any help will be appreciated. Regards to all.

 

[mfb]

$$\vec{F}=m\vec{a}$$
You can compare force and acceleration in each dimension separately. This is the acceleration of the center of mass and it neglects the interaction with the pivot (so it is valid only if the timescale of the punch is short enough).
If your accelerometer is not in the center of mass, things can get more complicated.

This is just based on momentum, you don't have to consider energy.

 

[gadong]

This is an interesting problem in applied physics.

It is not trivial, due to the variety of ways in which energy can be transferred (motion of bag, energy absorbed by bag, motion of the boxer).

The maximum angle of displacement of the bag from the vertical direction (after it swings away, like a pendulum from the punch) is a useful parameter as it can be used to compute the energy transferred to the bag (no need to measure acceleration along each axis after the punch).

However, I do not immediately see an easy way to determine how much energy has been absorbed by the bag. The mass of the boxer plays a part in the calculations.

 

[mrspeedybob]

The first question that comes to my mind is what exactly are you trying to measure. "impact of the punch" could mean peak force, average force, impulse, energy, power, or maybe the most useful measure is some other derived unit invented specifically for measuring punches.

What units do you want your results in?