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4-Participant

## Computing the punching force (when hitting a punching bag)

Hello!

You have a ground fixed punch bag (resting on a spring that's attached to a counterweight).
What is the minimum sensor setup in order to determine:

• the force of the punch in the bag
• acceleration of the punch
• the speed of the punches (for multiple punches)

Notes:

• no sensor must be attached to the person punching the bag, only on the bag
• bag is punched in a limited vertical area

• sensors
• calculations

Working as hardware engineer, I must admit I'm not that experienced with physics.

I've been trying to figure a way to solve it for a week now. What I thought of is mounting an IMU in the center of the bag and after that gather experimental data by hitting the bag with a pendulum. What's hard for me to determine is the force with which the bag is hit, how much of that force gets absorbed by the padding and the remaining force that drives the bag afterwards. Finding the acceleration and speed of the much would be pretty easy after finding the force, by applying Newton's second law.

Any help would be highly appreciated!

Check attachments section for some visuals on the problem.
Note: I'm sorry if I'm double posting this. For some reason the previous post auto-closed.

12 REPLIES 12
19-Tanzanite
(To:hgpt)

This is a Mathcad forum. If you want help with a Mathcad worksheet, please post the worksheet.

If you want help with a general engineering or physics problem you might get help here, but there are probably better forums (e.g. http://www.eng-tips.com/).

13-Aquamarine
(To:hgpt)

Hi,

to calculate the forces, accelerations and velocitys, you will have to make some measurements before starting calculations.

Is there any possibility to measure the contact-time?

The punch will be not elastic in the real situation, we will loose energy.

Basically you can start the calculation with this:

Volker
4-Participant
(To:vlehner)

You can assume a contact time of 30ms.
Considering the following as known:

There are multiple problems to be solved before taking real world measurements as:

• where are the IMU's going to be placed and why?
• how can you accurately measure the force applied by the pendulum
• what happens when multiple punches are thrown?

I started with the math the same way you did, but got stuck. Here is my progress (after many tries).

I was also thinking at analising the system as a black box and using Matlab System Identification Tool for finding the model, but then I will also need to know the applied force in order to link it to the acceleration of the bag.

13-Aquamarine
(To:hgpt)

We must search for a Law for the Spring.

The bag is a pendulum which has its dynamic with the spring.

I'm just searchig for it.

Then we can go on in calculations.

Can you give me some information about the spring?

For example stiffnes, wire-diameter, length (unloaded)

Volker
4-Participant
(To:vlehner)

Unfortunately, there's not that much info about the spring, apart from:

• wire diameter - 1 cm
• length - 20 cm unloaded

Theoretically, it should be solvable based only on IMU data (accelerometer and gyro) and maybe a load cell; this way anything that has to do with the spring gets to be bypassed.

13-Aquamarine
(To:hgpt)

@hgpt wrote:

Unfortunately, there's not that much info about the spring, apart from:

• wire diameter - 1 cm
• length - 20 cm unloaded

Theoretically, it should be solvable based only on IMU data (accelerometer and gyro) and maybe a load cell; this way anything that has to do with the spring gets to be bypassed.

Ok, if you will bypass the spring, you must measure the both velocitys of the punching body (before and after the punch).

You can do this with the elevation hight of the punching body after the puch.

With the difference of these two values for the speed and the delta t, the acceleration/Force would be no problem.

Then the sensor must be calibrated with this values.

I calculated the Punching-Force and acceleration approximately, see attachement please.

EDIT: The velocity of the bag you can calculate with the law of the impulse.

The absorbed Energy Delta W is a measurement for the acting Force (=resistance).

Good luck!

Volker
4-Participant
(To:vlehner)

The one thing that I do not understand is why is there a factor of 2x when calculating a_punch  ?

Apart from that, the math seems fine for calibration purposes and testing, but what happens when a real person hits it? There's no recoil of the punch, due to the nature of the impact being plastic.
Further more, imagine someone hits the bag when it is traveling from O1 to O with enough force to stop it, but not enough force to imply a movement back to O1 (the bag practically remains almost still for some time). The equations fail to model this kind of a situation.

There's one more thing mentioned in the problem: the bag is hit in a vertical space. Judging on this, one can say it's not always hit in the center of mass. Imagine this: you hit the bag with the same force:

• 1st time closer to the base
• 2nd time closer to the top

The speed of the bag will be different between the 1st and the 2nd hit, while the force is the same.  I guess one more thing that's to be taken into consideration is the torque that's applied relative to the mounting point of the base (the spring). I might be wrong, though.

Note: Due to the functions of the IMU acceleration on all 3-axis is provided as well as angle variation is time (due to gyro)

4-Participant
(To:vlehner)

Everything looks fine, but I don't quite understand one thing: why is there a factor of 2x that is multiplied to obtain a_punch ?

The model seems pretty good for calibration and testing, but I do not think it applies for a real human punch if you take into consideration the following:

• When it comes to a real punch, there's no recoil, due to the impact being somehow plastic.
• Hitting the bag multiple times.
• Imagine you hit the bag when it moves from O1 to O with just enough force to stop it, but not enough to bounce it back to O1. The bag remains still, the velocity is 0, thus, according to the equations, the force is 0; but it obviously is not.

• Imagine you hit the bag with the same force, but the projection of force does not go through the center of mass.
• 1st time you hit somewhere near the top end of the bag
• 2nd time you hit somewhere near the bottom of the bag

In both of the above situations you hit the bag with the same force, but due to the moment of force being different you end up with a different velocity, thus two different forces computed.

Due to my limited knowledge in physics, this was the hardest part for me and still is. Finding a model that fits the entire picture.

13-Aquamarine
(To:hgpt)

@hgpt wrote:

Everything looks fine, but I don't quite understand one thing: why is there a factor of 2x that is multiplied to obtain a_punch ?

because of the acceleration during Delta t is assumed to be as constant.

Volker
13-Aquamarine
(To:hgpt)
@hgpt wrote:
• When it comes to a real punch, there's no recoil, due to the impact being somehow plastic.
• Hitting the bag multiple times.
• Imagine you hit the bag when it moves from O1 to O with just enough force to stop it, but not enough to bounce it back to O1. The bag remains still, the velocity is 0, thus, according to the equations, the force is 0; but it obviously is not.

• Imagine you hit the bag with the same force, but the projection of force does not go through the center of mass.
• 1st time you hit somewhere near the top end of the bag
• 2nd time you hit somewhere near the bottom of the bag

In both of the above situations you hit the bag with the same force, but due to the moment of force being different you end up with a different velocity, thus two different forces computed.

Due to my limited knowledge in physics, this was the hardest part for me and still is. Finding a model that fits the entire picture.

If you want all this you need a simulation tool maybe for example MAPLE-Simulation.

To make that all in MathCad, i think it's very difficult.

In a model you can setup parameters, springs, pendulums, etc and describe them with parameters like stiffness, density, viscosity and all that stuff.

There is also an option to solve this problem for example in a CAD-SolidWorks Simulation-Tool.

There you can built a modell with all components (Bag, puncher, spring, etc.) and then you can start the simulation.

You can also define diagramms for the Force, speed, acceleration for all components and movement directions as well.

I have done many simulations in that way.

Todays Engineers choose this way because it is the fastest way to find out how a mechanical system reacts when initial physical quantities act on it.

So this should be your way to solve the problem you described (of course if you have the possibility to use such a simulation software)

Calculating this manually does not really make sense.

Volker
4-Participant
(To:vlehner)

I was thinking about simulation too, more specifically SolidWorks. I'm also a student, so acquiring the tool shouldn't be that difficult since they do have a student program. The real problem is knowing how to use it. Right now I have 0 experience using any CAD tool and learning how to use it takes a lot of time based on how complicated the tool is.  Also,  I didn't see any online tutorials about something similar as hitting a bag with a punch or any impact driven simulation.
I was thinking more about using Matlab System Identification Tool and considering the system a black box. This way the main goal becomes finding the transfer function of the system, by considering punch velocity, mass, and acceleration as input and bag's angular speed and position as output. What do you think of that?

13-Aquamarine
(To:hgpt)

I think you have to do it the hard way as i made: During my work as mechanical-engineer, i trained myself learning how to use the simulation tools nearly each minute of my free time. I started with easy problems and come up with more difficult tasks by time.

Now i'm an advanced user of this systems without any expensive training-center offered by CAD deliverer (about 700€ per day and user!!!)-but- this way was indeed not that easy to go.

You are a student, so i hope you have a bit more time for this.

As to simulation with blackbox-tools like them of Matlab, i have no experience with that, but it could be a way to go.

Try to find out what will be the best for you, i hope you'll be sucessful.

Volker
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