## Punching Bag - Physics problem

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hgpt
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### Punching Bag - Physics problem

A few days ago someone gave me the following problem:

You have a ground fixed punch bag (there's a base and a spring at the bottom of the bag)
What is the minimum sensor setup in order to determine:
1. the force of the punch in the bag
2. acceleration of the punch
3. the speed of the punches (for multiple punches)
Notes:
1. no sensor must be attached on the person punching the bag, only on the bag
2. bag is punched in a limited vertical area
1. sensors
2. calculations

Known things:
1. mass of the bag
2. mass of the punch
3. acceleration of the bag (by fitting an accelerometer)
4. high of the bag
5. bag is punched at a distance R of it's base

The problem is that all the scenarios need to be taken into consideration: [list=a]
[*] punching the bag when it's stationary
[*] punching the bag when it's returning to you
[*] punching the bag when it's going away from you
[*] series of punches

Any idea?

Sableagle
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### Re: Punching Bag - Physics problem

You get Taofledermaus to film it with his Chronos high-speed camera, which can turn "clink" into a graceful dance. If you can't get him, Brass Fetcher gets several frames in 1/3000 s, so should be able to film the impact and acceleration well enough. You'll need to account for parallax. I'd suggest placing a transparent scale in front of and another scale behind the bag at equal distances.

It might not be a good idea to measure the movement of the bag, though, because the bag is going to do a lot of changing shape. You may get better results by measuring the position of the fist. Wrap black, white and black tape around your arm to get a stripe that'll show very clearly and record where that stripe is. That'll give you your punch speed and acceleration, and frequency is pretty simple to calculate from interval.

How you know the mass of the fist and forearm I don't know. Without knowing that you can't convert from acceleration to force. For that matter, you've got an upper arm to consider, and probably the shoulder too.

If the accelerometer is in the combined centre of mass of itself and the bag and the punch is lined up with them, the initial acceleration will match the initial force, but then that spring will start resisting and damping the acceleration and you'll only be calculating net force, not the push force of the fist against the bag. You could measure the force required to hold the bag at a range of positions displaced from neutral, and use camera footage to find the position at the time of each reading from the accelerometer so you'd know how much to add to the force you calculate from the acceleration.

Alternatively, you could build a bench-like structure at just the right height, put a concrete skim over it to provide a level top, polish that as smooth as possible, build a wood frame to sit on two skateboards as a trolley, put a sandbag on (or, better, in) that wood frame and punch that on camera. It'd only give you one punch, so it won't measure force in a flurry of blows, but it would allow you to see just how fast you set a known mass of sand, canvas, wood and skateboards moving.

If you built such a structure with rigidity and tilted it to various angles, you could use a vector triangle to calculate the component of gravity along the slope towards the puncher, and then set it at an angle such that the flurry of blows would keep it at a steady position. You'd then know the average force over time of those blows, and that high-speed camera would let you calculate the contact time. With good enough resolution and frame rate (it's hard to achieve both without VERY bright light, so get some lights) you could work out position millisecond-by-millisecond, from that calculate average speed in each millisecond, from that calculate the average acceleration in each millisecond and from that get a graph of force over time, showing peak force not just average.

If you can't get the cameras, there are "laser microphones" that monitor the vibrations of a window pane to capture the sound within a room. One of those and the right software would probably allow you to get a graph of position over time with high resolution (high enough for the thing to capture human voices in the 290 to 1600 Hz range, anyway) that would give you the motion of the back of the punchbag but that's of limited use if you don't know how forces dissipate within it. Sand's known to be good at absorbing impacts, after all.

You've also got to account for the directions of the punches, because they won't all be coming from exactly opposite the laser, and as this isn't early-'90s DOOM and the punchbag isn't a square, any hit at an angle can't be resolved just by having two at right angles and using Pythagoras' Theorem.

I know what you could do! Move the punchbag against the wall so it can't move back when hit, then stand on the skateboard trolley and punch it and measure how fast you accelerate yourself backwards with each blow. After all, pushing yourself backwards towards the sensor is the same thing as pushing the bag, the house and the sensor forwards. That saves you building up a structure, because you can just find someone with a level polished concrete floor and borrow that, or even do this at a bowling alley as long as you use skateboards with clean, new wheels.

Oh, yes. Skateboards. Make sure they're identical. Don't want to be going in circles, do you?
Oh, Willie McBride, it was all done in vain.

LaserGuy
Posts: 4540
Joined: Thu Jan 15, 2009 5:33 pm UTC

### Re: Punching Bag - Physics problem

I think it would probably be easiest to stick a Wiimote into the bag. They're apparently quite fantastic 3-axis accelerometers.

I don't think any of the scenarios actually matter. I'd imagine that most implementations would be general enough to handle any of these cases without too much trouble.