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Slinging analysis from an overhead camera - slow motion video (Read 605 times)
IronGoober
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Slinging analysis from an overhead camera - slow motion video
Oct 6th, 2020 at 2:27am
 
I made an analysis of some slinging from and overhead viewpoint. It seems that a wider sweeping throw is key to more velocity. Not surprising in hindsight, but I didn't expect this result. It makes sense if you think about how pitchers get maximum velocity, they have maximum path length of their throw.

I was hoping to do more analysis of the angles of release and during the acceleration phase, but there was just too much noise in my data. My hand wasn't moving that much which made calculating the movement path difficult without smoothing it. (which is on the list of things to do).

I have a theory that the movement of the hand effectively gives the sling a much larger radius at the release point, so the typical argument that there are only microseconds error to be accurate is not valid. Because of the large effective radius, the angular error is much smaller which makes it easier for the human brain to calculate the release point. That is the thought anyway. I didn't prove that yet, but I'm heading in that direction.

I was able to do this by making a wooden "L" and lashing it to a step ladder. I rubber banded my wife's phone to it and then had a small bluetooth remote to trigger the video (got it bundled with a cheap tripod from amazon).

This was more work than I thought it would be. Kudos to Sarosh for all of his video analysis. I was really hoping to get the release of the projectile in frame, but I just didn't quite have it pointed in the right spot. I couldn't get much closer to the ladder without feeling like I would hit it when winding up.  I might need a bit more height to capture the entire wind up and release.

Oh well, next time.

https://youtu.be/doTYAGCTdog

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« Last Edit: Oct 9th, 2020 at 2:31pm by IronGoober »  

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Re: Slinging analysis from overhead - slow motion video
Reply #1 - Oct 6th, 2020 at 3:27am
 
This is really great work!

I absolutely agree with your points about the wider sweep. The general point is that in the sling motion the radius of curvature of the motion is almost never just the length of the sling, but is usually significantly larger.

Interestingly, I think there is a contrast with trebuchets here, where you generally want to slow the arm down close to the launch point - in order not to have a madly swinging arm left after the launch. That condition doesn't have to apply so much with a manual sling.

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Re: Slinging analysis from overhead - slow motion video
Reply #2 - Oct 6th, 2020 at 4:22am
 
Wow great stuff, I’ll be following your research for sure.
For me I’ve always felt that the relationship between “lag angle” and the power stroke of your hand to be the way to get the most power. So all the powerstroke transfers into the sling and the hand never chases the projectile. Just my thoughts I have no data or proof
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Re: Slinging analysis from overhead - slow motion video
Reply #3 - Oct 6th, 2020 at 6:26am
 
Great to see some experimental data on this, well done!

It would be interesting to see with a longer sling as this will inevitably increase the path length a fair bit too.

Quote:
I have a theory that the movement of the hand effectively gives the sling a much larger radius at the release point, so the typical argument that there are only microseconds error to be accurate is not valid. Because of the large effective radius, the angular error is much smaller which makes it easier for the human brain to calculate the release point. That is the thought anyway. I didn't prove that yet, but I'm heading in that direction.


I've always thought there was something like this going on. The sling projectile I feel is moving in almost a straight line at the point of release which allows decent horizontal accuracy without crazy good timing. If you were to just spin a sling in a circle and let go without any throw action it would surely be much harder to attain any horizontal accuracy.
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Re: Slinging analysis from overhead - slow motion video
Reply #4 - Oct 6th, 2020 at 6:59am
 
The lag angle is important because it reflects the core physics of the sling.

If you want to accelerate something, you must put energy into it, or 'do work' on it. The source of energy in this case is the motion of your hand, moving at any instant in some direction with a particular velocity.

At that same time, the sling is moving in a circle around the hand, by means of which the sling is tensioned, giving a force. Without this force you can't put any energy in to the sling at all.

But the most critical aspect is the angle between that velocity and the tension force, which is what I think Aussie coined as the 'lag angle'. The power transfer (the energy per unit time) to the sling from the hand is given by

    -Fv cos theta

with the minus sign because of the way the lag angle was defined. I wish I could get together a decent diagram, but I'm sorry I'm unable to do that at present.

There is then also an interesting balance which comes up and is superbly illustrated in IronGoober's video analysis.

You need to be moving the hand to accelerate the sling, but in doing so you tend to increase the radius of curvature of the path of the sling projectile and thus reduce the tension in the sling (given by mv2 /r), where r is the radius of curvature of the path at that point and NOT the length of the sling.





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IronGoober
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Re: Slinging analysis from overhead - slow motion video
Reply #5 - Oct 6th, 2020 at 10:38am
 
@Mersa Lag angles are on the to-do list, I've had similar ideas and wanted to try and confirm them.

@wanderer I'm glad to see some physics equations without having to find them myself.  I think that there will be a physiological limit on maximum lag angle/power transfer that can go into the sling, because our tendons can only handle so much.  I'm going to continue to bring this up, because it has been studied so much more than slinging, but in baseball pitching the limit to how fast a human can throw is the stress on the tendons in the elbow/shoulder. I think somewhere on the order of 80-90N is what a elite athlete can sustain.  Source: https://www.youtube.com/watch?v=8udNOTFiqUs We will likely run into a similar limit with the sling, using the type of motion I am. Piroutte style might be different, since there are different stresses involved.

But last night, I realized that I can accurately estimate where the ball is in my video when it goes out of frame because I have the length of the sling from previous frames (in pixels) and the strands are straight. It should be simple to determine where it would have been. This will allow me to make some better measurements for the last 4-5 frames. and look at the lag angles in more detail.
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Re: Slinging analysis from overhead - slow motion video
Reply #6 - Oct 6th, 2020 at 10:45am
 
IronGoober wrote on Oct 6th, 2020 at 2:27am:
This was more work than I thought it would be. Kudos to Sarosh for all of his video analysis.


Thanks! Nice job with solving the problem of the view angle, I had trouble since my slinging style is slanted or sidearm and I cant get a camera over me .

IronGoober wrote on Oct 6th, 2020 at 2:27am:
Because of the large effective radius, the angular error is much smaller which makes it easier for the human brain to calculate the release point. That is the thought anyway. I didn't prove that yet, but I'm heading in that direction.

since the path is not a circle that is the proof that every point on the projectile path has it's own curvature (in other words the curvature isn't a constant) and by having a lower curvature (bigger radius) for the same velocity(=dx/dt ) your dθ/dt is smaller dx=R*dθ => dθ=dx/R (bigger R gives smaller dθ where R has to do with the path and not the sling length)
It's not if but what style/technique/equipment makes the curvature smaller.

wanderer wrote on Oct 6th, 2020 at 6:59am:
You need to be moving the hand to accelerate the sling, but in doing so you tend to increase the radius of curvature of the path of the sling projectile and thus reduce the tension in the sling (given by mv2 /r), where r is the radius of curvature of the path at that point and NOT the length of the sling.


by length of the sling you mean stretch or the length?
I've been thinking how much energy is absorbed/lost by stretching in the cords or if the smoothness felt by using stretchy cords adds any benefit.

the lag angle with that cos(theta) explains very nicely why you shouldnt struggle before releasing that is when theta is close to 90° => power transfer is 0.

wanderer wrote on Oct 6th, 2020 at 3:27am:
Interestingly, I think there is a contrast with trebuchets here, where you generally want to slow the arm down close to the launch point - in order not to have a madly swinging arm left after the launch. That condition doesn't have to apply so much with a manual sling.


I dont know about this, I think it would be pretty awesome if the arm stopped by itself . with heavy stones it'll be easier but when going for speed there is going to be wasted energy.
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Re: Slinging analysis from overhead - slow motion video
Reply #7 - Oct 6th, 2020 at 6:17pm
 
Sarosh wrote on Oct 6th, 2020 at 10:45am:
I've been thinking how much energy is absorbed/lost by stretching in the cords or if the smoothness felt by using stretchy cords adds any benefit.


I think it depends on the release mechanics. If the hand is slowing down a lot, then maybe. If you look at this plot, the hand does slow down at the end (where the arm is almost fully extended and wrist action begins).  This could mean that some stored energy in the strings would have time to recoil and add energy to the projectile. But it would also add a component of velocity toward the thrower, which might not be beneficial.  Because of this, you'd have to release sooner and reduce the length of the power stroke.

Actually, I'll revise my statement. I think in the end, elasticity isn't beneficial for a sling for attaining more projectile speed.  It might be useful for a cleaner release though, because it could help get the sling out of the way of the projectile faster.

Hmm... that's a thought. What if we added a small elastic to the release cord side of the sling?? The elastic would be shorter than the release cord. This way, the sling still functions as intended, but the stored energy will be released only when the release cord is loosed. This way it will pull the release cord out of the way of the projectile faster... I might have to try this. It might make the loading and wind up weird, but once it gets going, it would be fine.. Just needs the length tuned properly.

Update: Added extrapolated data from calculated ball positions.
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« Last Edit: Oct 8th, 2020 at 12:06am by IronGoober »  

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Re: Slinging analysis from overhead - slow motion video
Reply #8 - Oct 6th, 2020 at 11:01pm
 
IronGoober wrote on Oct 6th, 2020 at 2:27am:
It makes sense if you think about how pitchers get maximum velocity, they have maximum path length of their throw.

I'm curious about how much of a difference the forward step makes.  Like you (and definitely others), I use a forward step when slinging.  What happens to the results if you don't take that step and just use a rotation of the body?  If you recreate this experiment, I would be interested to see that comparison.

Great stuff with this by the way.
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Re: Slinging analysis from overhead - slow motion video
Reply #9 - Oct 6th, 2020 at 11:18pm
 
I also feel that a forward step helps, but again I’m only hypothesising.
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Re: Slinging analysis from overhead - slow motion video
Reply #10 - Oct 7th, 2020 at 12:10am
 
joe_meadmaker wrote on Oct 6th, 2020 at 11:01pm:
'm curious about how much of a difference the forward step makes.  Like you (and definitely others), I use a forward step when slinging.  What happens to the results if you don't take that step and just use a rotation of the body?  If you recreate this experiment, I would be interested to see that comparison.


I'm glad this is of interest to this community. I really wish I had a better way of doing all of this. It was a real hack job. If I had a more streamlined way of doing it, I would do all of these suggestions.

I wanted to measure all 6 of my throws and then plot them all on the same plot for direct comparison, but just getting the 2 was like, 6 hours of messing around. Now that I have some of the workflow in place it would be easier. But I'd like to setup an automated tracking program, I was having a lot of trouble using any of the Fiji plugins to work as intended.  If this were better data I'd write a paper on it.  I actually think that would be a great accomplishment for the community, for us to gather our resources, share data and write an open source paper on slinging mechanics.

This paper on throwing mechanics was neat. I think it would be great if we could do something similar.
https://www.mdpi.com/2076-3417/9/5/999
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Re: Slinging analysis from overhead - slow motion video
Reply #11 - Oct 7th, 2020 at 3:20am
 
Alright gentlemen, here is my analysis of the lag angles. No interpretation yet. I stayed up too late finishing this. Darn Excel and its tiny parentheses!!

There is a lot of noise in the data at the point where my hand is changing direction. This is with using 3 point averaging of the positions to try and get it smoother.
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Re: Slinging analysis from overhead - slow motion video
Reply #12 - Oct 7th, 2020 at 4:16am
 
IronGoober wrote on Oct 6th, 2020 at 10:38am:
@wanderer I'm glad to see some physics equations without having to find them myself.

I feel the difficulty here is more one of knowing where to apply the equations meaningfully, and perhaps more importantly being able to explain the motions with high-school physics. (One can write full equations for a lot of this, but they will not mean much to anyone without a fair degree of specialist knowledge.)
That needs notions like the curvature of a general path in space (the trajectory) to be understood. The matter of the forces and torques relating to physical limits I have to admit I think less about, but they are certainly interesting!

Sarosh wrote on Oct 6th, 2020 at 10:45am:
by length of the sling you mean stretch or the length?
I've been thinking how much energy is absorbed/lost by stretching in the cords or if the smoothness felt by using stretchy cords adds any benefit.

I was referring to radii in the same sense as you were, as the radius of curvature of a path in space. As far a stretching, ie. strain energy stored in the cords of the sling, I do believe this has an influence mostlin in pouch behavior. Think that when you release the cord, how does the pouch 'know' you have done it? It's not instantaneous, but depends on the speed at which a strain wave will travel up from the release point to the pouch. A wave of compression, or ripple, traveling up the cord towards the pouch could certainly influence release characteristics, particularly the way the resulting impulsive torque on the projectile affects its spin.

- I see that point has been made later in the thread.. I had to write this without having read the following remarks properly.

Sarosh wrote on Oct 6th, 2020 at 10:45am:
I dont know about this, I think it would be pretty awesome if the arm stopped by itself . with heavy stones it'll be easier but when going for speed there is going to be wasted energy.

I think one always has to have some intent to reduce the arm speed for practical reasons, but I agree with your point. Can't resist pointing to a video channel which is by a young British engineer. He's into trebuchets and various other things, and his videos are concise, and I think really excellent merging of practical matters with what seems to be a very good understanding of the 'theory'.

https://www.youtube.com/channel/UC67gfx2Fg7K2NSHqoENVgwA
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Re: Slinging analysis from overhead - slow motion video
Reply #13 - Oct 7th, 2020 at 6:12am
 
Mersa wrote on Oct 6th, 2020 at 4:22am:
For me I’ve always felt that the relationship between “lag angle” and the power stroke of your hand to be the way to get the most power. So all the powerstroke transfers into the sling and the hand never chases the projectile. Just my thoughts I have no data or proof

That is exactly what the little equationlet that I posted shows. IronGoober wrote on Oct 7th, 2020 at 3:20am:
There is a lot of noise in the data at the point where my hand is changing direction. This is with using 3 point averaging of the positions to try and get it smoother.

Great work, and I well understand how much work these things can be! I'd suggest the plot before the cusp in not really much interest anyway - its just setting things up for the power stroke which begins as you accelerate beyond the cusp. To me the noise is darn good (ie. low) - amazing what a few years advance in video technology can do!

As far as the resolution to angle, I think there might be a change in sign going on towards the end, lost because of the arccos operation?

The paths show very clearly the hand path kind of trying to maintain as big an angle as possible, until basically one gets to the point where things are turning too fast or you run out of room to keep the move going.

re. taking steps forward, they definitely can help, but generally if one changes ones action to do that, if you keep the rest of your form similar you would expect to have to increase the length of the sling. There are scaling laws in the dynamics air resistance bends the solutions) which mean a longer path length for the drive has to scale with the sling length.
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Re: Slinging analysis from overhead - slow motion video
Reply #14 - Oct 7th, 2020 at 10:59am
 
wanderer wrote on Oct 7th, 2020 at 6:12am:
As far as the resolution to angle, I think there might be a change in sign going on towards the end, lost because of the arccos operation?


The lag angle I defined as the difference between hand trajectory and the hand to sling position. These two vectors.  It doesn't actually change sign if you think about it, me and the sling are always moving anti-clockwise, so their angular relationship should remain between 0 and ~90 degrees (it can go higher if my hand slows).

Here is my interpretation of the data assuming it is actually correct (there could be a mistake in the math), the climb to ~90 degrees is the wind up to get the sling in position for the power stroke.  This gave me insight as to where my spit-outs happen (loosing a stone early). Because of my hand motion, and the fact that I almost stop it completely, the lag angle becomes large as I'm not pulling the sling along to counteract drag, this looses tension in the sling and allows the projectile to fall out. After this, the power stroke begins. You can see that the lag angle rapidly drops from 90 degrees to zero, where the force on the sling is the most because I'm pulling in the same direction as the cords. Because of the acceleration, it starts to swing faster than my arm moves and the lag angle increases again. Eventually my arm moves as far as it can, and I start to roll my wrist, this puts the action closer in line to the sling cords and the lag angle decreases again. You'll notice the faster throw has a lower overall lag angle in the power stroke (but also a longer path length).

Sarosh, this last downturn with the lag angle shows that elasticity in the cords would be non-beneficial for this particular movement. The stretch would just be wasted as the forces would be stored in the sling and not transferred as efficiently to the projectile.
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