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Benjamite Accuracy Analysis (aka herding spherical cows) (Read 112 times)
NooneOfConsequence
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Benjamite Accuracy Analysis (aka herding spherical cows)
Jun 2nd, 2018 at 9:07am
 
Over in the General forum, Morphy asked what accuracy would be possible for an Olympics-level slinger at a 50% hit ratio. Jlasoud said 15cm at 30m. I said 30cm at 30m. Let’s put some math behind those guesses!

For the base analysis, we are going to have to create a few spherical cows (sorry vet Grin ).  Let’s assume spherical glandes (5cm diameter), circular targets, and no wind effects. Let’s also assume that Olympic sling engineers design a sling with zero variation in the pouch release timing.  Assume that the slinger’s statistical accuracy fits a distribution where 50% of the throws are within one standard deviation of the mean so that one standard deviation is the radius of the target plus the radius of the glande. The final spherical cow is a doozy... let’s assume that the ammo travels in a perfectly straight line to the target so we don’t have to account for multiple ballistic trajectories which could all achieve the same hit. All of these spherical cows allow us to reduce the problem down to a timing problem if we know the length of the sling and the rate of rotation (also assuming the sling only rotates around the hand... which is not true but that doesn’t matter because of our straight line assumption).

To be continued...
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“My final hour is at hand. We face an enemy more numerous and cunning than the world has yet seen. Remember your training, and do not fear the hordes of Judas. I, without sin, shall cast the first stone. That will be your sign to attack! But you shall not fight this unholy enemy with stones. No! RAZOR GLANDES!  Aim for the eyes! May the Lord have mercy, for we shall show none!“  -Jesus the Noodler
 
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NooneOfConsequence
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Re: Benjamite Accuracy Analysis (aka herding spherical cows)
Reply #1 - Jun 2nd, 2018 at 9:44am
 
Ok, so now we have collected our herd of rather plump and unrealistic cows, so let’s get into the sausage-making!

At a distance of 30m, the threshold for a hit on a 30cm target with a 5cm glande is +/- 17.5cm. The angular variation that still achieves a hit is 0.67 degrees (about half that for a 15cm target).  A sling would swingin a circular motion at some rate around 1-4 rotations per second just prior to release. If we go with the slowest rotation, 360 degrees per second, then the slinger needs to have a variation of +/-0.9ms in their release (400-500 microseconds for a 15cm target).

Is that possible? I don’t know. We would have to look at the biomechanics literature to see.

Of course if you put ballistic trajectories back into consideration, you may not need as much precision because multiple combinations of initial velocity and angle could result in a hit.
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“My final hour is at hand. We face an enemy more numerous and cunning than the world has yet seen. Remember your training, and do not fear the hordes of Judas. I, without sin, shall cast the first stone. That will be your sign to attack! But you shall not fight this unholy enemy with stones. No! RAZOR GLANDES!  Aim for the eyes! May the Lord have mercy, for we shall show none!“  -Jesus the Noodler
 
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NooneOfConsequence
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Re: Benjamite Accuracy Analysis (aka herding spherical cows)
Reply #2 - Jun 2nd, 2018 at 10:37am
 
So if ballistics matter and the glande doesn’t move in a straight line, here’s how a slinger controls initial velocity:
-Rate of rotation
-Forward motion of the arm (and the slinger)
-radius of rotation (sling plus bent arm)

Of these, the second one is the least significant, maybe adding a few meters per second at most. That means #1 and #3 are the big ones.

Let’s look at #3 first: as boundaries, the sling can rotate around the wrist or the shoulder with the arm fully extended. Let’s say that’s a possible variation of 0-80cm which can be added to the length of the sling itself.  With an 80cm sling you can double the speed by doubling the radius of rotation at a particular rotation rate. That gives a slinger a lot of control over the speed of the projectile even with the same throwing style and rotation rate. Realistically, this would be more of a fine tune control of the radius based on slight bends of the elbow.

Now for #1: I said previously that a reasonable rotation was 1-4 Hz.  If you are swinging around the shoulder at 4Hz with a 1m sling, the max linear speed is about 45m/s. That’s on par with the velocity estimates that people are seeing for long distance throws, so I think we’re in the right ballpark.

So to sum up: how hard you swing is the most significant factor with a variability of up to 400%
Fine tuning happens at the elbow, but different styles may change the speed by up to 100%
And that little lunge forward is good for squeezing out a little extra power.

All numbers are rough order of magnitude at best, and this is obviously oversimplified Smiley
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“My final hour is at hand. We face an enemy more numerous and cunning than the world has yet seen. Remember your training, and do not fear the hordes of Judas. I, without sin, shall cast the first stone. That will be your sign to attack! But you shall not fight this unholy enemy with stones. No! RAZOR GLANDES!  Aim for the eyes! May the Lord have mercy, for we shall show none!“  -Jesus the Noodler
 
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Re: Benjamite Accuracy Analysis (aka herding spherical cows)
Reply #3 - Jun 3rd, 2018 at 2:20pm
 
I guess the best way to test this is to let jaegoor throw 100 shots at different sized targets at different distances.

I suspect he puts in at least as much training time as many olympic athletes Thumbs Up
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woodssj
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Re: Benjamite Accuracy Analysis (aka herding spherical cows)
Reply #4 - Jun 3rd, 2018 at 11:03pm
 
That's not a lot of variation at all.

If we widen that up to a regulation target at 50 cm, using the regulation distances, this still leaves a tiny variance.

A cone of fire for a hit with any of these is small, and I understood that before. But this brings home exactly how hard it is: A .00067 Second window seems imperceptible!
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