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Slinging theories/explanations "internal ballistics" (Read 6862 times)
johan
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Slinging theories/explanations "internal ballistics"
Aug 16th, 2017 at 6:51am
 
this topic was inspired from here http://slinging.org/forum/YaBB.pl?num=1499008756/new

at the pisture below you can see how i understand slinging.
please focus more on the principles of the way of acceleration than on other details. it still needs a lot of refining. 

http://slinging.org/forum/YaBB.pl?num=1280933160/15
here Aussie (reply #16)
talks about trail angle. read it.....


the picture explains how you can't compare slinging to circular motion with radius of sling(or hand + sling). it's more dependent on hand path and style/technique
Quote:
in the case of an object that moves along a circular path with a changing speed, the acceleration of the body may be decomposed into a perpendicular component that changes the direction of motion (the centripetal acceleration), and a parallel, or tangential component, that changes the speed.

tangential component is what makes the throw more powerful...

if you don't understand the forces applied read here: https://en.wikipedia.org/wiki/Circular_motion,
https://en.wikipedia.org/wiki/Centripetal_force
or learn more about mechanics in the web.

pirouette styles opperate on the same principles(ellipse might be closer to circle).
i believe that linear style are more efficient than pirouette but pirouette has more energy capacity thus pirouette might result on faster/ more powerful throws.

put in here your ideas on how high velocities are achieved and what  can be done to achieve even more speed/ power
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sling_explan1.jpg (414 KB | 63 )
sling_explan1.jpg
 
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Mersa
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Re: Slinging theories/explanations "internal ballistics"
Reply #1 - Aug 16th, 2017 at 7:31am
 
I think there is a element of body movement. I think this is the extension that apex talked about . If you move forward when the pouch is behind you its adding force whether or not it's pirouette or a Byzantine. This then timed with the trail Aussie talks about and a good technique.
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JudoP
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Re: Slinging theories/explanations "internal ballistics"
Reply #2 - Aug 16th, 2017 at 7:46am
 
I want to look further into this later on when I have time but essentially, I still think that a circular motion model can approximate the tension through the arm and sling at point of release (with the inclusion of the arm of course).

No matter what complex combination of circles/ellipses leads to the throw, at the exact point of release it still appears that the projectile travels (roughly) perpendicular to the radius and the leading angle becomes small or 0.

Regardless of the wind up, at this small time interval around release the system is pretty much circular motion so:

F=(mv^2) / r

Should still apply at point of release.

The physics around the wind up and whether a sling of x size can actually be accelerated to that speed with air resistance etc seem to be a lot more complicated though.

For example to create some elliptical motion, may actually require more tension than circular motion at the point of release, but this wouldn't necessarily mean a faster moving projectile, just that the direction of the projectile is pulling more against your arm. Hope this makes some sense...

The whole thing is quite interesting so I might try devote some time to trying to hash out some physics to the whole thing. I've not really looked into elliptical motion before especially with considerations such as air resistance. So might be able to work some stuff out.
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Re: Slinging theories/explanations "internal ballistics"
Reply #3 - Aug 16th, 2017 at 10:14am
 
JudoP wrote on Aug 16th, 2017 at 7:46am:
The whole thing is quite interesting so I might try devote some time to trying to hash out some physics to the whole thing. I've not really looked into elliptical motion before especially with considerations such as air resistance. So might be able to work some stuff out.


Take for this once more a very "exactly" look at this video: https://www.youtube.com/watch?v=rzUAdkoAfbo - especially at the extreme slow motion of its first throw.

There happens something "crazy", because right before release (respectivley in the beginning of the last half rouund) the arm and hand already moves forward in a time, where the pouch still moves in counter direktion (means "back").
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Re: Slinging theories/explanations "internal ballistics"
Reply #4 - Aug 16th, 2017 at 12:33pm
 
in the graph above i have made the assumption that the tension of the sling is constant through out the throw, but in fact that won't be the case.

in reality i think it's more difficult to apply big forces at the end (extended arm) of the throw than at the beginning, so the blue force vector (tension of sling) will start big and become smaller while throwing.

the more ellipsoid the throwing motion is:
  • the faster your hand needs to be,the more difficult it is to apply force(accelerate)
    remember that the slingstone is going to travel faster than your hand most of the time during the throw
  • the easier it becomes for the arm to withstand the otherwise huge forces caused by small radius of curvature(of a more circular motion)


@JudoP i might be repeating myself here...
the law of physics you used (F=(mv^2) / r) applies to any motion of a body that changes direction (centrifugal acceleration).
You just used the wrong radius.
only in circular motion the radius of the circle equals the radius of curvature, here we don't have circular motion...

you could make make a rough example out of the above graph to understand the difference.

if above is in scale 1:20
then the sling is 80cm(=20*4cm)
let's say the slinger threw 100g stone 50m/s
1)doing it the wrong way and instead of radius of curvature we put the length of the sling 0.8m then F=312.5N
2) the right way would be : radius of curvature=(20*12cm)=2.4m
F=104.1N much less...

this also shows how bad use of long slings loses to good use of short slings

@Mersa the extension (Apex-apoc talks) comes from the combined movement of arm and body but is measured by the initial and last position of the arm

Apex-apoc's model has a multiplication  i don't understand and isn't explained

@Apex-apoc feel free to add your drawings and tables in this thread too.
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Re: Slinging theories/explanations "internal ballistics"
Reply #5 - Aug 16th, 2017 at 3:29pm
 
johan wrote on Aug 16th, 2017 at 12:33pm:
@Apex-apoc feel free to add your drawings and tables in this thread too.


Yes, thanks: My idea is to draw 24 circles in a linear row of 24 steps of (linear) "extension". On each circle the pouch (respektivley sling line) shows an other "time" - thats like the "second hand" on a watch (while moving the watch linear at the same time).

Each position of pouch than is a "red point" on his own circle (dial). If all red pointes will be connected through red lines, all red lines in this row of circles would build up a quarter of an ellipse (or something what is only similar to an ellipse). If this is done then also should be insert the parallelograms of vectors (force or velocity).

The distances between all circles of this row, of course had to increase from step to step (frame to frame) for showing the accerleration of the circle (while extension).

If this will explain and / or benefits something I hope than to see.

But I have already now the suspicion, that the flater "streched" parts of elliptical curve are longer and its lenght will be a measure for velocity (or force of acceleration) - similar to vectors.

So it would be nearly the same result as it is allready shown with my first drawing. But we will see ... perhaps!
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Re: Slinging theories/explanations "internal ballistics"
Reply #6 - Aug 16th, 2017 at 4:00pm
 
johan wrote on Aug 16th, 2017 at 6:51am:
put in here your ideas on how high velocities are achieved and what  can be done to achieve even more speed/ power


Three things in your drawing (in future we will need numbers for each new drawing) I do not understand:

1. Why is the "Sling = 4 cm" ?
2. Why is the path of hand a curve? (for extension I pull my hand from behind of me straight on / linear in direction of target).
3. Why is the "R" 12 cm only

Is your drawing not modelling a whole sling (which has more like 90 cm than only 4 or 12 cm)?

I mean is this a "scaled" drawing or is drawn here a minimal move of a hand only?

Scaled has this to be in anyway (because the screen is so small), but to scale "amounts" too is a little bit confusing. Thats like the remark "26,7 cm" to name the distance  between London and Berlin at a map.

I mean, what in reality is "100 cm" has also to be described as "100 cm" - regardless the scale.
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Re: Slinging theories/explanations "internal ballistics"
Reply #7 - Aug 17th, 2017 at 3:19am
 
@ Apex apoc
i think that i've already talked about that.
johan wrote on Aug 16th, 2017 at 6:51am:
please focus more on the principles of the way of acceleration than on other details. it still needs a lot of refining.


the drawing talks about how acceleration happens.
it's just an example...
but if want to put values to understand better as i did above (reply #4) then use whatever ratio you want, it won't change the general analogies. (i think this answers questions 1 and 3)


you can't find velocity from the above graph it's too generalised

2) i thought too that the arm goes straight but then i watched closely to some videos and made that conclusion. some people or styles may do it to greater extent than others.
is it good for speed? i don't know .
making better graphs or modeling real life powerful slingers vs noobs can answer some questions...
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Re: Slinging theories/explanations "internal ballistics"
Reply #8 - Aug 17th, 2017 at 4:08am
 
johan wrote on Aug 17th, 2017 at 3:19am:
2) i thought too that the arm goes straight but then i watched closely to some videos and made that conclusion. some people or styles may do it to greater extent than others.is it good for speed? i don't know .


You are right - my false: While doing the "extension" the hand turns necessarily around the joint of elbow (and shoulder). It does only "feel" like a linear move but is a (flat) curve.

Good to know!
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Re: Slinging theories/explanations "internal ballistics"
Reply #9 - Aug 17th, 2017 at 4:38am
 
Quote:
@JudoP i might be repeating myself here...
the law of physics you used (F=(mv^2) / r) applies to any motion of a body that changes direction (centrifugal acceleration).
You just used the wrong radius.
only in circular motion the radius of the circle equals the radius of curvature, here we don't have circular motion...


I think you may have missed one or more of my posts from the other thread.

The consideration of adding the arm into the radius was a simple error which I've rectified (more accurately the center of rotation might be the center of the torso rather than the shoulder).

I take your point that the motion is elliptical and not circular- my suggestion is that circular motion would probably approximate the behavior of the system at point of release.

If you consider circular motion vs elliptical the difference is that the velocity of the projectile is perpendicular to the direction of the radius at all times, whilst in elliptical it varies to tighter and wider depending on position in the curve (caused by varying centripetal force).

At the point of release on your diagram the velocity is more or less directly perpendicular to the radius to the center of rotation which means the motion is essentially identical to circular over this range (or at least a good approximation).

This should be true even with more complex behavior beforehand.

I'm not proposing a full mathematical treatment of the system here, only a relation that *may* hold accurate at the point of release only.

Another consideration is that the arm might not be fully straight at release, in this case the radius could be reduced and you could calculate the torque on extending the arm.
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Re: Slinging theories/explanations "internal ballistics"
Reply #10 - Aug 17th, 2017 at 4:39am
 
analysed some vids of me, see the pictures below.
fig8 modified and underhand

pictures are 2dimensions and it may confuse you because if the sling is canted to the picture, sling will appear shorter...
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Re: Slinging theories/explanations "internal ballistics"
Reply #11 - Aug 17th, 2017 at 5:05am
 
johan wrote on Aug 17th, 2017 at 4:39am:
fig8 modified and underhand


Also this picture (from Wikipedia / Onno) may be help to imagine where does extra accellerations come from (while slinging the last half round). Special here (mechanical "overhand style"): The path of "hand" while "extension" is a circle (respectively an orbit) too. Here the ellipse results from superposition of a circular move to another circular move. But I think this resulted path isn't really (called) an "ellipse", but a "klothoide" or "hypercyclus" ... or neither nor.

And still I think, the "extra accelaration" would be as higher as smaler the ellipse is (means: ... as higher the relation of smaler and larger axis is). So it would be better to hold the extension-path of slinging-hand as flat as possible.
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Re: Slinging theories/explanations "internal ballistics"
Reply #12 - Aug 17th, 2017 at 5:11am
 
Great diagrams guys
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Re: Slinging theories/explanations "internal ballistics"
Reply #13 - Aug 17th, 2017 at 12:36pm
 
I do not know much about math. I'm just throwing sling.  Cheesy

(But I was wondering if I would make a tutorial throwing of pirouette.)
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Re: Slinging theories/explanations "internal ballistics"
Reply #14 - Aug 18th, 2017 at 5:50pm
 
I've wondered a lot about this before.

Unfortunately, I don't have a camera that has enough fps to see my throws all that well. Even on my phone's "slow motion" setting (which is ~240 fps, but not really because of the way the shutter works), my arm moves too quickly to see the details of the throw -- even when I'm tossing pretty slowly.

Personally, I don't think that near the release the motion is super circular. This depends on your technique, but for fig-8 at least, it's much more elliptical during than circular. For something like apache, the motion is pretty circular.

I think if you are looking for the math, it's easier to figure it out for apache than most other styles due to the nearly circular motion. Part of the issue is that the sling does not extend straight out from your hand until the very end of the throw.

It is clear that the extra force comes from the extension of your arm by the sling, but beyond that, I'm not sure how to calculate it. I think it's very dependent on the slinger and their technique.
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