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The physics of the sling (Read 30316 times)
Hondero
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The physics of the sling
Aug 2nd, 2004 at 1:34pm
 
Well...  Humm...  Roll Eyes  this is a try to star the development of a physics of sling, in the same way that others sports like golf, baseball or tennis, that have in the net interesting pages on their particular physics. If there is a site in which that estudy on sling can be done, I am sure that it is here, between all interested people on the subject, proposing theories or commenting and debating those of others. So, since I have thought something on the matter, I´ll take the first step and hope you buddies to encourage to develop this study. Finally we could make a summary of everything debated, in the form of a theory and to put it in the articles section or another place readily accessible for use of the people.

Comparing the sling with the other sports of projectile or ball launching, being used the muscular force and by means of an instrument, like a racket or club, I have the pleasure to affirm that the sling is the most efficient instrument for  transmitting the muscular effort to the projectile. Tennis or golf loses a part of the muscular energy developed in the blow of the racket or club against the ball, that are temporary deformed and absorbs that part of energy.  In the best of the cases it is lost between 10 or 15 % of the energy. In addition, the air drag on the racket or club is greater than on the cords and pouch of the sling, if it is well designed.

Although the mentioned sports have a partly common physics, nevertheless there are many differences with respect to the projectile and the forces that affect it in their interaction with the air, the design and size, the speeds, the trajectories, etc. For that reason the development of a special physics for the sling is essential.

I´ve thought on a Index to develop, more or less like this:

1- Simulator of trajectories
2- Maximum speed to achieve with a sling
3- Optimal projectile weight.  
4- Optimal projectile shape
5- Optimal dimensions of the sling for maximum range.
6- Air drag on the sling
7- Maximum range with a sling
8- Best style for range or accuracy

Many things have been said yet in the forum about all this, and maybe they can be  reconsidered again.

I am preparing the first point for the next post  Grin.

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« Last Edit: Aug 19th, 2004 at 5:28pm by Hondero »  

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Matthias
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Re: The physics of sling
Reply #1 - Aug 2nd, 2004 at 5:16pm
 
Good job Hondero!

I'll throw in my vote that we add a (substantial Grin) "physics of the sling chapter" to "Project Goliath". I've been working on a couple of projects that evolved out of the last thread, so I hope to have some interesting info to contribute in the near future...

(unfortunately, my most recent "experimental" sling session came to a very abrupt end when my "aero" projectile disappeared into the woods. I'd like to believe that it was due to the incredible range but the truth is that the cords wrapped... can you "shank" a sling throw? - we need some better terminology)

Looking forward to reading your next post!

Matthias
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Yurek
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Re: The physics of sling
Reply #2 - Aug 2nd, 2004 at 6:47pm
 
Hondero,

I have read recent Chris' post too, so I think you both are thinking about the same initiative. Your post is an interesting challenge for us. I have declared my participation in the common project, just regardig the physics of slinging.

It would be good to treat the subiect in the two separate stages:

1. energy delivery to a projectile, that is just the physics of the throw (some biophysics and physics of a sling together);

2. physics of flight of projectile (using of delivered energy).

Of course, these two aspects have the common parts (for example, the mass of projectiles), which are important both during throwing and during flying.

We could also think about the third stage, which was been discussed on the forum:

3. Physics of a hit (impact), also using of delivered energy.

Of course, these aspects (threads) should go out from a short
and approachable introduction and drive to practical hints on the end.

I think the above partition isn't confliting with your index. It is possible to link the both things. What is your opinion?

In the begining, I think I could put something in your points: 2, 5, 7 and most probably put my two cents into the left points too. I am thinking about it all.

Jurek


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In the shape, structure and position of each stone, there is recorded a small piece of history. So, slinging them, we add a bit of our history to them.
 
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Hondero
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Re: The physics of sling
Reply #3 - Aug 3rd, 2004 at 5:27pm
 
Matthias, of course the physics of the sling can be a good chapter in the megaproject of the sling, the Goliath (good name Chris!), and in addition to be accessible separately in the site like a tool of work and orientacion for the slingers.

Yurek, it seems interesting to separately develop the physics of the throw as you say, although all the subjects are so related that there will be considered in different places. A correct and optimized style is an essential aspect in all the sports, that besides usually is performed the same way in each sport (serve in tennis, swing in golf, pitch in baseball). Here it would be necessary to speak of the different uses of the sling (distance, accjuracy, impact, penetration, etc) and the most effective styles in each case. Also it seems interesting to make an introduction to the subject, to detail an index, since as we are going to work in team it is the way of not losing in the great diversity of involved aspects. So I will delay the first point relative to the ballistic simulator and will try that introduction or exposition of the problem to be discussed.

1- INTRODUCTION
The throw begins with the development of a muscular effort that is translated in the acceleration of the sling. This muscular effort is a chained serie of efforts that are made with the hips, torso, shoulder, arm, forearm and wrist.  At the end the projectile is released with a kinetic energy that depend of its mass and the initial speed. Each slinger has a maximum force to develop, and therefore the obtained speed will be greater whichever minor is the mass of the projectile. The length of the sling influences the speed of launching, but not as much as it could seem, since after all the kinetic energy of the projectile comes from the muscular effort, which is limited, and as longer is the sling as much is the energy required to accelerate the projectile.
The projectile is affected in its flight by the air drag, which exerts a force that is proportional to the projectile frontal surface and to the square of its speed. It seems that the air drag it will affect more to the small projectiles that to the great ones, since its greater speed is more detrimental that its reduced section. For a same mass projectile, and therefore equal speed of launching, the use of dense materials, as the lead, provides small projectiles, of little frontal section and therefore the air resistance is smaller. To equality of size and different weight, the air resistance due to the frontal section will be equal, although the speed of the heaviest projectile will be smaller and the total resistance will be smaller too. All these factors are related in a complex way, and the best thing to calculate results is to have a balistic simulator. It avoids to enter complicated mathematical formulations, being enough the definition of the parameters to input.

Other factors to consider are the form of the projectile and its aerodynamic behavior. The fusiform projectiles present  less frontal section that the spherical ones for the same weight, supposing a flight according to the greater axis, or with little inclination. But the projectile must be thrown point-first and spinning on its axis to conserve the stability, which takes us to the study of the dynamics of the projectile within the pouch, or " interior ballistic".

The projectile surface can be important, offering smaller air drag the rough surfaces that the smooth ones, due to creation of turbulences that diminish the air drag Also this rugosity increases the Magnus effect, what can be used to get greater elevation of the projectile in the flight and prolongation of the range. But this effect will depend much on the density of the projectile and will be despicable for lead projectiles that are those that has better behavior for distance.

It is also important the sizing of the sling and its relation with the weight of the projectile. The cord and pouch air drag must be controlled, as well as the design of the pouch. It  could be said  that the sling must be designed for the optimal projectile and not contrariwise.

Well, I´m exhaust and have the feeling that all this is not much useful ??? ...and maybe I´ve forgotten some points to consider  for making the detailed index:Smiley.
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« Last Edit: Aug 4th, 2004 at 2:39am by Hondero »  

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Yurek
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Re: The physics of sling
Reply #4 - Aug 4th, 2004 at 7:42am
 
Great, Hondero!

I'm just preparing the article (chapter?) about the mechnics of a sling. It will explain why a sling gives so big advantage and will be closely related to your point nr 2. My consideration should bring us nearer to state the maximum sling velocity. I need more time to do it, however.  Maybe I will post in sections. I'm working in my language, so I have to make effort to translate it yet.

It would be good, if Chris moves this topic to the new section.

Jurek
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In the shape, structure and position of each stone, there is recorded a small piece of history. So, slinging them, we add a bit of our history to them.
 
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Chris
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Re: The physics of sling
Reply #5 - Aug 4th, 2004 at 11:37pm
 
You guys should make a formal comitment about working on the "Physics of The Sling" section.  I'll pencil you in and it will be all yours.  I think you two should co-author it.  Maybe rope Matthias in aswell, who has some great ideas. 

Think about all the different topics within this section you want to cover. 


• PHYSICS OF THE SLING
- releasing the retention cord causes the pouch to open, and the projectile to fly out tangentially.
- mechanical advantage of the sling.
- ratio of length to potential speed?
- drag, air resistance? 
- pouch design, and it's physics ramifications
- projectile design (tons of stuff to consider here, although don't get into historical evidence, as thats covered in other sections.) 

etc.

Develop this among yourselves (by email perhaps), present it to me, and We'll make an official update to the outline. 

Chris
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Hondero
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Re: The physics of sling
Reply #6 - Aug 5th, 2004 at 12:30pm
 
SIMULATOR OF TRAJECTORIES

There are many free simulators in the net but almost all are adapted to the speeds and ranges of golf, paintball or baseball, and are not too useful for the sling. I have chosen one of general purpose, that adapt very well to any sport, and in particular to the sling. The Link is:

http://www.sc.ehu.es/sbweb/fisica/dinamica/stokes2/stokes2.htm

The simulator is the one at the end of the page. It is in Spanish, but I´ll try to simplify its handling. The simulator draws the trajectories of a projectile for several angles, including the trajectory without air. The inputs are the speed and "c/m", being "m" the projectil mass and "c" = 0,5 x (drag coeff) x (air density) x (frontal section.) I have assume a drag coefficient for a sphere = 0,45, since the projectiles never are perfectly smooth (dg = 0,5).

Taking like a standard projectile a spherical one of stone, of 100 gr. and a speed of 200 Km/h, we´ll see the range of the Balearic champion of distance. The value of c/m is 0,0036 and the simulator say that about 180 meters would be reached with a launching angle of 40ª. It seems that the data of Vicente approximately agree in range and speed. We can see that the range without air is of 315 meters, thus it loses 43 % of range due to the air drag.

Now let us see to which speed would throw Larry Bray to get its record of 437 meters with a stone of 52 grams (the last verified weight): If the projectile had been spherical as in the previous case, the value of c/m = 0,00476 and he must have sent to 720Km/h, which is clearly impossible. But his projectile was oval and if we assume that flew perfectly oriented, the value of c/m is 0,003, which gives us a launching speed of 450 Km/h. This seems to be more logical. But in addition, the projectile was not perfectly oval, but something irregular, which perhaps would create some turbulence reducing drag coeff. to 0,3 (my estimation), and the value of c/m would be of 0.0025. Thus the necessary speed would be of 396 Km/h. The range  without air is now 1234 m, and the lose is a 63% of the range due to air drag.

( To be continued)  Grin
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Hondero
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Re: The physics of sling
Reply #7 - Aug 6th, 2004 at 5:26pm
 
RANGE WITH LEAD GLANDES

Let us see now the range that would have got Larry using a lead projectile of similar shape to the one of stone that he used and the same weight of 32 gr, that is to say, a small sort of glans not very perfected. I suppose the same CD = 0,3 and the value that we obtain for c/m is 0.00077. The speed of launching would be the same 396 Km/h that we had considered previously for the stone projectile. The obtained range would have been of 747 ms, a 70% longer than with the stone projectile. We see that now the lost of range with respect to the shot without air is only of 40%, whereas with the stone projectile it was of 63 %.

If my calculations are right this is astonishing!! With a lead glande even I could beat the present record!
Yurek, congratulations for your coming new record of distance with sling!!  Shocked Shocked

P.D  Well... let´s be a little humble...  Undecided , the most likely is that the little glans can´t fly perfectly point-first oriented and so its cd and the frontal section are greater. I guess cd =0.4 and c/m = 0.00125. The range would be then about  616 m. Also very good.
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Matthias
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Re: The physics of sling
Reply #8 - Aug 8th, 2004 at 12:01am
 
Lead is pretty sudcutive eh Hondero? Smiley I thought I was going to be able to cast a few this weekend and test all this out myself (having only ever thrown rocks and balls), but the ingots that I remembered seeing last time I was here turned out to be zinc rather than lead. I did collect my mold making gear though, so I'll (slowly) keep working on it.

I've been thinking this afternoon about the possibility of rigging up some kind of ballistic pendulum in support of our investigations into sling performance. The idea would be to sling a plastilene "glans" of varying weight at a heavy suspended target at very close range (all the easier to hit you with my dear Wink) and measure the deflection of the rearward swing. The total energy of the throw would then be determined, and with a known projectile weight the speed as well.

A series of increasing weights could then be compared (possibly also different throw styles and sling lengths) to allow us to start to build up a set of criteria for the "perfect" glans design. It might reveal some interesting "rules of thumb" such as "ideal ammo weight varies inversly with sling length" or other such nonsense, all of which would increase our knowledge base substantially.

The data would only be directly applicable to the test slinger, but eventually I suppose that we could build up a more complete picture.

I fully expect that the tests will show us that each person is most efficient when throwing his or her favorite ammo, having reached that decision by trial and error, but we never know.

The other idea I was tossing around today was to build a test projectile that had flashing led's. It is going to have to be pretty rugged, but flashing at ~100-200 Hz should allow better analysis of a throw than the frame by frame stuff that I did earlier. I'd like to try to use IR and a filter, but my digicam takes too big of a hit in the infrared range to make it viable. I guess that means that tests will have to be conducted in the dark/low light.

Matthias
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Re: The physics of sling
Reply #9 - Aug 8th, 2004 at 4:25am
 
Mathias, your experiments with the ballistic pendulum, throwing glandes at very close range  Grin, will be definitive. I think is the only way to know some critical thinks like the actual ratio weight-speed of the projectile. This will allow to conect the physic of the throw with the physics of the projectil fly and thus find the optimal weight of the projectil. This could be calculated theoretically, and Yurek (and myself too) is working on the subjet, but in my opinion the intrincacy of it is great and the results might be only rough.
I know you are a clever craftsman and can accomplish the task. I look forward to your experiments  Cheesy
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Re: The physics of sling
Reply #10 - Aug 8th, 2004 at 6:15pm
 
Hey, I had an idea about the physics of the sling section.  You all obviously know a lot more about the mechanics and everything, but for a book, you'll need something to draw the reader's interest.  It might be interesting to put some quotes about the amazing abilities of the sling as an introduction: (ie, "Among all these soldiers there were seven hundred chosen men who were left-handed, each of whom could sling a stone at a hair and not miss."), a quote from 3 or 4 thousand years ago.  I guess this is kindof a finishing touch type of thing, but I'll just throw it out there anyway.
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Re: The physics of sling
Reply #11 - Aug 8th, 2004 at 6:43pm
 
Hondero,

You are the most exemplary partner among us Smiley You one and only are doing the declared job as yet. I'm just trying to gather all my thoughts, but my mind is a bit lazy due to the hot and sunny summer we have Smiley Besides, I spend quite a lot time outdoors with my familly and also try to practice a bit, we need to use some our short summer. So, please be patient and give me some time.

That simulator really seems to be the best for our use among others we have, because it considers the drag coefficient and mass of projectiles. Your estimations looks likely.

Matthias,

I was been thinking about the ballistic pendulum too, but I haven't got the idea of the soft glandes (made of plasticine). Great idea! BTW, lead glandes during hiting concrete slabs with a big velocity, act very similar to plasticine Smiley Plasticine glandes would be also good for testing different its shapes, dimples etc. Looks like they are perfect, easy to changing test amo, but not during hot days, because they could become deformed during releases.

I also thought about stroboscopic photography, but I haven't a suitable lamp. I wonder, if there is a simple domestic way of doing it. Any ideas? Even useing a usual and cheap analog camcoder should be good too. It can be set at "high-speed-shutter mode". In this case we get the frames with clear pictures of the sling and projectile. If we know the distance between stone in following frames and the frequency of the frames, we are able to calculate the velocity of the projectile easily. I think it is a cheap and pretty accurate way. I already desrcibed that one on the forum sometime.

Quote:
The other idea I was tossing around today was to build a test projectile that had flashing led's.


I suppose, it would be enough to fix the led on the pouch and thin wires could be drawn along the retention cord. It would be cheaper and easier.

Jurek
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In the shape, structure and position of each stone, there is recorded a small piece of history. So, slinging them, we add a bit of our history to them.
 
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Re: The physics of sling
Reply #12 - Aug 8th, 2004 at 9:32pm
 
I acutally built a test rig for the BP this morning. I only had a few hours to spare, but preliminary results reinforce the idea that this would be valuable info. I ended up using a tennis racket as a target, which the plastelene sticks to quite nicely at thrown speeds. I tried projectiles of three masses, and recorded very repeatable results. At sling speeds, if anyone wants to make french fries, I'm your man...

I didn't want to use a flat plate due to the damping effect, so I'll have to rethink the construction a bit. For measuring deflection, I used a light cord that the pendulum pulls through a very slight friction fit connection. It worked well and is much easier to construct and less finnicky than the usual rigid swing indicators. If I have time before I head home I'll add some more mass to the proof-of-concept and figure out a way to reduce the penetration of the clay. Won't be quantifiable results, but interesting nonetheless.

As for the high speed photography. I think either strobes or leds on the sling/glans are the only options barring access to high speed motion cap equipment. I did some frame by frame analysis of some video but the frame rate is too low to adequately capture the "snap" and release phase of the throw. Putting the led's in the projectile allows use of an unmodified sling, which is nice. You would have to sling into a hanging backstop...

Glad you guys are moving along!

Matthias
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Re: The physics of sling
Reply #13 - Aug 8th, 2004 at 9:54pm
 
George Alsatian just submitted a pretty comprehensive review of the physics involved with slinging.  You should check it out asap in the articles section, and perhaps work with him developing the section.  I was pretty impressed with my quick glance through it.  I might print it out and read it thoroughly soon (just too busy now).  

Let me know what you think.
Chris
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Re: The physics of sling
Reply #14 - Aug 8th, 2004 at 10:05pm
 
One of those sections will definitely need to talk about the leverage and mechanical advantage of the sling. I have been thinking about that alot, so let me toss out some ideas.

If a person is throwing a rock, the speed of the rock is limited because of how fast your arm can move. Obviously, when you throw a pebble it hurts your arm because there is hardly anything to push against. And the converse, throwing a very large rock, you are limited because of sheer mass. But since kinetic energy is what we are aiming for (that is what causes damage when the projectile hits) there will be a peak kinetic energy that can be applied to a rock with the factors of the rock's mass and top speed of the throwing arm.

However, the sling provides leverage. Basically, when you double the length of the leverage arm (by attaching a sling to your hand), the work that it takes to accelerate a rock of the same size doubles. That way, you can throw a small rock that would normally hurt your arm at a slightly slower speed but get double the force applied to it. Basically, because the sling adds leverage it allows for the arm to accelerate small rocks without moving your arm too fast.

Sorry, I am having trouble articulating this. I had a terrible physics teacher, but I imagine after some instruction in college physics I will be able to explain this better.
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