General >> Project Goliath - The History of The Sling >> The physics of the sling

Message started by Hondero on Aug 2nd, 2004 at 1:34pm

Title: The physics of the sling
Post by Hondero on Aug 2nd, 2004 at 1:34pm
Well...  Humm...  ::)  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  ;D.

Title: Re: The physics of sling
Post by Matthias on Aug 2nd, 2004 at 5:16pm
Good job Hondero!

I'll throw in my vote that we add a (substantial ;D) "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!


Title: Re: The physics of sling
Post by Yurek on Aug 2nd, 2004 at 6:47pm

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.


Title: Re: The physics of sling
Post by Hondero on 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.

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::).

Title: Re: The physics of sling
Post by Yurek on 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.


Title: Re: The physics of sling
Post by Chris on 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.  

- 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.)  


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


Title: Re: The physics of sling
Post by Hondero on Aug 5th, 2004 at 12:30pm

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:

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)  ;D

Title: Re: The physics of sling
Post by Hondero on Aug 6th, 2004 at 5:26pm

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!!  :o :o

P.D  Well... let´s be a little humble...  :-/ , 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.

Title: Re: The physics of sling
Post by Matthias on Aug 8th, 2004 at 12:01am
Lead is pretty sudcutive eh Hondero? :) 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 ;)) 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.


Title: Re: The physics of sling
Post by Hondero on Aug 8th, 2004 at 4:25am
Mathias, your experiments with the ballistic pendulum, throwing glandes at very close range  ;D, 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  :D

Title: Re: The physics of sling
Post by solobo on 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.

Title: Re: The physics of sling
Post by Yurek on Aug 8th, 2004 at 6:43pm

You are the most exemplary partner among us :) 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 :) 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.


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 :) 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.

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.


Title: Re: The physics of sling
Post by Matthias on 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!


Title: Re: The physics of sling
Post by Chris on 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.

Title: Re: The physics of sling
Post by WildAtHeart on 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.

Title: Re: The physics of sling
Post by Hondero on Aug 10th, 2004 at 5:47pm
Don´t worry, Yurek, about your lazy holiday, I´m sure I can´t finish the task alone  ;D. Autumn will be a good time to work on physics.  Thinking of different ways to measure the initial speed of the projectile, as you and Matthias are talking, I see that another way, less accurate than the ballistic pendulum (wich is exact if well made), could be one working on the penetration of the projectile into a soft target. It coul be a first aproach, simple to make for  anybody. The kynetic energy of the projectile will be fully spent making the work of penetration. This work is the product of the penetration length and the resistance force of the material. This force would be calculated for a projectile from the resistance pressure (Kg/cm^2, etc) of the material, wich is a data of the manufacturer. It could be also easily calculated loading weights on the material until overcoming its resistance. From the equivalence "penetration work = kynetic energy" we extrac the speed.

A cheap an easy to get material would be the expanded polyethylene, that is used for modern targets in archery, though a material of very fine grain would be better and would provide more accurate messurements. If the plasticine were enough cheap as to make a big target...  ;D

Title: Re: The physics of sling
Post by Yurek on Aug 10th, 2004 at 7:28pm
Mechanical adventage of a sling.

We often can meet the opinion, that mechanical adventage of a sling relays on its ability to progresive accumulating the kinetic energy of the projectile in the rotary motion. In other words, one is able to get some relatively rapid turns of the sling in some unlimited time. Next, the sped up stone can be released in a suitable moment. Of course, that reasoning makes some sense, but doesn't explain the reason of the real efficiency of a sling.

Let's look on it closer. During a throw of a stone with the naked hand, we have the limited range of the hand motion. Assume, that the palm of our imagined thrower, during the throw, is able to travel the 1.8 m (S) along some curvelinear trajectory. He is very ambitious and want to beat the famous pitcher Nolan Ryan and accelerate the stone at the 55 m/s velocity (ca. 200 km/h)!.

Let's play a bit with a bit of physics.

For simplicity, let's assume that his hand is uniform accelerated (a = constans), from immobility at the 55 m/s. Since the increase of the velocity is lineal, then mean velocity (Vm) is equal to the arithmetical mean of the initial and final velocity:

Vm = (Vi + Vf)/2 = (0 + 55)/2 = 27.5 m/s

So we can calculate, what time of that throw (t) should be:

t = S/Vm = 1.8/ 27.5 = 0.065 s  !!!

As we can see, our thrower has very limited time for that acceleration.That time is terribly short! I'm not sure, if it is possible for human body, but maybe (we must verify it somewhere).

So, what can he do for geting the assumed final velocity (or even a bigger one)?

S = Vi*t + (a*t^2)/2        this is the well known eqution for the uniformly accelerated motion


t^2 = t*t
Vi - initial velocity
a - acceleration      

From this, we get:

a = 2 * (S - Vi*t)/t^2

For Vi = 0:

a = 2*S/t^2

So, since, he isn't able to shorten the time (it's pity, bacause it is a very strong factor, as we can see above), due to the limited mechanical power of his body, he may only lenghten the path of the acceleration. However, his hands are inextensible, so he will have to use just the sling.

Ineffective way of a sling using.

Our imagined thrower is an inexperienced slinger, so he will try to reach the assumed linear veloicty by progressive rotational speeding up of the sling. Saying simply, he will try to make the sling very fast whirled.

Let's check, how fast he should rotate his sling, in order to get the velocty of stone at the 55 m/s.

He has unlimited time for doing it (but only theoretically, he may die a natural death in the mean time). Starts slowly by a spacious arched movement of his whole arm. The faster rotations, the smaller circles are traced by the palm. When the sling stops to accelerate, palm still must rotate around the center of the stone (pouch) trajectory, because of, it must pull the cords a litlle agley to radius of sling rotation, in order to overcoming of the air drag of the sling. The picture below shows it.

Let's forsake a more penetraive analisis of that, but say only, that the smaller Driving/Centripetal force ratio, the smaller circle of the palm must be, for keeping the contant rotations up. The heavier stone, shorter and thinner is a sling, the more slight the palm movement can be, and vice versa. If our green slinger wants to keep really fast rotations, he shouldn't make spacious movement of his arm, due to its big mass (inertia).


R = 0.06 m     - radius of the palm rotation
L = 1 m        - lenght of the sling
m = 0.1 kg     - mass of the stone
Vf = 55 m/s    
T - time of the single sling turn

T = 2*pi*(R + L)/Vf = 2*3.14*(1 + 0.06) = 0.12 s

So, for keeping the stone velocity at the 55 m/s he should make the one turn during the 0.12 s.

This gives the speed of rotation:

1/0.12 = 8.3 turns/s    !!!

The centripetal force (Fc) for keeping up that orbit of the stome, amounts:

Fc = m*Vr^2/((R + L) = 0.1*55^2/(0.06 + 1) = 302.5 N = 30.8 KG   !!!

The 8.3 turns/s of the 30.8 KG force whirling around the palm, for sure, this is what, no normal man can do it! Unless, he is the Gigant, who has just got convulsions ;D I think, that average man can make mentioned sling rotated at the 4 turns/s, but it will be a big effort for his arm, and let him reach only the 26 m/s, what is very poor result. If he even use a double lenght (2 m) sling, for sure, want't be able to whirl it so rapidly.

We must also say a few words about accuracy of that method of slinging. Assume, that our slinger wants to hit the 1m x 1m target from the 20 m distance. His sling is rotating at 4 turns/s in the horizontal plane. In this case, the released projectile must be contained in the 2.9 deg angle. The sling runs that angle during 0.002 s (2.9/(360*4))! We can imagine, how it is difficult to feel so short moment during furious brandising with the tense and tired hand, practicaly it is beyond of human perception.

As we see, that way of slinging is full of faults. Although, let us to accelerate projectiles on the very long track (multi-rotations), but our hands are not able to manage so very quick and circular (recurent) motion, which causes so big stress.

We know, that some man (Larry Bray, David Engvall, for example) could throw projectiles with sling at quite a lot above 400 m, what require velocities at least 100 m/s, saying safely. They used sling not longer than 1.3 m and are not the Gigants ;) So we should think about some diferent, much more efficient way of using sling...


Uf! Enough for today. This is the first, short part of my virtual draft. It is very raw and probably contain quite a lot spelling and grammtical mistakes, if so, excuse me it. I hope there aren't content-related mistakes. This part rather treats about disadventages of a sling... or rather that method of slingin. Coments welcomed.


Title: Re: The physics of sling
Post by Matthias on Aug 11th, 2004 at 1:20am
Looks like you are on the right track Yurek. I certainly have the feeling while slinging that it is strength rather than speed that is limiting my range. Given a sling with little or no drag (there's that vacuum again) The amount of force you can put into the snap should be the limiting factor. I'd love to see a very high speed fram by frame analysis of a well executed throw - I think the forces/tensions achieved would surprise many of us...

I like the idea of projectile penetration too, but am hesitant based on too many years setting up experimental apparatus.

I think I "might" be able to swing a high speed strobe without spending any money. I'll build an LED enabled glans first. The unfortunate part is that with me as the only model, we won't be capturing the pinnacle of modern slinging by any means!


Title: Re: The physics of sling
Post by Hondero on Aug 11th, 2004 at 5:43pm
Yurek, your first work is very clear and didactic, an example to follow for all us. I´m sure that beginners fond of that way of spinning will forget it quickly, or will change to other sport like artistic skating  ;D.
I´m looking forward to read the next part about the dynamics of the efficient way of using the sling.

I´m preparing something about "optimal projectil weight". Maybe tomorrow I´ll post part of it.

Title: Re: The physics of sling
Post by Chris on Aug 11th, 2004 at 11:42pm
Can you guys write up a little outline for what you will cover in the Physics section.  i.e.:

- Mechanical Advantage (intro, why a sling works).
- Orbital/Rotational Physics (tangential releases, etc.)
- Drag
- Trajectories
- ....
- ....
etc etc.

I'm not a physics buff, so my outline isn't meant to be serious, but perhaps something like it.  I think will help you focus the section and help you divide up the topics among your selves (and have clean divisions).  I can also update the master outline with all the subtopics that will be included.


Title: Re: The physics of sling
Post by Hondero on Aug 12th, 2004 at 12:39am
Chris, I think that all this will come out a little anarchic at first, following the  interest each one has at each moment, like always happens in a forum debate. I think the debate is important even in this task, as a means to contrast ideas and theories with others. This way is also more fun and productive than to set up an index and "work" systematically on it :-/.  At the end all will be said and we can reorganize the subjet in chapters and to make a definitive structure and index.
In any case the points to work on, as we´ve said before, could include two main parts: Physics of the throw and physics of the proyectile fly. The first one, will consider the biomechanical aspects, the mechanic of the throw, the styles of throwing, the air drag on the sling, etc.
The second part will include the estudy of trajectories, the air drag on the projectile, aerodynamics, ballistic coefficients, maximun ranges, etc.
As a combination of the two parts, it can be considered the optimal weight and shape of the projectil, the optimal designe of the sling depending of the objet of its use, the tecnics of throwing to get range, penetration or impact, and so many subjets that are very interrelated and difficult to place in a precise place.
The organization work at the end will be interesting and valuable.
Well, this is only my opinion, and my way of work (only in these situations)  ;)

Title: Re: The physics of sling
Post by Matthias on Aug 12th, 2004 at 2:03am
Agreed. I think we are still in the stages of figuring out what we know (we know, what we don't know we know, known unknowns etc... :P) This one is going to be a fair deal tougher than just going out and collecting published work, citing some references and writing it up. We're in a position where we need to do some basic science before we can choose our targets (let alone hit them).

Chris' outline points are good ones, as are Hondero's up-thread. I think we'll get there, but it is going to take some time. If all the pieces that we're talking about come together this is going to be a heck of a seminal reference.


Title: Re: The physics of sling
Post by Hobb on Aug 12th, 2004 at 12:02pm

This one is going to be a fair deal tougher than just going out and collecting published work, citing some references and writing it up. We're in a position where we need to do some basic science

I'm lousy at physics, but I'm a statistician by trade.  If anybody ends up with some raw data in need of statistical analysis, or just needs some advice about experimental design, give me a buzz.

Title: Re: The physics of sling
Post by Hondero on Aug 12th, 2004 at 1:03pm

The common sense says to us that the heavier is a sling projectile at smaller speed we will be able to throw it and smaller range it will get, reason why we will use light projectiles to increase the range. It is the effect of "greater reach by speed".
But on the other hand, if we throw several projectiles of different weight at the same speed, the heaviest will reach greater distance since its stored energy will be greater, and the air drag will take more time in restraining it. It is the effect of "greater range by weight". As we see there are two opposed effects dealing with the weight, being more important one or another according to the weight that we are considering. If we suppose that we are using all our power of launching, an optimal weight will exist over wich the range will be smaller due to the superiority of the factor "greater range by speed", and also if the weight is below it, the range wiil be smaller too due to the factor "greater range by weight".
Evidently this optimal weight will be different for each slinger, since his muscular power will be different in general, and different therefore the relation weight-speed that he can obtain. This relation weight-speed of the projectile is related in the first place to the muscular behavior, it is to say to the own relation force-speed of contraction that the muscle is able to develop. This relation is expressed by the Hill´s formula, whose graphical representation is this:

As we see, as greater is the contraction speed of the muscle, less  is the force that it can develop. Evidently, both the speed and the force of contraction  will be transmited in certain proportion through the osseous system of the arm to the sling. One could think that the muscle is able to always develop the same maximum power, it is to say W=F*V = constant. Thus a diminution in the speed would make a proportional increase in the force. But the reality is more complex, like it can be observed drawing up the curve of power from the curve force-speed, that would be this:

We see that the maximum power is obtained for contraction speeds very reduced, of the order of 30% of the maximum speed. Nevertheless this fact does not worry us too much since in the sport we are considering we are located in the last third of the curve, that can be considered straight in first approach.

We have landed in the biomechanics. The arm, and in general the bones that take part in the launching are driven by muscles. The basic mechanical scheme is that of a lever leant on a joint and driven by a force applied near the joint that makes move the distant end and take to it a demultiplied force. It´s somehow like a little staff-sling. But in addition, the slinger model of propulsion is a set of conected levers that act in sequence, well coordinated, adding speed over speed to the hand. The hand, in turn, communicates this speed to the sling. And the question would be if we can substitute this compound lever for a single one at the time of making calculations to simplify them.

Well, this is the general exposition of the optimal weight problem. And for today it is enough  ???. It will continue.

Title: Re: The physics of sling
Post by Hondero on Aug 19th, 2004 at 4:53pm
The graph of normalized Muscle Force vs Velocity of contraction we have seen before shows the values of force and speed relative to the maximum values of these variables. We consider only the part of the curve between 0 and 1. The maximum force is the static weight that can support a muscle, and the maximum speed is the one at wich the muscle would contract without supporting any weight. Naturally, these maximums will be different for each slinger depending on their muscular structure. When we are considering not a single muscle but all the muscular structure implied in the launching with a sling, there are a serie of muscles and lever bones acting, being complex to establish an equivalent and simplified mechanics model, but in any case, given the muscular nature driving these levers, it is possible to accept as a first approach that the hand, driven by the shoulder and arm, follows a similar curve to the one considered for a single muscle,  been now the maximum values:

1- Maximum speed at which the hand can move without any weight;
2- Greatest weight supported at null speed (static weight in throwing position).

These maximum values can be messured or approached, like for example the launching speed of best pitchers (160 Km/h). For the calculations that follows I ´ve considered an average slinger, with a hand velocity of 100 Km/h and a static force in the hand of 5 kg (throwing position).
The useful range of the graph for our purpose will be the corresponding to projectile weights up to 250 gr., that is to say, for relative values of the force between 0,05 and 0. We are placed at the right end of the curve. If we expand this part of the graph we see that it can be considered a straight line, and its equation would be:

X = 130 - 3,25 * Y

And in addition:

Y (mm) = Y (gr)/6,25
X (Km/h) = 80 + 2/13 * X(mm)

With these simple formulas and the Simulator of Trajectories we can make several interesting simulations:

Let us take a 80 gr standard stone projectile (spherical shape for simplicity) and three slings:  long, medium and short, of lengths 105, 75 and 45 cm. respectively. Also let us consider the torque on the shoulder, being the shoulder the fulcrum, and the equivalent weights on the hand according to the length of each sling. In fact, in the launching, and depending on the style, the arm is partly folded at the beginning of snap, and soon it is stretched completely, that is to say, the length shoulder-hand is variable. In order to simplify the calculation we considered the lenght constant, about 70 cm, which corresponds with the arm length at the final powerful part of snap
Applying the previous equations and the Simulator we obtain the following values.

Sling-Length (cm).... Speed (Km/h)..... Range (m)
 105..............................210 ......................175,5
   75............................ 174,4................ ....140,5
   45 ............................146,7................ ....112.1

As we knew, to greater sling length greater range, but the increase in range is not as great as it could be thought. In addition, the air drag is different on the three slings and  difference in the ranges would be even smaller.
The long sling with respect to the short one has an increase in length of 133 %, but the increase in range is only of 56 %, that is to say, less than the half.

This optimal weight, as it´s said, could vary for each slinger. The slinger considered is the average one we have previously considered. We will choose the long sling, of greater reach. We´ll try with projectiles of weight between 50 and 100 gr.. since we suppose that among them it will be the optimal one. We´ll apply the previous equations and the Simulator:

Weight (gr).......... Speed (Km/h)................Range (m)
 45................................. 227.5........................ 178.2
 50................................. 225........................... 179,3  
 55................................. 222,5........................ 184,3
 60..................................220........................... 182.3

We see that for this slinger the optimal weight would be around 55 gr.
Curiously this weight corresponds enough with the projectiles of the last Guiness records, in spite of being the holders of greater power and range that the average slinger considered.

P.D. All this doesn´t  atempt to be exact calculations, but a general approach to the facts.

Title: Re: The physics of the sling
Post by Yurek on Aug 22nd, 2004 at 6:19pm


As Hondero mentined, Mother Nature has bestowed us with long bones of hand and tendons attached close joints. It has let us to make the rapid movements of hand and made us a quite good throwers, but, of not too heavy stuff. Fortunately, we have got also strong muscles of legs and trunk, of which we have learned use for more efficient throwing, over centuries of huntings, wars, plays and sports. So, there are the tested and efficient ways of throwing different things.

Therefore, it will be quite resonable, if our slinger would use one of these ways of throwing just for slingnig. For instance, the basebal pitcher's way (maybe, a bit modified, adapted to a sling motion).

Now, I try to explain how it working, using the simplified model.

Usually, the pitcher's palm is accelerated along some curved trajectory, because it mostly is a result of interfering rotatory motions of the hips, shoulders, arm, forearm and wrist. The acceleration surely changes along that composite curve.

For our purpose, let's assume, that that trajectory is circular and is a half of the full circle (180 degs).

Before we start our investigation of that throw, we should understand, how the cords behave during either a uniform rotation or eccelerated one, what forces act on a sling. That lets us to imagine how the trajectory of the stone looks.

Forces during a uniform rotation of the sling.

Here is the picture showing the forces during uniform rotations of the sling in the vacum (the air drag and gravity omitted):

Pic. 2

Practically, there is only a one external force, just the Centripetal Force, needed to keeping the circular trajectory of the stone (the Centrifugal Force isn't an external force, is only an inertial reaction to the curving the stone trajectory by the Centripetal Force).  

So, only job the palm must do, is pulling the cords with the Centripetal Force during the uniform whirling. No perpendicular to the radius, a driving force (which gives a torque) is needed, because there isn't an acceleration and air drag). After the release, the stone will start its stright travel along a tanget direction, with the same linear velocity, that had during the rotations (we know it from the Newton's First Law).

Angular acceleration = moment of interia * torque = 0  ---> torque = 0

In this case

radius of the stone orbit = radius of the palm orbit + lenght of the sling

Forces during an accelerated rotation of the sling

Now the case is a bit more complcated. When the palm accelerates, the cords become deviated to backward. The most short way of explanation, how it comes up to that deviation is, that a inertia of the stone (its mass) restrains its acceleration (First Newton's Law), saing simply, the stone "tries to delay itself". A deeper analysis of it would be very interesting, however for our purpose we skip it, as it is a bit complicated. Let's say only, the angle of the cords deviation results from a balance of forces. The picture below shows just these forces.

Pic. 3

Despite of common sense, tense sling works very similar to a stiff and light stick with a stone on the tip. But, there is one diference. We are able to provide the additional significant torque to a stick, by a suitable action of the fingers and wrist. In case of sling, it is almost impossible, bacause cords can't transfer any torque, due to its flexibility. In the other words, we are able to make the single stroke with stick using only our fingers and wrist, but try to do that with a relative long and sagging statically sling!
A stick is able to transfer either the torque or pulling or even pushing force, but cords only the pulling force! However, if one attaches a stick to fingers by a soft and short loop (or simply keeps the stick only beetwen the thumb and index finger), a stick would work almost exactly like a sling. In both cases, his palm only can pull these ones!

Consider, that just the pulling force is the only possible kind of interaction between slinger's palm and a stone! For lashing with a sitck, it is the strongest driving factor too, the figers and wrist action adds only some edge, in comparison to a sling.

So, there is the questions, how it is possible, that we are able to make so dynamic and spacious lash of a sling, only by pulling of the cords?

Look at the above picture (Pic. 2). During the acceleraton, the Pulling Force (Fp) transfered by the cords to the stone,  has the two component forces: the tangential one (Fa) and the radial one (Fcp). The first one (Fa) just transfers the torque to the stone and make it accelerated. The second one is the Centripetal Force, which keeps the stone on the curved trajectory. The forces Fai and Fcf are the interial reactions, the Fa "tries to restrain" the speeding up the stone, Fcf is the Centrifugal Force, which "tries" to make the stone trajectory just stright. They give the resultant force, the Fpi. Just this inertial resultant force (Fpi) determines the angle of the cords deviation from the radial direction, and a value and direction of the Pulling Force of the palm (Fp).

The mentioned forces are in a dynamic balance. The Fdi "tries" to deviate the cords to backward, but the Fcf "tries" to push them outside (erect them). They are changing their direction and value during the stone acceleration. It coerces a continous change of the cord deviations (the angle FI) and value of the Pull (Fp), acting on our fingers.

From the below formula (for the centrifugal force):

Fcf = [mass * (tangent velocity)^2]/radius

We see, that a value of the Fcf force is strongly dependend on the tangent velocity (^2). Therefore, that one must become higher and higher, since the stone is accelerated by the (Fa) force all the time. It causes, that the stone tends to go outside, what results in the additional rotation of the sling around the palm. As a result, the motion of the stone is compounded of the accelerated stone rotation around the centre of the circular orbit of the palm (our earlier assumptions), and of the accelerated rotation around the the palm (grip point).

The next picture shows what's going on.

Pic. 4

This is a quite likely sample, how the sling can run during a efficient stroke in a real conditions. W can see, that the stone accelerates more and more just in the last phase of the stroke, due to its high velocities (Fcf grows like tangent velocity^2) and due to decreasing the tangent stone acceleration (Fa decreases, bacause the arm and wrist become more and more erected, and additionaly more laden by the big Centrifugal Force). We can compare the Fcf to a (more and more stiff) spring, which is indirectly diffracted by the Fa, and which gives the kinetic energy back just before the release. That gives an additional spur for the stone, and makes a shape and lenght of the stone trajectory more beneficial, bacause lets us to release the stone in a much more profitable moment (I mean, more to forward, when the slinger's arm is alredy streched). You can see it on the above picture, that trajectory is a kid of a spiral. Of course, it isn't only possible variant in practice. It depends on a slinger's motion, his quickness, a leght of a sling, mass of a stone, and a few more factors. But, let's skip discussing it for the present, bacause, now we should start explore the adventage of our sling.

The adventage of the mentioned slinging way

Now let's play a bit with numbers again, and check what that adventage could be. The folowing analysis arises out of the assumption, that proceeding of the sling on the picture (Pic. 4) is similar to a real one during an efficient stroke.

Our assumptions:

R = 0.6 m              - radius of the palm circular trajectory;
                               (an result of the entire body motion);
L = 1 m                  - lenght of the sling;
THETA = 180 deg   - angle traced by the palm along the trajectory;
Vpi = 0                   - initial linear velocity of the palm;
Vsi = 0                   - initial linear velocity of the stone (assumption,
                               that the stone starts from the immobility is unrealistic,
                               especially for longer slings, because for doing an efficient stroke
                               we need some initial velocity for a proper tension of the cords);
t = 0.15 s               - time of the stroke (acceleration);

At my guess, that time practically could be even almost 50% shorter. This is the next parameter, we need to measure in a practice.

Vpf                 - final linear (tangent) velocity of the palm;
Vsf                 - final linear (tangent) velocity of the stone;
ap                  - mean tangent (along the trajectory) acceleration of the palm;
                      (constant equivalent of a variable acceleration);
as                  - mean tangent acceleration of the stone.

Let's calculate the mean tangent acceleration of the slinger's palm:

ap = 2*(S - Vpi*t)/t^2        

where Vpi = 0


Sp = 2*pi*R*(THETA/360)    - lenght of the palm arc

Sp = 2*3.14*0.6*(180/360) = 1.88 m

we get

ap = 2*1.88/0.15^2 = 167.1 m/s^2

Now we are able to calculate the final velocity of the palm:


ap = (Vpf - Vpi)/t         where Vpi = 0

we get

Vpf = ap * t = 167.1 * 0.15 = 25 m/s

Well, that velocity doesn't seem to be exaggerated, even for an average thrower.

Title: Re: The physics of the sling
Post by Yurek on Aug 22nd, 2004 at 6:37pm
Consider, that the stone traces a longer trajectory than the palm in the same time. On the above picture, we see, that the angle traced by the stone amounts 223 degs. As we know, the stone trajectory is composed of the circular motion around the slinger's pivot, and the circular motion around the grip of the cords.

Let's calculate a lenght of the first one.

If the sling doesn't rotate aroud the grip, the deviaton angle of the cords would be constant all the time. So, the stone would trace the half-circle. The radius of that half-circle we can calculate as one of the sides of the triangle designed of the arms R and L and the angle 180-120 deg (look at the start position of the sling on the above picture).

From the Law of Cosines (a bit trigonometry) we have:

radius^2 = R^2 + L^2 - 2*L*R*cos(180-120) = 0.6^2 + 1^2 - 2*0.6*1*cos(60) = 0.76 m

radius = 0.91 m

Then we have:

S1 = (180/360)*2*pi*radius = 3.14 * 0.91 = 2.8 m

Now, the lenght of the second "component" of the trajectory.

The angle of the cords rotation around the grip (palm) amounts (accordingly to the picture):

120 - 60 = 60 deg  

S2 = (60/360)*2*pi*L = 3.14*1/3 = 1.1 m

Then we have the entire lengh of the stone path:

Ss = S1 + S2 = 2.8 + 1.1 = 3.9 m

The acceleration of the stone we calculate in the same way like for the palm:

as = 2*(Ss - Vsi*t)/t^2          where Vsi = 0

as = 2*Ss/t^2 = 2*3.9/.015^2 = 346.7 m/s^2

So, the final tangent (muzzle) velocity is:

Vsf = as*t = 346.7 * 0.15 = 52 m/s = 187.2 km/h

So, now our slinger is able surpass pitcher Nolan Ryan's 45 m/s quite easy! All what he needs, is a 1 m long sling, nice stone and quite easy smooth stroke.

The adventage of the sling in this case amounts:

Adventage = as/ap = (2*Ss/t^2)/(2*Sp/t^2) = Ss/Sp

Adventage = 3.9/1.88 = 2.07

From the above contemplations and calculations we can conlude, that during the stroke a sling doesn't work exactly in the same way like a simple stright lever. The trajectory of the stone has the variable radius, so isn't circular (even if the palm traces a circle path). Despite the mean radius of the stone trajectory is smaller than the sum the L and R, the lenght of the path of the acceleration is significantly extended due to the additional rotation of the sling around the grip point. It is very efficient, when she sling is markedly deviated to backward in the first stage of the stroke and strighten itself just before the release. It lets to release a bit later, and better utilize the full motion of the forearm and wrist for the stone acceleration. Therefore, it is very important to drive the palm smoothly (it doesn't mean slowly) along a properly curved trajectory and keep a suitable ratio of Fa/Fcp. In the other words, The bigger a stone velocity, the bigger should be the palm acceleraton, and/or the more extended motion of the palm, the sling shouldn't "escape" permaturely. Fortunately, it naturally results from our's body mechanics. Describing of that questions by analytic equations would be complicated, as we should take into consideration a lot factors. The best way to find our OPTIMUM is understending how it works, and of course, a lot of practice, that gives just the feelling. Proper shots are felt as springy (just result of proper using of the "centrifugal spring") and pleasant, don't hurt our body (of course, a bit trained body). We get impression, that our forearm is just shot out to forward.

Now we try to check, what our slinger should do for... surpassing the curent record holders in slinging for  range...


Well, I'm not sure if I should reveal that secret here. So maybe it will be continued ;D Now I'm tired. Hondero and Matthias, thanks for the encouraging words. I'm happy, that there are as much as three person interested in that topic at least. So it is worth of our effort :D I was a bit off lately, so I have some arrears on the forum. I must yet read your Hondero last posts in this topic. I have find out some new interesting things in your post, especially the Hill's fromula charts. You both make a good job trying to measure slinging parameters. I would love, we get to know the exact trajectory of the palm and pouch, and the velocities and acceleratons in diferent points of these, during a efficient slinging.


Title: Re: The physics of the sling
Post by Hondero on Aug 23rd, 2004 at 1:26pm
Very interesting your analysis, Yurek!!. I think the position of the sling at the final stroke is quite accurate, though maybe it depends a little on the style you use. I´m addicted to accuracy and so my final stroke is very similar to a particular baseball pitch, describing the hand an almost straight trajectory from behind and ending with the arm streched towards the target. Thus the sling is more retarded at first and at the end it describe this aditional turn around the hand you say in a marked way. Other styles like Newmanitou or other guy whose name I don´t remember and that posted a good video, semms to have a snap with the sling almost like a continuation of the arm, in the upwards position.

The subjet is very interesting though it isn´t of general audience, but I  have to confess that I´m hooked.
I´have to modify a little my previous calculations considering this angle of the sling and the arm at the release in the general throwing style  ;).

Title: Re: The physics of the sling
Post by Yurek on Aug 23rd, 2004 at 6:13pm
Thanks Hondero,

Your posts I read with a great interest too.

though maybe it depends a little on the style you use

For sure, you are right. I think it also depends on the lenght of a sling, curvate of the palm trajectory, initial velocity of the pouch, distribution of the acceleration on the trajectory, air drag and indireclty on the mass (that slows down a slinger). So, there are possible different behaviours of a sling during the stroke. I believe there is the optimal one for a given L/R ratio, cosidering the velocity adventage.

I´m addicted to accuracy and so my final stroke is very similar to a particular baseball pitch, describing the hand an almost straight trajectory from behind and ending with the arm streched towards the target.

Yeah, it seems to match to the theory. I know you like rather shorter slings, as more accurate. Shorter ones more tend to escape ouside, because the cetrifugal force is inversely proportional to the radius of the trajectory (for a given tangent velocity, the smaller radius, the bigger Fcf). So, if your palm runs along rather flat curve, then it's radius is a bigger and the Fcf is smaller. Therefore the sling doesn't erect itself too early, what would extort a permature release, or stone would go more to the left (down) from target.

Other styles like Newmanitou or other guy whose name I don´t remember and that posted a good video, semms to have a snap with the sling almost like a continuation of the arm, in the upwards position.

If so, they would have to release too early (nearly the 3 o'clock or under the shoulder) or to send the stone sideward or into the ground :)

I  have to confess that I´m hooked

I'm afraid I'm too :D Does anybody know where I could find an Anonymous Slingsters ;D


Title: Re: The physics of the sling
Post by Hondero on Aug 24th, 2004 at 11:13am

We have seen that for the average slinger, throwing with spherical stone projectile, the optimal weight was of 55 gr. Nevertheless there are not much difference using others near weights. In fact, between 50 and 70 gr. the difference in range is smaller of 2%, barelly about four meters, which almost makes indifferent the use of anyone of these projectiles since other factors as small differences in the shape, rugosity of their surface or position of the projectile in the flight can compensate this difference.
I´m going to define a parameter ;D that I´ll call 2% RWI (Interval of Weights for Range variations of 2 %). For the average slinger this parameter would be then 50-70.

Now let us see the behavior of the lead projectiles, also of spherical shape at first,  in the hands of the average slinger:

weight (gr).....velocity (m/s)......range (m)
   20...................... 66.66................... 255
   30...................... 65.27....................262.5
   40...................... 63.88....................264
   50...................... 62.5..................... 262
   60...................... 61.11................... 258

We see that now the optimal weight is 40 gr. and the 2 % RWI is 30-50. The light lead projectiles are then more advantageous, and in addition we even see that the famous 20 grams small glandes reach a distance smaller only a 3,5 % than the optimal weight, which explains its frequent presence among archaeological glandes.

We have spoken until now of the optimal weight for the average slinger... but will be it the same one for a more powerful slinger? The common sense says to us that existing enough throwing power, the heavy projectiles are more advantageous due to their greater dynamic inertia and greater difficulty to be restrained by the air. The results of the simulation for a slinger with speed in the empty hand of 130 Km/h and a static force in throwing position of 10 kg are:

weight (gr).......velocity (m/s)........range (m)
    50....................... 85.76....................391
    60....................... 84.86....................395.8
    70....................... 83.95................... 399.2
    90........................82.15................... 401
  100....................... 81.25................... 401.4
  120....................... 79.44................... 398.2
  130....................... 78.54................... 396
  150....................... 76.73....................389

We see that the optimal weight is now of 100 gr. and the 2% RWI are 60-130. The evident conclusion is that the more powerful is the slinger more advantages will have using heavy projectiles, although we see that the margin of weights is rather wide and that it will be more important than the optimal weight the other mentioned factors that take part in the range, as the shape, the rugosity of the surface and the position of the projectile in the flight. These points will be the following ones to analyze (HELP, Matthias...  ;D)

Title: Re: The physics of the sling
Post by Matthias on Aug 24th, 2004 at 12:29pm
Yes, I've gone quiet - :) I'm following along... and doing some background work. Almost have a high speed strobe and photo/acoustic-trigger built! I'm hoping to be able to provide some classic "lead-glans-penetrating-pumpkin" shots for the gallery. Should be able to get nice attitude-on-impact shots as well (provided I can hit the target). Projectile shape is slow due to a lack of either tools or slinging space depending on where I am. I'm away until the 2nd, but might be able to convince my "almost as crazy as me" family to assist in some sling performance evaluation while I'm visiting. Northern Alberta (prairie) is good sling country. Might finally be able to recover some projectiles!

And what about our "ball series" experiments? Surely some of you guys have some tennis/golf/base/softballs?

Hey and didn't we have some stop-motion pictures promised? David_T mentioned them a while back.


Title: Re: The physics of the sling
Post by Thomas on Aug 28th, 2004 at 9:28am
I once made a simple device for measuring slinging force. It was a retention cord only, with a captive softball.Between the cord and  ball insert a short length of bungee. A piece of string is then used to remember the bungee stretch. Attach the string at one end of bungee and the other end across the bungee held fast by a rubber band. In use this assembly is whirled around to achieve the desired rate. The string has been drawn through the rubber band grip and will remember how far it was pulled. A weigh scale can be used to recover the force. I got approximately 20 pounds from the softball experiment. Of course this spinning achieved less than 70 mph! A recent post by Matthias dealing with a ballistic pendulum described a similar indicator idea. Someone could develop this into a real sling  and get reliable speed and force data. I don’t want to infer that elastic cords should be used in functioning slings.


Title: Re: The physics of the sling
Post by Hondero on Aug 30th, 2004 at 12:56pm

Although it´s somewhat incredible, the rugosity of the projectile has to do with the range, in the way of the golf balls, extending the reach, although not as much as in them because golf balls have less density and are affected in greater measure by this effect. Let us consider first a stone spherical projectile.

Re = Air density * Velocity * Diameter/air viscosity

Considering always the same projectile  Re= K1 * V

On the other hand :

Drag force Fd = Cd/2 *  air density * cross section * V^2  (CD = drag coefficient)

For the same projectile: Fd = K2 * CD * V^2

The drag force will vary then with the speed of the projectile, first by itself and secondly by its dependency of CD that varies with Re, that varies as well with V. The relation of CD with Re comes given from experimental form by the curves of Achenbach for spheres:

The upper curve, corresponding to smooth spheres, has an almost constant value around 0,5  until arriving at the point in which the speed of the projectile causes a turbulent air flow, falling drastically the CD. Nevertheless, the required speed for this it is higer than the maximum one that can reach a slinger, reason why hardly we will enter this favorable zone.

Nevertheless, if the sphere is rough, we see that the corresponding curve provides lower values of CD, now in the margin of speeds of the slinger. For that reason the air drag force will be smaller and greater the range. The curve shown corresponds to a projectile of rugosity K/D = 0,01250, wich expresses the ratio between the depth of the holes and the diameter of the projectile. Thus, for a projectile diameter of 4 cm the holes would be of 0,5 mm. A projectile like this is easy to make striking a smooth-stone around all their surface with another stone, or with a rounded hammer.

In order to calculate the increase of range of this rough projectil vs a smooth or polished one we will have to make approximated calculations, since the speed of the projectile will be changing as it goes being restrained by the air, and therefore will be changing its CD. In the picture I have selected two zones that corresponds to the variation of speed for projectiles thrown with two initial speeds: 55,55 and 120 m/s, that are the speeds of launching of the considered average slinger and of a recordman.
I have used the Simulator to get in both cases an aproach to the end speed of the projectile, that could be of about 25 m/s and 65 m/s respectively. As it is  very awkward to evaluate the effect of the changing Cd, I have taken an average Cd for each zone, as it is indicated in the figure. For a projectile of 100 gr. the calculated values of the range are:

Speed.......................55,55...........120 m/s
CD (Smooth) ........... 0,5............... 0,47
CD (rough)............... 0,272............0.37
Range (smooth )......167............... 353 ms
Range (rough )........ 208............... 409

We see that for the average slinger the increase of range with rough projectile is of 25%. The recordman, nevertheless, is penalized by the high end speed of the projectile, that does not take advantage of the zone of lower Cd.

The following calcualtions will be with lead projectiles, that surely also are influenced by this rugosity effect  (I progress little by little, but soon I´ll discover the carefully kept secret of Jurek... but I shall not disclose it  ;) )

Title: Re: The physics of the sling
Post by Hondero on Aug 31st, 2004 at 1:43pm
Before analyzing the rough lead projectiles, I want to show the Achenbach full graph, that includes a serie of curves corresponding to different rugosity, as it is seen in the figure. The curves can really be interpolated in a continuous way until arriving at the corresponding one to the perfectly smooth sphere.

We see as in each one of them the zone of minimum CD corresponds more and more at high speeds. Thus, our recordman of previous post, that had been underprivileged front to average slinger when using a projectile of rugosity 0.01250, does not have to do anything more than to use another projectile of smaller rugosity, like the one of 0.00150 to be able to get an average CD of 0.2, still smaller than the one of the average slinger, and to obtain therefore an increase of range with respect to the smooth projectile of 64%.

These so low values of the CD give rise to spectacular ranges, and make us to believe more and more in the possibilities of the sling if suitable projectiles are used. Each slinger has to choose the rugosity degree adapted to his power to get the best aerodynamic performances of the projectile. The suitable selection of the projectile plays then a decisive rol in the range, more than the simple power, and makes us imaging the high sophistication that could have the modern sling competition. After all, the sling, looking so simple, keep secrets that makes it a sophisticated weapon.

But coming back to the subject of the rugosity, we have seen that for a powerful slinger the optimal degree is quite small, and possibly a natural heavy grain stone without polishing, like the granite, provides the suitable value of rugosity. What we´ll have to avoid is the use of polished or very smooth projectiles.
Another observation is that it is not imperative for the slinger  to be a burly guy, and that a normal slinger, using a suitable projectile, can get excellent ranges.

Title: Re: The physics of the sling
Post by Yurek on Sep 2nd, 2004 at 3:03pm

but soon I´ll discover the carefully kept secret of Jurek... but I shall not disclose it


Ohh no! It isn't truth. I have just tried to share it all time. But maybe... a bit clumsily ;D

After your last lecture, I should try dimpled glandes again.


Title: Re: The physics of the sling
Post by Hondero on Sep 5th, 2004 at 3:32am

Let´s go on a little with this "saga" on projectiles that is almost arriving at the end. First I must say that the recordman considered until now, able to throw a projectile of 100 grams to 120 m/s seems at present some excessive, although it has helped us to get right percentage relations. The present real data of sling and baseball records indicates an approximate maximum power equivalent to the launching of 55 grams at 110 Km/h with a sling of 105 cm. This power match with a 100 gr. projectile thrown at about 105 m/s. Nevertheless we will continue considering this ideal recordman of the 120 m/s to make comparisons with the calculations made until now, although the ranges that we are going to see will surprise us a little.

I´ve used the same Achenbach curves that we saw for the stone projectiles, the one of 0,01250 rugosity for the average slinger and the one of 0,00150 for the recorman. Now the end speeds in both cases are greater since the lead projectiles has more dynamic inertia. These speeds are 40 and 90 m/s respectively, and the values corresponding to the average CD are 0,23 and 0.14.

Let us see the results in tables to not repeat the graphs:

Initial speed....................55.55.............120 m/s
End speed.........................40...................90 m/s
Average CD (smooth)......... 0,5.................. 0.5
Average CD (rough)............0.23................ 0,14
Range (smooth)................ 229................. 590 ms
Range (rough)................... 267.................990 ms

The increases in range for both slingers using the rough projectile are 17 % and 67 %. We see that the lead projectiles, that are smaller than those of stone (R.stone/R.lead = 1.6), accuse also widely the effect of the rugosity, contrarily whith what could be thought (I´m the first one surprised  :o)

Title: Re: The physics of the sling
Post by Hondero on Sep 8th, 2004 at 8:11am

Let us consider finally the famous effect of the shape and performances of glandes. The more trustworthy data on drag coefficients I´ve found are from H. Rouse (1946), and come expressed in the following curve:

The ellipsoid of the curve has a ratio between axes smaller than the typical glandes, whose average ratio could be 1:2.4, been the most fat of them about 1:2. Also the glandes have the ends more pointed and are more aerodynamic, reason why the values calculated here would be the minimal corresponding to a glans.

I consider again the two slingers of reference and their 100 gr projectile.  We obtain the following values:

Initial speed......... 55.55......... 120 m/s
CD......................... 0,1.............0.06
Range.................... 300............1280 ms

The increases of range in relation to spherical smooth projectiles are 31 y 116 % respectively. We remember that the speed of 120 m/s of our recordman is a little excessive, reason why the probable reach (for 105 m/s) would be of 1010 m. Also we have to not forget that this range is for a perfect orientacion point-first of the projectile, what will not happen exactly in practice although we use special throwing tecniques. In regard to the effect of rugosity I have not found any data, but given their aerodynamic shape, the rugosity could not play an important role, since the trail left by the glans is enough narrow and it would not be reduced as much as for the spherical projectile.

And since we are speaking of glandes we can consider also the glandes of stone that have been used in different times and places, and the clay glandes too that comes from the warlike origin of the sling (Neolithic). The values of Cd are the same that for lead glandes and we considere also the same projectile weight of 100 g. and the two speeds of reference.

Speed...........55.55 m/s.............. 120 m/s
Stone............ 277 ms..................1072 ms
Clay...............267 ms.................. 997 ms

Surprising! There is no excessive difference between glandes of lead, stone or clay!

Arrived at this point it is the moment for summarizing and put together in a table the results of the different calculations made with projectiles of different density, rugosity and shape. The data are corrected for a max. initial speed of 105 m/s.


Initial speed(m/s) ..................55.55..........105
Spherical smooth stone.................167.............319
Spherical rough stone...................208.............508
Spherical smooth lead...................229.............516
Spherical rough lead.....................267.............818
Elliptical lead (1:1.8 ) ..................300.............1010
Elliptical stone (1:1.8 ) ................277..............875
Elliptical clay (1:1.8 ) ..................267..............821

One first conclusion is the great importance of the characteristics of the projectile, that can triple the range for the same weight and are so  important as the power of the slinger.

Another observation is that glandes have an extraordinary performance, been their shape more important than the projectil density.

And a last one, among the many that can be done calculating ratios between the different modalities of projectile, is that the rough spherical lead projectiles can compete with glandes if these are thrown not well oriented point-first.

This takes us to the study of the throwing techniques and to the Yurek´s graphs to study the more suitable position. But that will be another day, after a rest of at least one month or so :D, when the secret to get the possible new Guiness record with lead (around 1000 m) will be eventually revealed  ;D.

Title: Re: The physics of the sling
Post by JohnHorn on Jan 5th, 2005 at 5:09am
Excellent in-depth writings you guys have here. Some of it goes over my head, though some of it I understand. :)

Now my question:
What is the likely and unlikely exit-velocities of a Balearic slinger with a 1-mina stone (436 gram) - also one must take into account that these are not regular people that have never slung before, they have probably slung so much to the extent that their arms have become especially adapted to it, as well as strong for the purpose. Even so, I don't expect a Balearic slinger to sling a 436 gram smooth stone with 100 m/sec. ;)

Also, what would the likely range be for a Balearic slinger?
I'm working on a realism modification for Rome:Total War. And we need to know what characteristics should apply.

I know Balearic slingers slung more for accuracy, and less for range as they used stones from the beginning, while the Rhodian slingers slung more for range using their lead glandes. Also, at what point in history did the Balearic slingers start using lead bullets? I know that Diodorus says they used 436 gram big stones in 311 BC.

Basically, I would just like to know the ranges for Rhodian lead slingers and 436g Balearic slingers respectively. Based on your experiences and guesswork of course. :)

Leshatt na'imot!
That's "for a good year" in Hannibal's own language

Title: Re: The physics of the sling
Post by Paul Bardunias on Mar 28th, 2005 at 4:40pm
Let me commend all of you on this site- very informative.  

I have a question that you might be able to answer.  Doesn't a Glans shaped projectile need to spin in a fashion akin to a rifle projectile in order to fly true?  If it is not spinning along its long axis, the shape seems to ensure that it will spin along its short axis and the same force that aids in rifling would now cause it to veer- assuming a symmetrically weighted glans.

I'm not sure how the spin would be imparted, but if it exists it probably has to do withthe release from the pouch.  Are the pouches on ancient slings different for "bullets" than for balls?



Title: Re: The physics of the sling
Post by Zwiebeltuete on Sep 23rd, 2005 at 8:38am
I began last year playing Golf and I noticed that it is not just the swing but many very important additional moves which makes the ball fly far. One very important move is the turning of the hip which might be comparable to the baseball step in slinging. Another move comes from the wrist where the club blade is turned and the club is additionally swung forward. Similar motions where the sling gets a kick with the wrist are probably also used in slinging.

Title: Re: The physics of the sling
Post by Gun on Sep 24th, 2005 at 9:45am

One very important move is the turning of the hip which might be comparable to the baseball step in slinging.

I use that method baseball step method. I call it the womens fast pitch softball throw. You get some longer ranges with it i believe.

Title: Re: The physics of the sling
Post by Rodders on Jan 9th, 2006 at 3:22pm
Almost obsessive. i have kept a diary of what works and what dont for the past three years. and in my best shots the energy starts from my legs surging up through the back, shoulders, forearm and final flick of the wrist a fair amount of passion tipped  malice i bang that shot out in a base ball come spear throw finnish. ow and hope i kill nothing but the undergrowth. ;) the point im making is for all the physics involved its still a case of skill, muscle, and hope to me.  8)

Title: Re: The physics of the sling
Post by simia on Feb 3rd, 2006 at 11:36pm
i was bord during study hall today so i came up with a  formula to calculate the speed of the projectile( not to bad for a freshman algebra 1 student) and looking for insite if it is correct.  .  then multiply the lenth of the sling, Both sides including the pouch, by pi.  you then divide this number by the time the total time it takes for the sling to make a full rotation.  this should give you the feet per second for the stone.  i couldn't get outside to get an accurate reading ( Ohio rain in febuary, suposed to snow 6 inches tomarro) but my calculations for indoors is about 90 fps but keep in mind that i just started slinging about 3 days ago so i probubly can get much higher the longer the sling and fast the swinging

Title: Re: The physics of the sling
Post by Matthias on Feb 4th, 2006 at 12:54am
Hey, Great (!) this thread got resurrected.

Simia - you are on the right track. Unfortunately, for most slinging styles, the majority of the acceleration is imparted during that last revolution. I use two styles predominantly: a single windup underhand/sidearm and the fig-8 (although I'm trying to develop a solid "Bernini" too*) During an underhand, I don't start putting enrgy into the throw until the sling is over my head, with only 180 deg left to travel. The fig-8 is similar, with most of the fancy footwork just being setup for a fast overhand swipe.

If you break down that last 180 deg further, you'll find that acceleration is usually increasing until the "snap" at release, where you spike. Velocity moves even faster. With a fig-8, I expect that I go from something closer to 10m/s up to 40-45 during the last 90 deg of the throw.

I did a quick analysis of some video a ways back and found that the timewise resolution was just too slow to work out the speeds in the last part of the throw. Durin ghte windup, 30 frames a second gives nice short steps, but the 40-70 that we are capable of ends up being too fast. You get something like 10cm, 10cm, 10cm 12cm, 80cm, where did it go ??? I'm still hoping to find/make a stroboscopic flash that can freeze the throw at (say) 200Hz steps, but no luck so far.


*note the newly named sling style... try it, you'll like it!

Title: Re: The physics of the sling
Post by bigkahuna on Feb 4th, 2006 at 5:04am
OK, How do you do a "Bernini"? ???

Title: Re: The physics of the sling
Post by simia on Feb 4th, 2006 at 10:51am
right i forgot to add in the speeding up of the last roitation and many tricks used to make the rock go faster.  i also made my formula for over headso it wouldnt work for many other methads.  how much was your high speed camera?  

Title: Re: The physics of the sling
Post by simia on Feb 4th, 2006 at 10:55am
by the way does the speed of the rock increace after you releace it (this is all from a geometry student so i mighht be missing a key componet later on in my student cureer

Title: Re: The physics of the sling
Post by Matthias on Feb 4th, 2006 at 12:20pm
No speeding up unless you have some sort of tricked out rocket assist glandes. This is a fundamental law of physics.

Most newish digital cameras, video cameras, webcams will give you 30 frames per second, but as I said, it really isn't fast enough. My attempt at getting around this is to use a long exposure (1-2 seconds) and a high speed stroboscopic flash. The other possibility is an external mechanical shutter.

(image by Andrew Davidhazy -


Title: Re: The physics of the sling
Post by Matthias on Feb 4th, 2006 at 12:22pm

wrote on Feb 4th, 2006 at 5:04am:
OK, How do you do a "Bernini"? ???



Title: Re: The physics of the sling
Post by bigkahuna on Feb 4th, 2006 at 5:02pm
Got it. :D     Thanks.

Title: Re: The physics of the sling
Post by simia on Feb 4th, 2006 at 5:34pm
a rocket assited rock interesting ;D

Title: Re: The physics of the sling
Post by DesertPilot on Aug 23rd, 2007 at 12:59pm
Are people still interested in studying the physics of the actual throw?  As someone who does this sort of thing for a living, I just couldn't resist the temptation to write a simulator.   I started with Yurek's post of several years ago, assumed the sling could be modeled as a coupled pendulum with the inner pendulum (the arm) with variable radius driven by an external torque (muscles, grunt, snort), while the outer pendulum is the sling.  Then I got carried away, added a crude Markov chain Monte Carlo procedure to optimize performance for different hand trajectories, and threw in simple graphics capability to create... RoboSlinger 1.0!  This was... way too much fun.  I'll try to attach a test run to this post.

NOTE: The hand trajectories I used during development are entirely unrealistic.  I rather doubt that for-real human beings, with actual shoulder and elbow joints, could ever throw in such a smooth spiral arc -- hence the name 'RoboSlinger'.  But this code can handle any type of throw for which one has data.  I've thought of some cheap simple ways one could photograph trajectories, measure velocities, etc., without fancy motion-capture equipment for a slinger with a reasonably flat and consistent overhand, horizontal, or underhand shot.  If anyone's interested, I can post details.  A figure-eight might be harder...

test_run_00a.jpg (176 KB | )

Title: Re: The physics of the sling
Post by Dravonk on Aug 23rd, 2007 at 4:04pm
Cool! In which system did you implement the simulation? And is it 3D or just 2D?

Title: Re: The physics of the sling
Post by DesertPilot on Aug 24th, 2007 at 1:45am

Dravonk wrote on Aug 23rd, 2007 at 4:04pm:
In which system did you implement the simulation? And is it 3D or just 2D?

I wrote it in MATLAB, and it should be fairly easy to port to other packages like IDL.  I'd be happy to send you the code if you're interested.  It could also be ported to C/C++, but that would lose the MATLAB user interface and graphics.  This version is simple 2D.  I plan to add 3D and the effects of gravity and air drag when I have a chance.  I could also imagine replacing that simple 'inner pendulum' with a full-fledged biomechanical simulation of the slinger's rotation and throw, but at that point, this would stop being a part-time hobby and become a full-fledged academic research project, and I can't imagine what funding agency would ever support such a thing.  NASA ('An Extremely Low-Cost Space Propulsion System')?  The DOD ('Robust Technology for Munitions Deployment')?  The EPA ('High-Speed Movement of Solid Debris')?  The Department of Agriculture ('A Portable Faunal Control Apparatus for Stock Managers')?   None of these alternatives seem likely :)

Title: Re: The physics of the sling
Post by Dravonk on Aug 24th, 2007 at 3:54am
Maybe it would run in Octave, too, that is a free software similiar to Matlab. I am definitly interested.

Maybe we could run the "virtual slinger" as a free software project here? I guess we have a few engineers and programmers here. Matthias made a simulator, too, didn't he? Maybe we could combine the efforts of the two first simulators to start the free project.

We could improve it over time to get it more and more realistic. The weight distribution of the arm and the strengths of the different muscles would be nice to know. But I have no clue where you might find that information.

And once we have got it realistic enough, we can put a self-evolving neural algorithm behind it so it tries out millions of different styles and tells us which style is the most effective. ;-)

(Yes, I like daydreams and high set goals...)

Title: Re: The physics of the sling
Post by Zwiebeltuete on Aug 24th, 2007 at 5:32am
There should be certainly very interesting results coming from such simulations, but I doubt I have enough knowledge to help in this area.

Title: Re: The physics of the sling
Post by wanderer on Aug 24th, 2007 at 8:28am
Desert Pilot,

Nice simulation. I think there's lots of interesting stuff to learn about the sling from examining the physics, even if some others here may not ;).

I'd be interested in the simulations you used - they sound pretty fancy, although most of the words you used seemed familiar!

Title: Re: The physics of the sling
Post by slingbadger on Aug 24th, 2007 at 10:26am
Another part of the physics of the sling is what happens after you release.
The angle and speed of the stone make a big difference in where things end up.
 A 45 degree angle launch will yield different results than a 30 degree launch.
Also, wind is a contributing factor. Iv'e deliberatly launched at an angle to winds to see what kind of curved path the stones take. Anyone familiar with a boomerang will know what that is about. I've had some interesting results.

Title: Re: The physics of the sling
Post by DesertPilot on Aug 24th, 2007 at 1:46pm

Dravonk wrote on Aug 24th, 2007 at 3:54am:
Maybe it would run in Octave, too, that is a free software similiar to Matlab...

It should definitely run in Octave.  I even had that in mind when I chose MATLAB.  If you let me know what way is most convenient for you, I'd be happy to send you the code.  (And yes, you can use it to try things like 300' slings with projectile velocities of Mach 1.2!)  I could also post the basic equations I used if anyone's interested.  There aren't very many, and people could ignore them as they saw fit.

I too have dreamed about the muscle/joint-movement/neural-network/genetic-algorithm idea to design... the Ultimate Throw!  But I tried something similar several years ago to evolve a robot walker, so I have a very good idea just how time-consuming such a project might be.  Still, I may have an idea where to look for throw measurements for baseball pitchers.  If I can find it, I'll post the links...

One thing I've noticed is that since the sling has a fixed length, it can only fit between the path of the hand and the path of the projectile in one particular way.  This means that in the absence of air drag, you can determine the complete trajectory, speed, and acceleration of the hand and sling from path information and launch velocity alone, without any other time data at all!  You could get the path information by taking a long exposure of a slinger with a white glove and a white sling pouch.  You could determine launch velocity by throwing the projectile at a projectile trap -- something like a bucket of mud -- hanging from a rope and measuring how far it swings.  In practice you'd need a good slinger with a consistent throw, and it would probably take many tries (and many buckets of mud) to get good data, but it might be worth a try.  I'll try to attach a diagram to show the camera setups for horizontal and vertical throws.  I apologize in advance for the poor quality of the art...

BothSlingers03.jpg (167 KB | )

Title: Re: The physics of the sling
Post by wanderer on Aug 26th, 2007 at 1:42am
You might also try a stroboscopic picture. With flourescent markers on the sling and the hand you should be able to manage a reasonable result by slinging illuminated by either a fluorescent light, or better maybe, a big street light.

As far as slinging at buckets of mud etc. I'm not sure many of us have had much success with ballistic pendulums, particularly if we have to back off the speed to be accurate enough to hit the thing.

Title: Re: The physics of the sling
Post by Dravonk on Aug 26th, 2007 at 9:15am

DesertPilot wrote on Aug 24th, 2007 at 1:46pm:
But I tried something similar several years ago to evolve a robot walker, so I have a very good idea just how time-consuming such a project might be.

Slightly different topic, but I am curious, how did it work? Did you actually build the walker?

Title: Re: The physics of the sling
Post by DesertPilot on Aug 27th, 2007 at 1:28am

wanderer wrote on Aug 26th, 2007 at 1:42am:
You might also try a stroboscopic picture. With flourescent markers on the sling and the hand you should be able to manage a reasonable result by slinging illuminated by either a fluorescent light...

...As far as slinging at buckets of mud etc. I'm not sure many of us have had much success with ballistic pendulums...

A flourescent light!  I never thought of that!  What an awesome idea!  I shall have to give this a try.  If all goes as planned, I'll be on vacation in Maine next week -- a land full of many small smoothly rounded rocks -- which should allow some opportunity for experiments.  Do you have any recommendations for a suitable (and inexpensive) digital camera?

I finally ran across some of the old posts about ballistic pendulumns, so I see what you mean.  I'll still try it myself, on the off chance that I might, in my naive incompetence, stumble upon some brilliant idea that greater minds than mine have missed, but I'll probably just add to the long list of Embarassing Experiences I've managed to accumulate over the years :)

Title: Re: The physics of the sling
Post by DesertPilot on Aug 27th, 2007 at 1:52am

Dravonk wrote on Aug 26th, 2007 at 9:15am:

DesertPilot wrote on Aug 24th, 2007 at 1:46pm:
But I tried something similar several years ago to evolve a robot walker, so I have a very good idea just how time-consuming such a project might be.

Slightly different topic, but I am curious, how did it work? Did you actually build the walker?

Alas, like all too many things in life, this idea never got past the simulation stage.  The biggest problem turned out to be modeling what happens when a foot hit the ground.  If I made the simulated ground too soft, it would sink under the robot's feet like a sagging trampoline.  If I made it too hard, the simulation could go unstable and shoot the robot into the air.  It was annoying... and also rather hilarious.  I could send you this code too, but this might be a complete waste of your time, because it was written in C++ using MFC for the graphics, and no one on Earth, including me, will ever be able to get the darn thing to run again.

Slings are more fun!  I just tried out some of the RoboSlinger results with my long-suffering indoor sling, and they seem to work.  But I'll save that for a later post 'cos I've already written too much this evening.  I have got to get that 3D version with gravity written!  Maybe next week...

Title: Re: The physics of the sling
Post by Dude on Sep 5th, 2007 at 10:59pm
***Update on the attached file- added 1 & 2 oz then added weight in grams to the oz listings for the     varous columes

I finially joined the Form and decided to add my 2-bits to the subject 8-)

I've attached a Zipped PDF file that I think does a fairly good job at helping one to see just what a Sling is capable of doing along side say...a standard pistol cartridge. I beleave that this should represent standard store bought loads.

Just a little background on the Calculations used

    Km/h = 1.6*MPH
    ft/sec = MPH*5280/60^2(60 squared)
    5280 ft per mile
    m/sec = km/h*1000/60^2(60 squared)
    1000 meters per km

    60^2(squared) gets the calulations down to the second

    Amount of Kinetic Energy = Weight of the projectile*Velocity in ft/sec^2(squared)/Constant

    Constant = 32.163^2(squared)*1
    Acceleration of Gravity = 32.163 ft/sec

Normally in the constant you will see instead of the number "1" for 1 pound, you will see the number "7000" because there are 7000 grains to the pound & bullet weight is in grains. Since that seems to be way too small of an increment of measurement for Sling Projectiles, I just left it at 1 pound.

I'm looking for ways to improve this, or add to it, or correct any mistakes

I hope this is of use to you; (13 KB | )

Title: Re: The physics of the sling
Post by Dude on Sep 6th, 2007 at 2:48pm
Would this apply? :-/

I been thinking about the pressure that is being applied to the bottom of a high heel, worn by a lovely women of course! Would this also apply to a projectile at it's point of impact for a given amount of kinetic energy as measured in foot pounds?

weight in pounds/area in square inches

100# petite woman with with 4" heel whose tip is .25 square inches = 1600 PSI
110# petite woman with with 4" heel whose tip is .25 square inches = 1760 PSI
120# petite woman with with 4" heel whose tip is .25 square inches = 1920 PSI just short of a TON

Looking at these numbers, I think I've lost any interest in having in having one walk on my back with heels. It would be very embarrassing explaining to the medical stall in the emergency room how I got all of the punture wounds in my back and vital organs ;).

If this would apply I have attached a Zipped PDF file that list the PSI for a given weight of 2 pounds to over 800 pounds for an area of .25 square inches or .0625 square inches; (10 KB | )

Title: Re: The physics of the sling
Post by curious_aardvark on Sep 7th, 2007 at 11:29am

Looking at these numbers, I think I've lost any interest in having in having one walk on my back with heels

lol that implies you'd thought about it before though ;-)

A slight play on words: The slinger of physics.
Gives you person who throws doctors around - I volunteer my gp who in the words of the specialist at the hospital is: 'f***ing useless !'

Title: Re: The physics of the sling
Post by Dude on Sep 23rd, 2007 at 5:14pm
Just to let you'll Know that I uploaded an update "Energy02" in reply #63 that compares differnt size projectiles and speed to varous sizes of pistol cartridges 8-)

Title: Re: The physics of the sling
Post by Trebuchet on Oct 3rd, 2007 at 9:44pm
You people never cease to amaze me.  Not only do you sling, but you apply the scientific method of research to your slinging.

In most of the technical threads I am WHOLLY out of my depth, but I enjoy reading them, if only to see the quality and intelligence of the people who contribute.

(No, I ain’t a bloody toady.  Just amazed, that’s all.)

I do have one idea for the “compound sling” forum I want to think about before I post.  If it works it might solve a few difficulties.


Title: Re: The physics of the sling
Post by kellymcdman on Oct 12th, 2007 at 1:01am
how do you quote part of what someone posts? cant figure it out.. anyway, as far as flashing sling ammo goes, has anyone been to a dollar store and bought one of those rubber balls that have a built in led flasher that blinks when you bounce it? might be a good start to blinking ammo. fun to launch at night, and go find too.. :)

Title: Re: The physics of the sling
Post by OrangeDuck on Oct 12th, 2007 at 1:04am

kellymcdman wrote on Oct 12th, 2007 at 1:01am:
how do you quote part of what someone posts? cant figure it out..

I really just wanted to do that to spite you  :D Basically what you do is press the quote button, and when ou go to the page where you write your response, what you quoted is within two codes which are within brackets. Just erase the part you don't want to be quoted.

Title: Re: The physics of the sling
Post by Dravonk on Oct 12th, 2007 at 1:05am

kellymcdman wrote on Oct 12th, 2007 at 1:01am:
how do you quote part of what someone posts? cant figure it out..

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