# "Force Wall" Effects in Slingshot Operation



## boby

I've attached a more detailed discussion. A summary of that follows:

The latex rubber used in slingshot bands is not an ideal spring-- there is what I refer to as a "force wall" that occurs when one stretches the bands more than about 5 times their unstretched length. In the force wall region, the bands become suddenly harder to pull back, almost like there is a mushy wall blocking further pull. What is not generally recognized is that *in this force wall region, there is relatively inefficient use of force for storing energy *in the rubber bands compared to away from the force wall. In fact in the extreme case, in which a force vs. pull-distance curve rises nearly vertically in the force wall region, one can pull with increasing force but get no more energy stored in the rubber. The underlying reason for this is that the energy stored in the the rubber bands is force times distance pulled, which is the area under the force vs pull-distance curve. A nearly vertical force slope exhibits an increase in force with no increase in this "stored energy" area. Of course we want to store as much energy as possible in the rubber bands, so that there is greater energy in the projectile once the pouch is released. So it is potentially sub-optimal to operate in the force wall region. Opposing this tendency, is that it it is beneficial to operate at large stretches, as this reduces the mass of the rubber bands, which would increase projectile speed. Hence it is usually best to operate near or only slightly into the force wall region. See the attached document for a graphical picture of force inefficiency in the force wall region.

It turns out there are two things that can be done to mitigate the effects of the force wall. The first approach is to use "tapered" or "pseudo tapered" bands (which softens the force wall). ("Tapered" bands are bands that are wider or thicker near the fork and taper to a smaller cross-sectional area near the pouch.) The second approach is to use stiffer (& therefore heavier) untapered bands (e.g., wider cuts for flat bands, or 1745 instead of 2040 for chinese tubes). In the attached, I give calculated results for latex sheet flat bands (from Hygenic Corp.), and for 1745, 2040, & 2050 chinese tubes (from Dankung). Either of these two approaches for a given band type can give similar projectile speeds AT FIXED FORCE for optimum designs, when the force for pseudo-tapered bands is high enough to involve the force wall region. However, if at lower forces one is NOT in the force wall region, pseudo-tapered bands have LESS energy stored in the rubber bands than untapered, and thus will always have lower projectile speeds. On the other hand, when pseudo-tapered bands result in more energy stored in the bands than untapered bands at the same force, it is NOT automatic that higher projectile speeds will result, because pseudo-tapered bands also weigh more than the corresponding untapered bands, which is detrimental to speed.

Several months ago in this slingshot forum I described a physics-based model that treated the slingshot rubber as an ideal spring. This model did not show a benefit for tapering under any circumstances, which a number of readers of this forum assured me was not their experience. When one looks at the energy stored in the rubber, as described above, it becomes apparent that the force-wall region (which only occurs for our actual non-ideal "rubber band springs") is a critical aspect for having beneficial effects from tapering. So in a revised physical model of slingshot operation, I calculate the energy stored in the rubber bands from the actual area under the force vs pull-distance curve, and do not assume an ideal spring. In this new model, tapering can be beneficial, but only for forces in the force wall region.

In the more detailed attached discussion, I compare calculated projectile speed for the 4 types of rubber mentioned above, at a variety of fixed forces, for both untapered and "pseudo-tapered" bands. ("Pseudo-tapered" bands here are considered to have on each arm of the slingshot, two bands connected to the fork joined to a single band connected to the pouch (with all being the same rubber type); I use this concept for the flat bands as well as the Chinese tubes.) The results show that pseudo-tapered *flat* bands are typically 2%-4% faster than the best *tube* choice AT FIXED FORCE and draw length, but also that untapered, but wider, flat bands can match or even slightly exceed the best pseudo-tapered flat band performance. An advantage to the untapered but stiffer band approach is that one operates at reduced stretch factor, further away from and less aware of the force wall. I prefer that feeling for target shooting. 1745 tubes were found to be typically only slightly faster than 2040 tubes (e.g., 2% or less) for optimal configurations and at constant force and draw length.

One needs to be aware of the force wall before comparing slingshots with different rubber. The force wall for flat bands is at about 7% higher stretch factor than for tubes. If one sets up the tubes to have the same unstretched length and draw length as the flat bands, one would be deep into the force wall region for the tubes and potentially wasting (e.g.) 5 pounds of force. In any case, there can be no meaningful comparison of bands if it is not done at constant force. Someone may say that "Brand X" flat band rubber is 5% faster than "Brand Y", but in fact these could even be the same rubber that just happens to have one type being (nearly unnoticeably) a few percent wider or thicker, and therefore having greater draw force. I encourage anyone making comparisons to spell out their force measurements.


----------



## SHTF Slingshots

So....If I pull my bands to roughly 500% stretch, they no longer store energy efficiently?

All I really got from that wall of text.

Thanks for taking the time to research this and write it all out.


----------



## LVO

I appreciate all the effort. A LOT of info in there.

but i think my brain pulled a muscle reading it. I'll try again after a good night's rest.


----------



## treefork

How does " force wall" relate to hysteresis ?


----------



## boby

Shtf Slingshots said:


> So....If I pull my bands to roughly 500% stretch, they no longer store energy efficiently?
> 
> All I really got from that wall of text.
> 
> Thanks for taking the time to research this and write it all out.


On the contrary, at roughly 500% stretch, the energy stored per pound of pull actually peaks (which is optimum). The problem is if you go to higher stretches the pull force is less efficient for storing energy in the bands, which enables the work-around of pseudo-tapering to be effective. Look at Figs. 2 & 6 in the attachment.


----------



## Charles

Since purely analytical approaches to slingshot matters seem so often to go awry (witness your comments about pseudo-tapered bands not giving higher velocities), it would be very interesting to see how your model compares to a great deal of experimental empirical data performed on a good test bed to eliminate human variables.

Here is one set of experimental data that I posted some time ago. The tests were done by me by hand, and not on a mechanical test bed. But I tried to be careful to control the variables as well as possible. To take just one simple example with which I am very familiar, doubled Alliance 105 bands do not in general yield as high a velocity as half doubled Alliance 105 bands.

http://slingshotforum.com/topic/11134-higher-draw-weight-does-not-always-result-in-higher-speed/?hl=%2Btaper+%2Bcutting

Since the chart I posted in that discussion seems to no longer appear, I will reproduce it here:









All of these tests were taken at the same draw length, and the draw weights were noted. I would also like to note that the Alliance Sterling #64 bands used for the braided bands are as far as I can determine made from the same material as the Alliance Sterling #105s.

Note that the tapered 105 consistently outperformed the straight 105 by a significant margin until very heavy ammo was used, and that the tapered 105 had a much lighter draw weight than the straight 105. Also note that half doubled 105 outperformed both the tapered and the doubled by a significant amount, straight across the board, and at significantly less draw weight than the doubled 105.

Also note that the braided #64 rubber bands outperformed the doubled 105 bands across all ammo weights, and at less draw weight.

Cheers ..... Charles


----------



## Rayshot

What I am curious about is; Are these findings from calculations or all of the findings from a relatively accurate practical exercise on all the band configurations?


----------



## boby

treefork said:


> How does " force wall" relate to hysteresis ?


Not related, except that if you hold a draw a long time, there is more hysteresis at higher stretch factors than lower. However Fig. 8 of the attachment shows that force drift for a held draw (a form of hysteresis) is the same for stretch factors of 4.5, 5.0, and 5.5 and is larger than for stretch factors of 3.5 or 4.0. The force wall begins just above a stretch factor of 5.0, so whatever hysteresis there is at a stretch factor of 4.5 is for a region away from/below the force wall.


----------



## boby

Charles said:


> Since purely analytical approaches to slingshot matters seem so often to go awry (witness your comments about pseudo-tapered bands not giving higher velocities), it would be very interesting to see how your model compares to a great deal of experimental empirical data performed on a good test bed to eliminate human variables.
> 
> Here is one set of experimental data that I posted some time ago. The tests were done by me by hand, and not on a mechanical test bed. But I tried to be careful to control the variables as well as possible. To take just one simple example with which I am very familiar, doubled Alliance 105 bands do not in general yield as high a velocity as half doubled Alliance 105 bands.
> 
> http://slingshotforum.com/topic/11134-higher-draw-weight-does-not-always-result-in-higher-speed/?hl=%2Btaper+%2Bcutting
> 
> Since the chart I posted in that discussion seems to no longer appear, I will reproduce it here:
> 
> 
> 
> 
> 
> 
> 
> 
> VelocityBandWeight.jpg
> 
> All of these tests were taken at the same draw length, and the draw weights were noted. I would also like to note that the Alliance Sterling #64 bands used for the braided bands are as far as I can determine made from the same material as the Alliance Sterling #105s.
> 
> Note that the tapered 105 consistently outperformed the straight 105 by a significant margin until very heavy ammo was used, and that the tapered 105 had a much lighter draw weight than the straight 105. Also note that half doubled 105 outperformed both the tapered and the doubled by a significant amount, straight across the board, and at significantly less draw weight than the doubled 105.
> 
> Also note that the braided #64 rubber bands outperformed the doubled 105 bands across all ammo weights, and at less draw weight.
> 
> Cheers ..... Charles


Charles,

I want to comment from two different angles. First, to be clear, when one uses the actual pull force vs draw curve to get the stored energy, there are times when pseudo-tapering wins over untapered for speed, and times when it doesn't. I'd be happy to compare speed calculations with your measurements or someone else's, but I can only do that for 2040, 1745, and 2050 (for which I have force and mass measurements). In addition to the data you provided, I would also need to know the draw length and the unstretched lengths of each section of rubber (e.g., the 1-band and the 2-band unstretched lengths), and the mass of the pouch.

The other angle for commenting has to do with a natural and appropriate suspicion for "theoretical calculations". A significant part of what I reported on had much less theory involved than a speed calculation-- it just looked at the force curves and noted that their shape led to less stored energy in the rubber when the forces were in the force wall region. See figures 3 and 4 of the attachment for a graphical view. This is a qualitative finding requiring little assumption and drives when tapering can be effective or not.


----------



## boby

Rayshot said:


> What I am curious about is; Are these findings from calculations or all of the findings from a relatively accurate practical exercise on all the band configurations?


The speeds are from calculations, not measurements. But there's a qualitative effect of force inefficiency that can be seen simply from force vs draw length measurements, which should thus provoke less suspicion than speed calculations. See especially Figures 3, 4 and 6 in the attachment. The relative inefficiency of forces in the force wall region to store energy in the rubber bands enables pseudo-tapering to sometimes be faster than untapered.


----------



## LP Sling

As a structural engineer I liked very much this study


----------



## Charles

You are attempting to measure "stored energy" by elongation of the bands. But that is not a good measure, in general.

Hooke's law, and variants of it, apply only for relatively small forces. Any real life standard stress/strain curve always shows a fall-off at some point ... all real elastic material has an elastic limit. Beyond that limit, the strain (elongation of an elastic band) begins to fall off. This is not new.

For example, look here:

http://en.wikipedia.org/wiki/Hooke's_law

You characterize that as the "force wall" ... all that is happening is that the band is reaching its elastic limit ... the point at which Hooke's law begins to break down. For most latex based material of the sort used in slingshots, when the band is stretched to about 5 times its original length, its ability to stretch further falls off rapidly until it breaks. Some material will stretch a bit further than 5 times before reaching the elastic limit, some will stretch less. This is not a new phenomenon.

For slingshots, what most of us are interested in is the delivered energy ... that is, the energy available to propel the ammo. The best measure of that is to look at velocities of ammo of varying weights.

For slingshot appropriate ammo, and slingshot appropriate draw weights, I will be willing to wager that pseudo-tapered bands will almost always deliver more energy (as measured by ammo velocities) than either single or fully doubled bands.

Cheers ..... Charles


----------



## boby

Charles said:


> You are attempting to measure "stored energy" by elongation of the bands. But that is not a good measure, in general.
> 
> Hooke's law, and variants of it, apply only for relatively small forces. Any real life standard stress/strain curve always shows a fall-off at some point ... all real elastic material has an elastic limit. Beyond that limit, the strain (elongation of an elastic band) begins to fall off. This is not new.
> 
> For example, look here:
> 
> http://en.wikipedia.org/wiki/Hooke's_law
> 
> You characterize that as the "force wall" ... all that is happening is that the band is reaching its elastic limit ... the point at which Hooke's law begins to break down. For most latex based material of the sort used in slingshots, when the band is stretched to about 5 times its original length, its ability to stretch further falls off rapidly until it breaks. Some material will stretch a bit further than 5 times before reaching the elastic limit, some will stretch less. This is not a new phenomenon.
> 
> For slingshots, what most of us are interested in is the delivered energy ... that is, the energy available to propel the ammo. The best measure of that is to look at velocities of ammo of varying weights.
> 
> For slingshot appropriate ammo, and slingshot appropriate draw weights, I will be willing to wager that pseudo-tapered bands will almost always deliver more energy (as measured by ammo velocities) than either single or fully doubled bands.
> 
> Cheers ..... Charles


I don't assume Hooke's law or the shape of the force vs draw curve. I use the measured force vs draw curve, and no matter what the shape of this curve, the area underneath it is the stored energy-- fundamental physics of energy being force x distance.


----------



## Arturito

Rubber is a non lineal elastic (deviates from Hooke law), practical ss elongation goes deep in non linear region, tapering makes the model more complex as there are infinite different sections in a different elongation states which also has different hysteresis losses (I am not denying a numerical model doesn't give some approximation, I did a computer model with finite elements and integration), for me it is all about experiencing with different setups, you can easily recognize which is better or worse even without a crony ...

Cheers

Arturo


----------



## Charles

boby said:


> I don't assume Hooke's law or the shape of the force vs draw curve. I use the measured force vs draw curve, and no matter what the shape of this curve, the area underneath it is the stored energy-- fundamental physics of energy being force x distance.


I never suggested that you Assumed Hooke's law ... you conducted the standard stress/strain experiment which is used in elementary physics labs by students to verify Hooke's law. What I did say is that the phenomenon which you want to label as "Force Wall" is the very standard observation which results from approaching the elastic limit of real materials.

Let me approach this matter from a slightly different way. You want to use "draw weight x distance" as a measure of the energy stored in the band. But of course this is a very crude approximation, as the final force is not applied over the whole distance ... the force at the beginning is 0 and increases (perhaps linearly, but probably not) until the final position. But let us leave that aside. Since in my examples, the original band length was the same for the entries and the draw length was the same, using your approach we can take the draw weight as an estimate (within some constant multiplier) of the energy. We can calculate the output energy in each case since we know the velocities of the projectiles and their weights. So we can get some estimate of the relative efficiency of the various arrangements by dividing the energy of the projectile by the draw force in each case. I have done the math for you, and here are the figures.

Relative Efficiency

Band  3/8 steel .46 cal lead .56 cal lead
52 gr 144 gr 270 gr

Tapered 105 .70 1.49 .78

Straight 105 .47 .99 .61

Tapered Doubled .43 1.01 .63

Half Double .28 .66 .42

64 Chain .28 .58 .34

Straight Double .18 .39 .29

So the tapered 105 was clearly more efficient than the straight 105, for all ammo weights. The half doubled was more efficient than the straight doubled, for all ammo weights. And the straight doubled had the lowest efficiency of anything.

I will say once again that high draw weight at a fixed draw length ("high stored band energy" to use your rather misleading way of putting it) does not correlate well with ammo velocity ... it does not correlate well with delivered energy.

I find that what slingshot shooters are most interested in is getting fairly high velocities with relatively light draw weights. Most slingshot shooters use a draw length of 30-40 inches. Most slingshot shooters use ammo weights between 50 and 200 grains. Most do not want a draw weight over 15 pounds, and would prefer quite a bit less. Most want a velocity around 200 fps. By those measures, and in those ranges, pseudo tapered bands will outperform singles, according to simple empirical tests.

Cheers .... Charles


----------



## crazyslingshot

profound research, It's the Physics paper


----------



## Popcorn

So, does any of this relate to the primary recapitulation of the stored 10X hyperbolic stretch factor which normally occurs during the latex vulcanization process, if it occurs in the final phase of the Lunar cycle?

Or not?


----------



## Charles

Popcorn said:


> So, does any of this relate to the primary recapitulation of the stored 10X hyperbolic stretch factor which normally occurs during the latex vulcanization process, if it occurs in the final phase of the Lunar cycle?
> 
> Or not?


Maybe ... but only on Tuesdays.

Cheers .... Charles


----------

