Can bands be too thin?

Have you tryed cutting some bands from a different peace of thera black. It might be possible that you just hit a bad spot even in the higher quality material it happens sometimes. Just a thought.

That's weird! Hmmm maybe because of a weak point or so. The TB should be good stuff. It's pretty new and from a

good batch. Friedrich

joseph_curwen, on 26 August 2010 - 07:34 AM, said:

Sorry, forget about it, i just read your other excellent post aboout longevity

perhaps you are over-drawing it during your tests? If you are only intending to use this for your daughter, perhaps you should test fire at a similar draw length.

I think the speed people use black to achieve might best be achieved with a longer strand of material, with less tension on the material. i'm just thinking in type here, but perhaps a more efficient form of speed would be achieved by an applied force on an object over a longer distance and time, rather than a sharp applied force over a shorter distance. hence the speed of butterfly shooting. perhaps the black theraband is reaching it's limit where your normal gold theraband is at it's optimum pull. for you, it is die-cut, so black might not work for you and you might have to hand-cut longer strands for yourself. but the situation - in my eyes - seems perfect for your daughter.

i haven't tired your bands, or any flat bands (other than some old botched up blue thera i got after breaking an ankle), but that sounds appropriate to me.

maybe you should just give a set to your daughter and see how long they last.

I am indeed over drawing them. I made the bandset for BB shooting, but you know the natural tendency is to draw till they stop. If your strength is much greater than the bands then you risk tearing them asunder. I originally posted this before I did my how-does-draw-strength-affect-accuracy post and now I realise that there is no point making bands so light that they are at near optimimal elastic efficiency for BBs because:

• Decreased draw strength has diminishing returns of accuracy as bands get super-light;
• They're not much faster - pouch weight starts to become significant; and
• They don't last as long.

I've shot several weights and brands of natural latex exercise bands: 0.35mm, 0.38mm, 0.50mm, 0.56mm, 0.65mm, 0.67mm. The common theme was that lighter bands always tore first. Tears once started, propagate quicker. Only thinnest bands tore from the centre. What I am concerned about is if we continue going thinner and thinner using Thera-band Blue or even Green, these bands are 0.30mm and 0.25mm thick respectively and the chance of a tear is much higher, especially when shooting heavier shot. Sure you'd be using greater widths, but if there is a defect or the bands were stretched unevenly, it may go at full stretch.

Also, with a thinner band you end up with fairly wide widths to deal with.

Dan, it is the speed that kills your bands.

If you go higher than 80 m/s, the bands will start to tear lengthwise. It always happens. If you go higher than 100 m/s, the band life is very short indeed.

My advise is to use heavier, larger ammo. I think that even a small child would be more happy with 10 or 12 mm marbles as the pouch is much easier to hold with a bigger ball inside.

Hi Dan,
it is true ,High speed kills bands fast. Also there is the manufacturing process. I have used a microscope on thin sheets of latex and they invariably have little air bubbles in them. these are weak spots as are spot marks caused by small foreign objects in the rubber that gets imbedded when they extrude sheet goods. Also when cutting latex or any rubber ,I use the "line marks" and cut with the grain,but then again I have cut against the grain and had them last pretty good. With rubber,I have found,it is always a surprise. Flatband

I'm going to bury this information deep down here in a comment in a long dead blog topic because that I am about to write is out there on the bleeding edge, a bit kooky and not at all thoroughly thought out. it's only intended for the technically inclined. Brace yourselves, lads.

I have a theory about why thin bands are faster. Actually, there are three theories, all of which will contribute in interrelated ways.

(1) Internal radial shear stresses

Rubber has a Poisson ratio of nearly 0.5. That means that rubber cannot change in volume when it is compressed or elongated. Instead, the rubber temporarily changes shape as long as the stress force is applied. For example, a stretched band will get thinner and narrower. That temporary conformational change is what gives rubber its strength. However, the uniaxial (single direction) stress of elongation become more triaxial (all three dimensions) in nature when the ratio of band length to cross section (specifically the average distance to the side) decreases. As rubber resists volume change, it also resists elongation at low ratios of band length to cross section.



The chart above shows how Young's modulus (E) is modified (E'/E) as a function of the ratio of distance to edge vs length of band. They used flat round sheets attached at their flat sides so they refer to length as 'thickness' and distance to edge as 'radius'. I believe the chart to be incorrect insofar as it should intercept the origin, by definition. Nevertheless:

• For short bands and for solids and thick walled tubes the effect will be greater as the distance to edge vs length is greater
  
• At the small values of a/h in slingshot bands, the slope of the modulus modification chart, approaches zero
  
• Note however that this chart is valid only for a relatively lower elongation than slingshot bands at full draw; within the inelastic transition, the effects will be much more pronounced.
  
• Note that significant internal stresses exist not only within solids, but within thick walled tubes. A tube is generally said to be thick walled when the ratio of the external diameter of the tube to the diameter of the internal hole falls to less then something in the order of 20:1 to 10:1.

This explains a some strange phenomena, such as why bands under high tension will split longitudinally before they split across the band, as long as there is nick or weak spot in the edge to form a cavitation failure stress riser/ initiation point.

For reference, here is a chart that shows the ratio of the average distance from a point within a band to the edge over the resting length versus the resting length of the band. For flat bands of reasonable width, it is not significantly dependent on the width of the band. The colour codes relate to Thera-band Gold, Silver, Black and Blue. Most chin draw bandsets are in the region of 150mm to 200mm long as tied.



Note that I previously had a hunch that the speed of a flatband was related to the ratio of the cross sectional area to the periphery, i.e. mathematically, the band thickness. My new understanding is exactly the same for flatbands, but penalises solids more. The only thing to note is that there is relatively little effect except at extraordinarily high elongations.

(2) Thermodynamics, or the speed of propagation?

If the effect of thickness on elasticity is not the cause, then is it some property of elastic itself?

Thin bands are known to reach an equilibrium state faster than thick samples. In dynamic (vibratory) measurements, some thicker samples never reach an equilibrium state. I don't think this is a thermodynamic effect, because the contraction of rubber is known to be an adiabatic process. However, it is also known that the speed of propagation of a wave in rubber is relatively slow. Therefore, it may be due to the speed of the elongation change propagating through the rubber as a result of interaction with the aforementioned internal radial shear stresses.

(3) Force/Inertia

I think the reason why narrow bands are faster has more to do with elongation than any property of rubber itself. Elongation is proportional to force and cross sectional area of the band. Therefore, lighter bands will elongate more by a given force. A band that is drawn out more will store more energy than a band that is drawn out to a lesser elongation. It will be less efficient in terms of energy out/in (resilience) and will suffer more mechanical damage (hysteresis), but will still deliver more energy on contraction for the same mass (inertia). Therefore, it will shoot faster.

Be careful when drawing! A thin band, especially a tapered band concentrates great tension forces in a small area. On a tapered band, this will be just in front of the pouch tie and the band can literally tear itself apart from the inside due to radial shear stresses. Initiating as a hole, it can quickly propagate up the band until it finds a place where it can pass to the side of the band and then snaps. This is the hole I noted in the original post.

Back to the original question, can bands be too thin? Ignoring the risk of band failure, then thinner bands will shoot faster. However, according to my theory, there should be limitations:

• When bands are maxed out (can't pull any longer) then thicker bands and thinner bands will offer similar speeds (observed?)
  
• When a heavier draw band is drawn to the same elongation then it should shoot a common dead mass faster because of the greater potential energy (yes, observed)
  
• When the dead mass is a greater component of total inertial mass, then the advantage of the light bands is less (yes, observed)

So that would say that thin bands will offer a greater advantage when shooting light projectiles from a light pouch and less advantage shooting with a heavier dead mass. For any given dead mass, you should see diminishing returns in increased velocity from thinner bands, while duly life falls precipitously.

It seems to me more investigation is needed. Obviously, I need to chart the velocities of bands of various thickness, but before I commit to doing a lot of new shooting tests, I have done some desktop number crunching.

I want to see if different thicknesses of Thera-band have different tensile properties.

Taking thickness measurements previously provided by Tex-shooter and force-elongation data provided by Thera-band, I have a chart of the force required to draw out a length of TB to 250% (e.g. resting length of 200mm drawn to 700mm). This is relevant because most people shoot at around 300% elongation. These force figures were carried out be researchers under ASTM conditions.



I normalised the other bands against TBG



This chart above shows that between 50% and 250% elongation, all thicknesses follow the same profile (none have reached the elastic transition)

Below, I have plotted the force required to draw a band to 250% elongation vs the thickness.



I see almost a straight line. The line must intercept the origin, as a band of zero thickness would require no force to draw it. The chart therefore shows a slight curve.

Let's see if we can replot the data normalising for tangential modulus of elasticity between 200% and 250% elongation or Young's modulus (E).



There is some spread due to the measurement of the band thickness, measurement of tension, conditions and/or the latex composition. Anyhow, I can see a relationship (whether it's statistically significant or not is another matter.) Thinner bands seem to be slightly easier to draw. This is consistent with my theory (1) above.

In case you want the data:

Colour Thickness (mm) Force@250%Elo(N) E(Mpa)
Gold 0.635 178 2.0
Silver 0.554 113 1.6
Black 0.381 78 1.3
Blue 0.305 60 1.6
Green 0.254 42 1.1
Red 0.203 31 0.9
Yellow 0.152 27 1.3

FYR, an independent study Santos et al, Nov./Dec. 2009 Mechanical evaluation of the resistance of elastic bands Rev. bras. fisioter. vol.13 no.6 São Carlos disagrees with me about the correlation of Young's modulus to thickness.



Note that they worked on die cut samples and not full widths and the results are presented at only 100% elongation, because the authors are sports scientists and when used in physiotherapy, Thera-band elongations rarely exceed 100% elongation.

Colour Force@100%Elo(N) E(Mpa)
Gold 12.1 2.75
Silver 8.6 2.43
Black 5.2 2.22
Blue 4.3 2.47
Green 3.7 2.31
Red 2.7 2.28
Yellow 2.4 2.56
Tan 2.0 2

I also suspect that they have incorrectly calculated E, using a secant modulus rather than tangential modulus.





I still see some correlation, but it's statistically tenuous, given standard errors of E in the order of +/-0.2

Note that the slope is less and their measurements are generally higher, consistent with secant modulus calculation at a lower elongation.

Above I wrote: This is relevant because most people shoot at around 300% elongation. Actually, I suspect many people shoot TBG at around 430% elongation where the bands stop.