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Hysteresis: Sapping Your Energy

Bands snap back with less force than it took to pull them. Latex and other elastics are are not like perfect springs. Some of the energy you put in drawing a band is wasted. It's primarily about internal friction and the energy is dissipated as heat, there's a little tearing going on, and a few other things, but the net effect is that quite apart from losses due to inertia of the bands and air friction, bands simply don't return as much energy as you put in.

To illustrate this, look at the chart below. I rigged up an 8" strip of 1" exercise band and loaded it with weights taking note of the elongation and then measured the elongation again as I took the weights off. The blue band represents the loading process which is like drawing the band, and the red band represents unloading, which is like shooting it, only without the effect of air friction (and some internal friction when contracting at high velocity, i.e. reality is worse still).

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You can see that the lines do not overlap. In fact, the contraction line is lower, which means that the contraction force is not as strong as the draw force. The bigger the difference, the worse it is. If you calculated the area of the gap, that's the energy lost. Here it's not too bad, but already a few Nm (a few foot-pounds in ordinary lingo). Compare the area under the red line with the area under the blue line; that's the band's efficiency.

It's worst just after the release. That's not good for a shooter, it's effectively a bit of let-off in the middle of the shot. So you're pulling hard and till your hand shakes and then you release the pouch, but then it falters. In car terms, it's almost like a flat spot in your engine performance as you accelerate away from traffic lights. Anyway, the pouch is falling and it actually dips more because it takes longer and so accuracy slips a bit too.

Yea, hysteresis is the enemy. I was on a mission to squash it and tried out different bands.

Thinner Bands and a strange twist

I think it was Jörg who explained Hysteresis most succinctly. He said that these inner frictions were caused by elastic molecules (let's not get into cross-linking here; the principle is sound) interfering with each other within the band and that the air doesn't so surface molecules had less interactions and worked with less friction. Therefore, thinner bands will always have less friction and the ideal band was as thin as possible so long as it could hold together.

I believed this and I still do, but here's where it gets funky. When I did the tests on three different bands of 0.69mm (XF-1065), 0.53mm (XF-1050) and 0.35mm (XF-1035) of identical rubber compound, the results were all over the place.

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The middle band looked the best and the others were worse.

How you draw a band makes a big difference

I rearranged the charts and quickly realised that the dominant determining factor was not how thin the bands were but how long they had been stretched to. The band that had been stretched modestly was the most energetically efficient, the one that had been stretched just into the elastic limit transition was markedly worse and the band that had been stretched deeply into inelasticity was so distressed that it lost almost a third of its contraction force before it had contracted enough to get its act together.

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The obvious conclusion should be that one shouldn't draw a band past the point where it begins to stiffen up.

However it's not that simple. Not by a long shot.

My head's going to explode!

You also have to take into account the total energy stored by over-elongation, which comes at no extra inertial cost. If you constructed a band with 22lbs draw using less elastic and pulled it further, it would be less efficient but there would be more force and more distance hence more energy put in than an equivalent band with 22lbs draw but more elastic under less strain. The curves are so complex and have so many non-linear inputs that it's getting beyond my math skills to forecast the velocity from a given bandset, mass and draw. There are other inputs like how long the band is held - not even that, the speed curve and pause of the draw and the speed of contraction - it's just impossible for me to do all that. I'll have to do it the traditional way with a Chrony and trial and error.

I'm going to press on though and see what empirical but qualitative things I can learn.

New possibilities are opening up

This is a fascinating subject. I've just scratched the surface, but the hole I have made has given me a glimpse of some strange possibilities. I've done lots of modelling as a scientist (biomedical) and as a financial guy and I realise natural systems like this can have multiple local maxima. That means for example, if you take an off the shelf fork and band set and it is entirely possible that different shot weights can be most efficient in terms of velocity or kinetic energy depending on how far you draw it, how fast you draw it, how long you hold it for, whether it is a smooth or jerky draw, the temperature, humidity and pressure density at the time and a myriad of other interrelated factors.

The way you deal with something as complex as this is you cut it into manageable chunks like a sushi chef cutting up an octopus. You take each factor and isolate it and see what the magnitude of effect is then see how the measure of fitness (e.g. the velocity) compares to the prediction, combining two or maybe three variables at a time until you have a model. In this case I need to redo all my numbers to see what they look like before the elastic limit (250%) and just into the inelastic transition (350%). There'll be more to test later, but by then my Chrony will have arrived.

Final Conclusion - for those of you who like to skip to the end

It's probably not wise to stretch the heck out of your bands on the draw because they won't work so well on the return.
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whipcrackdeadbunny
May 28 2010 07:30 AM

So, do you think that given consistent drawing time, the lightest bands have the best reaction time, and a shorter band length (I would also presume a band would have more inconsistencies in contraction with a longer band) would have the most efficient and reliable reaction limit; but the lighter bands would have a higher ratio of snapping, so a multi-layer light band set, might be the most reliable and efficient?
And we haven't had in the results of Jorg's tapering tests.


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ZDP-189
May 29 2010 06:19 AM

These are force-elongation and force-contraction charts for some popular bands. I gathered this data for my own use, but it may be useful to some other people as long as you take it for what it is.

  • Note that this data is not meant to constitute a review and its practical validity as a predictor of Kinetic Energy or Velocity is theoretical but unproven. P/E was calculated as the average of starting and ending steady-state traction force for each incremental distance from the back of the forks to the pouch on the contraction phase. It doesn't take into account several physical losses during full velocity dynamic contraction.
  • Results may vary from experiment to experiment due to inconsistent method, manufacturing tolerances and environmental conditions.
  • Data and charts are not meant to be comparative as experimental conditions were not exactly the same.
Hunter Bands from forum member fish

Specifications:
  • Mfr Rating (lbs) : ?
  • Mfr Rating (N) : ?
  • Length (mm) : 170
  • Width at fork (mm) : 27
  • Width at pouch (mm) : 21
  • Thickness (mm) : 0.72
  • Layers (x) : 2
  • Elastic : Thera-band Gold
As tested:
  • Max Force (N) : 92.7
  • Max Draw (mm) : 605 from fork to front of pouch
  • Max PE (J) : 23
  • Max PE/Force (J/N) : 0.24
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Experimental notes: I could have continued further, but the force numbers were so high I 'bottled it'. This just about touched on the draw distance where it started to stiffen a tiny bit. The bandset was a real performer with very low hysteresis and huge peak potential energy. These are very heavy bands, but I can pull more than twice force this at that length and it wouldn't have been beyond my comfort zone. In order to get the manufacturer's rating of 27J kinetic energy, I would have to draw further, to what would be for me a typical (for me) draw to under the chin. I would expect a little more hysteresis by this point, but I am confident the energy's there.

Express Bands from forum member Tex-Shooter

Specifications:
  • Mfr Rating (lbs) : 16
  • Mfr Rating (N) : 71 Tested to 64.5 at 780mm
  • Length (mm) : 230
  • Width at fork (mm) : 20
  • Width at pouch (mm) : 14.5
  • Thickness (mm) : 0.70
  • Layers (x) : 2
  • Elastic : Believed to be Hygenic natural latex .03" sheet
As tested:
  • Max Force (N) : 64.5
  • Max Draw (mm) : 780 from fork to front of pouch
  • Max PE (J) : 20
  • Max PE/Force (J/N) : 0.31
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Experimental notes: When I stopped, I was 10% below the manufacturer's rated draw force (despite being in a hot workshop without air-conditioning) and I don't think the bands were becoming inelastic yet. However I decided to stop because it was already equivalent to a chin draw for my diminutive stature compared to the typical American. The bands seem stretched razor thin and I wouldn't practically draw it another 10% back behind my jugular. These bands shoot with a pleasing amount of energy at this draw.

Field Bands from forum member Tex-Shooter

Specifications:
  • Mfr Rating (lbs) : 13
  • Mfr Rating (N) : 58
  • Length (mm) : 230
  • Width at fork (mm) : 17
  • Width at pouch (mm) : 12
  • Thickness (mm) : 0.75
  • Layers (x) : 2
  • Elastic : Believed to be Hygenic natural latex .03" sheet
As tested:
  • Max Force (N) : 43.1
  • Max Draw (mm) : 730 from fork to front of pouch
  • Max PE (J) : 13
  • Max PE/Force (J/N) : 0.30
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Experimental notes: When I stopped, I was 25% below the manufacturer's rated draw force (despite being in a hot workshop without air-conditioning) and the bands were a long way from becoming inelastic; hence the very low hysteresis. However I decided to stop because the bands seem stretched razor thin. These bands are light and accurate without being too week for reasonable sized shot of 6-8g.
 

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Excellent detailed summary, especially for the wonks who like to think about the mechanisms and complexity of multifactor systems and all. And as you pointed out several factors, especially including elongation factor, will play into this.

For a shorter / simpler real world test using just one type of band (and one type of tube) at a single elongation factor, see video below. I think the basic conclusions from this demo are that hysteresis is real, but for realistic hold times of a couple seconds or less the effect is minor (well under 10% loss of velocity).



 
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