Rubber length vs performance?

[oneoldude]

Hi,

I would like to propose a hypothtical to get some answers to help me understand speargun dynamics. Please humor me

1. Suppose we have four identical long spearguns with identical spears with wishbone slots all along their length so that band stretch can be easily varied.

2. Suppose we put one fat short band on one and and stretch the band to put one hundred pounds of force on the spear.

3. Suppose we put one fat long band on another and stretch the band to put one hundred pounds of force on the spear.

4. Suppose we put one thin long band on another and stretch the band to put one hundred pounds of force on the spear.

5. Suppose we put one thin short band on another and stretch the band to put one hundred pounds of force on the spear.

6. Then suppose we fire them all and measure what happens to spear travel.

Will there be any differences given that the spears are identical and the initial applied force is the same?

What factors and effects should be considered when desigining a speargun in regards to the diameter and length of the rubber?

Thanks

oneoldude.

 

[defofthecrown]

Well for starters my understanding is that pounds of force matters for loading, but not for firing. Example: You could have a gun vertical w/ the tip pointing at the ground. Then dead lift a 100lb block of lead w/ a wishbone and hook it on the spear. You have 100lbs of force but it will only fall at 9.8M/second squared b/c of gravity once the spear is released.

I think the elacticity of the bands is what matters. The faster they contract after being stretch, the more force will be applied to the spear and therefore the faster the acceleration (Keep in mind that mass x acc. =energy so spearshaft diameter is a fun argument too).

According to manufactures the 'ideal' stretch is around 300% it's also important to point out that the accumulation of power is not linear. In other words two identical bands stretch to 150% would not equal one identical band at 300%. Beyond 300% elongation power gain is purportedly minimal while band degredation is rapidly increased.

I don't have too much time rightt this sec, but this might give you a little reading to do. Note the loss of power as 'soak-off' over time and Mori's results for different batches of band material. http://rocknfish.com/Rubber_Test.html

 

[Alison]

LOL Ive just written and deleted a whole load of my thoughts that when I read it sounded dodgy to say the least, along the lines of rubber length and thrust rofl I shall abstain from this one

 

[Bill]

Fun question. Let's presume that the max distance, rubber keeper at the front of the gun to the far notch, is 48. The answer to the question that you didn't ask is, a 32 loop of rubber that measures 100# when on the rear notch will be optimum and the power will be close to 50*32 (pound centimeters or whatever). The force will reduce from 100 to 0 over 32 distances. Not linear though so I say about 50*32.
Other answers;
2. If it is fat enough a 24 loop will produce 100# on the 24 notch and the power will be close to 50*12.
3. For 100# the fat loop will have to be 48 and hooked to the 48 notch for a power of 50*24.
4. We already covered this, 50*32.
5. The shorter the loop, the less the power.
That's one opinion based on a lot of presumptions. The most important are; if you exceed 3 to 1 stretch, bad things happen and your limit of 100#. I actually decided, years ago, that two rubbers of different sizes and 50# each work better.
Aloha
Bill

 

[oneoldude]

FWIW, the question I have posed is not a trick question nor is it trivial. In looking at speargun designs I have seen that virtually all current guns are designed to use all the available spear length to hook up the bands. Some guns use thin rubber and stretch it all the way back when they could be made with thicker bands that might only reach to the middle of the spear and still get the same thrust only quicker. I asked myself, "Why?"

One answer might be that it, "looks right," and that is not a good reason for an implement with the purpose of sending a spear accurately to its target. Another answer might be the Tim Taylor solution, "More power, he, he, he." But that can cause problems with shaft bending and oscillation, loss of accuracy and power and results in thick shafts, channels and other bandaides to fix the too much power problems.

It would seem that if you could get the necessary power from shorter bands and place the wishbones closer to the front of the spear, a couple of problems might be minimized.

First, with less of the spear being put into compression during the initial flight phase, there will be less shaft bending and oscillation and therefor more accuracy and more ultimate power with less fiddiling to fix the bending problem in the first place.

Second, it may well be easier to stretch the bands onto the spear without requiring an extension (or as long an extension) behind the handle and still get equal or better results.

Short fat bands will most surely contract more rapidly and get their job done faster than long thin bands. Which is better, a short fast thrust or a long slow thrust with both acheiving the same terminal velocity?

I have read the "rockfish" site and it does not address the questions I pose. But it does bring up some issues. I am presuming that in all cases bands are not stretched beyond their normal 3:1 limit but are stretched to the 3:1 limit. Also, I presume that conventional guns of conventional sizes with conventional spears of conventional design are taken out of the equation. Lest you think I favor one design or another, that is not so. Thin shafts for small fish, thick shafts for bigger fish and monster shafts for monster fish are appropriate. American, Euro, pea shooter, tree trunk, who cares! In other words, if you were to start with a clean sheet of paper (and think out of the box) where would the best place be to put the wishbone on the spear and what strength and length of rubber would be best to send the spear quickly and accurately to the target.

The answer might be unusual and surprising. On the other hand it may well be that what is available is as good as it can possibly ever be. But I have a sneaky suspicion that what is available can be improved.

 

[Alison]

Acording to those in the know, 2 longer bands giving the same force as a thicker short one will provide a smoother power transfer with less shaft whip, hence greater accuracy but there I go again

 

[Huan]

The main reason that manufacturers do not put the spear notch in the middle of the spear is that it will weaken the spear right where the force(fish) is greatest.
have you looked at the dynamics of roller guns?

 

[Bill]

Did you read my answer? Comments?
Bill

 

[oneoldude]

Some Replies

Allison,

What you say makes sense. Two long narrow bands will accelerate more slowly than two short fat bands. If they are connected at the same place on the respective spear, the long narrow bands will allow the front of the spear to get going before bending while the short fat bands may well bend the spear. Question is what if the short fat ones are connected further toward the tip and there is less spear to bend? Then what?

Huan,

I think you are right that the spear will be weakened if a notch is placed in the middle of the spear. So let us use fins or pins on the spear for wishbone attachment. That will remove that variable. Yes I have looked at rollers. The ones I have seen seem to allow longer thinner rubber than would otherwise be possible due to space constraints. I suppose there could be certain leverage effects with multiple pullies but that is too complicated and bulky to be useful I suspect.

Bill,

Yes I have read your post. If I understand you correctly you are saying that 100# of total force delivered over a greater length is more powerful than 100# of total force delivered over a lesser length. I am not sure that is a correct proposition. Perhaps there is a physicist here who can answer that question. But it seems to me that if we use constant force units to make the analysis simple, if the spear were propelled by 100# for 1 ms. or 50# for 2 ms. or 25# for 4 ms. the total force would be 100# in all cases and the spear would go the same distance if all other factors remained constant. Any science guys out there?

Thanks

oneoldude

 

[Ntrik]

Not a science dude myself but the rule from my humble experience is the more rubber you have lengthwise or in girth the more powerful the shot will be. Do not confuse power with speed that is the subtle distinction here. A short thick band will deliver a fast explosive shot, but not a powerful one. With a thick long one the shot will be slower and more proggressive but will carry more punch.

 

[OregonSpearo]

The shaft will fire faster with the 2 short bands because they will pull it for a longer distance than the long band. The difference in pull is equal to the difference of length in between the long and the short bands.
It does not matter if the band is thick or thin, if they are the same length and both pull 100kg hence they are the same stiffness.

 

[Bill]

I'll stand by my original answers but now you've changed the question from 100# of force(peak) for 1, 2 or 3 ms to 100# for 1 ms 50 for 2 and 25 for 4. Since you changed the force, I'll get cute and change the length of the spear. Let's use shafts that fit the pull. A 2 foot shaft will weigh about 40% of the five footer and have close to double the 'muzzle velocity and energy but nearly the same momentum (penetration).
Bill

 

[oneoldude]

Re: Rubber length vs performance? (Long)

Sorry Bill, I was not trying to be cute with you. I was only trying to simplify a complex issue. It has been 45 years since I took my last physics class and I am a bit rusty.

Your posts have caused me to rethink the prior posts and I found a confounding requirement I added after your first post which was not part of the original question or your original answer. In reply to defofthecrown I stated that all bands should be stretched to a 3:1 ratio. That makes no sense in this discourse because if a short fat band were stretched 3:1 for a tension of 100# and then a same thickness long fat band were stretched 3:1, the long band would have much more than 100# on it. To improve the discourse we must say that no band shall be stretched more than 3:1 but that all bands shall exert the same pressure on the spear. Let’s say 100#. We must also keep in mind that well made bands (and springs) are essentially linear in stretch until they begin to permanently distort or become damaged. That is where the 3:1 rule comes from. Not a good idea to destroy your bands before their time by stretching them into oblivion. Also each band has its own constant called “k”. K is the band rating and tells you how much force is necessary to stretch the band one unit of length.

A little net research tells us that the total stored energy available in a stretched band or spring is called Potential Energy (PE). PE is all there is to send the spear forward. The more PE, the faster, harder and further the spear will ultimately go. The equation for PE is PE = ½ (k) (x) (x) where x is the stretch of the band in units from its unloaded condition to its loaded condition and k is that band’s constant. Whenever you see a squared item like x things will get interesting. Let’s see.

1.) First we will take a short fat band one unit long with a k of 50# per unit stretch. If we stretch it two units longer it will be three units long and at a 3:1 ratio putting 100# pressure on the spear and trigger.

2.) Next we will take a long fat band two units long with a k of 50# per unit stretch. If we stretch it two units longer it will be four units long and at a 2:1 ratio putting 100# pressure on the spear and trigger.

3.) Next we will take a short narrow band two units long with a k of 25# per unit stretch. If we stretch it four units longer it will be six units long and at a 3:1 ratio putting 100# pressure on the spear and trigger.

4.) Last we will take a long narrow band four units long with a k of 25# per unit stretch. If we stretch it four units longer it will be eight units long and at a 2:1 ratio putting 100# pressure on the spear and trigger.

If we calculate the Potential Energy (PE) from the equation above for each case in order, we get:

1.) PE = (50)(2)(2)/2 = 100
2.) PE = (50)(2)(2)/2 = 100
3.) PE = (25)(4)(4)/2 = 200
4.) PE = (25)(4)(4)/2 = 200

So Bill, if this is what you were trying to say, you are right. And Alison, keep the counsel of your cognoscenti. They know whereof they speak. I find it interesting that all cases load the trigger with the same pressure but the longer thinner bands provide twice the PE than the shorter fatter bands in the examples cited. So my conclusion is to use the longest thinnest bands that will get you the PE you need for the target species without exceeding the 3:1 ratio.

Thanks

oneoldude

 

[Bill]

"So my conclusion is to use the longest thinnest bands that will get you the PE you need for the target species without exceeding the 3:1 ratio. "

Since we agree on many things, your conclusion is very close to mine and few have entered the discussion, it might be best to let it drop. That's not my style and two months of doctor ordered inactivity have made me a little more stubborn than normal, but if you tell me to go away, I'll understand.

1. 50#/unit, 1 unit to 3 is 2 units stretch (3:1 ratio) and 100# (so far so good)
2. 50#/unit, 2 units to 4 is 2 units stretch but only 2:1 ratio and only 50#
3. 25#/unit, 2 units to 6 is 4 units stretch 3:1 ratio and 50#
4. 25#/unit, 4 units to 8 is 4 units stretch 2:1 ratio and 25#

PE1=100
PE2=50
PE3=100
PE4=50

Warning; the doctor is going to keep me off my feet and out of the water at least one more week. Any disagreement will be challenged and any questions, like how do you power a gun, may be answered with much verbiage.
Aloha
Bill

 

[oneoldude]

Re: Rubber length vs performance? (Long)

Bill, I think you need to re-think your approach. You are basing the PE on stretch ratio and that has nothing to do with it because the system is linear. The factor k defines the stretch in units, not ratios, for a given pull. So if k is one unit for each 50# it does not matter how long the band is.

Here is a possible experiment. If you take three fat bands: one of 1 unit length; another of 2 units; and another of 3 units; and hang them from one end then place 100# on the other end of each, the first will stretch 2 units and end up 3 unints long (3:1), the second will stretch 2 units and end up 4 units long (2:1) and the third will stretch 2 units and end up 6 units long (1:1.3). They will all stretch the same number of units. No more and no less. This is due to Hooke's law which states, "Elongation is proportional to force."

The equation for this phenomena can be written as x = (F)/(k) where x is stretch, F is force and k is the band constant. You will notice that length is not in the equation. So length is not a factor. For a band with a k of 1 unit for 50#, when 100# of force is applied, the band will stretch 100/50 units (2 units) no matter how long or short it is to start with as long as you do not exceed 3:1 stretch and damage the band. This does not change the fact that the stored energy in each fat band (PE) is exactly the same at 100#.

I also think you should think about the equation in my prior post. That equation is PE = 1/2 (k)(x)(x). You can see that x (elongation) is squared. That means that elongation myst be multiplied against itself to deternine PE and results in a non intuitive result that benefits narrow bands. The result being that a long stretchy (narrow) band can hold more energy than a shorter stiffer (fat) band for the same pull. It is like a lever. You have to pull the narrow band twice as far to load it with 100# and it will therefor store more energy (PE). It is an non-intuitive result and surprised the hell out of me!

Here are some sites that describe the phenomena:
http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/SHM/HookesLaw.html
http://webphysics.davidson.edu/Applets/animator4/demo_hook.html
http://www.kineticbooks.com/physics/16618/16639/sp.html

This is very useful information for me because it will help me to properly set up my gun without relying on intuition which is often wrong (as shown above). The equations are mathematical descriptions of how nature actually operates. And we all know that you disagree with mother nature at your own peril.

Thanks

oneoldude

 

[Bill]

Sorry to be so slow, but everything takes longer these days. I did the rethinking as you suggested and I think that "Elongation is proportional to force." means that your three rubbers will stretch the same ratio with the same force. After thinking about it, I decided that your 3 rubbers of one, two and three units is no different than one long loop with marked sections of one, two and three units. I marked the loop and used enough tension to stretch the one to three. Then I checked, the marks that were two units apart were now six and the marks that were three units apart were now nine (+/- 10%). That experiment didn't take long because all I needed to do was mark one of the rubbers on the big gun and cock it. The next experiment took a lot longer. I built another band one half the length of the big loop and connected them together at the wishbones. Looping them over the hitches and stretching them with the truck took a little time and I never got an exact 3:1 ratio but one measurement was close to 2:1 and they both measured the same ratio, more or less. The one unit loop stretched to two and the two unit loop stretched to four.
After all this it dawned on me that I could (and did) repeat your experiment in the house with elastic bands. I looped six (matched) bands together and measured the distances between the knots after I stretched the whole thing 3:1.
Thanks for the fun experiment, a shot of scotch will taste good before dinner.
Aloha
Bill

 

[Old Man Dave]

The answer to the problem lies in the practice. While it might be possible to calculate the theoretical outcomes, there are so many variables that this is of little practical use. After 40 years of firing all sorts of spearguns at all sorts of fish I have come to some conclusions. One long rubber streched back on the longest reach you can manage powering a thin spear produces the smoothest most accurate shot. However there is a maximum range and the lightweight spear only suits small to medium free swimming fish. Two rubbers on this type of gun produces more power but not much if any more range and is a lot less pleasant to use. You can however up the spear diameter and this is the way to go to produce a gun for larger free swimmers. The ultimate Tuna type gun uses heavy spear long rubbers at maximum arm strech to load them. Right now to short rubbers and/or short guns. The chief advantage is ease of loading due to shorter reach and most importantly high power at short range. If you try to shoot a heavy bodied fish at short range with a long range gun powered by long rubbers the spear lacks punch. Long rubbers accelerate the spear slowly and for the first foot or two have little penetrating force. Short powerful rubbers do deliver this punch but the spear lacks range an is not smooth. To summerise short rubbers produce high torque guns with lots of punch at short range but are nasty to shoot, innacurate and often frustratingly short on range. They are easyish to load and suit short thick spears. Use them on conger, grouper etc.They are the equivalent of shotguns. Long rubbers are best for free swimming fish at middle and long range. Use light spears and eat lots of bannanas so your arms are long enough to load them. Use one long rubber for small/medium fish like bass, snapper etc. Use multipul rubbers for bigger fish. These guns are rifles. One last point on a personal note I would not use short thick rubbers. If you need high torque power go pneumatic.

 

[oneoldude]

Dave,

You are a sharp eyed observer. Your observations are exactly what the physics equations predict. That, coupled with your practical advice, now gives me confidence that I can set up my guns without relying on incorrect intuitive notions that fall short of reality.

Thanks

oneoldude

 

[defofthecrown]

Oneoldude, I don't know that your varriable 'k' would be a linear constant before the 3:1 degredation. I think compressive strength or potential is independant of energy needed to stretch. As an example: It would take several tons of force to pull a stainless steel shaft into expantion, however when 'released' no energy is available for contraction. The energy is spent on breaking bonds, giving off heat etc and results in permanent deformation. It's the elacticity of the material that matters most. That being said I would find it impossible for a speargun band to realease the same amount of energy as it consumed to be loaded. Finite energy is lost as molecular bonds break, heat is generated, and then once fired via water resistance. The question is how much. Of course this is all academic and wouldn't even change your equation realtive to this experiment except to unilaterally lower the output.

 

[oneoldude]

Def,

Yes, you are correct. Indeed, the "soak off" of bands over time is part of what you describe as is the destruction of a band if over stretched. But for the purpose of understanding how these things work it is useful to presume perfect elasticity even though we know there will be some losses here and there.

The example you give of a shaft being stretched shows that some things make very bad springs or bands because they are not sufficiently elastic. Virtually any stretch on the stainless shaft damages the bonds, deforms the shaft and it will not spring back.

Also, that is not "my" k in the equation. I wish it were. Then it might be oneoldude's law instead of Hooke's Law

One more thing. In a prior reply to Huang I suggested that roller guns might not provide any benefits without compound rollers. I was wrong. The equations show that for the same force applied to a spear, longer thinner bands give a higher PE. Roller guns allow you to use even longer bands and therefore allow an even higher PE for a given force on the spear. That is a very significant advantage and a very good thing. I stand corrected.

Thanks

oneoldude