# Optimal tapers



## ZDP-189

Has anyone besides me done any testing on optimal tapers shooting over a chrony?

I know that most people don't go any more than 3:2 or 2:1 because they break early. That's not my problem, I have ample longevity and wonder if there is any benefit to being more aggressive.

I want to know if there is an optimum ratio to generate the highest velocity per peak draw weight.


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## gamekeeper john

i did a couple of tests with extreme tapers and the results was they were a lot faster than a slight taper at the same draw, on my own personal hunting catapult i use double theraband gold with a taper from 30mm to 10mm, these bands can launch a 12mm lead over 300fps !!! i get about 100 shots out of the band set, which i think is great, when hunting i only ever shoot 5 or 10 shots on each session, so this band set will last me 10 hunting trips







also i'm not using as much theraband because of the more extreme taper, -- gamekeeper john


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## bullseyeben!

This is gonna sound strange, but is a symmetrical taper, better than one that is a right angle at 1 bottom cnr? Ie- isosolese triangle vs a right angle? I hope someone understands lol


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## lightgeoduck

bullseyeben! said:


> This is gonna sound strange, but is a symmetrical taper, better than one that is a right angle at 1 bottom cnr? Ie- isosolese triangle vs a right angle? I hope someone understands lol


I understand what you are saying,, now we both hope someone can answer that









Great question.

LGD


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## AJW

Super question, it would make cutting somewhat simpler and cutting in pairs your remnant is always square.

Al


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## Wingshooter

That is the way I cut my bands. they seem to work just fine. Altho I have never compared the two for longevity. It is just simpler to cut that way.


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## AJW

Thanks Wingshooter, that's how I going to do it too. I just cut a set of 3/4 x 1/2 x 8 and how much easier and faster.

And a big Thanks to you bullseyeben for bringing it up.


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## ZDP-189

gamekeeper john said:


> This is gonna sound strange, but is a symmetrical taper, better than one that is a right angle at 1 bottom cnr? Ie- isosolese triangle vs a right angle? I hope someone understands lol


It's the same thing, because when you tie it, the _tips_ of the bands are just negligibly off. The angle on two _sides_ of the band are effectively the same. Especially on long bands.


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## Jacktrevally

I thought about this and this is not an easy matter to investigate into. I was thinking of any dynamics software, where I could analyse a band using finite element analysis! I know some expert in the field do it on sport equipment that flexes but in this case we are using an elastic material but we are interested in the energy stored and loss in the elastic material! Not impossible but I need to think how I can model that.

If someone can, then It's just simpler to change variables to accomodate various parameters like tapers and length.

If you have to investigate this by experiment, making a band longer to suit a draw an inch shorter will not have the same result for optimun taper. Whereas doing that on a program, this can give you the tapers in minutes to suit any draw you want! Now if you change material like latex, gum, latex with additives, all go back to the start but simpler with a program.

The program I'm talking cost about $33,000, used in aeronautical and complex structures. I've one of these at work, I'll not let all the secret out how I'll do an analysis like that but just a hint. You need to model a thin plate and subdivide tgat into elements and investigate stresses in the plate. Now you need a dollop of understanding how to used these thousand values as a result. Never tried but I think it's possible. But still thinking how to analyse the band as a projectile and deformation as it moves through air. As, when you do a taper, the narrower part recovers from it shape quicker than the wider part at the tip, the rubber creases! Optimum taper has to take this into account to reduce these creases!

Now for the theory, say you got a band load it, it stretches, the graph is in Theory exponent but it isn't as the band reaches a plastic limit!!!!

When you investigate an optimum taper the band must have the minimum energy loss through hyteresis! Therefore you'll have to find a relationship beween energy loss and optimum stretch (say 420-460)%. This will vary with tapers and length, so takes a long time to experiment!

Another thing is to integrate that 2 curves and find the energy loss. To put it in simpler terms, find the area between the two graph.

I've a feeling that straight cut tapers might not be the optimum, has anyone tried curve tapers, i.s a segmental shape type bands? Difficult to cut, needs a jig.

I stand corrected on all the above.


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## Charles

Straight cut experimentation is not so hard to do ... and would have to be used in any case to verify any computer model before one could/should have much confidence in that model.

My only go in this direction was my recent report about the effects of tapering Alliance 105 bands. See it here:

http://slingshotforum.com/topic/11097-pfs-over-300fps-with-single-gamekeeper-target-bands-and-95mm-steel-video/page__st__40

In the first case, I cut a taper from 5/8 inch to 0, making two pieces from one rubberband.

In the second case, I cut a taper from 5/8 inch to 5/16 inch.

The draw weight of the first case was 3.5 pounds. The draw weight of the second case was 4.5 pounds. When shooting 3/8 inch steel, the first case (extreme taper) gave a velocity of 172 fps. With the same ammo, the second case (less extreme taper) gave a velocity of 165 fps.

BUT their are complications. For one thing, band life comes into play. Extreme tapers have very short band life, as has been reported by many, many on this list. But suppose we just disregard band life for now.

Draw weight versus draw length is another complicating factor. If the bands were pulled to the same length, the extreme taper has less draw weight. If the bands were adjusted to have the same draw weight at a given draw length, the tapered band would have to be much shorter, assuming the two have the same thickness. The alternative would be to adjust the thickness of the more heavily tapered band until the draw weight at the given draw length matches the draw weight of the less tapered band. A manufacturer might be able to adjust thickness in this way, but most of us cannot. The best we can do is to add multiple layers of tapered bands of the same thickness.

A more important variable is projectile weight. Although the exteme taper did better on 3/8 inch steel, it would do worse on .44 caliber lead. In short, there is a trade off between the velocity effect of tapering and the mass of the projectile the band can effectively accelerate over the given draw length.

It seems to me that to be practical, a good place to start is with band material which many of us already use. Limit ourselves to methods that could be easily implemented by most of us. And then do a few experiments. By experiments, I do not mean the one-off sorts of things I just discussed. To be meaningful, one should cut at least 10 band sets of each taper, doing one's best to attach pouch and fork exactly the same. Probably should use a crossbow rig to eliminate variations in pouch hold and draw length. Do all shooting through a chronograph at exactly the same distance from the chronograph. And all shooting must be done with the same ambient air temperature. A variety of projectile weights should be used. Ideally, all projectiles should have the same physical dimensions to eliminate varaiable effects of air resistance on size of projectile. But I suspect such effects will be minimal given the types of ammo we usually use, so perhaps the size component could be ignored.

This all seems like a big job to me ... too big for me to do. But the results would be interesting. But I must say that I doubt that the differences would have much practical impact for most of us. However, I would be happy to be proven wrong!

So someone with a lot of time and the proper equipment can now just step up to the plate and have a shot!

Cheers ...... Charles


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## gamekeeper john

Charles said:


> Straight cut experimentation is not so hard to do ... and would have to be used in any case to verify any computer model before one could/should have much confidence in that model.
> 
> My only go in this direction was my recent report about the effects of tapering Alliance 105 bands. See it here:
> 
> http://slingshotforu...eo/page__st__40
> 
> In the first case, I cut a taper from 5/8 inch to 0, making two pieces from one rubberband.
> 
> In the second case, I cut a taper from 5/8 inch to 5/16 inch.
> 
> The draw weight of the first case was 3.5 pounds. The draw weight of the second case was 4.5 pounds. When shooting 3/8 inch steel, the first case (extreme taper) gave a velocity of 172 fps. With the same ammo, the second case (less extreme taper) gave a velocity of 165 fps.
> 
> BUT their are complications. For one thing, band life comes into play. Extreme tapers have very short band life, as has been reported by many, many on this list. But suppose we just disregard band life for now.
> 
> Draw weight versus draw length is another complicating factor. If the bands were pulled to the same length, the extreme taper has less draw weight. If the bands were adjusted to have the same draw weight at a given draw length, the tapered band would have to be much shorter, assuming the two have the same thickness. The alternative would be to adjust the thickness of the more heavily tapered band until the draw weight at the given draw length matches the draw weight of the less tapered band. A manufacturer might be able to adjust thickness in this way, but most of us cannot. The best we can do is to add multiple layers of tapered bands of the same thickness.
> 
> A more important variable is projectile weight. Although the exteme taper did better on 3/8 inch steel, it would do worse on .44 caliber lead. In short, there is a trade off between the velocity effect of tapering and the mass of the projectile the band can effectively accelerate over the given draw length.
> 
> It seems to me that to be practical, a good place to start is with band material which many of us already use. Limit ourselves to methods that could be easily implemented by most of us. And then do a few experiments. By experiments, I do not mean the one-off sorts of things I just discussed. To be meaningful, one should cut at least 10 band sets of each taper, doing one's best to attach pouch and fork exactly the same. Probably should use a crossbow rig to eliminate variations in pouch hold and draw length. Do all shooting through a chronograph at exactly the same distance from the chronograph. And all shooting must be done with the same ambient air temperature. A variety of projectile weights should be used. Ideally, all projectiles should have the same physical dimensions to eliminate varaiable effects of air resistance on size of projectile. But I suspect such effects will be minimal given the types of ammo we usually use, so perhaps the size component could be ignored.
> 
> This all seems like a big job to me ... too big for me to do. But the results would be interesting. But I must say that I doubt that the differences would have much practical impact for most of us. However, I would be happy to be proven wrong!
> 
> So someone with a lot of time and the proper equipment can now just step up to the plate and have a shot!
> 
> Cheers ...... Charles


your right charles, you dont get as much band life out of a more "extreme" taper, but on the plus side you are not using as much theraband (flatbands) on a more extreme taper, you would make 3 "extreme" tapered bandsets out of the same amount of theraband as u would use for 2 "slight" tapers, so overall theres not to much in it bandlife wise, but you get a faster shot with a greater taper? i hope u understand were i'm comming from lol -- gamekeeper john


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## Charles

gamekeeper john said:


> your right charles, you dont get as much band life out of a more "extreme" taper, but on the plus side you are not using as much theraband (flatbands) on a more extreme taper, you would make 3 "extreme" tapered bandsets out of the same amount of theraband as u would use for 2 "slight" tapers, so overall theres not to much in it bandlife wise, but you get a faster shot with a greater taper? i hope u understand were i'm comming from lol -- gamekeeper john


Absoultely, John. In the extreme case I was mentioning with the Alliance bands, I got TWO bands from ONE Alliance 105. When rigged up and shooting light ammo, they gave a higher velocity than using two bands, each made with a less aggressive taper from a separate Alliance 105. If cutting from a big sheet, then when properly laid out, you get more bands with a more aggressive taper; we have no disagreement there.

But I think band life is a bigger factor than the number of bands that you can cut from one sheet. In the example I mentioned, the bands with the most aggressive taper failed after about 25 shots. The bands with the less aggressive taper failed after about about 150-200 shots. For me, 25 is an unacceptable failure rate for less than a 10% increase in velocity. Now, everyone has their own limits in such matters.

In your case, with the taper you are using, you reported that you get a failure after about 100 shots, which you find acceptable when hunting. Some might want more band life, especially if they are not cutting their own bands. With a higher failure rate, one feels more of a need to carry a spare set of bands, probably with pouch attached ... or even a spare slighshot already made up. And it makes a difference where and how you are hunting. If I am walking a few fields not far from home, a higher band failure rate might be acceptable. If I am going off to a moose camp for a week in northern British Columbia, and I want to be able to do some plinking and perhaps shoot the odd grouse, I want a pretty low band failure rate.

In practical matters, do you carry spares into the field, or do you just abandon the hunt when the bands fail? Do you actually keep track of the number of shots you have taken while hunting, so you can begin to be warry as that number creeps up?

Also, those extreme tapers just will not handle heavier ammo ... there is a serious drop off in velocity as the ammo weight increases. I note that in your case you are using doubled taper bands, no doubt because an extreme taper on one band will not handle the heavy ammo.

Personally, I am fitting my "carry around" slingshots with tapered bands, but with fairly modest tapers. I like the lighter draw weight and the faster speed. But I personally cannot tolerate the very short band life with extreme tapers. I want to be able to shoot a handful of rocks from time to time; extreme tapers probably would not handle very well the weight of rocks I shoot. A failure once in a while is acceptable; but I do not want to have a failure every 20 shots or so.

Do not misunderstand me ... I am not against tapers at all. And I am interested in getting some empirical evidence on the velocity, taper, ammo weight, band longevity issues. I think it would be a lot of work to get that evidence, and I am not willing to do it myself ... I play around with it a bit, but will not do it in a statistically respectable way.

I think your decision to use double tapered bands on your hunting slingshots is perfectly rational. Everyone's situation is different, and there is no one solution that meets everyone's needs.

Cheers .... Charles


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## Jacktrevally

Extreme tapers are not the optimum as proven by Charles in his test, I've to agree on that!

But ZDP, is talking about optimum curve! I.e the retraction in relation to pull and elongation.


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## gamekeeper john

when you say the extreme tapers will not carry the heavy ammo, how heavy do you mean?
a double theraband gold set tapered from 25mm to 20mm will shoot a 12mm lead (10gram) over 250fps on a warm day,
a double theraband gold set tapered from 30mm to 10mm will shoot a 12mm lead (10gram) over 300fps on a warm day,
i would consider a 12mm lead as heavy?

i totally understand what you are saying about people who dont cut there own bands wanting more band life, thats why my cattys come with the slight taper of 25mm to 20mm to give a good balance of speed and band life,

and when hunting i always carry a spare set of bands with me, i can fit them to a frame in the OTT method in about 2 minutes with no tools, just wrap round about 8 times, then the last 2 times around your finger, then thread the last bit through the gap inbetween your finger and the theraband and pull your finger out,

i do understand that some people prefere power and some band life, thers no right or wrong answer, but me personally i would rather have a lead ball traveling at the rabbits head at 300fps and just change my bands more lol -- all the best john


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## spanky

Hi ZDP
I think i have a set of your bands,Tried them out this afternoon,They are really fast and hard hitting,Love the slin pouch as well.


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## Charles

gamekeeper john said:


> when you say the extreme tapers will not carry the heavy ammo, how heavy do you mean?
> a double theraband gold set tapered from 25mm to 20mm will shoot a 12mm lead (10gram) over 250fps on a warm day,
> a double theraband gold set tapered from 30mm to 10mm will shoot a 12mm lead (10gram) over 300fps on a warm day,
> i would consider a 12mm lead as heavy?
> 
> i totally understand what you are saying about people who dont cut there own bands wanting more band life, thats why my cattys come with the slight taper of 25mm to 20mm to give a good balance of speed and band life,
> 
> and when hunting i always carry a spare set of bands with me, i can fit them to a frame in the OTT method in about 2 minutes with no tools, just wrap round about 8 times, then the last 2 times around your finger, then thread the last bit through the gap inbetween your finger and the theraband and pull your finger out,
> 
> i do understand that some people prefere power and some band life, thers no right or wrong answer, but me personally i would rather have a lead ball traveling at the rabbits head at 300fps and just change my bands more lol -- all the best john


In my tests, a SINGLE tapered 105 band dropped down to about the level of an untapered band when I moved from 9 mm steel to 12 mm lead ... now of course that depends on the taper. Naturally, one solution to this situation is to put two tapered bands per fork, as you do. The trade off is that the draw weight of two bands is quite a bit more than the draw weight of one band. We give with one hand and take away with the other!!!

I agree with you that when hunting I would rather have a ball going at the rabbit's head at 300 fps than at 200 fps. Heck, I would rather have it going at 500 fps!!!! But there are costs for that kind of performance ... band life as we have discussed, and draw weight are two. And for me, the improved accuracy of the flatter trajectory of 300 fps or 500 fps would probably be completely off set by the decrease in accuracy of my having to pull that heavier draw weight and/or use a full butterfly technique. And in my opinion the bottom line when hunting is ability to cleanly kill the game. If I hit a rabbit in the head with a 12 mm lead ball at 200 fps, that rabbit is going to be just as dead as when I hit it in the head with the same ball at 300 fps or 500 fps. Dead is dead. Given that I personally am not going to have much assurance of hitting the rabbit beyond about 25 meters, a 12 mm lead ball starting at 200 fps will still have adequate killing power at 25 meters. So for me, jumping the speed much beyond 200 fps really has no upside, but some considerable downside. However, your situation and your abilities are very different from mine ... and the same is no doubt true of your customers. As I said before, your decision to use doubled tapered bands on your catapults is perfectly rational, and I have no quarrel with it.

Cheers ...... Charles


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## gamekeeper john

Charles said:


> when you say the extreme tapers will not carry the heavy ammo, how heavy do you mean?
> a double theraband gold set tapered from 25mm to 20mm will shoot a 12mm lead (10gram) over 250fps on a warm day,
> a double theraband gold set tapered from 30mm to 10mm will shoot a 12mm lead (10gram) over 300fps on a warm day,
> i would consider a 12mm lead as heavy?
> 
> i totally understand what you are saying about people who dont cut there own bands wanting more band life, thats why my cattys come with the slight taper of 25mm to 20mm to give a good balance of speed and band life,
> 
> and when hunting i always carry a spare set of bands with me, i can fit them to a frame in the OTT method in about 2 minutes with no tools, just wrap round about 8 times, then the last 2 times around your finger, then thread the last bit through the gap inbetween your finger and the theraband and pull your finger out,
> 
> i do understand that some people prefere power and some band life, thers no right or wrong answer, but me personally i would rather have a lead ball traveling at the rabbits head at 300fps and just change my bands more lol -- all the best john


In my tests, a SINGLE tapered 105 band dropped down to about the level of an untapered band when I moved from 9 mm steel to 12 mm lead ... now of course that depends on the taper. Naturally, one solution to this situation is to put two tapered bands per fork, as you do. The trade off is that the draw weight of two bands is quite a bit more than the draw weight of one band. We give with one hand and take away with the other!!!

I agree with you that when hunting I would rather have a ball going at the rabbit's head at 300 fps than at 200 fps. Heck, I would rather have it going at 500 fps!!!! But there are costs for that kind of performance ... band life as we have discussed, and draw weight are two. And for me, the improved accuracy of the flatter trajectory of 300 fps or 500 fps would probably be completely off set by the decrease in accuracy of my having to pull that heavier draw weight and/or use a full butterfly technique. And in my opinion the bottom line when hunting is ability to cleanly kill the game. If I hit a rabbit in the head with a 12 mm lead ball at 200 fps, that rabbit is going to be just as dead as when I hit it in the head with the same ball at 300 fps or 500 fps. Dead is dead. Given that I personally am not going to have much assurance of hitting the rabbit beyond about 25 meters, a 12 mm lead ball starting at 200 fps will still have adequate killing power at 25 meters. So for me, jumping the speed much beyond 200 fps really has no upside, but some considerable downside. However, your situation and your abilities are very different from mine ... and the same is no doubt true of your customers. As I said before, your decision to use doubled tapered bands on your catapults is perfectly rational, and I have no quarrel with it.

Cheers ...... Charles
[/quote]

thanks for the post charles,


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