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That's pretty cool. Thanks for sharing the video. ( we get to know you better with video ) I have a set of tex heavy bands in your taper set up. They rip 44 and 50 cal lead.
I bet those bands in that setup would kill a water buffalo!
I set up some Theratube Yellow in about this same configuration. It has an easy draw but smashes face with 5/8" steel!
 

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Man, you are shootin laser beams there Henry. Congrats on your 380 fps. I know you had fun making it, and more fun trying to beat it. Thanks for sharing your knowledge and talent with us.
 

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I've recently gotten back into shooting slingshots again and have followed with interest the discussion on Chinese tubes. As a retired physicist, I have time to try to make sense of the unexpected result that tapered bands (e.g., 4 strand mixed with 2 strand on each side) can outperform single bands (e.g. 2 strands per side). One can algebraically model a slingshot in which each side is composed of 2 strands in series, with each strand having different stiffness, mass, length, etc.. In the simplified case where the draw force is proportional to the amount of draw beyond the unpulled length (="draw length"), I did not find any advantage to pseudo tapered bands over untapered at CONSTANT draw length AND pull force; (by untapered, I mean constant band configuration all the way between pouch and slingshot "Y") . This calculation includes the mass of the rubber bands, the variation in velocity along the bands, and the mass of the pouch and projectile.

To get constant draw length and pull force for different types of bands, one needs to change the unstretched length of band(s). It seems that many on this forum are not aware of some general rules that can help understand observations. In particular, the pull force at a given draw can be doubled by doubling the number of identical strands side-by-side (i.e., in parallel) or by HALVING the UNstretched length of all bands. Alternatively, the pull force at a given draw length can be halved by halving the number of bands in parallel or by doubling the UNstretched length of all bands. This means that it is very important to carefully monitor the UNstretched length of bands as this can make more difference in stiffness than the band type (e.g., 2040, 1745, etc.).

I'm not sure why I didn't find it favorable to have pseudo-tapered bands at constant draw length & pull force. It is hard to know what the pull force is, so the various speed measurements that are being reported in this forum are hard to do at constant pull force. Also, if the pull force is reduced by tapering, it becomes easier to pull the pouch back and draw lengths are likely to increase as a result. Projectile speed is pretty sensitive to draw length, so an unplanned extra draw length could be contributing to a perception of higher speed for pseudo-tapered.

For the numerically oriented, the stiffness constants k (which have units of force / "draw length" ) combine in parallel like

k.effective = k1 + k2 (k1 & k2 in parallel),

while in series combine like

1/k.effective = 1/k1 + 1/k2 (k2 added to end of k1 (="series" connection)).

So be sure to report unstretched band lengths, and when possible control draw lengths and measure the force needed to achieve such draw lengths.
 

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Discussion Starter · #166 ·
Most of that is so far over my head that I won't even try to reply to it, but I will address one statement.

an unplanned extra draw length could be contributing to a perception of higher speed for pseudo-tapered.
There is no "perception" of higher speed. The speeds reported were measured with a Chrony. Few of us are interested in theoretical performance. We're looking for what happens in the everyday world. Few of us have or are willing to build special equipment to apply equal force to every shot, every configuration. Such information would be of little use in any case, since we just pull the bands back to a point which can vary depending on angle of shot, clothing, etc. and let go. It is useful to know which configuration will produce the most power or highest speeds. with the minimum draw weight. In every case I tried, the pseudo-taper configuration won handily. It produced the fastest speeds (380 fps) with light ammo and the most power (26+lb/ft - two pseudo-tapers per side) with heavy ammo.

Of course, if you were to do a series of tests and write them up in simple enough language for everybody to understand, I'm sure there would be a lot of interest.
 

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Theroy is theory, which is good within limits. However in real life with my slingshot I find that I am probably the biggest variable, either with my shooting or in making a band set as has been proven with my chrony. Including the variables in shot to shot or band set to band set my chrony tells me that I obtain higher velocity with a pseudo taper than a full loop and my fish scale tells me, as does my arm, that the draw weight is less. I am more inclined to believe my instruments than what should or should not be happening.
 

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I want to add to the analysis I described yesterday. There I looked at pseudo-tapered vs standard performance at constant pull force AND draw length BEYOND the unstretched length. A more appropriate comparison is at constant pull force and distance between anchor point (e.g. ear) and slingshot frame. This changes the conclusions but with a twist: pseudo-tapered configurations are beneficial over untapered configurations ONLY if the pseudo-taper has LESS band mass than the untapered-- a pseudo-tapered design with more mass than the untapered performs worse than the untapered design at constant pull force and anchor distance. For example, a standard chinese tube configuration for an untapered design has 2 bands on each side. Relative to that, a pseudo-tapered configuration with 1 plus 2 bands on each side gives better performance, while a pseudo-taper with 2 plus 4 bands on each side gives worse performance. This is not a surprise if you measure the various masses because the rubber bands (e.g. for 2040 bands) dominate all masses. E.g., for a typical untapered design, the bands weigh 8g, the pouch 3g, and the 3/8" steel ball weighs 3.5g.

I've included a pdf document that gives some calculation results plus commentary, and the function that calculated them. I am now comfortable that a rather standard physical model gives reasonable results-- and is much more convenient for understanding trends than building & testing different rubber band configurations. You may want to look only at the calculated results, but to understand the symbols used you may want to read the documentation comments at the beginning of the shown function. An example result:

For an anchor length of 30" & with 13.8 lb pull, a 3/8" steel ball has:
pseudo-tapered: 238 ft/s speed & 6.9 ft-lb energy
untapered: 205 ft/s speed & 5.1 ft-lb energy.
 

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Very nice, keep it up.

My first observation though is that you use a constant for koa - force per inch.

Others and myself have observed that this is not a linear rate.

Also it has been observed that rubber looses it's elasticity the longer it has been drawn out. Joerg S has studied this with the use of a thermal camera. Several members have also recorded slower speeds when the rubber is drawn for a period of time. DUGI demonstrates this quite effectively with his fast draw and shoot technique.
 

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Hrawk,
I am aware that F=k* DeltaX is an approximattion for rubber bands, and that there is hysteresis etc., but one would hope that it would be sufficient to understand the nature of pseudo-taper benefits or their lack, and I think that now this has been illuminated. By calibrating the rubber elastic (i.e., k) properties by using someone's measured velocity data (as I have done), one is closer to getting the velocity right at the expense of pull force. In any case, pull force is usually not measured carefully, and would depend on how long one holds the draw before releasing (because of the hysteresis effects). If there were more observations of time-dependent pull force and energy lost inelastically in the rubber, one might be able to make better fudge factors to account for these extra complications (perhaps an effective mass for rubber bands greater than the actual value?). From what I have seen in brief google searches, F=k*DeltaX is not off by more than ~25% when hysteresis & nonproportionality are included (except at extreme pulls near the rubber breaking point), so I am not motivated to get heroic about improving the calculations I have used, but if anyone has some practical suggestions, I'm all ears.
 

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Don't get me wrong man, I think what you are doing is great and those big words are downright sexy


If you need any specific test data let me know. I have a few sets of reasonably accurate pull scales as well chrony etc.
 

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boby,

That is some killer information that you are laying on us.. theories, science and math can be a good read for sure. As far as slingshots I am not an exact science kind of guy, but I do appreciate and find useful what others have put alot of effort in to sharing with the community... "Z" was a very scientific guy when he discussed slingshot theories. Hrawk as well puts up some excellent data information. Just keep in mind the nature of this thread and others of its kind. It gives us a practical image of what everyday shooters could experience with certain set ups. I don:t know the benefits of one or the other, but when I see 380fps coming from someone:s set up and compare it to their tests of other set ups.. it gives me a general idea what to expect when I make my generic adjustments for my shooting set up.

Everything serves its purpose in one way shape or form... and if you are up to the "challenge" it would be nice for you to share your knowledge in a thread/blog with tests and figures combined. It definitely seems you would be a big asset to the community by doing so.
 

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@Boby that explains why my pseudo tapered 2050 gave less performance than a full loop. I figured that I was on the back side of the curve and gave up testing early. 2050 is double the price of 1842 and 1745, and about 4x the 2040 and I wasn’t getting the expected results. I should point out that the factory full 2050 loop and the pseudo taper were from different manufacturers. The tests would have been more meaningful using the same lot. I have enough 2050 left to make a full loop and will go back and retest.
 

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Discussion Starter · #174 ·
I'm hoping to set a new personal speed record tomorrow morning. I fiddled a bit with dimensions, increasing overall rubber length to 7.0 inches. This allows me to stretch the set a couple of inches more and should increase velocity. First tests were encouraging. With a cooler temperature and only about 15 shots on the set, I recorded 375 and 377 fps. A few more breakin shots and a warmer temp should get me comfortably over 380 fps. This is with 2040 pseudo taper, 1:1 ratio and .25 inch steel. Total tube set weight with pouch tied is 6.25 grams/ 96.4 grains.
 
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