Primitive Archer
Main Discussion Area => Bows => Topic started by: Tuomo on December 07, 2025, 08:53:17 am
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What is the best shape for a reflexed bow? I experimented with the VirtualBow program to search for an answer. Shown here are five different reflexed designs, with a straight bow included for reference. All of the reflexed bows share the following characteristics:
* Length: 66", brace height: 6", draw length: 28"
* Draw weight: 50#
* Identical front profile, optimized for even stress distribution along the limbs.
* Taper rate 0.008
* Three-layer construction; only the core thickness is adjusted to achieve the 50# draw weight
* All reflexed designs have the tips reflexed by 100 mm (4"), measured from the belly side of the handle
* 10 grains per lbs -arrow
So, which shape is the best? By best, I mean the fastest and the one that stores the most energy. Why? Which design performs the worst, and why?
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This is my opinion.
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That design has broke flight records and won multiple IBO world championships.here is the caul.
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Here is a bambino backed Osage but I’ve done boo backed boo core and gemsbok horn belly and other combinations this boo backed Osage took some set throughout the limb. It’s best shot with a 462 grain arrow was 260 yds.
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This bow was designed by Alan Case. 64” long. I haven’t shot it in competition but it shot 460 grains 232 yds.
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So, which shape is the best? By best, I mean the fastest and the one that stores the most energy. Why? Which design performs the worst, and why?
Does maximim storage energy equate with performance?
I am curious if different designs of the same materiels are more or less efficient when delivering the energy to the arrow. (what weight arrows are you designing for?)
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I THINK that being said material qualities is huge in design with natural materials but also in general. It will affect the width and length of the limbs depending on the stress from reflex. And yes deflex in the handle and fades takes the stress out and makes the bow more efficient. That being said in flight you need limbs pushed to the max to achieve your goal. Just my opinion. That’s why my bows take more set . If I did it put the reflex In the ends my bows they may not take set. That design has smooth even draw weight and makes the bow pleasant to shoot. We all have our design choices though.
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Nice looking bows selfbowman. Not to high jack the thread but, what’s the wall board behind it made of.
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So, which shape is the best? By best, I mean the fastest and the one that stores the most energy. Why? Which design performs the worst, and why?
Does maximim storage energy equate with performance?
I am curious if different designs of the same materiels are more or less efficient when delivering the energy to the arrow. (what weight arrows are you designing for?)
Max energy storage absolutely does not equal performance. As a matter of fact, a bow could be made to store double its energy and only deliver to the arrow a small fraction of it. I struggles with my short recurve designs stringing energy, so I started focusing on what made them more efficient at delivering that energy. Eventually I got the design sorted out. Think, the energy consumed by the 1950s big engines, but how little they delivered. Same concept.
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Muskyman the long bows are on drywall . The recurve is floorings from Home Depot.
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Interesting question.
I’m not a number guy. And like already mentioned. Materials make a difference. And designs are high stress.
I’m guessing the program is with zero set?
I personally like shooting number 5 . I have a short draw though and I like the early string tension. It seems smoother at full draw also, but maybe that’s less stored energy?
I think if you could keep all the reflex with zero set the one with reflex all in handle seems like it might have the most energy?
I will be watching (-P
I want to know
Bjrogg
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All the shapes you show lack set, so that is a plus to begin with, and any one of them would make a fine hunting bow. I can confirm that. If you are shooting to make a wood flight bow maybe non of the above. If chrony numbers count, and all else being equal long sloping narrow recurved tips with very little deflex in the limbs that ended up with 2.5 inches of reflex is the fastest 35 lb. bow that I have made to date. With a 355 gr arrow at 25 inches of draw the bow shot from 158 to 162 through a chrony. You make fine looking heavy bows, and some laminate, so I can't speak to that. JME
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Having built only two computer design bows I will say this. Building a selfbow and achieving the spec are a challenge to say the least. The crown gets me every time. I built the second one by the dimensions and the force draw and bend profile. Laminate bows would probably be much easier. The next one build I will build it as close to the dimensions as possible before I put a string on the bow. I know I’m not going to be as perfect as the computer but I will have not stressed the wood in any way. The other trick will be matching the properties for the design. Since I know nothing about computer design I have to leave that to the smart guys. I do think that if the properties are put into the computer and the builder matches the dimensions it will turn out as predicted. That’s a lot to expect from a Texas cowboy.🤠🤠
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Since you are talking about laminated bows, I prefer #6. I think a bamboo backed osage or ipe, or a tri-lam is made for that deflex/reflex design. It makes an exceptional hunting bow that shoots as well as (or better) any glass bow.
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* Identical front profile, optimized for even stress distribution along the limbs.
* Taper rate 0.008
Usually you have to adjust taper to suit the front profile and side profile of a bow. Keeping them constant isn't typically optimal between designs. What front profile did you use? I stuck with a pyramid profile as it was easiest to get the stresses even along the limb and it never needed as much taper as you have, I was always around 0.003"-0.004" to get everything even on stresses.
So, which shape is the best? By best, I mean the fastest and the one that stores the most energy. Why? Which design performs the worst, and why?
Best will most likely be whichever one has the highest string tension at brace. Worst would be the lowest tension at brace.
I never considered a side profile like #2, I mostly stuck with circular reflex similar to #3. How does #2 compare to #3 on an F-d chart? It would be much easier to build #2 the way I was doing it.
#5 gave the smoothest draw curve for me, with a lot of early weight and no stacking. How does it look in your model?
Building a selfbow and achieving the spec are a challenge to say the least.
Yes it is. You need to be within 0.005" on the thickness at worst and it is hard to do that on a stave or board bow, especially if there is much thickness taper.
Laminate bows would probably be much easier.
I found that it was. I still ended up over thickness a bit, but that is better than under.
I do think that if the properties are put into the computer and the builder matches the dimensions it will turn out as predicted.
That was my experience with the two I did based on a model.
Mark
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I experimented with the VirtualBow program to search for an answer.......... optimized for even stress distribution along the limbs.
I am curious what your stress curve looks like. I posted about this earlier in
http://www.primitivearcher.com/smf/index.php/topic,72997.msg1024157.html#msg1024157
and would welcome any comments should you wish to reopen that thread.
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I wanted to do a small study on reflex shapes—bow designs that can realistically be built in real life. Even though theory and practice don’t always align, we should remember that there is always theory behind practical results. Yes, the zero set, but it doesn’t matter, because all the bows are similar except for the side profile. The only purpose of this comparison is to examine how different side profiles affect bow performance (10 gr/# -arrow) in theory.
“mmattockx” mentioned the front profile — it’s quite standard, adjusted so that with a 0.008 taper rate the stresses are distributed as evenly as possible along the entire length of the limb. But again, that doesn’t matter here, because the main purpose is to compare how the reflexed side profile affects the performance of a bow.
Regarding energy storage, it’s true that high energy storage does not necessarily mean that a bow will be fast. However, in this comparison the fastest bow has the highest energy storage, and it also has the highest efficiency, and unfortunately it has also the highest strain values.
Remember, the main goal is to compare different models in an idealized situation. How they are actually built in reality is a different matter, and there are many other variables involved, such as stability, material properties, and so on. However, there is still one model (side profile) that clearly outperforms the others (at least in theory...).
So far, one “correct” answer.
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I do think this is an interesting question.
My thinking that the one with all the reflex in the handle has the most stored energy is that “all the reflex is in the handle”.
Therefore all the working limb is able to use this reflex.
I have know idea if that is correct. It just seems to make sense to me.
But I could be totally wrong. Maybe reflex in a different area is better? Maybe more leverage further out the limbs?
Bjrogg
Thanks for post this Tuomo. I have wondered about these profiles myself
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Intersting experimantal setup Tuomo - that's exactly how software can make us wiser. Things like that are too difficult to examine in the real world!
I'm not surprised the d/r is the fastest - Still im curious to see your data.
However: Why do you use the same taper for all these bows? Different design needs different tapers. No wonder, the d/r is the most stressed - d/r needs stronger taper than the others or it will have too much bend on the inners which makes it of course fast but causing a lots of stress too.
However 2: The best shooters imho are not achieved by tillering to even strain anyways. They are just tillered so that the max strain does not exceed the capabilities of the wood. Within these boundaries you are looking for the fastest tiller, which never is even strain.
Simon
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Now we are getting to the core of bow design! And it seems that Simk knows something about bows (I knew that already...)!
Your questions:
Why the same taper? Because I didn’t want to optimize every bow model; I just wanted to compare different models while eliminating as many variables as possible. That’s why the front profile was quite normal—40 mm at the widest and 10 mm at the tips, with a realistic width taper. In computer models, you can always make the tips narrower and narrower to get more speed, but that isn’t reasonable in real life. Optimizing the taper rate has a very minor effect. When I used the same taper rate (0.008), every model had very similar stress curves, and the stresses were distributed quite evenly. So: little to no effect → no need to adjust it → fewer variables.
Your claim, “The best shooters, imho, are not achieved by tillering to even strain anyway,” is interesting—why do you think so? Let’s take the D/R design as an example. The more bending near the handle and the stiffer the limbs, the more energy is stored, right? Like the famous Möllegabet bow. But, as you said, D/R designs need more taper, which leads to lighter limbs and, in turn, a faster bow. So more taper → more evenly distributed stresses and lighter limbs.
I tried my D/R model using a 0.010 taper (more taper). It stored less energy (as expected) but had lighter limbs (also expected). However, it ended up a few fps slower due to the reduced stored energy. Most importantly, the maximum strain values were higher. With less taper (0.006), the limbs were a bit heavier, the bow was slower, and the maximum strain values were slightly higher. In VirtualBow, I get maximum speed and minimum strain when stresses are distributed as evenly as possible (within reasonable limits, of course).
When modeling, we can eliminate some variables, for example set, so the most meaningful ones (in terms of bow speed) are limb mass and stored energy. The side profile is linked to the stored energy, while the taper rate is linked to limb mass (at the cost of stored energy) and strain values. Then, you need to find the optimal solution for a specific side profile that minimizes limb mass and strain values. This solution produces the fastest bow.
In real life, we cannot “see” strain values, so it’s difficult to tiller perfectly, but we can learn a lot by using programs like VirtualBow. Of course, we also have to consider the real properties of natural materials (which we don’t really know…). My fastest bows have been "overbuilt" D/R-design, long, wide, minimally stressed.
I will publish my results tomorrow.
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My guts say that energy storage is less a matter of tiller than of bowlength and reflex.
To best use the stored energy it needs the optimized tiller. Tillershape is very important imho. and the max strain capacities of the material will define your tiller options.
Looking at actual flightbows I seldom see even strain in the limbs ;D With wood: the heavier the bow I make the more I go for even strain. The lighter the bow, the more I stress the wood and tiller. jm2c
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To best use the stored energy it needs the optimized tiller. Looking at actual flightbows I seldom see even strain in the limbs.
The question is that how do you optimize the tiller? What is the parameter which is altered? More bending towards the tips, or handle? Something else?
About flightbows (or any other bow), you cannot see the strains, it cannot be judged just according to the bending. It is impossible to know. For example, classic Turkish flight bow. It seems that they are bending mainly near handle area (sal) but they are stressed more along the limbs (up to kasan area) than it seems to be. If not, it indicates that there is unnecessary material (and thus mass).
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Guys I’m getting in over my head as usual but if the outer reflex is working reflex I think we might be getting a bit of whip affect. Giving you more energy in longer bows and heavier arrows. The shorter bows with lighter arrows with more strain on the inner limbs will give you more stored energy. This is just a guess like I said it’s over my head at this point. Think about the unwinding of the Turkish bows and they shoot lighter arrows farther. Not so good with heavier arrows.
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It seems that they are bending mainly near handle area...... If not, it indicates that there is unnecessary material (and thus mass)
I dont think so: The mass towards the outers is mainly needed for stability. If you want your outers stiff by purpose for some reasones then you keep them stiff of course and save mass by making them narrow.
And to me strain mainly is a function of bending radius vs thickness. And if that is correct you can actually see strain in the tiller. Look at Karpovitz idealized schemes.....or others....the bend and the strain are concentrated towards the handle. This is also why a d/r will do better than a straight limb....because you can move your bend closer towards the handle without overstraining weaker materials like wood.
Why it is better to have the bend closer to the grip still is an enigma to me - I just know it will make your bow faster as long as you keep your outers narrow and as light as possible. We of course also have that string angle thing.....the closer your bend is to the handle, the better your string angle at fd...but tbh, I never really understood the effects of string angle....I have discussed that topic with more than one physiscian but never got a reasonable answer - please enlight me :)
I'm also adding a picture of my fastest bows, which are a horn/sinew composites. And one of a horn bamboo longbow which is very similar to your model 3 (although very slim compared to your model. If my bows were evenly strained the wouldn't usually all fail in that same spot :OK
and btw Arvin: I think its true that the shorter bows outperform the longer ones with light arrows (due to shorter limb travel and higher dryfire speeds). On the opposite I dont think the longer bows have a advantage with heavier arrows at the same drawlength....that is a myth imho. These short reflexed bows can handle 10gpp very well.
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This has been a very educational thread. Thank you. It seems like there's going to be even more information added before it is complete. I'm not an engineer that understands all of these science/physics concepts, but I have made, owned, and shot a lot of bows and base my opinions on that. The fastest selfbow I ever owned/shot was made by Marc St. Louis. It was highly reflexed and also had static recurve tips. The bow shot a 10gpp arrow 199 fps. It has always been a quest for the best all-around combination of speed and shooting characteristics. Most of the speed bows didn't shoot my hunting weight arrows well or were not pleasant to shoot many arrows from a day. When I settled on the DR design it was just because it shot as fast as nearly all of them, plus it was very pleasant to shoot. I also agree that the design benefits from having the tapers correct. There is a fence 200 yards from my shop door, and it serves as a testing site when a bow is being made. It seems like the best ones will always send a 10gpp arrow over that fence...which is OK because it's my hay field on the other side of the fence. :) Thank you for the sharing of so much knowledge. :OK
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Bob, I dont think all the theories helped me a lot with my bowmaking. My most important lesson was: Make your bow look pleasant to the eye. a good looking bow usually is a good shooter.
For a wood only bow I'm very close with Arvins Design. I personally make them a little narrower and less pyramid but also put that slight reflex towards the outers. Those shoot very comfortable and plenty fast - I like others too, but I think this is my fav design for wood.
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Bob, I dont think all the theories helped me a lot with my bowmaking. My most important lesson was: Make your bow look pleasant to the eye. a good looking bow usually is a good shooter.
For a wood only bow I'm very close with Arvins Design. I personally make them a little narrower and less pyramid but also put that slight reflex towards the outers. Those shoot very comfortable and plenty fast - I like others too, but I think this is my fav design for wood.
simk, I absolutely agree. I forgot to mention your full draw photo posted earlier. The bow just looks too good not to be a great shooting bow. :OK
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I agree with you Bob on the Mark St Louis design. They are the fastest I have tested. They take a bit of skill and patience to pull off. To generalize a little bit I think it is safe to say that a simple composite bow ( wood or bamboo backed) will usually shoot about 10 Fps faster than a self-bow. So if we just talk self bows, I think it is safe to say that a straight pyramid self bow that is well designed with good wood and tillering will usually shoot between 168 fps to about 172 fps. If you go to an r/d design with 1 1/2" reflex, you are usually looking at 172 to about 176 fps. Recurves with about 2" behind the back usually about 175 to 182. There are a lot of exceptions.
My personal favorite is the R/d design and I am happy with anything over 172 for a self-bow. The difference is relatively small between the bows. For flight shooting the most important thing is getting the arrow out of the bow cleanly; that's why simple designs usually do well. You can lose a lot of speed in the first 10 ft of arrow flight if the arrow comes out sideways before it straightens out.
There has always been the catch-22 when it comes to energy storage VS efficiency. When you talk about efficiency, you are examining where your losses are. The two biggest and most controllable sources of loss are vibration and hysteresis caused by the set. The vibration can be reduced significantly by reducing the amount of working limb. This can also aggravate the set issue. The best way to mitigate that is to have the middle and inner limb do all the work and keep it wide. Extreme designs will usually shoot very fast for a few shots but quickly break down to mediocre performance if not designed properly. Wood has its limitations and a man has got to know his limitations.
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So more taper → more evenly distributed stresses and lighter limbs.......
I tried my D/R model using a 0.010 taper (more taper)...... the maximum strain values were higher.
With less taper (0.006).....the maximum strain values were slightly higher.
Was this with the same width width profile? A limb can be made stiffer, or for the sake of this discussion, less stressed, anywhere along the limb where the stresses are maxing out.
In VirtualBow, I get maximum speed and minimum strain when stresses are distributed as evenly as possible (within reasonable limits, of course).
In real life, we cannot “see” strain values, so it’s difficult to tiller perfectly, but we can learn a lot by using programs like VirtualBow.
visualing the stress curve with the program, is to me, its strongest feature.
The question is that how do you optimize the tiller? What is the parameter which is altered? More bending towards the tips, or handle? Something else?
In theory (and in generally accepted widsom), bend towards the handle does the most for energy storage. So for me, it becomes where a designer would seek to place the highest stress on the curve, but also keep it as level as possible without the stress curve peaking too much, finally deciding where along the limb length to have the stress curve begin its downward slope towards the tip where stress and bend is zero.
Looking foreward to your presentation!
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Here are the results I got from VirtualBow. Remember, no set, idealized situation, although 5 % damping in the model, 10 gn/lbs arrow, every reflexed bow’s tips are 100 mm (4") behind the belly side of the grip (thus about 70 mm from the back).
The deflex–reflex design performs well, while a handle-reflex design does not. The reason model 4 performed poorly is that the recurves didn’t open fully even at full draw; the string was still almost in contact with the base of the recurves.
Willie: Yes, in VirtualBow the ability to visualize the stress curve is a great feature. I also like the curvature graph—you can see exactly where the bow is actually bending.
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I also like the curvature graph—you can see exactly where the bow is actually bending.
Yes quite helpful with reflex/deflex and other profiles that are hard to judge when looking at the bow on a tiller tree.
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Thanks Tuomo!
I'd say the results are intersting to get a general idea about these designs. The setback handle being worst and the d/r best will will most likely match with reality.
However: Having the front profiles and tapers not optimized will distort the outcome relevant. Especially having the same front profiles on all bows neglects specific advantages/disadvantages of these designs. The recurves need a lot more mass on the outers to stabilize than a self-stabilizing longbow. In my experience the theoretical advantages of recurves and other complex designs over longbows mostly get consumed with the additional mass required. Therefore I would cast into doubt the "placements" 3-5 and also I think the gap between 1 and 6 is not that big.
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Very intresting Tuomo.
I think I shoot that bow Bob showed and it was a very nice shooting bow.
What would work best scaled down to a 24” draw.
I would be interested in the best performing length and reflex shape for a 24” @ 50 lb natural material Selfbow.
I’ve only done one deflex handle with static recurves . It was more draw length than I could comfortably draw at 28” .
Would the static tips in my bow add to much mass ?
It’s kinda hard to wrap my head around all the mechanics of a bow. Something so simple. Yet so complex.
Thanks for sharing
Bjrogg
I’d like to know the best front profile for it too.
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If we isolate the variables and assume that these bows are all evenly strained and 100% efficient then wouldn’t the difference come down to energy storage alone? I’m not sure what would make the difference just based on the unbraced profile. It’s hard to separate the real world effects that were used to making assumptions about such as strain, limb mass, hysteresis, limb vibration, etc.
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Simk: How do you optimize the front profile, and especially the tapers? The front profile is more of a practical problem, because in the model you can make it as narrow as you want, but in real life stability becomes a real concern. That’s the main reason I wanted to use the same front profile for every bow model.
As for the taper rate, I optimized it with strain distribution in mind. What would be a better approach? The 0.008 taper I used seemed to work well for every model.
Ryan: Yes, energy storage is mainly determined by the unbraced profile. That’s exactly what I wanted to examine, and of course the results of that difference also. All the “bows” had the same net reflex, yet they still behaved very differently.
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The design I’ve been using for years is closest to the third design. The speeds are close to what I get most of the time. I have had upward to 186 ft per second. Not often though. Interesting topic thanks for sharing. Notice the farther the tips get in front of the back of the bow the more speed. That’s with the deflex in the handle to help the stress on the inner limb.
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As for the taper rate, I optimized it with strain distribution in mind. What would be a better approach?
Model exceptional performing bows in virtualbow to find what the best strain distribution looks like.
Use this distribution model to test different degrees of deflex/reflex, different tapers and lengths etc.
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Nice idea, Willie, and definitely worth trying. But I see many problems as well. How can I be sure that strain distribution is the main feature of an exceptional bow? Why not mass or curvature distribution, or the side profile combined with some other parameter?
I don’t have an exceptional bow—just some good ones. Their common features are that they have minimal set and they are deflex-reflexed. Set is a material-related parameter, and when making wooden bows, minimizing set is only possible when strain is distributed as evenly as possible. I’m going to make some bamboo-horn bows in the near future, so with horn the set parameter is almost eliminated. Simk has made a lot of very fast horn-belly bows and has taken very good and reliable measurements of their performance (see Traditionell Bogenschiessen 117), so there is potential. But again, this is how we implement theory in a real-life bow.
So, I’m going to make deflex-reflex (or even deflex-reflex-recurve) bows with evenly distributed strain and test them. A long to-do list…
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yes, Tuomo, I had around 50 or so different bows from different bowmakers on the shooting machine....maybe post that in a seperate thread, its sure interesting.
How do you optimize the front profile
The longbow is self stabilizing when strung - you can make it as narrow as you like without getting into stability issiues. A recurve needs a certain width at its base. At the same spot the longbow can be made much narrower resulting in a different top profile and mass difference. Your experiment does not take in acount relevant specific characeristics of the design. Namely the lighter limbs of a longbow, and the extra mass of recurves. If we compare the experiment with reality we also must say, that you put recurves mainly on shorter bows - 68" is a bit long to make a recurve.
But this is all about fps. If we only talk about stored energy and sideprofile and leave the fps aside, this a very good experiment.
Shorter bows automatically store more energy - this we know - and also that reflex is another key factor. Now we have same length and same reflex. So the small differences we see come from the sideprofile (and tiller).
Maybe Tuomo could upload the force-draw-curves? Visualizing the stored energy? Maybe we see a nice hump in the curve of the d/r?
And Tuomo: Do these bows all have same length of string? Any Differences?
Gettin' curious again ;D
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yes, Tuomo, I had around 50 or so different bows from different bowmakers on the shooting machine....maybe post that in a seperate thread, its sure interesting.
How do you optimize the front profile
The longbow is self stabilizing when strung - you can make it as narrow as you like without getting into stability issiues. A recurve needs a certain width at its base. At the same spot the longbow can be made much narrower resulting in a different top profile and mass difference. Your experiment does not take in acount relevant specific characeristics of the design. Namely the lighter limbs of a longbow, and the extra mass of recurves. If we compare the experiment with reality we also must say, that you put recurves mainly on shorter bows - 68" is a bit long to make a recurve.
But this is all about fps. If we only talk about stored energy and sideprofile and leave the fps aside, this a very good experiment.
Shorter bows automatically store more energy - this we know - and also that reflex is another key factor. Now we have same length and same reflex. So the small differences we see come from the sideprofile (and tiller).
Maybe Tuomo could upload the force-draw-curves? Visualizing the stored energy? Maybe we see a nice hump in the curve of the d/r?
And Tuomo: Do these bows all have same length of string? Any Differences?
Gettin' curious again ;D
Do you still have the shooting machine set up? Im very interested in your experiments, please do post it, here or on another thread.
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Are you saying shorter bows store more energy? I believe this to be false I have never seen anything to support this.
Shorter bows automatically store more energy - this we know - and also that reflex is another key factor. Now we have same length and same reflex. So the small differences we see come from the sideprofile (and tiller)
I would agree that short bows tend to be more efficient. Many here will agree that right about 67" is an optimum length. .
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you are right Badger - I messed that up - the short bow does store less energy but is more efficient.
But why does it store less energy? String angle?
And why is it more efficient? Limb mass, limbtravel and inertia?
And why does the d/r in Tuomos experiment store more energy than the straight limbed bow? string angle?
Now: In practice we often see that short bows are faster — especially with light arrows — than the longer ones: is that maybe because limb mass and limb inertia (efficiency) matters more than stored energy?
If that is the case, when trying to make a fast bow, one should maybe focus more on efficiency than energy storage? How to optimize these contradictory facors?
Given that more stored energy usually means heavier and slower limbs, how do we find the sweet spot where arrow speed is maximized?
It must be where increasing stored energy starts to cost you too much efficiency by increasing limb mass and inertia.
Now where is that?
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Nice idea, Willie, and definitely worth trying. But I see many problems as well. How can I be sure that strain distribution is the main feature of an exceptional bow? Why not mass or curvature distribution, or the side profile combined with some other parameter?
you cant input a stress curve directly into Virtualbow as you can the profiles, but knowing what a good stress curve looks like can help you make the adjusments for your next iteration
when you look at arrow speed, also look at the stress curve for shape as well checking for max stress levels. Curve shape patterns will emerge with the faster arrow speeds. I never look at mass, if its too high, arrow speeds will suffer
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Simk has very good questions! I’ve been thinking about the same things, but I don’t have definitive answers either. Hopefully we can find some together. But here are my thoughts.
I don’t like string angle as a parameter, because it doesn’t have a precise definition. To define an angle, you need two intersecting lines. One of them is obviously the string, but what exactly is the other one? For example, in model 4, what is its string angle? Or model 5? Or with a recurve bow that has a circular arc at the tip – where do you draw the tangent to define the string angle? Sometimes string angle correlates with energy storage – smaller string angle → more energy storage – but I wouldn’t say they are always explicitly connected. Or at least, you shouldn’t focus too much on string angle, because it isn’t the parameter you should be looking at.
Why do shorter bows store less energy? First we should specify what we are comparing. By “shorter bow” I mean a bow that is short relative to the draw length. For a fixed draw length, a shorter bow must be drawn proportionally farther, and that leads to less stored energy.
You should think of a bow as a lever (or two-lever) system. It has a fulcrum and two lever arms. When drawing the bow, the effective lever arm length is decreasing. If we exaggerate a bit, think about a braced bow where the draw force direction is almost orthogonal to the limbs (or to the string, which transfers the force to the limbs), and then compare that to the extreme situation where the limbs are bent so much they are nearly parallel to the draw direction. At brace height, the limbs act like long lever arms; at full draw, they act like very short ones, approaching zero. Thus a bow acts like a variable-ratio lever, because its effective lever arm length changes throughout the draw.
Now remember that lever arm length affects the force needed: a long lever arm gives more mechanical advantage and therefore requires less force. Because of this, a longer-limb bow has more mechanical advantage near full draw than a short-limb bow. With a fixed draw length, when a short bow is drawn to full draw, its lever arms are shorter than those of the longer bow, which means it reaches higher draw force sooner. On the draw-force curve you will see this as the curve rising sharply – this is stacking – and stacking results in less stored energy overall.
But the most important point is that a short-limb bow’s limbs simply cannot bend much more near full draw. The lever system of the bow determines how the limbs bend and thus how they store energy. Therefore, short limbs cannot store additional elastic potential energy at the end of the draw.
The string applies the draw force to the limb tips, bending the limbs. This bending is what stores the energy. The limbs store elastic potential energy just like a stretched rubber band. The more you bend the limbs, the more energy is stored. The work done in drawing the bow is “force × distance”, and that is equal to the bow’s potential energy at full draw.
In physics, when you do work—like lifting a weight—the weight gains potential energy exactly equal to the work done. In the same way, the bow’s potential energy at full draw is exactly the work you have done in drawing it. You can calculate that potential energy by integrating the draw-force curve, i.e., by calculating the area under the curve.
Thus, you do work on the bow by drawing the string, which acts on the limbs, which act like levers and bend the limbs, which stores energy. The lever-arm behaviour determines how the draw force is applied to the bending of the limbs, which ultimately store the energy like springs.
In short, a bow is a complex system of energy-storing springs that also act as variable-ratio mechanical levers.
Here is small comparison made with VirtualBow-program, of short and long bow. Straight, normal front profile, taper rate 0.004 (evenly distributed stess).
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Are these real bow tests or computer-generated? I have never seen a 60" bow store that much energy unless it was a recurve with considerable reflex. Vibration or distortion of the limbs near the end of the power stroke is the area of the biggest losses. Reducing the amount of bending limb will also increase efficiency. You will see results here pretty quickly by just stiffening up the outer limb.
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Ive done a lot of study and thought on why short bows shoot light arrows better than long bows and can answer that one with certainty. The answer is horsepower vs torque. Short bows have high horsepower and long bows have higher torque. Small little 4 cylinder cars that are light weight can go super fast but a truck with an inline 6 can pull large weight uphill.
The answer is in the engine, and specifically has a lot to do with connecting rod length. The longer the connecting rod the more torque and slower the engine will rotate, vs a short stroke engine that will wrap up fast with a blip of the throttle. The shorter rods ( limbs ) allow for higher rotational speeds and more horsepower which a light load ( arrow ) can be accelerated from. The heavier the load the more torque required to motivate it.
Some comparisons can also be made to the draw length, which is why a longer draw will return at a slower rate than a shorter draw, but deliver more torque. An English longbow takes advantage of both situations. A short bow can be made to draw a long distance but the longer the draw the slower it will shoot a light arrow after a certain point. 22 to 23 inch draw seems to be the peak for super light weight arrow speed, and the arrows weight increases, so too should the draw length to gain the extra torque to speed that arrow up.
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to not confuse the thread we might stay a bit closer to the topic. The simple ( ;D) question actually seems: How and why does the sideprofile affect energy storage?
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to not confuse the thread we might stay a bit closer to the topic. The simple ( ;D) question actually seems: How and why does the sideprofile affect energy storage?
Lower string angles and preload from reflex is the simple answer. The entire limb responds to it's relative position to the string. Lower string angles allow for more weight up front because they build weight slower during the draw.
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I think a common issue with the R/d design versus a recurve is that they’re much harder to tiller. I assume this results in less even strain and a slower bow. Recurves are simple in comparison which may explain the difference by wood bow makers on average. I think it’s also easier to get more total reflex from a recurve than with a r/d bow. Seems like Fiberglass bows that can be designed so close to perfect are closer to what we’d see in a model versus real world averages.
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Here is small comparison made with VirtualBow-program, of short and long bow. Straight, normal front profile, taper rate 0.004 (evenly distributed stess).
I am using version 9.1 and do not recall seeing outputs for strain. Are you using a development version to get your strain values?
When I see such a difference between back and belly strains in your table, I suspect you are using different moe values or thicknesses for the back and belly layers, however the back and belly layers dont appear to be much different in thickness in the pics.
If modeling for basic shape/profile principles, why not just use a single layer?
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@ ryan, virtualbow outputs a graphic view as if on the tiller tree that one can reference for any stage of the draw when making tillering adjustments. Selfbowman had acess to a 36" printer and we once worked on enlarging Virtualbow plots to put behind bow when on the tiller tree.
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I am using version 9.1 and do not recall seeing outputs for strain. Are you using a development version to get your strain values?
Yes, I am using a development version 0.10. It has strain-values as an output, and you can give an fixed grains per pound -value for the arrow. It seems that it is also more accurate. Version 0.9.1 gives a bit skewed results.
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@ ryan, virtualbow outputs a graphic view as if on the tiller tree that one can reference for any stage of the draw when making tillering adjustments. Selfbowman had acess to a 36" printer and we once worked on enlarging Virtualbow plots to put behind bow when on the tiller tree.
That would be an amazing tool! I keep meaning to play with it but I haven’t gotten around to it yet.
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I think a common issue with the R/d design versus a recurve is that they’re much harder to tiller. I assume this results in less even strain and a slower bow. Recurves are simple in comparison which may explain the difference by wood bow makers on average. I think it’s also easier to get more total reflex from a recurve than with a r/d bow. Seems like Fiberglass bows that can be designed so close to perfect are closer to what we’d see in a model versus real world averages.
Wooden laminates are easy. I make a R/D model with VirtualBow, find a correct taper rate for specific front profile. Then I make the laminates (3–4, each tapering 0.000, 0.002 or 0.004), after gluing I shape the front profile and after rounding the corners the tiller is usually very close to "perfect". For example, that 98# bamboo-horn-laminate, I made two tillering rounds, maybe 15 minutes total. Thats it.
to not confuse the thread we might stay a bit closer to the topic. The simple ( ;D) question actually seems: How and why does the sideprofile affect energy storage?
Although I said that string angle isn't the best parameter to describe energy storage, it is still quite good to tell something about energy storage... Here is braced and drawn profiles of three of those models, and draw-force curves with straight reference line.
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Tuomo I really dig your D/R design. Would you be willing to share the parameters here?
I think a common issue with the R/d design versus a recurve is that they’re much harder to tiller. I assume this results in less even strain and a slower bow. Recurves are simple in comparison which may explain the difference by wood bow makers on average. I think it’s also easier to get more total reflex from a recurve than with a r/d bow. Seems like Fiberglass bows that can be designed so close to perfect are closer to what we’d see in a model versus real world averages.
Wooden laminates are easy. I make a R/D model with VirtualBow, find a correct taper rate for specific front profile. Then I make the laminates (3–4, each tapering 0.000, 0.002 or 0.004), after gluing I shape the front profile and after rounding the corners the tiller is usually very close to "perfect". For example, that 98# bamboo-horn-laminate, I made two tillering rounds, maybe 15 minutes total. Thats it.
to not confuse the thread we might stay a bit closer to the topic. The simple ( ;D) question actually seems: How and why does the sideprofile affect energy storage?
Although I said that string angle isn't the best parameter to describe energy storage, it is still quite good to tell something about energy storage... Here is braced and drawn profiles of three of those models, and draw-force curves with straight reference line.
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Tuomo I really dig your D/R design. Would you be willing to share the parameters here?
Here is VirtualBow model file, and measurements of the bow number 6.
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Thank you, will try it out.
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Thank you, will try it out.
Aussie, could you post the same for your design maybe in the other thread?
(just hoping to follow along here with virtualbow)
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Sure thing.
I'll try to post it this evening.
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Toumo, in an earlier post you asked about how to measure string angle?
This is what I would suggest.....
With a recurve you measure where the string touches the limb - measuring some kind of tangent does not make sense because the angle would stay the same (0) all the time.
At the end of the day we don't actually have to measure anything. Its enough if we understand the concept and know the general guidelines to keep the angle low.
cheers
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Ok, ok, for the scienece we measure :)
Are the pictures from bows 1, 4 and 6 Tuomo? If so:
Bow 1 angle 52.1 degrees - stored energy 101.3%
Bow 4 angle 53.9 degrees - stored energy 107.5%
Bow 6 angle, 49,9 degrees - stored energy 118%
with bow no 4 I'm not sure weather I measured correctly. Maybe measure from the very tip, and not the place where the string touches?
do you have the fd pic for the other bows too?
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Interesting analysis for string angle! Let's see what you can get from these. By the way, what is the program you use?
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Isn't it the shallow angle at brace that gives the high early draw weight and increases stored energy?
whereas excessive angle at full draw leads to stacking or an increase in apparent draw force but not stored energy?
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Good point willie. when the string touches the bow gets shorter virtually? complicated things. but something happening for sure, you can see that on the chart too. we here check only the angle at fd.
Tuomo, its autodesk fusion - pretty cool software for 3d design. they even had a FEA analysis addon, not for free version tough... :)
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complicated things. but something happening for sure, you can see that on the chart too.
a compressive force acting linear on the limb in addition to the compression due to bending?
maybe why such designs are more prone to compression failures?
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I misspoke earlier. It is the Gary Davis form that I adapted as my regular.
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I misspoke earlier. It is the Gary Davis form that I adapted as my regular.
I copied Gary's for at MoJam many years ago and it's the only reflex for I have ever used. My D/R form is an adjustable model that I also copied from a MoJam form that was made by Patrick Bumgardner.
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Patrick has made probably the most powerful bow for its draw weight ive ever seen. He isnt on here much anymore, but his handle is Lebhuntfish.
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Patrick has made probably the most powerful bow for its draw weight ive ever seen. He isnt on here much anymore, but his handle is Lebhuntfish.
It was built using this (his original) form.
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Isn't it the shallow angle at brace that gives the high early draw weight and increases stored energy?
whereas excessive angle at full draw leads to stacking or an increase in apparent draw force but not stored energy?
Yes, just like that! If you play with VirtualBow, you will find that the more string contact there is (especially with deflex–reflex designs), the more energy is stored. However, this requires that the string contact opens; in other words, there must be no string contact at full draw. See Model 4 with 90-degree recurves: because it does not open even at full draw, it is not a good design.
However, measuring the string angle at full draw is not very practical. As Simk said earlier, “It’s enough if we understand the concept and know the general guidelines to keep the angle low.” With the VirtualBow program, it is quite convenient to model different kinds of bows and gain a better understanding of bow behavior.