The best shape for a reflexed bow?

[willie]

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.

[Tuomo]

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.

[bjrogg]

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

[simk]

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

[Tuomo]

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.

[simk]

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  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

[Tuomo]

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).

[Selfbowman]

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.

[simk]

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 

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.

[Bob Barnes]

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.   

[simk]

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.

[Bob Barnes]

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.   

[Badger]

    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.

[willie]

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!