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.