Bow design and mechanics testing with PVC models

[joachimM]

Hi folks,
I've been having an argument to and fro on PA about the efficiency of strong recurves versus less recurved specimens (http://www.primitivearcher.com/smf/index.php/topic,56255.0.html)
Theory at least suggests that strong recurves ("hooks") are less efficient because during much of the draw these bows are actually shorter bows but carrying the tip mass of a longer bow. Even though such bows have a fatter force-draw curve, their efficiency is supposed to be lower because of the dead mass at the tip of the bows during much of the draw.

So I decided to test performance of two bows that only differ in their shape (strong recurve versus contact recurve), with the same bow mass, same peak draw weight, same brace height, same length of recurve but different angle.

The below pics show the two bows, and their FD-curve, plus the 163 grain arrow used to shoot the bows.
Each bow was made from a 1 m section of electric wire PVC pipe (16 mm diameter)

AAAH,  blasphemy!! PVC on PA!! - before you decide to lynch me: this is basically the same principle as the plastic food tray models Tim Baker advocated in TBB4. Plastic, yes.

The sharp recurve drew 16.8 pounds at 24", the contact recurve drew 16.7 pounds at 24". Each bow was shot and chronographed 12 times with the same arrow (c. 10 gpp), which was drawn to exactly 24" (one but terminal node of the arrow).

In order to get to the same peak draw weight, I had to deflex the sharp recurve a bit. At rest, the tips of both bows were level.
The draw-back of PVC bows is that you cannot tiller it by remove material, only by flattening it more or less. Since a contact recurve would be more stable at the tips than a sharp recurve, the tip mass could also be lowered. Here I couldn't do that. As a result, I expected both bows to perform equally, even though the sharp recurve stored more energy.

Here's the results
Average speed of contact recurve: 120.6 fps
Average speed of sharp recurve: 107.0 fps
Actually, the slowest shot with the contact recurve (114 fps) was higher than the fastest with the sharp recurve (111 fps).

So don't let force-draw curves fool ya. It's not about stored energy, what counts is the energy imparted on the arrow. Kooi & Bergman (1997) showed this extensively in their paper (google it to find the pdf).

Joachim

[scp]

This is just fantastic. Thank you.

[mullet]

Could you at least paint them brown?

[PlanB]

Just out of curiosity Joachim, would you mind testing them both with a heavier gpp arrow and a lighter gpp arrow?

[bubby]

For a control they should at least have the same amount of reflex these don't

[Knoll]

I enjoy reading your posts, fella.

[joachimM]

For a control they should at least have the same amount of reflex these don't

Bubby, these have the same amount of net reflex at rest. Both of these will break when drawn to 26" (I tested one till breakage). They are strained about equally right now.

Suppose  you just removed the deflex in the highly recurved bow, it would have higher peak draw weight and then you'll be comparing two bows with different draw weight, because they are strained differently. If I remove the deflex, the highly recurved bow will break at c 23". I could redesign it non-deflexed and draw it to 21" (and get the same peak draw weight of c. 17#), and draw the other one to 24". But then I would be comparing bows with different power strokes, and the slightly recurved bow would store a lot more energy. Again, not what we want.

This here shows that if you have two bows with the same peak draw weight, the one with the fatter force-draw curve (which results from the recurved design) will not necessarily shoot better. Rather the contrary.

This confirms what mathematic models indicate, but what few people believe, dismissing the maths because it's just theory.  I walked the walk.

[PEARL DRUMS]

Are you assuming, or do you know, wood would react the same way? A lot of questions come to mind when I compare wood and plastic. Mass weight, flexibility, tip weight, reaction speed, stored energy and so on. All you really proved was two pieces of plastic shaped in two different ways reacts almost the same.

[bubby]

Make the recurves the same length just bend one more to avoid lift off , apples for apples

[bubby]

that one bow isn't what i would even consider a contact recurve it is basically a flipped tip. I'm with Pearl and his breakdown

[PlanB]

JochimM, if arrow weight isn't matched to tip speed well enough the amount of energy transferred will vary. Particularly in a stacking bow. This is why I was curious about arrows with higher and lower gpp. There could be a sweet spot here for that weight for one bow and not the other that reverses itself for a different weight arrow.

Not trying to argue the "which bow type is better point," but very interested in energy transfer dynamics. I do agree that F/D curves give only the static picture, not the dynamic one, and I had already read the papers you linked to before. I just think this is an opportunity to see how these bows react individually to arrow weight. Will they maintain the same distinction for different purposes?

[Urufu_Shinjiro]

Precisely PlanB, we can see this looking at historical asiatic bows, the Ottomans for example used short ears contacting the string and they used lighter arrows, around 300-500g (I'm speaking in terms of war bows and arrows), whereas the Qing bows had exceptionally long ears and string bridges but they used arrows closer to English weights, 1000-1500g. I know ear length and recurve angle are not exactly the same but I suspect the principle is similar with respects to arrow weight.

[sieddy]

Posted by: mullet
« on: March 15, 2016, 04:30:26 pm » Insert Quote
Could you at least paint them brown

Lol! 

[joachimM]

that one bow isn't what i would even consider a contact recurve it is basically a flipped tip. I'm with Pearl and his breakdown

Both recurves/flipped tips are exactly the same length, one is shallow the other isn't. Whether it's a flipped tip or a recurve is semantics. One has immediate lift-off, the other doesn't. The point was to prove that a FD-curve can be deceiving.
 
Pearl Drums: did they react the same way? Hell they didn't!! Look at the figures: one bow is >10% slower than the other.
Do wood and PVC react the same way in a bow: essentially, they do. in straight bows, you get a linear increase in poundage when drawn further and further, in both materials. But you're straying from the mechanics question: this is a question of the interaction between strain, leverage, and tip mass addressed in theory by Kooi & Bergman 1997 (http://www.bio.vu.nl/thb/users/kooi/kobe97.pdf).

Now, some folks reacted "well you shouldn't have deflexed the sharp recurve"
So I removed the deflex. It now stores a ton more energy (because it's strained much more) and has a higher peak draw weight than the other bow (at 24"), but still doesn't shoot noticeably faster than the contact recurve with a nearly straight FD-curve. It's about the same (average speed 117 fps, 4 shots 24" draw. During the fifth it buckled -a compression failure in PVC bows-, proving that the deflex made sense to compare the bows).
Even though I'm comparing two bows with different peak draw weight, the one everyone thinks would shoot faster doesn't.

To level the playing field again, I drew the contact recurve 1" further, drawing close to the same peak draw weight (actually a tiny bit more). Instead of shooting an average of 120.6 fps, it now shoots on average 129 fps. Again, a lot faster than the sharp recurve strained about the same amount. Which is logic, as the power stroke was longer. But at the same level of strain, the functionally longer bow wins.

10 gpp is a pretty standard method of measuring bow performance. It's not about the absolute amount of energy transferred, its about the amount relative to the stored energy: efficiency. Shooting heavier arrows will reduce the difference between both bows, but will not remove it entirely (unless shooting extremely heavy arrows). Shooting lighter arrows will likely exacerbate the difference. But I don't have lighter arrows than 163 gr.

But it seems many are missing the point: FD-curves fool the arm, not the arrow. I don't see anyone commenting on the core of the matter. Everyone is trying to find a way out of what seems to be an uncomfortable situation.

So I say: prove me wrong! I feel like I did my fair share of empirically testing the mathematic models. Come with your own hard data instead of opinions. . Shoot two bows which have the same peak draw weight at the same power stroke, and which are strained the same amount (the mass principle is a good starting point to know this). And prove me that a bow with sharp hooks/ bow with a fat FD-curve shoots faster at 10 gpp than one with "flipped tips" / bow with nearly straight FD-curve.

Mullet: here ya go 

Joachim

[PlanB]

10 gpp is a pretty standard method of measuring bow performance. It's not about the absolute amount of energy transferred, its about the amount relative to the stored energy: efficiency. Shooting heavier arrows will reduce the difference between both bows, but will not remove it entirely (unless shooting extremely heavy arrows). Shooting lighter arrows will likely exacerbate the difference. But I don't have lighter arrows than 163 gr.

But it seems many are missing the point: FD-curves fool the arm, not the arrow. I don't see anyone commenting on the core of the matter. Everyone is trying to find a way out of what seems to be an uncomfortable situation.

Joachim, I wasn't trying to find a way out of an uncomfortable situation and I accept (and already agreed) that F/D curves don't necessarily represent what the arrow sees. I know 10 gpp is the usual standard comparison, and a dowel painted black can serve as a lighter "arrow" as far as a Chrony is concerned. I'm sure you have access to heavier arrows, and they don't have to be tremendously so. I was just curious if there would be a difference, and just how much difference there was. Of course you don't have to try them if you don't want. It was just a request.

As far as commenting on the core of the matter, here it is:

The string can only deliver to an arrow as much energy as that arrow RESISTS while moving. The resistance an arrow presents to the string takes two forms: inertia, and friction.

Ignoring friction, inertia is a result of mass -- the arrow's weight, in other words. A heavier arrow accelerates more slowly and absorbs more of the available energy.

A very light arrow has little inertia. That's a plus as far as speed goes. It can accelerate very quickly immediately after the string is released.

If a bow has very slow limbs / heavy tips, high stack, high internal resistance and a high draw weight, it may be possible for a light arrow to outrun the limbs (and string) soon after release. If so, it is gaining no energy at that point. No matter what the F/D curve says is the draw weight at that distance (and further along) before it leaves the bow. In fact, if the arrow nock is tight, it may actually be dragging the string with it.

A heavier arrow, accelerating slower, may absorb energy from release all the way to brace height, since it is not moving as fast as the limbs and string. It is also resisting the string more because of its inertia. It is technically a more efficient system, and its behavior will look a little more like the F/D curve, although it will never receive the forces that the F/D curve shows.

If those are extreme cases, it's also possible to imagine cases in between, where a light arrow receives a smaller fraction of the energy available than the heavier arrow from a somewhat faster bow, but where the differences are less extreme.

Since a light arrow mainly gets its energy from the furthest part of the draw, the difference in these classes of tip designs can favor (or not) that segment of the release cycle. So also can tip mass, and a whole lot of other variables. I personally think it would be very difficult to isolate all of the factors which contribute to initial limb tip speed.

In fact, testing arrows of different weights might be a very useful measure of whether a bow is slinging an arrrow for most of the draw length or only the initial part, and at what weight arror this transition occurs. And that is why I was just curious about the results using different arrows. Nothing personal, nor trying to prove anyone right or wrong.