Tiller shape vs front profile

[RyanY]

I think it’s helpful to think of these topics in terms of examples and thought experiments. Say you have a pyramid bow and a typical parallel limb taper (American longbow) bow and both have a circular tiller with the same amount of set. Which one would shoot faster and why? (Same poundage/draw length, length, etc. )

Since this is getting off topic and only Mark bit on this, I’ll give my thoughts on this scenario.

Starting with the pyramid bow because it seems easier to understand. 2” at the fade Straight taper to the tips very mild thickness taper in a real world scenario, let’s say 1” of set where the set is uniform along the whole limb (hypothetically), circular tiller. Now let’s design the parallel limb bow to try and take the same set with the same tiller shape.

We will say the second bow has limbs that are parallel in width to mid limb and then taper towards the tips. For the parallel width, if we start at 2” wide, the rest of the limb will have more width in terms of total back surface area. Keeping it 2” wide it would mean the inner limb would take the same set as on the pyramid bow. Given that the rest of the limb is wider than the pyramid bow it’ll have to be thinner to bend to the same degree. Being thinner, the back and belly are closer together and will stretch less resulting in less set in the rest of the limb. Remember the goal here is to make the bows have the same amount of set. We WANT the parallel limb bow to take a bit more set in this scenario so we will make it narrower, say 1.75”. Now that the inner limb is narrower but bending to the same radius as the pyramid bow, it’ll have to be slightly thicker for the same amount of force to bend it to that degree. Being thicker, the back and belly stretch a bit more resulting in more set getting us to that 1” mark. The bow is narrower than the pyramid bow in the inner limb but then becomes wider at the point where the pyramid bow narrows under 1.75”. The rest of the limb, again, being wider, will need to be thinner to bend to the same degree as the pyramid bow. The wider thinner cross section of the mid/outer limb is more massive than the narrower/thicker cross section of the pyramid bow. This moving mass robs the parallel limb bow of efficiency and thus it’ll shoot slower given that the set is the same and both bows store the same amount of energy with the same tiller profile.

Now, how would we make the parallel limb bow more efficient with the same amount of set? The parallel limb bow having more width and therefore mass in the mid/outer limb can afford to have that area bend more to both store energy and the shape of the bend results in less mass movement compared to the pyramid bow. F Where the bow takes set would move from the inner limb to more mid limb after making the inner limb thicker to resist the bend, take less set, and allow the mid/outer limb to bend more. This bow would be narrower than the previous one as we are less concerned about inner limb set and thus overall mass for the design is reduced. The energy storage will lower slightly as a result of a more elliptical tiller shape but the minor difference in this for same length bows with these profiles will be overcome by optimizing mass movement. This is why it seems most conservatively designed bows of differing styles shoot about the same speed if optimized.

To me, it’s pretty easy to understand why it’s helpful for bows to be tillered differently based on their width profile. Understanding exactly how to do this for every bow is a challenge given so many factors involved but low set with skinny outer limbs is a good start? It’s also possible that this one dimension of gaining efficiency isn’t the end all be all for arrow speed for other reasons (limb vibration comes to mind).

[SLIMBOB]

Scp. I think the conversation has gone, about as I would have expected, which is, not so bad. I have seen this for years on here. Somewhat “newish” folks asking well intentioned questions, that would be far more relevant and well received, if asked in a college classroom. No offense meant to those in pursuit of higher education, but this is not an exact science. Every type of wood comes with its  own peculiarities. Within a given species, the properties of one stave can differ pretty dramatically from its neighbor stave. To add to that, we are not building furniture, where somewhat exact dimensions can be plugged and played. We are asking a piece of wood to let us bend it, until it is near broken, and then do that again 5000 times. Without coming apart, all at once or a little at a time. That it is a moving target, and all the math in the world CANT tell you what kind of lead you need to take. Only lots of repetitive practice, until intuitively, without thinking, you can hit the center. Its not the answers that you may misinterpret, but the questions themselves. 

[scp]

You did say whatever mantra you’re talking about isn’t precise.

Seems like you want people to explain a complex concept simply enough and in a way that you believe it. These concepts are very complex and any distillation will be incomplete to some degree. If you want to understand something then it’s worth at least learning to use the language that is actually relevant in these discussions instead or asking others to try and understand your version of them.

Frankly I don't remember why I would have said the mantra is not precise, when it is not meant to be precise but just peculiarly specific. I must have been thinking that it lacks the depth of explanatory power.

This is a little better in that aspect:
"Bow limbs are tapered because the load changes along the length of the limb and you need less and less material to carry it as you move towards the tips. It is more structurally efficient to width taper than thickness taper and it results in lighter limb tips, which gives higher performance. ~Mark"

Or the "mass principle". These "principles" have some structural and functional information with more explanatory power.

But as Willie noted, those two probably conflict each other, because using thickness tapering of narrow limbs will usually make the bow lighter than using the width tapering on wide limbs. 

Now we need a deeper understanding.

[willie]

All generalizations are never as precise or exact as you tend to believe, even with good grounding in physics.

Some seemingly simple formulas in physics are actually empirical observations correct in 99% of cases, and are accepted as "generally" valid, at least until applied to the outliers.  Other formulas are by definition, derived from mathematical units. sorting them out is probally beyond the scope of this thread, as I haven't seen Kidder for a while. BTW, soil mechanics, or geophyiscal engineering makes use of a total stress vs unit stress concept, but it is the only field that I know of that does.

I think it might be quite unexpected, but I am using the bow making conversations here as a window into how people from diverse backgrounds interact to accomplish shared understanding of complex issues. So far, not that great.

After studying engineering long ago, I must confess I find the the study of the human condition to be much more of a challenge. I actually think we are doing quite well at finding a shared understanding. I was much impressed by the balance in Slim's reply #84
(and the fact that he still identifies as deplorable after 5 years, makes me chuckle every time he posts)

[Don W]

"I think it might be quite unexpected, but I am using the bow making conversations here as a window into how people from diverse backgrounds interact to accomplish shared understanding of complex issues. So far, not that great."

That has to be the understatement of the post.

I think a lot of use just want to know what direction to go in to make more efficient bows. I think Ryan and I are on the same path. (Although my path is a bit longer). I tend to immerse myself in a subject to try to keep my mind sharp. I'm self taught through two careers. I just want to learn what technique will get my progression to better, more efficient bows without actually building hundreds of them. So far all guidance has been vague and wide open to interpretation. I have always learned by doing, but typically one can find an example that can be precisely followed. O (-_)k, maybe with a precise example of a wood bow it will not come out precisely on the numbers, but it should get you to a working bow with working knowledge of how and why you got there.

[Del the cat]

"I think it might be quite unexpected, but I am using the bow making conversations here as a window into how people from diverse backgrounds interact to accomplish shared understanding of complex issues. So far, not that great."
I think that's a bit disingenuous.
You can't really expect people to follow the thread when it gets into lengthy maths/physics/spreadsheets/formulate etc, when it is expressed in brief sound bite style posts. (And I'm not into reading any referenced scientific papers).
Speaking for myself, I'm unlikely to ever be making bows by numbers or formulae (Although I have made bows from some basic Mary Rose figures).
To me tillering is only ever really be done by eye and feel, which is why I keep banging on about how and arc of a circle can at least be seen and judged as a start point... ok you can make it a tad more elliptical that that... BUT (IMO) you can't actually quantify or measure it in any meaningful way (other than going by the "no set" principle*)... if only for the simple fact that there is virtually no decent baseline or frame of reference from which to take measurements.
The esoteric technical points probably have some value if one was to make a bow using a CNC machine!
Del
* Using the "no set" principle is not going for "elliptical tiller" or "Tiller based on front profile" ... it is simply tillering for no set!
PS. I shall try very hard not to comment further on this thread

[Morgan]

I think with stave bows, the best you will glean is a general approach as opposed to hard and fast rules. I’ve learned a lot reading through just these posts here, and am so appreciative that many of you delve into the technical aspect of this stuff, because the discussions that you have opens my mind to understanding things that I did not previously.

[RyanY]

"I think it might be quite unexpected, but I am using the bow making conversations here as a window into how people from diverse backgrounds interact to accomplish shared understanding of complex issues. So far, not that great."
I think that's a bit disingenuous.

+1. Anytime someone takes this type of stance in a discussion it's always a last-ditch effort to stay on the high horse.

BUT (IMO) you can't actually quantify or measure it in any meaningful way (other than going by the "no set" principle*)... if only for the simple fact that there is virtually no decent baseline or frame of reference from which to take measurements.

You absolutely could do this but it would require measuring each piece of wood for it's individual properties and then making all your calculations based on that. 99.999% of bowyers don't have the knowledge or interest in doing this.

* Using the "no set" principle is not going for "elliptical tiller" or "Tiller based on front profile" ... it is simply tillering for no set!
PS. I shall try very hard not to comment further on this thread

The problem with only basing this on no set is that you can get overbuilt bows. This is why most average osage bows are probably overbuilt dogs. They take no set but have 1/2-5/8" wide tips with most of the bend in the inner 3rd of the limb resulting in a ton of moving mass. This is why it's helpful to compare bows such as in my example. The front view profile absolutely matters for reasons other than no set.

I demand a response.

[willie]

The problem with only basing this on no set is that you can get overbuilt bows.

Ryan, are you  referring to just building a bow with no set, or Badgers "No Set" tillering method?
With the latter method, you are actually detecting early indications of compression damage before set becomes apparent in the side profile. It does not indicate where the damage is about to occur if you do not reduce your weight goal though, so one should have a good idea beforehand which side profile is ideal for your chosen taper.

[Del the cat]

@RyanY
"...
I demand a response."

My response:-
<shrugs>
Del

[RyanY]

The problem with only basing this on no set is that you can get overbuilt bows.

Ryan, are you  referring to just building a bow with no set, or Badgers "No Set" tillering method?
With the latter method, you are actually detecting early indications of compression damage before set becomes apparent in the side profile. It does not indicate where the damage is about to occur if you do not reduce your weight goal though, so one should have a good idea beforehand which side profile is ideal for your chosen taper.

Not referring to that and that’s my understanding as well. If we use set as the only indicator for tiller shape then we can still get inefficient bows. Mass distribution and movement need to be accounted for as well like you are saying should be thought of beforehand. Maybe I misinterpreted Del’s last point.

[PatM]

How do you tiller a heavily  scalloped bow?

[mmattockx]

You absolutely could do this but it would require measuring each piece of wood for it's individual properties and then making all your calculations based on that.

It does. It isn't too much work to measure MOE of your material, which is by far the most important number to have. I now do a bend test sample for every bow I make to get MOE and go from there. I use more general limits for set based on larger samples from the same type of wood. David Dewey compiled a fair amount of sample data as has Alan Case.

In my case it is more time efficient to do this than to just hammer through making bows until I get enough experience to have it down. One thing I will say to all beginners is that it is completely worthwhile to tiller a few bows from scratch before trying to be more scientific as it helps develop your eye for how a bow should bend on the tree. I had one small tweak to make on my last bow that I made using David Dewey's spreadsheet and I never would have noticed it if I hadn't hacked at a couple from scratch before moving onto the more science based approach.

Another thing to realize is all my number crunching and design work only gets me maybe 95% of the way home. The inconsistencies in wood and the less than perfect nature of woodworking will always leave me needing to do a bit of tillering to finalize a bow. So science can replace a lot of the art, but not all of it, which is fine with me. There should always be a bit of magic mixed in there somewhere.


Mark

[scp]

"I think it might be quite unexpected, but I am using the bow making conversations here as a window into how people from diverse backgrounds interact to accomplish shared understanding of complex issues. So far, not that great."
I think that's a bit disingenuous.

+1. Anytime someone takes this type of stance in a discussion it's always a last-ditch effort to stay on the high horse.

Exactly. That's what philosophers do. They try to make people realize they don't actually know as much as they believe. And they are hated for that. Especially by those who need certainty in life.

No amount of math will solve all the problems of bow making with natural materials in any near future. We are not even at the stage of fully categorizing all the relevant factors involved, I guess. People love to pretend to know better than others. Philosophers love to pretend to know nothing when there are so many things we already know well enough.

Humility brings knowledge. Knowledge brings hubris. Saying things like these is just another desperate attempt to pretend to know more than we actually do. Nature laughs at our certitude. Who would have thought million of people would die so easily and unnecessarily in this age of science and technology?

[RyanY]

There should always be a bit of magic mixed in there somewhere.


Mark

Love this.