Tiller shape vs front profile

[Kidder]

A lot of very experienced bowyers refer to tiller shape matching the front profile. In another post I started I was referred back to TBB for this info. I’ve since gone through all four volumes, reading all the chapters on bow performance, tillering, etc. There is definitely reference to it, but for the life of me I cannot find a definitive statement on what proper tiller shape for various front profiles are, and importantly why they are that way. Can someone please explain this to me? Thanks in advance.

[Don W]

A lot of very experienced bowyers refer to tiller shape matching the front profile. In another post I started I was referred back to TBB for this info. I’ve since gone through all four volumes, reading all the chapters on bow performance, tillering, etc. There is definitely reference to it, but for the life of me I cannot find a definitive statement on what proper tiller shape for various front profiles are, and importantly why they are that way. Can someone please explain this to me? Thanks in advance.

Try vol 4, page 95. I've read it so many times I knew the image i was looking for 

[simk]

I'm only a beginner, but as far as I understood the width of the bow all over the limb corresponds the amount of bend and as a result in drawlength gained from that same spot. e.g. if you have a pyramid limb you gain most of your draw length from the inners, steadily decreasing towards the outers. jmy2c

[Kidder]

A lot of very experienced bowyers refer to tiller shape matching the front profile. In another post I started I was referred back to TBB for this info. I’ve since gone through all four volumes, reading all the chapters on bow performance, tillering, etc. There is definitely reference to it, but for the life of me I cannot find a definitive statement on what proper tiller shape for various front profiles are, and importantly why they are that way. Can someone please explain this to me? Thanks in advance.

Try vol 4, page 95. I've read it so many times I knew the image i was looking for 

That’s the one! I read that last night and again today. I guess the problem is I just don’t understand it in relation to the shape of the side profile. Goes to show that knowing and understanding are two separate things.

[BowEd]

Kidder....You might be over tihnking this.I think it has to do with whether you have parallel width or tapered width limbs.Tillering is all about your thickness taper.Your thickness taper will be more aggresive with parallel limbs than with tapered width limbs.
You can do combos' too.Parallel width a ways to say mid limb.Then tapered width a ways on the same limb with less aggressive thickness taper.Each has it's own degree of aggressivenss of thickness taper.
A person needs to keep in mind the amount of work a limb has on it's length and where that is.Page 117 in the TBB 4 book.The outer limbs don't work as hard as the inner limbs.It's for a D bow but still the analogy corresponds to stiff handled bows too.
A nice smooth ever increasing reflex of any degree from just outside the fades to the tip.
That's why reflex is held better on the outer limbs more so than on the inner limbs and there's no reason to over stress the inner limbs with reflex because it has to do more work which will create stress and set and lose the resilience of your wood there.
The old mantra of 0 to minute set on the inner limbs with enough width to handle the load.A little set midlimb,and paractically 0 to no set on the outer limbs.
Sounds confusing but it really is'nt.Once a person establishes a thickness taper on making different types of bows enough times it is'nt quite so confusing.
Example.
http://www.primitivearcher.com/smf/index.php/topic,67543.0.html

[willie]

Two given physics principles of bows
1. a limb has to taper either in thickness or width or some of both. 
2. any given thickness of any wood has a bend radius, that if exceded, creates set.

Consider the pyramid back profile with a width taper:
For a limb to have equal strain along it's length, it needs to be about the same thickness throughout it's length, and since the thickness remains even, it will result in a consistent bend radius, or a circular bend.

Since a straight limbed bow tapers in thickness, it should bend more as it gets thinner if the outer is to work as hard or be strained as evenly as the inner, yeilding a more eliptically shaped bend from the side view.

[SLIMBOB]

I agree with Ed completely, but I will add a few thoughts. Parallel limbs, as Ed mentioned, get thicker as you move from mid limb to fade. Thick wood can’t bend as far as thin wood without taking set or breaking right?  So the tiller shape ideally on that bow should be, less bend near the handle, and gradually more as you move mid limb. A pyramid bow gains little in thickness as you move toward the handle, therefore, being the same thickness along the limb, it can and should bend more circular than its parallel counterpart. That is the long and short of it. But this is all based on a perfect stave in a perfect world. Many are the times that I have ignored the whole thing. I made a bow some years ago, 2013 or so, that remains my favorite bow. Knotty Boy, if you care to look it up. It is a 66 inch Osage, bendy handle, covered with knots. I made it parallel from mid limb to handle. 1.5” wide. I kept the tiller circular because It was high crowned and I could not go much wider with it than 1.5” and I needed to compensate for the knots. All things equal, it violates the rule, but it shoots beautifully and has held up over time.

[RyanY]

The way I see it the reason for this is two fold. One, to make sure the limb is utilizing the mass where it needs to for low set. And two, for efficient movement of mass along the limb. For simplicity sake, a limb parallel it’s whole length should be highly elliptical and a perfect pyramid should be circular (slightly more inner limb bend) with variability between those extremes.

Areas of lower mass (width) should bend less than areas with more mass. This is because you need a certain amount of wood to do the work being asked of it. Narrower areas will need to be thicker to store the same energy but can’t bend to the same radius as wider thinner limbs.

As you get further out on the limb the mass has further to move during the power stroke. The more elliptical the bend the more efficient that movement of mass for any given profile. But that elliptical shape would have to be in balance with where the work needs to be done for low set.

Examples.
A pyramid bow with an elliptical tiller is more likely to take outer limb set though the movement of mass in the limb is quite efficient.
An American longbow (parallel width taper) with a straight thickness taper would bend a lot in the inner limbs with excessive mid and outer limb mass for low efficiency. It would also take set unless made wide to take the bend.

[SLIMBOB]

I agree with that Ryan. Mass placement and movement is part of the equation for sure. 
I will differ with you on one thing…and it is just my opinion, but the outer, more narrow limbs are under less stress, and can therefore bend in a circular manner, without the need for them being thicker to carry the load, as they are carrying less than the inner limbs.

[RyanY]

I agree with that Ryan. Mass placement and movement is part of the equation for sure. 
I will differ with you on one thing…and it is just my opinion, but the outer, more narrow limbs are under less stress, and can therefore bend in a circular manner, without the need for them being thicker to carry the load, as they are carrying less than the inner limbs.

Not sure what you’re referencing with regard to the outer limbs from my comment.

[SLIMBOB]

May be my interpretation of what you said is wrong, but paraphrasing, “areas of lower mass (width) need to bend less than areas with more mass…”

[RyanY]

May be my interpretation of what you said is wrong, but paraphrasing, “areas of lower mass (width) need to bend less than areas with more mass…”

That was a gross overstatement on my part. It’s definitely more complex than that. It’s difficult to describe the dynamics for a whole limb with each piece relative to each other.

[BowEd]

I meant to say and agree with what slimbob said about more extreme character bows.My thickness tapering descriptions were described for darn near perfect wood.Character bows with knots,pins,and whooptee doos, and wiggles can take longer to tiller.Before it's through you'll be using your eyes watching the bend and your finger tips feeling for irregularities to get to the final draw length.Unbracing checking for set along the way many times.

[SLIMBOB]

I think, at least in theory, a pyramid bow can have a near perfect circular tiller and be right. The more narrow mid limb bending in the same circular ark as the wider inner limbs, precisely because as you move outward (toward the tip) the limb is under less strain, and can therefore be more narrow and yet carry enough mass to handle the strain. Again, on a perfect stave in a perfect world. From a more practical stand point, adjustments are made to compensate for all kinds of irregularities that throw the theory a curve ball.

[bownarra]

Agreed, nothing more to add other than this principle is absolutely key to making good bows