Side/belly tillering

[Hrothgar]

Good refresher discussion. (Its easy to tell that Del has been up a few hours ahead of us   )

[BowEd]

I like to use a combination of both belly and side tillering on my bows.If my thickness taper and tiller is spot on even amounts of side tillering from each limb keeps it in tiller yet and reduces draw weight 8 times less than belly removal but reduces limb mass in the process.It's a way of zeroing in on things for the bow.Checking tiller and set all the time.

[Springbuck]

This sounds good. I'll break out the TBB and read your chapter, Again. Do you just use an average limb thickness to determine the different radii ( I don't think I've ever typed that word before )
[/quote]

No.  That's actually the whole point.  I hate dragging math into it, but......

Imagine taking some 2" wide boards and clamping them around a big curve, like say, a tractor tire.  Let's say the boards are five feet long, and the tractor tire is also five feet in diameter.  Ok?  Now, lets say that one of these boards is a full inch thick, and the other board is 1/4" thick.  On the tractor tire, the inch thick board is now scribing the arc of a circle and the diameter of that circle, on the belly would still be 60", BUT would be 62" on the back.  The thinner board has a 60" diameter bend on the belly, but only ma 60.5 diameter inch circle on the back.  So, 60:62 inch ratio for the thick board, and 60:60.5 inch ration on the thin one. Which one is under too much strain?

A certain thickness can only take a certain amount of bend.  Badger says 1% difference between inside and outside curve.   1% of 60 is 0.6 inches, and 1% of 62 is 0.62, right?  Thus, a 2" diameter difference is way too much, and you shouldn't try to bend a 1" thick piece into such a tight a circle.  But, a 1/4" thick piece can tolerate it easily.  My math is primitive, but it's for visualization.

So, we're back to "thinner wood can bend farther than thicker wood".  I tend to more or less calculate this where I want the limbs to bend the most, and then fudge it up where the limbs need to be thicker.

[DC]

But a bow limb is not 1/4 or 1" thick. It's 1/4 on one end and 1" on the other(sorta). What's the difference between the back and belly on that?

[PatM]

You're still striving for similar strain levels relative to how much the bow is bending in certain areas. So even though your depth and width may change, so does the  way the bow bends in those areas.

[Springbuck]

  Yeah, right.  So that means the thinner parts CAN bend to more curve than the thick parts.

  One of the best things I ever learned in bowyering was how to visualize a pyramid bow, with even thickness and a side taper like a long skinny triangle.  In theory, such a bow bends evenly (arc of a circle), because it's thickness is even, and the side taper is consistent. From there I can work out changes to the front taper in my head.  Like, if it DOESN'T taper side to side here, then it needs to taper back to front, and change the curve from arc to oval.  So, the 1% rule applies at any give section.  Thicker= less bend, thinner=more bend.

[joachimM]

Front profile has very little to do with tiller unless the bow is of constant thickness, see the miniature bow at the foot of this post on my blog, which illustrates the point:- http://bowyersdiary.blogspot.co.uk/2014/04/ashbow-re-try.html
Del

Del, great mini-bow you made and very illustrative. But I think you missed the point of the argument "front profile dictates tiller shape" that Steve makes in his TBB4 chapter on the mass principle. The bow you made will have a lot of excess mass at the tips, despite bending evenly in a semicircular tiller. It won't shoot as well as a normal pyramid bow of the same poundage. To get a bow with an ideal mass distribution for maximum performance, you end up with a bow whose tiller profile can be deduced from the front profile.
It doesn't mean you cannot make bows that deviate from that, but they won't be as efficient in storing energy for a certain amount of wood.

[loon]

Not as efficient in transferring energy, rather?
Korean bows are... parallel tillered? They're a rectangle in the front profile. Maybe that's why they don't seem to be as famous for flight archery as Turkish bows...
Makes sense that a pyramid bow would have lighter tips.

[joachimM]

Not as efficient in transferring energy, rather?

Yes, in theory. Not in practice.
 If you have wood that isn't strained as much throughout the bow, it means you have mass that is storing less energy than it could, because it is loaded below its maximum (or below the level of other parts). Excess mass is excess inertia and is mass that needs to be moved without doing its fair share.
"front profile dictates tiller shape" is all about equalizing strain throughout the working parts of the limb. In a pyramid bow, equalizing strain is achieved by an (nearly) even thickness throughout the limb.
Of course you can make a bow that doesn't follow that principle. But it will have a lower draw weight than a bow of similar wood mass that is tillered in that fashion.

[loon]

In theory, not in practice? So a parallel bow has a more stacky draw force curve than a pyramid bow, both with circular tiller?

I see stored/potential? energy as the integral/sum of the draw force curve, and transferred energy as the kinetic energy of the arrow, which is probably just stored energy minus handshock. Dunno about all that weird oscillation stuff.

A bow that's unevenly strained (parallel limbs) would store the same energy as a bow that is equally strained throughout the limbs *but bends the same*, but the uneven-strain bow transfers it less efficiently than a bow without extra mass. More handshock, less arrow velocity, but they'd both launch a broomstick at about the same speed since efficiency goes way up with projectile weight.

Blah terminology.