So I’m not the kind of person that can be given a problem and then drop it when I don’t find an immediate solution. It bugs me, it eats at me, and no matter how I try not to, my mind continues working on it till I figure it out. So, here is my proposed solution to the negative vs positive tiller quandary, which limb should be stiffer and why, as well as commentary on other bow-making observations. Along the way, I will state some things that we all already know (or at least maybe you do) as if perhaps not known before, not to promote the idea that I discovered it, but rather so that no assumptions are being made about what the reader knows/understands and nothing is taken for granted. So bear with me in that regard.
I’ve been teaching science/physics for more than 10 years now, so scientific methods and experimenting are pretty deeply ingrained in me by now. However, I didn’t want to experiment on perfectly good bow wood and invest a lot of time in making failures, so I opted for something quicker and less destructive. I took a 60” long 1” diameter pvc pipe I had laying around, and put holes in each end to serve as nocks for a pvc bow. It is uniform and elastic enough to make a good approximation of how a bow would behave. I then put spring scales at each end of a makeshift bowstring to be attached to the nocks, so this would register the force acting on each tip of the bow. I then proceeded thru trials of differing hand positions and nock points on the string and observed mainly 2 things: forces registered on the spring scales and the amount of tip deflection from the straightened position.
The first thing I noticed was the most startling, but was also a face-palm. No matter how I pulled and held the bow, the spring scales registered nearly identical forces at each end. My problem before this was that I was looking at the string as being divided in two segments (top and bottom), each attached in two places: at the tip and at the arrow nock point where they join. This was big time WRONG!! This would allow the segments to carry different forces depending on how the bow was operated (which was my previous thinking) , when IN FACT it is more like one string going one load to the other (tip to tip) with a pulley in somewhere between (the arrow nock/fingers). The tension is such a string is going to be uniform all the way through, allowing the force to be equal at both tips. This is HUGE!! With all due respect to Dean Torges, this was the fallacy in his representation of the bow as a seesaw with a fat kid and skinny kid. The bow system is much more complex that this, and simply cannot be represented this way. What’s the point?? Here it is: no matter where you grip the bow OR the string, the forces acting on each limb are the SAME! If one limb feels 20#, so does the other. If one feels 30#, so does the other. So, contrary to Dean’s thinking with the seesaw (with all due deference and respect), the shorter limb (top on an equal limb bow when measured from hand pressure fulcrum) does not bear a greater load, but the same load as the longer (bottom on equal limb bow).
WAIT A MINUTE!! You may say, “but then why does one limb obviously bend more than the other when forces aren’t centered?.” Good question, but the answer is NOT in the size of the force acting on them since these are equal. So do they bear equal strain? Depends on how you define strain. If strain is load, yes. As an engineer defines strain, I don’t think so (I believe it takes into account length of the deformed object), but going into that is over my head at the moment. Surely we have some engineer bowyers out there who could chime in on that one. But really, that is neither here nor there. Let me answer the question about the amount of bend in each limb a little in layman’s terms. When spine is measured for an arrow, length matters. A short arrow will bend LESS under the same load as a longer arrow (provided the distance from anchor point to load is greater on the longer arrow.). THIS is exactly why an equal limb bow tillered on the tree with fulcrum at geographic center will show MORE bend in the bottom limb than the top when gripped and shot conventionally. The lower limb, in effect, IS longer than the upper in this scenario, and being under identical load will have a greater amount of deflection at the tip than the upper for the SAME reason the longer arrow bends more than the shorter one under the same load.
So, why does it matter, since they are under the same load no matter how you design/tiller the bow?? Well, all the experienced bowyers will tell you (as they’ve told me), “it just don’t work buddy!” You’re bow may function now, but eventually it’s gonna malfunction. The tiller will get all screwy or it’ll just flat out blow on ya. Before I go into my proposed explanation for that, let me confirm that in my experimental bow, the longer limb ALWAYS flexed/bent/had more tip travel than the shorter limb. Period. Why? Because they are identical and have the same stiffness, they are subject to the principles above as applied to an arrow shaft. One question that remains (haven’t been able to go back and verify) is the ratio of limb length to deflection. Does a twice as long limb deflect twice as much, and show the same amount of deflection at it’s midpoint as the shorter limb (since equidistant from center)? I suspect the answer is yes. I know, I digress, and haven’t answered the question at to why such a bow will self-destruct if not adjusted in tiller. I believe the answer here is in timing. Let’s first assume both limbs have equal mass. If that is the case, then the acceleration of each limb at release is directly proportional to the force acting on each limb. Since we’ve already verified that is true, then we can infer that the limbs will in fact experience the same acceleration when the arrow is loosed. Anyone see a problem? I do. If one limb is bent further (the bottom in our equal limb length and strength bow), then it has further to move! This creates a timing problem. The top limb is gonna tend to finish before the bottom. I believe this causes the bow to retain more energy (rather than going to the arrow), and that energy remains in the lower limb and eventually destroys it, not to mention creates hand shock. That’s an unverified assumption, but I think it fits with our observations.
Fortunately, we already know the solutions to these problems. Make the lower limb stiffer (positive tiller), or make it shorter. All I’m proposing is hopefully an understanding of WHY these adjustments are necessary and why they work. So the seesaw analogy was definitely problematic and leads to some misunderstandings, but Dean was dead on in his solutions to these problems. What happens when we shorten the lower limb? It’s gonna flex less AND have less mass, and be more in time with the top limb, (this also fits with our equal force per limb idea!). What happens when we just positive tiller/make bottom limb stiffer? Well, limbs will have about the same mass, but will have close to the same amount of deflection and distance to travel home. Given the same force (again, verified), they will arrive in sync.
Well, there’s more to talk about on this (string angle and balance in the hand, split vs. three under, where are the fulcrums really located, etc.), but my brain hurts, and I’m tired, and it’ll have to wait. Feel free to comment on those, however!!
BTW: This is all perfectly in line with the advice given on this post and elsewhere, I guess I just had to figure it out fer myself as to why it works this way, and hopefully so I can be more thoughtful in future bow designs!
Happy shaving :D
Topic: Can we hash this out? neg vs pos tiller***Clarification (Read 1512 times)
