Beginner tillering questions for an ash Holmegaarden replica

[dvader]

I got curious about primitive bows a couple of months ago and decided to try it. I have no prior experience in either archery or bowyery but figured if the Danish could do it 8000 years ago with only stone tools, I could probably do it with modern tools. Sure, they had generations of experience but I have random people on the internet.

I started with an ash tree 7.5 cm in diameter and about 7m tall which I cut into pieces and split into halves. I got three decent pieces and one poor piece with a huge branch right in the middle. Since I'm a complete beginner, I figured I'd start with the poor piece and try to learn as much as possible from it. I've managed to get the bow into a rough shape and started tillering. It is currently bending OK and is about 28# at 15" (I haven't dared to pull it more than that yet).

I am currently a bit confused with the tillering. I see a lot of people tillering their bows to perfect semicircles or ellipses. That would make sense if the stick was perfectly straight to start with since you get the same stress/tension all along the stick. I started tillering for a nice semi circle but then my physics intuition told me that probably wasn't right. I should probably be looking for the same amount of movement along the stick. That is, if I want the same stress everywhere the deflection should be relative to the initial state and my final bow will look a bit crooked since my initial stick was. Is my intuition correct or have I missed something important?

I have attached two pictures that shows the current state of the bow. The first picture show the bow at rest and the second picture is at 15".  Directly to the right of the handle there is a natural curve in the wood and if you look at  on the 15" tillering picture, it looks like a weak spot since the bow seem to bend a lot there. But, when I pull the bow I don't see much movement at all so my intuition says it is actually too stiff.

Since I'm a beginner and have no experience to fall back on, I tried measuring the deflection (hence the red dots in the pictures) and I have attached the results. The first curve is from a spreadsheet where I calculated the change in angle at every red dot from 0" and 15". That is, at dot 2 I'm measuring the change in angle between dot 1 and dot 3. It seems to confirm my suspicion that the bow is not too weak at the handle (but further out on the right limb).

For those interested, I also tried some more advanced analysis by using spline interpolation through the red dots and plotted the corresponding derivatives along the bow. For the non-technical types, the top left graph shows the bow shape and the bottom left shows the curvature (second derivative which be an indication of  to stress/tension). The blue line is the bow at rest and the red line is the bow at 15". Just like the spreadsheet it seems to indicate that the curved area to the right of the handle is too stiff since there is not as much change as there is along the rest of the bow. But the main problem is probably the right limb where it seems to move too much. Does that make any sense?

Am I right in assuming that a good tiller means equal movement along the bow and not a perfect final shape? Do my current guesses about the stiff and weak spots seem reasonable? I am still learning the proper terminology so sorry for any confusions.

[DC]

I should probably be looking for the same amount of movement along the stick. That is, if I want the same stress everywhere the deflection should be relative to the initial state and my final bow will look a bit crooked since my initial stick was. Is my intuition correct or have I missed something important?

Yes

[mikekeswick]

I undersdtand you using the worst stave but you would have been better stacking the odds in your favour and using the best ones first!
The best/easiest/most failsafe method to determine the correct amount of stress on any bow is to watch the set (permanent deformation due to bending).
The rule of thumb for correct distribution of set is virtually none in the inner limbs, more as you get to mid limb and the rest out to the tips.
The reasoning being that any set in the inner limbs leads to a large loss of string tension, mid limb out has less effect on the tip position/string tension.
My advice is trace the bows side profile onto the floor/a wall etc and watch how it changes as you progress to full draw.
You are correct that the aim isn't to make perfect circles/ellipses at full draw UNLESS you have a flawlessly perfect stave to start with.
My advice with this particular bow is to get a heat gun and remove the deflex on the right limb next to the handle. Try to get both tips 'level' with each other relative to the handle. Staves where the limbs leave the handle at different angles aren't great when you are just starting out. It would also be worth heating this bow as ash responds very well to heat treating.

[willie]

Quit an an innovative approach for a "beginner". Tilllering a naturally bent stick is quite challenging.

Am I right in assuming that a good tiller means equal movement along the bow

Mostly, at least for those portions of the bow that you desire to have equal strain. Mike makes some good points about increasing the strain towards the tip,. or in the case of the holmegaard design, towards the outer fade where the nonworking "tips" begin. Another reason set is your best indicator, is that sometimes the wood it's self is not always consistent along the length of the bow.

 I am interested how you took your measurements, did you scale from a photograph? The method that Mike mentioned for monitoring set by tracing the resting profile as the bow is tillered out is common. A more precise measurement system, such as you have presented for observing limb curvature, could be useful.