Is there any correlation between design stress and performance? In other words, all else being equal, will a higher stressed design bow result in greater performance? One example of what I’m thinking is a 50# 66 inch bow versus the same 50# bow but only 60 inches overall. Assuming that is the case, will the performance degrade over time where the performance of the low stress design overcomes that of the high stress design after extended usage? Thanks for entertaining my wandering curiosity.
When I've previously said things along the lines of what I say below, I have attracted criticism for my expression of this craft as being too divorced from the romance of bowmaking by feel. However, given your question I feel an answer such as the below merits this sort of info. Using methodologies from materials science and mechanical engineering allows us to answer questions such as yours, and has helped me to personally teach maybe 180 students how to make dependable, high performance wooden bows.
Yes, there is a correclation between stress and performance. If the stress is very (very) low, it will be because the stress is being distributed across a whole lot of wood. Either through very long or very wide limbs (or both). If your bow is very high stress, it will be because the bow is very short or very thick (or maybe both).
In the former case, all that wood across which the stress is distributed presents a whole lot of excess mass. More of the energy stored in bending the bow has to be expended on accelerating the heavy limbs.
In the latter case, the bow gets dangerously close to having stress that either causes high amounts of set (which diminshes performance) or breaking (which summarily ends all performance). A bow which is tillered to a high level stress and repeatedly exposed to that stress is likely to deteriorate in performance over time. I understand that it's not uncommon for wooden flightbows last a few shots and then break down (or break up).
So the aim of the game is to find that amount of working stress that walks the fine line between sufficient wood to withstand the stresses over time, and of sufficiently high stress to minimise the mass. In your example of the two 50# bows, ideally they'd both have the
same amount of stress. There may be some who don't believe that, but mechanically it's true. A piece of timber with an ideal amount of working stress should be made into bows that experience that amount of stress regardless of the length or drawn shape.
While it is true that the variability of wood's mechanical properties can be quite broad, it is also the case that this phenomenon doesn't matter much so long as the stave is of sufficient size to extract a sample for bend testing first. There are probably many bowyers who would argue that this isn't 'listening to the bow/wood', but I'd argue that it is in fact listening very carefully after having asked the wood some very specific questions.
It is entirely possible to measure the mechanical properties of a piece of timber and from those calculations make a dependable, high performance bow. I've done it for years. What's more, I've outsourced the calculations to spreadsheets. I've written a reasonable amount about it here:
https://ozbow.net/phpBB3/viewtopic.php?f=34&t=5450 and here:
https://ozbow.net/phpBB3/viewtopic.php?f=34&t=13765. You can do the same with free software and engineer your own bows.
If you've the patience to go through that first link, you'll see its possible to make a bow with perfectly even stress and strain throughout the entire length of the bow, and that you can achieve this regardless of the particular drawn profile of the bow, be it English Warbow or short Mollegabet. If you go through the second, you'll see how I record bow properties in shorthand. Of note, by combining my bend test library with Tim Baker's, I found that while a wood like Rock Maple might vary in its mechanical proprties between samples, it is very often the case that the variation is sufficiently small not to matter a great deal.
I suspect the practice of rounding the bellies of yew bows is more a matter of convention than engineering best-practice.
AY
