I recently wrote a short entry on saw handle hang angles in which I alluded to providing a more technical analysis of the topic. After a few late nights, that analysis is ready to present in this post. This will be a bit more technical than the first one, and possibly of even less general interest.
If there is one concept that is drilled into the head of every engineering student, it is that the solution of any problem begins with the construction of a free body diagram that clearly shows all of the forces and their locations. The validity of the solution depends on the accuracy of this diagram.
The free body diagram of a backsaw is the starting point of this analysis. The remainder of it is largely a more rigorous confirmation of what was already covered in the first post. The major difference is the inclusion of the weight of the saw in the analysis. While this does not change our original findings, it does provide a third principle to take away from this mathematical exercise.*
This principle being that, as the weight of a saw increases, the teeth “bite” more deeply into the wood, allowing a greater proportion of the sawyer’s thrust to be directed parallel to the toothline (and less of it downward) by lowering the hang angle of the handle.
To avoid rendering issues, the free body diagram and its solution are presented in the following pdf file:
*In the event that you do not recall, or did not read (and who can blame you), the first two principles enumerated in the initial post, they are repeated below. -Ed.
“The first principle being that a saw with a higher hang angle will necessitate either adopting a more upright stance, lowering your work, angling the toe of the saw up, or some combination thereof. This assumes you are interested in the proper mechanics of sawing.
The second principle being that, ceteris paribus, as the hang angle increases, the rake angle needs to be relaxed to avoid difficulty in starting and catching in the middle of the stroke. This effect is much greater in rip saws than in crosscut saws.”
**A reader pointed out a mistake in the original version of this pdf. It has since been corrected. In the second to last paragraph, the first sentence began “Seeing that Fc can be …”. Fc has been replaced with Fb. -Ed., 30 April 2014