Further discussion of hang angles

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:

Backsaw fdb & solution**


*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

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5 Responses to Further discussion of hang angles

  1. Patrick Endicott says:

    Thank you for the excellent article on the hang angle
    I have read a number of article on the subject but they where so vague they did not say any thing
    I know on older saws the angle seams to be ~0 degreed are you aware of the reason newer saw have a high hang angle?

    Thank You

  2. admin says:


    I’m not sure why that change happened. Matt Cianci (The Saw Blog) might be a good person to ask. His knowledge of saw history is much greater than mine, and he is always happy to talk about them. You should be able to find his contact info on his website; if not, let me know and I will get it to you.

    Hang angle, as I measure it (and there is no standard definition, so others will do it differently), wasn’t quite 0 degrees. Referring back to an older post, the tenon saw in Smith’s key has a hang angle of about 16 degrees. How accurately this drawing reflects the actual saws is something I do not know. The Seaton Kenyon tenon saw (which I believe is pretty accurate), has a hang angle of about 22 degrees.

    This 18 inch Disston saw has a hang angle of about 26 degrees.

    It also seems (based on casual observation, and not actual measurements) that early, smaller backsaws (particularly dovetail saws) tended to have higher hang angles than later ones.

    I’m not sure what to take away from all of this, but it would be interesting to look into it further.


  3. Andy Lovelock says:

    Well I take my hat off to you sir. I can’t tell you how many times I’ve said to myself whilst filing saws “There must a formula for all this” and now you’ve come up with three. LOL. I’m going to re-read your PDF a few more times before thinking about posting a comment though.

    Regarding Patrick’s question, I’ve often wondered whether saw manufacturers started producing saws with a higher hang angle because people’s ability to sharpen them properly was decreasing. The higher hang angle would assist in keeping the teeth engaged in the wood due to the increase in downward force even when the teeth were less than sharp. Then again, the rake was also relaxed on later saws, so I’m not sure that theory holds water. I’ve also wondered whether the fact that carpenters found themselves working more with softwoods influenced the design of saws and their tooth geometry in later years.

    Great post Isaac.

  4. Bill Garver says:

    Great post! Exactly what I was looking for, so it saved me reading a bunch of other likely inadequate posts. I used to teach free body diagrams when in grad school and you would get an “A”. But only a 98, because there is a typo in the third word of the second to last paragraph, which makes the statement incorrect. You mean Fb, don’t you? 😉

  5. Isaac says:

    Prof. Ghosn, is that you?

    Sorry, he was my Mechanics professor, and I am still haunted by what was drilled into our heads in that classroom. In a good way, of course.

    Thanks for pointing that out. You are right, and I have updated the pdf. Thank you for taking the time to read and correct it. It is appreciated.


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