ideal edge/bevel angle

[brothers]

I've been trying to recall how to calculate the angle of the bevel that is required in order to make a good cutting straight razor. Someone once told me the ratio of (X)__________measurement to (Y)________ measurement (or something like that) should have an optimal score of 14 to 16. I need someone to please refresh my memory on how to measure a razor to see if the bevel/edge is optimal. Thanks in advance!

[drmoss_ca]

Dammit! Where did my long post go? I'll start again.

Imagine the blade seen end on, it will be a tall thin isosceles triangle, point down. Divide it into two right angle triangles by dropping a line through the centre of the spine's width down to the edge. Right angle triangles let us use trigonometry. If the spine has width s, then ½s will be the opposite side of our right angle triangle when considering the angle at the bevel, which we can call ϴ. Since each right angle triangle includes half that bevel angle, their included angle is ½ϴ for each. The line dropped from the spine to the edge is the blade width, w, and is measured from the widest point of the spine to the edge. This is our adjacent. Something like this:

IMG_0615.jpg (33.17 KiB) Viewed 6857 times

So from Mr Pythagoras, we know opposite/adjacent = tan½ϴ

That is to say, ½s/w = tan½ϴ
And thus for the whole bevel angle, s/w = tanϴ

So the ratio of spine width to bade width (measured from widest point of spine to edge) is the tangent of the bevel angle. Tangents for various angles are easily looked up, but to put you in the ballpark, the tangent of 15º is ~0.26. So if you had a razor with spine width of ¼" and a blade width of 1", you have a tangent of 0.25, you have a bevel angle of slightly less than 15º.

[brothers]

Just what I was looking for. Much obliged! Yesterday while I was wrestling with this, I was lucky enough to dig out the 14 -16 parameter, but I only got as far as figuring out measuring the spine and the blade width. The subject of trigonometry was never important when I was a student - just the opposite. With this crippling disadvantage it took me a while to conclude I should divide the width of the spine in half, and I completely overlooked the part about measuring the spine width at the widest point. I was measuring at the tallest point. Now that you've provided the link that will reveal how I can calculate and use the 14 -16 window I am hoping I will be able to judge razor capabilities. Highly useful information for which I am grateful.

[drmoss_ca]

What I have described remains true, no matter what happens to your blade. Some have delved deeper, and perhaps too deep, into how the bevel angle will change if the wear on spine width is not the same as wear on blade width. This requires more serious trigonometry:

http://straightrazorheaven.weebly.com/b ... ation.html

And all can be completely simplified by measuring your blade, no matter how worn or how old; spine width and blade depth from widest spine to edge still gives perfect accuracy for calculating bevel angle.

Me? I just shave with them and see if they work.

[drmoss_ca]

And, by the way, bevel width itself is a surrogate for bevel angle. Generally speaking, the wider the bevel, the narrower the angle. But some of that depends on grind. Here, you enter the territory of the expert, and I am a rank amateur.

[brothers]

Me? I just shave with them and see if they work.

That's what I do*.

*Anecdotally, there was a time I paid a premium for a one-off razor that was (briefly) a subject of discussion on more than one shaving forum. It turned out to be a dud as far as taking and holding an edge for only one or two shaves if any. So I eventually had an opportunity to discuss the problem with someone whose own custom razors continue to enjoy an excellent reputation. I would love to have one of his, but that's not likely. He was kind enough to educate me on my own failed custom razor, and it turned out that the geometry of the blade was simply and obviously wrong. I conducted the measurements several times to be sure, and it was proven that the failure was inevitable because the maker had missed his mark. It is for that reason that I've been subconsciously aware that there is such a thing related to well-engineered straight razors. In the real world, virtually all straight razors seem to have been forged and ground to the correct dimensions.