Thread: Calculating the bevel angle on a smiley razor

Originally Posted by celticcrusader

That's a good rule of thumb for selecting steel dimensions for a stock removal razor. Remember though, that the actual bevel angle is not directly determined by total blade width. The spine does not have a flat top, and the contact area is not at the very top of the spine.

For the obsessive, here is how to find the bevel angle.

1. Pick a spot on the razor, preferably near the midpoint of the blade.

2. Look for the top boundary of the spine's hone contact area, the flat strip of "hone wear" (I hate that expression!) on the spine. Measure from that upper boundary down to the edge, taking care not to ding the edge.This measurement is called "H", for "Hypotenuse", because it is the hypotenuse of a right triangle. The razor's geometrically significant points form an isoceles triangle, the base being a line through the spine and the apex being, well, the apex. The shaving edge. Or where the shaving edge will be when the razor is honed. Splitting this isoceles triangle in half, into two right triangles, makes calculation very straightforward.

3. At the same point on the upper border of the spine's contact area, measure the thickness of the spine. The thickness of the spine is the length of the base of the isoceles triangle, and since we want to work with the right triangle, we take HALF of the spine thickness, and call it "O", as in the Letter "O", for "Opposite".

4. Now you have two terms of the right triangle solution. Divide "O" by "H" to get "S", which is the Sine of the right triangle.

5. Find the angle that has "S" as its Sine. Now you have the acute angle of the right triangle, in degrees.

6. Because the right triangle is half of the isoceles triangle that represents the blade's geometry, double that angle for included bevel angle.

There are some common mistakes that will skew the results. One might use the entire spine thickness instead of half of it, and then not double the found angle. Seems simpler, right? But it is wrong. Or maybe regard the distance from top of spine bevel to shaving edge as the Adjacent side. This also is wrong, and will result in a small error. I have known guys to measure from the lower boundary of the spine contact area, which would only work if you measured thickness at the same place. However, thickness is measured at the thickest part of the spine, which is the upper boundary and not the lower. Finally, some guys will take the total blade width and try to plug that into the equation or an equation pulled out of raw imagination. This yields a solution that is significantly more acute than the actual bevel angle.

There is a spreadsheet on my growleymonster.com website, for those interested but who would rather not crunch the numbers. Not sure if I can post a spreadsheet here.

Once you have measured and calculated a few dozen razors, you will probably be able to eyeball the angle to better than a whole degree of accuracy. This is enough to tell you a lot about the razor. It may help you to decide whether to tape or not, or make a compound bevel, or diagnose shaving or honing failures. Tenth of a degree accuracy can be of interest or use when grinding or regrinding a razor. Otherwise it is of mostly academic interest, when you get finer than half degree accuracy. A tenth of a degree should certainly be undetectable when shaving. Still, if you are going to calculate the bevel angle, may as well do it correctly.

Originally Posted by CrescentCityRazors

That's a good rule of thumb for selecting steel dimensions for a stock removal razor. Remember though, that the actual bevel angle is not directly determined by total blade width. The spine does not have a flat top, and the contact area is not at the very top of the spine.

For the obsessive, here is how to find the bevel angle.

1. Pick a spot on the razor, preferably near the midpoint of the blade.

2. Look for the top boundary of the spine's hone contact area, the flat strip of "hone wear" (I hate that expression!) on the spine. Measure from that upper boundary down to the edge, taking care not to ding the edge.This measurement is called "H", for "Hypotenuse", because it is the hypotenuse of a right triangle. The razor's geometrically significant points form an isoceles triangle, the base being a line through the spine and the apex being, well, the apex. The shaving edge. Or where the shaving edge will be when the razor is honed. Splitting this isoceles triangle in half, into two right triangles, makes calculation very straightforward.

3. At the same point on the upper border of the spine's contact area, measure the thickness of the spine. The thickness of the spine is the length of the base of the isoceles triangle, and since we want to work with the right triangle, we take HALF of the spine thickness, and call it "O", as in the Letter "O", for "Opposite".

4. Now you have two terms of the right triangle solution. Divide "O" by "H" to get "S", which is the Sine of the right triangle.

5. Find the angle that has "S" as its Sine. Now you have the acute angle of the right triangle, in degrees.

6. Because the right triangle is half of the isoceles triangle that represents the blade's geometry, double that angle for included bevel angle.

There are some common mistakes that will skew the results. One might use the entire spine thickness instead of half of it, and then not double the found angle. Seems simpler, right? But it is wrong. Or maybe regard the distance from top of spine bevel to shaving edge as the Adjacent side. This also is wrong, and will result in a small error. I have known guys to measure from the lower boundary of the spine contact area, which would only work if you measured thickness at the same place. However, thickness is measured at the thickest part of the spine, which is the upper boundary and not the lower. Finally, some guys will take the total blade width and try to plug that into the equation or an equation pulled out of raw imagination. This yields a solution that is significantly more acute than the actual bevel angle.

There is a spreadsheet on my growleymonster.com website, for those interested but who would rather not crunch the numbers. Not sure if I can post a spreadsheet here.

Once you have measured and calculated a few dozen razors, you will probably be able to eyeball the angle to better than a whole degree of accuracy. This is enough to tell you a lot about the razor. It may help you to decide whether to tape or not, or make a compound bevel, or diagnose shaving or honing failures. Tenth of a degree accuracy can be of interest or use when grinding or regrinding a razor. Otherwise it is of mostly academic interest, when you get finer than half degree accuracy. A tenth of a degree should certainly be undetectable when shaving. Still, if you are going to calculate the bevel angle, may as well do it correctly.

Personally, I think your answer over complicates matters, I hone a hell of a lot of razors, and the simple facts are stick to a 4.2:1 ratio and you will be fine, it's not rocket science.

PS if you want to instantly find the angle just place the razor blade on a perfectly flat surface, then use a small digital bevel box place it on the spine to the razors edge there you have the angle.

Originally Posted by celticcrusader

Personally, I think your answer over complicates matters, I hone a hell of a lot of razors, and the simple facts are stick to a 4.2:1 ratio and you will fine, it's not rocket science.

PS if you want to instantly find the angle just place the razor blade on a perfectly flat surface, then use a small digital bevel box place it on the spine to the razors edge there you have the angle.

What ever seems to work for you or whatever you prefer. I seldom actually measure at all, TBH, but when I do, I go ahead and calculate correctly. It isn't complicated. Still taking only two measurements, then a few keystrokes on the calculator or in Python or look up on the spreadsheet. Easy Sneezy. Most of the time, just eyeballing it is good enough.

Originally Posted by CrescentCityRazors

That's a good rule of thumb for selecting steel dimensions for a stock removal razor. Remember though, that the actual bevel angle is not directly determined by total blade width. The spine does not have a flat top, and the contact area is not at the very top of the spine.

For the obsessive, here is how to find the bevel angle.

1. Pick a spot on the razor, preferably near the midpoint of the blade.

2. Look for the top boundary of the spine's hone contact area, the flat strip of "hone wear" (I hate that expression!) on the spine. Measure from that upper boundary down to the edge, taking care not to ding the edge.This measurement is called "H", for "Hypotenuse", because it is the hypotenuse of a right triangle. The razor's geometrically significant points form an isoceles triangle, the base being a line through the spine and the apex being, well, the apex. The shaving edge. Or where the shaving edge will be when the razor is honed. Splitting this isoceles triangle in half, into two right triangles, makes calculation very straightforward.

3. At the same point on the upper border of the spine's contact area, measure the thickness of the spine. The thickness of the spine is the length of the base of the isoceles triangle, and since we want to work with the right triangle, we take HALF of the spine thickness, and call it "O", as in the Letter "O", for "Opposite".

4. Now you have two terms of the right triangle solution. Divide "O" by "H" to get "S", which is the Sine of the right triangle.

5. Find the angle that has "S" as its Sine. Now you have the acute angle of the right triangle, in degrees.

6. Because the right triangle is half of the isoceles triangle that represents the blade's geometry, double that angle for included bevel angle.

There are some common mistakes that will skew the results. One might use the entire spine thickness instead of half of it, and then not double the found angle. Seems simpler, right? But it is wrong. Or maybe regard the distance from top of spine bevel to shaving edge as the Adjacent side. This also is wrong, and will result in a small error. I have known guys to measure from the lower boundary of the spine contact area, which would only work if you measured thickness at the same place. However, thickness is measured at the thickest part of the spine, which is the upper boundary and not the lower. Finally, some guys will take the total blade width and try to plug that into the equation or an equation pulled out of raw imagination. This yields a solution that is significantly more acute than the actual bevel angle.

There is a spreadsheet on my growleymonster.com website, for those interested but who would rather not crunch the numbers. Not sure if I can post a spreadsheet here.

Once you have measured and calculated a few dozen razors, you will probably be able to eyeball the angle to better than a whole degree of accuracy. This is enough to tell you a lot about the razor. It may help you to decide whether to tape or not, or make a compound bevel, or diagnose shaving or honing failures. Tenth of a degree accuracy can be of interest or use when grinding or regrinding a razor. Otherwise it is of mostly academic interest, when you get finer than half degree accuracy. A tenth of a degree should certainly be undetectable when shaving. Still, if you are going to calculate the bevel angle, may as well do it correctly.

I use this: https://www.calculator.net/triangle-calculator.html it's quicker faster, no halving spine etc. No mathematician here, not smart enough to do trig.

Originally Posted by Southbound

I use this: https://www.calculator.net/triangle-calculator.html it's quicker faster, no halving spine etc. No mathematician here, not smart enough to do trig.

I'm not smart enough to do trig either, but my calculator is. Spreadsheets work fine and are convenient, though, as long as they have the correct formula. Any popular spreadsheet should be correct.

Originally Posted by CrescentCityRazors

Remember though, that the actual bevel angle is not directly determined by total blade width. The spine does not have a flat top, and the contact area is not at the very top of the spine.

You measure the width of the blade from the apex of the edge to the top part of the hone wear, not the top of the spine itself. It is just that simple and it works.

http://www.coticule.be/wedges.html#:...round%20razors.

Be sure and open the Excel file for an illustration of that.

Bob

Originally Posted by BobH

You measure the width of the blade from the apex of the edge to the top part of the hone wear, not the top of the spine itself. It is just that simple and it works.

Exactly so. I thought I was more clear on that.

Originally Posted by CrescentCityRazors

Exactly so. I thought I was more clear on that.

Not in one paragraph.

Bob

That Excel file looks like the beginnings of the file you started for me, Bob. Way back when I wanted to keep this info and measure. I still have the same Spreadsheet you sent me, although it has changed many times. It still does that math for me and I use "IT only" for my calculations.