Bevel Angle Calculation

OK, so I'm trying to calculate bevel angles. I took Slash's advice and took it to my Excel program. Entered spine thickness in box A, blade width in box B and this formula in box C:f(x)=DEGREES(ASIN(A1/B1))*2

So for the first one, the spine thickness was .209 (thousandths), the width was .620 and it gave me an angle of 39.4 degrees. I know that can't be correct. I'm thinking it should be in the 15-20 degree range. I did another one, .208, .700 = 34.5 degrees ???

Do I have the wrong formula or am I doing something wrong? (I know nothing about Excel, never used it before)

You need to halve the spine thickness from your measurement.

I will send you a nice bevel angle calculator program.

For your first one I come up with 19.4º

The spine has to be halved, and blade width is from the edge of the spine wear that's furthest from the edge.


Online right-angle triangle hypotenuse/angle calculators work pretty well. Just gotta get the measurements right and maybe move a few decimal points around.

Thanks Gamma. It does seem that my formula is off by a factor of 2 somewhere.

What is the ideal angle range?

15-19º is common.

I think 16-17º is a good target most of the time.

Use google.

In google, type .209/2 you get .1045
That's 1/2 the spine thickness.
Divide that by the blade width - in google type .1045/.620. The result is 0.16854838709.
In google type - Arcsin 0.16854838709
The result is 0.169356801 rad. (radian)
In google type - 0.169356801 rad in degrees
result is 9.7º, multiply that by 2, result is 19.4º

you can use the scientific calculator in your computer too - hit shift then sin and the buttons shifts to arcsin/inverse sine. (sin[SUP]-1[/SUP])

Yep as others have said. The *2 is to correct for the fact that you're only calculating the angle of a single side of the blade (the adjacent side of the calculated angle is bisecting the blade edge to spine), so your opposite side in the arctan calc will be half the spine's width.

2*tan^-1((0.5*Spinewidth)/bladedepth) = total angle of a double-beveled blade (in this case a western razor, for a blade that is not honed even spine to bevel (for instance a razor honed in the past with an unknown quantity of tape or a knife) you have to use the bevel depth and width, rather than the entire blades)). I would assume for a Kamisori you'd simply remove both the 2 and the 0.5 from that equation (making it the formula for a single-bevel blade), but I'm not overly familiar with Kami's so there may be some deviation from a standard single bevel grind that I'm unaware of.

If your results are expressed in radians, then simply multiply by 180/pi or ~57.

drmatt357 said:

OK, so I'm trying to calculate bevel angles. I took Slash's advice and took it to my Excel program. Entered spine thickness in box A, blade width in box B and this formula in box C:

f(x)=DEGREES(ASIN(A1/2/B1))*2

So for the first one, the spine thickness was .209 (thousandths), the width was .620 and it gave me an angle of 39.4 degrees. I know that can't be correct. I'm thinking it should be in the 15-20 degree range. I did another one, .208, .700 = 34.5 degrees ???

Do I have the wrong formula or am I doing something wrong? (I know nothing about Excel, never used it before)

Click to expand...

There. Fixed it for ya. It should come out 19.41 degrees.

BTW I have a spreadsheet that you enter the smallest expected spine thickness and the smallest expected hypotenuse and it calculates a table of values for a pretty wide range. Handy reference when grinding down a razor. PM me an email address and I will email it. I tried to post it but the site won't let it post. Supposedly xls attachments are allowed but nevertheless...

But I will try to attach it here.

No dice. Says invalid file. Okay I changed the filename extension to .txt so just copy it and then change the filename extension of your copy to .xls and it should open. The two red boxes are the values you enter to seed the table. Then in Open Office you hit F9 and in Microsoft Office I don't know but look in the menu for "recalculate" or something like that.

Well shucky darn. I can't post a text file over 19kb and I can't post an xls file and I can't post a zip file. So I guess I just can't post this thing. Okay I will email it to you if you want it. But the corrected formula should work for calculating a single value.

I just google triangle calculator and punch in numbers.

thanks for that gamma, I didn't know the blade width only went to the edge of the spine wear closest to the cutting edge.

Gamma said:

The spine has to be halved, and blade width is from the edge of the spine wear that's closest to the edge.

Click to expand...

It would actually be the edge of the spine wear farthest from the edge. Nearest the edge will not be the full width of the spine. (You're thinking about it as if the spine is equal thickness at the top and bottom of its hone-wear, which can't be true since you'd have a single point of contact (zero thickness of spine-wear no matter how much the razor was honed)).

If you only measure to the inner line of spine wear, you'd also have to calculate spine width there, which would require setting the tips of your caliper on that line. Not terribly difficult, but it adds needless complexity when for most razors you'll get very close to the correct measurement just measuring the blade width and depth end to end. If you REALLY want to be accurate, caliper the spine-side limit of the hone-wear to the end of the spine and subtract that from your depth measurement. Eyeballing that on the first three razors I picked up, I'd estimate it's 1-2mm.

oh man. i have a math headache now.

Try this:

https://docs.google.com/file/d/0Bx16McVGFvBtdlNTTzNXYTV6bTQ/edit?pli=1

Is that a powerpoint presentation on bevel angles of razors? Or is my browser just making it appear that way?

blackhhawk said:

I just google triangle calculator and punch in numbers.

thanks for that gamma, I didn't know the blade width only went to the edge of the spine wear closest to the cutting edge.

Click to expand...

I was wrong - Ian is correct.

I goofed - I typed in haste without checking what I wrote.
My head was swimming from attempting to solve a huge issue/problem with an email client yesterday.

I'ts not the flat that is closest to the edge edge - and I am going to fix that now.
Doesn't even make sense that it could be the closest edge when you think of the triangle.
I was toast when I typed that post out.

Like Ian said, It's measuired from the edge of the spine-wear flat that is furthest from the edge.

Slash had a thread on this topic, it's buried somewhere - he uses the term bevel-width which sorta makes more sense in a way.
I thought I had it bookmarked but I don't.

Bart had a calculator up on coticule.be - not sure if it's still available.
Google works well enough for me. I rarely use the Calculator in my OS because Google is so easy.
Most of my math/conversions are done in Google actually.

Happens to us all. 99% of my posts are edited because I type faster than I think, reread them and realize what I said is either grossly erroneous due to a typo or grammatical error, or else is just completely unintelligible. I think I edited my first post in this thread about five times because even I couldn't understand what I wrote the first time... also the forum was brutally laggy... that's my excuse.

My brain hurts. I'ts still processing server/port combinations while mixing/matching the other variables.

At 10AM yesterday, my webhost bailed and said - 'sorry, we can't help you'.

Connection is still good - now I get to configure my IOS stuff. Yay.

Just hone it and shave.

Seraphim said:

Just hone it and shave.

Click to expand...

Truer words are hard to come by.

OK, I want to play too... I don't want to sound like a smarty pants here, but I am a licensed land surveyor. Measuring and calculating triangles is how I feed my kids. In a ridiculous display of "the economy sucks & I have too much time on my hands" I broke out the digital caliper and a small handful of blades - from a a brand new Filly to the crudest ebay blade - and (with the help of Autocad) did a little study on bevel angles. To level the playing field, I simply measured the width of the spine and the width of the blade at it's apparent widest point with no regard to spine wear, but noted the condition of the blade. Take this FWIW... I hope the graphic is helpful.

And when you are all done, I would not get too excited about having the exactly correct angle anyway; measuring the spine width and doing the calculations assumes the widest part of the spine is actually part of the plane between the cutting edge and the spine, which is usually not the case. So take whatever you calculate with a grain of salt regarding accuracy. That coupled with the fact that there really is no 'right' angle anyway.

Brian

Don't schools teach Trig anymore?