Sharpening & Calculating Ideal Bevel Height (trigometry!)

[BearShark44]

Hey folks, here’s a trig question just for fun. I’m looking for a way to gauge my sharpening accuracy by calculating what the bevel height (c) should be vs measuring actual with a ruler in mm.

1. When sharpening (I freehand, but w/ any method), if a proper bevel angle is held, shouldn’t the bevel height (c) be consistently the same # (mm) along the edge?

2. Is this formula right? (obviously a, b, and the referring angle are all variable based on the Spyderco model and preferred sharpening angle.)

3. If someone has digital calipers, what’s the opposite side (a) on their Delica 4? Does that # change negligibly along the edge?

[Danke]

Thanks for the homework

[benja-man]

As the blade gets thinner towards the tip, bevel height should theoretically decrease as well, I believe.

[kennbr34]

In my experience trying to do this, the problem is that the resultant calculation is extremely sensitive to the measurements of a and b. So in other words, you're more than likely only going to be able to reliably measure them to within +/- .005" but that can result in quite an extreme variance in the calculated angle.

Let's say for example that you have an edge that is .030" thick at the bevel shoulder, and the bevel face is .050" wide. (This corresponds to the factory geometry of my Manix 2)

asin((.030/2)/.050) * 180 / pi = 17.45 degrees

(The * 180 / pi is just to convert from radians to degrees. You don't need to do that if you're using a calculator you can set to use degrees.)

Now if you play around with those numbers to the tolerances I mentioned...

asin((.025/2)/.045) * 180 / pi = 16.21

asin((.035/2)/.055) * 180 / pi = 18.55

Now, +/- ~2.5 degrees may seem reasonable, but keep in mind that it becomes more difficult to get reliable measurements the smaller a and b get.

For example, let's say you're dealing with an edge that is .010 at the bevel shoulder and .020" wide. Right away your +/- .005" tolerance is going to be a much greater percentage of variance. It's really tough with calipers to take accurate measurements at this scale anyways, but then look at the way it affects the results...

asin((.005/2)/.015) * 180 / pi = 9.59

asin((.010/2)/.020) * 180 / pi = 14.47

asin((.015/2)/.025) * 180 / pi = 17.45

So suddenly the same -/+ .005" variance can lead to a ~8 degree +/- tolerance.

Given that the whole goal is to confirm how well you're sharpening to the angle you desired, it isn't very useful.

Personally, what I do is apply the same trig principles but measure the width of the blade as well as the distance from the spine to the hone surface. So for example if your blade is 1" wide, .125" thick and you hold the spine .375" from the hone surface...

asin(.375+(.125/2)/1) * 180 / pi = 25.94

The benefit of doing it like this is that you can put your blade on the hone surface, and raise the spine until you can visually confirm that your edge apex is in contact with the hone surface, and then measure the distance from the spine to the hone to estimate the angle, AND be able to use a much wider dimensional tolerance for nearly the same angular tolerance.

So for example...

asin(.350+(.125/2)/1) * 180 / pi = 24.36

asin(.400+(.125/2)/1) * 180 / pi = 27.54

So with a measurement that's +/- .025" you get a resultant angle calculation of nearly the same as you get with a dimensional tolerance of +/- .005" measuring things at the edge.

The best way to measure and confirm is with a laser goniometer.
https://www.gritomatic.com/products/las ... 181f&_ss=r

[horzuff]

Regarding #1 - This would be true assuming the blade is the same thickness behind the edge along the whole length of the knife which it almost never is ^^

[SaltyCaribbeanDfly]

I had pretty good grades in math growing up but after reading this thread my head is spinning

[JacksonKnives]

A laser "goniometer" is the only accurate/precise measurement I've seen.

http://bessex.com/forum/showthread.php?tid=338
Here's a DIY version I've had good success with.

Here's the way I think about sharpening accuracy:

Actual precision of angle makes little difference.

Repeatability makes more difference, but you're usually grinding away enough material that it doesn't change much if you are off 1-2° from the last sharpening session.

The "sharpie check" method is about as accurate as you can get for checking current angle vs last angle and is easy to do.

Repeatability from stroke to stroke (maintaining a consistent angle) is the most important challenge. Hence, the popularity of angle-guide systems with only vague calibrations.

[HolySteel]

The "sharpie check" method is about as accurate as you can get for checking current angle vs last angle and is easy to do.

The reason I prefer Spyderco stones over others is that, if I spray a little liquid on the stone, I get a suction feel when I have the blade at the correct angle. Then using the Sharpie when I strop just confirms that I have been consistently holding the angle correctly. Still, I use the diamond stone to get started on harder jobs. I have had no issues using this method but when I re-bevel a messed up edge, I couldn't tell you what angle results - just that it cuts how I need it to.

[bdblue]

Consider what the blade looks like before the edge is put on it. A flat ground blade will taper from the spine to the edge and will be thinnest close to the choil. At the tip it would be the same thickness as the rest of the spine. This won't work so the blade gets moved around a bit during grinding and isn't a pure flat plane. If done well then the edge will be the same thickness all the way along the edge. So if sharpened correctly the edge height would be the same all the way down. Sharpening correctly is going to be a problem so the edge height still might change a bit. Now consider a handmade knife that is hollow ground. It is a lot harder to maintain a uniform edge all the way to the tip, so consequently the edge height or the edge angle will suffer. I've had a lot of knives like this, both factory and custom. Come to think of it, I have a Manix 2 that I sharpened on a guided system and it has a higher bevel at the tip than it does at the choil. When reprofiling other knives I've noticed that it takes a lot of work near the tip to reach the edge and the bevel becomes relatively high.

[JacksonKnives]

The reason I prefer Spyderco stones over others is that, if I spray a little liquid on the stone, I get a suction feel when I have the blade at the correct angle.

I remember reading somewhere that we have the ability to feel incredibly tiny differences in surfaces (say, an offset in a pair of butted faces) that we could never see with our eyes.

I have no doubt that there are all kids of feedback mechanisms in sharpening that a master learns to feel. Kind of like playing a violin; your fingers remember and hold positions much better once you learn how to hear whether you're in tune.

[HolySteel]

The reason I prefer Spyderco stones over others is that, if I spray a little liquid on the stone, I get a suction feel when I have the blade at the correct angle.

I remember reading somewhere that we have the ability to feel incredibly tiny differences in surfaces (say, an offset in a pair of butted faces) that we could never see with our eyes.

I have no doubt that there are all kids of feedback mechanisms in sharpening that a master learns to feel. Kind of like playing a violin; your fingers remember and hold positions much better once you learn how to hear whether you're in tune.

Spyderco stones make it easy for anyone to get that 'feel', because they don't wear away;i.e-no dips like Arkansas stones get. The trade-off is that it takes longer to sharpen with them. I don't know the reasons for any of this, but I'm sure someone here can explain.

[kennbr34]

Come to think of it, I have a Manix 2 that I sharpened on a guided system and it has a higher bevel at the tip than it does at the choil. When reprofiling other knives I've noticed that it takes a lot of work near the tip to reach the edge and the bevel becomes relatively high.

I've noticed this too and think it's usually due to the distal taper and the way the stock if the blade thins out near the edge. The angle remains the same, but because the cross section of the blade where it's ground in is thinner, it results in a wider bevel.