A little math...

I am probably too lazy (or too dumb, you never know which at times) to figure this out.

Let's start with an 8 inch wheel. How high can I take my grind with above mentioned wheel before the hollow starts to get thick again? In other words, if I am grinding 1/8" stock blade, and the blade surface is 1", how high up can I take my grind before the curve of the wheel starts to move away from the blade surface? Is there a resource somewhere where this is all calculated according to wheel diameter, blade thickness, etc.?

Bob, Ben Ogletree (Knifemakers Guild member from Livingston, TX) did the math and prepared a chart. I am sure he would be happy to email you a copy. You can reach him at mayor@livingston.net. Tell him I said "Hello!"

If you get it, ask him for permission to scan it and post it. It would be a good resource!

I've seen a little cardboard slide rule of sorts somewhere that will give you the maximum height of grind for a given wheel on various thicknesses of material. I'll try to figure out where I saw it.

If all else fails simply figure out the arc height of an 8" circle that would give you about 1/16" base length. It is like drawing a right triangle inside of the circle and then calculating the corresponding lengths. Does this make sense?

Scrap that last reply, it is too much work.

K&G supply lists a slide rule as I described for $10 in their catalog.

If we can get a hold of the data, i will put it in our upcoming refernce area for all to use

Bunch of amateurs...

Here's the chart.

Wheel Diameter	Height of Grind
4"	Not too high
6"	A little higher
8"	Twice as high as 4"
10"	Pretty high
12"	Way up there

:

Doh!

and I thought it was gonna be hard : , sorry I can't help it. : : : . I knew this for years but just didn't know how to explain it!! :

You can tell a lot about your hollow grind with a strong light and your dial micrometer calipers.

With the jaws at right angles to the edge grip the bottom 1/8" to 3/16" of the hollows on both sides, straddling the edge. Try and rock the calipers. If there's slack at the tips when the edge is gripped tightly you've ground too high. If there's slack at the edge when the tips of the jaws are tight against the the sides of the hollow then you can grind a little higher. If the bottom 1/8 inch or so seems to be parallel and the jaws won't rock at all then it's just about right.

Magnifiers help when looking for the slack, however feel works pretty well. You can feel a 1/1000ths rock.

Hey, Ben! Delighted to see you here! Hope you didn't mind my using you as an information source. Again, welcome.

Okay...lets get serious. I put pencil to paper and put all this latent math background to work and after attempting to clarify the problem came up with a solution. Here is how I would state the original problem.

Given the barstock thickness, t, and the grinding wheel radius, r, what is the maximum height of the grind?

Here is where I made a few assumptions:
1) The edge of the knife was tangent to the grinding wheel.
2) The grind in the knife formed an arc on the wheel.

After doing a little trigonometry, I came up with this formula: max_height = r * sin(arccos(1 - t/2r)).

I ran some numbers for 1/8" barstock and found this:

8" diameter yields .70" max
10" diameter yields .79" max
12" diameter yields .87" max
15" diameter yields .97" max

I've not seen the tables and these numbers seem small, but I've checked the work. Do these numbers sound reasonable?

I will try to look at the problem a little differently and try again to see if I get the same numbers.

Interesting little problem.

Jeff Jenness

Well, I checked again and I trust the solution. The only problem with this solution is assumption (2)...I've seen some hollow grinding that seem to "stretch" the arc...it's all in how you use your grinder. I am curious if any hollow grinders here break assumption (2).

Looks just about right to me but keep in mind some makers start a little higher on the bar and drag the grind to the edge.

Thanks George for confirming this. So you do stretch the arc on the blade when grinding. I figure that most grinders rock the blade with a vertical angle of motion (same rotational axis as the wheel) to get a little more out of the height, but this cannot be calculated unless there is a maximum angle of rock. About what percent increase do you see from this most of the time? I guess I could give another formula where I add the angle of rock as another parameter...anybody interested?

Jeff