Trigonometry

Shmackey · Oct 20, 2005

Can anyone figure out what the new angles would be on the Sharpmaker if you put one of the rods underneath it in order to get more acute than 30 degrees?

I'm thinking of (1) putting a rod right under the middle, like a see-saw, and (2) putting a rod under the end. The see-saw method should get you a more acute angle, but I don't know what the angles would be.

MeDoctor · Oct 20, 2005

No, but that's a neat idea. It took me a couple of minutes to figure out what the heck you were talking about. Let's see... the thickness of the rod is one side of the right-triangle, 1/2 of the length of the SharpMaker is the hypotenuse. The angle formed where the SM touches the workbench would represent the shift in angle of the honing rod.

Better yet -- get a cheap protractor and measure it!

Shalom,
Mark

Cliff Stamp · Oct 21, 2005

The rods are 0.4 cm thick, the base is 19 cm long so the angle with the rod under one end is arctan(.4/19) = 1.21 degrees, as a quick approximation, arctan(x) ~ 60 * x, this would give 1.26, so you are shifting the angles by about one degree. If you put them under the middle you half the distance and thous double the angle arctan(.4/19/2)=2.41 degrees. You can just scale this with the thickness of the block, so if you put something with is twice as thick as the rod the angle is twice as high in both cases.

-Cliff

Don Luis · Oct 21, 2005

As Mark mentioned I suggest that you use a protractor, and use whatever you need to get whatever angle you want, I used to put a large hone in a vise at an angle and used a protractor. I was doing that when I was in junior high in the 60´s long before the times of the Sharpmaker, though I sharpened moving the blade horizontally rather than vertically.

Luis

Shmackey · Oct 22, 2005

Cliff, I think you have the formula right, but are you sure about the measurement of the rods? 0.4 cm sounds much smaller than the height of the triangle that is the cross-section of the rods.

daverave999 · Oct 22, 2005

I would have said it was nearer 1.1 cm (0.4 inch maybe?) and 19.5 cm long

In the middle, by my calculation:

arcsin (1.1/9.75)= 6.48°

which doesn't look quite right either...

Cliff Stamp · Oct 22, 2005

Shmackey said:
Cliff, I think you have the formula right, but are you sure about the measurement of the rods? 0.4 cm sounds much smaller than the height of the triangle that is the cross-section of the rods.

I thought you meant the safety rods, the honing rods are 1.13 cm high so the angle are 3.4 and 6.8 .

-Cliff

Shmackey · Oct 22, 2005

Cliff Stamp said:
I thought you meant the safety rods, the honing rods are 1.13 cm high so the angle are 3.4 and 6.8 .

-Cliff

Cool. So the see-saw method gets you a 23.2 angle, or 11.6 degrees per side (when subtracting from the 30-degree setting). Thanks!

MeDoctor · Oct 23, 2005

Cliff Stamp said:
I thought you meant the safety rods, the honing rods are 1.13 cm high so the angle are 3.4 and 6.8 .

-Cliff

I thought the same thing at first, then I realized that after you notch the center of the SM base to securely locate them the change in angle would be almost meaningless.

Shalom,
Mark

MeDoctor · Oct 23, 2005

Cliff,

Here's an example of why throwing ideas out into a public can be so useful. Shmackey spoke of setting up a "see-saw", which makes sense for alternating strokes between the left and right rods -- then you chimed in with the math and included the the possibility of putting the rod under one end, thereby halving the shift in angle. Then there's the use of the safety rods -- the 1 or 2 degree shift is perfect for a couple of final swipes on the fine or x-fine rods.

Shalom,
Mark

Joe Talmadge · Oct 23, 2005

Heh, I used to use a safety rod in the center (at the V apex) for a long time, and basically see-sawed it. Never actually measured it, and at some point decided it wasn't worth the trouble. But this thread definitely re-motivated me to try this out again.

If you're putting a stone under the base, are you planning to move the stone from one side to the other, or move yourself from one side to the other?

Cliff Stamp · Oct 23, 2005

One of the things I use this for often is knives with lopsided grinds, often I get knives ground at 15/25, now I could recut them to 15/15, but I like to work with the origional edge first and thus by putting something of the right height under the sharpmaker I can match the angles easily.

-Cliff