Lindsay Engraving System Math?

Hi, all - I use the Lindsay sharpening system. This sharpening system is based upon trig, with the two variables being the length of the graver in the holder and the height of the sharpening surface. I'd like to be able to shorten up the length of the graver, but I don't know the match to calculate the change to the height of the sharpening surface to get the same angles. Can anyone give me the right formula?

I knew I'd be sorry I didn't pay more attention in High School.....

Check your angle with a standard length graver. Then shim your sharpening surface till the shorter graver is at the same angle when jigged up. I am math challenged as well but I learned how to cope a long time ago!

Easy way to follow Southern Custom's advice: stand a piece of something (paper, cardboard, whatever) on the hone and draw a line along the top of the graver blank during the standard setup. Now you can easily tell when you have your different setup at the same angle.

Well. This is an excellent example of what happens when you get stuck on one possible solution and let the process become more important than the outcome. Thanks, Southern Custom and Steve for the excellent common sense solutions.

Cardboard, marker, touch of Kentucky windage, at least one eye, common sense, disengage the over-think routines... Check. Got it.

Maybe I'll make a product out of it and take it onto "Shark Tank".

Hi Bob,

Common sense seems easier than the math, but if you want a way to figure it out, here goes.

First, let's establish some givens so we can make sure we're solving the question you're asking. As I understand it, you want to shorten the length of the standard spacer (1.25") so you can make your gravers shorter, and you want to keep the same face angle (45 degrees). If I'm incorrect about that, ignore everything else that follows! Otherwise...

The template sharpening system is essentially a triangle. Short leg is the graver & its holder, long leg is the template, and we can ignore the hypotenuse. Since the graver is held at a 90 degree angle, we have some sort of a right triangle. Since the face angle of the graver is 45 degrees, the base angle of the template must also be 45 degrees, since the 3 internal angles of a triangle must add up to 180 degrees. If it weren't for the fact that the grinding wheel surface is shimmed up 1/2" from the base of the template, this would be an isosceles triangle, with both the short leg (graver and holder) and the long leg (template) actually the same length. Since there is a difference between the grinding surface and the base surface upon which the template rests, if you are going to shorten the graver length, you must either raise the height of the grinding surface and keep the base surface the same, or you must lower the base surface and keep the grinding surface the same height, or split the difference and do some of each - doesn't matter, just need to figure the height difference, once you determine how much shorter you want your graver.

To start, you must know the length of the short leg and the long leg. I'll use the measurements from my Universal 116 degree template. If you want to try this method, measure yours and use those numbers. The length of the graver, plus the holder, to the face of the template is 2". The length of the template is from the center of the mounting hole to the base, and mine measures 2.66". Once you have those measurements, determine the ratio of the long leg to the short leg, e.g. 2.66:2 = 1.33:1 The ratio, or multiplier is 1.33. I don't know how much shorter you want to make your gravers, but let's say you want to make them 1/4" shorter. If you shorten the spacer 1/4", the total length of the short leg goes from 2" to 1.75". Multiply the new short leg length by the multiplier, 1.33 and you get 2.3275". If we were going to shorten the template, you would make it 2.3275". Since we're not going to shorten the template, we can use the difference between the original long leg and the new long leg to calculate the new height difference. I don't have math symbols, so I'll write out what we need, and then I'll show the math to get there.

The height difference = the square root of 1/2 of the difference between the old and new long legs, squared

OK, let's work that out. We'll start at the end of the formula and work our way back to the beginning.
The difference between the old and new long legs = 2.66 - 2.3275 = .3325
the difference between old and new legs, squared = .3325 x .3325 = .1105562
1/2 of the squared difference = .1105562 x .5 = .0552781
the square root of .0552781 = .2351129
the height difference will be .2351129"

You must raise the grinding surface .2351129", or lower the base surface by .2351129", or adjust both by a combined amount that equals .2351129". Do you really need to carry out the calculations to 7 decimal places? Absolutely not! I'm just copying numbers off the calculator. Round off and you'll be in the ball park.

If you draw a picture of the sharpener in side view, you'd see that the difference in template length can be translated or calculated into the height differential. The template rests at an angle of 45 degrees. If you measure up along the template, from its base, the length of the difference, .3325", you could think of that as the hypotenuse of an isosceles triangle. Drop a line straight down from the upper end of the .3325 measurement, and that line is the height differential. Solve for that height difference by using the old a2 + b2 = c2, and that's where the formula I used above comes from. There are much more elegant ways to describe this, mathematically, but you need to invoke some higher level stuff like tangents and co-tangents, etc. If you understand my assumptions and how I got there, then that's all that really matters.

Seems like it should be simpler than all of that, but if you know your way around a spreadsheet program, you can write out the formula and get it to calculate the height difference from graver length with just a couple of clicks from here on out. Although once you figure out what you need, it probably won't change, and you might not ever need to figure it out again. Ha!

There is one fly in the ointment, though, and that is that this will work just fine for the face angle, because there's enough height in the template to accommodate the height difference. When you grind the heels, for example, you might not have enough template height, or length, to compensate for the relative change in grinding surface height. And, it might not work at all for the small templates which rough out the graver blank. Good luck!

Best regards,
Doug

Also if you want to alter the angle of the face Steve's site has a page on varring the length of the tube to what angle will be achived

Doug,
You owe me a beer! Reading that gave me a "math headache" !!! Only known cure........Sam Adams

Donny

My apologies, Donny!

I'm lickin' stamps and stickin' 'em on beer bottles as we speak. Just send me your address and I'll drop some off in the mail box on the corner!

Best regards,
Doug

all brand politics aside........ the GRS dual angle will do what you are wanting to do regardless of graver length. no extra trigonometry required. the face and heel geometries stay the same while the vertical automatically adjusts to fit whatever tool length.

Just cut abit off the other end if your holder can't accommodate the length.

i use lindsay and grs dual angle. lindsay sells good stuff, but you'll need a truckload of templates. his templates are designed primarily for one face/heel angle. the grs dual angler is much quicker to use. it has 2 , indexed protractors allowing any angle that you would want. including that pesky little bottom relief which is a good thing.