Tapering with SGA - math knowledge needed

Stromberg Knives

Stromberg Knives

strombergknives.com
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Jan 3, 2015
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856
Hey guys!

I'm using my surface grinder attachment for tapering tangs and spines. I like this process a lot, works great. But I've found that I'm having trouble finding the correct angle of the attachment depending on the thickness at the end and the length of the portion I want tapered.

I would like to be able to calculate the distance between the "tapering bolt head" and the magchuck, and put a correct size shim there. I thought I'd make some sort of excel matrix with the stock thickness, taper length and target thickness.

Unfortunately, my math keeps failing me. I have such a matrix for bevel grinding, but it returns the answer in degrees. And I can't seem to figure out how to convert those degrees to the distance between the bolt head and the magchuck.

Any mathematicians on duty today?

It would be greatly appreciated, thanks in advance.

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DevinT said:
Easy-peasy, rise divided by run, times length = shim thickness.

If you need to remove 1mm over 100mm in length, 1 divided by 100 = .01, .01 x 330 = 3.3. 3.3mm is the shim thickness. To taper the other side after tapering the first side, double the shim.

Hoss
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Godammit! That's a slick solution! Much appreciated! :thumbsup::thumbsup:
 
DevinT said:
Easy-peasy, rise divided by run, times length = shim thickness.

If you need to remove 1mm over 100mm in length, 1 divided by 100 = .01, .01 x 330 = 3.3. 3.3mm is the shim thickness. To taper the other side after tapering the first side, double the shim.

Hoss
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This is the easiest. It's just using proportions to match angularity without actually finding angularity.
 
kuraki said:
This is the easiest. It's just using proportions to match angularity without actually finding angularity.
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It's totally/technically wrong, and only works as a close-enough approximation when you're dealing with small angles.

You can expose the error of this approach by using an extreme example. Lets say I want to taper 1" over 3" on the knife. That is 18.43°.

Let's now use the rise/run math with those numbers:

1 / 3 x 330 = 110 shim thickness

Let's now use trig to check the angle with the 110 shim thickness, and the answer is 19.47° - an error of approximately 1°.
 
P.Brewster said:
It's totally/technically wrong, and only works as a close-enough approximation when you're dealing with small angles.

You can expose the error of this approach by using an extreme example. Lets say I want to taper 1" over 3" on the knife. That is 18.43°.

Let's now use the rise/run math with those numbers:

1 / 3 x 330 = 110 shim thickness

Let's now use trig to check the angle with the 110 shim thickness, and the answer is 19.47° - an error of approximately 1°.
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That's the error in your math. 1" taper over a 3" hypotanuese is 19.47 degrees.
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Just like 110 over 330 (inches so we're not mixing units)
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There's no cosine error in proportionally scaling a right triangle. It is debatable whether Stromberg's actually using a right triangle with a 330mm hypotanuese depending on whether it's actually set up like a sine bar and his 330mm is center to center of the cylinders. But for tapering tangs that error is likely insignificant enough to matter.
 
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kuraki said:
That's the error in your math. 1" taper over a 3" hypotanuese is 19.47 degrees.
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There was no error in my math, but you've got your finger on the pulse - misidentifying the hypotenuse is precisely where the confusion/error comes into play.

I never said hypotenuse - I said 1" taper over 3", which means 3" is the long side of the triangle.

If I said I want to taper 5" of the handle of a knife, obviously I'm talking about a measuring vector that runs parallel to the knife length, which is the long side of the resulting triangle. In no sane world would I refer to the hypotenuse of the triangle as the 'length' of the taper.

EDIT: while we're at it, it is also entirely wrong to say that the angle doubles if we double the shim length. 30 seconds on a calculator will confirm this.
 
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P.Brewster said:
There was no error in my math, but you've got your finger on the pulse - this is precisely where the confusion/error comes into play.

I never said hypotenuse - I said 1" taper over 3", which means 3" is the long side of the triangle.

If I said I want to taper 5" of the handle of a knife, obviously I'm talking about a measuring vector that runs parallel to the knife length, which is the long side of the resulting triangle. In no sane world would I refer to the hypotenuse of the triangle as the 'length' of the taper.
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Why wouldn't you when the hypotenuse is the length of the sine bar? Now I understand what you're saying, just not why you're looking at it from that perspective. I tend to assume if one is going to use proportional math they're going to compare the same feature.
 
kuraki said:
Why wouldn't you when the hypotenuse is the length of the sine bar? Now I understand what you're saying, just not why you're looking at it from that perspective. I tend to assume if one is going to use proportional math they're going to compare the same feature.
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You wouldn't use the hypotenuse because it is unknown at the start of the problem. If you did know (and use) the hypotenuse, then the simple approach would work, and be easier.

Again, in the real world, we are starting with a knife - we know the starting thickness, we know the final desired thickness at the thin end, and we know where on the knife we want the taper to stop. None of those number are the hypotenuse.
 
Yes, that's fair and now I understand better what you're getting at.

I'm only thinking about how I want the angles to be identical and any error can be fudged in the length, but I see your point. Mostly I was thinking you would know the hypotenuse because you could know the length of the scale.

If the length were critical you would just do the trig.
 
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No it will work, especially at the small angles necessary for tapering tangs.

If you wanted to have a precise scale length and precise angle, you would want to do the math. But we're talking like 1/2 an mm deviation for what you're really trying to accomplish.

Even if you did need a precise length, say on an integral guard knife with a tapered tang, you still wouldn't need the level of precision we're talking about to accomplish it since you could fit the scale after the fact.
 
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