I once posted this on another forum some time back, and since then I've been using it successfully so I thought I'd share it here. Basically I've seen a lot of stuff about finding angles by folding up pieces of paper, etc. and basically ways to find angles that aren't extremely precise. I decided to use some trigonometry and my calipers to get it a reasonably precise angle measurement.
The formula goes as so A = asin(d/w) * 180 / pi
A equals the angle that the blade is being held at, and d is the distance from the stone to the nearest edge of the spine ( if using the depth gauge of calipers to measure, one must subtract the width of the blade from the total measurement ) and the w is the width from the edge of the spine to the edge at the same location you measured d. The multiplication and division part is just to convert radians to degrees, if your calculator is already in degrees leave that part off. d and w should both be expressed in inches, I'm not sure how to do this in metric.
This doesn't so much work for a measure of the actual edge angle as much as it works for measuring what angle you're holding the entire blade to the stone in relation to the spine. Since you have your relief angle though, the actual angle measurement will be off a few degrees depending on how acute the relief grind is. At least this is what I've been told, I'm not a trig. major, I just have a little experience from my machining days. Either way +/- 5 degree angle is usually what I wind up with, and when sharpening it's not enough to make a real difference.
I don't really see how this is much different than other ways of measuring angles though, as the true measurement typically comes down to what angle the user is holding the blade at versus what angle the user holds the edge at. I've used the formula to match factory bevels with ease, so I figured I'd pass it on for use and critique.
The formula goes as so A = asin(d/w) * 180 / pi
A equals the angle that the blade is being held at, and d is the distance from the stone to the nearest edge of the spine ( if using the depth gauge of calipers to measure, one must subtract the width of the blade from the total measurement ) and the w is the width from the edge of the spine to the edge at the same location you measured d. The multiplication and division part is just to convert radians to degrees, if your calculator is already in degrees leave that part off. d and w should both be expressed in inches, I'm not sure how to do this in metric.
This doesn't so much work for a measure of the actual edge angle as much as it works for measuring what angle you're holding the entire blade to the stone in relation to the spine. Since you have your relief angle though, the actual angle measurement will be off a few degrees depending on how acute the relief grind is. At least this is what I've been told, I'm not a trig. major, I just have a little experience from my machining days. Either way +/- 5 degree angle is usually what I wind up with, and when sharpening it's not enough to make a real difference.
I don't really see how this is much different than other ways of measuring angles though, as the true measurement typically comes down to what angle the user is holding the blade at versus what angle the user holds the edge at. I've used the formula to match factory bevels with ease, so I figured I'd pass it on for use and critique.
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