Angle changes on the Wicked Edge – blade curves

[Geocyclist]

I don’t think so. With the brackets you are taking the arctan of tan(x) divided by sqrt(2). Or written differently you are taking the arctan(y) where y = tan(x)/sqrt(2)

If written this way it could be simplified: (arctan(tan(x)))/sqrt(2) = x/sqrt(2)

[Mark76]

If written this way it could be simplified:

Thanks for your reply Geocyclist! But it ain’t written that way… It’s slightly more complicated, which is why I wondered. But you also think it cannot be simplified any further?

Molecule Polishing: my blog about sharpening with the Wicked Edge

[Mark76]

Guys, it took a while, but I have written a revised version of the article. It now incorporates your comments (thanks!) and its scope is much broader. And hopefully the article is now easier to comprehend.

You can find it here: http://moleculepolishing.wordpress.com/2013/03/12/angle-changes-on-the-wicked-edge-revised/

Molecule Polishing: my blog about sharpening with the Wicked Edge

[Geocyclist]

I am glad I get to be the first to comment on this. Your write up is simply brilliant. :woohoo: (I tried to give more than 1 karma, but this doesn’t seem possible).

To close the loop how do we apply this the real world? I know with infinite blade shapes, etc. it may not be possible to write a single formula for this, but I think some reasonable generalities can be drawn, especially if we consider “traditional” blade shapes like clip points and exclude extreme shapes for the sake of simplicity.

1.) To minimize the angle change mount the tip within the radius, or to say it a different way the same distance from the pivot as the flat edge of the blade, i.e. like Curtis’s photo above with the tape measure. I guess the question is how well does the curve of the blade fit to a circle? If you mount the tip this way then the angle on the tip and flat will be equal. Will this “minimize” the difference of angle change along the curve or make it worse? From figure 1 this depends on how well the blade shape fits to a circle.

2.) It is agreed that the angle stays constant along the flat edge of the blade. Is it also correct to say it does not matter how the blade is mounted when it comes to the flat portion ONLY. For example, I normally mount the flat portion parallel to the base. If I mounted the spine flat against the depth stops so that the flat edge was not parallel it wouldn’t change anything ONLY in respect to the angle along the flat edge.

3.) Taking into account #2 above, you could get a better fit of the curve of the blade and the tip by adjusting the mounting angle. Is that correct? My thought is I can get a better fit by sliding the blade back to get the tip closer to the radius. Alternatively you could improve this by also tilting the tip down. (“could” – I know it ultimately depends on the blade and every knife is different). By tilting down I am thinking the tip will move closer to the radius.

Again, great job, this should go on the Wiki. “Finding the Sweet Spot 301”

[cbwx34]

Dammit Geocyclist, you made my head hurt with this one. :sick:

I think #2 is correct, you can tilt the blade up or down. At first I thought it was incorrect, because wouldn’t tilting the blade change the height in relation to the pivot? But then I realized that “parallel” is actually a relation to us (or the ground), and not the pivot. In other words, if I mounted the blade at a 20 deg. angle, but then tilted the whole WE 20 degrees, the blade would essentially be “parallel” again, the relationship never changes between the knife and the pivot.

So, with that in mind, in reference to #3, I don’t think tilting the blade will make the curve fit any better, since, with respect to the pivot, tilting the blade doesn’t change the relationship between the pivot and the blade.

To put it another way, if I look at Mark’s drawing correctly, tilting the blade would also “tilt” or move the circle too, since it’s based on the blade’s position. It wouldn’t stay in the same place while the blade moved.

Is that right? Seems so in my head (but at one time I thought the angle had to change along the straight part.) :dry:

[Mark76]

Thanks for the kind words, Geo. You make some interesting points.

You’re completely right about point #2! I knew that, but I never realized it so well: I always try to clamp a blade in horizontally, but that is not necessary! And indeed, as you note in #3, you may be able to get a better fit on the tip curve by not clamping in the blade horizontally. Tilting the blade down doesn’t matter for the straight portion of the edge, but it may matter for the tip. I have to experiment with this! (And you too 🙂 ).

Calculating the exact sweet spot is a challenge… Obviously it depends on the blade shape. It also depends on what exactly you call the sweet spot.

For example, in figure 1 of the blog post (see below) I positioned the knife such that the angle change at the end of the tip would be 0 degrees. The distance from the pivot point to the straight portion of the blade is not the same as the distance from the pivot point to the end of the tip (which, as someone wrote in another thread, is the recommendation in a book that treats guided angle systems). The distance from the pivot point to the straight portion of the blade is the same as the distance from the pivot point to the vertical line that touches the end of the tip.

However, there are two big buts:

• This only works for the “theoretical” knife shape used here. Most knives don’t have a tip that at the end points 90 degrees down. In fact, the angle change is the largest at the point indicated by the arrow In the above figure. Here the knife points about 45 degrees down. And many knives have a tip that about ends at 45 degrees… Here the angle change at the end of the tip could be made smaller by moving the knife slightly inward.
• Even for the knife in the figure the question is what the sweet spot is. At the end of the tip the angle change is 0 degrees and I calculated the angle change at the point indicated by the arrow. Call the angle change at the end of the tip a and the angle change at the point indicated by the arrow b. It might well be that it is possible to position the knife in such a way that abs(a-b) is smaller than b. I’m not sure, but intuition says this. Intuition also says that were only talking tens of degrees 🙂 .

For practical advice: I think it is a good idea to start to clamp in the knife such that distance from the pivot point to the straight portion of the blade is the same as the distance from the pivot point to the vertical line that touches the end of the tip. Depending on the blade shape it is then probably a good idea to move the blade slightly inwards.

What “slightly” is?… Food for thought. Fortunately the sharpie trick still works.

Molecule Polishing: my blog about sharpening with the Wicked Edge

[cbwx34]

For practical advice: I think it is a good idea to start to clamp in the knife such that distance from the pivot point to the straight portion of the blade is the same as the distance from the pivot point to the vertical line that touches the end of the tip. Depending on the blade shape it is then probably a good idea to move the blade slightly inwards.

Uh oh…. :S

I don’t agree with that… and that’s from reading your blog. In your blog you write:

Anthony did not only show that the sharpening angle remains constant along a straight line, but also along a circle around the pivot point.

So, wouldn’t you be closer to the actual angle being sharpened, by clamping the knife so that the tip/belly area is as close to this circle as possible? If you look at this picture…

… which is probably closer to most knife shapes, by your statement above, you’d be clamping the knife way forward of where it should be, while the picture shows clamping it closer to the circle will match the angle better. The farther you get from the circle, the more “off” the angle is correct? (How much, I’m not sure, but I would think you’d want to stay close.) Even the knife with the 90 deg. change… the angle would be closer if it was closer to the circle, not the vertical line that intersects.

Attachments:

• dia21.png

[Mark76]

Hey Curtis, you’re right. It really depends on the blade shape. If the blade is shaped like in figure 1, you probably need to move it in towards the pivot point somewhat. If it has got the “ideal” shape of figure 2, there’s no need to move it in or out at all.

The point is, no real knife probably has exactly one of those shapes, so it remains a bit of fiddling… But starting off where either the distance of the tip or the distance of the vertical line touching the tip equals the distance to the straight portion of the edge should bring you very close to the sweet spot.

Molecule Polishing: my blog about sharpening with the Wicked Edge

[wickededge]

This is a great topic and resource. Many thanks to Mark, Curtis and Lagrangian for all the very well thought out contributions!

Lately I’ve taken to using a combination of methods to quickly find the sweet spot on a given blade. First I set the depth key through the holes in the alignment guide and then place the key in the holes on the clamp. Next I rest the spine of the knife both pins, holding the handle of the blade with my left hand while taking note of where the section of blade directly above the clamp contacts my right guide rod. I then hold that point on the rod and rotate the rod toward the tip of the blade. I then adjust the blade accordingly such that the tip of the blade contacts the guide rod in approximately the same place as the section of blade directly clamp. I snug up the top screw and color in the bevels of the blade with a marker. From there, I observe how a fine stone tracks through the marker as described in the “Finding the Sweet Spot” tutorial. Sometimes I’ll also adjust the pitch of the knife as Mark and Curtis have mentioned, making note of the positioning for later touch-ups.

-Clay

[cbwx34]

But starting off where [strike]either[/strike] the distance of the tip [strike]or the distance of the vertical line touching the tip[/strike] equals the distance to the straight portion of the edge should bring you very close to the sweet spot.

I fixed this for you. 👿

Truth is, we may not be talking a big difference here… not really sure. I tried to do some measurements with the digital angle gauge… but that “3rd dimension” throws the readings off so that I couldn’t come up with an accurate comparison. The diagram Clay made can show a significant change depending on where the blade is set… here it’s much as 7-8 degrees. Not having the actual distance change between the two settings though makes it hard to evaluate.

Another thing worth mentioning is that part of the setting is affected by the fact that you’re sharpening into thicker metal also… so even if a “mathematical” determination could be made… the thickness would have to be accounted for too.

Interesting stuff though for sure. 🙂

[Mark76]

But starting off where [strike]either[/strike] the distance of the tip [strike]or the distance of the vertical line touching the tip[/strike] equals the distance to the straight portion of the edge should bring you very close to the sweet spot.

I fixed this for you. :evil:[/quote]

Well, I’m not sure you really fixed it 👿 . I really depends on the blade shape.

Take figure 1. Here the optimal position of the knife (in terms of the angle change being zero at the end of the tip) is when the distance of the vertical line touching the tip equals the distance to the straight portion of the edge. This is because the knife tip has such a profile that at the end it points straight down.

Now take figure 2. Here the optimal position of the knife is where the distance of the tip equals the distance to the straight portion of the edge. This is because the tip of the knife has a profile that aligns with the circle.

However, if you mean that in practice most tip profiles look more like the one in figure 2 than the one in figure 1, you’re right. Clay’s procedure (as well as Curtis’ one with a ruler) for finding the sweet sport should work well in this case.

The diagram Clay posted earlier is very insightful, but it does require proper intererpretation. The maximum angle changes I calculated are for the case in which you already have clamped your knife “properly”, i.e. there is at least one place on the tip curve where the angle change is zero. This is (almost) the case for the leftmost knife in Clay’s diagram. There the angle changes are relatively small. However, it is of course possible to move the knife out much further (as the rightmost knife in Clay’s diagram) and in that case the angle changes are be much larger.

Molecule Polishing: my blog about sharpening with the Wicked Edge

[Geocyclist]

Clay,

I think I do the same thing you do. After clamping I grab the 1000 diamond stone. Lay it on the edge so that the stone is straight up and even with the clamp (the stone is just about as wide as the clamp). I place tape on the stone even with the edge. Then I sweep the stone to the tip and see how much further the tape goes away from the edge. My goal has been to get the tip right up to the tape. For me the tape usually ends up 1/4 inch away from the tip. Just about all my knifes with any belly end up with a little more bevel at the tip. They look ok and I would much rather have a little more angle than less at the tip.

I do look first in the knife data base to see how far others have placed the tip into the vise.

Curtis has good point about blade thickness. For pocket knives with belly most all get thinner at the tip. My kitchen knives are uniform thickness all they way through on the other hand.

The marker trick only helps so much for me. If I am way off it show it. But when I take a factory edge of 20 to 15 the marker doesn’t work perfectly. By this I mean I can completely wipe off the marker with a stone but end up with more bevel at the tip.

[Author]

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