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Edge Angle, Angle Guide, and Blade Body Angle
#1
As some of you know, I've been using grepper's KallyRest on my Kalamazoo sander.  It has an adjustable angle guide, which is a table/rest that you lay the body of the knife on.

In previous sharpening adventures, I've used flat stones and plates and used wooden wedges as an angle guide.  With these, you put the wedge on the stone and then lay the knife body on top of the angle wedge.

Many blades are roughly triangular in cross section, even before you get to the edge bevel.  If you measure the included angle of the BODY of the blade, you normally will find that knives vary from around 3 degrees inclusive to fairly large angles.  I just measured a Cold Steel Recon Tanto and it showed over 12 degrees inclusive. 

So, if you want to know the true edge angle, and you're using an angle guide like I'm describing, you have to take into account the angle "offset" of the body.  In particular, one half of the included angle is the offset.  For a 3 degree inclusive blade, the offset is 1.5 degrees.

With a wedge where you set the body on top of the wedge, the edge is being lifted up by the body.  So you have to add the offset to the reference angle.  For example, if you have a wedge of wood cut at 15 degrees and you put a 4 degree inclusive knife on top of it, you have to add 1/2 of 4 degrees, or 2 degrees.  15 + 2 = 17 degrees.  17 degrees is the true edge angle that will be ground in. 

Or said the other way, if you want a 15 degree edge angle and you have a 4 degree inclusive blade body, you have to account for the 2 degree offset:  15 - 2 = 13.  You need a 13 degree WEDGE in order to produce a 15 degree edge angle on a 4 degree inclusive blade body.  

Here's where it gets interesting to me.  I've been doing these calculations for years and was pretty comfortable with them.  When I got the KallyRest and later an angle cube, I planned to do these calculations to put some really low edge angles on a few blades.  I'm planning on doing a few at 12 degrees per side and 10 degrees per side.  I started to do the subtraction in the previous paragraph and something didn't seem right to me.  I thought about it and drew some pictures.  It turns out with the KallyRest (or any similar "angle table") the math is backwards!

You see, with the KR, the angle is not a wedge you are sitting on top of.  Instead it's a SPACE between the table and the abrasive.  So, when you set the blade body on the rest and it has (for example) a 4 degree included angle, you are getting CLOSER to the abrasive.  With an angle wedge the body lifts further away from the abrasive!  The tool rest is backwards from this.  You get closer to the abrasive, therefore the edge angle is DECREASED by the body of the blade.  Wow.  I know, I know, it's just basic geometry but for me it was a wow moment.

Which means that if I set the KR to 15 degrees and I put my 4 degree (inclusive) blade body on it, I'm going to be grinding in a 13 degree edge angle.  Or said the other way, if I want a 15 degree edge angle on my 4 degree blade body, I have to add the offset.  15 (edge) + 2 (offset) = 17.  I need to set the KR to 17 degrees in order to get a 15 degree edge angle on this 4 degree blade body.

One of the blades I want to take to somewhere between 9 and 11 degrees (edge angle) is a full flat ground Delica.  I've measured it's body angle at 3.7 degrees inclusive.  So to take it to 11 degrees (edge). I need to set the KR to:  11 + (3.7/2) = 12.85 degrees.  Neat.

I might make a video about this.  I'm not sure if the words I've written are clear enough to get the meaning across.  Let me know if this makes sense and/or if anyone would like to see a video about this subject.

Thanks for reading.

Brian.
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#2
Chuckle, chuckle.  At first, I thought about it bass-ackwards too.
 
In your Powered Sharpener Setup Recommendations thread, Mr. Jan showed how he had made a 15° wooden angle guide for his grinder, but the bevels were coming out between 10° and 12°.  I replied to his post saying,Of course, a tapered blade placed flat on a 15° surface would not produce a 15° bevel due to the angle of the taper of the blade.  The weird thing is that I think that would increase bevel angle as opposed to decreasing it.

http://bessex.com/forum/showthread.php?t...59#pid5259
 
Then I actually placed a blade on the Kallyrest and gave it a little look-see.  I slapped my forehead and exclaimed, “doh!” shortly followed by,"duh!". For whatever reason, for me at least, it was natural to think about it backwards.
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#3
(03-10-2020, 03:48 PM)blgentry Wrote: You see, with the KR, the angle is not a wedge you are sitting on top of.  Instead it's a SPACE between the table and the abrasive.  So, when you set the blade body on the rest and it has (for example) a 4 degree included angle, you are getting CLOSER to the abrasive.  With an angle wedge the body lifts further away from the abrasive!  The tool rest is backwards from this.  You get closer to the abrasive, therefore the edge angle is DECREASED by the body of the blade.  Wow.  I know, I know, it's just basic geometry but for me it was a wow moment.

Which means that if I set the KR to 15 degrees and I put my 4 degree (inclusive) blade body on it, I'm going to be grinding in a 13 degree edge angle.  Or said the other way, if I want a 15 degree edge angle on my 4 degree blade body, I have to add the offset.  15 (edge) + 2 (offset) = 17.  I need to set the KR to 17 degrees in order to get a 15 degree edge angle on this 4 degree blade body.

Mr. Brian, you are correct!

The angle of the adjustable guide of the Kallyrest has to be increased by ½ of the (included) taper angle of the blade.

Jan

P.S.: Mr. Grepper, the figures from my example are biased, probably because the grind of the blade was convex. Numerically biased but qualitatively OK.


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#4
Another note on this:

How you hold the blade on the rest matters if the blade has more than one angle on it's body.  For example, the Recon Tanto has two main facets on the blade body.

https://www.amazon.com/Cold-Steel-49LRT-...B07BHGB22X

The part near the spine is almost flat stock.  If you press this back part against the rest, the included angle is less than 1 degree.  The front part of the body, near the edge, has a dramatic angle, which measures around 12 degrees included.  A huge difference.  Generally speaking, I will be holding a blade body so that the part of the body near the edge is touching the tool rest.  So in the case of the Recon Tanto, I would be using the angled part and would need to add 6 degrees to my angle on the KallyRest!

Ben Dale, the inventor of the Edge Pro, shows this exact "problem" or behavior on his product in some of his original product videos that I watched 10 to 15 years ago.  At the time, I "got it", but it all seemed way too complicated.  Now I think it's neat.  Time flies.  Smile

Brian.
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#5
[quote pid='5268' dateline='1583876934']

I might make a video about this.  I'm not sure if the words I've written are clear enough to get the meaning across.  Let me know if this makes sense and/or if anyone would like to see a video about this subject.

Thanks for reading.

Brian.
[/quote]

I'll bite... Video please...
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#6
(03-12-2020, 07:43 AM)chino Wrote: [quote pid='5268' dateline='1583876934']

I might make a video about this.  I'm not sure if the words I've written are clear enough to get the meaning across.  Let me know if this makes sense and/or if anyone would like to see a video about this subject.

Thanks for reading.

Brian.

I'll bite... Video please...
[/quote]
I, am interested in a video -
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#7
Perhaps this will help clarify.

For demonstration, the knife taper is 10° inclusive (5° each side).

The knife rest is angled to 20°.

This will produce a 15° bevel.  To make a 20° bevel, the rest would have to be set to 25°.  This is because the blade is lifted off the rest by 1/2 the inclusive taper angle of the blade.

Angle the rest at (desired bevel angle + .5 * inclusive taper angle of the blade)

   

Conversely, if the knife was being sharpened on the bottom side of the blade instead of the top side, 1/2 the inclusive blade taper would have to be subtracted from the rest angle.
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#8
I'm not good at math, but I understand with the help of the posts. Thank you.

To measure the knife angle, what tool are you using? Angle cube?

Thanks everyone!
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#9
(03-25-2020, 06:47 AM)chino Wrote: To measure the knife angle, what tool are you using? Angle cube?

That's what I've done.  Seems to work well.  I demoed this in my video but.... the video didn't come out well so I didn't post it.  I'm going to redo it... probably. 

Brian.
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#10
(03-25-2020, 01:34 PM)blgentry Wrote:
(03-25-2020, 06:47 AM)chino Wrote: To measure the knife angle, what tool are you using? Angle cube?

That's what I've done.  Seems to work well.  I demoed this in my video but.... the video didn't come out well so I didn't post it.  I'm going to redo it... probably. 

Brian.

Alright, at least I know (sort of, lol)
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