How to calculate the projection as a function of bevel angle for LN Honing Guide

[Thomas Wilson]

The Lie Nielsen honing guide instructions give a list of the projections for bevel angles of 20, 25, 30, … 50 degrees but not a formula for intermediate values or for jaws other than the standard jaws. I took this problem as a challenge and solved it. My question is whether anyone here is interested in my formula or the derivation.

I did a cursory Google search of the internet to see if someone else had reported a formula. I did not find a formula but I did find another forum on which a person asked the if anyone knew the formula (he called it the protrusion). He only got ways to find it by trial and error or measure it with a protractor or angle gauge.

I will take the time to make a drawing and show the math tomorrow if there is any interest.

[Robert Hayward]

I have an interest, thanks for the offer.

[Jack Frederick]

LN have a link on their site for a…what to call it, a board with assorted dimensions, distances to set reference blocks to set the angle. I made one years ago and it has worked well for me. I just packed it up for the move or I’d post a pic.

[Jack Frederick]

Tried to do a link, but it is an “angle setting jig PDF under sharpening.

[Thomas Wilson]

Here you go.

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[Thomas Wilson]

Tried to do a link, but it is an “angle setting jig PDF under sharpening.
Thanks Jack. I meant a math formula for projections that would be used to set up the jig.

[Derek Cohen]

Just place the blade in the guide and use an angle box or a protractor to set the angle wanted.

Then mark/measure the projection involved.

The blocks in front of the grinder are stops for angles for BU blades ...

https://i.postimg.cc/4xb204gH/5.jpg
Regards from Perth

Derek

[Thomas Wilson]

Tried to do a link, but it is an “angle setting jig PDF under sharpening.
Thanks Jack. I am talking about a mathematical formula to calculate the distances versus bevel angle. The formula I found can be used to set up a similar jig with different dimensions or find the distance for an intermediate angle like 27 degrees. I don’t think many will find a use for the formula. I just like to solve math problems.

[Thomas Wilson]

Just place the blade in the guide and use an angle box or a protractor to set the angle wanted.

Then mark/measure the projection involved.

The blocks in front of the grinder are stops for angles for BU blades ...

https://i.postimg.cc/4xb204gH/5.jpg
Regards from Perth

Derek
Can’t fool me Derek. That's a grinder not a formula.

Since you hone freehand, you may not know about the jig LN gives a plan for to set the projection of the blade in front of the guide.

Never mind. I see your projection setting stop blocks at the bottom of the picture. I am giving a way to calculate the set back if you need one that LN did not provide or for another Eclipse style honing guide.

[Thomas Wilson]

I made a sign error in the derivation above, tried to delete the figures but it did not work. The following pages are correct. Sorry for the error.

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[Rob Luter]

LN have a link on their site for a…what to call it, a board with assorted dimensions, distances to set reference blocks to set the angle. I made one years ago and it has worked well for me. I just packed it up for the move or I’d post a pic.

The link is shown below.

https://d3h1zj156zzd4j.cloudfront.net/pdf/honing-guide-062719-1.pdf

[Tom M King]

I didn't read all your post. With that in mind, I don't like projection method of setting a jig by because it doesn't take into account the thickness of the cutter. I made these where the thickness doesn't matter at all, and can be used with any jig. No calculations required, and Very quick to set anything by. Nothing fiddly about them, and repeats the same angle every time.

[Greg Parrish]

Could you possibly take Tom's approach and use a protractor/angle finder in the same way, only setting the offsetting angle? So rather than 30, set the protractor/angle finder at 150. In my head that seams to work with the chisel once set into the honing guide, but maybe I'm not thinking of something.

[Thomas Wilson]

I didn't read all your post. With that in mind, I don't like projection method of setting a jig by because it doesn't take into account the thickness of the cutter. I made these where the thickness doesn't matter at all, and can be used with any jig. No calculations required, and Very quick to set anything by. Nothing fiddly about them, and repeats the same angle every time.

I like it. There is more than one way to skin a cat.

[Derek Cohen]

Could you possibly take Tom's approach and use a protractor/angle finder in the same way, only setting the offsetting angle? So rather than 30, set the protractor/angle finder at 150. In my head that seams to work with the chisel once set into the honing guide, but maybe I'm not thinking of something.

Greg, did you read my post (earlier)?

Regards from Perth

Derek

[Greg Parrish]

Derek, I did but I think my head was still swirling from trying to understand Thomas' math equation. I see now that you were advocating that exact same thing. Thank you for the clarification.


Greg, did you read my post (earlier)?

Regards from Perth

Derek

[Thomas Wilson]

Could you possibly take Tom's approach and use a protractor/angle finder in the same way, only setting the offsetting angle? So rather than 30, set the protractor/angle finder at 150. In my head that seams to work with the chisel once set into the honing guide, but maybe I'm not thinking of something.
Sometimes there is a problem with width or length of the angle measuring device such that you can’t get it to align with the blade without interference. There are solutions to that as well, like Tom’s custom width and length angle blocks.

I find that measuring small angles is harder to do accurately than measuring small lengths. So I like the projection jig. With a math formula for the projection, I have no need to measure the angle. I also like a good math problem. I’m also great fun at parties.

[Reed Gray]

Well, I guess I could do the math, but for me, I would just divide the difference between 2 settings. Personally, I wouldn't worry about anything beyond about 5 degree increments. Don't see the need for them either...

robo hippy

[Gary Focht]

I tried to stay out of this thread, but as long as we are discussing angle setting jigs…


Here is my version for the Lee Valley Eclipse style jig. It has one board and one fence. Adjustable for angle and micro bevel. Don’t really know microbevel angle, but probably 2-4 degrees depending on which angle I’m doing. It varies, but is consistent for that angle. Both lower and upper settings.

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[Thomas Wilson]

I tried to stay out of this thread, but as long as we are discussing angle setting jigs…


Here is my version for the Lee Valley Eclipse style jig. It has one board and one fence. Adjustable for angle and micro bevel. Don’t really know microbevel angle, but probably 2-4 degrees depending on which angle I’m doing. It varies, but is consistent for that angle. Both lower and upper settings.

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Gary,

The thread has turned into a thread about jigs for setting bevel angle. I tried to turn the herd but it was a stampede.

Your jig is innovative and compact. Certainly worth sharing. I like it. If you take some measurements of blade projection and dimensions of the Lee Valley honing guide, I can tell you the angles. :)

[Thomas Wilson]

The initial problem that prompted me to figure out the formula for blade projection was the Veritas sharpening instructions that suggested chisels narrower than 1/2” should be sharpened to a primary of 25 degrees and a secondary of 27 degrees. Chisels 1/2” and wider are recommended to be sharpened at 30 and 32 degrees. The Lie-Nielsen guide does not list 27 and 32. Lie-Nielsen also does not give projections for the other jaws they sell. I wanted to fix that.

Here is a table for all the angles and all the jaws I wanted.
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Here is how I measured the guide parameters.

G the width of the guide front to back
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R+r the height of the guide from top of blade to bottom of roller
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and 2r the diameter of the roller


I got a slight difference between my results and the Lie-Nielsen values so I investigated. The differences are shown in the rightmost columns in the table. The greatest difference occurs at 20 degrees.

There is a problem with measuring angles less than the bevel of this test blade. The back of the bevel touches before the tip. To check angles less than the bevel of the blade of 25 degrees I had to turn the blade upside down in the holder and subtract the thickness of the blade from R. The blade thickness is 0.102”.

Here is how I set up the Wixey angle gauge on the guide to check angles. The bench is level within 0.2 degrees which I account for using the relative angle feature of the Wixey gauge.
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My formula is accurate. LN is off a bit. I do not know why.

[Thomas Wilson]

I tried to cancel a post that had rotated images without submitting it. Then I started a new post in which the erroneous photos had been deleted. Apparently the images were still there at attached thumbnails.

Here is the correctly rotated measurement of the roller diameter that put the post over the 8 image limit.
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[mike stenson]

I'm going to ask a stupid question here. The angles are, IMO, pretty arbitrary. In other words, if you're off a degree or two it doesn't seem to matter. Am I missing something?

[Thomas Wilson]

I'm going to ask a stupid question here. The angles are, IMO, pretty arbitrary. In other words, if you're off a degree or two it doesn't seem to matter. Am I missing something?
I think your opinion is pretty common. My opinion is that is is pretty easy to get an accurate number. With a combination square and a sharp pencil, you can make a reference mark on a scrap board and set an exceedingly accurate bevel angle. No one else had shared a formula anywhere that I found so I put mine here for anyone who is curious.

Bevel angle does affect cut quality, cutting force, edge durability, and a lot of things. People here do discuss optimum bevel angles for chopping and paring, for planing, for different woods, etc. To share experience or to use experience other people have shared on the effect of the bevel angle in this forum, you need to know what it is. From an engineering perspective, a difference of 25 vs 27 degrees is significant, like 8%. Forces and loads, to a first approximation, are proportional to the angle, so 8% also.

[Tom M King]

Do you use a different formula and stop block for each thickness of cutter? Projection the same for an old Stanley iron and a new thick iron?

I made my setting jigs in about 10 minutes one morning in 2016 (I think it was). I made a quick jig to cut the little blocks at a complementary angle on my miter saw. No calculations were required. I just made them quickly to see if I liked them, with plans to make "better" ones out of Corian if I liked them. They've worked just fine every since for some number of hundreds of sharpening sessions, good enough that I haven't made the Corian ones yet.

They are at least as quick and easy to use as a projection jig. You just loosely put the sharpening jig on the tool well back from where it will end up, hold the cutter in place against the angle piece, slide the jig down until it touches the surface, and tighten it. The same setting jig repeats the same angle every time, for any cutter, any thickness of cutter, and any sharpening jig combination without changing anything. Thickness of chisel or iron matters not.

I haven't ever heard of anyone else making any to try. It seems like everyone thinks the projection method is better somehow. I don't. I did use one for a long time when I only used the original Eclipse, but it's long since been thrown away.

When I had helpers, I hired people that no one else would hire. They never did learn to read a tape measure, but they could sharpen anything as good as I could using my system which included these setting jigs.

[Thomas Wilson]

The Lie-Nielsen jig registers the top of the blade in a wedge shaped grip between the jaws. Hence the top surface of the blade is always the same distance from the centerline of the roller. Thickness of the blade does not affect the relationship between projection and angle. The classic Eclipse must work a bit differently. I do not have one. The Veritas Mk.II references to the bottom of the blade but it comes with a setting gauge.. The Veritas Side Clamping references to the top like the Lie-Nielsen. I could add a parameter for the thickness of the blade to the formula for jigs that reference the bottom of the blade.

Your jig is very clever and easy to use. I can see that and I do like it.

I have no jig at all, just a pencil line on a board. I extend the blade of a combination square to the projection length corresponding to the desired angle and scribe a line across the end of the square on the board. It is even easier to make and I can adjust bevels in fractions of a degree. I maintain that it is easier and more accurate to measure and mark a length on a board and align the blade and guide to it than to cut an angle for your jig's angle block and align the guide and blade to it. Angles are harder to measure than lengths. But I will not argue the point further than that.

I am sure you would have been a great boss to work for and learn from. We need to get together sometime.

[Derek Cohen]

Thomas, it needs to be said that the absolute angle of the bevel is relatively unimportant. You need just to be in the ball park (i.e. close). There are no Bevel Police coming to check your angles. What is most important is repeatability, that is, being able to return to the same setting (on your guide) each time you sharpen. Calculating angles is a waste of energy. Get it close (digital box) and set a projection stop. Done.

Regards from Perth

Derek

[Thomas Wilson]

Thomas, it needs to be said that the absolute angle of the bevel is relatively unimportant. You need just to be in the ball park (i.e. close). There are no Bevel Police coming to check your angles. What is most important is repeatability, that is, being able to return to the same setting (on your guide) each time you sharpen. Calculating angles is a waste of energy. Get it close (digital box) and set a projection stop. Done.

Regards from Perth

Derek

Derek, I solved a woodworking math problem. It was not a hard problem. I thought the work was interesting, useful, and original so I shared it here. I still feel that way. The energy is small. The accuracy is great. Give it a try.

[Patrick McCarthy]

Tom, much appreciated. Thank you. Patrick

[Jim Koepke]

An Eclipse style guide was given to me and is used occasionally. It has the projections for a few angles embossed on the siide.

For a shop rigged guide a much easier way was found.

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It was easier to align the angle on a piece of tile by using the bevel already on the blade.

The exact angle of a blade never stopped it from cutting if it was off by a degree or two.

Sometimes it is better to forget about all the calculations and permutations and just get the job done.

There are advantages to being lazy.

jtk


Whenever there is a hard job to be done I assign it to a lazy man; he is sure to find an easy way of doing it.
— Frank B. Gilbreth Sr. (“Popular Science Monthly” in 1920)

[Joel Gelman]

https://bluesprucetoolworks.com/products/sharpening-square

I understand this thread is about angles between standard (Eg. 25, 30 degrees), but the broader subject is how to set and check angles when sharpening. I came across the Blue Spruce Sharpening Square and just purchased one. I could not find info on it on this forum. Maybe silly purchase as I have been known to buy things I find out later I did not need, but it is because of my lack of still I though this would help me check my work. Just an FYI rather than starting a separate thread. I suppose with this one could check to see if something is in between 2 standard angles, but then it would not tell you the exact angle/

[Jim Koepke]

I suppose with this one could check to see if something is in between 2 standard angles, but then it would not tell you the exact angle/

Is there an advantage to knowing the exact angle?

With a bit of use and training your eyes you can be close enough. I like the Veritas guide for ~$10

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Many other retailers sell similar gauges.

jtk

[Richard Verwoest]

Thank you Thomas. Sometimes I wonder why people share anything here. Some of the replies are very discouraging.

[Warren Mickley]

Thank you Thomas. Sometimes I wonder why people share anything here. Some of the replies are very discouraging.

I agree.

I remember in trigonometry class people were saying "I am never going to use this." Years later they claim they went to high school, but it doesn't show.

[Jim Koepke]

I agree.

I remember in trigonometry class people were saying "I am never going to use this." Years later they claim they went to high school, but it doesn't show.

The only trigonometry in my high school math classes was how to use the trig tables and to remember Chief SOH CAH TOA. Geometry was one of my subjects, but trigonometry didn't interest me much until college.

The tables still come in handy at times.

The tables are available on line. A little measuring and some math can work this out easily.

Though the only time the angle on an edge is of much importance to me is when the edge is being renewed on my powered set up.

Not far off subject the book Euclid's Door (Lost Art Press) reveals how a lot of this can be determined without a lot of math.

Tom shows a great set up for setting angles. With something like that one could likely make some shims to vary the setting by a degree or two if so desired.

jtk

[mike stenson]

I agree.

I remember in trigonometry class people were saying "I am never going to use this." Years later they claim they went to high school, but it doesn't show.

Thanks for reminding me why I took a long break.

[Thomas Wilson]

I want to apologize to the forum for posting something that caused controversy. In particular, I apologize for responding directly to most people and answering their objections and criticisms of my post. I held my ground. This served only to continue the controversy, I should have let their and my posts stand on their own merit. That is what I will do in the future. If you ask me to clarify something I will try to answer. A question mark will be my cue to respond.

[Greg Parrish]

I want to apologize to the forum for posting something that caused controversy. In particular, I apologize for responding directly to most people and answering their objections and criticisms of my post. I held my ground. This served only to continue the controversy, I should have let their and my posts stand on their own merit. That is what I will do in the future. If you ask me to clarify something I will try to answer. A question mark will be my cue to respond.

Thomas. Don't get bent out of shape over it. I think its great that you figured out the math equation. Mind you, I still contend I may need my teenager to help me understand it. LOL Some healthy debate and argument is good for a family, even a Sawmill Creek Family. If everyone thought alike and did things the same way, we would never get anywhere new. I personally do not know enough about sharpening to truly make use of your formula, so I'll personally stick to the basic LN provided measurements, but I did save a copy of the math so that one day I can refer back to it if needed. Cheers and again chin up. Greg

[Tom M King]

I think it was all fine. Someone may have even learned something along the way.

[mike stenson]

I want to apologize to the forum for posting something that caused controversy. In particular, I apologize for responding directly to most people and answering their objections and criticisms of my post. I held my ground. This served only to continue the controversy, I should have let their and my posts stand on their own merit. That is what I will do in the future. If you ask me to clarify something I will try to answer. A question mark will be my cue to respond.

I don't think you did a thing to apologize for Thomas. It seems that pretty much anything around here can be suddenly controversial. More over, I think that a free exchange of ideas is healthy. I also believe that questioning things and disagreeing with thoughts are a fundamental part of that. Unfortunately, things generally devolve into patronization and outright derision far too often.

[Thomas Wilson]

I don't think you did a thing to apologize for Thomas. It seems that pretty much anything around here can be suddenly controversial. More over, I think that a free exchange of ideas is healthy. I also believe that questioning things and disagreeing with thoughts are a fundamental part of that. Unfortunately, things generally devolve into patronization and outright derision far too often.

Thank you Mike for responding. I was indeed concerned for you. The thread went off the rails and your reaction was undoubtedly shared by many. It caused me to review my posts and to consider how I might have contributed. I found that I had responded when no response was required. That is what needed apology. For certain, my feelings were not hurt then or now.. Please stay and contribute. You are a valuable member.

[Jim Koepke]

I want to apologize to the forum for posting something that caused controversy. In particular, I apologize for responding directly to most people and answering their objections and criticisms of my post. I held my ground. This served only to continue the controversy, I should have let their and my posts stand on their own merit. That is what I will do in the future. If you ask me to clarify something I will try to answer. A question mark will be my cue to respond.


Thomas. Don't get bent out of shape over it. I think its great that you figured out the math equation. Mind you, I still contend I may need my teenager to help me understand it. LOL Some healthy debate and argument is good for a family, even a Sawmill Creek Family. If everyone thought alike and did things the same way, we would never get anywhere new. I personally do not know enough about sharpening to truly make use of your formula, so I'll personally stick to the basic LN provided measurements, but I did save a copy of the math so that one day I can refer back to it if needed. Cheers and again chin up. Greg


I don't think you did a thing to apologize for Thomas. It seems that pretty much anything around here can be suddenly controversial. More over, I think that a free exchange of ideas is healthy. I also believe that questioning things and disagreeing with thoughts are a fundamental part of that. Unfortunately, things generally devolve into patronization and outright derision far too often.

Thomas, maybe I should apologize to you if my responses caused you pain.

In open discussions there are going to be many thoughts that do not always align. This is especially true when it comes to the topic of sharpening.

Stay the course, for many mathematical equations can an exciting passion. In my college days they excited me. Now that I'm an old fart, not so much.

jtk