Extension Calculator Finest abrasives. Microbevels front and back. Use a jig. Copyright (c) 2002-17, Brent Beach

## Contents

1. Introduction -
2. Geometry - The mathematics, part 1.
3. Extension Calculator - Calculate the extension for your jig/iron/angle.
4. Setting the extension
5. Many Jigs - Why one is not enough.
6. Tapered Irons - What thickness do you use for a tapered iron?

## Introduction

This Extension page explains the geometry behind the jig and provides a calculator and tables which will allow you to set your jig to any desired bevel angle.

### Naming the parts

There are seven things to know in order to specify all the angles. Five have to do with the blade and jig, two with the slips used to produce the (second and third) microbevels. The names used in these pages:

1. Bevel jaw

The jaw on the bevel side of the tool. Its height, along with the extension, determine the front bevel angle.

The jig has two jaws - the bevel jaw and the back jaw. Typically the bevel jaw is from 1 inch to 2 inches tall, although the bevel jaw if slanted (more below) can be 5 inches or more tall.

2. Back jaw

The jaw on the back (non bevel) side of the tool. It's height, along with the extension, determine the back bevel angle. It is usually quite thin - starting at 1/8 inches.

3. Jaw Angle

All of my early jigs had square jaws. The blade and jig front form a right angle triangle. This is fine for longer tools. For short tools, or when you want a longer range of motion, an angled jaw works better.

Slanted jigs increase the distance from the tool edge to the jig base. This can be important for short chisels and plane irons, as well for grinding the primary bevel. In both cases a slanted jig increases the length of the sharpening motion, improving control and speed.

The blade is held between the bevel and back jaws. You will need to find out the thickness of your blade. If you don't own a digital caliper or micrometer, and don't know the thickness of your blade, use the default blade thickness of 0.09 - an average thickness.

5. Bevel Angle

The angle you want to get on the first abrasive, without any slips.

If you are honing, this is the angle of the first microbevel. For plane irons, I usually use a first microbevel angle of 29 degrees.

The honing angle is fixed by these 5 values. If we want to hone at a different angle, we have reset to the extension for that angle. We can avoid resetting the extension by putting a slip under the base of the jig. When honing the jig rests on the slip and the slip skids along the glass. This little bit of extra height slightly increases the honing angle.

This slight increase in honing angle means that when we start honing on the next finer abrasive the tool is resting on the edge. Only the edge is touching the abrasive. With very fine abrasives metal removal is very slow. By isolating the abrasive action to the edge we can remove the correct depth of metal even though we are using a very fine abrasive.

1. Short slip

The short slip is used under the jig with the second abrasive to produce the second microbevel (the first microbevel is produced using no slip). I usually use a short slip that is around 0.06" thick. With a taller jig, you might want a slightly thicker short slip.

2. Tall slip

The tall slip is used under the jig with the third abrasive to produce the third microbevel. It should be about 50% thicker than the short slip (mine is 0.1" thick).

### What are extensions?

For a given jig, the angle at the edge depends on the extension - how far the tool edge is from the front of the jig. So, extension is the single essential measurement you will have to make each time you use the jig.

However, aside from determining the sharpening or honing angle, the extension has one other important effect on honing - it determines the range of motion of the jig. Range of motion is the amount you can move the jig on the glass sheet without the tool falling off the abrasive or the jig running into the abrasive.

I have found that a range of motion over 4 inches is pretty good for honing. For grinding, where more force is required, an 8 inch range of motion is much better.

Why is this important? It turns out that the beginning and end of each honing motion are the toughest bits. This is where you will make all the mistakes. The middle portion, once you have reached operating speed, is error free. The longer the range of motion the better will be your honing success.

If range of motion did not affect how well you hone or grind we would be satisfied with one jig for all our work. We could make, for example, a 1" high jig and be done with it. Most jig manufacturers were done with it at that point.

We increase this range of motion two ways. First, by making the jig taller. For every inch we add to the jig height we add 2 inches to the range of motion. Unfortunately, we also add 0.87 inches to the amount of blade extending from the front of the jig. This is fine for longer tools like full size plane irons. It stops being a solution quickly for shorter tools like some chisels and short plane irons. It is a real problem for very short tools like knives (short from spine to edge).

The second way we can increase the range of motion is by using an angled jaw on the jig. More on this below.

So, you want a jig size that lets you maximize the range of motion - to the extent you can given the length of the tool you are honing.

### How tall should my jig be?

I have made many jigs over the years, most between 1 1/2 inches and 2 1/2 inches tall. I make them quickly and throw ones that don't work into a box. A large box.

You can reduce the number of failed attempts by using the Jig size from blade length calculator below. It lets you work from the length of your plane iron or chisel to the correct size of jig. The basic problem is that the jig must grip about 3/4" of the blade. The maximum extension is about 1 inch less than the blade length.

Generally you want a jig that gives a range of motion over 4 inches if possible, 8 inches for grinding. Balancing large range of motion with the size of the tool you are honing is the essential first step. The Jig size from blade length calculator lets you design an appropriate jig.

### Page history

When I first made these jigs, I started with a table of jig sizes. I struggled to make the jig parts exactly the size given by the table. With the introduction of this extension calculator page, you can make the jig any size you want (depending on the wood you have), then use the calculator to find the correct extension for that jig. If you have a piece of scrap 1-7/8" tall, don't plane it down to 1-1/2", use it as it is.

As well, I made all my early jigs with the thin side 1/8" thick, because that was the size in the tables I have worked out by hand. The calculator lets you specify the thickness of the thin side. Now you can select a thickness that produces the back bevel angles you want.

As well, for years I used slips with thicknesses 0.06" and 0.10". The calculator now lets you supply slip thicknesses. The key is that the first slip add about 2 degrees, the second slip about half that again. Once you have your jig made, use the calculator to find slip thicknesses that complement its dimensions.

I no not expect people to use the tables any more. I have moved them off to another sheet.

The Calculator was updated in June, 2006 to show the back bevel angle as well, both for the basic jig and for the jig with slips!

The Calculator was updated in October, 2006 to handle non-square jigs. These jigs are most useful when grinding the primary using a bench stone, or sharpening chisels.

This was was updated in July 2011 to change the terminology. Now, the jaw on the bevel side of the tool is called the bevel jaw. That on the back side of the tool is called the back jaw. (Changed from tall and short, respectively.)

## Geometry

The angle the plane iron makes with the abrasive is determined by the sizes of the parts of the jig, the blade thickness, and the amount the edge extends beyond the front of the jig. The formula that relates the variables:

 E = (Tj + Tb) / Tan(A) Tj - jig height (bevel side) Tb - thickness of the blade A - angle at the edge E - extension of blade edge from the front of the jig

This formula assumes that the jig has square jaws. The formula that applies when the jaws are not square is only slightly more complicated and has been incorporated into the calculators below.

The new angle, called the Jaw Angle, is angle at the jig face. The default is 90 degrees. By using lower angles, you can increase the distance between the blade edge and the jig front, giving you a longer range of motion during sharpening. With a 45 degree jaw angle, you can use the full length of an 8" oil stone when grinding a typical bench plane blade.

Jigs with this shape are also useful with short chisels. Usually with short chisels the edge can only extend an inch in front of the jig, so the distance between the chisel edge and the jig front is quite small. With an angled jig you can make a 5" tall jig with a 35 degree jaw angle that allows a 5" range of motion with the shortest chisel.

This angling of the jaw face does not assist back bevel honing in the same way. In fact, it reduces the distance from the blade edge to the leading edge of the short jaw, reducing the range of motion. For this reason, jigs with jaw angle other than 90 degrees would typically be used only for front bevels, not for back bevels. They are most useful for

• grinding plane irons, or
• grinding or honing chisels.

## Extension Calculator

Here are four calculators.
1. Use the first calculator if you have a jig and know the angle you want -- it will calculate the extension in imperial units.
2. Use the second to calculate the extension in metric units.
3. Use the third if you have a blade and an angle you want -- it will calculate the jig size you need (imperial only).

The calculators now have 7 inputs that let you define a variety of different jigs and honing situations.

Referring again to the Sketchup model:

1. Bevel jaw height

The height of the jaw on the bevel side of the tool, along with the extension, determine the front bevel angle.

The jig has two jaws - the bevel jaw and the back jaw. Typically the bevel jaw is from 1 inch to 2 inches tall, although jigs with a slanted jaw can be 5 inches or more.

2. Back jaw height

The height of the back jaw, along with the extension, determine the back bevel angle.

3. Short slip height

The short slip is used under the jig with the second abrasive to produce the second microbevel. I usually use a short slip that is around 0.06" thick. With a taller jig, you might want a slightly thicker slip.

4. Tall slip height

The tall slip is used under the jig with the third abrasive to produce the third microbevel. It should be about 50% thicker than the short slip (mine is 0.1" thick).

5. Jaw Angle

All of my early jigs had square jaws. I have recently been experimenting with jigs which hold the iron at larger angles to the jig front face. Such slanted jigs increase the distance from the tool edge to the jig base. This can be important for short chisels and plane irons, as well for grinding the primary bevel. In both cases a slanted jig increases the length of the sharpening motion, improving control and speed.

If you don't own a digital caliper or micrometer, and don't know the thickness of your blade, use the default blade thickness of 0.09 - an average thickness.

7. Bevel Angle

The angle you want to get on the first abrasive, without any slips.

If you are honing, this is the angle of the first microbevel. I usually use a first microbevel angle of 29 degrees.

### # 1 Extension from jig size and angle - Imperial units

Fill in the 7 numbers for your particular case and click the Calculate button to find the extension required.

Outputs include:

• the extension, to the nearest 32nd of an inch.
• the distance along the glass from the front of the jig to the back of the bevel, in inches. This distance is the range of maximum motion of the jig. Usually you will use an inch less than this.
• the actual front bevel angles.
• the actual back bevel angles.

 Inputs bevel jaw height inches back jaw height inches short slip height inches tall slip height inches jaw angle degrees blade thickness inches bevel angle degrees Outputs Extension + / 32nds inches Base of jig to blade (range of motion) inches Actual angles ... no slip degrees ... short slip degrees ... tall slip degrees Back bevel angles ... no slip degrees ... short slip degrees ... tall slip degrees

### # 2 Extension from jig size and angle - Metric units

Fill in the first 7 numbers for your particular case and click the Calculate button to find the extension required.

NOTE: Although this calculator uses metric units, it uses a period '.' rather than a comma ',' as the decimal point. Thus 3 1/10 cm is written 3.1 (not 3,1).

This calculator shows the extension, to the nearest mm. Default sizes of the various jig components in metric:

 Short slip .2 cm Tall slip .3 mm

Outputs include:

• the extension, to the nearest mm.
• the distance along the glass from the front of the jig to the back of the bevel, in cm. This distance is the range of maximum motion of the jig. Usually you will use a couple of cms less than this.
• the actual front bevel angles.
• the actual back bevel angles.

 Inputs bevel jaw height cm back jaw height cm short slip height cm tall slip height cm jaw angle degrees blade thickness cm bevel angle degrees Outputs Extension cm Base of jig to blade (range of motion) cm Actual angles ... no slip degrees ... short slip degrees ... tall slip degrees Back bevel angles ... no slip degrees ... short slip degrees ... tall slip degrees

### Jig size from blade length

You have a plane iron or a chisel and want to make a jig for it (and all its similar pals).

As mentioned before, generally we want a tall jig because that maximizes the range of motion when honing or grinding. A range of motion shorter than 1 inch is quite hard to use. A range of motion around 3 or 4 inches is quite comforatble. I find that any jig over 2" tall works pretty well. Much taller and they become a little unwieldy.

Width We also have to decide the appropriate width for the jig. Generally, because the back jaw (the thinner jaw) will bend if the jig is a lot wider than the tool, we want the jig to be a bit more than 1 inch wider than the tool. This 1 inch allows for the space taken up by the screws and T-nuts plus a bit of leeway in tool width. You can use the same jig for a 1/2" wide chisel as a 1" wide chisel, but probably not for a 2 inch wide chisel.

Thickness Jig thickness is not as important, but it does matter. Most of my jigs are made from standard 3/4" stock. I have made jigs from 1/2" stock but they tend to be more fragile. The jig grips the tool on the front and back face. If the jig is over 1/2 inches thick this grip is usually pretty good.

Height Get the appropriate height from this calculator. For that you need:

1. the length of the blade less the thickness of the jig. This gives you the maximum extension.
2. the thickness of the blade at typical extensions.
3. the average honing angle you want.

### # 3 Jig size from blade length

For example, I have a bench chisel that I want to hone. The chisel is just over 3" long. I will be using 3/4" thick wood for the jig. That means I will be able to have an extension of not much more than 2 1/8". At that extension, the chisel is 0.22" thick. (Notice the plus sign in the blade extension box - writing 2 1/8 does not work).

 blade extension inches blade thickness inches bevel angle degrees jig height + / 32 inches

NOTE: If you put the jig height from the second calculator into the first calculator, the blade extension calculated may be a little different from your number in the second calculation. This is rounding error from working in thirty-seconds of an inch.

In metric:

 blade extension cm blade thickness cm bevel angle degrees jig height . cm

## Setting the extension

I use a combination square to set the extension. If a short movie would help, you can watch me set the extension here.

A little tricky the first time, with a little practice you should be able to set the extension in under a minute.

Get the extension you need from the extension calculator. Having gotten it you might write it on the jig.. I have a printed table of of blade extensions for various first microbevel angles I use for various blade thicknesses.

Set that extension on your combination square.

With the iron in the jig, tighten the screws until iron can move in the jig, but not slip out. With the blade of the combination square against the jig and the iron against the square, set the extension.

Flip the square over and make sure the side of the iron is square to the front of the jig.

A little bit more tightening of both screws and I'm ready to sharpen.

Perhaps surprisingly, the iron rarely slips inside the jig once the nuts are tightened. This wide beech jig has excellent grip.

As well, even after hundreds sharpenings, the jig shows little wear from sliding on the glass and the glass in scratch free.

Many people who use jigs that rely on blade extension make up a jig to simplify extension setting. At its simplest it is a strip of wood nailed to a board, the distance you want from the edge. You then push the jig up against the edge of the board and push the blade forward to the stop.

This is quick and accurate and fine if you only need one or two extensions. This model shows two stops - one for plane irons in a 2" square jig, one for 1/4" thick chisels in a 2" slanted jig.

## Many Jigs

I have made many different sized of jigs over the years, to accommodate different sizes of blades.

 2" tall, 3" wide This is the most used size jig. It works for most bench plane irons. 2" tall, 3-3/4" wide For the wide blades use in #7 and #8 planes. 1-1/4" tall, 3" wide For short blade, like block plane blades, where the extensions required for the taller jigs are greater than the blade length. You might consider a slanted jig for these blades.

My first instinct was to suggest using the thickness where the jig grabs the blade. Thinking it over a bit I concluded this was wrong.

First, until you know the extension you don't know where to measure the thickness. Duh! You could put a thickness into the calculator, get the extension, measure that distance from the edge, get a new thickness, put that thickness into the calculator, rinse, repeat, ...

Even that will not get the correct answer because all the calculators assume the sides of the blade are parallel.

This sketchup model shows the tapered plane iron, drawn from a blade I have. The jig size was arbitrary.

Rather than a single blade thickness, you need to supply two thicknesses and two lengths:

• Tj - select some point on the blade well away from the edge, scratch the blade, measure the thickness on the thin side of the scratch.
• Te - seclect a second point closer to the edge, scratch the blade, measure the thickness of the thin side of the scratch.
• D1 - measure the distance between the scratches
• D2 - measure the distance from the edge to the closest scratch.

The calculator uses these thicknesses and lengths to calculate the taper angle. It uses the taper angle to compute the correct extension - the distance from the edge to the jig face perpendicular to the jig face (not along the upper blade face).

### # 4 Extension calculator - tapered blades

 Inputs Tj thickness near jig inches Te thickness near edge inches D1 distance Tj to Te inches D2 distance Te to edge inches bevel face jaw height inches back face jaw height inches short slip height inches tall slip height inches jaw angle degrees honing angle degrees Outputs Extension + / 32nds inches Base of jig to blade (range of motion) inches Actual angles ... no slip degrees ... short slip degrees ... tall slip degrees Back bevel angles ... no slip degrees ... short slip degrees ... tall slip degrees

### Error Analysis

How much of a difference does it make to use the tapered blade calculator? Not a lot.

Using this calculator and this blade (the thicknesses and distances in the model) and specifying a 2" jig this calculator gives an extension of 3 28/32".

Working back from this extension in the sketchup model, I find the thickness there is 0.16907.

Putting that thickness in the original calculator we get 3 29/32" extension.

Specifying a honing angle of 28.9 or 28.8 degrees in the tapered blade calculator give an extension of 3 29/32".

So, the error using the original calculator is no more than 0.2 degrees *** provided you enter the thickness at the extension it calculates. Getting the correct thickness could take several interations of the calculator: guess an extension, measure the thickness there, enter that thickness in the calculator, calculate, measure the thickness at the calculated extension, update the blade thickness input to the calculator, calculate, ...

### Grinding Error

If you grind using one of my jigs and a stone, using the tapered blade calculator will give you the correct grinding extension.

If you grind using some other jig, their extension setting is probably wrong.

If you grind using a belt sander, setting the tool rest to the desired grinding angle will get the wrong angle at the edge. The edge angle will be the tool rest angle minus the taper angle. If you grind using a grinding wheel, the usual tool rest setting algorithms will yield the wrong tool rest angle. Again, the error will be small and should not affect honing much.

## Lost?

Try looking around the site map. You can also reach the site map from the little map at the top of each page.