# Dovetail geometry



## zxxer12 (Feb 8, 2005)

Are there any good primers on the relationships between dovetail angle, diameter and depth of cut vs material thickness, etc.

I'm getting ready to cut some dovetails and want to learn some more about the basics of the joint.

TIA


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## Dewy (Sep 15, 2004)

The reply depends on whether you intend making hand cut dovetails or use a router to produce them.
Hand cut dovetails usually have a 7° or 8° angle depending on the material.
Dovetail cutters are usually similar angles and the fit depends on the depth you set the cutter at.
Tight fit, lower the cutter slightly.
Loose fit, raise the cutter slightly.


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## zxxer12 (Feb 8, 2005)

What is the relationship between material thickness and bit size, same different??

Does material 3/4" thickness require minimum 3/4" long cutting section on the bit??

Does the template determine the bit angle ??

I have a Stotts and his wbsite talks about an 8 Deg. bit but what about 7 or 9 deg.??


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## Mike (Nov 22, 2004)

Zxxer, I dont think there is per say a standard for dovetails. Many of the jigs work off similar dimensions but I think that is mostly a copycat situation. Some of the nicest looking pieces have high angles or double dovetails, spacing set to all different patterns to create unique designs. Obviously a jig is designed to work in a certain set up, with a certain combination of rules. This does not mean it wont work when you change some of the parameters, just that you will need to confirm the results are what you are looking for.


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## Dewy (Sep 15, 2004)

zxxer12 said:


> What is the relationship between material thickness and bit size, same different??
> 
> Does material 3/4" thickness require minimum 3/4" long cutting section on the bit??
> 
> ...


It depends on whether you want through dovetails or half blind dovetails.
The angle is personal preverence when hand cutting dovetails.


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## jeff12002 (Mar 1, 2005)

With regards to the stots jig, look closely at the jig. The taper on the tapered fingers is 8 degrees, just like the 8 degree bit you use with the other side of the template. A 7, or 9 degree bit with this jig, will not produce tight fitting joints.


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## Cummins92 (Nov 14, 2004)

Zxxer12,
Router cut dovetails are determined by available cutter angles. So, I think this begs the question, are you going to custom grind dovetail cutters or have them custom gound? Or, are you looking for visual relationships? Perhaps a design manual that talks about proportions would help. Can't help you there. I have a Craftsman Dovetail Jig where all the spacing and angles are fixed. I precut one dovetail, measure the width and angle with a dial caliper, refer to trig tables, move dovetail jig with dial caliper measurements, move router depth with dial caliper measurements, finish cut. It's worked perfectly so far. Good Luck with your search and have fun.


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## tdshepard (Nov 8, 2009)

*There is a simple relationship*

Hi. I'm a brand new member here, and this is an old thread. I don't really see an answer to the original question here. So it seems I have something to offer.

Many decades have passed since my F in shop class, I have 4 college degrees, and I am doing much better now. I am a "re-beginner" at woodworking.

Here is the math. If the explanation below is hard to visualize, please tell me. I can put an illustrated version on my web site.

Draw a sketch of the interface between the two dovetail-joined parts. It should look like a jagged line of opposing trapezoids. I'll try to do that with ascii art here (if you used a fixed-width font, it might work):

----- ----- -----
\ / \ / \ /
----- ----- -----

It doesn't matter whether this is a blind or through dovetail joint. The analysis below focuses only on the geometry of the joint interface. (How that lines up with your workpiece determines what kind of dovetail joint it is.)

Define some variables:

h = depth of cut (distance from top to bottom of my diagram above)

d = diameter of router bit at widest point

p = period of the dovetail pattern (distance from corner of one tail (or pin) to the next tail (or pin)

e = angle of dovetail bit. This is the angle between any of the slanted lines in my diagram and the vertical, and corresponds to the way bit angles are defined in typical bit specifications. (The total angle subtended by the bit, a pin, or a tail is 2e.)

The universal relationship between these variables is

h sin(e) = d - p/2

I just purchased an Incra Incremental Positioning Jig Model 25971. It comes with a couple of templates, one for box joint and another for dovetails. These templates are only good for two particular dovetail bit geometries and a couple of stock thicknesses. Rather than buy more templates, I can use this formula to make my own, for any bit geometry and stock thickness.

The distance between any line and the next in an Incra template is p/2, and the distance between any A line and the next A line or any B line and the next B line is p.

All I have to do is check and maybe calibrate the scaling accuracy of my printer and I can crank out any template for any geometry with a simple computer program. The printer scaling can even be slightly off, and the Incra incremental positioning jig will get it perfect as long as p is an integral multiple of 32nds of an inch.


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## Bob N (Oct 12, 2004)

Hi Thomas and welcome to the forum. Thanks so much for such an excellent reply even if the thread is old. I am sure many here will benefit from the time you have taken to do this.

We hope you will elect to participate often, you have much to offer it appears.


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## tdshepard (Nov 8, 2009)

tdshepard said:


> h sin(e) = d - p/2


Oops! Slight mistake here. That should be a tangent function, not a sine function. That is,

h tan(e) = d - p/2

For the small angles typical of dovetail bits, it doesn't matter too much, because then sin(e), tan(e) and e (if in radians) are all approximately the same. And you're probably going to begin by making a test cut and adjusting the bit height (h) to get a good fit anyway.

Also, while I am splitting hairs, it wouldn't surprise me if the angles given on the bit packages are actually rounded to only 1 significant digit. When I set up to do dovetails on a router, rather that using trig functions, I just use the approximate relations

tan (14) = 1/4
tan (10) = 1/6
tan (9) = 5/32
tan (7) = 1/8


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## garycurtis (Sep 17, 2007)

There are some rules, in fact. Smaller angle dovetails are suitable for hardwoods. In softwood, because the tail might pull out of the pin, or because the wood might actually break, you must use the larger angle dovetail bits.

Generally available bits are carbide tipped, so the angles are usually rather clumsy looking. The carbide cutter is brazed to a steel shank, and the resulting profile is thus a dead giveaway that the joint created is machine made.

Handmade dovetails can be quite thin (given the limits of the wood strength) and elegant. One company makes very small angle bits out of HSS. Not as strong or durable as Carbide, but the results are beautiful. Go to The Craftsman Gallery, chipsfly.com. The drawer bits (some as small as 6 °) must be used carefully in hardwoods. They break easily.

Gary Curtis


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## bobj3 (Jan 17, 2006)

8 deg.
16 pc 8mm Shank Dovetail Router Bit Set For Leigh Jig - eBay (item 140360137847 end time Nov-22-09 10:23:27 PST)

7 and 8 deg.
11 pc 1/2" SH Dovetail Router Bit Set For INCRA Jig - eBay (item 130345416442 end time Nov-24-09 10:42:09 PST)

========


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## anotherBob (Oct 28, 2009)

garycurtis said:


> There are some rules, in fact. Smaller angle dovetails are suitable for hardwoods. In softwood, because the tail might pull out of the pin, or because the wood might actually break, you must use the larger angle dovetail bits.


This is pretty much as I understand it too, info gleaned from others...



garycurtis said:


> Generally available bits are carbide tipped, so the angles are usually rather clumsy looking. The carbide cutter is brazed to a steel shank, and the resulting profile is thus a dead giveaway that the joint created is machine made.
> 
> Handmade dovetails can be quite thin (given the limits of the wood strength) and elegant.


Dittos, but most of us don't have the time or patience or whatever to make James Krenov style dovetails, but can all appreciate how beautiful they are, and serve as inspiration. Myself, I've only ever done one project, a small bookcase, in hand cut dovetails... just to learn and try. Was inspired by one of Krenovs' books enough give it a go. They turned out pretty good for a first time effort... but let's just say, that you couldn't make a living out of doing them at the speed that those went, _and_ they were not as thin.  The router lets you cheat the "paying-your-dues" part, but the tradeoff is like you said... a dead giveaway.



garycurtis said:


> Handmade dovetails can be quite thin (given the limits of the wood strength) and elegant. One company makes very small angle bits out of HSS. Not as strong or durable as Carbide, but the results are beautiful. Go to The Craftsman Gallery, chipsfly.com. The drawer bits (some as small as 6 °) must be used carefully in hardwoods. They break easily.


Think these are what you're talking about:

Individual Bits: The Craftsman Gallery, chipsfly.com

8-degree 3/16" HSS Dovetail Bit
8-degree 3/16" HSS Dovetail Bit: The Craftsman Gallery, chipsfly.com

I never knew anyone made these... so, thanks!


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## garycurtis (Sep 17, 2007)

The HSS bits I have and use are one piece. No brazing. So the smallest, used for drawers, are so narrow as to be almost unbelievable. And when the wood project is finally assembled, you cannot distinguish them from handmade dovetail joints.

At the other extreme, this same company makes and sells a 28mm dovetail bit. That's about 1 1/8" in diamter. I made 20 feet of knockdown (no glue) wall benches out of 2x6 and 4x4 douglas fir timbers using sliding dovetails for the legs, aprons and stretchers with this bit. I can stand on the bench tops. 

Seeing as the bits are HSS, I made the cuts less aggressive by hogging out an initial trench using a half inch carbide spiral bit and then following up with the dovetail. I sharpen all my HSS bits with a light pass of a diamond paddle and, so far, haven't seen a noticeable reduction in bit diameter. I love HSS because the edge can be honed so fine. 

But they won't last forever. 

Gary Curtis


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