Stock preparation for tapered tenon cutter

Question

I’ve got a Veritas tapered tenon cutter and feel like I am missing something obvious for using it efficiently.

Suppose I have a square chair leg 4 cm (1 1/2 in) thick, and I want to create a tapered tenon on it. The cutter is about 3 cm (1 1/8 in) at the wide end and about 1.6 cm (5/8 in) on the narrow end. Obviously, I need to remove some material first to start using the cutter. I have 2 very closely related questions:

1. Which shape should I impart on the leg before applying the cutter? Reduce to a cylinder that barely fits the wide end? Reduce to a cone with approximately the same included angle as the cutter? A cone with a smaller angle?

2. What is an efficient way to achieve the above shape? I have chisels, block & jack planes, a flat bottom spokeshave, a travisher, rasps, hand saws. I don’t have a lathe, or a drawknife, or a bandsaw (any of those seem like they would save a lot of effort). I could consider getting a drawknife.

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What I’ve tried so far was to reduce to a cone with approximately the right angle. A wide chisel with the bevel up removes the initial material quickly, then a spokeshave to refine. (I’ve tried the jack plane but it’s a bit heavy to go back and forth on such a short section.) Then apply the cutter, inspect the marks it left where it stopped, thin the material up to the marks with a spokeshave, repeat. It took me about 1h per leg. I know things take what they take, but it feels like I am missing something and could be done much faster!

Answer 1

After some experimentation, some new tools and some math, I believe I have arrived at a reasonably efficient method. My last attempt took 13 minutes including marking, as opposed to over 1h in the original question :)

Which shape should I impart on the leg before applying the cutter?

A reduced cylinder is fine, however it’s no easier to create than a cone (maybe even harder) and gives more work to the tenon cutter.

Trying to cut a cone with a matched included angle is a fool’s errand. If you get even a slightly steeper angle than needed, the cutter will eventually encounter a section thicker than its opening and will stop cutting. You will find yourself trimming down the offending sections again and again. To illustrate (exaggerated, not to scale):

Starting with a lower-angled cone (say, 10˚) is the way to go (drawing not to scale):

What is an efficient way to achieve the above shape?

Some math

First, determine the length of your 10˚ cone. You will need to know the width of your stick (W) and the desired diameter of the tip (w). For the latter, I went with 17 mm, which is a little over 5/8”.

To calculate the length, l, use the following formula: l = (W - w)/2 / tan(10˚/2). For example, with a 37 mm wide stick this yields (37-17)/2 / 0.087, which is about 115 mm.

Marking out

Transfer the cone length and the tip diameter to the stick:

Roughing out

Taper to the marks with a drawknife.

Make sure the “shoulders” all around the cone are straight or (failing that) ever so slightly concave, but never convex (otherwise you might have an overly thick section the cutter can’t enter):

Applying the cutter

Now use the tapered tenon cutter. If it gets stuck on an overly thick section, find the offending bumps and trim them away with a drawknife:

Done

Once you reach your desired depth, you are done!