Women in Dreams & Geometry
This post is totally suitable for work.
“To see the next part of the movie,” the woman’s voice said through a speaker, “you must first solve this puzzle.”
I looked down at my lap in the movie theater and there were six walnut dowels. The puzzle: Figure out how to drill six holes in a block of wood so the walnut dowels all appeared to be one piece of wood.
“That’s impossible,” I muttered to myself. But I started drilling and – damn – within a few minutes, I’d figured it out.
Elated, I woke up in my bed, shaking off the dream of the movie theater. The solution to the walnut dowel puzzle was also the answer to the chair geometry problem I’d been working on all week.
I’ve written about “sandwich drilling” in the past. You can see my first write-up about it here. Or you can download “The American Peasant” for free here and read the chapter on the “Peasant Chair” for a more polished presentation. Basically, sandwich drilling is a way to drill all the mortises in a chair’s arms and backrest by stacking them up on the seat, clamping them down and drilling through the whole pile.
Sandwich drilling saves time and makes the drilling more accurate. The mortises all match in angle because they were drilled simultaneously.
So far, I’ve used the technique on a few chair designs, including the chair in “Build a Chair from Bulls%$t” (also a free download). But until today, all the angles I’ve used have been simple, non-compound angles. For my next Chair Freak, however, the backrest angles needed to be compound angles. And the chair’s five back sticks had to be drilled at three different angles.
It’s a thing of nightmares. Or so I thought (thank you, woman on the speaker in my dream).
The solution came rapidly because my brain works mostly in inches and feet, aka “base 8” and “base 12.” If I’d been thinking in metric, I’m not sure the answer would have come so easily. (I’m not arguing one system over another. I use both. But understanding the measurement system that dead chairmakers used for their chairs helps me get into their heads.)1
Here’s the “eureka” bit. The old chairs I’m studying use angles that are related. The chair on my bench today uses 3.8°, 7.5° and 15°. These three angles describe the chair’s entire backrest.
The outside sticks lean back 15° and splay out 7.5°. The adjacent sticks lean back 15° and splay out 3.8°. And the center stick leans back 15° – no splay.
The endless-forehead-slapping moment came when I realized what happens when you drill a hole at each of those angles in 1"-thick material. The 1"-thick material is the key to the puzzle.
A 3.8° angle shifts the centerpoint of a drill bit 1/16" in 1"-thick material.
A 7.5° angle shifts the centerpoint of a drill bit 1/8" in 1" material.
And a 15° angle shifts the centerpoint of a drill bit 1/4" in 1" material.
Knowing that, it’s easy to lay out a compound angle when drilling through a 1"-thick arm. Let’s say you want the bit to exit in the center of the arm on its underside. Plot the hole on the top of the arm. Now shift the center point 1/4” down and 1/8" to the side. Tilt your drill 15° back and 7.5° to the side. Drill. You’ll hit the desired center mark on the underside of your arm.
This simple trick makes compound sandwich drilling a breeze. Stack the arm on top of the seat. Put the centerline of the arm on the centerline of the mortise in the seat. Shift the mortise location as noted above, tilt the drill and go for it.
Of course, I dislike drilling while following two sliding bevels, so I used the Chairpanzee to turn the two drilling angles into a sightline (65.4°) and a resultant (16.4°).
If all this is making your head hurt, I empathize. I have not gotten more than four hours of sleep for the last four days. Finally, my brain relented and explained it in a dream.
More details to come on this technique soon.
When Will the Chairs End?
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