Tools and externalities

Following on my previous post: In trying to define a “traditional” tool I raised the issue of toolmaking. But the way a tool is made has implications for the maker of the tool as well as (if not more than) for the end user.

The low stages of my scales suggest a toolmaker who pursues a craft in a small shop: people who make wooden molding planes, for example. That may be a kind of ideal, but it isn’t always practical.

In the middle are small, semi-industrial operations in the U.S., Canada, and Europe, with relatively few workers, an emphasis on craft, and a working environment that is, for lack of a handier term, more or less flat, in that it minimizes the distance and distinction between labor and management workers being given latitude for authority and the owner is not only capable of doing some actual work but even now and then does it. That, at least, is the kind of working environment I would prefer for myself, whether as a worker or a manager ( I have been both).

At the high end of the scale, you have machine parts cranked out by machines wherever labor is cheapest for the profit of corporate shareholders.

If I value the way I work, surely I ought to try to extend that privilege to others? That’s merely the golden rule. So I might say, as a third principle, that “A tool (and its components) should be made by workers who work as the user would want to work and who are treated as the end user would want to be treated.”

Hand tools and “traditional woodworking”

When I asked recently “What is a ‘hand tool,’ anyway?” I considered two fairly literal definitions of a hand tool: a tool held and operated with the hands, and a tool powered exclusively by the hands (or possibly by other body parts). Neither was really satisfying. Here’s another, more complicated idea that comes up in conversations about hand tools: the idea of “traditional woodworking.” Continuing my list, I could say that

3. A hand tool reflects traditional woodworking practice.

But what do I mean by traditional?

Here we go again.

What is a “hand tool,” anyway?

When I describe my work I usually say that I do “hand-tool woodworking,” or that I work primarily or exclusively with hand tools. Nobody has ever asked me what I mean by “hand tools,” so presumably everyone has a clear idea in his or her head what I mean… or rather what they think I mean. What do I mean? What’s a hand tool, anyway? And why do I use them, as opposed to… whatever hand tools are opposed to?

Maybe this seems like a facile question. I don’t believe it is. Nor an unimportant one. If I’m only using the term for introductions at parties and taglines on business cards, then I suppose it doesn’t matter much what I mean, but if I’m trying to make serious decisions about work, then it matters a great deal. It matters in conversations with other woodworkers who use machines, and who are apt to see a hand-tool-first or hand-tool-only approach as stupidity or snobbery—opinions that I can’t refute if I can’t clearly define what I’m doing and why.

Most important, it matters in making decisions about what tool to use for a job. We all have standards by which we evaluate and adopt (or decline to adopt) technology, but few of us actually know what they are — or have considered what they should be.

But it’s also the kind of question a guy with advanced degrees who has written cultural history starts thinking about while he’s in his second hour of sawing and planing 8/4 oak. Not just why don’t I buy a freaking bandsaw? but no, really, why don’t I? This need to define my terms was made rather more urgent, if ironically also more quixotic, by my experience teaching homeschool environmental science last spring. When my daughter suggested writing her final paper on means of reducing or eliminating single-use plastics, I told her she had better start by defining what a “single-use plastic” was. She spent three months, wrote nearly five thousand words, and still never quite managed a precise definition, but by the end she knew a hell of a lot more about what she didn’t know. She grew wisely ignorant, you might say, as opposed to being merely a clever fool. Which I believe to be an improvement.

So let me see if I can become at least more wisely ignorant. This will take awhile to suss out; I’ll only get started today, and I’ll post new ideas as I think of them, revising my thinking as I go. Consider this an invitation to think along with me.

I can think of several qualities that might qualify a tool as a “hand tool,” but none of them is sufficient as a definition. Let’s start with two.

Small arcs of large circles: A calculator for cheaters and engineers

finishing the coffee table

This week I am finishing my splay-legged coffee table… in the dining room, because the humidity is such that I don’t trust oil to dry in the workshop. I will have more to say about (and better photos of) this piece, which posed several, ah, interesting challenges, but for now let’s talk about this one, which I’ve faced before and will face again: constructing small arcs of large circles.

There are three long arcs of circles on this table, at the ends of the top and on the undersides of the aprons. The longest has a lengths of 23 inches and height of 1 inch — a radius of some five feet, so actually constructing the circle was straight out. I could probably have drawn the shortest one freehand to within sawing and shaving tolerances, but the longest moves so slowly that I didn’t trust myself. I’ve been known to use Affinity Designer (Adobe Illustrator for people without corporate budgets) to draw ogees when I couldn’t get what I wanted with French curves, but I can’t print something 23" long. What to do?

What George Walker and Jim Tolpin call artisan geometry has solutions for practically every design problem woodworkers face, including this one. What you do, is draw a half-circle with the height of the arc you want, then proportionally expand that arc using station points, from which you can build a form for bending a batten or simply sketch a template:

constructing an arc from station points

But while this method works well for doubling or tripling the length of the arc, it isn’t really practical for stretching it by a factor of twelve.

Finally, like all good craftsmen, I fell back on the training I received as a young apprentice: I used trigonometry. Knowing the length and height of an arc one can, using trigonometry, determine the radius of the parent circle, then plot coordinates of station points in terms of the horizontal distance from the center of the baseline and the height of the arc at that point. Of course, one doesn’t want to have to do those calculations thirty-odd times for a single project, so I wrote a bit of code to do it for me. And since I assume other people have similar challenges, I made the calculator available on my website.

To use the calculator, input the width and height of your arc, the horizontal interval (along the baseline) between the points you want to plot, and the desired precision. The coordinates will be generated in ordinary fractions of an inch, to the desired precision (up to 1/64 inch). If desired, you can also see decimal values.

A calculator for constructing small arcs of large circles

If you want to understand the math, my explanation follows.