Sunday, February 16, 2020

Deriving the Forumulas for Sightline and Resultant angles

Warning for adults: This post is primarily about math. If you're a math phobe, hate math, whatever, you should hit the eject button now! For an excellent, math-free approach to the same topic, go here. This warning is only for adults--teenagers can do this stuff easily.

I've been too busy making planes to dabble in chairmaking lately, but it's never far from my mind. Chairmakers and planemakers have a lot in common, and a number of folks--like Caleb James--do both at a very high level.
I first read about sightlines and resultant angles eight years ago, when I checked Drew Langsner's book out of the public library. In use, it's the simplest, most intuitive way to drill chair mortises. The only difficulty is coming up with the numbers. I know of five ways to do it:
So, do you need a sixth approach? Probably not. But I do! I've always used the numbers in Langsner's book, but I hate relying on a table of calculations without understanding where they come from, and why they work. I need to know what's under the hood and how it was made--maybe you're the same. Plus, if the apocalypse comes and sweeps away all my books, I'll still be able to make Windsor chairs in the post-nuclear hellscape.

Edit: If you just want the formulas for sightline and resultant angles, skip to the bottom of the post, where I give the two formulas and walk through a brief example. If you want to understand how the formulas are derived, read on.
To derive the formulas, we only need a bit of high school (sophomore year) math. We need to know SOHCAHTOA, and the inverses of the three basic trig functions. If you've forgotten this stuff, brush up with the linked explanations. I'll wait.

Oh, you're back? Great. I'll start with Galbert's method of drawing the rake and splay. Imagine dropping a plumb line from the top of a chair leg down to the floor. You'll form two triangles, one in side view (rake) and one in front view (splay). Now imagine flopping those triangles down on the floor to get a two-dimensional view, and you'll get this:

Since the the height is the same in both views, I've labeled them both with an arbitrary unit of one. As you'll see, this will be key to finding our formulas.
Next, label the rake and splay angles, r for rake and s for splay. Draw the rectangle defined by the rake and splay axes, and add in a diagonal. This is the sightline. You can think of the lower right vertex as the point where the bottom of the chair leg would sit.

Now we're ready to find the lengths of the rake and splay lines in terms of r and s. Using the tangent identity,
and similarly,

Here's what we've got so far.

Now we need a way to find the sightline angle--let's call it l--and to find the length of the sightline in terms of our other measurements.
The sightline angle is easy. Using the tangent identity again,

File this away for later--we'll use it to find our actual sightline angles.
Finding the length of the sightline is a little more complicated. Since it's the hypotenuse of a triangle, we'll need our sine function:

Now do a little algebra to isolate the "sightline" variable, and you'll get

Here's what we've got so far.

The last thing we need is a way to find the resultant angle, which I'll label t°. Let's draw one more triangle, defined by the common height and the sightline.

Using the tangent identity,

And now we've got the two formulas we need. Let's get rid of the confusing letters and use words instead:


Now let's look at an example. To find the angles we need to build a chair, we just have to punch the numbers into a calculator, and use the inverse tan (tan -1 ) button. Let's say we want 12° rake and 14° splay. For the sightline,

Now plug .851 into the inverse tan function:

So 40.4° is the sightline angle.

For the resultant angle:

Plug .327 into the inverse tan function:

And 18.1° is the resultant angle. Now, go make some chairs!

Sunday, August 4, 2019

After Four Years, It's Time For a Raise

Badger plane with open tote, referred to in some old catalogs as "jack badger."
Four years ago, I launched my planemaking business with a post titled "The Traditional Double-Iron Wooden Plane is Back." Since then, I've made a lot of planes, written a couple articles, lectured at various venues including Colonial Williamsburg, and demonstrated my wares at Handworks and many Lie Nielsen hand tool events.

Through it all, my prices haven't changed. Meanwhile, tariffs have raised the cost of materials for my blades and cap irons, PayPal takes a hefty cut of almost every plane I sell, and inflation, even at a measly two percent, adds up after a few years. So, it's time to raise prices a bit. I haven't settled on the exact numbers yet, but they will be in the 10-15% range, with the small smoothers going up the least, and the big try plane going up the most.

Here's the good news: It will take a few weeks to get these prices published on my website. Until then, the current prices are still in effect. So if you've been on the fence about ordering, now's the time to lock in the old price. Just go to my website and click on "how to order."

A quick note on pricing: In general, my customers have been very understanding, but I occasionally meet folks who think my prices are outrageous. And I get where they are coming from: We live in a world of mass-produced, dirt cheap consumer goods, and a lot of people see everything through that lens.

But here's the deal. I make my planes one at a time, or in small batches of two or three. Everything is meticulously custom fitted. Most of the work is done with hand tools. It's labor intensive and very time consuming. And believe me, I'm not getting rich off this. Much like folks who make custom furniture or musical instruments, I do this because I love doing it, and I'd be really happy just to be able to pay myself a living wage. I'm eternally grateful to have customers who understand this and are willing to pay for quality.

One more note on orders: My website currently claims a lead time of 3-4 months. That is probably a bit optimistic--in practice it's been more like 4-5 months, and I'll note that on the website when I change the prices.

In other news, I'm adding a few more planes to my catalog. Badger planes, like the one pictured at the top, can be ordered right now--just email me for pricing. Here's an Instagram clip of the badger in use--it is a really fun plane to make shavings with! In addition, I'm getting very close to being able to offer a dado plane for sale. To the best of my knowledge, no one is currently making a traditional beech dado plane, so I'm pretty excited about getting that off the ground. Stay tuned for more info. After that, I hope to finally get toothing planes into the mix as well.

To everyone who's bought a plane or otherwise helped me over the last four years, thank you. I hope to keep doing this for many, many years to come.

- Steve Voigt

Friday, March 15, 2019

Low Budget, High Vise

Back in 2011, Chris Schwarz wrote about the Etaux, a vise produced by Forge Royale in the early 20th century.

A few years later, Benchcrafted came out with a commercial version, which they call the Hi-Vise. The Benchcrafted hardware is top notch, but I wanted to build a low budget version using inexpensive hardware, some of which I already had lying around. I finished mine up in December and have been using it ever since. It's definitely one of the more useful shop fixtures I've ever made. So, here are a few pics and a brief description, should you want to make your own.

I based the construction around a Lee Valley tail vise screw (about $40) and a couple 9" veneer press screws (I had a box of these screws I bought years ago when they were cheaper; they are around $25 now). The Forge Royale originals, pictured above, also used two screws (theirs were wood) to hold the vise to the bench.
Forge Royale's more expensive version (above right), like the Benchcrafted vise, used a cast iron cross mechanism to regulate the jaw opening, while the cheaper version used a threaded rod with a nut that spins on it. For my version, I used a traditional parallel guide and pin. I've had the parallel guide on my main vise for about seven years and have always been happy with it: it's cheap, dependable, and bomb-proof.

The basic idea is that the parallel guide slides between the the two lower arms, and the tail vise screw slides between the upper arms, as shown below.

The lower arms have to be fairly thick (mine are 8/4) to accommodate the nuts for the veneer press screws. The upper arms can be thinner (mine are 5/4); just make sure they are far enough apart that the tail vise nut will fit in between. Also, note that the arms are about half an inch proud of the sides of the jaws. In Benchcrafted's version they are flush, but that wouldn't have worked here.

Some hack saw work was required for this job. I cut about 6" off the tail vise screw to save weight and space. I wanted a maximum opening of 8", so size yours to whatever you want to be able to hold.

I also cut down the handles of the veneer press screws, and filed them until they were comfortable to operate. As purchased, they are too wide and will bump into each other. Cutting them down also prevents me from torquing down too hard and over-stressing the dado joints that the lower arms fit into. These dados take a lot of force, so make sure you pin them to the sides of the fixed jaw, and don't put the holes for the veneer screws too far from the jaw (mine are 1-1/4" O.C. from the outside edge of the jaw).

I don't have a lathe, so I made some fairly fancy looking octagonal handles. There are definitely cheaper and easier ways to go, but this worked for me. I needed a new handle for my main vise anyway, so I made two.

Even before the handle was done, I was using the vise to hold the end caps while I beveled them.

A couple more dimensions: My vise is 4-1/2" wide, and the tops of the jaws are 8" above the bench top. I sized the dimensions to fit what I do: my plane totes are 5" or  5-1/2" long, so I wanted the vise to be narrower for easy access.

Overall, I'm incredibly pleased with this vise. I use it all the time for shaping totes, filing my planemaking floats, and other miscellaneous tasks.

If you make your own, I recommend using the excellent Benchcrafted instructions as a starting point.

- Steve Voigt

Thursday, December 13, 2018

Three Things David Pye's "The Nature and Art of Workmanship" Is Not About

Gouge cut detail, jack plane.

Recently Christopher Schwarz wrote a pair of posts on David Pye, the influential designer, critic, and woodworker who coined the phrase “workmanship of risk.” Chris’s take is as controversial and thought provoking as you’d expect, and it’s motivated me to write down some of my own thoughts on Pye. Like Chris, I first read Pye's book (The Nature and Art of Workmanship, published in 1968) years ago, and I've returned to it many times since.

I’m not here to argue with Chris, a terrific writer who has done more for the craft of woodworking than, well, just about anyone. But I’d like to try and rehabilitate Pye’s ideas from decades of misuse and misunderstanding. As Chris himself says, people love to take Pye’s pet phrase out of context and use it in ways that would've horrified him. So let's start by examining three common misconceptions about Pye's writing.

It’s Not about Screwing Up

Pye’s definition of workmanship of risk is pretty well known: It is workmanship in which “the quality  of the result is not predetermined, but depends on the judgment, dexterity, and care which the maker exercises as he works. The essential idea is that the quality of the result is continually at risk during the process of making.” 
This passage, with its connotations of daredevil craftsmanship, is very suggestive, but it’s only part of the story. Pye valued workmanship of risk for its "diversity," a catch-all term he used to convey qualities such as variety, uniqueness, and subtlety.

Consider the gouge cut in the photo above. I make these cuts freehand, so each one is a little different. The surface varies subtly from the surrounding areas that were planed, scraped, or chiseled. And yes, there is risk of failure: Sometimes the cuts are great, more often they’re decent, occasionally they’re barely acceptable. But I think what Pye would've appreciated about them was not the possibility of failure, but the fact that the surface bears traces of having been worked by an actual human being. Risk is a means, not the end: "There is much more in workmanship than not spoiling the job, just as there is much more in music than playing the right notes."

If the phrase “workmanship of risk “ is poorly understood, then its corollary, the "workmanship of certainty," is even more so. Pye starts by noting that the workmanship of certainty is “always to be found in quantity production, and found in its pure state in full automation. In workmanship of this sort, the quality of the result is exactly predetermined before a single salable thing is made.” To illustrate this concept, Pye contrasts the act of writing with a pen, clearly the workmanship of risk, with the operation of a printing press. He notes that while it took a great deal of skill to create the metal typeface and machinery necessary for printing,

But all this judgment, dexterity, and care has been stored up before the actual printing starts.  Once it does start, the stored up capital is drawn upon and the newspapers come pouring out in an absolutely predetermined form with no possibility of variation between them.

This passage is frequently misinterpreted by Pye’s critics, who object on the grounds that printing presses or other machinery may take great skill to operate. But Pye's point is not that it’s easy to run a printing press, or that nothing can go wrong with machinery. He’s simply observing that all the  copies of today’s newspaper that come out of the press will look the same. A skilled operator may be able to keep the machinery running more smoothly, and he may have fewer mangled copies of the paper that end up in the dumpster. But his copies of the paper will look the same as those of a less skilled operator, just as all the copies of an IKEA table will look pretty much the same, regardless of whether Sven or Birgit was running the machinery that day. It’s not the certainty of never screwing up that Pye is talking about; its the certainty that the objects of mass production will lack any meaningful variation.

At some point you might be wondering, doesn’t this risk/certainty thing just boil down to hand made vs. machine made? That is certainly the message many have taken from Pye, but as we will see, nothing could be further from the truth.

It's Not about Hand Tools

When someone uses the phrase "workmanship of risk" in a woodworking blog, it's often to extol the virtues of, say, cutting to a line with a hand saw, rather than feeding the board to a table saw. The former obviously requires more skill, and the risk of cutting poorly may be higher, but the broader implication is that hand tools in general are the workmanship of risk, while power tools are the dull, plodding workmanship of certainty. This is the framing that Chris Schwarz objects to, and rightly so.

But Pye actually takes the opposite tack. He begins the chapter "Is anything done by hand?" with two contrasting examples: A dentist drilling into a tooth with a handheld power drill, and a workman operating a hand-cranked drill press (like a post drill). The obvious point here is that the machine operation is full of risk, while the hand tool operation has very little (Pye amusingly notes that it has perhaps 5% risk because "if the hand-workman is fool enough he may break the drill"). The purpose of these examples, says Pye, is to show that "to distinguish between the various ways of carrying out an operation by classifying them as hand or machine work is…all but meaningless."

See, the whole reason Pye resorted to the categories of risk and certainty is that he wanted to avoid the dichotomy of hand vs. machine made. Pye sees "hand made" as a historical term people use to describe pre-Industrial production, but it's a highly inaccurate term, since many trades have actually used machines, more broadly defined, for centuries. Think of the loom, the lathe, or the potter's wheel.

Ultimately, Pye's purpose was to distinguish between highly automated mass production on the one hand, and the individual craftsman or small shop on the other.  "Workmanship of risk" was a useful way of describing what the individual craftsman did, regardless of whether that involved hand tools, power tools, or (more likely) both.

It's Not About Your Table Saw

After reading Pye's example of the drill-wielding dentist, one might conclude that cutting to a line with a band saw, which involves a modest amount of skill, is workmanship of risk, while ripping a board on a table saw, which requires little, is workmanship of certainty. Or, to cite another example, cross-cutting exactly to the line with a back saw vs. squaring up the work on a shooting board.

Nope, says Pye. "All workmen using the workmanship of risk are constantly devising ways to limit the risk by using things such as jigs and templates. If you want to draw a straight line with your pen, you do not go at it freehand, but use a ruler, that is to say, a jig."

Pye is distinguishing here between individual operations that involve more or less risk, and an overall framework of risk or certainty. He continues:

In fact, the workmanship of risk in most trades is hardly ever seen, and has hardly ever been known, in a pure form, considering the ancient use of templates, jigs, machines, and other shape-determining systems, which reduce risk. Yet in principal the distinction between the two kinds of workmanship is clear, and turns on the question: "Is the result predetermined and unalterable once production begins?" (emphases mine)
 To put this in concrete terms: If you are making a cabinet in your shop, you are engaged in the workmanship of risk, because you have control over the quality of the result. It doesn't matter whether you are doing the work with handsaws, planes, and chisels, or with a table saw, power planer, and router table. The latter approach may take more steps to limit risk, but that's what craftsmen have always done within an overall framework of the workmanship of risk.

On the other hand, to take another example of Pye's, suppose your job is to feed raw steel rods to a machine that then "turns out hundreds of finished bolts without anyone having to look at it." Now you're engaged in workmanship of certainty, because as Pye just said, the result is "predetermined and unalterable once production begins." And remember, "predetermined and unalterable" doesn't mean that nothing can ever go wrong; it means rather that the worker has no direct control over the quality of the work.

Now, we could quibble with this; we could say that the machine operator must know when to change or sharpen the cutting tool, or the bolts will be ruined. But all this means is that a bit of skill and risk has been injected into the workmanship of certainty, just as those practicing the workmanship of risk are introducing a modicum of certainty by using templates and jigs. The categories of risk and certainty are extreme poles, and as Pye suggests are rarely seen in pure, unadulterated form. But even so, the distinction is clear: As a Supreme Court justice said of pornography, we know it when we see it.

Finding a Place for Crafsmanship

It's now fifty years since Pye wrote The Nature and Art of Workmanship, and much has changed. At the time, Pye was worried about the possibility that craft would disappear entirely, and that we'd be living in a world where all products were mass produced. So an important part of his philosophizing is about trying to find a place for craftsmanship in a world in which it seemed to be rapidly vanishing.

Pye wasn't a hopeless romantic or a Luddite, and he wasn't nostalgic for a bygone era. He didn't believe that workmanship of risk was better than workmanship of certainty: He points out, for example, that cars produced by workmanship of risk would be fantastically unaffordable by just about everyone. So he recognizes that the affordable mass production of consumer goods has enormous benefits, but at the same time he insists that traditional tradespeople (cabinetmakers, for example), practicing the workmanship of risk, produce things that have unique aesthetic qualities that the workmanship of certainty can never duplicate. He writes that the crafts "ought to provide the salt--and the pepper--to make the visible environment more palatable when nearly all of it will have been made by the workmanship of certainty."

Not everyone will agree with my interpretation of Pye, and that's OK. But having lived with his ideas in my head for a long time, I'll sum them up this way: Make stuff. Make it however you want, use whatever tools you want, limit risk to the extent that you need to. Skill is important, but "what matters most in workmanship is not long experience, but to have one's heart in the job and to insist on the extreme of professionalism."

Tuesday, December 4, 2018

A Badger Plane

It's been a while since I posted about a new plane, but this one's pretty unusual, and pretty interesting to make. Badger planes were very popular in Great Britain in the 19th century, but never really caught on in North America. They were typically used for planing large rabbets and making raised panels.

A badger plane is a top escapement rabbet plane, which means that it shoots the shavings out of the top, just like a bench plane.  The mortise of a badger is not only skewed, it's rotated 10 degrees about its vertical axis. If that's making your head hurt, perhaps some pictures will help.

I didn't take many pics during the construction of the plane, but here are a couple that show the rotation and skew.

Here's a shot of the wedge in mid-construction. I'm using a gouge to rough out the ramp; afterwards I'll finish with a chisel.

The cutting iron and cap iron both need to be skewed of course. Making a skewed cap iron from scratch was simpler than I expected, and much easier than trying to modify and existing cap iron.

Once the mortise was done, it was time for the body details. I built this plane for the purpose of finishing the grips of side escapement planes, so I decided to make it unhandled and 10" long, basically a large smoother. I have read on the Interwebs that badger planes have to have handles, but if we go to primary sources, we see that's not true. Here's a clip from the 1909 Preston catalog, which listed badger planes in both smooth and jack sizes, the latter with three different types of boxing! Ah, the good old days.

Anyway, here's a shot of the heel of the plane, which is quite comfortable actually. There's also a step cut into the right side, which makes the heel smaller and easier to hold, and also makes the mortise appear more symmetrical when viewed from above.

As I mentioned, the badger plane was popular in Britain but never really caught on here. I'm not sure why. The badger excels at making large rabbets that are tear-out free. That's not something that's needed in typical furniture making, but for a planemaker it's essential. There are a couple metal planes designed to do this job, but they don't do it as well. The Stanley 10-1/4 or 10-1/2 can plane large rabbets, and the double iron will control tear-out better than any other method, but the lack of skew makes the plane harder to push. Similarly, the Stanley 140 will plane a wide rabbet, and the bevel up iron can be sharpened with a steep angle to combat tear-out, but that high angle makes the plane a bear to push, and the block plane format is not ideal for heavy work.

The badger on the other hand combines skew, a double iron, and good ergonomics to make easy work of those wide rabbets. To close, here's a short video clip of the plane in action.

Tuesday, January 23, 2018

New year, new planes, new shows

For the first two and a half years of business, I've concentrated on the core of of the three essential bench planes--the jack plane, the try plane, and the coffin smoother. This year, I'm starting to expand my offerings. The first of these is the rabbet plane, pictured above.

My rabbet planes are bedded at 50° and can be ordered either square or skewed. A nominal 1" iron is standard, but if you are looking for a different width, just ask. These planes have custom irons that are 5/32" thick--a bit thicker than what most other makers offer. They have a very solid feel in the cut.

I'm also adding a new bench plane, which I call the Mini-Smoother.

I jokingly refer to this plane as the cure for the common block plane, because I built the first version of this plane about four years ago, and I haven't used my block plane since. The design has been honed a couple times, and I think it's just about perfect now. The plane is comfortable to use with one hand or two. It has a 1-1/4" double iron and is 5-1/4" long.

This is just the beginning. In the near future, I plan to roll out a number of new planes. Moving fillisters will be next, followed by dado planes, and then we'll see what's next. Toothing planes? Miter planes? Stay tuned.

I'll be doing a couple Lie-Nielsen Hand Tool Events this spring. This weekend, January 26-27, I'll be at the Chicago School of Woodworking. In March, I'll be at Urban Specialty Woods in Huntington, NY. If you're in the neighborhood, stop by, say hi, and try some wooden planes!

Finally, a reminder: If you'd like to see more regular photos from my planemaking biz, check out my Instagram feed.

Monday, October 9, 2017

New Article in Popular Woodworking

In this month's issue of Popular Woodworking, I have an article (my first!) on making a double iron coffin smoothing plane. Here's a link to a description of the article, and here's a link to purchase, should you be so inclined.

I didn't choose the title--Popular Woodworking likes puns more than the NY Post does!--but I'm very happy with how it all turned out. Megan Fitzpatrick originally asked me to write a seven-page article. A few months later, I emailed her to say "I have a problem. I've written 15 pages and I'm not done yet." But somehow, she managed to condense it down to 10 pages, without omitting any essential content.

I tried to put everything I could think of into this article, but after it was done, I realized there was one thing I didn't mention: no matter how complete an article is, it can never substitute for learning at the School of Hard Knocks. I tried to include everything I've learned over the past five years about avoiding all the pitfalls in planemaking, but you know what? The only way to really learn about those pitfalls is to experience them. You'll probably make some mistakes on your first plane. You might even have to start over. But if you want to make a plane, persevere, and you'll get there. I won't pretend it's easy, but it's not rocket science, either.

If anyone out there has comments or questions, feel free to post below.