Now, I’m an electric guy. Not as in “exciting”, but as in “I like power tools”. Despite that, I have taken a fancy to some very old tools, those being the divider and the sector. I got this bug while reading the really nicely put together book called, “By Hand And Eye”, by George Walker and Jim Tolpin.
In this book, they show that design is about harmonic visual proportion and that, rather than using a tape measure and math, design is most easily accomplished using a very, very old design process. This process starts with some fundamental dimensioning. For furniture that means dimensioning for the space the object will occupy and dimensions that work for a human body, such as seat height, arm length, or eye level. With those dimensions in mind, the task turns to design and that is where we use the divider and sector.
The divider provides your fundamental dimension, that from which all your other dimensions are derived. A divider looks like a compass, but it has two points rather than a point and a pencil-lead marker. It is common to have two or three dividers, all set to commonly used dimensions found in your project (as you design and develop them) and the sector is used to rapidly make whole-number multiples of a fundamental dimension. I don’t want to steal the thunder from George and Jim, so suffice it to say that whole-number multiples make the world go ’round, and I’ll move on to what I really want to show, which is the building of a sector.
Building a Sector
Good luck finding a sector at WoodCraft, or Rockler, or WoodWerks, or Highland Woodworking, or Veritas, Lee Valley, or Amazon or eBay. You have to make one, but it’s easy.
First, find yourself some hinges. You can use any small, cheap butt hinge from a hardware store. I bought solid brass hinges online somewhere, but as I was examining some dividers I recently bought on eBay, I found that one of them had a broken spring. Bummer about that, but the hinge was really great, with a brass decoration, so I decided to use that for my sector. As I mentioned, you can use a cheap but hinge. There is a video below (How To Use a Sector) that shows a sector made using a simple butt hinge, so watch that before sawing a perfectly good divider into pieces.
Here you see that I sawed the hinges off and threaded holes in them for brass screws. The two legs I sharpened and now use as awls or center punches.
Second, get some nice, straight wood sticks. I had some poplar hanging around, so I used that. I tapered the legs just for appearance.
Third, fasten the two sticks using the hinge. I mortised them flush with the inside face of the sector sticks. That way my starting point for distance increments can be the center of the hinge.
step four, divide the length into 13 equal parts and mark both legs of your sector alike. Yes, 13.
“13” And The Golden Ratio
The reason to number to 13 is because of the Golden Ratio. If you don’t know what that is, look here: Design Using the Golden Ratio
The Golden Ratio number is 1.618, or its reciprocal, 0.620. It turns out that 13 divided by 8 is 1.625, which is a whole number ratio and is close enough to 1.618 that they eye can’t tell the difference.
Using The Sector
To use the sector you set some real some real dimension as the distance between the same point on each leg, then transfer the multiple you want from the sector using dividers. So, if you have a drawer that is 7.3594733 inches high and you want the drawer above it to be just two thirds of that height (remember, whole numbers), you simply set the bottom right corner of that drawer face to the “3” on one sector leg, and the top right corner on the “3” of the other sector leg. Now, without moving the sector, take your dividers and set the distance between the “2” markings on each leg. Transfer that to your work piece, or a story stick and you have your dimension with no fussy math. Look at this very short video and it will be clear: How To Use A Sector
Mark Your Sector Using Fundamentals
Writing this description reminds me of the beauty of using pointy things to mark your work and how it can help you draw your sector divisions. You use dividers and a marking knife … and a square. Estimate about a 13th from your starting point to near the end of the sector leg. Set the divider to that dimension. Now walk it from your beginning point 13 times. If you are too long make it shorter, too short make it longer. Trial and error a few times.
Once you have that measurement, start from the hinge end and for each step of the divider poke an obvious mark for each of the increments. Grab your square and marking knife. Put the tip of the marking knife in the first point mark. Slide the square up to the edge of the knife. Pull the knife along the square edge to the inside edge of the sector leg and be sure to cut a good notch in that top corner. Move the square to that inside face, put the knife in that edge cut, slide the square up to it and cut a line in the inside face. Repeat for all 13. Now close the sector legs and transfer your marks using the knife and square.
Once you have all your knife marks, draw over them with a fine point marker. The cut lines will stay visible so you still have that very fine accuracy. Number the marks 1 to 13 starting at the hinge end.
Design Is Fundamental
Read the book, “By Hand And Eye”. Think like a designer who is a craftsman. Be a designer first. Just as your craftsmanship improved, your design eye will develop too. These tools will help you do that by abstracting away the math.