Recently I had an order for a turned lavatory stand that presented some unique challenges. It was 16 at the top, 3 at the bottom, 32 tall and needed to have room internally for the plumbing. I decided to make it from 8/4 cherry and use 8 compound mitered staves for the construction. Using the Table Saw Miter Angles program from www.turnedwood.com it was a simple matter to figure out that the slope was 11 degrees, each stave was 6.83 wide and 32.7 long, the miter gauge angle was 4.519 degrees and the blade tilt angle was 67.935 degrees. Using 2 stock, this would give me a wall thickness of 1.548. The easy part was done and now I had to set the blade angle. While no stranger to segmented turning I had never worked with compound miters. I was entering the world of compound miters where confusion and profanity reign.
I didnt feel comfortable that any of the commercial products I had seen would give me the accuracy I needed and they were all too expensive to try on a whim. Finally the solution hit me! It is simple, cheap, requires no special tools to make and the construction tolerances are not critical.
First lets start with a simple geometry lesson.
Depending on which vendor you talk to, a saw blade that is at a right angle to the top is at 90 degrees or 0 degrees. For this article it is 90 degrees. Its my article so I get to decide. Split that hair on your own time!
The angle wanted for the saw blade is between side A and side C, angle AC. Side C is the plane of the saw blade. If I want to know the length of side A and know the length of side C and angle AC then the cosine of angle AC times side C gives me the length of side A. The longer side C is the less measurement error creeps into AC.
Example A:
Side C = 69
Angle AC=45 degrees
Cosine 45 * 69 = 48.7904 on length of side A
So if I tilt the blade until side B crosses side A at 48.8 the saw blade is at 45 degrees. This is the maximum that most saws will tilt hence is the maximum length needed for side A.
Example B
Side C = 69
Angle AC=67.935 degrees
Cosine 67.935 * 69 = 25.92 on side A.
Now for the construction. I used a piece of 3 by 12 3/8 aluminum plate with a 5/8 hole (saw arbor size) drilled in the plate, 2 from one end. I then bolted 1 square tubing (side C) to the plate. The tubing is centered on the arbor hole. To the tubing I pop riveted a 50 piece of 1 aluminum angle stock (side A). The pop rivet is pivot point AC. Side A has a tape measure pop riveted on it and the start of the tape is centered on the pop rivet holding the 2 pieces (side A and side C) together. This is pivot point is AC. From point AC, I measured 69 on side C (point CB) and attached ½ aluminum angle (side B). I used 69 because that is maximum length I could use without hitting the shop ceiling. This piece is attached with a wood screw that screws into the wood plug inside the end of the square tubing and the hole in side B is drilled in the angle of the stock allowing side B to pivot freely. Now I installed the tool on the saw. Height of side A above the saw table is not critical as long as it is parallel to the saw table. Side B was too long to swing down over the table and needed to be cut off. To find the length needed I cranked the saw to 45 degrees according to its gauge and cut side B off so that it swings freely over the table and extends below side A. The excess was rubber banded to the inside of side B. This allows me to adjust length of side B so that it extends below side A as I change angle AC.
Considerations:
None of the lengths of my version are critical and should be adjusted for your location. The longer side C is, the more accurate angle AC will be but also the more it will bend under gravity. With side C at 69, one degree is over 1 on the scale on side A and accuracy within 1/8 degree is not hard to achieve. Side B can be made using a string and weight, but is very slow to stop swinging and is very sensitive to any vibration. Pivot point CB is centered on the tubing. On my original version I attached side C to an old saw blade and that worked fine. This article is for a right tilting saw. For a left tilt make a mirror copy.
The same process works fine to set the miter angle but is much easier. Based on the assumption that the saw blade is 90 degrees to the front edge of the saw top and that the right edge of the top is parallel to the saw blade. The front edge is side A and the right side is side B. Now we need to compute the length of B.
The formula is sin of AC * side A = B
AC = 30 degrees
Sin 30 * 50 = 25 on side B