In chair making there are all kinds of angles to deal with. I never just use one method for every task. It would be great if I could but considering the pieces I want to make it just requires a variety of approaches.
With windsor chairs we often talk about angles such as splay, rake, sighting, and resultant. Figuring these is often done with a trigonometry chart or some similar method to take our splay and rake and make a sighting and resultant angle to simplify drilling. This works well because we have a nice center line to use as a reference and everything can relate to that. However what do you do when you start to throw in some odd lay outs that don't relate well to that set up.
Consider the three legged candle stand that I have pictured Above. First there is no common center reference line that all the legs would share that would give you one convenient sighting and resultant angel. That is easily simplified by just sharing a common resultant angle and then drilling them every 120˚ in relation to one another, moving around the center point of the table top.
The harder part is figuring the stretchers that are tipped down in one direction and up in the opposite, as well as, being 60˚ in relation to each other and entering the legs that are at a resultant angle of 6.5˚ sighted from the center of the table top. This can make you start scratching your head as to how you will figure these angles and then drill them accurately. Well, it is time to put the calculator down, the angle gage, protractor, or whatever it is that you might think to use in this instance, and just use some practical thinking.
First, I know that, in the simplest therms, I simply want to drill a hole in one leg that is in line with another hole on an opposite leg. In other words to go from point A to point B, whatever that angle might be in relation to anything else. So then, why not just drill from point A to point B. Let me show you how I do just that, rather than take my measurement, disassemble things, and then drill, only to put it all back together again.
Below I show the two points I want to connect.
Second, I know that in order to do that I need to keep everything lined up just as it will be in its final constructed position. Since my top is so thin and doesn't have enough surface within the joint to hold the leg at the correct angel while applying pressure from drilling, I constructed this base, pictured below, that will keep all the legs at the point where they are intended to be placed at the floor. There are holes drilled at the proper locations and the end of the legs are placed in those holes. (I wouldn't do this, if drilling for a typical chair leg, since the seat is thick enough to hold the leg at the correct angle while I drill.)
Third, I need to make sure that all my legs are at 90˚when sighted 120˚, relative to one another from my center point, to confirm that my resultant angles for all legs will be what I intended. I do this by checking all three legs like I show in the photo below. Now comes the drilling!
I didn't have anyone to take a shot of me doing the drilling so, in the photo below, I simply show the drill bit in the leg after drilling to show how I line the shaft of the bit to correspond with one hole location while drilling into the opposite hole location. Ok, but you say, that my hole is not in line with the other hole, it is offset to the outside of the leg. This is simply brought into line by turning the leg a few degrees to line it up. This is not a problem if you are doing something like a side stretcher for an H pattern undercarriage. Since only one stretcher enters each leg then you can turn it a few degrees and everything is in line. But this case is different since we have two stretchers entering each leg. Take a look at the next photo.
Notice that when drilling the lower hole on the same leg I simply drill with my shaft on the inside of the opposite leg, rather than from the outside, thus offsetting it in the same direction. Now that both holes are drilled proceed with turning the leg a few degrees and the holes line up.
If you want to keep all the growth rings in perfect orientation to the table top or seat then simple turn the leg a few degrees prior to drilling so it will fall back in place after everything is assembled.
So, there you have it. Drilling angles without complex calculations. I hope this helps you expand your design possibilities.
Remember when drilling to let the drill do the work. A light touch and a little practice will make drilling this way quite successful. If you grind your own drill bits, then use a shallow relief angle brad point which will make your dill bit less aggressive, aiding in control while using one hand. If you need some advice on drill grinding, check out Peter Galbert's blog post here. A must see.