shop math help needed

[Alan Turner]

HELP!! Some time ago, in FWW, there was an article, or a sidebar, on a trig based formula for converting two angles to one angle, as in for drilling. If you want to drill a hole that is 15.7 degrees off of vertical in one direction, and 7.2 degrees off of vertical at 90 degress to the first angle, that can be converted to a single angle, using trigonometry. Build a jig or sled to that single angle, line up a line drawn between the centers of a pair of opposite holes with the center of the column of a drill press, and you have it. I think the article or note was in connection with drilling the splayed leg holes on a windsor chair.

With this method, one need not build a sled for the first angle, and then tilt the DP table to the other, and then try to hold the stock without being clumsy.

I can't locate this article in the FWW index, and wonder if someone can help with the Issue number.

Thanks for helping someone with all too many senior moments these days.

Alan

[Greg Mann]

Talk about Senior moments. It was 1972 when I did this for a grade. I think this is what you are looking for. I wrote it in what I think are descriptive terms so that it makes sense (I think). I don't know how better to format it to allow its acceptance. Just to make sure, we put your example through a CAD sketch and got the same results, so I think it will be valid. Usual cautions here: I'm not a real mathmetician, I just play one on the internet.

ArcTan of resulting angle = Square Root of (Tan of first angle)squared + (Tan of second angle)squared

Arc Tan of R<SUP> </SUP>= √ (Tan15.7)squared + (Tan7.2)squared

ArcTan of R = √ .079 + .016

ArcTan of R = .3082

R = 17.1278 degrees


Greg

[Alan Turner]

I'll test drive it. Thanks so much.
Alan

[John Gregory]

This is another example of the remarkable resource the members of Saw Mill Creek are.

[Chris Padilla]

Alan,

I dunno if Greg is correct because I am not following what exactly you are setting up and I am not following your description of the problem. Is this a 2D problem or a 3-D. Are you tilting the table of the Drill press to drill off of 90 degrees in two directions? I wanna figure this out because this sort of stuff drives me nuts until I can figure it out but I just don't understand the problem to begin with. Anyone, anyone?

[Greg Mann]

Of course I'm right, Chris. John just descibed me as part of a wonderful resource.:D
It was my understanding that Alan was indeed describing a coumpound angle, or 3D problem.

Greg



Alan,

I dunno if Greg is correct because I am not following what exactly you are setting up and I am not following your description of the problem. Is this a 2D problem or a 3-D. Are you tilting the table of the Drill press to drill off of 90 degrees in two directions? I wanna figure this out because this sort of stuff drives me nuts until I can figure it out but I just don't understand the problem to begin with. Anyone, anyone?

[Chris Padilla]

Okay, I have confirmed Greg's findings. I bow to the master. :)

However, I messed up my reference and found the wrong angle since I got 1 over what Greg got. No problem, 90 degrees minus my answer is Greg's answer...the correct one I might add! :)

Here it is in an equation format:

http://members.roadfly.com/agent99/eq.jpg

Alpha is the angle you are looking for and theta and phi are the two given angles. Make sure your calculator is in degrees and you'll need t use the Arctan, Inverse Tan, or Tanª where the superscript a is -1, to get the angle you want.

[Alan Turner]

Chris,
The problem is how to drill 4 precisely correct holes, two pairs of diagonals really, that round tenons on leg ends will go through, on a rectangular bench, such that each leg is splayed to the side (looking at an elevation from the long side perspective) 15.7 degrees, and then viewed from the end splayed 7.2 degrees. I have historically drilled these by setting a shop made angled jig at one angle, 7.2 deg. front to back, and then tilting the table 15.7 degrees. But, it is really just one angle, for which I would build a wedged table, if I can align a line through the center points of the diagonal holes. It is that angle that I seek.

I worte this just as you were posting your second response. Did we understand each other correctly?

This is a great place!

Alan

[Greg Mann]

Crown Molding: calculate compound ;) , cut, cope, cuss, caulk, chill.... :D

I found a couple other formulas in my old Mechanics Vest Pocket manual but I don't have my RPN brain with me to confirm, so I will stick with the rather cumbersome solution I posted earlier for now. If it works in San Jose that's good enough for me.

This was posted on the Knot's for you and I think it will work too.
V = acos(cos(R) x cos(T))


Greg

[Alan Turner]

Thanks to all for your help.

Alan

[Doug Shepard]

Boy do I feel stupid. I got my degree in Math and Computer Science. In theory all this should be familiar enough to comment. In reality, it just means I've forgotten more math than most people ever learn.

[Mark Stutz]

All this ArcTan stuff is making my head spin this early in the morning on a Sat! :D Guess I need another cup of coffee.

Greg...1972....WOW....I was doing this for a grade around then. :eek: Didn't understand it then :o and couldn't begin to remember it now ;)

[Greg Mann]

All this ArcTan stuff is making my head spin this early in the morning on a Sat! :D Guess I need another cup of coffee.

Greg...1972....WOW....I was doing this for a grade around then. :eek: Didn't understand it then :o and couldn't begin to remember it now ;)
Mark,

There was a brief time period in the early seventies when I learned compound angles and used them everyday. It really was fun, but times have changed with CAD systems and all. Our skillsets change and our memory fades. It was reassuring that I could still pull it up. Now if I could still run that quarter-mile like I used to. ;)

Greg