math help needed

[Donald A. Fortune]

Greetings to all-- I am in need of some help in the math area-- Im making a jig to cut a neck pocket in a solid body guitar and was wondering what the angle in inches is for a 3 degree angle.
I believe that if you have a 6 degree angle then the formula is 1/2 inch per foot.
(correction accepted)
thanx in advance for any help...
Donald

[Dan Gibbs]

Howdy :)
Here ya go.... go to this page: http://primeshop.com/access/woodwork/anglecalc/

I tinkered around with the numbers in the calculator using 12 (inches) as our fixed "run" and toyed with the "rise" number to get the requested 3 degrees. The magic number there is 0.62872 which results in an angle of 2.99925 degrees. You'd need to keep adding more precision past the decimal to approach any closer to 3 degrees and this calculator has a fixed number of five digits past the decimal. That's in the 10/1000th's anyway and prolly impossible for us to resolve in the real world with Harbor Freight tools :)

If you like fractions a bit more than decimals, we can change 0.62872 to a nearer common fraction of 0.625 which just happens to be 5/8". I got this result from this webpage: http://www.webmath.com/dec2fract.html
I also just remembered that 0.625 seemed like a standard fraction and that page confirmed it as 5/8".


Dan Gibbs :)

[Bob Webster]

Okay, Donald, the formula is x=tan(A)X12, which reads as "the tangent of the angle A times the 12" run". X is the movement perpendicular le to the 12" run. I hope that's the number you're looking for.

For a 3deg angle, x=0.629", or only 0.004" fatter than 5/8". For a 6deg angle, x is not ~1/2". Instead, x=1.261", or 0.011" fatter than 1 and 1/4". Hope that helps.

Cheers,
Bob

P.S. Duh. I didn't see Dan's response when I signed in to answer this one. We're in heated concordance.

[Brent Hutto]

I just always remember the identity x=sin(x) for small x and do it in my head. You gotta be able to work in radians though. ;-)

[Bob Webster]

Brent, the sine function is the wrong one to apply. Sine(angle) is the ratio of the opposite side to the hypotenus of the triangle. Donald's 12" represents the adjacent side of the triangle and so you have to apply the function tangent(angle) = opposite/adjacent, or in Donald's case, opposite/12".

Bob

[Brent Hutto]

Hmmm, I thought sin(x)=tan(x) for small x as well. I guess I depend on that "small x" to cover a multitude of sins.

P.S. Just to show my true geek colors, I'll also point out that the errors in these two approximations work in opposite directions for modest violations of "small x". Two wrongs may not make a right but they sometimes partially cancel out.

[Bob Webster]

Yeah, they do approach each other at very small angles. Sin 3deg = 0.05234 and tan 3deg = 0.05208. The difference in calculated rise would be 0.00086". At the level of precision and accuracy that most of us work to with a router, the errors would probably be undetectable. That's why God made shims, right? The dust thrown off by the router is probably 20X bigger that the error.

Bob

[Brent Hutto]

And it's why for every mathematician God made ten engineers and for every engineer, ten craftsmen.

And I guess we could add for every craftsman at least a hundred shims!

[Ron Frazier]

I believe if you will check the pocket is not cut on a angle. The neck is tapered from first fret to the end so that will be your angle.

Ron

[Bob Webster]

Pretty shoddy, Ron, throwing facts into the stew. Bad attitude.

Bob

[Brent Hutto]

Yeah, nothing puts a crimp in a good math discussion like the so-called "Real World".

[Donald A. Fortune]

Hi Ron- Dont mean to disagree with you or start up something that I cant gracefully back out of ,HOWEVER, I'm starting from scratch and the neck that I'm making is ded flat where it mets the body so therefore I need to taper the pocket in order to make the strings go to the top of the bridge and not have a mile and a half of clearance under them.
MEANWHILE-- I thanks to all who got into this descussion because it brings bk some of my math lessons which I should remember but didnt in this case.............
Donald

[Bob Webster]

AAAhhhh, now we come to the crux of the problem. It's the action you're trying to manipulate. Wish we'd known that 11 posts ago. You're thinking that you need to taper the floor of the pocket so that a flat thickness neck heel will have the right approach angle to the bridge area, right? This is basically going to establish a forward pitch to the nut end of the saddle. Or is it a backward pitch that you think you need?

A last comment is that a 3deg angle seems pretty huge. Your best next move is to draw out the whole action, nut to bridge with fingerboard included, and see exactly what kind of pitch you need. Forget angles for the moment. Do you have a thickness sander, like a Performax, perhaps? It could help in the solution.

Bob