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Trigonometry problem

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I was lazy one in the trigonometry class at highschool and I went to the fine arts academy instead of a technical university.. so I know nothing about trigonometry and maths :D

Well here's the problem:

If we know the values of x and z in this triangle, how do we find the angle at the corner A? Or do we need another value?


Lets say x=4 and y=8, what is the Â?

And yes, I need this for angling the neck pocket..B)

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yes, on a scientific calculator, you type in TAN X/Y

its easy to remeber how you know weather to use SIN COS or TAN

what do you do when you stub your toe?


(soak a toa, hahahaha, aint i a comedian?)

yep yep, special thanks to my math teacher Mr. burns for drilling trig into my head!!


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Forgive me for raining on your nerd parade, but unless you like unnecessary calculations, there are better ways to do this. String length is roughly 2/3rds neck, 1/3rd body. And it makes an "X" not a triangle (or two opposing triangles) I don't know the nerd math name for that, though. But basically for every increment you lower the headstock along that plane, you raise the bridge by twice that distance. Consider the neck joint your fulcrum.

I was (I emphasize "was") good at math back in the day. But the reason I don't like to get so technical about it is because there are so many other factors. First, is your neck angle calculated assuming a straight neck? Once relief is applied to the formula your bridge needs to be lowered, since the relief begins around the 15th fret, and affects the general trajectory of the neck angle. Second, and perhaps more importantly bridges have so much adjustability that you really need only to get within range. Third, the desired action and string gauge can result in over 1/8" of bridge height movement. Often we do neck angle before installing the frets. Do you know the fret size you'll use? Because that changes the string height too. I have a method that precisely calculates neck angle but its built into a jig I made, so its done in real-time rather than with formulas.

Please recognize and apply the tongue-in-cheek factor (we'll call it "n") and apply it to the previous "nerd" comments. It's really my own insecurity coming through (we'll call that "e") plus years of real experience with many guitars (call that "r") and finally my arrogance ("d") and you will realize that I am really just:

n x e + r + d = Ha! You guys are nerds for even reading this far! You probably thought I would say that I was a nerd too! Well think again nerds! :D

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I always remembered it by

"Silly Old Hitler Couldn't Advance His Troops Over Aston"

I lived near a place called Aston, so I guess some teacher made that up a while back... lol... Trig is easy... especially the stuff you do in secondary school...

it get's more complex when you get sin curves and having to find intersects and all sorts of weird stuff like that in college... man college maths really bites! lol... So glad I'm at Uni now and the maths we have to do is a lot easier... well... apart from the binary and hexadecimal sum's... bah!

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I have a method that precisely calculates neck angle but its built into a jig I made, so its done in real-time rather than with formulas.

Let's see the jig!

I don't have pics but its basically a flat piece of MDF that you rest the body on. And it's just for solidbodies. It's two pieces really, one that stays flat on the bottom and one that ramps up when you thread it. The body is secured with clamps, or in the case of my Radius bodies, I have to use tape (lots) because you can't get a good grip. I suppose I could make extenders for my clamps to get them farther into the body and over to the flat surfaces. But I only use it to cut the angle. I use a hand router to route the cavity first, to about 90% of its final depth. Or in the case of putting angle into a factory guitar with the pocket already cut, I just go right to the jig.

Anyway, I have threaded inserts in the top MDF up by the neck area, and as I rotate the bolts in there, it simply elevates the neck side of the body. Then I use my multi-speed drill press as an overhead router with a 1/4" pattern cutting bit to re-route the bottom of the cavity to the appropriate depth and it puts the angle right in. Since the MDF that the body is on spans the whole length of the body, it's not a 2:1 ratio like I said above. Whatever the height of the neck side of the jig is, plan on reducing that by 1/3rd, since the saddle point is usually about 2/3rds the distance from the neck pocket to the strap button. (by the way, I haven't used it on an explorer or anything like that) So I've always ended up with exactly the right height in bridge if I use that formula. Basically the bridge will elevate by 2/3rds the distance you've raised the neck end of the body. If you wanted to make it more sophisticated, you'd actually pivot the top piece along the saddle intonation line. Then you'd have a 1:1 ratio of elevated height to increased bridge height.

On some guitars I don't want the bridge to move at all. I just want the neck to sit lower in the neck pocket for better access and a sleeker, lower profile guitar front. So then I deepen the neck pocket and angle it at the same time. It's pretty easy, basically it works out to where if you've deepened it by 1/8" for example, then on the jig you also need to put 1/8" of tilt, and the bridge location stays the same.

When I made it I used Strat dimensions, and I did get real nerdy and I did a lot of math. So I hope everyone knows I was just fooling around. Most guitars will have the saddle point right at 2/3rds of the way between the neck joint and the butt end of the guitar. So if you use the butt end of the guitar as the fulcrum you'll be okay. But I thought the idea of coming at it from overhead, and moving the workpiece instead of trying to make a router template that angled was a pretty good idea, and I can put a precise angle in a solidbody in a matter of minutes. Truth be told you don't really need the clamps or the tape, as long as you are holding the body in place while you move the jig. Also I have an oversized table for the drill press.

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Cool thanks. I have a neck routing jig too: neck pocket jig. It works very well but I need to make revision 3 with the angle adjusters like you use. This would make it more useful. For now I have been using shims if I need them but I would rather have some adjustment.

Thanks for the detail in your post. I appreciate it!

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I love it being threaded. You can leave it set so that if you reassemble the guitar and want a little more angle, its right where you left it. Plus you can make sure it's flat and not leaning to one side or the other. I did my classical on it just like your single cut in the 6th picture from the top. It's a "real" top w/bracing on a hollowed back. I layed the neck in real deep, and angled it. So there's only about 3/16ths of body wood under the neck. The neck is almost the same depth as the body. I did all the wood removal with the hand router though, including the exact fitting, so then the pattern cutting bit just followed the pocket but put the final angle and depth in it. My hold downs are like yours too, but they're wood and I use leather as the safety pad. And they can be bigger because they aren't in the way of the router, since I'm routing from overhead.

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