Maths boffin angle and curves stuff.

[liam_fnq]

If I built a guitar with say, a 15' radius back, would the angle that the back meets the sides be the same all the way around.

* I know that technically it's a straight line meeting a curve so there is no angle as such but lets just talk about a tangent across the first 5mm or so of the back.

[kiwigeo]

Is this question related to cutting a binding ledge?

[Nick]

If your sides are parallel (i.e the upper bout bend is parallel with the lower bout) & your back is a constant 15' radius then I would say it should be the same all the way around Liam. The back has such a "large" radius that any variation would only be in the range of minutes of a degree maybe even only seconds of a degree, hardly enough to concern any routing of binding channels e.t.c.

[Trevor Gore]

If I built a guitar with say, a 15' radius back, would the angle that the back meets the sides be the same all the way around.

No. The angle that the tangent to the domed back makes with the sides will vary by ~1.5 degrees if the sides are more-or-less constant height all round (i.e. no big wedge).

[kiwigeo]

If I built a guitar with say, a 15' radius back, would the angle that the back meets the sides be the same all the way around.

No. The angle that the tangent to the domed back makes with the sides will vary by ~1.5 degrees if the sides are more-or-less constant height all round (i.e. no big wedge).

Can we have the equation please?

[Trevor Gore]

Can we have the equation please?

You mean you can't do it in your head?

OK. What you're looking for is the included angle between the slope of the tangent to the back dome and the sides at the edge. The largest variation in slope will be between where the guitar is narrowest and where it is widest (longest). The dome is 15 feet, which I'm calling 5m (or 5000mm). The half narrowest width is at the waist, call it 240/2 = 120mm. The half length is 500/2 = 250mm. The included angle between the tangent to the dome and the side is acos(120/5000) at the waist (88.62 degrees) and at the ends is acos(250/5000)= 87.13 degrees. Difference between the two is 88.62-87.13 = 1.49 degrees (i.e. ~1.5 degrees). If you can't immediately see the acos relationship, just sketch it out and you'll see it.

[kiwigeo]

Can we have the equation please?

You mean you can't do it in your head?

No I can't....that's why I became a Geologist. My brother is the mathematician in my family...an honours degree in maths and currently teaching maths in Bhutan.

[Trevor Gore]

My brother is the mathematician in my family...an honours degree in maths and currently teaching maths in Bhutan

Well, it sounds like you both share an interest in mountains...

[Nick]

No. The angle that the tangent to the domed back makes with the sides will vary by ~1.5 degrees if the sides are more-or-less constant height all round (i.e. no big wedge).

Geez is it that much?! I would have said (well I did before ) it was only in the seconds & minute range but there you go the maths prove me wrong, I'll just keep my mouth shut while we have a doctor in the house .

[Taffy Evans]

Hmmmmm, I don't understand a word. All I worry about is that the back meets the side at the time of gluing with as close a fit as I can get and that the router follows the shape of the back.

[kiwigeo]

Hmmmmm, I don't understand a word. All I worry about is that the back meets the side at the time of gluing with as close a fit as I can get and that the router follows the shape of the back.

They're Boffins mate.....

[Lillian]

They are just explaining why your binding jig indexing off of the sides is a good thing.

[kiwigeo]

They are just explaining why your binding jig indexing off of the sides is a good thing.

Trev likes to put a "bulge" in his sides so indexing of the side of his guitars probably wouldnt work too well.

[Trevor Gore]

The "bulge" is a lot smaller than the curvature given by 5m radius; but, anyway, a Jim Williams type binding router (two point support) or a vertical axis binding machine (as per the book) will still work fine. A "rolling pin" binding router, if you have the nerve to use one, might be somewhat more problematic, but this will probably be the least of your problems if you're using one of those things.

[Dominic]

Think of it this way, the top which is a part of a sphere sits on sides that come up to meet it vertically all around so the sphere is not changed. Now the closer you get the centre of the top the closer to 90 degrees you will be the angle betwee the sides and the top. Alternatively, the further from the centre, the further you are travelling around the sphere which at some point goes from being horizontal to vertical. So the waist is likely to have the flatest angle. The head and tail blocks that are furthest away from the centre will have the steepest angles.
Dom

[liam_fnq]

You're a legend Dom. Your post caused the penny to drop.

Thanks.

[Taffy Evans]

I'm still waiting for my penny.

[nnickusa]

I'm with you, Taffy. I just clean up the sides until the top and back fit nice.....Does my head in, all this math, and I sometimes wonder if it's truly needed. I mean, if you go into a guitar shop, and pick up 10-20 acoustics, you'll like the sound of them to different degrees, and some you'll just hate, and if lucky you'll find one you love.

What do I know? I'm just a hack in this game.....

[charangohabsburg]

As it had been said before, when registering from the sides when cutting the binding rebate the difference of those angles does not matter at all. If you still want to know what angles these are, here my attempt to explain them:

In the following drawing the circle section represents the back doming, the red line the body width at the waist, and the black line the body width at the lower bout. Everything within the drawing NOT to scale!

2012_D70_5540.jpg (52.84 KiB) Viewed 18634 times

As per the second figure which represents one of the sides, the widest (highest) point is at the waist (red), and the narrowest (lowest) is at the lower bout (black), the width difference is d (green).

Going back to the first figure you can see that the angle b between the horizontal line and the tangent of the doming (-circle) at the waist is slightly different from angle a between the horizontal line and the tangent of the doming (-circle) at the lower bout. This is why one should not register from the domed back (e.g. its tangent) when cutting the binding rebate.

[kiwigeo]

http://en.wikipedia.org/wiki/Mathematical_anxiety

[Trevor Gore]

Does my head in, all this math, and I sometimes wonder if it's truly needed. I mean, if you go into a guitar shop, and pick up 10-20 acoustics, you'll like the sound of them to different degrees, and some you'll just hate, and if lucky you'll find one you love.

And that epitomises the problem. If you're a custom builder it helps if the client likes the guitar you just built for them. There's more than one way of doing that, but I don't like a crapshoot.

[nnickusa]

Trevor, I agree with you. I am not, however a custom builder. Look, I reckon that if you have a good "ear" for what the various bits sound like as you're doing the build, and the experience to "know," or guess, what will be a good fit, that would about do it.

I've read mountains of stuff, here and on other forums, about frequency responses and Helmhotz(?) stuff, but in the end, it's what it sounds like to my ear that counts.

My comment re: 10-20 acoustics in a shop was mostly referencing the fact that all the parts get spit out identically dimensioned, taking in no account of the individual characteristics of EACH bit of timber, resulting in a wide variety of sounds from otherwise identical instruments. The people making them could just as easily be making socks, banana bread, or toyotas....

I might add, I'm a crap player, but have fun noodling around with guitars. What I enjoy about the build process is that, 1. I seem to be much better at that than at playing and 2. that I'm making a beautiful instrument that I, and others, will enjoy. It's my understanding that Stuart Newman in Byron is a similarly unaccomplished player, but his instruments are, it seems, well-regarded....

I don't know, I wonder if all the super science, and hoodoo stuff is needed. Seems that if you're good at hearing your guitars as you build them, you'd turn up a pretty good guitar. Not that I don't ant to have a read through your books.....

Quick question Trevor. Have you done any emperical studies to determine whether the "average" player can tell the difference between your work and a decent guitar from, say Martin or Cole Clark? I'm not challenging the legitimacy of your work, which I acknowledge, but wonder HOW MUCh of a difference it would make to Joe Blow....

[kiwigeo]

Quick question Trevor. Have you done any emperical studies to determine whether the "average" player can tell the difference between your work and a decent guitar from, say Martin or Cole Clark? I'm not challenging the legitimacy of your work, which I acknowledge, but wonder HOW MUCh of a difference it would make to Joe Blow....

I've picked up a few Martins in shops of late and haven't been that impressed. I also had a Cole Clark in my shop for repairs and the quality of build on that instrument...well let me just say it made my first build look like a work of art.

Yes some of the maths in Trev and Gerards books is scarey but Im a maths dunce and Im still getting a shitload of useful information out of the books. Have a read of the books and then lets revisit

[68matts]

Let me just say this Nick, I was in Sydney earlier this week and went to one of the large franchised guitar stores in the city . I played some top shelf Cole Clarkes, some high end Matons and Martins as well as a couple of pretty expensive Gibsons. None of these impressed me nearly as much as a couple of Trevors guitars that I played earlier this year. I know it's hard to compere, with them being played in a completely different setting and months apart, but as you said it comes down to what you like in an instrument and for this inexperienced builder and very average player there's a hell of a difference.

[nnickusa]

Martin, Matt, that's sort of my point. I think MY two efforts are better than most name guitars I've played, both vintage and new, bar the expected learning curve issues in fit and finish. Sound-wise, I'd stack them up against my mate's Fat Lady 3, no worries.

My question is more related to qualitative differences, not quantitative ones. You can show me as many response curve charts, etc, etc as you like, but does it make that much of a difference to the average player.

I appreciate that being able to reproduce a set of responses from, evidently, any set of timbers is of great use to the professional builder who is seeking to set themselves apart from everyone else. But, doesn't making each and every guitar's response identical also eliminate the contributions of diverse timbers and other elements?

This is sort of where I've gotten with electrics. I think the electronics and signal path have significantly more to do with the sound, tone, sustain, etc than does the timber of the electric guitar. For example, simple physics(the only kind I know) suggests that any tremolo will reduce sustain, simply because you have a moveable component to the strings vibration, which provide a dampening effect, whil a hard tail will retain it....

I don't know, just trying to make a couple guitars that look and sound nice up in the backwater that is Byron....