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Hi,

I have started putting together a workbench dedicated to guitarmaking. Inspired by Dave Fifields post about his compound radius jig i decided to build something similar.
i sat down with autocad for a few minutes just now to look at how the radiuses would be.
In my mind it makes sense to have the compound radius correspond to the fretboard taper, so with a 1 3/4 at the nut and 2 1/4 at 12th fret would mean, according to my calculations, that a 12" radius at the nut is a 19.859..." radius at the 12th fret(on a 25.4" scale). This meaning that the axle holding the jig together is to be set at an angle of 32degrees in relation t the FB.
Am i onto something here?

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Frank

If you wanted a true conical section with a 12" at the nut, I come up with 15.428" radius at the 12th,, leaving you with an angle of about 15 degrees of the axle to the board.

If you're using the axle style system and want the board flat under each string line right off the tool, then you may be bound to following these cone rules. There's really no reason that your start to end radius ratios have to coincide with a cone though, other than the convenience of this style tool. If you're willing to use a tool more like Tracy's thickness sander style, or are willing to do a bit of final truing by hand, you can choose any start and end radius you like. Just choose the radius on each side and connect them with a straight line, splayed out in relation to the fingerboard width. This would not always coincide with a true cone, but there's no reason it has to and allows you to choose any start and finish you desire.

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Eschew obfuscation, espouse elucidation.

if the side of the FB is to have the same thickness along the lenght i need to keep it at 32degrees, but maybe that doesn't matter.

I have searched the archives for compound radius, but there seems to be a lot of different opinions on this.

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Frank

Perhaps someone else should check my math, but I'm fairly certain that if you wanted a 12" radius at a 1.750" nut and a 2.250 width 12th fret, you would need a 15.428" radius at the 12th, requiring a 15.662 degree angle if you wanted a straight board under each string coming off a axle mounted radiusing jig. My numbers would put a 32 degree angle as leaving notable relief under the outer strings if the center were straight.

We seem to be at about 2:1 difference with our numbers, so it's likely a simple formula glitch on one side, but I'm fairly comfortable with my results (keeping it mind, these are 1:30 AM results ).

If using an axle-style fingerboard shaper, you would need to maintain a constant section of the circle as it widens in accord with the fingerboard width to keep a line under each string straight. Starting with a 12" radius and 1.750" nut width (or cord), this would leave you with a 8.363 degree section of the circle. That same 8.363 degree section at a 2.250" cord at the 12th fret would leave you with a 15.428" radius at that point. This in turn would result in a 15.662 degree angle on a 25.4" scale board (no compensation to actual string length is considered here, but I doubt it would affect more than 1/8 degree difference).

I'm wondering if your calculations are giving you the entire angle of the cone, rather than the half of it that would be required for setting up the jig. Again, I would love it if someone double checked my numbers, but I think they are on. Then again, I'll never rule out a moment if someone were to correct me.

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Eschew obfuscation, espouse elucidation.

You're probably more right thn me when it comes to the math of things, i don't know how this is normally done.
i just decided for a 12"radius at the nut, then measured the side of the FB and used that height at the 12th fret to get the radius there(if that makes sense at all )

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Frank

Hi,

I'm in the process of building one of these too. So I thought I would check your numbers with mine. I'm coming up with a 19.826 radius at the 12th fret and an axle angle of 31.64 degrees. That's with a 1.75 nut and 2.25 at the 12th fret.

I'm designing mine so I can change the pivot for different fingerboard tapers. I layed out my current fingerboard with a 2.15 string spacing at the saddle, because that's what my bridge pin holes are drilled at, and a 1.75 nut. I want an 11" radius at the nut and a 19" radius at the 20th fret, so not quite as radical as above. This works out to a 24.7 degree axle angle. You can get quite a variety of angles depending on what fingerboard taper you use.

I'm trying to keep a constant fingerboard edge thickness for the length of the board. I'd be interested in hearing what others are using for their axle angle.

Cheers,
Kirt

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Horton, MI

David is correct. The angle is a little over 15 degrees.

Dave F.

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Cambrian Guitars

"There goes Mister Tic-Tac out the back with some bric-brac from the knick-knack rack"

Hmmm, not seeing it. Here's my drawing.



1.75 at the nut, 2.25 at 12th fret. 12 radius at the nut. The .0319 distance from top of the crown to the edge remains the same for the whole length. This yields a 19.83 radius at the 12th.

What am I not seeing? (head scratching emoticon)

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Horton, MI

I understand you're getting the 31.64 degrees from the 19.826 radius, but I can't figure out where you're getting that radius from. Any insight as to the thought here?

The width of the board represents the chord of a circle at that point. From a 1.75" chord at a 12" radius, it's easy to determine that it represents an 8.363 degree section of the circle. If you want to use the perfect cone method from an axle shaper, you need maintain constant section of the cone as the width spreads. This is where I 'm arriving at the 15.428" 12th fret radius. A 19.826" would represent a 6.505 degree section of the circle, which would leave your string lines crossing over the cone, no longer parallel to it's surface. I think I misspoke this in my previous post, but if the center were set as straight this would result a slight hyperbolic (or is it parabolic?) backbow curve on the edges.

The real world differences would probably be easily reconciled with a few swipes of of a leveling plane, but at this point I'm just interested in where the math glitch is. We are certainly using two different means to come to our results, but I'm not sure how you're getting yours, or if there's a crucial error somewhere in mine?

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Eschew obfuscation, espouse elucidation.

Ah, I see where we differ. (simultaneous postings)

It looks like you're considering the profile at the two points (nut & 12th) with the goal of maintaining the same thickness on the edges and center at both points. Thing is, that won't guarantee straight lines between the nut and 12th, or beyond. Those two radius when connected would not result straight lines under each string. I'd have to think on it a bit to better understand what the results of your method would be though.

Thinking of it in terms of the cone that the axle shaper cuts for you I think is key.

Man, I wish I could draw this out on computer like you do. I suppose I could scan in my pencil and paper chicken scratch, but I didn't exactly sketch them out for presentation.

Oh, and my end angle was off in a post above as well. I had the arms mounted wrongly to the axle in my mind and was thinking of the board as hypotenuse, rather than adjacent to the angle we want. 15.1 degrees would be my answer, rather than the 15.6 I wrote before.

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Eschew obfuscation, espouse elucidation.

exactly what i was thinking, i got 32 degrees only because i had decimals turned off in autocad.
I have no experience with compound radiuses or guitar building in general for that matter, so i should be shooting for an angle 15,1 on the axle? how do you calculate that?

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Frank

As an afterthought, if you wanted ideal numbers it should all be calculated from the string spacing at the nut and 12th rather than fret board width, as the strings don't necessarily spread at the same rate as the board. Minor difference, and would probably put the end angle right at about 15 degrees even.

If you want to make a conical fret board and aim for a flat surface beneath each string, the rule to follow is this.

The length of each string should lie directly in the plane of a radius of the cone.

I find the easiest way to calculate this is to use the triangle created by the cord and radii. Then for simplicity of the right triangle, I make all my calculations from half of that triangle, or centerline to radius to 1/2 the chord, if that makes sense. You can determine the opposite angle of the chord easily enough, which would be half of the section of the circle. You can then use that angle to determine the end radius for any board width (or string spacing as it may be) along the board to maintain a constant cone. This will then ensure a straight line under each string.

Am I making sense? Terminology and description is certainly one of my weaker points in mathematics.

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Eschew obfuscation, espouse elucidation.

I see what your doing David. Your keeping a constant angular section of the circle. Like this?



With the 15.428" radius at the 12th fret, the edge of the fingerboard would be about .009" thinner there than at the nut.
Can't say that's bad though. Not a huge difference in 12.7 inches.

More head scratching to be done.

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Horton, MI

Thank you Kirt. Yes that's what I'm doing, but didn't have the software to easily draw it. To be honest, I hadn't even considered the idea of a consistent thickness at the edge, but only achieving a flat line on the surface directly below each string. The thickness at the edge could be made consistent easily enough during the setup of the tool though. Just set the sander or router level with the edge rather than the center of the board, placing the small thickness variation in the center and leaving the edge consistent.

Of course everyone has to admit we're really probably splitting hairs to extreme levels here. A single radius board is far far from meeting the criteria we're trying to figure in every aspect, and they still work okay for most. Might as well shoot for perfect though, even if were only to matter in the abstract, eh?

Wrapping your mind around the fretboard radius issue can seem a pretty abstract thing. The end goal in each system though is primarily to leave a straight flat surface directly under each string. This can correspond with a cone shape in particular circumstances (like the tool being discussed here), but doesn't need to if you wanted a different start to end ratio. If the desired start and end radii and chord (or width) did not end up on the same angular section of their respective circles, you can still make each line under each string straight. The resulting shape just would not be a section of a cone and would not work as ideally with this style tool.

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Eschew obfuscation, espouse elucidation.

Thanks alot this really cleared things up for me

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Frank