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Old 09-27-2014, 02:15 PM
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Default Question re conical fretboards

I am about to commence the shaping the fretboard for my first "proper" (I hope) guitar, and I am planning on doing a conical radius (or "compound radius" if you prefer) .

I rather like the idea that John Arnold mentioned on here some time ago ... he said that he shaped his boards starting with a defined radius at the nut, and maintains a constant center thickness and a constant edge thickness. I seem to recall that Charles Tauber said that was his preferred method as well.

Am I right in thinking that doing it this way, there is one, and only one end radius which satisfies these conditions for any given nut width, end width, and nut radius ? ie if you start off with a given radius at the nut, then the radius at the end is predetermined ?

I am 99.99 % sure that such is the case, but just wanted confirmation from those who have actually done it.
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Old 09-27-2014, 03:46 PM
LouieAtienza LouieAtienza is offline
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The radius at the end is predetermined because the width (chord) and height (sagitta) are defined...

Or are you trying to reel me in?
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Old 09-27-2014, 04:13 PM
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I don't have the calculations at hand but you are looking for equal sagittal depth assuming the fretboard thickness was not tapered to begin with.

However question: aren't conical fretboards not truly conical but instead have multi-radiuses which are blended one into another?
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Old 09-27-2014, 04:27 PM
LouieAtienza LouieAtienza is offline
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I posted all my math long ago on the old MIMF... my conclusion is that you can have a fretboard that's a true regular conical section (albeit varying thickness) or the so called "compound" radius fretboard which I conjectured to be the sectin of a slanted, or elliptical cone. Or you can just start with a cylindrical section and true the string paths. Even an untrued 12" radius cylindrical fretboard has a max error of about .015" which is easily trued.
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Old 09-27-2014, 04:34 PM
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Originally Posted by LouieAtienza View Post
The radius at the end is predetermined because the width (chord) and height (sagitta) are defined...

Or are you trying to reel me in?
Now then Louie, would I do a thing like that ...although I did have you in mind as i was typing the post.



Quote:
Originally Posted by rick-slo View Post
I don't have the calculations at hand but you are looking for equal sagittal depth assuming the fretboard thickness was not tapered to begin with.

However question: aren't conical fretboards not truly conical but instead have multi-radiuses which are blended one into another?

Yes, the fretboard starts off at a constant thickness, but tapered to the required widths (which will be 1.75" at the nut and 2.5" at the end.

The fretboard surface is actually a true section of a cone.

My nut radius will be 14", and it works out that with a 1.75" wide nut and a 2.5" wide fretboard end, the radius at the end will be 20" exactly.
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Old 09-27-2014, 05:06 PM
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Originally Posted by murrmac123 View Post
The fretboard surface is actually a true section of a cone.
How do you sandpaper a true conic versus blending one radius form shape into another?
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Old 09-27-2014, 06:02 PM
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How do you sandpaper a true conic versus blending one radius form shape into another?
Ah right ... I thought you were querying the mathematics of the construction.

As far as the practicalities are concerned, I don't know how others have done it, but for my own part I intend to set up a 14" radius template at the nut end and a 20" radius template at the other end, and handplane the fretboard between the two. If the process were mechanized it would be a relatively simple matter to construct a swinging jig which could hold the fretboard and pass it over a router ... or of course the fretboard could be stationary and the router could be guided similarly instead.

Manually done , it is much like sanding the frets on a fretboard using a flat sanding beam ... if you follow the string path you end up with a compound radius, even if the fretboard is cylindrical.

EDIT : I think I see what you are saying Rick ....you are envisaging a succession of shaped concave sanding blocks, perhaps one at 14" radius, one at 16" radius, one at 18" radius and one at 20" radius and blending the various radii (radiuses) together. No, I agree, that would not produce a true conic surface.
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Old 09-27-2014, 10:16 PM
LouieAtienza LouieAtienza is offline
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Murray, Murray, Murray... If you recall, for a fretboard to be a true regular cone section, the lines below each string on the board should converge to a common point. But since this has been ruled out by virtue of the crown and edge of the board being parallel, they cannot converge, therefore it is NOT a conical section.

Also if you remember, if your fretboard surface is a true conical section, then the frets do not lay on a perfect radius. This is because the slots are cut normal to the surface, while the circular sections of a cone are perpendicular to the cone center. If you left the fretboard as is the frets would actually follow an elliptical path.

When two radii are selected (or any curve for that matter) and the fretboard is trued along the splay of the strings a "ruled surface" is created. It also follows a proportional relationship between distance and curve just like a conical section or "compound radius."

In a true conical fretboard, the end radius is determined by the nut radius and taper of the board (or string splay.) The center height wil then be higher at the end than the nut.
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Old 09-27-2014, 10:20 PM
LouieAtienza LouieAtienza is offline
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Quote:
Originally Posted by murrmac123 View Post
Ah right ... I thought you were querying the mathematics of the construction.

As far as the practicalities are concerned, I don't know how others have done it, but for my own part I intend to set up a 14" radius template at the nut end and a 20" radius template at the other end, and handplane the fretboard between the two. If the process were mechanized it would be a relatively simple matter to construct a swinging jig which could hold the fretboard and pass it over a router ... or of course the fretboard could be stationary and the router could be guided similarly instead.

Manually done , it is much like sanding the frets on a fretboard using a flat sanding beam ... if you follow the string path you end up with a compound radius, even if the fretboard is cylindrical.

EDIT : I think I see what you are saying Rick ....you are envisaging a succession of shaped concave sanding blocks, perhaps one at 14" radius, one at 16" radius, one at 18" radius and one at 20" radius and blending the various radii (radiuses) together. No, I agree, that would not produce a true conic surface.
Check out Charles Fox`s fretboard shaping jig for a staionary belt sander, it's the same idea. Either way care must be taken to move or plane with the string lines, as any angling can create a low spot.
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Old 09-28-2014, 05:15 AM
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Quote:
Originally Posted by LouieAtienza View Post
Murray, Murray, Murray... If you recall, for a fretboard to be a true regular cone section, the lines below each string on the board should converge to a common point. But since this has been ruled out by virtue of the crown and edge of the board being parallel, they cannot converge, therefore it is NOT a conical section.

Also if you remember, if your fretboard surface is a true conical section, then the frets do not lay on a perfect radius. This is because the slots are cut normal to the surface, while the circular sections of a cone are perpendicular to the cone center. If you left the fretboard as is the frets would actually follow an elliptical path.

When two radii are selected (or any curve for that matter) and the fretboard is trued along the splay of the strings a "ruled surface" is created. It also follows a proportional relationship between distance and curve just like a conical section or "compound radius."

In a true conical fretboard, the end radius is determined by the nut radius and taper of the board (or string splay.) The center height will then be higher at the end than the nut.
Louie, you are absolutely correct ... very clearly and succinctly explained.

Now that you have pointed it out, it all comes back to me ... I wish that MIMF thread were still around ...
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Old 09-28-2014, 08:44 AM
LouieAtienza LouieAtienza is offline
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Originally Posted by rick-slo View Post
How do you sandpaper a true conic versus blending one radius form shape into another?
I remember reading of one builder who had a conical sanding block CNCd to create such a surface. In this case sanding would have to be done across the grain, and finished up along the string paths with a flat beam. You can also check out the Charles Fox belt sander jig (which was adapted by Somogyi) .
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Old 09-28-2014, 12:57 PM
Howard Klepper Howard Klepper is offline
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Quote:
Originally Posted by murrmac123 View Post
I am about to commence the shaping the fretboard for my first "proper" (I hope) guitar, and I am planning on doing a conical radius (or "compound radius" if you prefer) .

I rather like the idea that John Arnold mentioned on here some time ago ... he said that he shaped his boards starting with a defined radius at the nut, and maintains a constant center thickness and a constant edge thickness. I seem to recall that Charles Tauber said that was his preferred method as well.

Am I right in thinking that doing it this way, there is one, and only one end radius which satisfies these conditions for any given nut width, end width, and nut radius ? ie if you start off with a given radius at the nut, then the radius at the end is predetermined ?

I am 99.99 % sure that such is the case, but just wanted confirmation from those who have actually done it.
Murray, you are correct in your assumption. [a quote from Mel Brooks, BTW]

But--John and Charles are describing a conical surface fretboard. They are not giving a method of construction. It would be impractical to construct the board by repeatedly measuring the sagitta and side wall height and adjusting them to remain equal over the length of the board. The method of construction should be a mechanical jig that will yield a conic surface, or a hand method that will do the same. One such mechanical system can be seen on Grizzly Industrial's site--look for their fretboard radius sander.

While the hand methods (there are a few different ones) may lack mechanical precision and be impractical for a factory (which does not want to rely on individuals' hand skills), they are every bit as good for a skilled hand builder. This is so because the deviations produced from the ideal surface will vary by no more than a couple of thousandths of an inch, which is greater accuracy than you achieve when installing the frets. You will still level the frets along the string paths, and any deviation in the board's surface will be eliminated in that process.

Moreover, the ideal conical surface is not the only one that works, for both theoretical and practical reasons. You can deviate from it while maintaining a board that is perfectly straight under each string path, if you allow variation in the board's side height. This can be up to several thousandths of an inch and never be seen or cared about.

You can also improved the playability of a guitar that will be used for bent ("choked" in some sources' terminology) by increasing the radius more than the taper of the board would dictate as you go toward the body. That will decrease the sagitta if the side height is maintained, which allows the bent notes to not fret out (by bending, the string is no longer over a level fret top path--it starts lower down on the curve, and can buzz against the next fret or two). Or you can decrease both sagitta and side height toward the body end to give clearance for bent notes. I find that the decrease in sagitta is necessary for good electric guitar setup.

And last, you may want a bit of dropoff on an acoustic guitar to provide a cushion against the eventual change in neck angle. That will depend on player preferences and how much the upper frets are to be used.
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Old 09-28-2014, 02:50 PM
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Excellent observations, Howard, and the "fine tuning" tips much appreciated.

My modus operandi as far as getting the compound radius is concerned is definitely to do it by handplaning ... the fretboard will be stuck down with double sided tape onto a wooden block the same length as the fretboard, and the 14" and 20" radius templates (made of aluminum plate)will be screwed onto either end of the block. Then it's just a matter of planing the radius close enough on both ends and removing the bulk in the middle, finishing off with a flat sanding beam. Leastways that's the plan. (it goes without saying that the fret slots will be already cut, prior to the tapering to width )

I have seen pics of the various jigs available to automate the process ...very impressive they are too, but I want to do as much handwork as possible on this instrument.

I would appreciate any comment on the method I used to arrive at the two radiuses. I didn't do a calculation involving the sagitta and the chord at the fretboard end ... maybe I should have.

I know I want a 14" radius at the nut (which is 1.75" wide), so that's a given. I then divided the circumference of a 14" radius circle by 1.75 ... the result turns out to be 50.26.

So I then figured out that for the end radius, if the width is 2.5" I need the radius of a circle whose circumference, when divided by 2.5, also gives a result of 50.26. My reasoning was that this will in fact give a very close approximation to a true conic surface.


So ...

C/(2.5) = 50.26 therefore ...

C=(2.5)*(50.26) = 125.66

Therefore the radius R is given by
R=125.66/(2π) =20.

I find it quite astonishing btw that the result of any calculation involving π yields an exact integer , but that's what my calculator says.

Hopefully the calculations using the sagitta and the chord will give the same result.
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Old 09-28-2014, 03:48 PM
Howard Klepper Howard Klepper is offline
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Originally Posted by murrmac123 View Post
Excellent observations, Howard, and the "fine tuning" tips much appreciated.

My modus operandi as far as getting the compound radius is concerned is definitely to do it by handplaning ... the fretboard will be stuck down with double sided tape onto a wooden block the same length as the fretboard, and the 14" and 20" radius templates (made of aluminum plate)will be screwed onto either end of the block. Then it's just a matter of planing the radius close enough on both ends and removing the bulk in the middle, finishing off with a flat sanding beam. Leastways that's the plan. (it goes without saying that the fret slots will be already cut, prior to the tapering to width )

I have seen pics of the various jigs available to automate the process ...very impressive they are too, but I want to do as much handwork as possible on this instrument.

I would appreciate any comment on the method I used to arrive at the two radiuses. I didn't do a calculation involving the sagitta and the chord at the fretboard end ... maybe I should have.

I know I want a 14" radius at the nut (which is 1.75" wide), so that's a given. I then divided the circumference of a 14" radius circle by 1.75 ... the result turns out to be 50.26.

So I then figured out that for the end radius, if the width is 2.5" I need the radius of a circle whose circumference, when divided by 2.5, also gives a result of 50.26. My reasoning was that this will in fact give a very close approximation to a true conic surface.


So ...

C/(2.5) = 50.26 therefore ...

C=(2.5)*(50.26) = 125.66

Therefore the radius R is given by
R=125.66/(2π) =20.

I find it quite astonishing btw that the result of any calculation involving π yields an exact integer , but that's what my calculator says.

Hopefully the calculations using the sagitta and the chord will give the same result.
It won't be an integer if you carry it out to enough places. The closeness to 20 is an artifact of your choices for fretboard taper and nut radius.

By the way, you are introducing a trivial variation by measuring the chord at the nut and then using it for the arc. Doesn't matter in the end. I commonly go from a 12" radius at the nut to 20" at the end, and my board does not have quite as much taper as yours will (I fix the nut and 12th fret width--usually 2-1/4" for a 1-3/4" nut--and then let the end width just be an artifact of those numbers and the number of frets) --that would raise the side height of the board a bit at the body end, but I do a little bit of fall-away and the side height ends up even. Or even enough to the eye; the side is not the playing surface.

Sanding the compound radius by hand works fine, and you don't need radiused sanding blocks--I like to use a hard rubber block of the kind sold in automotive finishing stores for some flex. You will be sanding along the string paths, which gives a smooth change in radius. More recently, to save time and arms, I get close to my conical surface on the belt sander, but this is risky and I don't recommend it unless you already have a good sense for how much wood you will be removing.

Remember--you will eliminate any tiny variations from ideal when you file the frets, and that won't call for more than a couple of thousandths here or there.
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Old 09-28-2014, 03:51 PM
LouieAtienza LouieAtienza is offline
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Originally Posted by murrmac123 View Post
Excellent observations, Howard, and the "fine tuning" tips much appreciated.

My modus operandi as far as getting the compound radius is concerned is definitely to do it by handplaning ... the fretboard will be stuck down with double sided tape onto a wooden block the same length as the fretboard, and the 14" and 20" radius templates (made of aluminum plate)will be screwed onto either end of the block. Then it's just a matter of planing the radius close enough on both ends and removing the bulk in the middle, finishing off with a flat sanding beam. Leastways that's the plan. (it goes without saying that the fret slots will be already cut, prior to the tapering to width )

I have seen pics of the various jigs available to automate the process ...very impressive they are too, but I want to do as much handwork as possible on this instrument.

I would appreciate any comment on the method I used to arrive at the two radiuses. I didn't do a calculation involving the sagitta and the chord at the fretboard end ... maybe I should have.

I know I want a 14" radius at the nut (which is 1.75" wide), so that's a given. I then divided the circumference of a 14" radius circle by 1.75 ... the result turns out to be 50.26.

So I then figured out that for the end radius, if the width is 2.5" I need the radius of a circle whose circumference, when divided by 2.5, also gives a result of 50.26. My reasoning was that this will in fact give a very close approximation to a true conic surface.


So ...

C/(2.5) = 50.26 therefore ..

C=(2.5)*(50.26) = 125.66

Therefore the radius R is given by
R=125.66/(2π) =20.

I find it quite astonishing btw that the result of any calculation involving π yields an exact integer , but that's what my calculator says.

Hopefully the calculations using the sagitta and the chord will give the same result.
Pi does NOT need to come into the equation. Let's say your fretboard is 18" long from nut to end. Your taper over 18" is .75". Divide 1.75 by .75 you get 2.33333. Multiply by 18 and you get 40, which is the distance from nut to converging point of the fretboard. Add 18 to get the distance to the fretboard end. The end radius is found by ratio. 14 x 60 / 42 = 20

You won't always get a round number. I use an 17" long board tapering from 1.75" to 2.25" with a 12" nut radius which works out about 15.4" at the end..
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