MIMF

Hi.
I posted here because 'bending' seems to be a notion more commonly associated with solid bodied etc etc (not exclusively of course) and a main motivation for using them conical fretboards that is..

If we take a cone that is about 30" high from the centre of the bottom circle and drop a line vertically from the apex ( the point ) it hits the centre of the circular bottom.

All the points on the line projected HORIZONTALLY (parallel to the bottom surface) to the surface will define an individual radius. that is a circle at the level of any point.

eg a 10" rad at a higher point than a 16" rad closer to the bottom.

all very well.

but the fingerboard isn't built that way.

To excise the fingerboard from the surface of the cone at radii of 10 and 16 inches respectively and lie it on a neck the 'sample' would be cut perpendicular to the surface of the cone. If it was cut along the line of the radius the line of excision would be inclined to the surface not right angled. Well - sand it square - no problem. but then the radius isn't 10 (or 16) anymore it would be slightly less.

So in designing a process for a cnc machine to cut a compound radius from a blank what is done?

Is close enough good enough? or is there some transformation done so that on the fingerboard blank the result is an actual 10 to 16 'conical' surface? If so what is the transformation?

Rhino 5 is hard enough for me already!!

Am I worrying too much?

Thanks,
Rob.

You are worrying too much me thinks.

If I were to hand you a neck with a radius of 10.0373" vs a true 10", do you think you could tell? I couldn't.

In any case, what I have done in Rhino is create a truncated cone with a 10" radius circle on to and a 16" radius circle on the bottom, separated by the length of the fretboard. Not all fretboards are exactly the same, but I usually use a 25" scale length on a fretboard cut at the theoretical 23rd fret. I don't have the exact number, but it is somewhere close to 19". Then I draw a chord on each circle, nut width on the 10" circle and the width of the fingerboard on the bottom circle. Connect the ends of the two chords, trim away the outside parts of the truncated cone and I'm left with a fingerboard.

I've been pretty happy with the results and have never worried that the radius wa "off" because the arcs of the truncated cone are not perpendicular to the surface of the fingerboard. What is the "right" radius for a fingerboard anyway?

I was trying to think of an optimum compound radius, and came up with this:
Let's say the scale is 25", string spread at the nut is 1.5" and at the bridge 2"
So the taper is (2-1.5)/25=.02
If the 23rd fret is 18.25" from the zero fret, and the radius at zero is ten, the radius at 23rd should be
10+.02*18.25=10.365 and the arch on the bridge would be 10+.02*25=10.5. Plus maybe another 1/16th or so on the bridge radius because it is actually a bit above where the fretboard would be if extended to the bridge.
This would have the strings sitting on a cone which is the same shape as the fret board, and have the action on all strings the same.
I don't think it really addresses the issues of chocking out at all.
And the 10-14 or 10-16 compounds seem in practice to work well.
But I am having trouble visualizing what happens to the action as you get into more conical compounds. It seems like there must be some danger zone or area if you get to radical. Sometimes looking at a radical situation helps me understand the normal situation.
So what happens if the bridge is flat and the radius at the nut is tight.
Does anyone have the software modeling to lay this out and see if there are any potential problems. I keep thinking it is in the 5th to 8th fret areas on the outside strings, but I really can't get a handle on it.

Dave Weir wrote:I don't think it really addresses the issues of chocking out at all.
And the 10-14 or 10-16 compounds seem in practice to work well.
But I am having trouble visualizing what happens to the action as you get into more conical compounds. It seems like there must be some danger zone or area if you get to radical. Sometimes looking at a radical situation helps me understand the normal situation.
So what happens if the bridge is flat and the radius at the nut is tight.
Does anyone have the software modeling to lay this out and see if there are any potential problems. I keep thinking it is in the 5th to 8th fret areas on the outside strings, but I really can't get a handle on it.

I think the easiest way to answer the this Question is to build a model of several boards and doing real wold analysis. I am sure there are guy with cnc's out the that would be willing to cut several fretboards for you if you paid. I have been on some other boards on face book lately and they have many that offer cnc services. But as I have seen in the different radius from 10 to 20 there is less visual difference looking on end as there is from 6.5 to 10 which is much easier to see. and I suspect is you looked at say a cello or violin finger board the difference is even more apparent to the naked eye. So to my way of thinking if you can easily see the curve the string will be even more likely to fret ou on string bends.

Normally, the smaller radius will choke out before larger radius; whether it is conical or not; all other things being equal; your results may vary; no warranty implied; don't hold me to this.

I can make any compound radius board I want so don't really need to hire someone with cnc to do that. I think differences of how the strings lay on a straight 12 or 12-14 are very small and a computer model might show it more accurately than an actual neck.
I agree the small radius are always going to chock out more than a flatter neck.
There are always compromises and you just need to work out for yourself what you prefer. Personally, I've never felt any preference for a small radius, so a conical board doesn't matter much. I like being able to use one size caul for fretting. I can see some theoretical advantage to the slight cone, like 10 to 10.365, but haven't convinced myself its worth the trouble of 23 different size cauls, or revamping my whole fretting procedure.
I guess back to the original post, to me a 10/16 board is so far from "ideal" that the tiny difference in how lay the section of the cone onto the neck would matter at all. It should work fine.

I've designed them on solidworks and autodesk by building a construction line the length of the fretboard, and then creating a rectangle at each end with equal height sides and overall width corresponding with the width at the nut end and bridge end respectively. Then I draw a circle of the radii I want for each end, and apply tangency constraints at the upper corners of each rectangle. From there it's a matter of trimming out the unwanted lines and then using the loft function to join the two entities using the length construction line as an extrusion path.

This will give you a slightly taller apex at the nut end of the neck due to the tighter radius, , although because that end of the fretboard is usually ~ .5" narrower, the difference is negligible and can easily be compensated for in setup, at least by my understanding.

Disclaimer: I've thought about this, but I've never done it. So take this with lots of salt.

It seems to me the reason to have a compound radius fingerboard is because it gets wider from the nut end to the high end, so if the radius doesn't change, the fingerboard sort of drops away further the wider it gets. Thinking along those lines leads me to think that following the string path is one way to approach this question. So if we pick our favorite radius at the high end and measure the drop directly underneath each string, then we take those same "drop" numbers down to the nut end of the neck and put them under the strings in their new narrower positions, and plot that curve we will have the radius at the nut end. In practise my inclination would be to radius the fb to the widest (high end) radius and set a router to the depth of the end of the fb and run it back to the nut end following the string path for each string. then you'd have to round out the flats created by that procedure, which I would probably do with a card scraper. One thing left to sort out would be the radius of the saddles at the bridge. They would be flatter still because the strings are still wider. It shouldn't be a problem as long as you had individually adjustable saddles like on a strat. A tunomatic style would require a bunch of filing on the inner saddles, but that's probably doable.

Having said all that, I've never experienced much of a problem with regular single radius fingerboards that would make this necessary, but then I don't worry too much about super low action.
Jim