Official Luthiers Forum!

Reading back through some previous posts, more than one person suggested that it may not be worth the trouble to do a compound radius on acoustic guitar fretboards. I just got my first compound-radiused fretboard set up, and it worked out very nicely (and wasn't *that* much extra work).

I think I have an idea of why you could make the case that it doesn't make that much of a difference on an acoustic, but could someone who understands the concepts better than I do explain it in 2-3 sentences? Just the basic pros and cons?

TIA,

_________________
Ken Mitchell
Durham, NC

Most people don't spend much time doing large bends in the upper registers of an acoustic. A compound radius allows you to have lower action up and down the neck without fretting out when performing large bends. This was pretty apparent on old Fenders that had 7" and 9" neck radii. The 7" is brutal! I never really notice a problem on anything 12" and larger though I'm sure some people do.

A 9.5 or flatter radius is flat enough that I can dress a compound radius into the fret plane (the tops of the frets) and still do large bends, acoustics have 12 or flatter fretboards usually. Also the taper of a guitar fretboard is not extreme, unlike a bass guitar, which has an extreme taper AND a long length, exaggerating all the problems.

_________________
Old growth, shmold growth!

It's my understanding form reading Mario's past post over at MIMF that it's lower action without fret buzz even for hard strumming Bluegrass players which he makes a lot of guitars for.

Right, because with a compound radius each string lies in it's own straight string plane, rather than with a cylindrical radius when the neck is straight, the outer edges roll away and are in effect backbowed. If you put a little reliefe in a compound radius, all the strings gain relief whereas with a cylindrical radius, the neck requires more relief to the middle strings to gain a slight relief to the outer strings.
However, a cylindrical fretboard radius can have the fret plane compound radiused with no extra effort, for those who always dress their frets before final setup. (there are those who feel that with properly seated frets dressing is unnecessary) This is what I do. I feel that for guitars, unless you have a Floyd Rose system, where the geometry of the fretboard has to conform to pre-machined metal parts, a compound radius fretboard plane is unnecessary since the frets can be compounded and gain the same benefit, unless you're already jigged up for compound radii.

_________________
Old growth, shmold growth!

Being able to bend strings without fret buzz is a fringe benefit of having a compound radius...not the primary objective. Lower action is the goal of a compound radius which I think is beneficial to all acoustics that employ a radiused fretboard.

In a nutshell, a compound radius compensates for how string taper affects string height over the length of a radiused fretboard.

Compound radiused fretboards and flat fretboards maintain the height relationship of each string to the fretboard whereas a constant radiused fretboard does not. Assuming a tapered neck, with fixed radius fretboards the height relationship of the D and G strings (the two middle strings) to the fretboard will be nearly linear whereas the high and low E strings will see a non-linear increase in height from the nut to the bridge. If the strings were parallel all the way down the neck the height relationship would be linear but because the strings taper outward towards the bridge, the outside strings are higher off the last frets if the fretboard doesn't compensate for the string taper.

Therefore, with a compound radius fretboard, one is able to set the action height of the high and low E lower than with a constant radius fretboard. The B and A string can also be set a bit lower too.

_________________
I read Emerson on the can. A foolish consistency is the hobgoblin of little minds...true...but a consistent reading of Emerson has its uses nevertheless.

StuMusic

I love me some compound radius on a fretboard.

_________________
"Act your age, not your shoe size" - Prince

Me too. I go 15-21 on mine. When I play my Gibson AJ, it sure feels awkward in comparison IMO.

Agreed. A little compound goes a LONG way to making the instrument more enjoyable to play.

Dave F.

_________________
Cambrian Guitars

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

Just to get an idea of the numbers involved....

I'm assuming a 1.7" nut, 12" radius and 22 fret neck, 25" scale length. The neck at the 22nd fret is 2.152" (this just happens to be what I calculated for one of my neck/bridge combinations). I assume a worst case of the string being aligned with the very edge of the fingerboard.

The sagitta of the arc at the nut is .03", that is with a 12" radius the fret at that point is .03" lower than it is at the center of the fingerboard. At the last fret (22nd fret), the sagitta is .048". That's a pretty dramatic difference but what we really want to know is not how much it changes, but how much it changes from a straight line. So if we turn this into a line, we get the equation:

y = .001X + .03 (where X is the position in inches of the fret we care about).

So that is what a straight line would look like.

Now let's pick a fret in the middle, which is about at the 8th fret, and see how the two differ.

A straight line at the 8th fret would be at a height of .001*9.251" + .03 = .039"

The sagitta of the arc at the 8th fret is .039"

So for a 12" radius, it's within <.001" deviation from a straight line right up to the 22nd fret.

If you repeat all of this for a 9" neck, the results are much different. The sagitta comes in at .052", but the straight line would come in at .049", so you're a full .003" taller in the middle of neck than you'd like to be.

Incidentally, the formula to calculate the sagitta is:

r - sqrt(r^2 - L^2)

where r is the radius of the neck, and L is the distance from the center of the neck to the point you want to measure. So the sagitta for a 12" radius neck at the nut for a 2" nut width is:

12 - sqrt(12^2 - 1^2) = 12 - sqrt(144-1) = .042"

I think I got that right. Hopefully someone will muster up some energy and maybe double check my allergy induced delirium.

I don't think there's really any point, or at least I certainly don't have a point to make, but for me it's just interesting to get a feel for the things I can calculate and measure because there are so few of them.