Gotoh Floyd Rose non-standard radius, compound radius board, and saddle shimming

[rundgrenrules]

I see plenty of information out there in regards to how many saddle shims to use on a standard OFR or other Floyd with a built-in 10" radius, but none for the Gotoh brand Floyd which comes with a roughly 14" radius saddle setup.  I have a 12"-16" compound radius so I am aiming for around 18" radius at the bridge, and I have a set of shims (used previously to set a 10" radius Floyd Rose 1000 series to 18").  My question is, does anyone know the math on how many saddles to use under the outer E, A, and B strings to take a 14" radius up to 18"?  I have the standard .15mm shim set.  I know its an odd question, but I can't figure it out myself.

 

[amigarobbo]

:icon_scratch:

Not the most helpful of replies, but I went for a straight 10" neck just to keep it simple, my brain couldn't cope with anything like that.

 

[Logrinn]

Or another simple answer:
put one shim each under the b and A saddles and two each under the e and E saddles.
String it and play.
If it feels ok stop, otherwise add another shim under each of the four saddles and try again.
Repeat if necessary.

 

[Cagey]

Dontcha just love Floyds? For as complicated as they are, they still don't have any adjustment for individual string height, and setting intonation requires a special tool as well as the patience of a saint, as does changing strings. How they still sell those things is a mystery for the ages.

Anyway, the OFR is actually a 12" radius, but they ship with a shim installed under the middle 4 strings to make it a 10" (roughly). When you adjust for an 18" with that bridge, you pull the original shim. So, if the Gotoh is starting at a 12", then the compensation needed to get it to an 18" is going to be the same as that for an OFR.

 

[Mad Hatter]

String it up, and measure your action at the 12th or 17th fret on the D and G strings, then measure the action for the outside strings.  The difference is what you need for shim thickness to make them all the same.  Tear it down, pop the needed shims in, and you should be good to go.

 

[rundgrenrules]

Thanks Everybody!  I think measuring and adding shims to compensate based off that string measurement is the way to go per MadHatter.  According to the Gotoh website, the bridge has a 350mm radius with no shims under the saddles, so thats roughly 13.75".  Im going to string it up, set the high E and low E strings to the same height with feeler gauge, and measure the difference. 

 

[rundgrenrules]

So I realized that i could use AutoCAD to figure out the exact difference between the two radii.  Created a circle with an 18" radius and one with a 14" radius and superimposed them, then measured the difference at intervals representing the string spread.  Two spacers on the outer strings and one on the A and b strings will get me plenty close.  Thanks all!

 

[Cagey]

That's a good solution. Have to remember that one. I wanted to hook you up with a spreadsheet another member here created a while back with the math to calculate for any radius, but he hasn't been around for a while and the link to the 'sheet is dead. So, I'm glad you got an answer after all, and thanks for sharing.

 

[Strat Avenger]

Still don't get why people think they need a 18" radius bridge for a 16" radius neck. Your fretboard does not extend all the way to the bridge saddles. In any case, shimming those bridge saddles is easy. You want no shims under the D and G saddle.  One shim under the A and B, and 2 shims under the high and low E.

 

[bagman67]

Still don't get why people think they need a 18" radius bridge for a 16" radius neck. Your fretboard does not extend all the way to the bridge saddles.

Well, if you look at the compound radius fretboard as a section of a cone (which it is), and you keep your action at a pretty consistent for the length of the fretboard, then it does flatten out to 18" or thereabouts at the bridge.  It may not make a huge difference, but it's a difference that matters to some players.

 

[Strat Avenger]

Still don't get why people think they need a 18" radius bridge for a 16" radius neck. Your fretboard does not extend all the way to the bridge saddles.

Well, if you look at the compound radius fretboard as a section of a cone (which it is), and you keep your action at a pretty consistent for the length of the fretboard, then it does flatten out to 18" or thereabouts at the bridge.  It may not make a huge difference, but it's a difference that matters to some players.

I'm assuming this is because the nut is a 10" radius.  If the fretboard were a straight 16", wouldn't 16" @ the bridge be just right?

 

[Cagey]

Yes.

 

[stratamania]

Here is a very good explanation of compound radii with useful pictures and diagrams.

Compound Radius Explained

 

[DustyCat]

Wow! That's genius!
OP is saying that the cone off the compound radius neck keeps extending past the 22nd fret, and by the time the strings pass the pickup, the bridge will have an even flatter radius at 18"

Intonation improvement?
What does the spacing of the strings feel like at the 20-22nd frets with that compensation?

 

[Fat Pete]

Wow! That's genius!
OP is saying that the cone off the compound radius neck keeps extending past the 22nd fret, and by the time the strings pass the pickup, the bridge will have an even flatter radius at 18"

Intonation improvement?
What does the spacing of the strings feel like at the 20-22nd frets with that compensation?

Changing the radius wouldn't affect intonation (as you'd want to set this after the shim change anyway).

The string spacing, as viewed from above, wouldn't be affected either, but the actual 'point to point' spacing would be reduced slightly by increasing the radius - by about 0.0024" (about a quarter of the thickness of a high e string).

The significant change is that action of the middle strings is improved. The 'error' on the g and d strings is about 0.03" with a 12" radius.

I've drawn it out - just for the fun of it.

The lower pic is a 'real world' approximation with the whole thing canted up by 0.254" to give the low strings more room to move. (Just to illustrate/exaggerate that any fixed/semi-fixed bridge is going to be something of a compromise compared to a unit with individual string height adjustment.)

Disclaimer: the numbers quoted are based on a string spacing of 10.75mm (apologies for the mixed units but that was the first thing that came up on Google images). Likewise, quoting numbers down to 1/10,000ths of an inch is pretty silly as the bridges wouldn't be built to those sort of tolerances anyway. Also, I can't be bothered trying to get my head around whether the actual string radius is larger than the fingerboard radius or just the same radius shifted up.