Well, I worked out the math as a prelude to figuring out the code. Hope it makes some sense to you :
The distance between 1st and 6th strings on my floyd is
2 1/8" (2.125".) Numbers have been rounded to nearest 0.0001"
6 5 4 3 2 1
<-c3->
<------c2------>
<-----------c1----------->
let c1 = 2.1250" # distance between 1st and 6th
let c2 = (3/5)* c1 = 1.2750" # distance between 2nd and 5th
let c3 = (1/5)* c1 = 0.4250" # distance between 3rd and 4th
let r0 = 15" # starting radius
let r1 = 10" # ending radius
function calculate_height_d (r, c) {
# takes radius and string distance as args: r and c
d = sqrt(4*(r*r) - (c*c))/2
return d
}
# let d10, d20, d30 = the calculated distance using c1, c2, c3
# with the formula: d = sqrt(4*r*r - c*c)/2
# and r0.
let d10 = calculate_height_d (r0, c1)
let d20 = calculate_height_d (r0, c2)
let d30 = calculate_height_d (r0, c3)
d10 = 14.9623"
d20 = 14.9864"
d30 = 14.9985"
# let d11, d21, d31 = the calculated distance using c1, c2, c3
# with the formula: d = sqrt(4*r*r - c*c)/2
# and r1.
let d11 = calculate_height_d (r1, c1)
let d21 = calculate_height_d (r1, c2)
let d31 = calculate_height_d (r1, c3)
d11 = 9.9434"
d21 = 9.9797"
d31 = 9.9977"
Now here's where it gets confusing :-).
Since in this case, we're going from a radius of 15 to 10, the 1st/6th
strings will be untouched, with shims needed for the 2nd/5th and
3rd/4th strings. If we went from a radius of 10 to 15, the 3rd/4th
would stay the same and the others would need to be shimmed.
let d20_diff = d20 - d10
let d30_diff = d30 - d10
d20_diff = 0.0241"
d30_diff = 0.0362"
let d21_diff = d21 - d11
let d31_diff = d31 - d11
d21_diff = 0.0363"
d31_diff = 0.0543"
let shim_for_3rd_4th_strings = d31_diff - d30_diff
let shim_for_2nd_5th_strings = d21_diff - d20_diff
shim_for_3rd_4th_strings = 0.0181"
shim_for_2nd_5th_strings = 0.0122"
so basically, you'll need two shims of about 0.0181" for your 3rd and 4th strings and two of about 0.0122" for your 2nd and 5th strings to change it from the 15" radius to 10" radius. Of course, as I said several times before, you could have "trial and error"-ed it, but math is fun, right? If anyone sees any errors above, please post any corrections.