Question on FR 66s

Bill, John, Lew and others, I would like to have your opinion about the following calculations I made regarding the geometry of the FR-66S with a SPU (52 mm length). Please correct me if I'm wrong.
The effective length of the FR-66S with needle to arm distance of 50 mm is 307 mm.
Draw a imaginary line (line 1) between the needle and the pivot, which is the same as the effective length.
Draw another line (= line 2) from the needle, parallel to the head shell.
Between line 1 and line 2 there is an angle, which is the offset angle (16.8 degrees for the FR-66S).
So the projection of line 1 on line 2 is cosine of 16.8 degrees * 307 mm = 293.9 mm (right triangle).
293.9 mm + 2 mm (because the length of the SPU is 52 mm) = 295.9 mm.
The new effective length will be: 1/cosine 16.8 degrees *295.9 mm = 309 mm.
If we want to have an overhang of 12 mm, the P2S distance would be: 309 mm - 12 mm = 297 mm.

Chris

Hello John_Gordon,

I do like the way that your mind works through these well thoughout solutions...scientific, without a hint of marketing, thank you!

Cheers

Thanks, John. As it happens, I own both an original metal Dennesen and a UNI. I tend to use the Dennesen only to set P2S. (I mark the desired distance on a piece of white paper and then set up the Dennesen so its pointy end is on one mark and the center of the spindle hole is over the other mark. Then set the adjusted Dennesen on the spindle and "Bob's your uncle".) I don't like using it for cartridge alignment because I have a very difficult time seeing its grid and sensing the position of the little dimple that marks the target for the stylus tip. (Also, many of the vintage Japanese tonearms are not meant for Lofgren A.) The UNI is a little better for that purpose. As I mentioned privately, I have a bias against twisting the cartridge in the headshell, based on one bad experience doing that. So I tend to favor using the geometry for which a particular tonearm was designed.

John,
If one were to do the calculations as you suggest......with and SPU or FR-7 type of fixed headshell......surely the Off-Set angle cannot be changed?
Nor can the Overhang or Effective length.
The only parameter able to be changed is the Pivot to Spindle distance?
To calculate the new P to S....one needs to know accurately (to within 0.1mm) the 'actual' Overhang Distance.
To do this with a 'J' shaped tonearm like the FR-66s.....one needs to set up the arm accurately to the recommended P to S Distance (295mm) and then measure the stylus point Overhang?
One would imagine that the FR-7 series (because they are made by the same manufacturer as the tonearm) would be spot-on the specified 12mm?

The problem that Jazzdax poses

The length of the SPU is 52 mm instead of the 50 mm recommended by Ikeda.

does not necessarily indicate a 2mm difference in stylus Overhang?
One would need to accurately measure this as I describe..... before plugging those figures into the Vinyl Engine Calculator to ascertain the new P to S distance and the consequent new Null Points with the accompanying distortion figures.

There must be a way....but for the life of me I can't see a way to accurately measure this Overhang to within 0.1mm?

Thuchan has a fine collection of SPU cartridges.
I suspect he uses his original Ortofon tonearm to run them?.........but I wonder how he sets their geometry and whether he has mounted them in the FR-66s?