Dear @thom_at_galibier_design : Nice to see you in Agon again.
I only want to make some comments about the information in that link:
first is that J.Ellison made his spreadsheet geometries named/labeled it in the rigth way ( because he knows very well the Löfgren w.papers. ): Löfgren A and B.
Baerwald has no merit on those alignments other that his solution 4 years latter to Löfgren was exactly the same/similar to Löfgren A. I’m not saying it’s a copy but certainly nothing new or better than Löfgren or a modification.
second is that Stevenson made as Löfgren 2 solutions: Stevenson A and B where the latter is similar to Löfgren A alignment. Not only you but even the tractors manufacturers never specify the correct way: Stevenson A. Are important this issues? well I think it’s. Other issue about is that you named uni-din where this is not a universal alignment an even is not a new equations solution but only a manipulation parameters using Löfgren solution and it’s too what SAT tonearm designer did it ( to set up the cartridge to his tonearm. ) with that kind of manipulations to the original input parameters : innermost groove and outermost groove radius values. These kind of manipulations means that you, me or any one else can have our personal alignment if we want it. You can do it through the Ellison spreadsheet or through the VE alignment calculator. Not big deal as the Löfgren solutions. Btw, VE calculator has the advantage that at the same time gives you both Löfgreen ste up parameters and Stevenson A too and diagrams/charts with the 3 alignments curves to compare visually between them.
in the link I pasted :
" In contrast, the math developed by Löfgren (and subsequently used by Baerwaald), derives a unique set of 3 parameters (effective length, mounting distance and offset angle). "
Not exactly as you specified it and please let me explain about because I think is way important to any audiophile:
what are the input parameters used in the Löfgren equations that used he?
only 3: effective length, innermost groove radius and outermost groove radius and from those 3 input parameters the Löfgren equations solutions gives/output parameters: both null points ( inner/outer ), off-set angle, overhang and linear offset. The pivot to spindle distance then comes from an atritmetic subtraction: EL - overhang.
Been mathematics we can do whatever we want as could be to have a TT convenience P2S distance and use this parameter in those equations making the changes necessaries but is only a manipulation of the original equations/parameters and not a new alignment. As I said It’s only mathematics.
In reality the Stevenson A is an extreme input parameter change/manipulation ( innermost groove radius. ) but this gentleman made something truly different to what existed and some tonearm designers choosed Stevenson A alignment.
Again good to know from you.
R.
