Dear Gentlemans: First than all I want to say again that I'm not questioning any single protractor ( including all the ones named in this thread. ), I'm not questioning VPI undisclose protractor parameters or the DT ones but the " concept " that some tonearms needs " dedicated " geometry set up, first question here: why not all tonearms?
In reality the Löfgren and copy equations/solutions are to determine the exact point/place and " direction/orientation " where the tip on the cartridge stylus must be to fulfil a criterion that could be defined by the cartridge/tonearm owners or the explicit criterion on Löfgren A/B Stevenson or what ever for any given tonearm geometry design ( inclusive you could note VPI site that the designer never talk about: " our specific tonearm geometry " and he don't speaks about because he knew on the subject. Neither Stevenson. )
These are some of those criterion for set up parameters calculations:
+++ Löfgren A and is the solution that gives you the lowest possible amount of tracking error at the inner, centre and outer grooves while keeping this error equal at all 3 points. +++++
+++ Löfgren B and will gives you the lowest overall tracking error of any alignment method but with slightly higher error at the beginning and end of the record than the A method. +++++
++++ Stevenson - a variation on Löfgren geometry optimized for low distortion at the inner groove at the expense of increased distortion elsewhere. +++++
VPI, in reality ( I could be wrong, so crrect me if I am. ) take the criterion to have the lowest distortion in the last 1/3 of the recorded area ( something similar to Stevenson, but not the same. ). For doing this what VPI made was to change one of the three input data on the Löfgren equations ( this is an option but he can determine the desired null points and works for a derivation of the inner groove radius. The result is the same ), the change was in the most inner groove distance ( that in the case of Stevenson he made that that input data coincide with the inside null point and that's why in the last one groove the distortion is cero. ) for change the null points in a way that fulfil that criterion but the foundation of any of these changes are still the Löfgren equations that any one can " manipulate " by algebra to fulfil his criterion.
The undisclose VPI set up parameters IMHO was something with almost no reason for that because in the very first moment that his tonearms and VPI jig/protractor be on customers hands it was very easy to know those set up parameters and this is what happen when VE people take their knowledge and time to analize which were those set up parameters and when they have on hand run calculations against Löfgren A/Baerwald and B . Well you can read it here:
www.vinylengine.com/vpi-tonearm-geometry.shtml.
You can note that in the models 10 and 10.5 even in the last 1/3 of the recorded area ( VPI criterion ) the Löfgren distortion is lower.
Through the thread I posted several times the importance of those three data inputs on the calculations and what happen if we change it:
+++++ I repeat again, in the Löfgren and clones solutions/equations you need three and only three input data for the calculations: tonearm effective length, most outer groove distance and most inner groove distance and is according these three numbers ( that you can choose as you want it. and for any reason you have. ) that you calculate the overhang and offset angle. +++++
+++++ In my last post before the one I sended to you I explain the Stevenson approach as an example on how we can manipulate/change the input data to achieve a different set up parameters. +++++
+++++ We don't need any other geometry parameter to make a tonearm/cartridge set up: effective length, overhang and offset angle are all we need. Even we don't have to care on the null points.
The null points are calculated and used for other things than stylus-cantilever/tonearm geometry set up. +++++
+++++ The Stevenson A cloned/solution ( adopted by several Japanese tonearm manufacturers. IMHO with out in deep analysis. ) is not something with " new " equations, Stevenson only wanted that at the inner groove the tracking error be cero so he taked one of the three input numbers ( in the Löfgren formulas. ): most inner grove distance as one null point and that's all.
This " solution " gives you almost cero tracking error/distortion in the last 30 seconds of a LP with a higher distortions on all the remaining LP surface than in any other " solution ". +++++
+++++ Any one of us can change ( in the Löfgren equations. ) this same input number and Voilá! we have a " new " Perry/Jones/Lopez/etc solution!!!. +++++
+++++ Now, if we change the data input to force better " figures " at inner groove that could be in detriment of higher distortions in the other 90% of the remaining LP grooves +++++
As any one can read on those Graeme F. Dennes white papers any change on that input data makes a change on null points. In those equations the null points are not input data but a calculation output of the equations. Of course, in mathematics you can re-arrange by algebra and could make that the null points be data input.
So, it is IMHO that the criterion is what define those three input data for calculate: overhang, offset angle and null points positions and not the " specific tonearm geometry ".
Other that the most inner groove distance ( inpput data ) we can change ( if the slots's length in the headshell permit it. ) the tonearm effective length data for a higher one to achieve better distortion figures but again not because tonearm geometry it self.
I could be wrong but in this thread and all over the net there is no single real scientific evidence that that is true.
Anyway, I think too that in one or other way the discussion was a learning one and I say this because due to many of the persons posts in the thread I was wrong when I thinked that some of you were " familiar " with all the terms ( terminology ) used on the subject and the most important the meaning of each term.
What's true is that today our knowledge level on the subject is higher than " yesterday ".
regards and enjoy the music,
Raul.
