Why use a super accurate cartridge protractor

I am not a mathematician but doesn't the geometry change slightly with every moment when stylus is moving along? So, yes, perfect alignment at every moment would be great if it was possible. The trick is to find an acceptable compomise. By ear.

Dear Cocoabaroque, when Loefgren and Baerwald calculated the respective tangential curves (Baerwald/Loefgren A and Loefgren B), they did do it for monophonic records to be tracked with round styli of approx. 60 µm radius.
Stereo microgroove and fine line or similar styli with polished area of 1µm x 5-6µm weren't in sight at all.
A stereo record's groove is not a homogenous track at all and the differences in radii between the groove's two walls do increase with decreasing distance to the spindle.
In other words: the tracking conditions for a stereo stylus do change ever more towards the groove's lead out.
That's why some designers did choose alignments different from the "old masters" and that's a reason why so many modern audiophile records have rather long dead wax - avoiding the ever more problematic situation close to the inner label.
When Loefgren made his calculation's, our grandfathers were young men and our parents were in pampers. This was almost half a century before micro-ridge, vdH 1 or fine line styli first saw the light of day or the walls of a MFSL LP.
A spherical 60µm needle tracking an old wide groove record has a much easier job.
No worries there about soundstage recreation, increasing differences between left and right groove wall contact areas.
Keep enjoying the discussion - off for 2 week holiday in Africa now,
D.

Cocoabaroque,

Are we not taking it on faith that the great masters of cartridge alignment(!)--Lofgren, Baerwald, Stephenson, etc knew what they were doing even though they disagree amongst themselves?

You don't have to take anything on faith, it is not a matter of "faith". The only reason we can all actually talk about alignments and geometry and use the words to describe them is because Loefgren, (and Wilson before him in the 20's) spent many hours (without calculators or computers) to figure out from first principles how to minimise tracking error and then tracking distortion.

Subsequently Baerwald, Bauer, Stephenson et al came up with variations based on those calculations, which have different perpectives, but in no way disagree. Rega doesn't use a "special" alignment. It is just not Loefgren A IEC. Stephenson IEC is simply a Loefgren A with inner radius around 54.8mm which places the inner null at 60.3mm, the IEC inner radius.

Dertonarm is correct in saying that conditions change as the radius decreases, but the calculations for minimising tracking error are the same as they always have been. It is the distortion caused by that error that is the issue...

Which is why he is advocating different alignments. But these alignments are still predicated on the Loefgren equations and merely reflect his preferences as to where the equations should be weighted. This can now be done by anyone and his brother, who (unlike Loefgren) has access to the excellent Vinyl Engine calculators. In the same way that Stephenson came up with his variation, we can enter minimum and maximum radii such that the shape of the distortion curve suits our purpose for the records we have.

However, as far as I know, no one has yet come up with a formula which has been designed to use different weightings (other than those for average distortion (Loefgren B), or for minimising/equalising distortion peaks (LoefgrenA))

Whatever our reasons, in coping with tracing distortions caused by using modern stereo (versus old mono) stylii, Dertonarm and the rest of us are basically still using Lofgren A, with variations in input parameters.

Although all this doesn't address the issue of how significant are errors in set up in relation to the distortions at particular radii.
.

Moonglum,

After the first 60 tries (yes you read that correctly) I was still unhappy with the final cart position which often ended up with an estimated 0.2mm offset from target in any given direction(!!!). I finally got the perfect result (and was only truly happy) after 70 tries...

Interesting to hear your take - I would imagine that +/-0.2mm is pretty good and that 0.5mm is more typical. I have played around trying to estimate how accurately I could set the offset angle, as I think that is the real unknown when it comes to talking about accuracy, and reckon +/-0.25 degree is the variation.

However, no protractor manufacturer, as far as I know, actually says either how accurately their protractor is made, or how accurate, precise and repeatable are the setups typically achieved with their device. In particular, regarding offset angle. So, is a Mint more accurate than a Denessen, a DB, a Wally tractor, a Feickert? How to measure this?

Löfgren just used euclidean geometry - as does did everybody before/after him in the past 2260+ years in the western hemisphere - be it in tonearm geometry or any other geometrical topic related to mechanics and 3-dimensonal space on earth.
He was however unquestioned the first to muse and care about giving phono playback an optimized geometric solid basis.
And every analog audiophile should be grateful for his attempt.
I for one certainly am.
Viewed in the light of fact that there is a wide diversity of stereo records since 1958 with groove cut area varying by a wide margin, his preferences and weightings aren't as universal applicable as they were in 1934/38.