John G,
A few comments...
#1) I have nothing to say on his or your comments on antiskate and SME. I have seen no vagueness of analysis on 12" vs 9". Given what you say later in your post, it is pretty obvious you have a simple explanation (but you did not give your analysis either). I think if it is obvious to you, it may also be obvious to others. It is to me. If you have additional complex analysis of the differences, please share. I think 'analysis' of 'why' old full-length records should have different innermost and outermost grooves is kind of a moot point. They are different (at least mine are). If one has looked at enough records, one may notice patterns among periods, recording companies, cutters, etc. I think that noting the difference and applying math to it to achieve better set up where desirable is easy, and I think that is what he has done. Standard geometry using standard assumptions does not always produce lowest possible distortion except in the case when the record has the same dimensions as the standard assumptions AND one does not prioritize low distortion in one part of the record over another.
#2) I don't find him unclear on geometry issues at all. As far as I can tell, he has stipulated everything you have written. He shouldn't have to as the math does not change. He mentioned in these fora, that given his parameters and listening preferences, he had found a better way (than the manufacturer's stated geometry, or standard Baerwald geometry using manufacturer's stated effective length) to set up a particular tonearm. Others pestered him on it, and he politely refused to be harassed. The effort spent by one person in particular on harassing him about this subject could fill a small magazine issue, and may have closed down two threads. I thought it would do this thread in, but he left some hints about it, and I did some analysis to figure out Dertonarm's 'geometry' including the "weightings" you speak about. It took me about 10mins to come up with it. If you did not read the analysis above, the short version is that assumes IEC records, and is basically a cross between Stevenson's 'tilt' and Lofgren A's curve shape. It achieves lower average distortion in the place where he wants to achieve lower distortion (second half of the record), and achieves sharply lower average distortion in the last 10% of the record for long records than either of the standard setups, especially when those tonearms/carts have been set up for DIN. It is, as he has stated, entirely a matter of choice based on his record selection and his priorities on where on the record he wants to hear his distortion (or lack of it). It is decidedly not 'new math'.
#3) I think all of us, including the dastardly Dertonarm, get that minute changes and ball-busting accuracy requirements for one or two of the parameters will necessitate the same accuracy requirements for ALL the geometric inputs (though inner-most groove by its very nature must have some flexibility because one does not newly align (or set up a new headshell) for every particular length). If you read his posting history, it is blatantly obvious he shares your opinion. On the other hand, bad implementation of offset angle is bad - on any geometry on any tonearm.
As an aside, as far as I can tell, the supplied lengths and angle for your signature tonearm don't match the null points noted in the manual. Not having seen the supplied protractor, I can only presume it was in fact like a jig so that people could set their cart perfectly straight without deviating from appropriate offset angle, and then the overhang would fall into place shown on the protractor. Using the accuracy as stated, one would not have come up with the same null points as you did, which means that anyone using a protractor other than yours would have been off Baerwald by a decent bit, even if they had managed to get the offset angle and mounting distance perfect.
#4) If you read his posting history, you can glean a fair bit of his history (who he is, what he has done, etc). A little bit of digging and you can find more. I don't know him personally but have discovered a little on these threads and more elsewhere. Without doing the digging on you, one would not know who you are either. As to the protractor, other people challenged him on the subject, and rather than complain about being attacked, he made it. He is now offering it out. Is it more expensive than a laminated piece of cardboard? Yes. Is it for everyone or is necessary for achieving good sound? No. But neither is a gold-plated tonearm with diamonds on the headshell.
If you have but one or two tonearms, it may not be for you. If you have a half dozen, it may be cheaper than buying a half dozen protractors specifically designed for those half dozen arms. One could obviously make one's own 'mirrored' protractor using a CAD program, printing on clear plastic and mounting that on cardboard with some aluminum foil in between. But that is beyond most people who don't have CAD design experience. I don't have anything better than SketchUp, which is kind of a PITA to use, and I figure that if I don't like mine, I can probably sell it and not lose too much money on it. And in the meantime, I will have a cheaper tonearm-specific protractor for my more than half-dozen arms than I would if I bought just one. And I will have a universal protractor which will work on other tonearms. And I expect that it will be easy to use so that my conscientious set up will take less time and back pain than it would otherwise. I know nothing of the extra goodies/modifications yet other than what he has written, so cannot comment. You could send him an email and ask him yourself.
A few comments...
#1) I have nothing to say on his or your comments on antiskate and SME. I have seen no vagueness of analysis on 12" vs 9". Given what you say later in your post, it is pretty obvious you have a simple explanation (but you did not give your analysis either). I think if it is obvious to you, it may also be obvious to others. It is to me. If you have additional complex analysis of the differences, please share. I think 'analysis' of 'why' old full-length records should have different innermost and outermost grooves is kind of a moot point. They are different (at least mine are). If one has looked at enough records, one may notice patterns among periods, recording companies, cutters, etc. I think that noting the difference and applying math to it to achieve better set up where desirable is easy, and I think that is what he has done. Standard geometry using standard assumptions does not always produce lowest possible distortion except in the case when the record has the same dimensions as the standard assumptions AND one does not prioritize low distortion in one part of the record over another.
#2) I don't find him unclear on geometry issues at all. As far as I can tell, he has stipulated everything you have written. He shouldn't have to as the math does not change. He mentioned in these fora, that given his parameters and listening preferences, he had found a better way (than the manufacturer's stated geometry, or standard Baerwald geometry using manufacturer's stated effective length) to set up a particular tonearm. Others pestered him on it, and he politely refused to be harassed. The effort spent by one person in particular on harassing him about this subject could fill a small magazine issue, and may have closed down two threads. I thought it would do this thread in, but he left some hints about it, and I did some analysis to figure out Dertonarm's 'geometry' including the "weightings" you speak about. It took me about 10mins to come up with it. If you did not read the analysis above, the short version is that assumes IEC records, and is basically a cross between Stevenson's 'tilt' and Lofgren A's curve shape. It achieves lower average distortion in the place where he wants to achieve lower distortion (second half of the record), and achieves sharply lower average distortion in the last 10% of the record for long records than either of the standard setups, especially when those tonearms/carts have been set up for DIN. It is, as he has stated, entirely a matter of choice based on his record selection and his priorities on where on the record he wants to hear his distortion (or lack of it). It is decidedly not 'new math'.
#3) I think all of us, including the dastardly Dertonarm, get that minute changes and ball-busting accuracy requirements for one or two of the parameters will necessitate the same accuracy requirements for ALL the geometric inputs (though inner-most groove by its very nature must have some flexibility because one does not newly align (or set up a new headshell) for every particular length). If you read his posting history, it is blatantly obvious he shares your opinion. On the other hand, bad implementation of offset angle is bad - on any geometry on any tonearm.
As an aside, as far as I can tell, the supplied lengths and angle for your signature tonearm don't match the null points noted in the manual. Not having seen the supplied protractor, I can only presume it was in fact like a jig so that people could set their cart perfectly straight without deviating from appropriate offset angle, and then the overhang would fall into place shown on the protractor. Using the accuracy as stated, one would not have come up with the same null points as you did, which means that anyone using a protractor other than yours would have been off Baerwald by a decent bit, even if they had managed to get the offset angle and mounting distance perfect.
#4) If you read his posting history, you can glean a fair bit of his history (who he is, what he has done, etc). A little bit of digging and you can find more. I don't know him personally but have discovered a little on these threads and more elsewhere. Without doing the digging on you, one would not know who you are either. As to the protractor, other people challenged him on the subject, and rather than complain about being attacked, he made it. He is now offering it out. Is it more expensive than a laminated piece of cardboard? Yes. Is it for everyone or is necessary for achieving good sound? No. But neither is a gold-plated tonearm with diamonds on the headshell.
If you have but one or two tonearms, it may not be for you. If you have a half dozen, it may be cheaper than buying a half dozen protractors specifically designed for those half dozen arms. One could obviously make one's own 'mirrored' protractor using a CAD program, printing on clear plastic and mounting that on cardboard with some aluminum foil in between. But that is beyond most people who don't have CAD design experience. I don't have anything better than SketchUp, which is kind of a PITA to use, and I figure that if I don't like mine, I can probably sell it and not lose too much money on it. And in the meantime, I will have a cheaper tonearm-specific protractor for my more than half-dozen arms than I would if I bought just one. And I will have a universal protractor which will work on other tonearms. And I expect that it will be easy to use so that my conscientious set up will take less time and back pain than it would otherwise. I know nothing of the extra goodies/modifications yet other than what he has written, so cannot comment. You could send him an email and ask him yourself.