Two Protractors - Only One Aligns

PS - even though the tonearm is 10", if the effective length is 265mm (10.8"), perhaps it is not surprising that the PTS length that works is 250mm.  When I google PTS lengths for other 10" tonearms (not many hits) I see values ranging from around 228 to 232mm.  When I look at 12" tonearms, I see values on the order of 295mm. (this is also where my SME is set).  Using proportionality between 230 - 295, a 10.8" tonearm would have a value of 256mm.  So it seems I am in the ballpark.

I starting to not trust the TTB Protractor!!!  

@wlutke The MINT was made for a 12-inch tonearm that has a P2S of 290mm.  Is it possible that a 12"/290mm combination has the exact same null points as a 10"/250mm combination?  I haven't yet achieved a perfect alignment with the MINT and the 10" tonearm, but preliminary results lead me to believe that I likely could.

@lewm  - I’m surprised at how inaccurate the TTB is. I tried multiple P2S values and I couldn’t get close for any of them. After lining up the outer null point, the inner null point was always at least a centimeter off. @wlutke - are you saying that there is no universal 2-point protractor - that all protractors must be made based on the P2S and the effective length of the arm? How is it that TTB seems to be selling a universal protractor with no mention of fitting to these parameters? Does it have to do with pointing the guide line to the pivot point? Can someone direct me to a reference that I can read to familiarize myself with the math and geometry of this situation?

@lewm One thing that is unique about this tonearm is that I can change the P2S over a wide range without moving the mount, as the arm that leads to the pivot swings. This can be seen on the link in my first post. Thus I can change the P2S from 230-270mm.  I can also change the overhang by +/- 4mm with the slot on the headshell, and I can change the offset angle significantly since the headshell is only attached with one bolt.  With all this adjustability, I may be able to line up the proper offset angle and null points with the mint protractor made for my unique tonearm combo.  Does this make any sense?

@wlutke I get what you are saying, and agree that the arc should be flatter for a larger P2S (or a longer effective length).  However, if the null points are the same for both configurations, perhaps this doesn't matter.  By definition, the null points are the two points where the cantilever is tangent to the record groove, and this is not effected by the "curvedness" (or flatness) of the arc.  I think the difference is that a flatter arc will create less error at locations away from the null points. That is why a 12" tonearm is preferred over a 10" tonearm.

I found a good turntable geometry calculator on this website. This calculator shows that for any given P2S, the zero radii are the same.  What changes is the effective length and offset angle required to meet the null point requirements.  For example, calculating the zero radii for a 250mm and 290mm P2S, I get the same zero radii (63.32, 119.63) with the following differences:

P2S                        250              290
Eff. Length              264.79         302.84
Off. Angle                20.25           17.61

I guess the cool thing about my tonearm is that the offset angle is adjustable, because the headshell is attached at only one point and can be rotated.  Thus, if I am able to find a P2S that works for the effective length of the tonearm, I can adjust the offset angle accordingly. Early indications suggest that I can accomplish that with the MINTLP - but I haven't confirmed that yet.

Where I get confused is applying the protractors.  My MINT and TTB protractors both have the same zero radii (67 & 121 mm) which differ slightly from those calculated above (don't know why, maybe different calculation method).  But they are clearly offset from one another in a different manner.  So if I could lay them on top of one another, the two null points would not line up, even though they use the same zero radii. That probably reflects the difference in P2S, and the TTB must have some assumed value of P2S.  The problem is that both protractor manuals state that you should fix the protractor - so that the differing offset makes it either possible or impossible to match the two null points on the protractor. If the only requirement is that at each zero radius the cantilever is tangent with the grooves, couldn't I simply rotate the protractor and use the lines on the mirror to make sure that the angle is correct?

@lewm Is this to suggest that a dedicated protractor is needed for every possible effective length?  See my post above.  If that is the case, the TTB would be misleading.  Must have something to do with pointing the orientation line on the TTB to the pivot point.  But even when I come close to doing that, my alignment with the TTB sucks.

I think the unique thing about this "Musical Life Conductor SE" tonearm is that I can alter the P2S, the offset angle, and effective length (3% range).  My question stands: if I can match the two null points with the correct angle so the cantilever is tangent to the grooves (defined by the protractor grids), is it OK to rotate the protractor during alignment?

@wlutke I get what you are saying: 

As the stylus traces the flatter arc, the stylus tracing angle changes less in relation to the grooves. The Mint inner and outer null alignment lines will be more near parallel to each other to compensate. Overhang may be different in order to compensate as well.

But shouldn't the alignment lines be parallel to the grooves if they occur at null points?  This makes the cantilever parallel to the grooves.  I think what changes is the angle between the alignment lines and the stylus arc on the MINT.  These are not perpendicular, and differ at each null point.

If I am being thick, forgive me - I appreciate your help.  Peter

@mulveling Thanks for the suggestion.  I will get a Geo-Disk.  The SMART-Tractor is way too expensive for me.  But I still want to make sure I can achieve 2-point alignment as well.

@lewm Sorry I missed your post at 8:05am before writing the one above.  I will need to see if the stylus follows the arc on my MINT - but it probably won't, because I'm using a 10" tonearm and the MINT was set up for a 12" tonearm.  The arc HAS to be different, and this is why less error occurs with a longer tonearm. But this doesn't mean that meeting the two null point requirements is not sufficient for getting proper alignment, right?  Although I know that I am close, I haven't yet fully confirmed that I can meet both null point requirements with the MINT without rotating the protractor.

@lewm Thank you! I think I’ll sell my TTB on ebay! I was just going online to purchase a Feickert when I saw your post coming in! Paid the extra $$ for 2-day delivery so I can get this thing wrapped up over the weekend.

Just checked the retail price for the TTB. $20. I think I’ll give it to a budding vinylphile...

@lewm That is the rub!  The company is no longer in business.  I guess I need a contact in the German audio industry to track down the manufacturer - no luck googling thus far.  I will operate within normal ranges.  The pivot to stylus distance can only  vary by a small amount, which means the P2S range is pretty tight as well. 

Folkfreak and LewM. Thanks! You guys rock!