LP Thickness/Taper

I find your picture interesting in that the outer rim is not resting on the turntable platter. Since the rim and center are considerably thicker to suspend the playing surface off of the platter. And I would imagine that the 180 gram pressings have different relative thickness between the outer grooves versus center playing area.

My guess is that the pressing process plays an important part as the puck is pressed from the center out as pressure is applied. Maybe the bulk or mass of the puck causes a restriction equalization of pressure across the diameter. Although I would also think that the manufacturer of the press would have accounted for this after all these years of vinyl manufacturer. It would be interesting to run this same experiment on records based on the manufacturer of each pressing machine. 
Kudos to you for taking time to do this, but although I don’t see that your motive is my curiosity, but I find it intriguing none the less.

However if I interpret your motive or question. I don’t know how a tonearm setting can be set to anticipate and compensate for this variance. Once again I am reminded of an article which I think Michael Fremer wrote about the playback of vinyl contradicts logic on many planes. But thankfully it does it as well as it does.

thank you for this food for thought 

@theo 

I find your picture interesting in that the outer rim is not resting on the turntable platter.

Many turntable platters are designed like that because the outer rim of the record is much thicker than the grooved portion.  By hanging the thicker, outer portion off the platter, better contact between the record and platter is made.  That's an old Goldmund Relief Mat. It looks like they chose the perfect diameter as the LP begins to get thicker right at the edge of the mat.  In fact, the entire mat fits the LP like a glove.  It perfectly matches the contour.  It even matches the stepped portion of the label area.  It's more apparent when the image is viewed full size.

However if I interpret your motive or question. I don’t know how a tonearm setting can be set to anticipate and compensate for this variance.

Any arm with adjustable azimuth will be able to compensate.  You just need to figure out a way to adjust azimuth while taking that 0.12 degrees into account.  I've figured out a way to do exactly that and will be testing soon.

I always check azimuth in the middle of a thrift store record. And several 1/1000ths of an inch matters not! Not in the real world!!

I always set all cart adjustments with it aligned exactly half way in the middle of the record. On my VPI Classic TT it specially matters for VTF and anti skate. But it would also be beneficial for azimuth if all records are built like the one you tested, which I doubt. Anyway, to test a cart alignment either at the beginning or at the end of a record makes no sense at all. Always test the middle for the best average adjustments. 

Since the angle of incline appears to be constant from outer to inner grooves, seems to me if you set azimuth correctly at any point on the LP surface, there would be no problem related to a changing azimuth angle.

Another vote for the middle. 

Every record is different depending on the flatness of the shellac master. What does it mean? Absolutely nothing. The geometry of the groove depends entirely on the orientation of the cutting head. It stays perfectly vertical regardless of the thickness of the record.

The tip of all styluses is radiused and does not have to be perfectly perpendicular to the groove. 30 seconds one way or the other is not a problem. Some  styluses like the Replicant 100 are more pointy (the radius is smaller) and are more exacting. 

ketchup, I can appreciate your logic concerning the mat you have and I agree on a hard mat that makes sense as the only way to go. However I have a felt mat on my Rega and would think that the vinyl rests with a fair distribution of pressure across the playing surface. In addition to that I have recently added a Michell clamp to my TT and hope add to that equalization of pressure. I do realize that the raised edge and lable area have been on records for as many years as I can recall, of course that practice goes back to the days of stacking records on automatic turntables. A practice that hasn't been used for decades, so it kind of suprises me that modern day records are still pressed in this manner. But I guess it does drastically reduce the chance of the stylus exiting the record off the lead in. 

But again at the end of the day, I appreciate the time and effort you spent pointing out the variance in thickness. I found it mind provoking in the physics that a tonearm and cartridge must overcome in revealing the information found in these "somewhat" flat peices of vinyl. 

Theo has it. LPs were thicker at the edge and at the label so the lps didn't scratch each other when they dropped from a changer onto the spinning disc below.
I had a Garrard SL95, Dual 1219 and a trusty Benjamin Miracord 50H. Amazing machines.

And then there was DynaFlex...

@lewm 

Since the angle of incline appears to be constant from outer to inner grooves, seems to me if you set azimuth correctly at any point on the LP surface, there would be no problem related to a changing azimuth angle.

You are exactly right.

Just measured another one for fun This was a 158 gram Hickory. The thickness of the grooved portion ranged from 0.053" at the beginning of the first track to 0.063" at the end of the last track. This means that the top surface of the LP will be at a 0.18 degree angle if it’s laying on a flat/level platter, or your azimuth will be off by 0.18 degrees if you set azimuth with a mirror on your platter.

That’s a lot. I just had two precision shims next to each other that measured 0.0 degrees and 0.12 degrees, and it was very easy to see the difference.