LP Thickness/Taper

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.