Lathe tool height

[Ken226]

It's almost the same as checking the headstock to the bed. Any difference in centre height makes such a small difference. Remember; this is a lathe not a cylindrical grinder.
If a tool is 0.015 below centre does the error remain constant or does it vary? It seems to me that the theoretical triangle shape varies depending on the distance from the centre.
Nobody sets their tool within half a thousandth !! - it's a lathe.

Yea, the error definitely varies. And non-linear in magnitude.

As the diameter gets smaller, the error gets bigger quickly.

A thought experiment: If the tool were .015" below center, when the part diameter gets to .03" in diameter, you wouldn't be cutting anything anymore.

Because you'd have a .03" diameter nub above the tool.

 

[Parlo]

Exactly .

Perhaps the experiment could be repeated to show the repeatability on the x axis. This has more effect on the diameter.