Improving lathe turning accuracy.

[tonyfoale]

If you use this idea, be careful when using a carriage stop to turn up to a shoulder. Arccos(arcsin(0.1)) = 0.995 so the tool will move closer to the shoulder by an amount only a tiny bit smaller than whatever you dial in on the compound.

Marv,

You are right and wrong, arccos returns an angle not a relative length. arcsin also returns an angle which we usually express in deg. or radians. If in deg. then it 5.74 but that is an invalid argument for arccos. If in rads then it's 0.1 and arccos = 84.3 deg or 1.47 rads, neither equals 0.995.
However, cos returns a relative length and Cos(arcsin(0.1)) does = 0.995.

Of course you are right about turning to a stop, you must allow for the self evident fact that winding the compound rest in with a shallow angle will invalidate the carriage stop setting.