How to measure female taper with ball

In this post I will guide how to measure female taper with two balls and Vernier caliper.
α: haft taper angle
R: radius of the large ball
r: radius of the small ball

Step 1: Drop the small ball in to the taper and use the Vernier caliper to check distance of 1st ball.

Step 2: Drop the larger ball in to the taper and use the Vernier caliper to check distance of 2nd balls.

How to calculate taper angle?

As picture above, Sinα =O2O3/ O1O2 = (R-r)/(A-B-R+r)

You can see this video below for more detail.