To calculate the side force needed to slide a ball plunger out of its detent hole, refer to the free-body force diagram to the left.
End force (F) depends on how far the spring will be compressed, which depends on how far away from the sliding surface the ball plunger is installed. Maximum spring compression and end force occur as the ball breaks out of its hole.
A CL-40-BP-3 ball plunger (1/4-20) exerts an initial force of 4 lbs, a half-way force of 8 lbs, and a final force of 12 lbs. With a 90° countersink angle and half-way compression:
To obtain full locking torque, countersink the installation hole to avoid cutting the locking element. Countersink at a 90° angle to a diameter 1/32" larger than the major thread diameter. Then, as you screw the plunger into its hole, the locking element will be compressed, not cut.