Trigonometry help please, plunge depth for a v cutter!

[cncJim]

Hello,

I am trying to calculate the required plunge depth for a v cutter needed to produce a given diameter of hole.

Can someone explain the formula I need?

Thanks!

--------------------------------------------------
EDIT:

Answer:-

Z = Depth of cut
d = Required diameter of cut
a = Cutter tip angle in degrees*
f = Flat spot
r = Tip radius

V Groove type cutter with no flat spot.
Z=d/(2*tan(a/2))

V Groove type cutter with flat spot.
Z=(d-f)/(2*tan(a/2))

V-Groove type cutter with a radius tip.
Z=r-(r^2-d^2/4)^0.5, for Z<=2r
Z=r+(d-2r)/(2*tan(a/2)), for Z>2r

Ballnose type cutter.
Z=r-(r^2-d^2/4)^0.5, for Z<=2r

* The TAN() function in some applications (such as Excel) require the angle to be expressed in radians, Not degrees. Convert degrees to radians - Radians = angleInDegrees x (PI/180)
So in excel the first formula above would become:-
Z=d/(2*tan((a*(PI()/180)/2))