[FCGears] Calculating the root diameter of a bevel gear

[ppedrosa]

I'm looking into cutting away the bevel gear "saw" that is generated by FCGears along a line that is perpendicular to the pitch angle line starting from the root of the gear.

I don't want to hardcode any values so I'm trying to figure out the formula for the radius of the root of the gear at the base of the gear.

I was able to figure out the radius of the tip of the tooth using the addendum and also the root "base" using the dedendum (ie clearance = 0) but I can't figure out how positive clearance is applied to the tooth. I tried to calculate variable clearance by extending the dedendum (figure out the angle of dedendum + clearance) and also constant clearance by using a line that is parallel to the dedendum angle line at distance clearance from the dedendum angle line but neither worked

Any help would be appreciated