Dougal;Based on what assumptions?
Coarse threads or fine?
Mismatching elastic modulus of the bolt and socket?
What level of friction between threads (any lubrication)?
Linear elastic thread behaviour or yielding?
Three threads in 6061 aluminium can be stripped out very easily. Try it if you don't believe me.
Three diameters for reusable aluminium threads is a safe level for the worst case. It holds after bolts have been removed and refit many times.
In contrast one of the designers at my last job had M6 cap screws threading into 4mm of mild steel. Several of them stripped out during assembly of the brand new machine.
Is 3x diameter a engineering standard ? Is it for Aluminum and steel or both ? Not being an engineer, I am always trying to learn more.
So for a 1/2" bolt your suggesting the tapped hole be 1.5" deep ?