I'm building a phase control system for simple power control to a given load (heater for example).
I need an equation to find the relationship between angle of TRIAC firing vs power delivered to load (in percent).
Let's say that my AC mains frequency is 60Hz. If I need to delivery 50% of power to the load I need to fire the TRIAC every half half wave of the AC (every 4.16ms after the zero-crossing). However, since you all know the power line is not linear, but a sine function, so I cannot get a simple rule of three to find the power x time relationship.
What I need is an equation that solves for a given power (eg. 35%) I get the time after zero-crossing that the TRIAC needs to be fired.