So no formula? Not even as a starting point?
Linear power supplies are fairly challenging to model numerically, partly because there are so many variables that all matter enough to worry about. Start with the transformer--you have to know its effective output source impedance and reactance. The rectifiers have a varying V
f and shutoff characteristics.
However, if you want a method of estimating needed capacitor size, I'd use a first-order hold-up approximation to start At 60 Hz, you get an incoming peak every 8.3ms. Assume the capacitor charges to that peak and then determine what minimum the voltage must stay above as the capacitor discharges (the hold-up threshold). Figure out how large the capacitor must be to supply the load current for 8.3ms without dropping more than the difference between your peak and the holdup threshold.
A 1F capacitor will drop 1V every second as it delivers 1A. So C = 1A*1s/1V = 1F. Sub in your values, say you're willing to accept 5V of ripple and the load current is 500mA. C = 0.5*.0083/5 = .00083F or 830µF. Now factor in some second order corrections such as the capacitor not actually charging to the peak (due to resistance) and the hold-up time actually being less than 8.3ms because the rising wave will catch up some time before the peak. Both of these factors reduce the needed size, perhaps to about, hmmm, about 500µF or so?