If you will pardon an old fella here, the formula is AIRMANSHIP and EXPERIENCE.
The variables are infinite, distance of parallel downwind, head or tail wind on base, airspeed and weight to name a few.
You can't do a base turn on numbers alone you have to look out on a visual circuit. Most SOPs state 25 deg normal/30 max, so start off hard and ease out to final, monitoring the sink and C/L closure rate. Remember that the sink can sneek up on you in the turn.
Radar vectors being a different kettle of fish as the vector is usually 30/40 angle off and to an ILS or radial.
Most flight directors predicate at approx 25 deg bank achieved at 3 per sec average in and out of the turn in still air, which we never have.
Flight directors can be used in a visual circuit but have to be adjusted to what you are doing rather than you following what they tell you to do, which can be "fun" if you dont change your usual mindset.
I came from a jet operation in Aust where 95% of our approaches were visual 3 legs of a circuit. I now do 99% vectors to final and the rare visual ones are sometimes not pretty to watch, it's all experience and recency of the operation.
PM me if you wish.
