I’m not even sure if this is a safe/allowed procedure at controlled airports so it is purely hypothetical.
Assuming there are calm winds at the field, is there a way to calculate the distance your plane must be from the centerline (see “x”) of the runway while on downwind, so that once you start your turn to base and final thereafter, in a constant rate turn (assume 3 deg./sec.), that you will end up rolling out on the centerline of the runway?
Speed changes (slows) by 27 knots from the beginning of the turn to the end of the turn.
Essentially, if I wanted to execute an 180 degree turn at 3 deg. per second, while slowing the airplane from traffic pattern speed (90 kts) to final approach speed (63 kts), how far away would I need to be from the runway while on downwind before beginning the maneuver? The goal is to be able to use this on any plane given their own specific traffic pattern speed and final approach to landing speed.