How could I calculate the correct distance from the runway to be able to fly a continuous downwind to final turn?
Turning at 3 deg/sec, a 180-degree turn will take 60 seconds. If the entire turn is performed at 63 knots, the aircraft will travel 1.05 nautical on a half circle (assuming zero wind). The radius of the circle will be the circumference, 2.10 divided by 2*pi = 0.3342 nm. Therefore, x = 2*0.3342 = 0.6684 nm.
If starting at 90 knots and slowing down to 63 knots, the trajectory will not be a a semi-circle but rather a section of a spiral. The starting radius will be 0.4775 and the final radius 0.3342. In this case, x will be approximately 0.8117 nautical miles. To get an exact value for x, an integration must be performed.