Better circling with math.
Roger Kontak's article "Circling with Precision" (October 2005 IFR) was very interesting and thought-provoking. However, the math for the opposite-end approach, though accurate, was perhaps a little challenging under real-time conditions just underneath the cloud base. The penultimate section was entitled "Making it Simpler," and I'd like to suggest a way to do just that.
I like standard-rate turns! They are easy to maintain manually and the autopilot can do them hands-off. Also, their parameters are easy to remember: 120 seconds circumference, 40 seconds diameter (OK, 39.2 seconds).
The illustration assumes a 5,000foot runway and a circling minimum of 500 feet AGL.
The procedure is quite leisurely and almost automatic--no calculations and it stays within the VMA for all aircraft categories.
First, get to the MAP and maintain minimum until you've lined up with the runway and crossed the threshold to get a reading on the windsock. This is where altitude hold on the A/P really helps. Also, this might be a good time to program "Set OBS and Hold" on the GPS if you have one so as to give you added situational awareness.
Then, when you're ready (say, 10 seconds after crossing the threshold) start a standard-rate turn to 45 degrees off the runway. Time for one diameter (40 seconds +/- a little bit to allow for any cross-wind) then start the standard-rate turn back to the runway. Maintain minimum until 90 degrees to the runway and it's in clear view. Turn off the A/P (if you're using one) and hand-fly the airplane to a perfect landing on the VASI or PAPI. Since it's all geared to standard-rate turns, it's easy and safe to increase or decrease bank angle under visual control.
Read this once and I bet you can recall it next month when you need it!
Timing for 40 seconds will give you one standard-rate turn diameter for any true airspeed--a clever solution. When it comes to real-world application, success will depend on when you start that 45-degree turn and what correction you allow for the winds. As we said before, try this on a clear day with a safety pilot so that we don't get nasty letters from the lawyer representing your estate.