Good post Bill.
I would also add that if you ride any distance on a singlespeed freewheel or single fixed, it is advisable to get a handle on your natural cadence for pushing the bike along at a comfortable cruising pace, then you will be able to fine tune the gear.
As Bill says, he found his comfortable cadence for riding on the flat and when a hill appeared, his cadence dropped. On a singlespeed, this happens and there will be a gear which suits flat and hills. The steeper the hill, the lower the speed and cadence. When you become a master of spin and grind; and get the gear right for you, long rides on a fixed will be a real treat.
Owners of Sturmey AW3 will know that the range of ratios is not wide enough; and the steps between gears is too wide. The bike can be geared for mostly hills or geared for mostly flat. Knowing my natural cadence, I can use an 18, 19 or 20 rear sprocket depending on the terrian I'm to ride.