With the recent talk of interval timers, I have to mention my swimming trip timer.
My wife and I like to leave our watches at home when we go to the lake in the summer. We want to get home at the time promised to those left behind, but neither of us is good at sensing the passage of time. There is a clock in the car but it's 5 minutes walk from the beach to the car park, so checking is not convenient. We tend to schedule things so that we get an hour at the lake, so I wanted to devise a 1-hour timer based on the sun (specifically on azimuth change). I knew that tan(15) is very close to 0.25 so at first I just poked a stick in the ground, measured off 4 hands along the shadow and one hand sideways, and marked the spot. When the shadow moved to my mark it was time to go. Towards the end of this summer I improved the scheme to allow for the fact that the sun's azimuth changes less in the late afternoon than in the early afternoon. I needed a smaller timer angle later in the day, which is the same as using a bigger radius. Ah ha! The clock hour is getting bigger as the afternoon goes by. Could I use that to determine radius? After a bit of trail and error and some calculations on a spreadsheet, I found a magic formula as follows: measure off as many units as the hour shown on the clock when we arrive at the car park, then go one unit sideways. That is, if we reach the lake at 3.30 pm (DST), I measure 3.5 units of radius for 1 unit sideways. It's as simple as that. We're at 45 N, the lake is only warm enough for swimming from mid-July to mid-Sept and we only go in the afternoon, arriving there between 3 pm and 6 pm. I calculated that in theory the method is good to within about 6 minutes given these constraints. In practice, limited testing of my new formula gave one occasion where it was wrong by more than 15 minutes -presumably the stick wasn't upright or if I didn't get the sand level, or perhaps I've got the formula wrong. But overall it seems close enough for us. My spreadsheet calculations showed that at my latitude the best results happen when the radius is Local hour + 1.25. We're at W63, and the 1.25 part is conveniently cancelled out by using daylight saving time and by our offset from the timezone meridian. Presumably equivalent rules could be found for other latitudes, but without the handy cancellation of the fixed adjustment. Steve
