samuelson measured: David's Blog: Navigation ? sextant and GPS

Sunday, January 27, 2013

David's Blog: Navigation ? sextant and GPS

Navigation ? sextant and GPS

There was a man on the radio this week talking about his sextant ? which was over 100 years old when he bought it some time ago. This was the only navigation instrument available to sailors for over a century. When searching for info for this entry I found a reference to Robin Knox Johnson?s circumnavigation of the globe 44 years ago ? he had no radio, a barometer from a pub and a sextant. How things have changed! GPS, now on most mobile phones can locate your position to within a metre or so.

Sextants rely on the knowing the exact time to calculate the position in fact the British admiralty sponsored the development of the first accurate timepiece that could go to sea ? pendulum clocks aren?t much use in a seaway! The balance wheel was the solution to this problem.

GPS rely on timing, too, but rather more precisely that a maritime chronometer. The basis for GPS is a series of satellites that orbit the earth ? not in synchronous orbits like communications satellites ? but with a period of just under 12 hours. These are equipped with extremely accurate atomic clocks. A GPS receiver will receive signals from at least four satellites and will calculate the distance from each based on the time take for the signal to reach the receiver from the satellite. It then calculates the position based on a mathematical principle called trilateration. This involved calculating the intersecton of the four or more spheres that are defined by the timings. Thinking of this in 3 dimensions is quite tricky (I always have to get an orange out when I try to think of the geometry of the earth!) In two dimensions, it?s a little simpler: here?s a local example. Suppose I?m 2.81 miles from Gt Missenden, 2.59 miles from Wendover and 3.33 miles from Princes Risborough. The first distance gives me a circle.?

The second ties the position down to two possible points

The third fixes me at Little Hampden

Now try to imagine this in three dimensions ? intersections of spheres. The calculation to achieve a position is pretty complicated. GPS devices can also calculate the position in a number of formats including the GB OS grid reference. I?ve put a map on the waymark outside outside our house with a grid reference read from my GPS. Lots of walkers stop to look ? but I?m not sure if the reference means anything to many of them!