★ CODING ★ LISTINGS ★ FOLLOW THE SUN TO THE S. POLE (COMPUTING WITH THE AMSTRAD) ★ |
| Follow the Sun to the S. Pole (Computing with the Amstrad) | Coding Listings |
ALEATOIRE looks skyward for an answer to navigation problems ONE of the great myths of British history is that in January 1912 Captain Scott arrived at the South Pole only to find, to his great surprise, a tent and flag left there by the Norwegian explorer Amundsen. Furthermore we have the impression that Scott took a few photographs, then almost immediately started on his fatal return journey and only failed to reach safety by a mere 11 miles. The fact is that in those days any navigation near the Poles was very inaccurate. Amundsen arrived near the Pole by dead reckoning on December 15, 1911, but then wrote: "Of course we are not exactly at the South Pole - but we must be very close", by which he meant he must be within 10 miles of this imaginary point. Amundsen then set about calculating his position as accurately as possible with the equipment available, a sextant and a chronometer. In good conditions these can fix a position to about one nautical mile or one minute of arc on the earth's surface, which is 6080 feet. Actually the chronometer was useless for the time being because Amundsen no longer knew which time zone - hence longitude - he was in. He had to observe the sun for a period of 24 hours to find the time and direction of its zenith - highest -position, and reported: "It is interesting to watch the sun wander round the sky at about the same altitude day and night. I think we are the first to see this strange sight". Eventually Amundsen found he was at longitude 120 degrees East and latitude 89 degrees 54 minutes South - about six minutes of arc or six nautical miles from the Pole. The next day he travelled this distance by dead reckoning and then took observations for another 24 hours. He now knew that he must be within about a mile of the Pole so he sent out two men on skis to box the area with flags. Subsequent analysis by a committee decided that one of these men must have passed within 200 metres of the actual point - a remarkable performance. Still not absolutely sure of direction Amundsen then retraced his tracks, left a black flag some 15 miles from the Pole on about the 160 East meridian and then picked up his 169 Now both Amundsen and Scott were aware of each other's presence and purpose on the polar plateau and the black flag, deliberately left in the path of Scott's approach, was there to tell him that Amundsen had won the race. One month later the flag was found by Lieutenant Henry Bowers R.N. who had been included in Scott's party at the last minute when it was belatedly realised that only he could navigate accurately in this featureless region. Oddly enough the flag, which might have saved their lives, was almost completely ignored and the British party wasted three precious days in the area trying to make more accurate measurements than Amundsen. In the course of this exercise they found Amundsen's spare tent and flag but the irony is that, lacking ski expertise and so being unable to box the area, they never actually got closer than one mile to the Pole. I will now attempt to show that given ideal conditions, instruments and a calculator, sun navigation is not difficult in principle and can even become an interesting puzzle. The earth is a sphere 360 x 60 = 21,600 nautical miles in circumference. It rotates once every 24 hours and is tilted 23.44 degrees to the plane of its orbit around the sun. On December 21, just after Amundsen's survey, the South Pole is at its maximum tilt towards the sun (see Figure I). Now consider Amundsen's observations on December 16. If he had been exactly at the Pole he would have observed the sun to be at 23 degrees 23 minutes and still slowly rising. Figure I: Earth tilt of South Pole towards the sun is maximum about December 21 >> What he actually observed was a minimum of 23 degrees 17 minutes at 1600 GMT rising to a maximum of 23 degrees 29 minutes 12 hours later -0400 GMT on December 17. Hence his position was six miles from the Pole on longitude 120 East. To check this enter Program I which, using the SIN function, simulates the changing tilt of the earth as it travels around the sun. First test it by assuming that the date is December 21 and you are at the South Pole -90. It's a puzzling place, since your longitude can be any number from 0 to 180 degrees East (+) or West (—) and your watch can only give a global time, GMT, or the time of the sun's crossing the Greenwich meridian. The input is therefore: Day, Month 21,12 |
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