Hello Frank and all, I am surprised that no-one has yet give a definitive answer to your puzzle. The clues have all been posted. The dip correction (0.97 * sqrt h)gives the change in altitude with height. The path of the setting sun is described by the angle Psi( where Cos Psi = Sin Lat / Cos Dec). From these two relationships and some guesses on your friends location, I conclude that he had not just 4, but over 7.5 seconds to climb to the next deck. His feat of witnessing the instant of sunset three times in one evening now becomes plausible, if not quite credible.
The weather ship that he was on must have been a typical coast guard ship. I have assumed decks at 16, 25 and 36 feet above the water line. This makes the square roots easy (4, 5 and 6). Approximating the 0.97 factor in the dip equation as ~1.0, the difference in dip correction between the decks is 1 minute of altitude. If the sun sank straight down as it does at the equator, this would give the time angle of 4 seconds per deck as you mentioned. But this ship was not likely to be on the equator, but somewhere near the British Isles. I am assuming a latitude of 55 degrees and a summer solar declination of 15 degrees. Solving Cos Psi = Sin Lat / Cos Dec with these inputs gives the angle Psi as ~32 degrees. This is the angle the sun's path makes with the horizon as it crosses at sunset. From simple geometry of the triangle with the altitude of 4 seconds, the hypotenuse (the suns's path) is 7.5 seconds. (4 sec / sin 32). This would allow sufficient time to climb to the next deck but little time for viewing the green flash phenomenon. The green flash is a new tangent to go off on. Jules Verne used it for the story line in his novel "Le Rayon Vert". The physics, although complex, are now better understood. I have enjoyed many Great Lakes and ocean sunsets but I must confess to never consciously observing the phenomenon. When I first heard of it while vacationing in Hawaii, I dismissed it as an urban legend. Now I know what to look for. A web search on "green flash" will bring up lots of interesting URLs. A couple are: <http://pw2.netcom.com/~flzhgn/grnray.htm> for pictures, or <http://mintaka.sdsu.edu/GF/index.html> for the Green Flash Home Page. How many of you have seen the phenomenon? Roger Bailey Walking Shadow Designs 51 N 115 W (and surrounded by the Rocky Mountains which give local "sunsets' when the solar altitude is 13 to 17 degrees) At 03:55 PM 1/30/99 +0000, you wrote: >Hi John and others in the golden west, > >You make the case that the sun truly sets earlier than it appears to do. >If, as you say, 34 minutes of arc represents 2.26 minutes of delayed >sunset time due to refraction, we are getting into seconds. In that >case we must do what the Nautical Almanac does not, and consider the >height of the observer's eye. > >The late Mr. E.W. Barlow, a meteorologist in the British Met. Office >once told me that while serving aboard one of the ocean weather ships he >saw the green flash (visible under very clear conditions at the moment >of sunset) three times at a single setting. This he said he achieved by >moving to successively higher decks as the sun went down. > >Pondering this, I have reckoned that if the decks were, say, ten feet >apart he would have about four seconds to move from one deck to the >next. I wonder if, being prepared, such a feat would be possible and >whether anyone else has ever attempted it. Or was he just hauling my >leg? >Frank > > >-- >Frank Evans >
