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Mark Knudsen You wrote:

Question? There is a U Tube program were a man used a board with a wire to cast a shadow , he marked the points of the shadow with a pencil every couple of minutes than recorded the time. At the peak , shortest shadow he recorded thi time Ned used it to calculate from GMT for his longitude  is this simalar to what you are doing with graph paper. If I remember he was only point something of a kalometer off. Comments please.

All these methods rely on the principle that if you stand in the same spot and observe the Sun, it will describe an arc in the sky and reach its highest point at local noon.  If you can measure the Sun’s highest altitude and know its declination, you can calculate your latitude very simply.  It’s called Meridian Passage Latitude or Mer-Pas.  If you are able to mark the exact Greenwich Time the Sun reaches its highest point you can also work out your longitude.  For centuries the main problem was knowing exact Greenwich Time, but in this day and age, that is no longer a problem.  However, unless you’re starring in a movie, the problem of spotting the exact time the Sun is at its highest altitude still remains, because close to that point, the Sun’s altitude varies very slowly, perhaps less than two minutes of arc over ten minutes of time.  This is a particular problem with an aircraft sextant where aiming can be very subjective, even for the same observer from second to second.  The slightest change of pressure on the index thumbwheel can easily put two minutes of arc onto the altitude counters.  Therefore, a four minute time error in spotting Mer-Pas time is not out of the question, and what would give you a whole degree of longitude error.  Hence the need to take a series of observations from about 30minutes before until about 30 minutes after the expected Mer-Pas time, and then to fold the paper over and try to balance both sides in order to find the centre of the arc, as Frank suggests.  You need a really exaggerated vertical scale to get a good attempt at this.

Shadow methods simply replace the need for a sextant by measuring the length of a shadow and using trigonometry.  They commonly came up in books with titles like ‘A hundred and one things for boys and girls to do in their holidays’ and ‘A charismatic teacher’s guide to teaching trigonometry’.  I’ve toyed with the idea, but you need a good imagination and have to be prepared to be disappointed.  You need a clear sky and a strong Sun to get a sharp shadow edge; flat, level ground or surface; and those who must be obeyed mustn’t mind it all happening over lunchtime.  You still have to be able to mark the point directly below the shadow item in order to define the vertical and have somewhere to take the base measurement from.  With care, luck, and a big enough model, you might get reasonable latitude, but IMHO it would be hopeless for determining longitude.   If you just wanted time, a simple Sun dial might be a better bet.  DaveP