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David Harrison
Thank you for the photographs.  Clearly, I didn’t explain what I wanted very well.  However, I’ve managed from the side view that you posted.  Hopefully, you can see from the diagram below what Geoffrey was saying.  If the Sun is higher in the sky than 53 degrees, it’s shadow will not reach the numbers.  In the Northern summer, the Sun reaches 23.5 degrees above the Equator, and this affects how high it is in the sky at noon.  Below 60.5 degrees latitude North the Sun would be greater than 53 degrees high in the sky at noon, so the device would be no good for mad dogs or Englishmen.  That’s not to say it wouldn’t be OK earlier or later in the year or earlier or later in the day, but you get the idea.

Looking at uses, I can see three possible uses for the device.  You could use it to take bearings on points to produce lines of position.  You could set the azimuth disc reading corresponding to your desired direction of travel.  Then, holding the device with the arrow pointing forward, walk, ski, or ride in such a direction that the shadow of the sun forms a solid line through zero. In difficult conditions, you could send a walker, skier, or rider ahead; then hand wave them into position.  Then catch them up.  I’ve used this technique successfully in the English Lake District in mist with a magnetic compass.  It’s slow but surprisingly accurate. 

Regarding the formulae, testing means examining at least 16 possibilities, possibly 24, and using up a lot of backs of envelopes.  You need to look at least four heading sectors, before and after noon above Cancer and below Capricorn.  So far I’ve found they work on for all headings or bearings north of Cancer before noon. DaveP