Let me introduce a couple of comments on Bill Gottesman's formula to
calculate the declination
of a wall (a lot of thanks Bill and Roger!). Sorry if they are on his
original article, but like many
members on the list I do not have access to it
[1st] We can trace a lot of references to this formula in many
classical gnomonics books. In fact
his square is a smart kind of 'fake vertical gnomon'. For instance, in
pag. 75 of Savoie's "La Gnomonique"
you can see the same formula generalized for any inclination of the wall.
By the way, perhaps we could avoid the problem of the double solution by
posing it as an arctg(),
because most programs include the useful function atan2(x,y). Therefore
the formula would be something
like:
tan(A-D) = sqrt(cos²(h) - sin²(h_eq) ) / sin(h_eq) -> D = A - atan2(
sin(h_eq) , sqrt(...) )
where h_eq is the 'equivalent altitude' of the sun over the wall,
calculated as tan(h_ea) = L(gnom)/L(shad).
If am not completely sure that this would always work well, but it's an
alternative option
[2nd] Yvon Masse describes in his web a wonderful procedure to
calculate simultaneusly the inclination
and declination of any wall just using a single measure like that by
Bill (well, we must measure as well how
much the square diverges from the greatest slope line). See the link at
the NASS.
Ah, and I forgot a small piece of advice: make sure that the square lies
perfectly perpendicular to the
wall's surface. Otherwise you might introduce an unnaceptable amount of
error!
Best regards,
Anselmo Perez Serrada
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