Hi Gianni,
Thank you for your splendid response...
> I hope that our Emails, interesting for us, don't bore
> other readers :-)
I promise this one will be short!!
Oh, and your image arrived first time (a little corrupted but
I could read it).
This time I agree with EVERYTHING in your reply.
> For a declining sundial I think that the direction of the axis
> of the hole should coincide with the intersection of the plane
> of the equator with the substyle plane (hour plane normal to
> the dial and on which the polar style lies)
Ah. Now that IS a good rule and, as you say, it works for walls
that face east and west too.
> In the figure....
Yes, I agree with your calculations.
> CAMERA OBSCURA MERIDIANA
I am most grateful to you for your comments here. You are, of course,
absolutely right to use sin(h) cubed. I was comparing solid angles.
You compare brightness which is definitely better.
> sin(45+dec) x sin(45+dec) x sin(45+dec) x sin(45+dec+ang)
Yes!! Agreed.
> I try to explain this in the note at the end, so the readers not
> interested can jump it :-)
Yes, your explanation is very eloquent and easy to follow.
I see from a very old message that I once omitted a sin term before
and you corrected me. I must do better!
> Then in my opinion the function to use is
>
> sa(dec,ang) = sin(h) x sin(h) x sin(h) x sin(h+ang)
> or
> sa(dec,ang) = sin(45+dec) x sin(45+dec) x sin(45+dec) x sin(45+dec+ang)
Yes but we must change the name...
I chose sa for Solid Angle. My function is correct for comparing solid
angles but solid angles are not (quite) what we want!!
Using your function, the King angle is now 108.829 degrees...
sa(+23.5,108.829) = 0.038 = sa(-23.5,108.829) = 0.038
This is very academic! The plane of the hole almost aligns with the sun
at the summer solstice. The difference is only 2.67 degrees. The hole
would have to be in a very thin part of the wall or the summer solstice
point would get no light at all.
You could make the hole elliptical which would help...
If the height of the hole is 20,000mm then the hole could have a
major axis of 160mm and a minor axis of 20mm. This would give you
an image all year I think.
At the summer solstice 1/R would be about 3000 and at the winter
solstice 1/R would be about 450 which is acceptable. Unfortunately,
at the equinoxes, 1/R would be about 400 which is getting rather low.
I don't think Cassini would accept that!
I think we can conclude this most interesting exchange.
I must find an English church which will let me try some experiments!
Thank you again
Frank
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