Hello, Alberto!
Yes, it does make a fine math problem, one you have to solve numerically
using a computer. You will indeed need two spindle-shaped gnomons, one
for spring and one for autumn. Mathematically speaking, the gnomons are
however infinite surfaces, that is, they flare to infinity near the times
of solstices! So, a totally accurate solution working throughout the
year does not exist. Various approximative solutions abound, of course.
I once wrote a report which contains all the math and lots of pictures:
K. Ruohonen: Designing Sundials by Matlab and Maple. Tampere University
of Technology. Department of Information Technology. Mathematics
Software Report 9 (1994)
It is also available in the net (in Postscript):
ftp://ftp.cc.tut.fi/pub/math/ruohonen/Raportit/PRep9/
(For those interested, the math is here formulated using matrices
and vector calculus.) In principle, the sundial face could be arbitrarily
oriented but the gnomon surfaces tend then to be very complicated. Simple
things like time shifts are easily incorporated.
Best regards
Keijo Ruohonen
>
>Very clear, David.
>Thank you also for the marvelous photo .
>My doubt is for plane dials however oriented :
>in this case does exist a shape of the gnomon good for all the hour lines ?
>This could be a fine math problem to solve, but I'm lazy !
>
>Best regards
>
>Alberto Nicelli
>
>> ----------
>> From: David Higgon[SMTP:[EMAIL PROTECTED]
>> Sent: martedì 15 settembre 1998 10.18
>> To: all
>> Subject: gnomon shape and EoT
>>
>> <<File: CONNOISB.JPG>>
>> Alberto,
>>
>> Yes it is, is the short answer. In fact you will need two shaped gnomons
>> -
>> one for the spring and one for the autumn. For each gnomon to stay in one
>> piece, it has to have some notional diameter to which the EoT is added or
>> subtracted. In the morning one side of the gnomon will cast the shadow,
>> whilst in the afternoon it will be the other side. This means that at
>> noon
>> there are two parallel lines, separated by the notional diameter of the
>> gnomon. This allows for the change of which edge of the shadow you read.
>> I don't know if I've explained this as clearly as I should, but if you
>> need
>> more information, drop me an email.
>>
>> My father makes an equatorial dial with just such gnomons and I have
>> attached a photo of one - I hope it's not too big a file (apologies if it
>> is).
>>
>> Regards,
>>
>> David Robert Higgon
>> London
>>
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Keijo Ruohonen Tampere University of Technology
[EMAIL PROTECTED] Department of Mathematics Voice (+358) (3) 3652420
http://www.cc.tut.fi/ Tampere, FINLAND Fax (+358) (3) 3653549
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