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I thank John Carmichael for his interesting
experiment on the different types of nodi since I am very interested in this subject ;
I agree completely with the
analysis made by Frank King in his Email (August 6) I think however that the experiment with the
disk with the hole can give
distorted results since the plane of the hole has been taken orthogonal to the
style and parallel to the plane.
In this way the image of the hole, when it is
visible, is perfectly circular ,
but its brightness decreases very quickly when the angle between the hole axis
and the rays from the sun increases. In the second Johns experiment this angle is
around 80.1° and causes, as clearly
Frank has shown, the disappearance of the image of the hole itself. I would like to point out however that in a horizontal
sundial, for a place with latitude = 45°, the rays of the sun have this
inclination only around 1h before the sunset or after the dawn and therefore
only in extreme points of the dial.
As King has already written the ratio R=( Distance hole-shadow / Diameter of
the hole) = 558 : the spot of light decreases in brightness when this ratio R
gets over the value 107.5 and
disappears when it becomes greater than 200-300 ( around ). When the ratio R becomes very great, in practice higher than 400-500 (pin-hole or stenopeic hole), the
spot of light has no more the shape of the hole but it is the image of the sun ,
whatever is the shape of the hole itself. --------------------------- I think that it is advisable that the plane of the hole is a polar plane with the hole axis on the intersection
among the equator and the meridian planes. Obviously the image of the hole now appears
elliptic and no more circular. In this way, at noon, the angle between the
rays from the sun and the hole axis
is always less than 23.5° and also on the winter solstice
the ratio R = 48 and the spot of light is clearly
visible. Also in the extreme points of the dial the
things improve.
A hour before sunset we have: - on summer solstice the angle between Suns
rays and hole axis = 41.3°; the observer sees the hole (that
appears elliptic) under the angles 26 x 36 '. The ratio R =99.4 - on the equinoxes the angle between rays and
hole axis = 35°; the observer sees the hole with axis
of 32x39'. The ratio R=106. -on winter solstice the angle = 53.7° and the
observer sees the hole with axis of
18x 30 '. The ratio R =190
Therefore only under these extreme conditions
(1h before the sunset in winter) the spot of light if greatly attenuated. Best wishes Gianni Ferrari
P.S.
- In Cassini sundial in S. Petronio (Bologna) the ratio R = ( Distance hole-spot / Diameter of the
hole) changes from 1070 to 2670 during the year
P.P.S. Here
the weather is very hot ,
and I hope that mine calculations are correct :-) |
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