Anselmo Perez Serrada asked:
> Imagine an oriented wall (gnomonic declination equals to 0 deg in
> one side and 180 deg in the other), all of us know that the southern
> side is exposed more time to sunlight than the northern one, but where
> is this difference bigger? It is clear that in the equator and in the
> North Pole the rate is 50% to 50%, ie., both sides receive the same
> amount of sunlight through a whole year, so there must be in the middle
> some latitude where the difference becomes maximal. Which is that
> latitude?
What a relief to learn I'm not the only one who frets over such obscure
questions. ;-)
A few years ago I put my computer to the task of grinding out plots of the
annual percentage of sunlight available to dials at various orientations
and for various latitudes. I employed the straightforward, brute-force
computational approach. (My goal: to use the data to derive good approx-
imate expressions for predicting how many hours an arbitrary planar surface
receives sunlight. I've yet to work out these approximations, however.)
Here's a synopsis of my results;
Percentage of Annual Sunlight
on a Vertical Planar Dial
Latitude South-Facing North-Facing
-90 50.0 50.0
-80 42.4 57.6
-70 33.2 66.8
-60 21.2 78.8
-50 17.9 82.1
-40 17.8 82.2
-30 20.7 79.3
-20 32.5 67.5
-10 41.5 58.5
0 49.0 51.0
+10 56.5 43.5
+20 65.9 34.1
+30 78.3 21.7
+40 81.5 18.5
+50 81.4 18.6
+60 78.1 21.9
+70 66.0 34.0
+80 57.2 42.8
+90 50.0 50.0
Some highlights:
* The greatest percentage of available sunlight for a south-facing
vertical dial occurs at latitude +45 degrees. (Likewise for
north-facing vertical at latitude -45 degrees.) How much so?
If the weather is perpetually cloud-free, and if there are no
obstructions -- houses, trees, hills, etc. -- then a dial so-
oriented receives impinging sunlight 82% of the time the Sun is
above the horizon. Obviously, then, a north-facing vertical at
the same latitude only gets 100% - 82% = 18% of the available Sun.
* One would expect a direct-south vertical on the equator to receive
the same amount of sunlight as a direct-north vertical. This is
true to first order. But upon closer inspection, a slight asymmetry
is evident: a north-facing surface actually receives a tad more
sunlight throughout the year (51% versus 49%), a direct consequence
of the Sun dwelling longer in northern declinations because of the
Earth's slightly eccentric orbit.
* These results show there's good reason for vertical direct-south
dials to be more popular in north-temperate latitudes than in
tropical or arctic climes.
~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~
Mark Gingrich [EMAIL PROTECTED] San Leandro, California
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