Calculating Noon Sun Angle:
When you are looking at the altitude of the sun in relation to the angle of
the earth’s tilt, you begin to understand how and why we have seasons on
this planet. Because the earth is tilted at 23.5 degrees, the sun’s energy is
diffused over a greater surface area as the angle of the earth’s surfaces
increases north or south from the Equator.
As stated in your textbook, pg. 48, the only point receiving incoming solar
radiation or ‘insolation’ perpendicular (at right angle, or straight overhead)
to the surface of the earth is called the Subsolar Point. The Subsolar Point
occurs moving north or south of the equator between 23.5 degrees north
(Tropic of Cancer) and 23.5 degrees south (Tropic of Capricorn) and
energy in these areas is more concentrated. All other locations north of the
Tropic of Cancer or south of the Tropic of Capricorn therefore receive less
energy at a greater angle. The more you increase the degrees of latitude,
the greater this influence on seasonal variation.
The Noon Sun Angle is one way to develop an understanding as to the
angle of insolation making its way to the surface at any location. The sun
can only go as far as straight overhead – once earth rotates past noon, the
sun begins its decent in the sky. So, the maximum angle of the sun can
only be 90 degrees, which is the Subsolar Point.
Therefore, if you know the latitude of your location, and the Subsolar Point
on a certain date, you can figure out the Noon Sun Angle. When you know
that, you will see the reason why days are shorter or longer during the
various seasons.
This is an example of how to calculate the Noon Sun Angle. You are
looking for the angle of the sun in the sky from where you are standing.
Find: The Noon Sun Angle in San Diego (32º North Latitude) on October
20.
Start with recognizing whether the location you are calculating for is north
or south of the equator. You know from the problem that the given location
is 32º North Latitude. Now, go to your Analemma.
The Analemma shows the path of the Subsolar
Point throughout one calendar year. You will
look to the outer edge of the Analemma for the
Month. Then, find the exact day for the problem
that you are given. Now, follow a straight line
across to the center black-and-white measure
line. That will give you the altitude in degrees of
the sun on that date. You will notice that the
Equator is not at the crossing of the figure 8 on
the Analemma, but at the date of the Vernal and
the Autumnal Equinox.
If the Subsolar Point is north of the equator and
your location is north of the equator, you will need
to subtract one from another. If the Subsolar
Point is south of the equator and your location is
north of the equator, then you will add the two
degrees.
On October 20 the Subsolar Point is 10º South
Latitude
So, make a drawing of the
location, the line of the equator
and the Subsolar Point (from
your Analemma) on paper.
This will enable you to decide
whether the degrees are going
to be added or subtracted. It’s
a simple calculation to figure
out what the Noon Sun Angle
is at your location on that day.
This is your formula to calculate the Noon Sun Angle:
90- (Degrees of latitude of your location +/- Subsolar Point) = Noon
Sun Angle
The final equation that looks like this:
90 - (32+10) = 48 degrees
In other words, the sun will only get 48 degrees high in the sky, so it must
be autumn! The sun will rise later and set sooner, and the weather will be
cooler.
If the Subsolar Point is on the same side of the equator, your equation
would look different:
90 - (32-10) = 68 degrees
The Subsolar Point is now higher in the sky, and it is springtime.
Also, on the analemma, remember to double check whether the Subsolar
Point is North or South of the Equator in relation to your location.
Remember: If the Subsolar Point is on the same side of the equator as
the location, subtract. If the Subsolar Point is on the opposite side of the
equator as the location, add.