Solar Geometry

Solar Geometry refers to the position of the sun on any day in relation to the earth.  It is used when finding sunrise and sunset, determining where to place solar panels on a house, best direction to build a house for maximum solar exposure so it doesn't get too hot in the summer.

First off, the location of the sun is represented by two coordinates, much like a point on a graph.  Instead of using x and y, they use the solar azimuth which refers to the clockwise movement between the sun and the cardinal direction of true north and solar altitude or elevation which is the angle of the sun from the horizon.

Then there is solar declination which is the angle of the sun's ray as it is extended to the center of the earth and the equatorial plane.  If you look at a graph of the solar declination over the period of a year, it resembles a sine curve between 23.5 degrees and -23.5 degrees.  At the Vernal and Autumnal Equinox, the declination is zero while at the Summer Equinox is + 23.5 and the at the Winter Equinox it is -23.5 degrees.

There is also solar noon defined as when the rays of the sun are hit perpendicular to the planet based on the longitude and noon occurs at exactly the same time everywhere along the longitude.  These are some of the basic terms. 

Penn State has produced a 68 page activity guide covering everything from longitude to latitude, to earth's orbit around the sun but towards the end, it provides information on solar position.  This section includes the three steps needed to calculate solar time using standard time, an equation of time for the position and date, and the longitude correction. The longitude correction is expressed in either degrees or radians based on preferred use. All the equations needed for students to calculate the solar time for their location or any location around the world.

Once the solar time is calculated, the activity has students calculate the solar declination for a specific location. Now a student has everything needed to calculate the sun's position in the sky.  This information is important if someone is planning to install solar energy.

This site has some great diagrams complete with all the mathematical equations for solar geometry. The diagrams provided show how the angle of the sun changes the amount and direction of light which is used to create a sun's path for a specific location which is used when planning and installing solar energy.

Finally, Teaching Engineering has several lessons which could be used to reinforce the above math.  One lesson has students learning more about solar angles and tracking systems, determining the amount of solar energy available at a specific place and time, learn about the maximum power point of a photovoltaic cell, and ways to increase the amount of solar energy hitting a cell. 

Let me know what you think, I'd love to hear.  Have a great day.