Understanding the solar tracker problem

Before embarking on the design of the solar tracker you must make sure that you thoroughly understand the nature of the problem. For this reason, you need to ask yourselves the following questions:

1. How does the sun move in the sky relative to a fixed point on earth? You intuitively know that the sun rises from an easterly direction, then moves across the sky towards the west, and disappears in a westward direction. But you need to better understand the nature of this movement. For example, from which exact direction does the sun rise, and how does this direction change throughout the year?
2. How do you determine the sun’s position in the sky relative to a fixed point on earth? What kind of coordinates do people usually use to determine the position of the sun in the sky?
3. Surely, you are not the first to think about designing a solar tracking system. How did people solve this problem and what kind of designs have they come up with?

The apparent motion of the sun across the sky

For an observer on earth, there are two elements to the sun’s apparent motion across the sky. An east-west element and an elevation (or altitude) element. The east-west element, as shown in part a of the diagram below, describes the sun’s motion as it moves from east to west. The elevation element describes the sun’s changing altitude above the horizon as it moves from east to west, as shown in part b of the diagram below.

The sun’s apparent motion during any single day is a combination of these two elements and follows an arc-like path. It rises from an easterly direction and its elevation gradually increases above the horizon as it moves towards the west. The sun reaches its highest altitude in mid-day when it is exactly south of the observer. The sun then keeps moving westward but its altitude decreases until it disappears into a westerly direction.

In the southern hemisphere, eg in Australia, the sun also moves from east to west but it culminates in the north. For simplicity, in the remainder of this design problem, we will restrict our discussion to the northern hemisphere. But the same concepts and designs apply to the southern hemisphere as well.

View the full size version of the sun’s motion diagram

The diagram above shows the two elements of the sun’s motion in the sky:

• Part a shows the east-west element of the sun’s motion.
• Part b shows the elevation element of the sun’s motion. The sun’s altitude increases from sunrise to noon, when it reaches its highest point in the sky, then decreases from noon to sunset.

Changes in the sun’s path in different seasons

For simplicity, when we speak we say that the sun rises from the east and sets in the west. But this is not always true. The sun only rises from due east (exact east) and sets into due west in only two days each year. In fact, during winter months the sun rises from a south easterly direction and sets into a south westerly direction. And in summer months, it rises from a north easterly direction and sets into a north westerly direction. But the exact direction and time of sunset and sunrise depends on the latitude of the point on earth where the observations are made. It also depends on the time of year.

Scientists have devised mathematical formulae and charts that determine the sun’s path at various times of the year. For example, the chart below, describes the sun’s east-west motion at various dates for the city of Rotterdam in the Netherlands.

View the full size version of the sun’s east-west motion diagram

The chart shows that in winter the sun’s arc, hence the day, is quite short. And at the shortest day of the year, which occurs on December 21st, the sun rises from the south east and sets into the south west. Conversely, in summer the days are quite long. And during the longest day of the year, which occurs on June 21st, the sun rises from the north east and sets into the north west. Only on March 20th (and September 23rd) the sun rises due east and sets due west. Furthermore, in summer the sun reaches a much higher elevation at noon time compared to winter.

So what implications does this have on solar trackers? Solar trackers must be able to rotate their payload (eg solar panels) horizontally from east to west to follow the sun as it moves from east to east. They also must be able to rotate the payload vertically from a horizontal direction to a vertical direction to follow the sun as it moves up and down the sky.

The azimuth and the altitude of the sun

In astronomy, the position of any celestial object, such as the sun, relative to a fixed point on earth, such as an observer, is determined by two angles called the azimuth and the altitude as shown in the diagram below. The azimuth angle is usually measured from the true north direction, and the altitude angle is measured from a horizontal line that extends from the observer’s location towards the local horizon.

Hence in this method of determining position, an object that is due north has an azimuth of 0˚, and one that is due east has an azimuth of 90˚. Similarly, an object in the horizon has an elevation of 0˚, and an object right above the observer has an altitude of 90˚.

Tracking celestial objects

The problem of tracking celestial objects, the sun included, is not new. Astronomers have long ago devised designs of mounting mechanisms that allow telescopes to track celestial object. One such design is shown in the following photo. This design is known as an alt-azimuth (or altazimuth) mount because it allows the telescope to be rotated to track the altitude and azimuth of any object.

In this design, the telescope is mounted so that it can rotate around two perpendicular axes as shown in the following diagram.

Altazimuth mounting arrangements are also used to orient other devices such as radars, guns, and solar mirrors. The photo below shows an an array of mirrors mounted on an altazimuth mounting mechanism.

The photo above shows an array of flat mirrors mounted on an altazimuth mounting apparatus. The array can be rotated around a vertical axis to track any azimuth angle of the sun. The apparatus also allows rotating the array around a horizontal axis to track any altitude angle of the sun.

Solar tracker types

Different types of solar trackers are in use today. Solar trackers can be classified into two types with respect to the number of rotation axes: single axis and dual axis trackers. A single axis solar tracker only allows the panel to follow the sun as it moves from east to west. In other words, a single axis tracker only allows for the changing azimuth angle of the sun. But, it does not account for the changes in the sun’s elevation angle as it rises into the sky then falls back into the horizon. Single axis solar trackers are simpler to design and build but they cannot make the panel to directly face the sun all the time. An example of a single axis solar tracker is shown in the photo below.

A dual axis tracker on the other hand can follow the sun in two directions (eg azimuth and altitude) and hence can be made to directly face the sun.

Additional resources

These external videos contain useful information about the sun’s motion and solar tracking systems.

The apparent path of the sun

This video explains the apparent motion of the sun at various times of the year.

How solar trackers work

This video explains solar tracking and presents a dual-axis solar tracker.

Full text description – Alt-azimuth mount