Harnessing the Sun with Precision

Orienting the Heliostat Mirror

To accurately reflect sunlight from the sun toward a target, a heliostat mirror must be precisely oriented. This orientation is determined by calculating the Pointing Vector \( \mathbf{P} \), which tells the mirror which direction its surface normal should face.

Using Azimuth and Elevation

The directions to both the Sun and the Target are defined by their azimuth and elevation angles, relative to the heliostat. These are then converted into 3D direction vectors:

• Sun Vector \( \mathbf{S} \): direction from mirror to the Sun.
• Target Vector \( \mathbf{T} \): direction from mirror to the target location.

The Pointing Vector Formula

To find the required orientation, we calculate the vector that bisects the angle between the Sun and the Target. This is done using the following formula:

This equation produces a unit vector that bisects the angle between the Sun and the Target, which is the correct direction the mirror’s surface normal should face.

Example: Calculating the Pointing Vector

Let’s say the Sun is at an azimuth of 120° and an elevation of 45°, while the Target is at an azimuth of 60° and elevation of 10°, relative to the heliostat. Convert both into 3D direction vectors using spherical to Cartesian conversion:

Next, add the two unit vectors and normalize the result:

Convert \( \mathbf{P} \) Back to Azimuth and Elevation

To control a heliostat’s motors, the 3D pointing vector must be converted back into azimuth and elevation angles:

This tells us the mirror normal should be tilted upward by about 29° and rotated to an azimuth of ~84° to accurately reflect sunlight from the Sun toward the target.

Controlling the Heliostat

The azimuth and elevation angles derived from \( \mathbf{P} \) are passed to the heliostat's actuators to adjust tilt and rotation. This enables precise, real-time tracking and reflection onto a fixed receiver.

Note: Azimuth refers to how many degrees you are from True North(Not Magnetic North!), Elevation is how many degrees you are away from a Horizontal Plane in relation to the earths surface at a given point.

A common method of reaching azimuth and elevation is simply by using a dual axis stepper motor design, with the correct design you should be able to reach all angles needed for the Pointing Vector.