Equations for solar tracking

TL;DR

This paper provides essential geometric formulas for a solar tracker system using two mirrors, aiding atmospheric research by improving Sun tracking accuracy in spectroscopic measurements.

Contribution

It compiles and illustrates key geometrical formulas for a common two-mirror solar tracker used in atmospheric spectroscopy.

Findings

Formulas enable precise Sun azimuth and altitude calculations.

Illustration with a practical tracker prototype.

Improved accuracy in solar tracking for atmospheric experiments.

Abstract

Direct Sun light absorption by trace gases can be used to quantify them and investigate atmospheric chemistry. In such experiments, the main optical apparatus is often a grating or a Fourier transform spectrometer. A solar tracker based on motorized rotating mirrors is also needed to direct the light along the spectrometer axis, correcting for the apparent rotation of the Sun. Calculating the Sun azimuth and altitude for a given time and location can be achieved with high accuracy but different sources of angular offsets appear in practice when positioning the mirrors. A feedback on the motors, using a light position sensor closed to the spectrometer is almost always needed. This paper aims to gather the main geometrical formulas necessary for the use of a widely used kind of solar tracker, based on two 45{\deg} mirrors in altazimuthal set-up with a light sensor on the spectrometer, and to illustrate them with a tracker developed for atmospheric research by our group.