When we want a shorthand to describe spatial relationships on continuous surfaces that are sphere-like, as with the Earth and the surrounding sky and stars, we choose to use Greek letters. In contrast, when we are trying to communicate things like linear distances, lengths, time, or simple Cartesian coordinates, then we will tend to use Roman letters for our shorthand.

You may notice in your reading of older textbooks that several systems of sign convention for the angles have emerged for practical use. Also, the various systems can have different approaches to azimuth that we should be aware of. For instance, the software SAM (System Advisor Model) will use both the $360^\circ$ clockwise standard (from Meteorology) as well as the $\pm180^\circ$ standard used extensively in the component-based models of TRNSYS and SAM. We will be sure to become familiar with both.

Below are four tables showing the Angular Symbols for Standard Solar Relations.

### General Angles

Angular Measure | Symbol | Range and Sign Convention |
---|---|---|

altitude angle | $\alpha $ (alpha) | 0^{o} to + 90^{o}; horizontal is zero |

azimuth angle | $\gamma $ (gamma) | 0^{o} to + 360^{o}; clockwise from North origin |

azimuth (alternate) | $\gamma $ (gamma) | 0^{o} to ±180^{o}; zero (origin) faces the equator, East is + ive, West is - ive |

### Earth-Sun Angles

Angular Measure | Symbol | Range and Sign Convention |
---|---|---|

latitude | $\varphi $ (phi) | 0^{o} to ± 90^{o}; Northern Hemisphere is +ive |

longitude | $\lambda $ (lambda) | 0^{o} to ± 180^{o}; Prime Meridian is zero, West is -ive |

declination | $\delta $ (delta) | 0^{o} to ± 23.45^{o}; Northern Hemisphere is +ive |

hour angle | $\omega $ (omega) | 0^{o} to ± 180^{o}; solar noon is zero, afternoon is +ive, morning is -ive |

### Sun-Observer Angles

Angular Measure | Symbol | Range and Sign Convention |
---|---|---|

solar altitude angle (complement) | ${\alpha}_{s}=\text{}1\text{}-\text{}{\theta}_{z}$ ${\alpha}_{s}=1-{\theta}_{z}$ (alpha _{s} is the complement of theta_{z}) |
0^{o} to + 90^{o} |

solar azimuth angle | ${\gamma}_{s}$ (gamma _{s}) |
0^{o} to + 360^{o}; clockwise from North origin |

zenith angle | ${\theta}_{z}$ (theta _{z}) |
0^{o} to + 90^{o}; vertical is zero |

### Collector-Sun Angles

Angular Measure | Symbol | Range and Sign Convention |
---|---|---|

surface altitude angle | $\alpha $ (alpha) | 0^{o} to + 90^{o} |

slope or tilt (of collector surface) | $\beta $ (beta) | 0^{o} to ±90^{o}; facing equator is +ive |

surface azimuth angle | $\gamma $ (gamma) | 0^{o} to + 360^{o}; clockwise from North origin |

angle of incidence | $\theta $ (theta) | 0^{o} to + 90^{o} |

glancing angle (complement) | $\alpha =1-\theta $ (alpha) |
0^{o} to + 90^{o} |