Recall from EME 810 the following four tables showing the Angular Symbols for Standard Solar Relations. These angles are detailed in the D&B textbook in section 1.6. These angles are all critical to the calculation of solar energy on any given surface at some orientation. To calculate the energy balance across any time scale with respect to the incident solar radiation, you must know the geometric relationships that define the spherical realities of planetary motion relative to the sun for specific tilted surfaces on the planet. Each piece is defined relative to another piece. For example, a solar panel may have a tilt, beta, but that tilt is relative to the horizontal surface on the planet, not relative to the sun. Greek symbols, often with a subscript, are used to ensure clarity through unique identifiers for each angle. Additionally, the sign convention for each angle is critical, as an incorrect sign or origin can lead to drastically incorrect results. Be careful when performing calculations to ensure that each angle and sign is correct.

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

Altitude Angle | α (alpha) |
0^{o} to + 90^{o}; horizontal is zero |

Azimuth Angle | γ (gamma) |
0^{o} to + 360^{o}; clockwise from North origin |

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

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

Lattitude | ϕ (phi) |
0^{o} to ± 90^{o}; Northern hemisphere is +ive |

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

Declination | δ (delta) |
0^{o} to ± 23.45^{o}; Northern hemisphere is +ive |

Hour Angle | ω (omega) |
0^{o} to ± 180^{o}; solar noon is zero, afternoon is +ive, morning is -ive |

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

Solar Altitude Angle (complement) | α_{s} = 1 - θ_{z} (alpha_{s} is the complement of theta_{z}) |
0^{o} to + 90^{o} |

Solar Azimuth Angle | γs (gamma_{s}) |
0^{o} to + 360^{o}; clockwise from North origin |

Zenith Angle | θz (theta_{z}) |
0^{o} to + 90^{o}; vertical is zero |

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

Surface Altitude Angle | α (alpha) |
0^{o} to + 90^{o}; horizontal is zero |

Slope or Tilt (of collector surface) | β (beta) |
0^{o} to + 360^{o}; clockwise from North origin |

Surface Azimuth Angle | γ (gamma) |
0^{o} to ±180^{o}; zero (origin) faces the equator, East is + ive, West is - ive |

Angle of Incidence | θ (phi) |
0^{o} to + 90^{o} |

Glancing Angle (complement) | α=1−θ (alpha) |
0^{o} to + 90^{o} |