What is the solar altitude and azimuth angle and how to calculate

What is the solar altitude and azimuth angle and how to calculate

1.1 Sun altitude and azimuth

1.1.1 Definition of solar altitude and azimuth

Everyone knows that the sun rises from the east, passes through the sky, and then sets from the west. However, if you want to accurately determine its position, you must use the apparent position of the sun to represent it. The apparent position of the sun refers to the position of the sun as seen from the ground, which is represented by the two angles of the sun’s altitude and the sun’s azimuth. The altitude angle of the sun refers to the angle between the light from the center of the sun and the local horizontal plane, that is, the angle between the incident direction of the sun and the ground plane. The height of the sun actually refers to the angle (Figure 1-1).

Sun altitude and azimuth

Figure 1-1 Sun altitude and azimuth

1.1.2 The influence of the height of the sun on the strength of the solar thermal energy obtained on the surface of the earth

The height of the sun is the most important factor that determines the strength of the solar thermal energy obtained on the surface of the earth. Its value varies from 0° to 90. It is zero at sunrise and sunset, and the sun is 90° on the zenith. The azimuth of the sun is the position where the sun is. It refers to the angle between the projection of the sun’s rays on the ground plane and the local meridian. It can be roughly regarded as the angle between the shadow of a straight line erected on the ground and the true south. The azimuth angle is zero in the positive south direction, negative from south to east to north, and positive from south to west to north. If the sun is in the positive east, the azimuth is -90°, and when it is in the northeast, the azimuth is -135° , The azimuth angle is 90° in the west, and ±180° in the north. In fact, the sun does not always rise in the east and set in the west. Only on the two days of the spring and autumn equinox, the sun rises in the east and sets in the west. At the summer solstice, the sun rises from the north of the east, at noon (not 12 noon Beijing time, but the time when the center of the sun is exactly on the meridian, that is, the moment when the azimuth of the sun changes from a negative value to a positive value), The value of the sun’s altitude angle is the largest in a year (except the north and south poles), and then it falls from the northwest. At the winter solstice, the sun rises from the southeast, at noon, the value of the sun’s altitude angle is the smallest in the year, and then sets from the southwest. Therefore, the value is larger in summer, smaller in winter, maximum at summer solstice, and minimum at winter solstice.

In the northern hemisphere, during the half-year from the spring equinox to the autumnal equinox, the sun rises from the north-east direction (azimuth angle of 0°-180°) and sets in the north-west direction (azimuth angle of 90°-180°); and from During the half-year from the autumnal equinox to the vernal equinox of the following year, the sun rises from the south-east direction (azimuth angle of -90~0°) and sets in the south-west direction (azimuth angle 0°~90°).

1.1.3 The significance of the sun’s height to the use of solar energy

The strength of the ground receiving sunlight is closely related to the height of the sun. There is a big difference in the intensity of light between morning and evening and noon because of the difference in the altitude of the sun. On a sunny day, the intensity of sunlight is proportional to the sine of the sun’s altitude. Therefore, understanding the sun’s altitude angle is of great significance for analyzing the solar light intensity on the ground and how to use solar energy.

The azimuth of the sun determines the incident direction of the sun, and determines the lighting conditions of the hillsides in various directions or the buildings in different directions. When the sun’s altitude angle is large (for example, greater than 80°), the sun is basically located near the zenith, and the influence of the sun’s azimuth angle is small at this time.

The altitude of the sun changes with latitude and time. Therefore, the solar radiation intensity is different at different latitudes and different times. Because the solar altitude angle of the area between the Tropic of Cancer and Capricorn is relatively large, and the solar altitude angle of the area north of the Tropic of Cancer and south of the Tropic of Capricorn decreases with increasing latitude, the solar radiation reaching the upper boundary of the earth’s atmosphere is along the latitude. The distribution is uneven, gradually decreasing from low latitudes to high latitudes; because the solar altitude angle of the area between the Tropic of Cancer and the Tropic of Cancer changes little during the year, while the solar altitude angle of the middle and high latitude areas changes during the year. Therefore, the annual change of solar radiation intensity in low latitude areas is small, and the annual change of solar radiation intensity in high latitude areas is large.

1.14 Calculation of the solar altitude angle

The solar altitude angle (using H to represent this angle) can be calculated with the following calculation formula:

         sinH=sing∮sindδ+ cos∮cosδcosωτ

 In the formula, the declination angle of the sun is represented by δ, the geographic latitude of the observation point is represented by middle, and the local time (hour angle) is represented by τ. Use ω to represent the angular velocity of the earth’s rotation, which is almost a constant, that is, 15%/h. As the sun rises and sunsets, the sun’s altitude angle is constantly changing within a day at the same place. The angle is 0° at sunrise and sunset, and the sun’s altitude angle is the largest at noon. The hour angle at noon is 0° (negative before noon, positive after noon), the above formula can be simplified to:

sinH=sing∮sinδ+cos∮cosδ

In the formula, H represents the altitude of the sun at noon. From the trigonometric formula of the sum and difference of the two angles, we can get:

sinH=cos(∮-δ)

Therefore, for the northern hemisphere, H=90°-(∮-δ); for the southern hemisphere, H=90°-(∮-δ).

Here are two examples to illustrate the calculation of the altitude angle of the sun at noon.

[Example 1] Calculate the altitude angle of the sun at noon on the Tropic of Sun in the summer solstice.

Solution: δ=23°27’ ∮=-23°27’

H=90°-(δ-∮)

  =90°-[23°27’-(-23°27’)]

  =43°06’

Therefore, the altitude angle of the sun at noon on the Tropic of Sun in the summer solstice is 43°06’.

[Example 2] Calculate the altitude angle of the noon sun on the Arctic Circle on the vernal equinox.

Solution: δ=0° ∮=66°33’

H=90°-(δ-∮)

  =90°-(66°33’ -0°)

  =23°27’

Therefore, the sun angle at noon on the Arctic Circle on the vernal equinox is 23°27’.

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