Handbook of air conditioning and refrigeration / Shan K

3.24 CHAPTER THREE
● Solar altitude angle � (Fig. 3.7a and b) is the angle ROQ on a vertical plane between the sun’s ray
OR and its projection on a horizontal plane on the surface of the earth.
● Solar azimuth � (Fig. 3.7a) is the angle SOQ on a horizontal plane between the due-south direction
line OS and the horizontal projection of the sun’s ray OQ.
● Solar declination angle � (Fig. 3.6) is the angle between the earth-sun line and the equatorial
plane. Solar declination � changes with the times of the year. It is shown in Fig. 3.6 on June 21.
● Surface-solar azimuth � (Fig. 3.7a and c) is the angle POQ on a horizontal plane between the
normal to a vertical surface OP and the horizontal projection of the sun’s rays OQ.
● Surface azimuth � (Fig. 3.7a) is the angle POS on a horizontal plane between OP and the direction
line SN.
● Latitude angle L (Fig. 3.6) is the angle S�O�O on the longitudinal plane between the equatorial
plane and the line O�O that connects the point of incidence of the sun’s ray on the surface of earth
O and the center of the earth O�.
Hour Angle and Apparent Solar Time
Solar Angle Relationships
Hour angle H (Fig. 3.6) is the angle SOQ on a horizontal plane between the line OS indicating the
noon of local solar time t ls and the horizontal projection of the sun’s ray OQ. The values of the hour
angle H before noon are taken to be positive. At 12 noon, H is equal to 0. After 12 noon, H is negative.
Hour angle H, in degrees, can be calculated as
H � 0.25 (time in minutes from local solar noon) (3.49)
The relationship between apparent solar time t as, as determined by a sundial and expressed in apparent
solar time, and local standard time t st, both in minutes, is as follows:
(3.50)
where M � local standard time meridian and G � local longitude, both in degrees. In Eq. (3.50), t eq,
in minutes, indicates the difference in time between the mean time indicated by a clock running at a
uniform rate and the solar time due to the variation of the earth’s orbital velocity throughout the year.
The relationship among the solar angles is given as
sin� � sin� sinL � cos� cosH cosL (3.51)
and
Angle of Incidence and Solar Intensity
t as � t eq � t st � 4(M � G)
cos � �
sin� sin L � sin �
cos� cos L
(3.52)
The angle of incidence � (Fig. 3.7a) is the angle between the sun’s rays radiating on a surface and
the line normal to this surface. For a horizontal surface, the angle of incidence � H is ROV; for a vertical
surface, the angle of incidence � V is ROP; and for a tilted surface, the angle of incidence � � is
ROU. Here, � is the angle between the tilted surface ABCD and the horizontal surface.
Let I DN be the intensity of direct normal radiation, or solar intensity, on a surface normal to the
sun’s ray, in Btu/h�ft 2 (W/m 2 ). In Fig. 3.7b, I DN is resolved into the vertical component RQ � I DN