Table 170 497 



SOLAR ALTITUDE AND AZIMUTH 



The altitude and azimuth of the sun are given by 



sin a = sin <p sin 8 -f- cos cos 5 cos h ( 1 ) 



sin a = — cos 8 sin h/cos a (2) 



and 

 where 



= altitude of the sun (angular elevation above the horizon), 



(j> = latitude of the observer, 



8 = declination of the sun, 



h = hour angle of sun (angular distance from the meridian of the observer), 



a = azimuth of the sun (measured eastward from north). 



From equations (1) and (2) it can be seen that the altitude and azimuth of the sun are 

 functions of the latitude of the observer, the time of day (hour angle) and the date 

 (declination). 



Table 170 provides a series of charts, one for each 5 degrees of latitude (except 5°, 

 15°, 75°, and 85°) giving the altitude and azimuth of the sun as a function of the true 

 solar time and the declination of the sun in a form originally suggested by Hand. 1 

 Linear interpolation for intermediate latitudes will give results within the accuracy to 

 which the charts can be read. 



On these charts, a point corresponding to the projected position of the sun is deter- 

 mined from the heavy lines corresponding to declination and solar time. 



To find the solar altitude and azimuth: 



1. Select the chart or charts appropriate to the latitude. 



2. Find the solar declination 8 corresponding to the date in question from Table 169. 



3. Determine the true solar time as follows : 



(a) To the local standard time (zone time) add 4 minutes for each degree of longi- 



tude the station is east of the standard meridian or subtract 4 minutes for 

 each degree west of the standard meridian to get the local mean solar time. 



(b) To the local mean solar time add algebraically the equation of time obtained from 



Table 169; the sum is the required trice solar time. 



4. Read the required altitude and azimuth at the point determined by the declination and 



the true solar time. Interpolate linearly between two charts for intermediate latitudes. 



It should be emphasized that the solar altitude determined from these charts is the 

 true geometric position of the center of the sun. At low solar elevations terrestrial 

 refraction may considerably alter the apparent position of sun. Under average atmos- 

 pheric refraction the sun will appear on the horizon when it actually is about 34' below 

 the horizon; the effect of refraction decreases rapidly with increasing solar elevation. 

 Since sunset or sunrise is defined as the time when the upper limb of the sun appears 

 on the horizon, and the semidiameter of the sun is 16', sunset or sunrise occurs under 

 average atmospheric refraction when the sun is 50' below the horizon. In polar regions 

 especially, unusual atmospheric refraction can make considerable variation in the time of 

 sunset or sunrise. 



The 90° N. chart is included for interpolation purposes, the azimuths lose their direc- 

 tional significance at the pole. 



Altitude and azimuth in southern latitudes. — To compute solar altitude and azimuth 

 for southern latitudes, change the sign of the solar declination and proceed as above. 

 The resulting azimuths will indicate angular distance from south (measured eastward) 

 rather than from north. 



iHand, I. F., Heating and Ventilating, vol. 45, p. 86, 1948. 



(continued) 



SMITHSONIAN METEOROLOGICAL TABLES 



