THE UNIVERSITY OF MICHIGAN INDUSTRY PROGRAM OF THE COLLEGE OF ENGINEERING STUDIES ON DAYLIGHT AVAILABILITY R. A. Boyd Research Physicist University of Michigan March, 1958 IP-279

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Studies on DAYLIGHT AVAILABILITY R. A. Boyd The University of Michigan Engineering Research Institute Synopsis To util-ize solar energy advantageously for the lighting and heating of buildings, additional data are required on the availability of daylight and solar heat for variously oriented surfaces, and for nuimerous geographical locations. This study presents data on daylight availability at Ann Arbor, Michigan) for the period March, 1953, to March, 1954, and correlates these data with theoretical considerations and climatological data as recorded by the U. S. Weather Bureau. Introduction Only meager data are:available on- the variability of exterior daylight intensities. References on. this subject are widely scattered.l2'3'5' and only a few of these3'56 are available as illumination literature. To afford additional data in. this direction, a study was undertaken on the availability of daylight at Ann Arbor, Michigan, for a period to include all seasons, these findings then correlated with theoretical considerations and climatological data as recorded by the U!. S. Weather Bureau. Measurements recorded are for the period March, 1953, to March, 1954.

Recording Equipment All measurements were made with a group of five photocells (Fig. 1) mounted on the roof of the Daylighting Laboratory, The University of Michigan, so that an unobstructed view of the sky could be obtained, the cells facing north, south, east, west, and toward the zenith. The supporting shield, painted flat black, reduced the light reflected from the "ground" to a minimum of approximately four per cent.. The photoelectric cells were model 856, as supplied by the Weston Electrical Instrument Corporation. Each cell was equipped with a Viscor filter to provide it with the same spectral sensitivity as the human eye, and was placed in a watertight case. A metallic film filter and depolished flashed opal disc were sealed in place over the face of each cell. A multipoin~t Speedomax Recorder, with appropriate shunts, was used for the recording. Each of the five circuits was provided with five shunts so that the Recorder response could be varied as the photocell response varied. The values of the shunts and the density of the metallic film filter for each cell were selected so that the Recorder response was directly proportioned to the illumination incident on the cell. The photocell case and the opal disc were so designed that the unit obeyed the cosine law of illumination. The maximum error of this corrected unit for undirectional illumination is four per cent, and that occurs for an angle of incidence of 80 degrees. For measuring the illumination due to a uniform hemispherical source, such as a sky having a uniform brightness, this photocell has an error of less than one per cent. The photocells were initially calibrated and periodically checked with 1000- and 5000-watt incandescent lamps of known candlepower. For the higher intensities, corresponding to direct sunlight conditions, the photocells and metallic film filters were calibrated separatly and then combined to avoid errors due to lack of application of the inverse square law. 2

Data Recorded Data were collected with weatherproof cells during most of the working days from March 1, 1953, to March 1, 1954, regardless of exterior weather conditions, The number of days in each month for which data are available are: Month Number of Days March, 1953 18 April, 1953 20 May, 1953 19 June, 1953 22 July, 1953 22 August, 1953 20 September, 1953 19 October, 1953 17 November, 1953 20 December, 1953 21 January, 1954 19 February, 195- 21 238 Tabulation of Data Since the recorder provided approximately one intensity reading per photocell each minute, more data were collected on the recorder charts than could reasonably be analyzed for this study. Consequently, it was decided that footcandle readings for each photocell would be selected on a 15-minute-interval basis, from 8 a.m. to 5 p.m. each day. Such a tabulation gave the intensity of daylight, in footcandles, every 15 minutes, on north, south, east, and west vertical surfaces, and on a horizontal surface. One aim of this study was to correlate the recorded intensities with the degree of cloudiness and percentage of possible sunshine as specified by the U. Weather Bureau. The nearest weather station to Ann Arbor is at Willow Run, whic records the degree of cloudiness but not the percentage of possible sunshine. The lU. S, Weather Bureau indicates the degrFee of cloudiness as tenths of the entire sky, 0 to 3 tenths being clear, 4 to 7 tenths partly cloudy, and 8 to 10 tenths cloudy. These data were obtained for the entire year from the Weather Bureau Station at Willow Run.

An overcast sky is one for which the cloud formation is so dense that all vertical surfaces are equally illuminated. As the cloud density decreases, the sky brightness becomes non-uniform, and consequently the variation in vertical surface illumination with orientation of the surface becomes greater. In an attempt'to obtain some correlation between the measured intensities and the degree of cloudiness, the readings were classified on the basis of the ratio of maximum to minimum vertical surface illumination. The classes are as follows: M1ax Class Ratio Mn A 1.0 to 1.5 B 1.5 to 2.5 C 2.5 to 3.5 D > 3.5 May 5, 1953, was one of the days during which all four of these conditions existed. Figure 2 shows the variation of the illumination on the four vertical surfaces and on the horizontal surface, with the readings marked according to the above classification. The readings were plotted as recorded; no attempt was made to account for light reflected to the vertical surfaces from a particular, foreground. Every reading, for the entire year, on the 15-minute-interval basis, was classified in this manner. Table I shows a comparison, for each month, of the following: 1. Percentage of all days, designated as cloudy, partly cloudy, and clear by the U. S. Weather Bureau. 2. Percentage of all days for which recordings were made, designated as cloudyy partly cloudy, and clear by the U. S. Weather Bureau. 3. Sky cover, in tenths, for the entire month, 4. Sky cover, in tenths, for the days for which recordings were made. 5. Percentage of the total number of readings, 8 a.m. to 5 p.mo designated as being in classes A, B, C, and Do

This table indicates that the distribution of cloudy, partly cloudy, and clear days for the recorded periods is just about the same as for the entire year. The table also indicates that the days designated as cloudy by the Uo -S. Weather Bureau are not all overcast days. On the average, it takes the sum of Class A, Class B, and Class C conditions to equal approximately the percentage of days designated as cloudy. To obtain maximum information from these data, they have been tabulated in several different ways. Each tabulation will be presented and explained in the following sections. In the consideration of the increase in vertical surface illuminations due to light reflected from a foreground, it has been assumed that (1) the quantities measured included a negligible amount due to ground reflection because of the black shield, and (2) for a foreground with a reflectance of 25 per cent, the increase in north, south, east, and west vertical surface illuminations would equal 12.5 per cent of the horizontal surface illumination. Time'Intensity Graphs In the daylighting of schools, offices, small factories, shopping centers, and the like, it is of interest to know what percentage of the time of occupancy the exterior illumination of a particular surface is above a specific value. Such a presentation has been made for the periods 8:30 acm. to 3:30 p.m. for the entire year, and for the school year (September through May), and for 8 a.m. to 5 p.m. for the entire year. In plotting these data, the morning and afternoon values for east and west exposures have been kept separate. These data are presented in Figs, 3 to 8 as follows: Figure Coverage Foreground Reflectance 3 8:30 amo to 3:30 p.m. - School Year Negligible 4 8:30 a.mo to 3:30 p.m. - School Year 25% 5 8:30 a.m, to 35:30 p.m. - Entire Year Negligible 6 8:30 aomo to 3:30 pom. - Entire Year 25% 7 8:00 a.mo to 5:00 p.m. - Entire Year Negligible 8 8:00 a.m. to 5:00 p.m. - Entire Year 25%

Average Illumination The average illuminations for classifications A, B, C, and D, for the period 8:30 a.m. to 3:50 p.m., were calculated for each month. These averages for each exposure, without and with consideration of ground-reflected light, are presented in Table II. This table also shows the average illumination for each exposure for the sum of Classes A, B, and C and for the sum of Classes A, B, C, and D; the averages are weighted on the basis of percentages of time involved. The average illuminations for all conditions for the period 8:00 a.m. to 5:00 p.m. are given in Table III, again without and with consideration of groundreflected light. Overcast and Cloudy Sky Conditions Overcast and cloudy sky conditions are of particular interest because it is generally considered that for these periods exterior illumination is inadequate for daylighting purposes. This opinion is prevalent in connection with the daylighting of schools. Table IV shows the average external illuminations for each month for the school period 8:30 a.m. to 3:30 p.m., for the overcast, and cloudy sky conditions. Overcast sky conditions are represented by Class A and cloudy sky conditions, by Classes A, B, and C. The vertical surface illumination is given as the average of the values for north, south, east, and west exposures. Table IV also gives the ratio of horizontal surface illumination to vertical surface illumination for each month. Sun and Clear Sky Conditions It is also of interest to consider the variation in exterior illumination for a cloudless day. One day each month was selected as being the best from this point of view, and the data were plotted. Four of these graphs are presented as follows: Figure 9 March 20, 1953 Figure O10 June 235 1953 Figure 11 September 28, 1953 Figure 12 December 16, 1953

These data were plotted without consideration of additional ground-reflected light. As an indication of the total luminous energy that is incident directly on the specific surface during the period of one day, between the hours given, the area under each of these curves was measured, and the results, in 1000 lumenhours, are listed in Table V. In Fig. 13, these same values of total luminous energy are plotted against noon-sun altitude for the day of measurement; the altitude scale is divided into two parts to separate the values for the two halves of the year. For convenience, the altitude scale is also divided into months with specific dates designated. The continuous curves are drawn to give some indication of the total luminous energy, 8:00 a.m. to 5:00 p.m., for any clear day of the year. Exterior Daylight Intensities of 1000 and 2000 Footcandles 6 In a paper on the availability of daylight at Port Allegany, Pennsylvania, data were presented showing the number of hours per day, between 8:00oo am. and 5:00 p.m., that the illumination of particular surfaces was above 1000 and 2000 footcandles for each month. To allow direct comparison of these data with the data for Ann Arbor, a similar analysis has been made of the Ann Arbor data; the results are presented in Fig. 14. Discussion of Results Some previous papers7 on the availability of daylight and solar radiation have attempted to relate the average intensity for cloudy days to the average intensity for cloudless days through the percentage of possible sunshine. In the absence of percentage of possible sunshine figures for Ann Arbor, approximate values have been obtained by averaging the available figures for East Lansing and Detroit. Utilizing these figures, an attempt will be made to relate cloudy day conditions to those for cloudless days. From Fig. 13 it is possible to determine the average illumination, Io, for *7

each month, 8:00 a.m. to 5:00 p.m. for each exposure, assuming that all days are cloudless or reasonably so. Then the average illuminations shown in Tables II and III can be related to these to obtain the ratios listed in Table VI, where R1 is the ratio Qf the average illumination for strictly overcast sky conditions (Class A) to Ib, Rz is the ratio of the average illumination for cloudy sky conditions (Classes A, B, and C) to I, and Rs is the ratio of the average illuminations for all conditions to Io0 8 Angstrom has suggested that an equation of the form Q/Qo = a + bS represents the relation between sunshine, S (expressed as a fraction of the possible number of hours), and the ratio of the average radiation, Q, on a horizontal surface to the corresponding average radiation, Q0, during cloudless days, where a and b are constants. Using the data of Table VI for a horizontal surface, it appears that I = Io (0.32 + 0.68 ), (1) is a reasonable expression, where Io is the average illumination for the month, assuming all days to be cloudless, and I is the average illumination for the month having 100S per cent of possible sunshine. The values of Io, RlIoJ 0.32 Io1 R3Io, and I for the 12 months are shown in Fig. 15. Setting a = 0.32 indicates that when S = 0 the sky is overcast and the average illumination is 0.32 Ioo It appears that the agreement of 0.32 Io to R1Io and I to R3Io is quite good, considering the uncertainty in S. Reference to Table VI will indicate, however, that an equation of this form cannot be used to represent the conditions for a vertical surface since R1 is not a constant or nearly so. An equation that represents fairly well the conditions for the south vertical surface is: I = Io [S + 0.95 (l-S) sin2 a/2], (2) where c is the average noon sun altitude for each month. The values of Io, R1Io, R3Io, 0.95 Io sin2 a/2, and I for the 12 months are shown in Fig, 16.

A similar expression I = Io IS + 0.44 (1-S) sin a/2], (3) represents the conditions for east exposure in the forenoon and for west exposure in the afternoon,values of Io, R110, R3Io, 0.44 Io sin a/2, and I are given in Fig. 17. Equations (1), (2), and (3) represent fairly well the data of Table VI, and were formed to give I = I0 when S = 1.0, and average values for overcast sky conditions when S = 0. Equations (2) and (3) are for direct light only, and do not attempt to include an added vertical surface component due to ground-reflected light. Since total radiation intensities were not measured at Ann Arbor or Willow Run during the period the data of this paper were collected, these daylight intensities cannot be related to total radiation. When the distribution of brightness of an overcast sky has been measured, it can generally be represented by Bg = B (a + b sin @), where Bg is the sky brightness at an altitude 9, B is the sky brightness at the zenith-, and a and b are constants. It is because of such facts that Class A conditions were selected as those for which the ratio of maximum to minimum vertical surface illumination did not exceed about 1.5. Values of the constants a and b that have been used are a = 0.4, b = 0.6, and a = 1/3, b = 2/3. An integration of this expression for an unobstructed horizontal surface and for an unobstructed vertical surface gives a ratio for total horizontal to total vertical surface illumination of 2.42 and 2.52, respectively, for the two sets of constants. In Table IV such ratios are presented for average values of horizontal and vertical surface illumination for Class A conditions and for the sum of conditions of Classes A, B, and C. It will be observed that these ratios for the summer months agree quite well with the theoretical values; however, for the winter months the ratios are close to 2.0, which is the theoretical ratio for a sky of uniform brightness. 9

In the daylighting of buildings, the interior illumination is usually related to the exterior illumination of the surfaces containing the fenestrations. Some attempt has been made to establish average values for exterior illuminations due to overcast sky conditions; values of 500 and 1000 footcandles have been used for vertical surfaces, and 1000 and 2500 footcandles for a horizontal surface. The data of this study indicate that for strictly overcast sky conditions, and with average foreground reflectance, the average vertical surface illumination, between 8:30 a.m. and 3:30 p.m. is 1140 footcandles for the entire year and 960 footcandles for the school year. The corresponding figures for a horizontal surface are 2030 footcandles for the entire year and 1670 footcandles for the school year. For the period of 8:00 a.m. to 5:00 p.m. the figures, of course, will be somewhat lower. In any case, these data indicate that 1000 footcandles for a vertical surface and 2000 footcandles for a horizontal surface are reasonable averages for this location. It should be realized, however, that minimum exterior illumination conditions do not only relate to overcast skies. Clear sky conditions for vertical surfaces not receiving direct sunlight or appreciable ground-reflected light should also be included. Comparison of Class D and Class A averages for north exposure, Table II, indicatesthat they are comparable. When the ground-reflected light is appreciable, the overcast sky conditions do represent the minimum. One reason for establishing an average minimum exterior illumination is that for this value the interior illumination should be Just adequate for the task involved. The percentage of time for which the exterior illumination, for all conditions, is above a specified level is given in Figs. 3, 4, 5, 6, 7, and 8. In the case of 1000 footcandles for a vertical surface and 2000 footcandles for a horizontal surface, Fig. 8 indicates that for the period 8:00 a.m. to 5:00 p.m. for the entire year, these values will be exceeded 67 per cent of the time for a horizontal surface and 75 per cent of the time for a vertical surface with south exposure. 10

In considering such figures, it should be realized that the data of this study are for one of the three districts in the United States having the lowest percentage of possible sunshine. The U. S. Weather Bureau9 extensively records solar radiation on a horizontal surface and collects illumination data at only a few geographical locations. More extensive data, showing total radiation and illumination for vertical surfaces, are required to obtain a correlation between solar heat and luminous energy intensities and atmospheric conditions. Recording devices designed specifically for such research are needed to avoid the time-consuming methods of tabulation and analysis used in presenting the data of' this study. ACKNOWLEDGEMENT The collection and initial tabulation of the data of this study were accomplished through the use of funds supplied by the Kimble Glass Company, a subsidiary of Owens-Illinois. The author is grateful to this Company for its support and permission to use the data in this publication. The author also wishes to thank the Director of the Engineering Research Institute fot making funds available for the preparation of the manuscript. 11

REFERENCES 1. "Variations in the Total and Luminous Solar Radiation with Geographical Position in the United States," Herbert H. Kimball, U. S. Weather Review, November, 1919. 2. "Daylight Illumination on Horizontal, Vertical and Sloping Surfaces,'" Herbert H. Kimball and Irving F. Hand, U. S. Weather Review, December, 19220 3. "Variations of intensities of the Visible and of the Ultraviolet in Sunlight and in Skylight," William Kunerth and Russell D. Miller, Transactions, I.E.S., 27 (1932), 82-940 4. Technical Data on Weston Photronie Cells, Weston Electrical Instrument Corporation, Cir. B20B, October, 1944. 5. "The Amount of Luminous and of Ultraviolet Solar Radiation Received on Certain Vertical Planes," William Kunerth, Russell D. Miller, and Herbert Harley, Transactions, I.E.S., 32 (1937), 315. 6. "Availability of Daylight," H. F. Kingsbury, H. H. Anderson, and V. U. Bizzaro, Illuminating Engineering, p. 77 (February, 1957). 7. Smithsonian Meteorological Tables, Sixth Revised Edition, Washington, D. Co, 1951. 8. AngstrOm, A,, Medd. Stat. Met. Hydr. Astr., Vol. 4, No. 3, 1928. 9. Climatological Data, U. S. Department of Commerce, Weather Bureau. 12

RECORD OF CLOUDINESS 8o00 a.m. to 500 p.m. —March 1953 through February 1954 Percent of All Days Percent of Measured Days Sky Cover Percent of Readings Month Partly Partly All Measured Class Class Class Class Cloudy PClear Cloudy Clear Cloud Cloudy Cloudy Clear Days DaDys A B C D March 84 10 6 88 6 6 8.6 8.7 47 16 9 28 April 74 13 13 70 10 20 7.6 7.2 34 13 5 48 May 58 29 13 68 26 6 7.2 7.9 40 17 7 36 June 40 43 17 41 36 23- 6.2 5.9 17 13 10 60 July 29 42 29 32 41 27 5.5 5.5 20 13 10 51 August 23 26 51 20 20 60 4.2 3.8 7 7 5 81 Sept 20 37 43 16 42 42 4.3 4.2 10 10 4 Oct 23 23 54 24 12 64 4.0 3.8 17 4 2 77 Nov 53 17 30 55 15 30 6.3 6.3 37 11 6 46 Dec 64 23 13 52 29 19 7.5 6.8 37 10 8 45 Jan 74 16 10 84 5 11 8.2 8.7 70 6 4 20 Feb 61 14 25 57 19 24 7.1 7.0 50 8 2 40 Avg 50 25 25 50 22 28 6.4 6.3 32 11 6 51 TABLE I

AVERAGE ILLUMINATION IN FOCITCANDLES Classes A, B, C, and D —8:30 a.m. to 3:30 p.m. I Number Percent Foregound Reflectace-Neg Foreground Reflectance-25 Class Horizontal of l/4 hr of Time Horizontal North South East West North South East West A 374 68 720 340 380 350 370 430 470 440 460 o B 37 7 1560 570 1190 720 900 770 1390 920 1100 C 23 4 2750 730 1960 1190 940 1070 2300 1530 1280 s- D 112 21 2740 730 4810 2000 1400 1070 5150 2340 1740 i Average Classes A,B,C 900 380 530 420 440 490 640 540 560, Average Classes A,B,C,D 1300 450 1430 755 645 610 1590 920 810 >- A 284 50 1140 550 610 550 590 690 750 690 730 ~ B 44 8 2600 860 1970 1330 1170 1180 2300 1650 1490 > C 12 2 2340 790 2230 1510 1160 1080 1520 1800 1450 s D 229 40 3370 580 5260 2340 1490 1000 5680 2760 1910, Average Classes A,B,C 1390 600 830 690 670 770 1000 860 840, Average Classes AB,C,D 2180 590 2600 1350 1000 860 2870 1620 1270 A 223 50 2200 890 1000 930 940 1170 1280 1200 1210 B 15 3 3020 1040 1700 1320 1420 1420 2080 1700 1800 C 52 12 4080 1110 3250 1940 1850 1620 3760 2450 2360 o D 158 35 5720 840 5330 3730 2010 1550 6040 4440 2720 Average Classes A,B,C 2580 930 1450 1140 1130 1260 1770 1460 1450 Average Classes A,B,C,D 3680 900 2810 2050 1440 1360 3270 2510 1900 A 196 33 2590 990 1110 1030 1100 1310 1430 1350 1420 0o B 91 16 4110 1230 2220 1670 1720 1740 2730 2180 2230 r C 28 5 5330 1240 3070 2220 2020 1910 3740 2890 2690 r D 272 46 6790 910 4520 3060 2830 1760 5370 3910 3680, Average Classes A,B,C 3310 1080 1610 1330 1370 1490 2020 1740 1780 Average Classes A,B,C,D 4910 1000 2950 2130 2040 1610 3660 2740 2650 TABLE II

Number Percent Fore gound Reflectance-Ne Foreround Reletance Class Horizontal of 14 hr of Time North South East West North south East West A 230 41 2740 1050 1170 1130 1150 1390 1510 1470 1490 B 81 15 4270 1500 2160 1730 1740 2030 2690 2260 2270 c\ C 42 7 5500 1510 3060 2070 2430 2200 3750 2760 3120 D 205 37 7870 1190 4220 2590 3350 2170 5200 3570 4330 S Average Classes A,B,C 3400 1210 1620 1380 1430 1630 2040 1800 1850 Average Classes A,B,C,D 5050 1200 2580 1830 2140 1830 2210 2460 2770 A 104 17 3260 1230 1540 1390 1320 1640 1950 1800 1730 ~L B 97 16 4770 1290 2270 1750 1750 1890 2870 2350 2550 < C 74 12 7570 1490 3580 2430 2500 2440 4530 3380 3450 D 340 55 8450 1160 3920 3630 2910 2220 4980 4690 3970 e Average Classes A,B,C 4950 1320 2310 1800 1800 1940 2930 2420 2420 Average Classes A,B,C,D 6880 1230 3200 2810 2410 2090 4060 3670 13270 knA 140 23 3240 1080 1490 1260 1330 1470 1880 1650 1720 B 86 14 4610 1340 2290 1890 1830 1920 2870 2470 2410 C 66 11 7540 1310 3510 2310 2390 2250 4450 3250 3330 > D 321 52 7930 1150 3270 3740 3060 2140 4460 4730 4050 D Average Classes A,B,C 4580 1210 2190 1680 1730 1780 2760 2250 2300 Average Classes A,B,C,D 6320 1180 2850 2750 2420 1970 3640 3540 3210 r., A 38 7. 2910 1190 1440 1050 1320 1550 1800 1410 1680 o\ B 38 7 3500 1180 1980 1410 1470 1620 2420 1850 1910 C 28 5 5250 1080 2610 1650 2340 1740 3270 2310 3000 D 468 81 7650 1000 4610 3890 2430 1950 5560 4840 3380 Average Classes A,B,C 37401900 1160 1900 1320 1630 1630 2370 1790 2100 Average Classes A,B,C,D 6910 1030 4100 3400 2280 1890 4960 4260 3140 TABLE II (continued)

Number Percent Horizontal' 1 Number Percent ~ ~~Fo0reground'-Reilectance —Neg..Foreground'-Reiflectance —25 Class ~of 1/4 hr of T ime North South East West North South East -West A 52 10 2480 970 1280 1140 1050 1280 1590 1450 1360 B 59 11 2670 920 1620 1050 1400 1250 1950 1580 1750 ~, C 29 6 3810 990 2490 1390 1890 1470 2970 1870 2770 D 577 73 6650 790 568o 3530 2540 1620 6510 4560 5570 -4 Average Classes A,B,C 2780 970 1700 1150 1570 1520 2050 1500 1720 Average Classes A,B,C,D 5610 840 4610 2890 2220 1540 5310 5590 2920 a) AveaeCassABI A 81 17 1200 510 570 56o 560 660 720 710 710 \ B 22 5 2000 720 1360 970 1220 970 1610 1220 1470 C 9 2 2930 870 2500 1250 1730 1240 2870 1620 2100 D 368 76 5210 650 6350 2980 2810 1300 7000 5650 546o 0 Average Classes A,B,C 1500 610 920 730 810 800 1110 920 1000 oAverage Classes A,.BCD 0' Average Classes A,B,,CD 4320 640 5050 2440 2330 1180 5590 2980 2870 A 205 37 1130 510 640 550 600 650 780 690 740 r-B 50 9 2040 740 1630 1140 1000 990 1880 1590 1250 C 28 5 2470 720 2410 1460 920 1030 2720 1770 1250 D 265 49 3080 560 5190 2360 1570 950 558o 2750 1960 w Average Classes A,BC 1430 580 990 750 710 760 1170 950 890 Z Average Classes A,B,C,D 2240 570 3050 154o 1150 850 3550 1820 1410 A 211 39 820 370 470 420 440 470 570 520 54o ON B 55 10 1590 600 1300 800 940 800 1500 1000 1140; C 40 7 1980 660 1900 1030 1140 910 2150 1280 1590 D 239 44 2350 510 4290 1660 1550 8oo 4580 1950 1640 Average Classes A,B,C 1100 460 790 570 620 600 930 710 760 Average Classes A,B,C,D 1650 480 2330 1050 940 690 2540 1260 1150 TABLE II (concluded)

AVERAGE IITLUMINATION IN FOOTCANDLES 8:00 a.m. to 5:00 p.m. Month Horizontal | Foreground Reflectance Neg Foreground Reflectance 2 North South East West North South East West Jan 1954 1140 420 1420 630 680 560 1560 770 820 Feb 1954 2120 530 2640 1130 1300 790 2900 1390 1560 March 1953 3450 840 2530 1660 1680 1270 2960 2090 2110 April 1953 4560 860 2650 1900 2150 1430 3220 2470 2720 May 1953 4920 1110 2140 1850 2050 1720 2750 2460 2660 June 1953 6180 1120 2800 2750 2580 1890 3570 3520 3350 July 1953 6190 1130 2680 2770 2690 1900 3450 3540 3460 August 1953 6400 980 3750 3150 2710 1780 4550 3950 3510 Sept 1953 5050 760 4260 2770 2660 1390 4890 3400 3290 Oct 1953 3900 570 4660 2050 2510 1060 5150 2540 3000 Nov 1953 2020 475 2720 1150 1230 7350 2970 1400 1480 Dec 1953 1470 420 2170 870 910 600 2350 1050 1090 Avg 3950 770 2870 1890 1930 1260 3360 23580 2420 TABLE III

AVERAGE TTLLUMINATION Overcast and Cloudy Sky Conditions-8:30 a.m. to 3:30 p.m. Class i Class A Classes A+B+C.....,, -' J.... A+B.+C Month t Avg V.S.. Avg V.S.I. Avg H. S. I. H. S. I. Neg GrF 25) GrF Neg Grd 25% Grd (FtC) (FtC) Neg Grd Neg Gd 2%Gd t(FtC) ( FtC)... Jan 1954 360 450 720 440 550 900 2.00 2.04 Feb 1954 580 720 1140 700 870 1390 1.97 1.99 March 1953 940 1220 2200 1160 1480 2580 2.534 222 April 1953 1060 1380 2590 1350 1760 3310 2.44 2.45 May 1953 1130 1470 2740 1410 1830 3400 2.42 2.41 June 1953 1370 1780 3260 1810 2430 4950 2.38 2.73 July 1953 1290 1680 3140 1700 2270 4580 2.43 2.69 August 1953 1250 1610 2910 1500 1970 3740 2.33 2.49 oco Sept 1953 1110 1420 2480 1300 1650 2780 2.24 2.14 Oct 1953 550 700 1200 770 960 1500 2.18 195 Nov 1953 580 720 1130 760 -940 1430 1.95 1.88 Dec 1953 430 530 820 610 750 1100 1.91 1.80 Average Entire Year 890 1140 2030 1130 1460 2640 2.22 2.23 Average School Year 750 960 1670 940 1200 2040 V.S.I. - Vertical Surface Illumination,H.S.I. - Horizontal Surface Illumination

TOTAL LUMINOUS ENERGY 1000 Lumen-Hours Sun and Clear Sky-8:00 a.m. to 5:00 p.m. Date South East West Horizontal Jan 22, 1954 51.6 16.1 18.1 24.2 Feb 17, 1954 54.5 20.1 22.7 54.2 March 20, 1955 52.1 50.4 27.5 54.5 April 21, 1953 37.6 27.8 29.4 69.3 May 28, 1953 31.8 55.0 24.5 76.5 June 25, 1955 25.9 51.2 25.0 78.5 July 24, 1953 33.2 54.7 29.7 77.7 August 20, 1955 41.3 32.6 52.6 66.8 Sept 28, 1955 55.7 28.2 28.5 50.8 Oct 29, 1955 58.1 20.4 24.9 35.7 Nov 17, 1955 49.7 17.0 17.8 25.2 Dec 16, 1955 47.5 14.2 15.6 20.5 TABLE V

COMPARISON OF CLOUDY AND CLOUDLESS DAYS 8:00 a.m. to 5:00 p.m. Jan Feb Mar Apr May June July Aug Sept Oct Nov Dec Percent Possible Sunshine 31 44 38 43 52 70 75 76 75 70 40 32 Avg Noon Sun Alt 27.5 35 46 57 66 70.5 69 62 51 40 30 25.5 Horizontal Surface Io 2700 3720 5500 7280 8250 8640 8560 7670 6250 4670 3110 2310 R1 0.23 0. 30 0.38 0.33 0.32 0.34 o.36 0.36 0.36 0.23 0.33 0.32 R2 0.29 0,. 36 0.44 0.42 0.40 0.52 0.53 0.45 0.40 0.29 0.42 0.43 R3 0.42 0.57 0.63 0.63 0.60 0.72 0.72 0.83 0.81 o.83 o.65 0.64 ro 0 South Vertical Surface Io 5600 5900 5640 4560 3600 3170 3420 4420 5450 6170 5840 5280 R1 0.068 0.103 0.16 0.22 0.27 0.42 0.41 3 0.22 0.086 0.098 0.083 R2 ~~0.094 0.143 0.23 0.32 0.37 0.64 0.60 0.39 0.29 0.138 0.150 0.140 R3 0.25 0.45 o.45 o.58 0.59 0.88 0.78 o.85 0.78 0.76 0.47 0.41 East or West Vertical Surface Io 1800 2300 2900 3170 3170 3170 3360 3560 3330 2750 2080 1670 R1 0.144 0.26 0.31 0.33 0.35 0.44 0.41 o.35 0.35 0.20 0.25 0.23 R2 0.171 0.31 0.38 0.42 0.44 0.58 o.54 0.43 0.40 0.27 0.31 0.32 R3 0.28 0.53 0.58 0.64 0.62 0.84 0.81 0.82 0.82 0.83 0.57 0,53 ICo* 3200 4100 5000 5700 5600 5700 5000 6300 6000 5000 3670 2830 R1i* 0.109 0.134 o.19 0.18 0.20 0.24 0.21 0.17 0.19 0.112 0.15 0.15 R3* 0.28 o.46 o.47 0.56 0.52 0.76 0.73 0.77 0.76 0.80 0.50 0.47 *For east in a.m. or west in p.m. TABLE VI

LIST OF FIGURES Figure 1 Photocell Arrangement (photograph) 2 Exterior Illumination-May 5, 1953. Designation of Classes A, B, C and D. 3 Availability of Daylight. 8:30 a.m. to 3:30 p.m. -School Year. Negligible Foreground Reflectance. 4 Availability of Daylight. 8:30 a.m. to 3:30 p.m.-School Year. Foreground Reflectance-25f. 5 Availability of Daylight. 8: 30 a.m. to 3:30 p.m. — Entire Year. Negligible Foreground Reflectance. 6 Availability of Daylight. 8: 30 a.m. to 3:30 p.m. -Entire Year. Foreground Reflectance-253. 7 Availability of Daylight. 8:00 a.m. to 5:00 p.m.-Entire Year. Negligible Foreground Reflectance. 8 Availability of Daylight. 8:00 a.m. to 5'00 p.m. —Entire Year. Foreground Reflectance-25%. 9 Daylight Intensity. Sun and Clear Sky. March 20, 1953. 10 Daylight Intensity. Sun and Clear Sky. June 23, 1953. 11 Daylight Intensity. Sun and Clear Sky. September 28, 1953. 12 Daylight Intensity. Sun and Clear Sky. December 16, 1953. 13 Total Luminous Energy per Day. Sun and Clear Sky-Negligible Foreground Reflectance. 8:00 a.m. to 5:00 p.m. 14 Average Number Hours per Day-8:00 a.m. to 5:00 p.m. Illumination Above 1000 and 2000 FtC. 15 Average Illumination. Horizontal Surface —8:00 a.m. to 5:00 p.m. Calculated and Measured. I = Io (0.32 + 0.68S) 16 Average Illumination. South Vertical Surface —8:00 a.m. to 5:00 p.m. Calculated and Measured. I = Io [S + 0.95 (1-S) sin2 a/2] 17 Average Illumination. East Vertical Surface in a.m. West Vertical Surface in p.m. 8:00 a.m. to 5:00 p.m. Calculated and Measured. I = Io [S + 0.44 (l-S) sin cz/2]

Fig. 1. Photocell arrangement.

EXTERIOR ILLUMINATION MAY 5, 1953 __ Designation of classes A, B, C and D A A A B B B B B A B C D DC D B A A A A A A A A B B C D D D D D D'D D D D 10,9000 9000 8 9 11 12 1 2 3 4 5 8000 7000 -' 6000 zi HORIZ.___ 5000 2 )4000J_ 3000 2000 1000 E- _ 8 9 10 11 12 I 2 3 4 5 E.S. TIME Fig. 2

10,000- -.... l l _ 9000 8000 __ 7000 86000 _ __- _ m e _. 5000 4000 3000 ____ W(P.M.) S E(A.M.) HORIZ. 200i0 100I IE(P.M \, AVAILABILITY OF DAYLIGHT W(MA.M.) - school year 100 400 10 20 30 40 50 60 70 80 90 100 200 AVAILABILITY OF DAYLIGHT 8:30 A.M. to 3:30 P.M. - school year Negligible foreground reflectance PERCENTAGE OF TIME - ILLUMINATION ABOVE INDICATED VALUE Fig. 3

10,000 9000 8000 \ ___ 7000 6000% _. F... 5000 4000 3000 17 w(P.M.) O7uX, ____ E(A.M.) __. aooo 900 1000 0 00 700 600 300 200 AVAILABILITY OF DAYLIGHT 8:30 A.M. to 3:30 P.M. - school year Foreground reflectance - 25% 100, I 0 10 20 30 40 50 60 70 80 90 100 PERCENTAGE OF TIME - ILLUMINATION ABOVE INDICATED VAIUE Fig. 4

10,000 9000 8000, 7000 HORIZ. 6000 5000'x'' 4000 ": \ E(A.M.),- r W(P.M. 300 _0 2000,00 W(A.M.) 8:30 A.M. to 3::30 PM. - entire year 00 I I........1.. 900 0 10 20 30 40 50 60 70 80 90 00 8:30 A.M. to 3-30 P.M. - entire year PERCENTAGE OF TIME - ILLUMINATION ABOVE INDICATED VALUE Fig. 5

10,000 I - - - 9000 _..... 8000 v.\ _ HORIZ. 6000 6000..... _ __. HO R __.. 5000 - 0W(P.M.) 4000 3000, W M 2000 W(A.M.) E(P.M.) 1000 o 900 800 700 600 300 200 AVAILABILITY OF DAYLIGHT 8:30 A.M. to 3:30 P.M. - entire year Foreground reflectance - 25% 100 I i I I I I 0 10 20 30 40 50 60 70 80 90 100 PERCENTAGE OF TIME - ILLUMINATION ABOVE INDICATED VALUE Fig. 6

10,000 -- 9000 M 8000 ___. 7000 5 00 A.50 E(A.M.), e 3000 10. 1 I\\,.... I 2000 X00, N -- W(A.M.) 1000. 700,.,AILABILITY k \'I 400 300 i.__ 200.. AVAILABILITY OF DAYLIGHT 8:00 A.M. to 5:00 P.M. - entire year 0 10 20 30 40 50 60 70 80 90 100 PERCENTAGE OF TIME - ILLUMINATION ABOVE INDICATED VALUE Fig. 7

10,000 9000 C 7000 26000, w(P..M.) 5000 1 I~e~ E(A.. 4000 O D IE(P'-x.. 0 900. 800 l 700 300 200 AVAILABILITY OF DAYLIGHT 8:00 A.M. to 5:00 P.M. - entire year Foreground reflectance - 25% 100 I I I I I I I I - O 10 30 00 50 60 70 80 90 100 PERCENTAGE OF TIME - ILLUM1NAI0N ABOVE INDICATED VALUE Fig. 8

I I' i..... I I I I I I I DAYLIGHT INTENSITY Sun and clear sky.. - March 20, 1953 10,000 IZ 9000. 8000 - I —t- I I ) 2 < X XI I_ I _, 8000 W 0.- 4000- _._ __ __ __f01 3000 / _ 6000-. 5000 - 0-, _S, __8 9 10 11 12 1 2 3 4 5 E.S. TIME Fig. 9

I ~~~~I! I I i DAYIGHT INTENSITY Sun and clear sky 11,0 June 23, 1953 __ 10,000 __ __ 9000 -,," 5000 7000'~~~~i. 10 -' 6000 /" ~' 500'0' o, I \ S 4000 s o~~~~~~~~~~~~,o 3000 2000 " 008 //,.,, /~ 8 9 10 11 12 1 2 3 4 E.,S. TIME F 10g. 10

- - I... - DAYLIGHT INTENSITY Sun and clear sky September 28, 1953 10,000... 9000. 8000.._ _,. E S 7000,,. 6000 0 x' 2 4000-,/ —,, ~-.-/4-,8 9 10 I 1 2 1 2 3 4 E.S. TIME Fig. i11

-..... l.. DAYLIGHT INTENSITY -I. ISun and clear sky December 16, 1953 10,000................. 9000 - S -. 8000.._ 7000 6000 _ _ _/ _ _ _ ___ _ 5000...... 4000 OR'' 1000- /,._ 100 - - -\/ - \ - - - - - 8 9 10 11 12 1 2 3 4 5 E.S. TIME Fig. 12

'~~~~~ I! I I I.... i I I [ I I! [ " TOTAL LUMINOUS ENERGY PER DAY Sun and clear sky - negligible foreground reflectance 8:00 A.M. to 5:00 P.M, Ill 80 HORIZ. x x 40 - 0 30 E- _. 20 -x- j-'/~ 10 - JUNE -EC. JAN. FEB. MAR. APR. MAY IJULY AUG. SEPT. OCT. NOV. 1522 17 15 20 15 21 282315 15 20 15 28 15 9 51716.x x 15 xx 1 XX l5S>X x x XX xxlxx X xx xx -x x - x i 11.5_241 I 15. 27.5 24.5 31.5 41.5 51.5 61.5 71.5 61.5 51.5 41.5 31.5 24.5 27.5 SUN ALTITUDE AT NOON Fig. 13

AVERAGE NUMBER HOURS PER DAY - 8:00 A.M. to 5:00 P.M. Illumination above 1000 and 2000 FTC. 9 _ HORIZ. 8 0._., 2000 FTC. 7/ 6 z -t o, J z:~~~' EE:lp Mi~~~~~~~~~~~~,.0 00 0 ~- /,\ -' 7II/ a= 0 4'' i I I I I. 9 HORZ. 8 1000 FTC. a " I~- / ~ ~~~~ -ar 4 3 3= DEC. JAN. FEB. MAR. APR..AY JUE.JULY AUG. SEPT. OCT. NOV. DEC. JAN. MONTH Fig. 14

AVERAGE ILLUMINATION Horizontal surface - 8:00 A.M. to 5:00 P.M. Calculated and measured I = 1o (0.32 + 0.68 S) 9.000..-. - 8000 / 7000 Ol/ 6000 /,I 5000 o /I 4000 -/ 31 44 38 43 52 70 75 76 75 70 40 32 PERCENT POSSIBLE SUNSHINE Fig. 15

AVERAGE ILLUMINATION South vertical surface - 8:00 A.M. to 5:00 P.M. Calculated and measured I=Io [S+ 0.95 (1 - S) sin2 a/2] 8000 7000 -...... 6000 - -"_.. 5000 31 4000 75 76 75 70 40 32 FigR3 6 2000 " 1000 ~-C!0.95 Jo SIN r/2 R..I..._RiI0 JAN. FEB. MAR. APR. MAY JUNE JULY AUG. SEPT. OCT. NOV. DEC. MONTH 31 44 38 43 52 70 75 76 75 70 40 32 PERCENT POSSIBLE SUNSHINE 27.5 35 46 57 66 70.5 69 62 51 40 30 25.5 AVERAGE NOON SUN ALTITUDE Fig. 16

AVERAGE ILLUMINATION East vertical surface in A.M. West vertical surface in P.M. 8:00 A.M. to 5:00 P.M, Calculated and measured I=Io [ + 0.44(1 - S) sin a/2] 8000. -----—. 7000 -~o~~~~~~~~oo M" -~ 5000.....'............ ~ "~ " 40003 2 70 75 76 75 70 40 32 PERCENT POSSIBLE SUNSHINE 3000. 69 62 51 40 30 25.5 AVERAGE NOON SUN 0.44IoALTISINTUDE F'ig. 17 JAN. FEB. MAR. APR. MAY JUNE JULY AUG. SEPT. OCT. NOV. DEC. MONTH 31 44 38 43 52 70 75 76 75 70 40 32 PERCENT POSSIBLE SUNSHINE 27.5 35 46 57 66 70.5 69 62 51 40 30 25.5 AVERAGE NOON SUN ALTITUDE Fig. 17

UNIVERSITY OF MICHIGAN 3 1111111015 02523 04601111111 3 9015 02523 0460