xt7nvx05zt21 https://exploreuk.uky.edu/dips/xt7nvx05zt21/data/mets.xml   Kentucky Agricultural Experiment Station. 1972 journals 208 English Lexington : Agricultural Experiment Station, University of Kentucky Contact the Special Collections Research Center for information regarding rights and use of this collection. Kentucky Agricultural Experiment Station Progress report (Kentucky Agricultural Experiment Station) n.208 text Progress report (Kentucky Agricultural Experiment Station) n.208 1972 2014 true xt7nvx05zt21 section xt7nvx05zt21 S Z R d' t' Sl ji
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By B. Barfneld, J. Hall and J. Walker * Progress Report 208
UNIVERSITY OF KENTUCKY :: COLLEGE OF AGRICULTURE :: AGRICULTURAL EXPERIMENT STATION
Department of Agncultural Engmeermg In cooperatnon wnth Natlonal Weather Servace
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 I CONTENTS
PAGE _
Introduction ....................... 3
Description of the Tables and Graphs .............. 3 4
Discussion of Data ..................... 4 i
Literature Cited ...................... 4
Appendix I: Tables and Graphs ................ 5
Appendix II: Procedure for Calculating the Ratio of Solar Energy l
Falling on Sloping Surfaces ................ 14
Appendix III: Computer Program ............... 15 ·
-2.

 Solar Radiation on Sloping Surfaces in Kentucky
By B. BARFIELD, ]. HILL, and]. WALKER*
The amount of solar energy (radiation flux) reaching the surface of the earth greatly
affects many agricultural and industrial activities. This amount of energy is influenced by time of
year as well as by the slope of the surface and the direction which the surface faces (aspect). This
is known as the slope-aspect effect. A casual observation of the difference in snow cover and in
A the timing of tree leafing on north and south facing slopes can reveal the difference in solar
energy reaching the slopes. Casual observation, however, does not indicate which slope and aspect
will receive the most or the least energy for any period of the year.
Most textbooks on climatology refer to the slope-aspect effects on the quantity of solar _
energy reaching the surface   Equations are also available (2) for making calculations of the
slope-aspect effect for any given date. Making use of these equations by hand computations is
time-consuming; however, the use of computers makes extensive calculations practical.
‘ The purpose of this report is to provide a set of tables and graphs showing the effect of
the slope and aspect on the solar energy falling on a surface for each month of the year for the .
state of Kentucky.
DESCRIPTION OF THE TABLES AND GRAPHS Y
The amount of solar energy striking a surface at any time depends on the angle between
the surface and sun and the brightness of the sun. This is shown graphically in Appendix II. If the
solar intensity is known or can be assumed, calculations can be made of the amount of energy
falling on any surface at any instant of time.
Climatological observations of solar energy are usually made on a horizontal surface;but
in most applications involving solar energy, one is interested in the ratio of daily or monthly total
energy reaching a sloping surface as compared with the horizontal surface. To determine this
ratio, one has to account for the variation in angles between the surface and the sun during the
l day. The procedure for accounting for this variation and taking the average is shown in Appendix
II. The calculated ratios are shown in Appendix I for each month of the year for Kentucky
(average latitude 37.5°N).
Table 1 in Appendix I shows the average amount of solar energy falling on a horizontal
surface on a clear day in Kentucky for each month. It also shows the long-term average daily ’
radiation by months. The long-term average accounts for the effects of cloudiness. Figures 1
through 12 in Appendix I show the ratio of energy falling on a sloping surface to that on a
A horizontal surface for varying aspects (slope orientations) and months of the year. Figure 13
shows the effect of slope and aspect averaged over the entire year. For a given slope and aspect,
one could multiply the ratio found in Fig. 1 through 13 by the appropriate value in Table 1 and
determine the amount of solar energy reaching the surface on a clear day or the long-term daily
average which accounts for cloudiness. For example, consider a slope of 10 degrees facing SSE
(150°) during january and june. The ratio of energy reaching the slope to that on a horizontal
surface is given in Figs. 1 and 6 as 1.29 in january and 1.04 in june. The long-term average
reaching a horizontal surface is given in Table 1 as 610 BTU/ft2 day in january and 2120
BUT/ft2 day in june. Making the appropriate multiplication, the energy on the average which
reaches the slope in january is 1.29 x 610 = 787 BTU/ft2 day and injune is 1.04 x 2120 = 2205
BTU/ft2 day.
*Associate Professor of Agricultural Engineering; Advisory Agricultural Meteorologist, National Weather Service;
and Professor of Agricultural Engineering.
.3-

 The graphs in Figs. 1 through 12 are symmetrical; hence, only half of each graph is
shown. To prevent "cluttering" the graphs, a portion of the curves was drawn on the left half of
the graph and the remainder on the right half of the graph.
DISCUSSION OF DATA
One potential use of the data presented is in the location of plant beds. Plant beds should
, be located to get the maximum solar energy falling on the surface. During the months of April
and May, for example, the maximum solar energy falls on the slope of l5° facing south as shown
in Figs. 4 and 5. During these months, however, there is very little variation in the amount of
energy received on a 15° slope varying between ESE to WSW. Hence, a plant bed would be nearly
optimally located on a l5° slope facing anywhere between ESE and WSW.
Another potential use of the information is in the location of sites for exposing material .
to the sun to be dried. The materials to be dried could vary from lumber to digested sludge. As
with the previous example, the dryer should be located and tilted so that the maximum solar
radiation would be received on the surface during the drying period. In this application, one ·
would need to consider the average expected solar energy for the months that the dryer would be
operated. .
A use of the data in which solar energy minimization is of interest is in the location of
winter sports areas. To minimize snow melt, a slope aspect relationship should be selected which
minimizes incoming solar energy.
A major potential use of the data could be for the determination of the solar intensity
impinging upon windows in any type of structure. Because the data consider all slopes from
horizontal to vertical, the intensity upon windows in either walls or sloped roofs can easily be l
determined. By appropriate use of glazing transmission data, the direct solar heating load within
the structures can be determined. Possible uses of this information include the orientation of
greenhouse benches and the orientation of homes and other buildings for minimum air condition- _
l ing and heating loads.
Several interesting observations can be made from the information on the graphs. One can
observe for any given month that the maximum ratio will be for some angle on a south-facing
slope. This angle is small in the summer months and large in the winter months. During the
winter months, south-facing slopes have the largest ratio regardless of the angle. During the
summer months, steep angles have a maximum ratio for SE and SW angles. This is because the
sun will never be perpendicular to south-facing slopes which have steep angles.
LITERATURE CITED
1. Geiger, R. 1966. The Climate Near the Ground. Harvard University Press, Cambridge.
2. American Society of Heating, Refrigerating, and Air Conditioning Engineers. 1967. Handbook of
Fundamentals. New York.
-4-

 APPENDIX I:
TABLES AND GRAPHS
Table 1.—Average Solar Energy on a Horizontal Surface in Kentucky (Btu] sq ft/day).
Long Term Average
Month Clear Day (Considering Cloudiness)
january 1 ,035 610
- February 1,41 3 85 0
March 1,869 1,120
April 2,207 1,550
May 2,434 1,900
june 2,503 2,120 »
july 2,42 6 2,030
August 2,252 1,770
September 1,641 1,5 30
October 1,557 1,180
` November 1,134 810
December 91 8 590 ‘
Table 2.—Relationship Between Slope Angles and Percent
Slope.
Angle Slope in Percent
e (degrees) (Ft of Fall per 100 Ft)
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1 1.7
2 3.5
_ 5 8.7
1 0 17.0
15 27.0
30 57 .0
45 1 00.0
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75 37 3.0
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.12.
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EE
-J-IO
O
cn
—l5
-20
‘ -25
JAN FEB MAR APR MAY JUN JUL AUG SEPT OCT NOV DEC
Fig. 15.—S0lar declination.
-13.

 APPENDIX II
PROCEDURE FOR CALCULATING THE RATIO OF SOLAR ENERGY
FALLING ON SLOPING SURFACES
The amount of solar energy striking a surface depends on the brightness of the sun "B"
and the angle between a line perpendicular (normal) to the surface and the sun. This angle "0S" is
known as the incident angle. When the incident angle is zero, the sun is perpendicular to the
surface. The amount of solar energy "Q" reaching the surface can be calculated from the
equation
· Q = B cos0S (1)
The incident angle can be calculated from the equation
cos0S = cosB cosy sinE + sin[3 cosE (2)
where B is the solar elevation angle, ·y is the wall-solar azimuth, and E is the slope angle of the _
surface. These angles are shown graphically in figure 14. The wall-solar azimuth can be calculated
from
v = W + W, (3)
where (lz is the wall azimuth (aspect) and xlxs is the solar azimuth. For a given surface, the slope
angle and wall azimuth will remain the same throughout the year. For given values of solar _
azimuth and elevation, then one can calculate the energy falling on the sloping surface with angle
E and compare that to a horizontal surface where E is zero.
The solar elevation and azimuth angles can be calculated from the equation
sin{3 = sin<$ sinL + cos'6 cosL cosH (4)
where 6 is the solar declination angle, given in Fig. 15, L is the latitude, and H is the hour angle
of the sun which can be calculated from the time of day.
The hour angle of the sun can be calculated to within 4 degrees of accuracy by the
equation
No. of hours from `
¤0¤¤ mdard me Actual 1%.....
H E 15 X +if a`m` + [Longitude — Longitude] (5)
-1f p.m.
The reference longitudes are 75°W, 90°W, 105°W, and l20°W for Eastern, Central, Mounta.in,and
Pacific time, respectively. Obviously, for hour angles prior to sunrise and after sunset, H has no
meaning. The hour angle can be calculated for sunrise and sunset from the equation
1
Hsumisc = cos- [tan8 tanL] (6)
A further description of Equations 1 through 6 is given in the ASHRAE Handbook of
Fundamentals  
A computer program was developed using slightly modified forms of Equations 1 through
5 to make calculations for each hour of the day throughout each month. Calculation is made of
the total daily energy falling on a sloping surface and on a horizontal surface, then the daily ratio
is computed and averaged over the month. This is done for 19 different slope angles and 19
aspect angles.
The computer program for making these calculations is given in Appendix IH.
The only variable is the latitude of the location being considered. The input on each card
is the name of the month being computed, the julian day number of its first day, and the total
number of days in that month. The program can be used for only selected months or 12 cards
can be entered to make the calculations for an entire year.
-14-
. l"*· (

 APPENDIX III:
COMPUTERPROGRAM
C SOLAR
C
C
C THIS IS A PROGRAM TO DETERMINE THE RATIO OF THE SOLAR RADIATION ON A
C HORIZONTAL SURFACE TO THAT RECEIVED ON A SLOPING SURFACE FOR ALL
C COMBINATIONS OF SLOPE ORIENTATION AND INCLINATION.
C
V C
IMPLICIT REAL (A-Z)
INTEGER DAYNO, HR, DCTN,NODAYS• IMAGE»A,B,J,N,X,Y
REAL*8 MONTH
DIMENSION MOFCN(20,36D, Z(3I•20}•AZANGL(31,20I
C ESTABLISH THE LATITUDE
10 LAT=37.5
R=57.29578
- SINLAT=SIN(LAT/R)
COSLAT=COS(LAT/RI
C READ THE DATA CARD INDICATING THE NAME OF THE MONTH TO BE CALCULATED,
C THE DAYNUMBER OF THE FIRST DAY, AND THE TOTAL NUMBER DF DAYS IN THAT
C MONTH.
20 READ(5•1001•END=130) MONTH, DAYNO,NODAYS
1001 FORMAT (A8•1Xv2I3l *
» C COMPUTE THE POSITION OF THE SUN FOR EACH HOUR OF EACH DAY IN THE
C MONTH AND PLACE IT IN AN ARRAY BY DAY AND HOUR.
DO 40 N=1•NODAYS
DO 30 HR=4•20
C FIRST• COMPUTE THE DECLINATION OF THE SUN, DELTA
SOLHR=I2.0—HR
HRANGL=(SOLHR*15.0)/R
A= DAYNO+N·173
C=.987*A
DELTA=23.5*COS(C/R)/57.29578
C Z IS THE ZENITH ANGLE OF THE SUN AND AZANGL IS THE AZIMUTH DF THE
C SUN COMPUTED FROM DUE SOUTH.
Z(N•HR)=ARCOS(SINLAT*SIN(DELTA)+COSLAT*COS(DELTA)*COS(HRANGL)I
AZANGL(N•HR)=ARSINI-(COSTDELTA)*SIN(HRANGL)/SINIZ(N•HR))l) ,
30 CONTINUE
40 CONTINUE
_ C SET THE INCLINATION OF THE SLOPE• I
DO 100 X=1,l9
I=(5*(X-1))/R
COSOFI=COS(I)
SINOFI=SIN(I)
C SET THE DIRECTION, B INITIALLY TO DUE NORTH AND CHANGE IT BY
C INCREMENTS OF 10 DEGREES.
DO 90 Y=1•19
B=Y·1
C INITIALIZE THE MONTHLY FRACTION TO ZERO BEFORE STARTING ON A
C DIFFERENTLY ORIENTED SLOPE.
MOTOT=0.0
C COMPUTE THE ANGLE BETWEEN A LINE NORMAL TO THE SLOPE AND DUE SOUTH.
APRIME=((I0*B)+I80)/R
IF IAPRIME .GE. 6.2832) APRIME=APRIME•6.2832
DO 80 N=I•NODAYS
C INITIALIZE THE TOTAL DAILY RADIATION ON THE HORIZONTAL SURFACE AND ON
-15.

 C THE SLOPE TO ZERO.
TOTHOR=0.0
TOTSLP=0.0
DO 70 HR=4.20
C IF THE SUN IS BELOW THE HORIZON• THERE IS NO RADIATION STRIKING THE
C SLOPE.
IF (Z(N.HR) .GE. 1.57079) GO TO 50
C COMPUTE THE HORIZONTAL ANGLE BETWEEN THE SUN AND A NORMAL TO THE
C SLOPE.
DIFF= AZANGL(N•HR) - APRIME
C COMPUTE THE RADIATION FALLING ON THE SLOPE ASSUMING THE INCIDENT
A C RADIATION IS UNITY.
QS=COSIZ(N.HR))*COSOFI+SIN(Z(N•HR))*SINOFI*COS(DIFF)
C WHEN QS IS NEGATIVE. THE RADIATION IS FALLING ON THE BACK OF THE
C SLOPE AND NONE IS REACHING THE FRONT.
IFIQS .LE. 0.0) QS=0.0
C COMPUTE THE RADIATION ON A HORIZONTAL SURFACE ASSUMMING THE
C INCIDENT RADIATION IS UNITY.
QH=COS(ZIN•HR))
GO TO 60
50 0S=0.0
OH=0.0
C SUM THE HOURLY RADIATION 0N THE SLOPE AND ON THE HORIZONTAL SURFACE.
60 TOTHOR=TOTHOR+QH
TOTSLP=TOTSLP+QS
70 CONTINUE
C AT THE END OF THE DAY, COMPUTE THE FRACTION OF THE RADIATION
C RECEIVED ON THE SLOPE TO THAT RECEIVED ON A HORIZONTAL SURFACE.
DAYFCN=TDTSLP/TOTHOR
C SUM THE DAILY FRACTIONS TO OBTAIN THE TOTAL FOR THE MONTH.
MOTOT=DAYFCN+MOTOT
80 CONTINUE
C DIVIDE THE MONTHLY TOTAL BY THE NUMBER OF DAYS IN THE MONTH IN ORDER ’
C TO OBTAIN THE AVERAGE MONTHLY RATIO OF RADIATION ON THE SLOPE TO
C RADIATION ON A HORIZONTAL SURFACE FOR THE GIVEN SLOPE.
MOFCN(X»Y)=MOTOT/NOOAYS
C INCREMENT THE INCLINATION AND ORIENTATION OF THE SLOPE TO OBTAIN V
C ALL POSSIBLE COMBINATIONS.
90 CONTINUE
100 CONTINUE
110 WRITE (6•1002 ) MONTH
1002 FORMAT ('1',42X•'DURING '•A8•' THE FRACTION OF THE SOLAR RADIATION
X ON'/•43X,'A HORIZONTAL SURFACE WHICH IS RECEIVED ON A SLOPE IS:')
WRITE (6.1003)
1003 FORMAT ('0'•47X.'SLOPE ANGLE IN DEGREES (0 IS LEVEL GROUND)')
WRITE(6•1004) (J. J=5•90•5)
1004 FORMAT ('0'.22X.'0',18I5)
OO 120 Y=1•19
B=Y·1
DCTN=I0*B
IMAGE=360-DCTN
WRITE(6,1005) DCTN• (MOFCN(X•Y)• X=1•19)• IMAGE
1005 FORMAT (14X•I3y3X.19F5.2•4X.I3)
120 CONTINUE
GO TO 20
130 STOP
END 2M-3-73
-16.