• TABLE OF CONTENTS
HIDE
 Copyright
 Front Cover
 Movement of the sun
 Using the shading factors
 Back Cover






Group Title: Florida Cooperative Extension Service circular 515
Title: Factors for determining shading patterns in Florida West Palm Beach and vicinity
CITATION PAGE IMAGE ZOOMABLE PAGE TEXT
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00049251/00001
 Material Information
Title: Factors for determining shading patterns in Florida West Palm Beach and vicinity
Series Title: Circular Florida Cooperative Extension Service
Physical Description: 27 p. : ill. ; 23 cm.
Language: English
Creator: Buffington, Dennis E
Sastry, Sudhir K ( Sudhir Kartikeya ), 1952-
Black, Robert J ( Robert John ), 1942-
Publisher: Florida Cooperative Extension Service, Institute of Food and Agricultural Sciences, University of Florida
Place of Publication: Gainesville
Publication Date: 1981?
 Subjects
Subject: Shades and shadows   ( lcsh )
Landscape architecture -- Florida -- West Palm Beach   ( lcsh )
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
non-fiction   ( marcgt )
 Notes
Statement of Responsibility: Dennis E. Buffington, Sudhir K. Sastry and Robert J. Black.
General Note: Cover title.
Funding: Florida Historical Agriculture and Rural Life
 Record Information
Bibliographic ID: UF00049251
Volume ID: VID00001
Source Institution: Marston Science Library, George A. Smathers Libraries, University of Florida
Holding Location: Florida Agricultural Experiment Station, Florida Cooperative Extension Service, Florida Department of Agriculture and Consumer Services, and the Engineering and Industrial Experiment Station; Institute for Food and Agricultural Services (IFAS), University of Florida
Rights Management: All rights reserved, Board of Trustees of the University of Florida
Resource Identifier: oclc - 08818063

Table of Contents
    Copyright
        Copyright
    Front Cover
        Page 1
        Page 2
    Movement of the sun
        Page 3
        Page 4
    Using the shading factors
        Page 5
        Page 6
        Page 7
        Page 8
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
    Back Cover
        Page 28
Full Text





HISTORIC NOTE


The publications in this collection do
not reflect current scientific knowledge
or recommendations. These texts
represent the historic publishing
record of the Institute for Food and
Agricultural Sciences and should be
used only to trace the historic work of
the Institute and its staff. Current IFAS
research may be found on the
Electronic Data Information Source
(EDIS)

site maintained by the Florida
Cooperative Extension Service.






Copyright 2005, Board of Trustees, University
of Florida



































































Dennis E. Buffington is an Associate Professor in Agricultural Engineering, Sudhir K.
Sastry was a graduate student in Agricultural Engineering, and Robert J. Black is an As-
sociate Professor in Ornamental Horticulture, Institute of Food and Agricultural Sciences,
University of Florida, Gainesville 32611.








FACTORS FOR DETERMINING
SHADING PATTERNS
IN
FLORIDA
West Palm Beach and Vicinity

Dennis E. Buffington, Sudhir K. Sastry, and Robert J. Black


Patterns of shade cast by an object, either natural or man-made, are often
needed to utilize or avoid the shade. To locate the shading pattern cast by
any object, the specific time (month, day, and hour), latitude and longitude
of the location, and the physical dimensions of the object casting the shade
are required. The shadow dimensions can then be calculated by applying
earth-sun angular relationships. Mathematical relationships of the earth-
sun angles have been known for centuries, but it becomes very tedious to
use the relationships to calculate shading patterns for several hours of a rep-
resentative day of each month throughout a year to describe necessary
shading patterns for a design.
The object of this circular is to present tabulated values to use for the de-
termination of shading patterns throughout the year for any described shad-
ing device. Examples to illustrate the use of the tabulated values are
presented. The tabulated values were computer calculated specifically for
the West Palm Beach location from the mathematical relationships of the
earth-sun angles. By using the tabulated values presented in this circular,
one can easily determine shade patterns for the West Palm Beach location,
without having a knowledge of earth-sun angular relationships.

Movement of the Sun
The sun appears to move across the sky in a circular arc from the east
horizon to the west horizon. The sun is directly over the equator on the vernal
equinox (around March 22) and the autumnal equinox (around September
22). On these two days and only on these two days each year the sun
rises due east and sets due west. Between the vernal equinox and autumnal
equinox the sun rises north of east and sets north of west. On the summer
solstice (around June 22), the sun is at its highest point in the sky. On this
day, the sun is directly over the Tropic of Cancer (23.5 deg North latitude).
The summer solstice day has the longest daylight period in the year in the
northern hemisphere. On this day, all locations farther north than the Arctic
Circle (66.5 deg North latitude) have continuous light for 24 hours.
During the fall and winter months, the sun rises south of east and sets
south of west. On the winter solstice (around December 22), the sun is di-
rectly above the Tropic of Capricorn (23.5 deg South latitude). On the winter








solstice day, the sun is at its lowest point in the sky and corresponds to the
shortest daylight period of the year in the northern hemisphere. Continuous
darkness is experienced on this day for all locations in the Arctic Circle.
Factors for determining shading patterns (shade projection factors and
azimuth angles) are presented for West Palm Beach, Florida in Tables 1
through 12. Publications containing the shading factors for ten other Flor-
ida locations are available from your County Extension Office. When cal-
culating shading patterns for any given location, refer to Figure 1 to determine
the nearest city for which a publication with shading factors is available.


Figure 1. Florida regions with publications available on factors for determining
shading patterns.


,^'~ P








Using the Shading Factors
Precise shadow locations can be determined by using the azimuth angles
and shade projection factors presented in Tables 1 through 12. The data
presented are for the 1st, 8th, 15th, and 22nd day of each month for West
Palm Beach, Florida (26.7 deg North latitude; 80.1 deg West longitude). For
each day, data are presented for all daylight hours (from within one hour of
sunrise to within one hour of sunset). The time of day is expressed as East-
ern Daylight Savings Time from May through October. For the remaining
months of the year, the time is expressed as Eastern Standard Time. The
azimuth angle is defined as the angle of the sun's rays in the horizontal plane
measured from south. The shade projection factor is the shade length per
unit height of the object casting the shade. The shade projection factor is
dimensionless, so it can be used with either English or metric units.
A positive azimuth angle is measured as the number of degrees clock-
wise from the south axis; a negative azimuth angle is measured counter-
clockwise from the south axis. Azimuth angles before solar noon are neg-
ative; after solar noon, azimuth angles are positive. Solar noon corresponds
to the time when the sun is due south and is at its highest point in the sky
for that day.
Data presented in Tables 1 through 12 are useful for determining shading
patterns cast by an object onto a horizontal surface. The shadow will be
shortened if the surface slopes upward, or elongated if the surface slopes
downward away from the shade-casting object. To illustrate the use of the
data in the tables, consider the following examples.
Example #1
It is important to know the location of the shadow from a shading device
for various times of the day for many different days throughout the year to
fully utilize the shade cast by the shading device. After having determined
the shading locations, one can properly site the shade device to maximize
the shading benefits.
Suppose that a horizontal trellis is to be built near West Palm Beach to
cover a picnic area. The dimensions of the trellis are 30 ft (9.1 m) wide and
80 ft (24.4 m) long, with a flat roof 12 ft (3.7 m) high. A scaled sketch of the
trellis is presented in Figure 2. Whenever using the data in Tables 1 through
12, it is always necessary to indicate clearly the direction of the north axis
and to also indicate the scale of the drawing.
For example, to calculate the shadow location at 6 p.m. on June 22, read
the values of 1.9 for the shade projection factor and 103.80 for azimuth an-
gle from Table 6 for 6 p.m. on June 22. For each corner point of the trellis
that is 12 ft (3.7 m) high, the corresponding shadow location is determined
by projecting 22.8 ft (1.9 x 12 ft high) or 7.0 m (1.9 x 3.7 m high) along the
prescribed azimuth angle of 103.80 clockwise from the south axis. The four
shade points are then connected to define the shade location cast by the
trellis as shown in Figure 2.








-- 30 FT.-1

J03.8-'^ ^






SHADE
STRUCTURE 80 FT





SUN'S
RAYS
SCALE
03.8*- N 0 5 10 20'
"--


Figure 2. Shading pattern at 6 p.m. on June 22 for a horizontal shading device 12
ft high.




Example #2
Trees, vines, shrubs, and espaliered plants will protect buildings from in-
tense solar radiation, thereby reducing energy expenditures for air condi-
tioning. Trees are probably the most effective form of vegetation for reducing
solar radiation effects on buildings. A well-designed landscape (including
precisely located trees) will reduce energy expenditures for a building and
enhance its beauty at the same time. Estimates on the potential savings of
energy conserving landscapes are variable, but generally fall within the
range of 20 to 30% in Florida.
Data in the tables can be used to determine the shading patterns from
trees and shrubs. Suppose you have a large tree canopy approximately cu-
bical in shape. Top height is 32 ft (9.8 m); height from ground to bottom of
canopy is 8 ft (2.4 m); and canopy length and width are 40 ft (12.2 m). A top
view of the canopy is shown in Figure 3. The shading pattern cast by the tree
at 3 p.m. on December 22 is calculated by using the shade projection factor
of 2.0 and azimuth angle of 41.60 from Table 12 for 3 p.m. on December
22. The four shadow points corresponding to the four corners of the canopy
bottom are located by multiplying the shade projection factor, 2.0, by the
height to the bottom of the canopy, 8 ft (2.4 m). The corresponding points








are projected 16.0 ft (2.0 x 8 ft) or 4.8 m (2.0 x 2.4 m) on the prescribed
azimuth angle of 41.6'. Similarly, shadow points corresponding to the four
corners of the canopy top are located 64.0 ft (2.0 x 32 ft) or 19.6 m (2.0 x 9.8
m) or, the same prescribed azimuth angle. The shading pattern is deter-
mined by connecting six shadow corner points with the remaining two
shadow corner points inside the shading pattern. (The two inside points are
shading overlap.)
Consider the case of a canopy of several trees approximately rectangular
in shape. The top height is 35 ft (10.7 m); height from ground to bottom of
canopy is 9 ft (2.7 m); canopy width is 24 ft (7.3 m); and canopy length is 70
ft (21.3 m). A top view of the canopy is sketched in Figure 4. The shading
pattern cast by the canopy at noon on December 22 is determined by using
the shade projection factor of 1.2 and azimuth angle of -5.60 from Table 12.
Four shade points corresponding to the bottom of the canopy are located
10.8 ft (3.3 m) on the -5.60 azimuth angle. Four shade points corresponding
to the top of the canopy are located 42 ft (12.8 m) on the same azimuth
angle. As shown in Figure 4, the overall shading pattern is defined by con-
necting the individual shading patterns corresponding to the top and the
bottom of the canopy. The shading pattern for 5 p.m. on April 1 is also
shown in Figure 4.
--SPF= 2.0








40 FT-----




40 F TREE I
CANOPY

SCALE

/,j N 5 10 20'
/ o^AZIMUTH
/ ANGLE
SUN'S
RAYS
Figure 3. Shading pattern at 3 p.m. on December 22 for a cubically shaped tree
canopy.












12 NOON
DEC. 22


5 P.M
APRIL I


SCALE
0 5 10 20


Figure 4. Shading patterns at noon on December 22 and 5 p.m. on April 1 for an approximately rectangular canopy of several trees.



















% %3 ;-- 9-.


5 P.M.


0 5 10 20


Figure 5. Shading patterns at 9 a.m., noon, and 5 p.m. on July 1 for a conically
shaped canopy.


9 A.M.


12 NOON


S.RF. 1.7
S AZ. ANGLE -102.3*













S.PF. = .4
_ AZ. ANGLE= -84.2"











S.PF.= 1.1
AZ. ANGLE= 98.3








Shading patterns for a conically shaped tree with a canopy base diameter
of 25 ft (7.6 m), a top height of 35 ft (10.7 m), and base of canopy height of
4.5 ft (1.4 m) are shown in Figure 5 for the times of 9 a.m., noon, and 5 p.m.
on July 1 in West Palm Beach. Figure 6 presents the shading patterns on
August 8 at 10 a.m., 2 p.m., and 6 p.m. for a cylindrically shaped tree with a
canopy diameter of 12 ft (3.7 m), a top height of 30 ft (9.1 m), and a base of
canopy height of 3.5 ft (1.1 m).
Example #3
One of the most effective ways to conserve energy when air conditioning
a building is to shield the windows from solar radiation. Trees and other
landscaping materials provide a natural, effective means of externally block-
ing the radiation from the window.

-- S. P. = 1.1
*' ,, AZ. ANGLE -88.8


10 A.M.


/ 39.
2 PM.


S. P. F = .2
AZ. ANGLE = 39.0*


S. P. F.= 2.0
AZ. ANGLE = 96.0*
2.0_x 30'I 60'


,6 P.M.


0 5 10 20


Figure 6. Shading patterns at 10 a.m., 2 p.m., and 6 p.m. on August 8 for a cylin-
drically shaped canopy.








Proper tree placement becomes especially critical when one desires to
use the tree(s) to provide shade on a certain window during a certain period.
Consider the example of the west-facing wall of a residence as shown in Fig-
ure 7. It is desired to place a conically shaped tree (as described in Figure
5) with a height of 35 ft (10.7 m) at a specified location so that the major
portion of the large, patio glass doors will be shaded at 4 p.m. on August 8.
Some recent studies have shown that the first week of August generally cor-
responds to the time of maximum ambient temperature and the period of
peak energy utilization of residential air conditioners in Miami and probably
most of Florida. During this week of peak energy usage, the daily maximum
usage normally occurs between 4 and 5 p.m.
In this case, one must determine the height that the shade "climbs up the
wall" of a vertical surface. The data presented in Tables 1 through 12 are
appropriate for this case with some procedural modification. The distance
that the shade will project up a vertical surface is expressed below in Equa-
tion 1.


h'= h (X/SPF) [1]
Where:
h' = height of shade on vertical surface
h = height of object casting the shade
X = horizontal distance from object casting the shade to the vertical
surface
SPF = shade projection factor (from Tables 1 through 12)
A negative or zero value for h' indicates that the vertical surface is not being
shaded at that particular time. Equation 1 can be rearranged to solve for X,
the horizontal distance from object casting the shade to the vertical surface,
as it is below.
X = SPF* (h h') [2]



If it is desired for the conically shaped tree to shade a major portion of the
glass doors at 4 p.m. on August 8, then one must specify that the shadow
point of the top of the tree project at least higher than the top height of the
doors in this case, 6 ft 8 in (2.0 m). For a specified shade projection of 8
ft (2.4 m) up the west-facing wall, the horizontal distance to locate the tree
from the wall is calculated as 21.6 ft (6.6 m) according to Equation 2 for the
shade projection factor of 0.8 from Table 8 at 4 p.m. on August 8. The tree
should then be sited 21.6 ft (6.6 m) from the centerline of the window on
the prescribed azimuth angle of 81.80. The shading pattern on the west-
facing wall is shown in Figure 7. The shading patterns for 3 p.m. and 5 p.m.
for this same case are shown in Figures 8 and 9.














I I I
r___,_1---^






-1 I
S.I


I I
II








SCALE
O 5 10 20'













Figure 7. Top and side views of shading patterns from a conically shaped canopy
on a residential building at 4 p.m. on August 8.












AUGUST 8
3:00 RM.


rr1





I I
I I
I I










--I---


SCALE
0 5 10 20'


Figure 8. Top and side views of shading patterns from a conically shaped canopy
on a residential building at 3 p.m. on August 8.


a a,













AUGUST 8
5:00 PRM.


N

SCALE
0 5 10 20


Figure 9. Top and side views of shading patterns from a conically shaped canopy
on a residential building at 5 p.m. on August 8.


El E E







TABLE 1. SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR WEST FALM BEACH. FLORICA FOR JANUARY




JANUARY 1 JANUARY 8 JANUARY 15 JANUARY 22

EASTERN SHADE SHADE SHADE SHADE
STANDARD PRCJECTICO AZIMUTH PFCJECTION AZIMUTH PROJECTION AZIMUTH PROJECTION AZIMUTH
TIME FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE


8 AM 6.2 -58.3 6.3 -59.3 6.3 -60.6 6.1 -62.1

S AM 2.8 -49.4 2.8 -50.6 2.7 -51.9 2.6 -53.4

10 AM 1.8 -38.2 1.8 -39.4 1.7 -40.8 1.7 -42.3
01
11 AM 1.4 -24.0 1.3 -25.3 1.3 -26.6 1.3 -28.0

12 AM 1.2 -7.1 1.2 -8.2 1.1 -9.3 1.1 -10.3

1 FM 1.2 10.8 1.2 10.1 1.1 9.4 1.1 9.0

2 PM 1.4 27.2 1.4 26.9 1.3 26.7 1.2 26.9

3 PM 1.9 40.8 1.8 40.7 1.7 40.9 1.6 41.5

4 PM 3.1 51.4 2.9 51.6 2.7 52.0 2.6 52.8

5 PM 8.5 59.9 7.3 60.1 6.4 60.7 5.6 61.6










TABLE 2. SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR %EST PALM BEACH. FLORIDA FCR FEBRUARY




FEBRUARY I FEBRUARY 8 FEBRUARY 15 FEBRUARY 22

EASTERN SHADE SHADE S-ADE SHADE
STANDARD PROJECTION AZIMUTH PROJECTION AZIMUTH PROJECTION AZIMUTH PROJECTION AZIMUTH
TIME FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE


8 AM 5.5 -64.6 5.0 -66.4 4.5 -68.4 4.0 -70.5

9 AM 2.5 -55.9 2.3 -57.7 2.2 -59.7 2.0 -61.8

S 10 AM 1.6 -44.7 1.5 -46.5 1.4 -48.4 1.3 -50.4
0)

11 AM 1.2 -30.0 1.1 -31.5 1.0 -33.1 1.0 -34.7

12 AM 1.0 -11.6 0.9 -12.4 C.9 -13.1 0.8 -13.7

1 PM 1.0 8.9 0.9 9.1 0.8 9.6 0.8 10.4

2 PM 1.1 27.8 1.1 28.8 1.0 30.3 0.9 32.1

3 PM 1.5 42.9 1.4 44.4 1.3 46.3 1.2 48.5

4 PM 2.3 54.5 2.2 56.1 2.0 58.1 1.9 60.4

5 PM 4.7 63.5 4.3 65.2 3.9 67.2 3.6 69.4





TABLE 3. SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR %EST PALM BEACH, FLORIDA FOR MARCH


MARCH 1


MARCH 8


MARCH 15


MARCH 22


EASTERN SHADE
STANDARD PROJECTION
TIME FACTOR


7


8

9

- 10


11

12


1

2


3


4


5


23.6

3.6


1.9


1.2

0.9

0.7


0.7

0.9


1*2


1.8

3.3


AZIMUTH
ANGLE


-80.0

-72.7

-64.0


-52.5

-36.4


-14.2


11.6

34.4


51.1


62.9


71.9


SHADE
PROJECTION
FACTOR


14.3

3.2


1.7


S11

0.8

0.6


0.6

0*8


1 1

1.7


3. 1


AZIMUTH
ANGLE


- 82.2

-74.9

-66.2


-54.7

-38.2

-14.6

13.2

37.1


54.0


65.7


74.5


SHADE
PROJECTING
FACTOR


10.1

2.9


1.6


1.0

0.7


0.6

0.6

0.7


1.1


1.6

2.9


AZIMUTH
ANGLE


-84.4


-77.2

-68.5


-57. 0

-40.1


-15.0

15.3


40.3


57.2


68.6


77.3


SHADE
PROJECTION
FACTOR


7.7

2.7


1.5


1.0

0.7


0.5


0.5

0.7


1.0


1.6


2.8


6 -M -. 79.- -2.2 81-8 10. --.5 9.0 87.2


AZIMUTH
ANGLE


-86.7

-79.5


-71.0


-59.5

-42.2

-15.3

17.7

43.9


60.6


71.7


80.1


- - - - - - - -- - - - - - -- -


79o3 12.2 81.8 10.3


84.5 9*0 87.2


6 FM 15o1







TABLE 4. SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR WEST FALM BEACH. FLORIDA FOR APRIL


--------------------------------------------------------------------------------

APRIL 1 APRIL 8 APRIL 15 APRIL 22

EASTERN SHADE SHADE SHADE SHADE
STANDARD PROJECTION AZIMUTH PFCJECTION AZIMUTH PROJECTION AZIMUTH PROJECTION AZIMUTH
TIME FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE
--------------- ---- -------------------- ----------


7 AM 5.8 -89.S 4*9 -92.1 4.3 -94.2 3.9 -96.4

8 AM 2.3 -82.9 2.2 -85.2 2.0 -87.5 1.9 -eS.9

9 AM 1.4 -74.6 1.3 -77.2 1.2 -79.8 11t -82.5

S 10 AM 0.9 -63.4 0.8 -66.3 0.8 -69.3 0.7 -72.5
00

11 AM 0.6 -45.7 0.5 -48.5 0.5 -51.8 0.4 -55.4

12 AM 0.4 -15.8 0.4 -16.2 0.3 -16.9 0.3 -17.9

1 PM 0.4 22.2 0.4 25.9 0.4 30.2 0.3 35.0


2 PM 0.6 49.6 0.6 53.9 0.6 58.4 0.5 63.0

3 PM 0.9 65.7 0.9 69.4 C.9 73.0 0.9 76.6

4 PM 1.5 76.2 1.4 79.3 1.4 82.4 1.4 85.3

5 PM 2.6 84.2 2.5 87.0 2.4 89.7 2.4 92.3

6 PM 7*7 91.1 7*0 93.7 :.4 96.2 5.9 98.6





TABLE 5. SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR WEST PALM BEACH, FLORIDA FOR MAY


MAY 1 MAY 8 MAY 15 MAY 22
--------- -------------- ------- -- ------

EASTERN SHADE SHADE SHADE SHADE
DAYLIGHT PICJECTION AZIMUTH PROJECTION AZIMUTH PROJECTION AZIMUTH PROJECTION AZIMUTH
SAVINGS FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE
TIME
-- -------- ------------------------- -------- ------------- -----------


7 AM 20.6 -105.2 14.9 -107.0 12.2 -108.6 10.7 -110.0


8 AM 3.5 -98.9 3.3 -100*8 3.2 -102.5 3.0 -104.0


9 AM 1.8 -92*7 *17 -94.8 1.7 -96.8 1.6 -98.5


10 AM 1.1 -e5.8 1.1 -88.3 1.0 -90.7 1.0 -92.7

11 AM 0.7 -76.7 0.7 -79.9 0.6 -83.0 0.6 -85.7


12 AM 0.4 -60.7 0.4 -65.1 0.4 -69.6 0.3 -74.0


1 oM 0.2 -20.1 0.2 -22.7 C.2 -26.6 0.1 -32.0


2 PM 0.3 41.9 0.2 47.7 0.2 53.5 0.2 59.1


3 PM 0.5 68.7 0.5 73.0 C.5 76.8 0.5 80.2

4 PM 0.8 80.9 0.8 84.0 0.8 86.7 0.8 89.0


5 PM 1.3 88.8 1.3 91.3 1.3 93.4 1.2 95.3


6 PM 2.3 95.3 2.2 97.4 ;.1 99.3 2.1 100.9


105.1 4.5 106.5


103.4 4.8


7 PM 5.4


101.5


5. 1






TABLE 6. SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR WEST FALM BEACH& FLORIDA FOR JUNE


JUNE 1 JUNE 8 JUNE 15 JUNE 22

EASTERN SHADE SHADE SI-ADE SHADE
DAYLIGHT PROJECTION AZIMUTH PROJECTION AZIMUTH PROJECTION AZIMUTH PROJECTION AZIMUTH
SAVINGS FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE
TIME


7 AM 9.7 -111.6 9.5 -112.5 9.6 -113.1 10.0 -113.4

8 AM 3.0 -105.8 3.0 -106.7 3.0 -107.3 3.0 -107.6

9 AM 1.6 -100.5 1.6 -101.5 1.6 -102.2 1.7 -102.5

10 AM 1.0 -95.2 1.0 -96.4 1.0 -97.2 1.0 -97.5

0 11 AM 0.6 -89.0 0.6 -90.7 C.o -91.7 0.6 -92.2


12 AM 0.3 -79.3 0.3 -82.1 0.3 -83.9 0.3 -84.6

1 PM 0.1 -42.0 0.1 -49.3 0.1 -55.1 0.1 -58.4

2 PM 0.2 65.9 0.2 69.3 C.2 71.3 0.2 71.4

3 PM 0.4 E4C. 0.4 85.8 .0.4 86.9 0.4 87.1

4 PM 0.8 91.6 0.7 92.9 C.7 93.5 0.7 93.7

5 PM 1.2 97.3 1.2 98.2 1.2 98.8 1.2 98.e

6 PM 2.0 102.6 2.0 103.3 1.9 103.7 1.9 103.8

7 PM 4.2 108.0 4.0 108.7 3.9 109.1 3.7 109.1




TABLE 7. SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR WEST FALM BEACH. FLORIDA FOR JULY


JULY I JULY 8 JULY 15 JULY 22


EASTERN SHADE SHADE SHADE SHADE
DAYLIGHT PROJECTION AZIMUTH PROJECTION AZIMUTH PROJECTION AZIMUTH PROJECTION AZIMUTH
SAVINGS FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE
TIME


7 AM 11.0 -113*4 12.2 -112*9 14.1 -112.2 16.9 -111.2

8 AM 3.1 -107.5 3.2 -107.1 3.3 -106.3 3.5 -105.1

9 AM 1.7 -102.3 1.7 -101.8 1.8 -100.9 1.8 -99.6

10 AM 1.0 -97.3 1.1 -96.6 1.1 -95.5 1.1 -94.0


11 AM 0.6 -91.9 0.7 -90.9 0.7 -89.4 0.7 -87.4

12 AM 0.4 -84.1 0.4 -82.7 0.4 -80.3 0.4 -77.1

1 PM 0.1 -58.5 0.1 -55.8 0.1 -51.3 0.2 -45.9

2 PM 0.2 68.6 0.2 64.3 0.2 58.6 0.2 52.3

3 PM 0.4 86.1 0.4 84.3 0.4 81.8 0.4 78.6

4 PM 0*7 93.0 0.7 91.9 C.7 90.3 0.7 88.2

5 PM 1.1 98.3 1.1 97.5 1.1 96.2 Iel 94.6

6 PM 1.9 103.3 1.9 102.6 1.9 101.5 1.9 100.2


7- -M -. 108.6 3.7 107.9 10. 3.8 105.8


7 PM 3.7


108*6 3.7 107.9 3.7


107.0 3.8 105.8







TABLE 8. SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR WEST PALM BEACH, FLORIDA FOR AUGUST


AUGUST 1


AUGUST 8


AUGLST 15


AUGUST 22


SHADE
FFOJECTION
FACTOR


3.7

1.8

el

0.7

0.4

0.2

0.2

0.4

0.7


1.2

2.0


EASTERN
DAYLIGHT
SAVINGS
TIME


7PM--- 4.1 103.7- 4.3- 102.0-'~' 4.8 100.2" 5 98.


SHADE SHADE SHADE
AZIMUTH PROJECTION AZIMUTH PROJECTION AZIMUTH PROJECTION AZIMUTH
ANGLE FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE
--------- -- -----------------------------------------


-103.0 3.8 -101.2 4.0 -99.2 4.2 -96.9

-97.2 1.9 -95.2 1.9 -92.9 2.0 -90.4

-91.1 1.1 -88.7 1*2 -86.1 1.2 -83.2

-83.7 0.7 -80.6 0.7 -77.2 0.7 -73.5

-71e5 0.4 -67.0 0.4 -62.2 0.5 -57.3

-37.4 0.2 -31.8 0.2 -26.5 0.3 -21.8

43E. 0.2 39.0 0.3 35.1 0.3 32.0

73.3 0.4 69.4 0.5 65.5 0.5 61.8

84*6 0.8 81.8 0.8 78.9 0.8 75.9

91.8 1.2 89.6 1.3 87.3 1.3 84.9

97.8 2.0 96.0 2.1 94.0 2.3 91.9


8

9

10

A 1


12




2

3

4


5

6


103*7 4.3 102*0 4.8


100.2 5.4 98.3


7 PM 4&1





TABLE 9. SHADE PRCJECTICN FACTORS AND AZIMUTH ANGLES FOR WEST PALM BEACH, FLORIDA FOR SEPTEMBER




SEPTEMBER 1 SEPTEMBER 8 SEPTEMBER 15 SEPTEMBER 22

EASTERN SHADE SHADE SHADE SHADE
DAYLIGHT FFCJECTION AZIMUTH PROJECTION AZIMUTH PROJECTION AZIMUTH PROJECTION AZIMUTH
SAVINGS FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE
TIME


8 AM 4.5 -93.4 4.7 -90.7 .0O -88.0 5.3 -85.3

9 AM 2.1 --6.6 2.1 -83.7 2.2 -80.8 2.3 -77.9

10 AM 1.2 -78.7 1.3 -75.5 1.3 -72.2 1.3 -68.9


w0 11 AM 0.8 -68.0 0.8 -64.1 0.8 -60.2 0.9 -56.4

12 AM 0.5 -50.2 0.5 -45.5 0.6 -41.1 0.6 -37.1

1 PM 0.3 -16.1 0.4 -12.8 0.4 -10.0 0.5 -7.7

2 PM 0.4 29.0 0.4 27.4 0.5 26.1 0.5 25.1

3 PM 0.6 56.S 0.6 53.9 0.7 51.3 0.7 48.8

4 PM 0.9 71.8 1.0 69.0 1.0. 66.4 1.1 63.8

5 PM 1.4 81.3 1.5 78.9 1.6 76.5 1.7 74.1

6 PM 2.5 88.7 2.7 86.5 3.0 84.3 3.3 82.1


95.4 8.4 93.3 11.3


7 PM 6*7


91.2 17.4 89.0









TABLE 10. SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR WEST PALM EACH, FLORIDA FOR OCTOBER


----- ------------- ------------------

OCTOBER 1 OCTOBER 8 CCTCBER 15 CCTOBER 22


EASTERN SHADE SHADE SHADE SHADE
DAYLIGHT FPOJECTION AZIMUTH PROJECTION AZIMUTH PROJECTION AZIMUTH PROJECTION AZIMUTH
SAVINGS FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE
TIME
TIME -------------_ _______ __ __ __- -


8 AM 5.8 -81.8 6.4 -79.1 7.1 -76.5 8.0 -74.1

9 AM 2.4 -74.2 2.5 -71.4 2.6 -68.7 2.8 -66.2


10 AM 1.4 -64.8 1.5 -61.8 1.5 -58.9 1.6 -56.4


11 AM 0.9 -51.8 1.0 -48.6 1.1 -45.7 1.1 -43.1

12 AM 0.7 -32.6 0.7 -29.6 0.8 -27.1 0.9 -25.0

1 PM 0.6 -5.3 0.6 -3.9 0.7 -2.8 0.8 -2.1

2 PM 0.6 23.9 0.7 23.1 0.8 22.2 0.8 21.3

3 PM 0.8 46.0 0.9 44.0 1.0 42.2 1.1 40.4


4 PM 1.2 60.8 1.3 58.6 1.4 56.4 1.5 54.4

5 PM 1.9 71.2 2.1 69.0 2.3 66.8 2*5 64.7


6 PM 3.9 79.2 4.5 77.1 5.2 74.9 6.1 72.8
S----------- --------------- -------------------------







TABLE 11t SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR VEST PALM BEACH. FLORIDA FOR NOVEMBER


NOVEMBER 1


EASTERN SHADE
STANDARD PROJECTION
TIME FACTOR


AZIMUTH
ANGLE


NOVEMBER 8


SHADE
PROJECTION
FACTOR


AZIMUTH
ANGLE


NOVEMBER 15


SHADE
PROJECTIC.
FACTOR


AZIMUTH
ANGLE


NOVEMBER 22


SHADE
PROJECTION
FACTOR


7


8


ra



11


12


1


2


3

4


10.1


3.1


1.8


1.2


1 0


0.9


0.9

1.2


1.7


2.8


-71.0


-63.1


-53.2


-40.2


-22.8


-1. S


20.0


38.0

51.6


61.9


12.5


3.3


1.9


1.3

1. 0


0.9


1.0

1.3


1.8


3.0


-69.1


-61.3


-51.4


-38.6


-21.7


-1.5


19.0


36.4

49.8


60.0


14.5

3.6


2.0

1.4


1.1

1 .0


1.1


1.3


1.9


3.2


-67.5


-59.7


-50.0


-37.4

-2101


-1.7


18.0


34.9


48.1


58.3


24.4


3.9


2.1


1.5


1.2


1.1


1. 1


1.4


1.9

3.3


5 P4 7.7 70.0 9.0 68.1 10.3 66.3 11.5 64.7
-------------------------- ----------------------------------


AZIMUTH
ANGLE


-66.2


-58.5


-48.9


-36.5

-20.7


-2.1


16.9

33.4


46.5


56.7


__________ ____ _I__~~_ ___________ ____ ____ ___ ________ __ ___ _____ __ ___ ______










TABLE 12. SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR WEST PALM BEACH, FLORIDA FOR DECEMBER




DECEMBER 1 DECEMBER 8 DECEMBER 15 DECEMBER 22


EASTERN SHADE SHADE SHADE SHADE
STANDARD PROJECTION AZIMUTH PROJECTION AZIMUTH PROJECTION AZIMUTH PROJECTION AZI UTH
TIME FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE
---------------------- -------------- ---------- -------- -- ------- -------------------------


8 AM 4.4 -57.5 4.9 -57.1 5.3 -57.1 5.7 -57.3

9 AM 2.3 -48.1 2.4 -47.8 2.6 -47.9 2.7 -48.3


10 AM 1.6 -36*0 1.6 -36.0 1.7 -36.3 1.8 -36.9
0)

11 AM 1.2 -20.8 1.3 -21.1 1.3 -21.7 1.4 -22.6

12 AM 1.1 -2.9 1.2 -3.7 1.2 -4.6 1.2 -5.6

1 PM 1.2 15.5 1.2 14*3 1.2 13.2 1.2 12.2

2 PM 1.4 31.7 1.5 30.4 1.5 29.3 1.5 28.3

3 PM 2.0 44.7 2.0 43.4 2.0 42.4 2.0 41.6

4 PM 3.5 54.8 3.5 53.6 3.4 52.7 3.3 52.0

5 PM 12.3 62.9 12.1 61.7 11.4 60.8 10.2 60.2
------------------------------------------------------------------------------------------------- ------








Future publications in this series will focus on: 1) assessing the econom-
ics of various landscaping features for conserving energy in residences; 2)
determining the optimal tree location in order to maximize the economic
benefits of the shade for conserving energy in heating and cooling in a spec-
ified structure; and 3) providing climatic data in a useful form for assessing
the potential benefits of the various climatic factors in Florida. It is intended
that all of these publications will be specifically written to apply to each of
the eleven Florida locations shown in Figure 1.







University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - - mvs