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

S11
CIRCULAR 511

FACTORS FOR DETERMINING
SHADING PATTERNS
IN
FLORIDA
Jacksonville and Vicinity

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

fTI
t~, a;~n d

A,
i*L

FLORIDA COOPERATIVE EXTENSION SERVICE
INSTITUTE OF FOOD AND AGRICULTURAL SCIENCES
UNIVERSITY OF FLORIDA, GAINESVILLE
JOHN T. WOESTE, DEAN FOR EXTENSION

Dennis E. Buffingion 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 Agricullural Sciences,
University of Florida, Gainesville 32611.

FACTORS FOR DETERMINING
SHADING PATTERNS
IN
FLORIDA
Jacksonville 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 Jacksonville 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 Jacksonville 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 Jacksonville, Florida in Tables 1 through
12. Publications containing the shading factors for ten other Florida loca-
tions are available from your County Extension Office. When calculating
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.

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 Jack-
sonville, Florida (30.5 deg North latitude; 81.7 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 Jacksonville 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 1.7 for the shade projection factor and 101.20 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 20.4 ft (1.7 x 12 ft high) or 6.3 m (1.7 x 3.7 m high) along the
prescribed azimuth angle of 101.20 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.

101.20

SUN'S
RAYS

----- 30 FT.---

---

SHADE
STRUCTURE gOFT

1L.-----
20. 4/

SCALE

S 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 2.2 and azimuth angle of 39.10 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, 2.2, by the
height to the bottom of the canopy, 8 ft (2.4 m). The corresponding points

are projected 17.6 ft (2.2 x 8 ft) or 5.3 m (2.2 x 2.4 m) on the prescribed
azimuth angle of 39.10. Similarly, shadow points corresponding to the four
corners of the canopy top are located 70.4 ft (2.2 x 32 ft) or 21.6 m (2.2 x 9.8
m) on 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 1.4 and azimuth angle of -7.1 from Table 12.
Four shade points corresponding to the bottom of the canopy are located
12.6 ft (3.8 m) on the -7.1 azimuth angle. Four shade points corresponding
to the top of the canopy are located 49.0 ft (14.9 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.

t----------------
------- ---
40 FT.

40 F TREE
CANOPY ,

SCALE

0 5 10 20'
/.' AZIMUTH
SUN'S 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

I71

2-5 A5 s7.5<
SCALE

N 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.

81.90

s.

*r:~I

S.PF. = 1.7
--- AZ. ANGLE = -100.7

S. F. = .4
AZ. ANGLE= -75.4"

12 NOON

S PF = I.I
aZ. ANGLE = 94.30

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.

S7 ~ '5

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 Jacksonville. 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. F. = 1.2
,/ -r AZ. ANGLE = -86.3*
-]6.30

10 A.M.

S.PF. = .3
AZ. ANGLE = 25.50

/ 2 PM.

S.PE = 1.9
AZ. ANGLE = 93.30

J1 .9 x 30' = 57

.m.p.m. .. ---

6 P.M.

N 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 18.9 ft (5.8 m) according to Equation 2 for the
shade projection factor of 0.7 from Table 8 at 4 p.m. on August 8. The tree
should then be sited 18.9 ft (5.8 m) from the centerline of the window on
the prescribed azimuth angle of 75.70. 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.

AUGUST 8
4:00 PM.

N

SCALE
0 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.

r"9~1 a a. Ei

I"
-- 2

,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.

SCALE

0 5 10 20

11

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.

TABLE t1 SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR JACKSCNVILLE, FLORIDA FCR JANUARY

JANUARY 1 JANUARY 8 JANUARY 15 JANUARY 22

EASTERN SHADE SHADE SHADE SHADE
STANDARD PROJECTION AZIMUTH PROJECTION AZIMUTH PROJECTION AZIMUTH PROJECTION AZIMUTH
TIlE FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE FACTOR ANGLE

8 AM 9.6 -58.7 9.8 -59.8 ?.6 -61.0 9.0 -62.5

S AM 3.4 -49.5 3.4 -50.7 3.3 -51.9 3.2 -53.4

10 AM 2.1 -38.3 2.1 -39.5 2.0 -40.8 2.0 -42.2
01
11 AM 1.6 -24.6 1.6 -25.8 1.5 -27.0 1.5 -2p.3

12 AM 1.4 -8.5 1.3 -9.6 1.3 -10.6 1.2 -11.6

1 PM 1.4 8.5 1.3 7.7 1.3 7.1 1.2 6.6

2 PM 1.6 24.6 1.5 24.1 1.5 23.9 1.4 23.9

3 PM 2.1 38.3 2.0 38.1 1.9 38.2 1.8 38.7

4 PM 3.4 49.5 3.2 49.6 2.9 49.9 2.7 50.6

5 PM 9.6 58.7 8.1 58.9 6.9 59.3 6.0 60.2

TABLE 2. SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR JACKSONVILLE* FLORIDA FOR FEBRUARY

FEBRUARY I FEBRUARY 8 FEBRUARY 15 FEBRUARY 22

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

8 AM 7.7 -64.9 6.7 -66.7 5.8 -68.6 5.0 -70.6

9 AM 3.0 -55.7 2.8 -57.5 2.6 -59.4 2.3 -61.3

S 10 AM 1.8 -44.4 1.7 -46.1 1t6 -47.9 1.5 -49.7

11 AM 1.4 -30.2 1.3 -31.6 1.2 -33.0 1.1 -34.5

12 AM 1.1 -12.9 1.1 -13.6 1.0 -14.3 0.9 -14.9

1 PM 1.1 6.3 1.0 6.4 1.0 6.7 0.9 7.3

2 PM 1.3 24.5 1.2 25.4 1.1 26.6 1.0 28.1

3 PM 1.6 39.9 1.5 41.2 1.4 42.8 1.3 44.8

4 PM 2.4 52.1 2.3 53.6 2.1 55.4 2.0 57.6

5 PM 5.0 61.9 4.4 63.5 4.0 65.4 3.6 67.5

TABLE 3. SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR JACKSCNVILLE, FLORIDA FOR MARCH

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

MARCH 1 MARCH 8 MARCH 15 MARCH 22

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

7 AM 137.9 -80.6 27.0 -82*7 14*6 -84.9 9*9 -87.0

8 AM 4.3 -72.6 3.8 -74.7 3.3 -76.8 3.0 -79e0

9 AM 2.1 -63.3 2.0 -65.4 1.8 -67.5 1.7 -69.7

10 AM e14 -51.6 1.3 -53.5 1.2 -55.6 11t -57.8

I1 AM 1.0 -36.0 0.9 -37.5 0.8 -39.1 0.8 -40.9

12 AM 0.8 -15.5 0.7 -15.9 0.7 -16.2 0.6 -16.6

1 PM 0*8 8.2 0.7 9.4 0.7 10.9 0.6 12.8

2 PM 0.9 30*1 0.9 32.4 0.8 35.1 0.7 38.1

3 PM 1.2 47.2 1.2 49*8 1.1 52.7 1.0 55.9

4 PM 1*8 60.0 1.7 62.6 1.6 65e4 1.6 68.3

5 PM 3.3 69.9 3.1 72.4 2.9 75.1 2.7 77.9

6 PM 13.0 78.2 10. 8. 8.8 _83.3 7.6 86.0

6 PM 13.0

78.2 10.4 80.7 8.8

BJJ 7~ 86.6

TABLE 4. SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR JACKSCNVILLE, FLORIDA FOR APRIL

APRIL 1 APRIL 8 APRIL 15 APRIL 22

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

7 AM 6.8 -90.0 5*6 -92.1 4.8 -94.1 4.2 -96.1

8 AM 2.6 -82.1 2.3 -84.3 2.2 -86.5 2.0 -88.7

9 AM 1.5 -73.0 1e4 -75.4 1.3 -77.8 1.2 -80.2

00 10 AM 1.0 -61.2 0.9 -63.7 0.8 -66.3 0.8 -69.1

11 AM 0.7 -43.8 0.6 -46.0 0.6 -48.6 0.5 -51.5

12 AM 0.5 -17.1 0.5 -17.5 0.4 -18.1 0.4 -19.0

1 PM 0.5 16.0 0.5 18.7 0.4 21.8 0.4 25.2

2 PM 0.7 43.0 0.6 46.8 0.6 50.8 0.5 54.8

3 PM 1.0 60.7 0.9 64.2 0.9 67.6 0.8 71.1

4 PM 1.5 72.7 1.4 75.7 1.4 78.7 1.3 81.6

5 PM 2.5 81.9 2.4 84.6 2.3 87.3 2.2 89.8

6 PM 6.4 89.8 5.8 92.4 5.3 94.9 4.9 97.2

TABLE 5. SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR JACKSCNVILLE* FLORIDA FOR MAY

MAY I MAY 8 MAY 15 MAY 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 23*2 -105.8 15.7 -107.5 12.4 -109.0 10.7 -110.4

8 AM 3.7 -98.6 3.4 -100.4 3.3 -102.0 3.1 -103.5

9 AM 1.9 -91.4 1*8 -93.4 1.7 -95.2 1.7 -96.9

10 AM 1.2 -83.3 1.1 -85.6 1.1 -87.8 1.1 -89.8

S 11 AM 0.7 -72.8 0.7 -75.6 0.7 -78.4 0.7 -80.9

12 AM 0.5 -55.6 0.4 -59.1 0.4 -62.7 0.4 -66.2

1 PM 0.3 -20.7 0.3 -22.6 0.2 -25.2 0.2 -28.5

2 PM 0.3 29.8 0.3 33.6 0.3 37.4 0.2 41.0

3 FM 0.5 60.0 0.5 63.8 0.5 67.3 0.4 70.4

4 PM 0.8 75.2 0.8 78.2 0.8 80.9 0.7 83.1

5 PM 1.3 85.1 1.2 87.5 1.2 89.6 1.2 91.4

6 FM 2.1 92.9 2.0 95.0 2.0 96.8 1.9 98.3

100.0 4.2 101.9

7 PM 4.5

4.0 103.6

105.0

TABLE 6. SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR JACKSCNVILLE. FLORIDA FOR JUNE
-- ------------------------------------------------

JUNE 1 JUNE 8 JUNE 15 JUNE 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 905 -112.0 9.2 -112.8 9.2 -113.4 9.6 -113.8

8 AM 3.0 -105.2 3.0 -106.1 3.0 -106.7 3.1 -107.1

9 AM 1.7 -9808 1.7 -9908 1.7 -100.5 1.7 -100.8

10 AM 1.0 -92.1 1.0 -93.3 1.0 -94.1 1.1 -94.5

11 AM 0.7 -83.9 0.7 -85.5 0.7 -86.6 0.7 -87.1

12 AM 0.4 -70.7 0.4 -73.1 0.4 -74.8 0.4 -75.6

1 PM 0.2 -34.0 0.2 -38.0 0.2 -41.4 0.2 -43.7

2 PM 0*2 45.1 0.2 46.9 0.2 47.5 0.2 46.7

3 PM 0.4 73.S 0.4 75.5 0.4 76.4 0.4 76.4

4 PM 0.7 85.7 0.7 86.8 0.7 87o4 0.7 87.5

5 PM 1t1 93.4 1.1 94.3 1.1 94.8 1.1 94.8

6 PM 1.8 100.0 1.8 100.7 108 101.1 1.7 101.2

7 PM 3.5 106.4 3.4 107.1 3.3 107.4 3.2 107.4

8 PM

JULY 15 JULY 22

SHADE
PROJECTION
FACTOR

7

8

9

10

% 11

12

1

2

3

4

5

6

7

SHADE
AZIMUTH PROJECTION
ANGLE FACTOR

10.5

3.2

1.7

1.1

0.7

0*4

0.2

0.2

0.4

0.7

1.1

lo7
1*7

3. 1

-113.7

-107.0

-100.7

-94.4

-86.9

-75.4

-44.5

43.8

75.2

86*8

94.3

100.7

106.9

SIADE
AZIMUTH PROJECTION
ANGLE FACTOR

11.7

3.3

1.8

1.1

0.7

0.4

0.2

0.2

0.4

0. 7

1.1
lo7

1.7

3. 1

-113.4

-106.6

-100.2

-93.7

-86.1

-74.3

-43.6

40.3

73.4

85.6

93.4

99.9

106.2

SHADE
AZIMUTH PROJECTION
ANGLE FACTOR

13.5

3.4

1.8

1.1

0.7

C04

0.2

0.2

0.4

0.7

1.1

1.7

3.2

-112.7

-105.8

-99.4

-92.7

-84.7

-72.4

-41.4

36.4

70.9

83.9

92.1

98.8

105.3

8 PM 10.2 113.6 10.3 113.0 10.9 112.1 12.1 110.9

EASTERN
CAYLIGHT
SAVINGS
TIME

16.4

3.5

1.8

1.1

0.7

0.4

0.2

0.2

0.4

0.7

1.I

1.7

3.3

AZIMUTH
ANGLE

-11l .7

-104.7

-98.1

-91.2

-82.9

-69.8

-38.4

32.5

67.8

81.8

90.5

97.5

104.1

_ _- ------ --------- -------------------------------------------------

JULY 1

JULY 8

TABLE 8. SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR JACKSONVILLE, FLORIDA FOR AUGUST

AUGUST 1 AUGUST 8 AUGLST 15 AUGUST 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

8 AM 3.8 -102.7 4.0 -100.9 4.2 -s8.9 4.5 -96.7

9 AM 1.9 -95.9 2.0 -93.9 2.0 -91.7 2.1 -89.3

10 AM 1.2 -88.6 1.2 -86.3 1.2 -83.8 1.3 -81.0

S 11 AM 0.7 -79.5 0.8 -76.6 0.8 -73.5 0.8 -70.2

12 AM 0.5 -65.2 0.5 -61.4 0.5 -57.4 0.5 -53.3

1 PM 0.3 -33.3 0.3 -29.5 0.3 -25.7 0.4 -22.1

2 PM 0.2 28.0 0.3 25.5 0.3 23.6 0.4 22.3

3 PM 0.4 63.1 0.5 59.6 0.5 56.4 0.5 53.3

4 PM 0.7 78.3 0.7 75.7 0.8 72.9 0.8 70.2

5 PM 1.1 87.7 1.2 85.6 1.2 83.3 1.3 81.0

6 PM 1.8 95.1 1.9 93.3 2.0 91.4 2.1 89.4

102.0 3.7 100.4 4.1

7 PM 3.5

98.6 4.5 96.8

TABLE 9. SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR JACKSCNVILLE. FLORIDA FOR SEPTEMBER

SEPTEMBER 1 SEPTEMBER 8 SEPTEMBER 15 SEPTEMBER 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

8 AM 5.0 -93.3 5.3 -90.7 5.8 -88.1 6.4 -85.4

9 AM 2.2 -85*6 2.3 -82.8 2.4 -80.0 2.5 -77.2

10 AM 1.3 -76.8 1.4 -73.7 1.4 -70.6 1.5 -67.5

f 11 AM 0.9 -65.2 0.9 -61.6 C.S -58.1 1.0 -54.6
CA)

12 AM 0.6 -47.3 0.6 -43.3 0.7 -39.6 0.7 -36.1

1 PM 0.4 -17.5 0.5 -14.6 0.5 -12.1 0.6 -9.9

2 PM 0.4 21.0 0.5 20.4 C.5 20.0 0.6 19.6

3 PM 0.6 49.5 0.7 47.2 0.7 45.1 0.8 43.2

4 PM 0.9 66.5 1.0 64.0 1.0 61.7 1.1 59.5

5 PM 1.4 77.7 1.5 75.4 1.6 73.2 1.7 71.0

6 PM 2.4 86.4 2.6 84.3 2.8 82.2 3.2 80.1

7 P M-- - - - -- 6 8 -- 9 0 1 5 8

7 PM 5.6

94.0 6.8 92.0 8.8

90.0 12.5 88.0

TABLE 10* SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR JACKSCNVILLE, FLORIDA FOR OCTOBER

OCTOBER 15

OCTOBER 22

SHADE
PROJECTION
FACTOR

AZIMUTH
ANGLE

-82.0

-73.6

-63.6

-50.5

-32.2

-7.6

19.1

41.0

56.8

68.3

77.4

SHADE
PROJECT ION
FACTOR

8.3

2.9

1.7

1.1

0. 8

0.7

0.8

1. 0

1.4

2.1

4.3

AZIMUTH
ANGLE

-79.4

-70.9

-60.8

-47.6

-29.5

-6.2

18.7

39.4

54.8

66.3

75.4

SHADE
PROJECTION
FACTOR

SHADE
AZIMUTH PROJECTION
ANGLE FACTOR

-76.9

-68.4

-58.2

-44.9

-27.2

-5.1

18.2

37.9

52.9

64.3

73.4

12.0

3.3

1.9

1.3

1.0

0.9

0.9

1.1

1.6

2.6

6.0

OCTOBER 1

EASTERN
DAYLIGHT
SAVINGS
TIME

OCTOBER 8

8

9

10

II

12

1

2

3

4

5
S
6

AZIMUTH
ANGLE

-74.5

-66.0

-55.8

-42.6

-25.4

-4.3

17.6

36.5

51.1

62.4

71.4

_ ___- --- -- --- ---- ------------------------ ---------------------

_______ _____I_____________________________I____

TABLE 11. SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR JACKSCNVILLE* FLORIDA FOR NOVEMBER

NOVEMBER I NOVEMBER 8 NOVEMBER 15 NOVEMBER 22

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

8 AM 3.7 -63.1 4.1 -61.3 4.6 -59.9 5.1 -58.7

9 AM 2e0 -52*8 2.2 -51.2 2.4 -49.8 2.5 -48.8

3 10 AM 1.4 -39.S 1.5 -38.4 1.6 -37.3 1.7 -36.6

11 AM 1.1 -23.3 1.2 -22.4 1.3 -21.7 1.3 -21.4

12 AM 1.0 -3.6 11 -3.5 1.1 --36 1.2 -3.9

1 PM 1.0 16.7 1.1 16.0 1.2 15.1 1.3 14.2

2 PM 1.3 34.5 1.4 33.1 1.4 31*8 1.5 30.5

3 PM 1.8 48.7 1.9 47.0 2.0 45.4 2.1 43.9

4 PM 2.9 59.7 3.1 58.0 3.4 56.3 3.6 54.8

5 PM 7.7 68.7 9.3 66.9 10.9 65.2 12.5 63.6

TABLE 12. SHADE PROJECTION FACTORS AND AZIMUTH ANGLES FOR JACKSCNVILLE. FLORIDA FOR DECEMBER

DECEMBER 1 DECEMBER 8 DECEMBER 15 DECEMBER 22

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

B AM 6.0 -57.8 6.8 -57.4 7.7 -57.4 8.5 -57.7

5 AM 2.8 -48.1 3.0 -47.9 3.1 -48.0 3.3 -48.4

S 10 AM 1.8 -36.1 1.9 -36.2 2.0 -36.5 2.1 -37.1
0)

11 AM 1.4 -21.5 1.5 -21.8 1.6 -22.4 1.6 -23.2

12 9A 1.3 -4.6 1.3 -5.3 1.4 -6.1 1.4 -7.1

1 PM 1.3 12.9 1.4 11.9 1.4 10.8 1.4 9.8

2 PM 1.6 28.9 1.6 27.7 1.6 26.6 1.6 25.7

3 PM 2.2 42.2 2.2 41.0 2.2 40*0 2.2 39.1

4 PM 3.7 53.0 3.8 51.8 3.7 50.8 3.6 50.1

5 PM 13.9 61*8 14.0 60.7 13.2 59.7 11.8 59.1

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.

LANDSCAPING
FOR
ENERGY
CONSERVATION

This publication was promulgated at a cost of $926.75, or61.7
cents per copy, to help Florida residents calculate shading
patterns. 11-1.5M-81

COOPERATIVE EXTENSION SERVICE, UNIVERSITY OF FLOR-
IDA, INSTITUTE OF FOOD AND AGRICULTURAL SCIENCES,
K. R. Tefertiller, director, In cooperation with the United States
Department of Agriculture, publishes this information to further the
purpose of the May 8 and June 30, 1914 Acts of Congress; and Is -
authorized to provide research, educational Information and other
services only to Individuals and Institutions that function without regard to race, color,
sex or national origin. Single copies of Extension publications (excluding 4-H and Youth
publications) are available free to Florida residents from County Extension Offices.
Information on bulk rates or copies for out-of-state purchasers is available from C. M.
Hinton, Publications Distribution Center, IFAS Building 664, University of Florida,
Galnesvllle, Florida 32611. Before publicizing this publication, editors should contact
this address to determine availability.