energy saving by proper tree plantation

\PERGAMON Building and Environment 23 "0888# 454Ð469

9259Ð0212:88:, ! see front matter Þ 0888 Elsevier Science Ltd[ All rights reserved

PII] S 9 2 5 9 Ð 0 2 1 2 " 8 7 # 9 9 9 3 5 Ð 7

Energy saving by proper tree plantation

S[ Raeissi\ M[ Taheri�

Chemical Engineering Department\ Shiraz University\ Shiraz\ Iran

Received 03 May 0886^ received in revised form 19 May 0887^ accepted 05 September 0887

Abstract

A model is presented to predict the e}ect of trees as passive cooling options on buildings[ A computer program is written to

calculate hourly cooling load requirements by the numerical solution of the energy balance equation for the building[ This simulation

is validated by comparison with _eld data taken from an actual house in Shiraz\ Iran[ A guideline is presented for optimum tree

plantation concerning energy saving[ Results indicate that for the house under study "of popular size in Shiraz# cooling loads may

be reduced by 09Ð39) by appropriate tree plantation[ Þ 0888 Elsevier Science Ltd[ All rights reserved[

Keywords] Trees^ Shading^ Passive cooling

Nomenclature

CF fractional cloud cover\ dimensionlessD instantaneous di}use solar radiation ðW m−1Łf "t# heat ~ux de_ned in eqn 3 ðW m−1Łh heat transfer coe.cient ðW m−1 K−0ŁIh instantaneous direct solar radiation on

horizontal surface ðW m−1Łk thermal conductivity ðW m−0 K−0Łl�\ m�\ n� direction cosines of sun beams\

dimensionlessqsky sky radiation per unit area ðW m−1ŁQAI cooling load due to air in_ltration ðWŁQC cooling load due to air conditioners ðWŁQdw heat transfer rate through doors and windows

ðWŁQf heat transfer rate through ~oors ðWŁQI cooling load due to lights\ appliances\ occupants\

etc[ ðWŁQR heat transfer rate through roof ðWŁQw heat transfer rate through outer walls ðWŁRt radius of treet time ðsŁT temperature ðKŁTsky sky temperature ðKŁx distance from outer surface of roof or walls ðmŁz9 lowest height of roof

Greek symbols

a absorptivity of surface\ dimensionless

� Corresponding author[ Tel[] 99 87 60 292960^ fax] 99 87 60 41614

g wall azimuth anglegs solar azimuth angleo emissivity\ dimensionlessu angle of incidence ðdegŁuz zenith angle ðdegŁs Boltzmann constant ðW m−1 K−3Ł

Subscripts

A ambientb center base of treec center of spherical shaped treeg groundL inner surface of roof or wallsN generic point in spaceR room "inside of building#T points on treeO outer surface of roof or walls

0[ Introduction

In early times\ before the invention of mechanicalforms of refrigeration\ ingenious uses were made of theavailable sources of coolness to provide thermal comfortin hot climates[ Due to the shortage of nonrenewableenergy sources and environmental pollution problems\once again e}ort is being made to reduce the high energyconsuming methods of mechanical refrigeration and airconditioning\ and instead to establish systems whichmake use of {natural cooling| with even higher e.cienciesthan in the past ð0Ł[ Of the many available systems forreaching this goal\ tree plantation is a delightful option

S[ Raeissi\ M[ Taheri : Buildin` and Environment 23 "0888# 454Ð469455

achieving much more than just energy saving] reducingnoise and air pollution\ modifying temperature and rela!tive humidity and having great psychological e}ects onhumans[ Trees can modify both the microclimate arounda building and the macroclimate of a region[ The sig!ni_cance of trees as passive options is in the charac!teristics of growing leaves in the hot summer monthswhen shading is most needed and loosing them in thecool winter season when shading is not desired[

The variability of the elements involved in the treeÐenvironment interaction\ makes the establishment ofdesign guidelines very di.cult\ but there seems to be agrowing interest in this subject in literature[ The advan!tage of using trees for summer shade has been pointedout in a large number of references\ but very little datacan be found giving quantitative information about thee}ects of trees on shading[ Kay et al[ ð1Ł presented tech!niques using diagrams for the estimation of the solaraccess to buildings[ Maksoumi ð2Ł used scale models oftrees for determining the resulting shadow patterns[Budin and Budin ð3Ł and Sassi ð4Ł described mathematicalmodels for shading calculations and Fanchiotti et al[ ð5Łpresented some applications of a computer program indetermining the shadows cast by obstructions[ Sattler etal[ ð6Ł calculated the area and position of shadows castby trees on a surface of any orientation and inclination[In the present work a computer program is written whichpredicts the position of shadows cast by trees on buildingsat di}erent hours in a day and di}erent days of the year[The overall cooling load reduction caused by shadowson di}erent facing walls and windows is also predicted bythe program and a guideline is presented for appropriaterelative positioning between buildings and trees for Shi!raz and similar latitudes[

1[ Theoretical model of the building

To calculate cooling loads in summer\ by assumingthat the air inside a building is at constant temperature\the energy balance for the building is ð7Ł

Qc �QR¦Qw¦Qdw¦Qf¦QI¦QAI "0#

Due to the time dependent terms on the right side\ thisequation must be solved numerically[

1[0[ Calculation of heat loads

The loads due to the ~oor\ lights\ appliances\ occupantsand in_ltration are estimated by the methods given in theASHRAE Handbook of Fundamentals ð8Ł[

1[1[ Heat ~ux through roof and walls

Heat transfer through the roof and walls is determinedby solving the unsteady state heat conduction equation

numerically[ This is done by dividing the roof and wallsinto three!dimensional space nodes and determining thetemperature of each node at successive time intervals[Assuming that the net radiation on the inner surfaces isnegligible\ the boundary condition at these surfaces is ð7Ł]

−k1T

1x bx�L

�hL"TL−TR# "1#

Where L is the thickness of the roof[ At the outer surface\other than convection from the ambient air\ there is alsoa net heat ~ux to the surface caused by radiation[

−k1T

1x bx�9

�hA"TA−TO#¦f "t# "2#

The radiation ~ux denoted by f "t#\ may be divided intoseveral parts\ each acting parallel to each other\ namelydirect and di}use solar radiation and sky radiation[ Forhorizontal roofs\ f "t# will take the form ð7Ł

f "t#� a"Ih¦D#¦qsky "3#

Ih and D\ the instantaneous direct and di}use solar radi!ation on horizontal ~at surfaces in W m−1 are determinedby the empirical equations given by Daneshyar ð09Ł forradiation in Iran

Ih � "0−CF#"840[44ð0−exp=−9[964"89−uz#=Ł#"cos uz#

"4#

D� 0[321¦1[096"89−uz#¦010[2CF "5#

where CF is the fractional cloud cover\ and uz is thezenith angle in degrees[ The net radiation from the sky iscalculated using

qsky � os"T3sky−T3

O# "6#

in which

Tsky � 9[9441T0[4A "7#

For vertical walls the net radiation ~ux takes the formð7Ł]

f "t#� 6aIh

cos u

cos uz

¦D

1¦

rg

1"Ih¦D#7¦

qsky

1"8#

where u is the angle of incidence of solar radiation on thewall\ rg is the re~ectivity of the ground\ and the 0:1multipliers are the shape factors of vertical surfaces tosky and ground[ Of course each wall is treated separatelysince the radiation incident upon it di}ers with direction[In this manner the temperature pro_les of the roof andwalls are set up for each time step\ from which the heat~ux through the slab is easily obtained[

S[ Raeissi\ M[ Taheri : Buildin` and Environment 23 "0888# 454Ð469 456

1[2[ Heat ~ux through windows

The transmittance\ re~ectance\ and absorptance ofglass windows are functions of the angle of incidence ofradiation\ which itself varies throughout the day[ Thus aprecise numerical approach is set up which\ after esti!mating the angle of incidence of direct solar radiation ateach time step\ will determine the transmissivity\ re~ect!ivity\ and absorptivity of the glass for both direct anddi}use radiation at that time step[ This is followed by theestimation of the glass temperature by use of an energybalance written around the glass[ Finally the load due towindows is estimated as the sum of transmittance andconductance of the windows[ Windows facing di}erentdirections are also treated separately due to the variationsof incident solar radiation ð7Ł[

2[ Simulation of trees

In order to _nd where the shadows of a tree will be atdi}erent hours of a day throughout the year\ threeelements must be taken into account] the tree geometry\the position of the sun in the sky at the required timesand the position of the surfaces to be shaded[ It has beensuggested that any tree can be typi_ed either as having aspherical\ conical or cylindrical shape or as being theresult of some sort of combination of these shapes[ Inthis work the geometry of the shadows are obtained bythe method of Sattler et al[ ð6Ł[ A system of coordinateaxes is considered with origin O\ on the bottom left!handcorner of the surface in question\ so that the z!axis pointsto the zenith and the x! and y!axes are on the horizontalplane\ with the x!axis pointing outwards from the surfaceand the y!axis pointing to the right[ A sun ray can bereferred to in relation to this system of coordinate axesby means of its direction cosines\ which are the cosinesof the angles that the sun ray makes with the positivedirections of the coordinate axes[ Thus\ if the surface tobe shaded by the tree has a wall azimuth angle g\ solarazimuth angle gs\ and solar altitude angle hs\ then thedirection ratios de_ning the sun beam will be

l�� cos hs cos "g−gs# "09#

m�� cos hs cos 0p

1¦g−gs1 "00#

n�� sin hs "01#

2[0[ The geometry of the shade of spherical shaped trees

A spherical shaped tree will be speci_ed by the coor!dinates of its center Xc\ Yc\ and Zc\ and its radius Rt[ Theintercepts of the sun|s rays with a spherical tree producea cylinder of shade[ When incident on a ~at surface\ thiscylinder of shade will de_ne an ellipse as can be seen in

Fig[ 0[ The shadow of a spherical shaped tree[

Fig[ 0[ For a vertical wall de_ned by x�9\ the resultingellipse will be ð6Ł

"0−m�1#y1"0−n�1#z1−1m�n�yz¦1"m�k−Yc#y

¦1"n�k−Zc#z¦c� 9 "02#

where

k� l�Xc¦m�Yc¦n�Zc "03#

and

c�X1c¦Y1

c¦Z1c−k1−R1

t "04#

On the other hand\ the roof can be expressed by

z�zO−x tan a "05#

where zO is the lowest z value on the roof\ and a isthe inclination of the roof[ Thus\ the intersection of thecylindrical shade with the roof is given by ð6Ł

ð0−"l�−n� tan a#1¦tan1 aŁx1¦"0−m�1#y1

−1"l�−n� tan a#m�xy−1ðXc¦zO tan a

−Zc tan a¦"l�−n� tan a#"n�zO−k#Łx

−1ðYc¦m�"n�zO−k#Ły¦z1O

−1ZOZc−n�1z1O¦1kn�zO¦c� 9 "06#

2[1[ The geometry of the shade of conical and cylindrical

shaped trees

In their simulation\ Sattler et al[ ð6Ł assume that bothconical and cylindrical shaped trees have vertical axesand that they have bases normal to their axes[ In orderto _nd their shadows it is necessary to project as manypoints as possible from two circles "cylinder# or one circleand one point "cone# onto a plane\ considering parallels


Fig[ 1[ The shadow of a conical shaped tree[

to the solar beam through these points and then to drawthe contours of the shadows by linking these projections"see Figs 1 and 2#[

The base of a cone or cylinder is a circle that can bedescribed by radius Rt and the coordinates of its center"Xb\ Yb\ Zb#\ with respect to the coordinate system[ Theequation of this circle will be

"x−Xb#1¦"y−Yb#

1 �R1t "07#

and

z�Zb "08#

The equation of the straight line parallel to the sun!beam containing a generic point in space with coordinatesXN\ YN\ and ZN will be

x−XN

l��

y−YN

m��

z−ZN

n�"19#

By giving an adequate value to y "or x# in eqn "07# thecorresponding value of x "or y# is calculated[ This can berepeated for points 0\ 1\ [ [ [ \ n\ positioned on the base

Fig[ 2[ The shadow of a cylindrical shaped tree[

"cone# or bases "cylinder# of the tree[ The pairs of coor!dinates found in this manner] "X0\ Y0#\ "X1\ Y1#\ [ [ [ \ "Xn\Yn#\ together with the z!coordinate of the tree base\ canthen replace the values of XN\ YN and ZN in eqn "19#\thus determining as many points as needed to be pro!jected onto the walls[

In order to draw the contours of a shadow\ it is impor!tant to calculate the coordinates of the points positionedbetween straight lines and curves\ where a transitionoccurs on the contour of the shadow[ These points canbe found by projecting the corresponding points on thetree surface\ with coordinates Zb or Zt belonging to thebase of a cone or cylinder and XT and YT\ onto the planein question[ XT and YT are estimated by

YT �Yb2Rt0l�1

m�1¦l�110

1 "10#

XT �Xb¦m�

l�"Yb−YT# "11#

Similarly\ the projection of the top of the cone can befound by replacing the value of ZN in eqn "19# by thecorresponding z!value of the top of the cone and x and y

by Xb and Yb[

3[ Experimental procedure

The residential building under experiment is a one!storey house with no common walls with other buildings[This case study is situated in Shiraz\ Iran\ at an altitudeof 0380 m\ latitude angle of 18[5> N and longitude angleof 41[42> E and is directed towards the south[ It is cooledin summer by an evaporative water cooler[ The househas a ~oor area of 039[44 m1 and a height of 2 m[ Walland glass areas are given in Table 0 for each side of thebuilding ð7Ł[

A program is set up to simulate the thermal behaviorof the house[ Cooling loads are calculated for each hourand summed up over 13 h to obtain the daily total coolingload[ Numerical values of the constant parameters usedin this simulation are given in Table 1[

Table 0

Wall and window "glass# area of test building

Direction Wall area ðm1Ł Glass area ðm1Ł

South 16[14 13[51

West 21[16 2[65

North 35[09 4[84

East 17[58 6[02

S[ Raeissi\ M[ Taheri : Buildin` and Environment 23 "0888# 454Ð469 458

Table 1

Constant values used in the simulation of test building

Ambient air]

Wind velocity 09 km h−0

Average relative humidity 9[13

Pressure 74299 Pa

Roof]

Roof thickness 9[21 m

Emissivity 9[77

Conductivity 9[610 W m−0 >C−0

Density 0599 Kg m−2

Speci_c heat 739 J Kg−0 >C−0

Walls]

Wall thickness 9[21 m

Emissivity 9[4

Conductivity 9[78 W m−0 >C−0

4[ Results

The validity of the simulation program has _rst beenchecked by comparing the actual sensible cooling andheating provided by the cooler and heater with loadsestimated by the program for a few random days insummer and winter[ The results of these comparisonsare given in our earlier paper ð7Ł[ Good matching wasobserved for both seasons[ This validated program wasthen used to study the e}ects of tree shadows on coolingloads of buildings[

As an optimum sunshine shielding system\ cylindricaltrees were chosen side!by!side and touching each other[By noting that the rays of sunshine are all parallel\ it isnot the actual dimensions of the tree!wall geometry thatare important\ but rather the various ratios of the lengthsð6Ł[ Thus the ratio of tree height to distance from wall"Zt:X# was varied for each wall of the house[ The daychosen for this analysis was 10 June since it is the longestday of the year[ The estimated results are shown in Figs3 and 4[ The e}ect of the ratio of tree height to treedistance on heat ~ux through windows is given in Fig[ 3for each side of the building and Fig[ 4 shows the samee}ect for the walls[ As shown\ heat ~uxes through southand north faces are not much altered by trees in summer^north faces barely receive any sunshine and south facesreceive high noon sunshine which is better blocked byoverhangs than trees[ Both east and west windows andwalls\ receiving low morning and afternoon sunshine\ aregreatly a}ected by trees[ Increasing the tree height todistance ratio has larger e}ects at lower ratios but startsto level o} at ratios of 2Ð3[

As an overall energy guideline for tree plantation atlatitudes of about 29>\ it is suggested to use coniferoustrees on east and west faces of a building whenever thesewalls are exposed[ By taking into account the maximumobtainable height of the chosen trees\ they should be

Fig[ 3[ E}ect of tree height to tree distance on heat ~ux through window

on 10 June\ Zb:X � 9[1[

Fig[ 4[ E}ect of tree height to tree distance on heat ~ux through walls

on 10 June\ Zb:X � 9[1[

planted at a distance which ful_lls the criterion of height:distance× 2Ð3[ Evergreens are not desirable on east andwest sides[ North facing walls and windows do not receivesummer sun so design is not based on shadow e}ects\ butplanting a condensed row of evergreen trees and busheson this side can help block cold north winds in winter[South face plantation is left to the personal preference ofthe habitants but use of evergreens should be discardedto prevent shadows in winter[

Tables 2 and 3 give the daily cooling load and thepercentage of reduction of the load for the test buildingon 10 June for cases where there are no trees\ trees withheight:distance�3 on east\ west\ and both east and west


Table 2

E}ect of tree shadows on overall daily cooling load of test house on 10

June with no ambient air temperature reduction

Trees on Cooling load ð097 JŁ ) Reduction

No sides 6[34 *

East side 6[99 5[9

West side 6[03 3[1

East and West sides 5[58 09[1

Table 3

E}ect of trees on overall daily cooling load of test building on 10 June

with 2>C ambient air temperature reduction

Trees on Cooling load ð097 JŁ ) Reduction

No sides 6[34 *

East side 3[672 24[7

West side 3[758 23[6

East and West sides 3[368 28[8

sides[ To show the e}ect of shading alone\ the resultsof Table 2 are for the imaginary case of no ambienttemperature reduction caused by trees[ It is seen that treeshading alone reduces cooling load by 09)[ In reality\trees contribute even more than this[ Due to their evap!oration and perspiration\ they can also reduce the tem!perature of the ambient air "either microclimate ormacroclimate#[ Experimental measurements in Shirazshowed that in summer\ the temperature in a heavy treepopulated area was about 1Ð4>C less than an area wherevery little trees were found[ The extent of ambient airtemperature reduction caused by trees in a particularlocation is a very complicated function of the surfacearea covered by trees\ the number of trees per unit area\size and type of trees\ and the rate of irrigation[ Withpresent knowledge\ it is almost impossible to exactlydetermine the temperature e}ects of trees in a particularsite[ But to have an approximate\ cooling loads werealso estimated by taking an average ambient temperaturereduction of 2>C caused by trees[ The results presentedin Table 3 show the overall e}ect of shading and tem!

perature reduction of green trees[ It is seen that up to39) reduction is obtainable with correct plantation[

5[ Conclusions

Trees are ideal passive options decreasing summerloads by blocking sunshine and reducing ambient airtemperature\ while having insigni_cant e}ects in winterby loosing their leaves[ Thus correct tree planation oneach side of the building is important and can lead todesirable energy e}ects[

Trees can act complementary to window overhangs\ asthey are better for blocking low morning and afternoonsun while overhangs are better barriers for high noonsunshine[

Acknowledgements

The authors wish to acknowledge Shiraz UniversityResearch Council for their _nancial support[

References

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energy saving by proper tree plantation

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