Analytical investigation of collector optimum tilt angle at low latitudeOgboo Chikere Aja, Hussain H. Al-Kayiem, and Zainal Ambri Abdul Karim

Citation: Journal of Renewable and Sustainable Energy 5, 063112 (2013); doi: 10.1063/1.4829434 View online: http://dx.doi.org/10.1063/1.4829434 View Table of Contents: http://scitation.aip.org/content/aip/journal/jrse/5/6?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Design and realization of a novel sun tracking system with absorber displacement for parabolic trough collectors J. Renewable Sustainable Energy 5, 033108 (2013); 10.1063/1.4807476 Effect of temperature and concentration on commercial silicon module based low-concentration photovoltaicsystem J. Renewable Sustainable Energy 5, 013113 (2013); 10.1063/1.4790817 The optimum tilt angle for flat-plate solar collectors in Iran J. Renewable Sustainable Energy 4, 013118 (2012); 10.1063/1.3688024 Optimum sizing of air heating collectors J. Renewable Sustainable Energy 1, 043101 (2009); 10.1063/1.3166862 Determining optimum tilt angles of photovoltaic panels at typical north-tropical latitudes J. Renewable Sustainable Energy 1, 033104 (2009); 10.1063/1.3148272

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Analytical investigation of collector optimum tilt angleat low latitude

Ogboo Chikere Aja,a),b) Hussain H. Al-Kayiem,a)

and Zainal Ambri Abdul Karima)

Mechanical Engineering Department, Universiti Teknologi PETRONAS,Bandar Seri Iskandar, 31750 Tronoh, Perak, Malaysia

(Received 25 March 2013; accepted 25 October 2013; published online 26 November 2013)

An analytical investigation on the optimum tilt angle for solar collectors at low

latitude, a case study of Universiti Teknologi PETRONAS (UTP), 4.39�N and

100.98�E, Malaysia is presented in this work. The study employed Hay, Davies,

Klucher, and Reindl (HDKR) anisotropic sky model to evaluate the available

hourly solar radiation on inclined surface using the location metrological data.

The tilt angles considered were 0� to 30� in step of 3� with the inclusion of the

location latitude angle. The study employed the ratio of global solar radiation on

tilted surface to the global solar radiation on horizontal surface in the decision of

the optimum tilt. The system equations were converted to MATLAB codes to

solve for the optimum tilt angles. The results show that the optimum tilt varies

monthly but gave zero degree for south facing collector for the months of April to

August; thus, the investigation also considered north facing orientation for the

months of April to September. The optimum annual tilt angle for the location

using the tilt to horizontal radiation ratio was found to be equal to the location

latitude angle. Using the conventional average of the monthly optimum tilt

angles, the annual optimum tilt angle was found to be 9.75� for south facing

collector. Considering seasonal optimum tilt angle for the location using the tilt to

horizontal radiation ratio, 18� facing south was found to be the optimum tilt angle

for rainy season (September to March) and 15� facing north for dry season (April

to August). Employing the average of monthly optimum tilt method, the seasonal

optimum tilt angle was found to be 17� for rainy season and 12� facing north dry

season. The effect of dust on the collector was considered with reference to

literature and the annual tilt angle of 15� facing south was recommended for the

location in the case of large solar collector that cannot be monthly or seasonally

adjusted. VC 2013 AIP Publishing LLC. [http://dx.doi.org/10.1063/1.4829434]

NOMENCLATURE

E equation of time

i number of data

I solar radiation intensity

kT clearness index

L longitude

LST local solar time

LSN local solar noon

n number of day (January 1st ¼ 1)

a)O. C. Aja, H. H. Al-Kayiem, and Z. A. Abdul Karim contributed equally to this work.b)Author to whom correspondence should be addressed. Electronic mail: fajannl@yahoo.com

1941-7012/2013/5(6)/063112/17/$30.00 VC 2013 AIP Publishing LLC5, 063112-1

JOURNAL OF RENEWABLE AND SUSTAINABLE ENERGY 5, 063112 (2013)

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N number of years the data were collected

R radiation ratio of tilt surface to horizontal surface

t time

TC time correction factor

x different hourly solar radiation on horizontal for each mean day for the nine years

�x mean hourly solar radiation on horizontal for each mean day for the years

Subscripts

b beam

c cover

cs circumsolar

d diffuse

g ground

hz horizon

iso isotropic

loc location

o extraterrestrial component

opt optimum/optimum

r reflection

sc solar constant

s solar

T tilt

TZ time zone

z zenith angle

1 before

2 after

Greek letters

1 latitude

c surface azimuth

d declination

b inclination/tilt/slope

h incident angle

x hour angle

q ground albedo

r standard deviation

I. INTRODUCTION

Solar collectors (mainly flat plate collectors) installation may be fixed or tracked depending

of choice and the requirement.1 Tracking mechanism is employed to keep the collector surface

perpendicular to the incident beam radiation but for flat plate solar collector, fixed orientations

are more common because flat plate collectors can absorb both diffuse and direct radiation.

Some other reasons for the choice of fixed tilt for flat plat collectors might be due to architec-

tural integration of solar collectors to other fixed structures like the building roof; the marginal

economic return of a solar collector tracking mechanism may be low for geographic regions

with high percentage of the incident solar radiation.2 The performance of a solar collector is

highly influenced by its orientation towards the incoming solar radiation which is a factor to

determine the available solar radiation to surface.

The intensity of extraterrestrial solar radiation in space is approximately constant but gets

reduced by clouds, dust, and shades on passing through the atmosphere to reach a body

063112-2 Aja, Al-Kayiem, and Abdul Karim J. Renewable Sustainable Energy 5, 063112 (2013)

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horizontally fixed or tilted on the earth’s surface. The solar radiation reaching the earth’s sur-

face is in the form of direct (beam radiation) and diffuse (scatter radiation) which depends on

the cloudiness or clearness of the sky and seasons at the location.3,4 However, harnessing the

optimum solar radiation available at any location is of primary interest for solar system design

and installation. The quest to access the optimum solar radiation available at a location prompts

the search for best orientation for the installation of fixed tilt solar collectors. Literature has

shown that for fixed oriented solar collector, the rule of the thumb is that the collector should

be mounted such that its tilt angle from the horizontal be equal to the latitude angle of the loca-

tion and its azimuth angle (c) facing south for location in the northern hemisphere or facing

north for locations in the southern hemisphere but small deviations in azimuth angles of 10� to

20� from due south/north may have little or no effect.2,5 Some studies have shown that opti-

mum tilt and azimuth angles selection are not solely a function of latitude but include the cli-

matic condition of the location with emphasis on weather effects such as cloud cover.2,5–7

Nijegorodov et al.8 studied the optimum tilt (bopt) of absorber plate, variously orientated at dif-

ferent latitudes and reported that cloud cover has significant effect on determining the optimum

tilt angle of solar collector. Ahmad and Tiwari9 theoretically modeled and evaluated the tilt

angle for the solar flat-plate collectors using daily average solar radiation and found that the tilt

angle has some relationship with the weather (season). Agarwal et al.10 employed average daily

solar radiation model to evaluate the optimum tilt angle for Nandha (Haryana) and Delhi using

solar radiation data from the respective locations and inferred that the weather has effect on the

decision of the optimum tilt angle. Some investigators have made different recommendations

for the optimum tilt, based on the latitude.

Considering location latitude as a factor for optimum tilt angle decision, Gunerhan and

Hepbasl11 found the average annual optimum tilt for collectors in Izmir, Turkey,

(1¼ 38:46�N) to be 35.8� which is approximately the location latitude. Lunde12 suggested op-

timum tilt angle as (16 15�), Kalogirou13–15 suggested optimum tilt angle to be (16 10� to

15�) depending on application; while Duffie and Beckman3 used (1 þ 15�) 6 15� in their

book. Asl-Soleimani16 reported an annual optimum tilt angle of 30� for maximum yearly energy

generation of a grid connected photovoltaic (PV) at Tehran (35.7�N), which a bit lower than

the local latitude. Sunderan et al.17 used average monthly solar radiation model to theoretically

evaluate the optimum tilt angle for PV modules at Ipoh, Malaysia (4.6�N, 101�E) and their

results reported monthly optimum tilt angle to be 1-d; when bopt is positive, the system should

face South (c¼ 0�), and when bopt is negative, the system should face North (c¼ 180�). They

suggested that the PV modules should be aligned facing North for the months of April to

August and face due South for the months of September to March for the location which is

contrary to the conventional orientation which suggests that for location in the northern hemi-

sphere, the collector should face due south all year round. Oko and Nnamchi4 used daily solar

radiation model to evaluate the optimum tilt for collector situated at the low latitude in Nigeria

(4.858�N–13.02�N) and found optimum tilt correlation for the different months, season, and an-

nual. The result of the correlation using latitude 4.858�N gave the monthly optimum tilt angle

in the range of 4� to 18.84�, while the seasonal optimum tilt angle was 11.24� for dry/harmattan

season (November–March), 8.8� for rainy season (April to October), and the annual optimum

tilt angle was found to be 9.4�. Okundamiya and Nzeako18 investigated the effects of orienta-

tion on the power generated by a south facing PV for latitudes 6�N to 13.02�N. Their results

indicate 0� as optimum tilt for months of April to August and monthly optimum tilt angle range

of 3�–39� for latitude 6�N (between September and March) while they found the annual opti-

mum tilt angle for the location 6�N to be 12�. Elhassan et al.19 experimentally investigated the

optimum tilt angle for Kuala Lumpur using PV modules and inferred that the annual optimum

angle was 15� facing due south. Saadatian et al.20 reported annual optimum tilt angle for Kuala

Lumpur as 10�. Yakup and Malik,21 used monthly average solar radiation model to determine

the monthly, seasonal, and annual optimum tilt for a location at low latitude (Brunei

Darussalam, 4.82�N, 114.77�E) and their result reported annual optimum tilt angle 3.3�. Kacira

et al.22 modeled and estimated optimum tilt angles for a PV panel installed in Sanliurfa,

Turkey using daily solar radiation. Their result showed variation in the monthly optimum tilt

063112-3 Aja, Al-Kayiem, and Abdul Karim J. Renewable Sustainable Energy 5, 063112 (2013)

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angle with minimum tilt angle of 13� in June and maximum tilt angle of 61� in December.

Ibrahim23 used daily global solar radiation on a horizontal surface to model the optimum tilt

angle for Cyprus (35.23�N, 33.61�E). The results showed that seasonal variation can give

nearly optimum energy capture where winter months have optimum tilt angle of 48� (1þ 13�), summer months 14� (1-21). Elminir et al.24 performed a statistical comparison of ac-

curacy of solar radiation on tilted surface estimation for three anisotropic models

(Tamps–Coulson, Perez, and Bugler) and used Perez’s model to determine the optimum collec-

tor slope. Their results inferred that during the winter months, the maximum daily solar radia-

tion was received on a south facing collector with tilt angles around 43.33�, whereas during the

summer, the maximum daily solar radiation was incident on a nearly horizontal surface and the

annual optimum tilt angle from their study was approximately equal to the location latitude

(29.85�N). Ulgen25 used daily solar radiation model to evaluate the optimum tilt angle for max-

imum solar radiation capture solar collector surface at Turkey (39.2�N, 34.07�E). The study

found that the optimum tilt angle varies between 0� in June and 61� in December. In winter

(December, January, and February), 55.7� tilt angle was recommended, in spring (March,

April, and May) 18.3�, in summer (June, July, and August) 4.3�, and in autumn (September,

October, and November) 43�. The annual optimal tilt using average of monthly optimum tilt

was found to be 30.3�. Another study on optimum tilt by Nijegorodov and Jain26 reported that

the output of the PV arrays could be increased by 20%–25% at almost no additional investment

if the collector could be installed at a slope equal to the mean monthly slope for the site loca-

tion and slope adjusted once in a month. The report of Nijegorodov and Jain26 shows that fixed

tilt favors flat plate collectors. Dust is another design factor that affects the performance of so-

lar collector.

Considering the effect of dust on the performance of solar collectors, El-Nashar27 studied

the effect of dust deposition on evacuated tube solar collectors and found that dust deposition

can cause 10%–18% drop in glass tube transmittance which was reported to cause 60% drop

in the collector performance. The reduction in glass transmittance depends strongly on the

dust deposition density in conjunction with plate tilt.28 In similar consideration, Zorrilla-

Casanova et al.29 inferred that dust deposition changes the dependence on the angle of inci-

dence of solar radiation on surface. In the study on effects of dust on the performance of PV

panels, Sulaiman et al.30 found that dust accumulation on PV surface can reduce the system’s

efficiency by about 50%. Similarly, Yaghoubi et al.31 in their study inferred that an amount

of 1.5 g/m2 dust deposition on collector can reduce the instantaneous performance of collec-

tors up to 60% and the average performance during the dust deposition up to 37%.

Investigation on the effect of dust accumulation on tilted collector located in Kuwait by

Sayigh et al.32 showed a reduction in plate-transmittance from 64% to 17% for tilt angles of

0� to 60�, respectively. It can be seen that higher tilt decreases the effect of dust deposition

due to safe cleaning. A review study by Mani and Pillai33 on the impact of dust on solar PV

performance recommended tilt angles higher than the location latitude for locations at the

low latitudes—wet tropical with temperature range of 20–34 �C, so as to reduce dust accumu-

lation. Considering Malaysia which has weather condition characterized by average ambient

temperatures between 26.0 and 32.0 �C, relative humidity of 80%–90% and daily solar radia-

tion intensity range from 4.21 kWh/m2 to 5.56 kWh/m2,34 wet tropical climate located at the

low latitude, it would be prudent to consider the effect of dust as recommended by Mani and

Pillai.33

Several investigations have been conducted to achieve optimum solar radiation capture at

different locations on the earth surface, while the studies related to Malaysia and other coun-

tries in the low latitudes are few. From literature, there are varying reports of optimum tilt

angle for Kuala Lumpur in Malaysia which has same climate with the location of case study.

Similarly, the available works in the literature employed daily and monthly average solar radia-

tion in their models which might reduce prediction accuracy. This work employs hourly solar

radiation model to evaluate the optimum tilt angles (monthly, seasonal, and annual) for the

location. The main objective of this work is to determine the optimum tilt angles for fixed solar

collector for low latitude using hourly solar radiation model.

063112-4 Aja, Al-Kayiem, and Abdul Karim J. Renewable Sustainable Energy 5, 063112 (2013)

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II. ESTIMATION OF SOLAR RADIATION ON TILTED SURFACE

The solar radiation reaching a surface in space varies at the range of 63.3% due to varia-

tion in sun-earth distance. The extraterrestrial solar radiation reaching a surface in space at any

time of the year can be evaluated from1,3,15,35

Io ¼ Isc 1þ 0:033cos360n

365

� �� �coshz; (1)

where Io is the extraterrestrial radiation for a specific day while Isc is the solar constant

(¼1367 W/m2), n is the day’s number in the year with 1st January as 1, hz is the zenith angle

of the sun.

The extraterrestrial solar radiation on a horizontal surface per hour was calculated from

Io¼12x3600

pIsc 1þ0:033cos

360n

365

� �� �x cos/cosdðsinx2�sinx1Þþ

2pðx2�x1Þ360

sin/sind

� �� �;

(2)

where 1 is the latitude of the location, d is declination, x1 and x2 are hour-angle at 30 min

before and after the hour under consideration.

To determine the declination angle and the hour angles, Eqs. (3) and (4) were used,

respectively,

d ¼ 23:45 sin 360284þ n

365

� �; (3)

x ¼ ðLST � LSNÞ � 15�; (4)

where LST¼ local solar time and LSN¼ local solar noon.

LST is the supposed time of the location considering the location longitude with reference

to the prime meridian while LSN is time when the sun is at the meridian of the observe (the

location of study). To evaluate the solar time and hour angles, it is important to evaluate the

time correction factor from equation of time. The equation of time (E) (in minutes) is an empir-

ical equation employed for the correction of the earth’s orbit eccentricity and its axial tilt

E ¼ 9:87sinð2BÞ � 7:53cosðBÞ � 1:5sinðBÞ; (5)

where

B ¼ 360

365ðn� 1Þ: (6)

The Time Correction Factor (in minutes) accounts for the variation of the LST within a given

time zone due to the longitude variations of the location with the time zone longitude which

also incorporates the equation of time (E),

TC ¼ 4ðLTZ � LlocÞ þ E: (7)

The constant 4 stands for time (minutes) as it takes the Earth to rotate 1�, LTZ is the time zone

longitude while Lloc is the location longitude.

LST and LSN can be evaluated using Eqs. (8) and (9), respectively, where tl is the local time

LST ¼ tl þ TC.

60; (8)

LSN ¼ 12þ TC.

60: (9)

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The incidence angle of beam radiation on a horizontal surface (zenith angle, hz) can be eval-

uated using

hz ¼ cos�1ðcos / cos d cos xþ sin / sin dÞ: (10)

Similarly a relationship for the incidence angle of beam radiation on a tilted surface, hi, can be

evaluated utilizing geometric principles as

hi ¼cos�1ðsin / sin d cos b� cos / sin d sin b cos cþ cos / cos d cos b cos x

þsin / cos d sin b cos c cos xþ cos d sin b sin c sin xÞ

!: (11)

Only some percentage of the extraterrestrial solar radiation impinges on the earth surface due

to cloud and dust in the atmosphere. To evaluate the available solar radiation on a tilted surface

on the earth, the direct radiation (Ib) and diffuse radiation (Id) on horizontal surface are eval-

uated from the measured global hourly solar radiation I, where global radiation equal to the

sum of diffuse and beam radiations. The usual approach is to correlate the fraction of hourly

radiation on horizontal plane which is diffused, Id/I, with the hourly clearness index kT,3

kT ¼ I.

Io; (12)

Id

I¼

ð1� 0:09kTÞ;ð0:9511� 0:1604kT þ 4:388k2

T � 16:638k3T þ 12:336k4

TÞ;0:165;

for

for

for

kT � 0:22

0:22 < kT � 0:80

kT > 0:80

;

8><>: (13)

Ib ¼ I � Id: (14)

When the total radiation on a horizontal surface is known, the radiation on a tilted surface can

be estimated (Eq. (15)),3

IT ¼ IT;b þ IT;d�iso þ IT;d�cs þ IT;d�hz þ IT;r; (15)

where I is the incident radiation, the subscripts b, d, iso, cs, hz, and r represent beam, diffuse,

isotropic, circumsolar, horizon, and reflected radiation streams and subscript, T, denotes the

tilted surface.

The reflected energy terms seem impossible to evaluate in full detail, to account for build-

ings, ground, trees, etc., the changing solar radiation incident on them and their changing reflec-

tance.3 Adopting a standard practice of assuming one surface reflectance, which is a horizontal

and diffusely reflected ground,3 Eq. (15) can be rewritten as

IT ¼ IbRb þ Id�isoFc�s þ Id�csRb þ Id�hzFc�hz þ IqgFc�g; (16)

where Rb is the ratio of beam radiation on tilted surface to beam radiation on horizontal surface

Rb ¼Ib�T

Ib�h¼ Ib�h coshi

Ib�h coshz¼ coshi

coshz: (17)

To evaluate Rb near sunrise and sunset, Eq. (18) was employed,

Rb ¼ Rb;ave ¼a

b; (18)

a ¼ðsin / sin d cos b� cos / sin d sin b cos cÞx2 � x1

180p

� �þ�ðcos / cos d cos bþ sin / cos d sin b cos cÞðsin x2 � sin x1Þ

��ðcos d sin b sin cÞðcos x2 � cos x1Þ

0BBBB@

1CCCCA; (19)

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b ¼�ðcos / cos dÞðsin x2 � sin x1Þ

�þ ðsin / sin dÞx2 � x1

180p

� �� �: (20)

Approximating the ground as an infinite horizontal surface, an inclined surface to the horizontal

will have a view factor for diffuse sources on the collector from both the sky and the ground.

The view factors for sky and ground are

Fc�s ¼1þ cos b

2

� �; (21)

Fc�g ¼1� cos b

2

� �; (22)

where b represents the collector tilt angle to the horizontal. Ground reflected diffuse radiation

is determined using the total solar radiation incident upon the ground, and the surface albedo or

diffuse ground reflection qg (¼ 0.2 for bare ground and 0.7 for snow ground).3

For the evaluation of solar radiation incident on tilted surface, IT, many models have been

developed, of varying complexity as the bases for calculating IT which are based on Eq. (15).

The difference in the models is largely in the way the diffuse terms are treated. This paper

employs Hay, Davies, Klucher, and Reindl (HDKR) anisotropic sky model which uses Eq. (23)

to evaluate the diffused radiation. HDKR model predicts results closer to measured values and

it is recommended for collectors with surface azimuth of 0� facing the equator,1,3

Id;T ¼ Id ð1� AiÞ1þ cos b

2

� �1þ f sin3 b

2

� �� �þ AiRb

� �; (23)

where

Ai ¼ Ibn.

Ion¼ Ib

.Io

(24)

and

f ¼ffiffiffiffiIb

I

r: (25)

Substituting the diffused radiation on tilted surface as in Eq. (23) into the global radiation on

tilted surface as in Eq. (16), HDKR anisotropic solar radiation on tilted surface gives

IT ¼ ðIb þ IdAiÞRb þ Idð1� AiÞ1þ cos b

2

� �1þ f sin3 b

2

� �� �þ Iqg

1� cos b2

� �: (26)

III. METHODOLOGY

This analytical investigation used HDKR anisotropic solar radiation model to evaluate the

direct and diffuse radiations and subsequently the solar radiation on tilted collector surface

from global solar radiation on horizontal surface data from Ipoh and UTP metrological stations

with focus on achieving the best fixed orientation for a solar air collector system that was to be

installed at UTP (4.39�N and 100.98�E). The solar radiation data from Ipoh metrological station

(4.58�N and 101.083�E) covers seven years (2003 to 2009), while the solar radiation data from

the University Metrological Station covers two years (2010 to 2011). First, the two different

data were checked for consistency in the different year’s data to know the variation using the

mean days of each month (Table I) for the nine years data. The standard deviation was

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considered per hour and the maximum value in the standard deviation was about 20% as was

observed close to sunrise and sunsets hours and below 10% at midday using

r ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi

1

N � 1

XN

i¼1ðxi � �xÞ2

r; (27)

where

�x ¼

XN

i¼1xi

N; (28)

where r is standard deviation; N is the number of years the data was collected; i is the number

of data, x is the different hourly solar radiation on horizontal for each mean day for the nine

years, and �x is the mean of the hourly solar radiation on horizontal for each mean day for the

years.

For this investigation, a computer program was developed in MATLAB to evaluate Eqs.

(1)–(26) for the location taking the surface azimuth to be zero degrees (facing due south) for

the initial study and an extended investigation for azimuth angle of 180� for the months of

April to August. The tilt angles were varied within the range 0� to 30� (approximately the loca-

tion latitude and maximum declination angle of the earth) at an interval of 3� with the location

latitude included in the tilt angles investigation. The reflectivity for the ground (qg) was taken

to be 0.2 (Refs. 1 and 3) as there are no snow fall at the location. The results assume that

future weather conditions will be statistically equivalent to the weather conditions from 2003 to

2011 as the variation in the already existing data considered for the 9 yr was negligible consid-

ering the mean hourly solar radiation for mean days of each month. The results are meant to

provide the best information possible in order to assist in the design and installation of fixed tilt

solar systems at the low latitudes.

IV. RESULTS AND DISCUSSION

The global solar radiation on tilted surface was calculated using Eqs. (1)–(26) and the ratio

of available global radiation on tilted surface to global radiation on horizontal surface, Rb, also

evaluated using

Rb ¼IT

Ih; (29)

where IT is the evaluated global radiation on tilted surface and Ih is the measure global radia-

tion on horizontal surface at the location.

Rb was calculated for south facing collector inclined at (3� to 30�) from the horizontal

position. All calculations were based on the HDKR anisotropic sky diffuse radiation model, and

ground reflection is assumed perfectly diffuse with ground reflectance, qg, value of 0.2. The

result, as in Table II, shows that at high tilt angle during the months of April to August; when

the sun is at the northern hemisphere, Rb was less than one. The ratio of global solar radiation

on tilted surface to global radiation on horizontal surface helps in proper decision of the tilt

angle as it is the ratio of solar radiation that can be received by a tilted surface to that on a hor-

izontal surface at same time of the day.

TABLE I. Mean days for each month and the day number in a year calculation.

Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec

Mean day 17 16 16 15 15 11 17 16 15 15 14 10

Day No. 17 47 75 105 135 162 198 228 258 288 318 344

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From Table II and Figure 1, the analysis of the average ratio of radiation on tilted surface

to horizontal surface (Rb,ave) shows that annual maximum energy for fixed tilted surface facing

due south at the location can be obtained using the tilt angle near or equal to the location lati-

tude as can be seen in the case of tilted angles of 3� to 6� for the location of study (UTP). It

was found from literature, that the decision of annual optimum tilt angle for collectors was

based on average of the monthly optimum tilt angle. For monthly tilt angle variation, optimum

tilt angles for each month are as in Table II. The average of monthly optimum tilt angle nor-

mally gives less value of radiation ratio (Rb,ave) compared to considering the average ratio of

radiation on tilted surface to horizontal surface (Rb,ave) for different angles and taking the aver-

age for the 12 months of the year. Evaluation using the method from literature (average of the

months optimum tilt angle) showed that the annual optimum tilt angle for a south facing collec-

tor at the location (UTP) was 9.75� with Rb,ave of about 1.06 compared to an average maximum

Rb,ave of 1.0681 for tilted collector at an angle equal to the latitude of the location. Considering

dust effect on collector glass transmissivity, this work recommends 15� as optimum tilt for

south facing collector all year round at the location (UTP) as in Table III.

TABLE II. Ratio of global radiation on tilted surface to global radiation on horizontal surface for a collector with c¼ 0�

for a whole year.

Daily Rb at different Solar collector’s tilt angles

Month 0.00� 3.00� 4.39� 6.00� 9.00� 12.00� 15.00�

Jan 1.0000 1.1110 1.1199 1.1298 1.1466 1.1611 1.1736

Feb 1.0000 1.1431 1.1500 1.1573 1.1692 1.1789 1.1863

Mar 1.0000 1.1082 1.1094 1.1101 1.1099 1.1075 1.1030

Apr 1.0000 0.9983 0.9957 0.9900 0.9778 0.9636 0.9474

May 1.0000 0.9962 0.9875 0.9770 0.9560 0.9332 0.9087

Jun 1.0000 0.9907 0.9806 0.9684 0.9443 0.9184 0.8907

Jul 1.0000 0.9762 0.9669 0.9558 0.9336 0.9097 0.8842

Aug 1.0000 0.9985 0.9918 0.9834 0.9663 0.9473 0.9265

Sep 1.0000 1.0960 1.0949 1.0931 1.0882 1.0814 1.0725

Oct 1.0000 1.1640 1.1685 1.1732 1.1801 1.1848 1.1874

Nov 1.0000 1.1150 1.1223 1.1302 1.1434 1.1545 1.1635

Dec 1.0000 1.1191 1.1298 1.1352 1.1493 1.1615 1.1716

Rb,ave 1.0000 1.0680 1.0681 1.0672 1.0637 1.0585 1.0513

% Gain 0.00 6.80 6.81 6.72 6.37 5.85 5.13

Daily Rb at different Solar collector’s tilt angles

Month 18.00� 21.00� 24.00� 27.00� 30.00� Rb,opt b,opt (�)

Jan 1.1838 1.1919 1.2029 1.2015 1.1978 1.2029 24.00

Feb 1.1949 1.1943 1.1933 1.1915 1.1893 1.1949 18.00

Mar 1.0964 1.0877 1.0771 1.0644 1.0499 1.1101 6.00

Apr 0.9294 0.9096 0.8880 0.8647 0.8398 1.0000 0.00

May 0.8825 0.8549 0.8258 0.7954 0.7637 1.0000 0.00

Jun 0.8615 0.8307 0.7985 0.7650 0.7303 1.0000 0.00

Jul 0.8571 0.8286 0.7987 0.7676 0.7353 1.0000 0.00

Aug 0.9040 0.8798 0.8540 0.8266 0.7978 1.0000 0.00

Sep 1.0618 1.0493 1.0349 1.0188 1.0010 1.0960 3.00

Oct 1.1872 1.1854 1.1811 1.1746 1.1660 1.1874 15.00

Nov 1.1704 1.1751 1.1784 1.1778 1.1768 1.1784 24.00

Dec 1.1798 1.1860 1.1902 1.1925 1.1924 1.1925 27.00

Rb,ave 1.0424 1.0311 1.0186 1.0034 0.9867 1.0969 9.75

% Gain 4.24 3.11 1.86 0.34 �1.33 9.69

063112-9 Aja, Al-Kayiem, and Abdul Karim J. Renewable Sustainable Energy 5, 063112 (2013)

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The ratio of radiation on tilted surface to horizontal surface of 0� surface azimuth is shown

in Figure 2 for monthly optimum tilt, average optimum annual tilt based on average maximum

radiation ratio, optimum annual tilt based on average of optimum monthly tilt, and recom-

mended optimum tilt for self cleaning of the surface. Figure 2 shows the average daily solar

radiation at the different optimum tilts for a year.

It is important to note that the recommendation of 15� tilt is for self cleaning of the collec-

tor and reduction of dust accumulation as the months of April to August falls in the dry season

at UTP, Malaysia. From physic point of view, objects such as the dust particles are more stable

when the tangential component of the center of gravity of the body to the resting surface is

small, which is the case of a body resting on a surface at small inclination angle. The tangential

component will be zero when the surface is horizontal. At higher collector tilt angle, the tan-

gential component of the center of gravity of dust particles is increased; therefore, they can be

toppled off the collector surface under the influence of external natural forces like wind and

rain. The 15� tilt angle will reduce dust accumulation and also achieve near optimum solar radi-

ation capture in the location. This is well described in Figure 3 which shows the daily solar

radiation at the location for collector inclined to the horizontal at angle equal to the location

FIG. 1. Annual average daily solar radiation at different surface tilt for 0� surface azimuth and the ratio of radiation on tilt

surface to radiation on horizontal surface.

TABLE III. Predicted monthly and annual optimum tilt of collectors facing due south.

Month Monthly b,opt (�) Annual tilt from Rb,ave Average tilt from months optimum tilt Recommended annual tilt

Jan 24.00 4.39 9.75 15.00

Feb 18.00

Mar 6.00

Apr 0.00

May 0.00

Jun 0.00

Jul 0.00

Aug 0.00

Sep 3.00

Oct 15.00

Nov 24.00

Dec 27.00

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latitude angle, 9�, 15� and monthly optimum tilt variation. It was found that monthly adjusting

the collector to the monthly optimum tilt angle lead to 9.69% gain of solar radiation incident

on the surface but from the month of April to August will surfer some losses due to high depo-

sition of dust on the horizontally set collector. Similarly, using the location latitude angle as

FIG. 2. Ratio of radiation on tilted surface to horizontal surface of 0� surface azimuth, for collector at 0� (horizontal), 4.39�

(location latitude angle), 9�, 15� surface inclination, and monthly optimum tilt angles.

FIG. 3. Daily solar radiation for 0� (horizontal), 4.39� (location latitude angle), 9�, 15� surface inclination, and monthly op-

timum tilt angles.

063112-11 Aja, Al-Kayiem, and Abdul Karim J. Renewable Sustainable Energy 5, 063112 (2013)

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annual optimum tilt as evaluated will achieve 6.81% gain of solar radiation (Table II) but will

face similar problem of dust accumulation all year round. The use of 10� optimum tilt angle

will yield about 6% solar radiation gain while 15� optimum tilt can yield about 5.13% gain of

solar radiation. The tilt angle range of 10� to 15� is good for low latitude, but considering the

dust effect but this work recommend 15% because of the dry seasons associated with locations

at the low latitudes. The average daily solar radiation for some important tilt angles is plotted

in Figure 3.

TABLE IV. Ratio of global radiation on tilted surface to global radiation on horizontal surface for a collector with c ¼ 0�

for months of September to March and c¼ 180� for April to August.

Daily Rb at different Solar collector’s tilt angles

Month 0.00 3.00 4.39 6.00 9.00 12.00 15.00

Jan 1.0000 1.1110 1.1199 1.1298 1.1466 1.1611 1.1736

Feb 1.0000 1.1431 1.1500 1.1573 1.1692 1.1789 1.1863

Mar 1.0000 1.1082 1.1094 1.1101 1.1099 1.1075 1.1030

Apr 1.0000 1.0839 1.0846 1.0849 1.0838 1.0806 1.0752

May 1.0000 1.0954 1.0974 1.0992 1.1010 1.1008 1.0987

Jun 1.0000 1.0987 1.1033 1.1082 1.1156 1.1209 1.1242

Jul 1.0000 1.0883 1.0958 1.1039 1.1174 1.1289 1.1545

Aug 1.0000 1.1011 1.1057 1.1105 1.1178 1.1267 1.1258

Sep 1.0000 1.0960 1.0949 1.0931 1.0882 1.0814 1.0725

Oct 1.0000 1.1640 1.1685 1.1732 1.1801 1.1848 1.1874

Nov 1.0000 1.1150 1.1223 1.1302 1.1434 1.1545 1.1635

Dec 1.0000 1.1191 1.1268 1.1352 1.1493 1.1615 1.1716

Rb,ave 1.0000 1.1103 1.1149 1.1196 1.1269 1.1323 1.1364

Season 1 1.0000 1.1223 1.1274 1.1327 1.1410 1.1471 1.1511

Season 2 1.0000 1.0935 1.0974 1.1013 1.1071 1.1116 1.1157

Daily Rb at different solar collector’s tilt angles

Month 18.00 21.00 24.00 27.00 30.00 Rb,opt b,opt (�)Energy gain

for b,opt %

Jan 1.1838 1.1919 1.2029 1.2015 1.1978 1.2029 24.00 20.29

Feb 1.1949 1.1943 1.1933 1.1915 1.1893 1.1949 18.00 19.49

Mar 1.0964 1.0877 1.0771 1.0644 1.0499 1.1101 6.00 11.01

Apr 1.0678 1.0584 1.0469 1.0335 1.0182 1.0849 �6.00 8.49

May 1.0946 1.0886 1.0807 1.0711 1.0596 1.1010 �9.00 10.10

Jun 1.1255 1.1248 1.1221 1.1174 1.1108 1.1255 �18.00 12.55

Jul 1.1536 1.1534 1.1506 1.1455 1.1382 1.1545 �15.00 15.45

Aug 1.1253 1.1229 1.1219 1.1164 1.1088 1.1267 �12.00 12.67

Sep 1.0618 1.0493 1.0349 1.0188 1.0010 1.0960 3.00 9.60

Oct 1.1872 1.1854 1.1811 1.1746 1.1660 1.1874 15.00 18.74

Nov 1.1704 1.1751 1.1784 1.1778 1.1768 1.1784 24.00 17.84

Dec 1.1798 1.1860 1.1902 1.1925 1.1924 1.1925 27.00 19.25

Rb,ave 1.1368 1.1348 1.1317 1.1254 1.1174 1.1368 18.00 13.68

Season 1 1.1535 1.1528 1.1511 1.1459 1.1390 1.1535 18.00 15.35

Season 2 1.1134 1.1096 1.1044 1.0968 1.0871 1.1157 �15.00 11.34

063112-12 Aja, Al-Kayiem, and Abdul Karim J. Renewable Sustainable Energy 5, 063112 (2013)

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Maximum radiation for the months of April to August, at the location was at horizontal

surface (0�) or at low tilt angles close to zero degree. Similar observations has been recorded in

literature for locations in the northern hemisphere during the summer period.8–11,17,18,21,22,24,25

Some investigations,8,17,21 show tilt angles of negative values for the summer months of April

to August in the northern hemisphere which can be translated as reverse surface azimuth

(c¼ 180�). This work extended its investigation to study the effect of surface azimuth

(c¼ 180�) for the months of April to August to find the monthly optimum tilt angles for collec-

tor at the location. Contrary to the principle that collectors in the northern hemisphere should

face south, using the ratio of global radiation on tilted surface to global radiation on horizontal

surface, it was found that there is radiation gain when the surface are tilted and surface azimuth

changed to 180� for the months of April to August as can be seen in Table IV. Optimum tilt

angle for monthly adjustment in the location of study is as shown in Table V with the collector

facing north during the months of April to August.

The result shown in Table V evaluated the monthly optimum tilt angle, seasonal optimum

tilt (considering April to August), and annual optimum tilt. Taking average of the optimum tilt

for the months of September to March that are most favoured by surface azimuth of zero

degree, the optimum tilt angle for the season is about 17� and between April and August, the

seasonal optimum angle was found to be 12� facing north. This study in line with the effect of

dust on performance recommends 15� tilt for the seasons and surface azimuth of 180� for April

to August. The result on Table IV gave 18� as the annual tilt considering the maximum radia-

tion ratio average for the year. It was also found that for seasonal evaluation of the radiation ra-

tio, 18�, was the optimum tilt angle for season 1 (September to March) while 15� was the opti-

mum tilt for season 2 (April to August).

Based on the analysis shown on Tables IV and V, selected optimum tilts radiation ratios

are plotted in Figure 4 which emphasizes the energy gained by a surface at different tilt angles.

Using the average of seasonal optimum tilt angle (season 1¼ 17� and season 2¼ 12�) for the

two seasons, the solar energy gain on tilted surface per year was about 13.60% but in same

analysis it was found that the gain using the radiation ratio optimum tilt (season 1¼ 18� and

season 2¼ 15�) for the two seasons was 13.77% gain. Also, using a seasonal optimum tilt angle

of 18� for both seasons gave 13.68% gain; a seasonal optimum tilt angle of 15� for both sea-

sons gave 13.64% gain while changing the collector tilt to the monthly optimum tilt angle

yielded 14.55% gain of daily solar radiation. The average daily solar radiation on different tilt

angles are shown in Figure 5.

TABLE V. Monthly, seasonal and annual optimum tilt of collectors at low latitude with seasonal azimuth rotation.

Month

Monthly opt tilt

at c¼ 0

Monthly opt tilt

at c¼ 180

Seasonal tilt

at c¼ 0

Seasonal tilt

at c¼ 180

Suggested seasonal

tilt at c¼ 0

Suggested seasonal

tilt at c¼ 180

Jan 24.00 … 17.00 … 15 …

Feb 18.00 … … …

Mar 6.00 … … …

Apr … 6.00 … 12.00 … 15

May … 9.00 … …

Jun … 18.00 … …

Jul … 15.00 … …

Aug … 12.00 … …

Sep 3.00 … 17.00 … 15 …

Oct 15.00 … … …

Nov 24.00 … … …

Dec 27.00 … … …

Average 16.71 12.00

063112-13 Aja, Al-Kayiem, and Abdul Karim J. Renewable Sustainable Energy 5, 063112 (2013)

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The result of the monthly optimum tilt angle was compared with already existing work

from literature as shown in Table VI. The result correlates closer to Sunderan et al.17 model

which was a study conducted for a nearby location and also shows similar trend with

Nijegorodov et al.8 model.

Both Sunderan et al.17 and Nijegorodov et al.8 models when deeply inspected are functions

of location latitude and declination angle. But in Nijegorodov et al.,8 the model used multiplier

for the location latitude and increased the declination angle. The results of this work show

closer result to the result of Sunderan et al.,17 which presented the optimum tilt angle to be

equal to location latitude (Ø) minus the declination angle.

FIG. 5. Average daily solar radiation for collector seasonal optimum tilt angle.

FIG. 4. Radiation ratio for collector seasonal optimum tilt angle.

063112-14 Aja, Al-Kayiem, and Abdul Karim J. Renewable Sustainable Energy 5, 063112 (2013)

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V. CONCLUSION

The study considers hourly solar radiation using HDKR anisotropic diffuse-sky radiation

model to evaluate the available solar radiation on inclined surface, and used radiation ratio to

determine the monthly and annual optimum tilt angle for south face solar collector at low lati-

tude. It was found that the optimum tilt for April to August at the low latitudes for south facing

collector was 0� thus this work extended its investigation on evaluating the optimum tilt angle

for April to August by using surface azimuth of 180� (collector facing due north) and the result

shows that during the season when the sun is at the northern hemisphere (passed the latitude of

the location/observer), the surface azimuth should be changed to face due north. The optimum

annual tilt angle for the location using the tilt to horizontal radiation ratio was found to be

equal to the location latitude for a south facing collector located in the northern hemisphere.

Taking average of the monthly optimum tilt gave the optimum tilt for south facing collector for

the location was 9.75�. Considering seasonal tilt angle variation, It was found that the optimum

tilt for the months of September to March has monthly tilt average of 17� facing due south and

12� tilt facing due north for the months of April to August while employing tilt to horizontal

radiation ratio method, the seasonal optimum tilt was 18� facing due south for the months of

September to March, and 15� due north for the months of April to August. The result of the

monthly optimum tilt angle from this work was compared with already existing work from lit-

erature as shown in Table VI and the result correlates closer to the model by Sunderan et al.,17

which was a study conducted for a nearby location and also shows similar trend with

Nijegorodov et al.8 model. Objects including dust are more stable when the centre of gravity is

lower, while increase in center of gravity of the object causes overthrow with little external

force. At higher tilt angle, the wind/rain can sweep off the dust particles out of the collector

surface easily. The effect of dust on the collector was considered with respect to literature rec-

ommendations; 15� annual tilt due south for the location was recommended for large solar col-

lector that may be difficult to be undergoing monthly or seasonal tilt angle adjustment. It is rec-

ommended from the result that monthly manual adjustment of the collector be employed for

collectors that can be adjusted and also considering the surface azimuth change for the months

of August. The result showed that about 14.55% of solar radiation available at the location can

be gained when the collector is tilted monthly to the monthly optimum tilt angle and surface

azimuth orientation for the collector. About 9.7% solar radiation can be gained for a south fac-

ing solar collector that is monthly adjusted which does not undergo surface azimuth adjustment.

With an annual optimum tilt angle of 4.39�, the solar radiation gain was 6.81%, while at 9.75�,the solar radiation gain was 6% and for 15� optimum tilt angle; the solar radiation gain was

5.13%.

TABLE VI. Comparison of present analysis with Nijegorodov et al.8 and Sunderan et al.17

Month Nijegorodov et al. model, bopt(�) Sunderan et al. model, bopt(

�) Opt. tilt, bopt

Jan 0.89Ø þ 29� 32.91 Ø-(�20.9�) 25.29 24.00

Feb 0.97Ø þ 17� 21.17 Ø-(�13.0�) 17.39 18.00

Mar Ø þ 4� 8.39 Ø-(�2.4�) 6.79 6.00

Apr Ø � 10� �5.61 Ø�(9.4�) �5.01 �6.00

May 0.93Ø � 24� �19.92 Ø-(18.8�) �14.41 �9.00

Jun 0.87Ø � 34� �30.18 Ø-(23.1�) �18.71 �18.00

Jul 0.89Ø � 30� �26.09 Ø-(21.2�) �16.81 �15.00

Aug 0.97Ø � 17� �12.74 Ø-(13.5�) �9.11 �12.00

Sep 0.89Ø � 2� 2.39 Ø�(2.2�) 2.19 3.00

Oct Ø þ 12� 16.39 Ø-(�9.6) 13.99 15.00

Nov 0.93Ø þ 25� 29.08 Ø-(�18.9�) 23.29 24.00

Dec 0.87Ø þ 34� 37.82 Ø-(�23.0�) 27.39 27.00

063112-15 Aja, Al-Kayiem, and Abdul Karim J. Renewable Sustainable Energy 5, 063112 (2013)

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ACKNOWLEDGMENTS

The authors would like to acknowledge Universiti Teknologi PETRONAS (UTP) for the tech-

nical and financial support. The main author appreciates, UTP for supporting his Ph.D. study under

the GA scheme.

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