Depósi o de in es igación de la Uni e sidad de Se illa
h ps://idus.us.es/
Es a es la e sión acep ada del a ículo publicado en: This is an accep ed manusc ip
o a pape published in:
Renewable Ene gy (2014): 08/10/2024
DOI: h ps://doi.o g/10.1016/j. enene.2014.05.020
Copy igh : © 2014 Else ie L d. All igh s ese ed.
El acceso a la e sión publicada del a ículo puede eque i la susc ipción de la e is a.
Access o he published e sion may equi e subsc ip ion.
“This is an Accep ed Manusc ip o an a icle published by Else ie in [Renewable
Ene gy] on [2014], a ailable a : h ps://doi.o g/10.1016/j. enene.2014.05.020”
1
Ene gy e iciency and ligh ing design in cou ya ds and a iums: A
p edic i e me hod o dayligh ac o s
Au ho ’s name and a ilia ion:
Ignacio Acos a, Ins i u o Uni e si a io de A qui ec u a y Ciencias de la Cons ucción, Uni e sidad de Se illa.
P o esso PhD. Co esponding Au ho .
Ca men Va ela, Ins i u o Uni e si a io de A qui ec u a y Ciencias de la Cons ucción, Uni e sidad de Se illa.
Resea che .
Juan F ancisco Molina, Ins i u o Uni e si a io de A qui ec u a y Ciencias de la Cons ucción, Uni e sidad de Se illa.
Resea che PhD.
Jaime Na a o, Ins i u o Uni e si a io de A qui ec u a y Ciencias de la Cons ucción, Uni e sidad de Se illa.
P o esso PhD.
Juan José Send a, Ins i u o Uni e si a io de A qui ec u a y Ciencias de la Cons ucción, Uni e sidad de Se illa.
P o esso PhD.
Co esponding Au ho :
Ignacio Acos a, Uni e si y o Se ille, Co esponding Au ho
Tel. numbe : 0034647550654
Email: [email p o ec ed]
Pe manen add ess:
Ins i u o Uni e si a io de A qui ec u a y Ciencias de la Cons ucción, Uni e sidad de Se illa, 41012 Se ille. Spain.
Abs ac
The p ope design o cou ya ds and a iums is key in p o iding su icien dayligh inside buildings as well as majo ene gy
sa ings in elec ic ligh ing. Al hough a sui able design equi es calcula ions using ligh ing simula ion so wa e o complex
algo i hms, a chi ec s lack a quick and p ecise p ocedu e o de e mine p ope design. The aim o his esea ch is he e o e o
o e a as accu a e me hod o de e mining he dayligh ac o o di e en poin s on a ec angula cou ya d o he cen al
space o an a ium, based on he a iable geome y and e lec ance o he inne su aces. Fi s ly, dayligh ac o s a e de ined
using measu emen s in scale models in an a i icial sky and alues ob ained in eal cou ya ds unde eal o e cas skies. The
sky componen is subsequen ly de ined based on ea lie s udies and T egenza algo i hms in o de o quan i y he e lec ed
componen . Following he cu e i ing p ocess, a p edic i e me hod o dayligh ac o s is de ined and compa ed wi h he
p e ious measu es. The compa ison demons a es ha he p edic i e me hod o e s an a e age accu acy o o e 90% based on
a quick and easy calcula ion. Finally, he ene gy sa ing in elec ic ligh ing is quan i ied ollowing he p edic i e me hod
es ablished.
Keywo ds: dayligh ac o , cou ya d, a ium, p edic i e me hod, dayligh au onomy, ene gy sa ing.
2
1. In oduc ion and objec i es
1.1. S a e o he a
The p ope design o cou ya ds and a iums is essen ial o he p o ision o su icien dayligh inside buildings, p oducing a
no iceable educ ion in ene gy consump ion in elec ic ligh ing [1]. Acco dingly, many esea che s ha e ied o de e mine he
implica ions o geome y and quali ies o hese a chi ec u al esou ces in he ene gy pe o mance o buildings [2,3,4],
es ablishing new design p inciples and me ics o assess he use o na u al ligh .
Mo eo e , dayligh ing imp o es isual pe cep ion [5] and p omo es he synch oniza ion o he ci cadian s imulus [6], esul ing
in imp o ed com o and heal h condi ions o occupan s [7] while good cou ya d o a ium design also p o ides imp o ed
he mal com o [8,9] and passi e en ila ion o he en i e building [10].
The s udy o dayligh in cou ya ds and a iums has ex ended om he p ocedu es p oposed in classic ea ises [11] igh up o
he mos cu en esea ch based on compu e simula ions [12,13]. Ea ly pape s on his subjec analyzed sola adia ion in
cou ya ds and a iums and i s in luence on dayligh illuminance, igno ing any o he implica ions in building design. Fo
example, Mohsen’s esea ch [14] de eloped a ma hema ical p ocedu e ha simula es he in e ac ion o sola incidence on
cou ya d loo s. Howe e , due o i s impo ance in ligh ing and he mal com o as well as i s impac in ene gy sa ings he
li e a u e abou cou ya d design has inc eased signi ican ly in he las 10 yea s. In subsequen s udies [15,16,17] he esea ch
ocused on he ene gy e iciency p o ided by p ope cou ya d design, analyzing he ligh ing and he mal beha io o he
building acco ding o he a iables es ablished. Se e al au ho s ha e analyzed he dayligh dis ibu ion on loo s and walls in
a iums [18,19,20] in an a emp o es ablish a p ope design acco ding o di e en a iables. Howe e , mos o his esea ch
was based on speci ic clima e condi ions o geome ic limi a ions, making i di icul o ind a uni e sal me hod which helps o
de e mine he illuminance in cou ya ds o a iums [21].
Dayligh illuminance can be de e mined using wo main me ics: dayligh ac o and dayligh au onomy. The dayligh ac o
(DF) co esponds o he a io o dayligh illumina ion a a gi en poin o ha o he ligh ecei ed on a ho izon al plane om an
unobs uc ed o e cas sky [22]. Nowadays, his is he mos widesp ead me ic in he s udy o dayligh ing [23,24,25]. The
dayligh ac o is conside ed a s a ic me ic, ha is o say, i depends only on he geome y and quali ies o he a chi ec u e,
since loca ion and o ien a ion a e i ele an in ela ion o an ideal cloudy sky [26]. The e o e, he dayligh ac o ep esen s he
po en ial illuminance a a gi en poin o he wo s case scena io unde o e cas sky condi ions. Mo eo e , dayligh au onomy
(DA), p oposed in 1989 [27] and ede ined by Reinha e al. [28], is de ined as he pe cen age o he yea when a minimum
illuminance h eshold is me by dayligh alone. The e o e, he highe he dayligh au onomy, he lowe he ene gy consump ion
in elec ic ligh ing. Unlike s a ic me ics, dayligh au onomy depends on he wea he condi ions and loca ion o he space, as
well as occupancy hou s and blind con ol by occupan s. Al hough dayligh au onomy can almos ce ainly de ine ene gy
3
sa ings mo e accu a ely han me ics based on s a ic clima e condi ions [29], he g ea e complexi y o his me ic, suppo ed
by a high numbe o a iables, makes he de ini ion o a p edic i e me hod almos impossible. I is o his eason ha mos o
he p edic i e me hods de eloped a e based on he dayligh ac o me ic [21].
As seen in he de ini ion es ablished by he CIE [22], dayligh ac o s can be de e mined as he sum o h ee componen s: he
sky componen (SC), which ep esen s he dayligh p o ided di ec ly om he sky; he ex e nally e lec ed componen (ERC)
p oduced by he e lec ion o he sky componen on he ex e io su aces; and he in e nally e lec ed componen (IRC)
gene a ed by he e lec ion o he sky ligh on he in e io su aces o he space.
The sky componen (SC) a a poin can be ob ained ollowing he analy ical o mula ion ha conside s he luminance
gene a ed by he isible ac ion o an o e cas sky. T egenza [30] de e mined he algo i hms o calcula e he sky componen
h ough e ical and ho izon al openings. The T egenza equa ions a e cu en ly used o assess he accu acy o ligh ing
compu e p og ams [31], and in he speci ic case o cou ya ds and a iums, he equa ions we e simpli ied by Acos a e al. [32]
o p oduce a simple calcula ion p ocedu e wi h an a e age ma gin o e o lowe han 2%.
Usually, he ex e nally e lec ed componen (ERC) is de ined as a ac ion o he sky componen [33], depending on he
dis ance om he ex e io geome y and i s e lec ance. In he case o cou ya ds and a iums, he ERC is negligible, as he e
a e usually no obs uc ions om he zeni hal dayligh .
The quan i ica ion o he in e nally e lec ed componen (IRC) depends on he endless e lec ion o dayligh on he inne
su aces o he cou ya d o a ium, conside ing he e lec ance (how much ligh is e lec ed) and he e lec ion (how ligh is
e lec ed) in each ligh bounce [22]. The e o e, gi en his complex de ini ion, he IRC canno be based on analy ical
calcula ions. Acco dingly, ini ial p edic i e me hods o quan i ying he IRC [34,35] a e based on ligh e lec ion hypo heses,
p incipally on he heo y o he in eg a ing sphe e [36]. Howe e , his heo y was suppo ed by simple geome ies which a e
no applicable o complex a chi ec u e. A ew decades la e , he p edic i e me hods o calcula e he IRC we e based on cu e
i ing p ocedu es, usually on ma hema ical unc ions i ed o he da a ob ained om ligh ing simula ion p og ams, building
moni o ing, o scale models [19,25,37,38]. One o he speci ic p edic i e me hods o de e mine he IRC in cou ya ds was
de eloped by Acos a e al. [39]. Howe e , his me hod is based on a cu e i ing p ocess a gued om he da a collec ed om
ligh ing simula ion p og ams, a oiding compa ison wi h eal o scale models. The simula ion p og ams a e limi ed by a
maximum numbe o e lec ions (in he case o ay- acing p og ams) o by a Lambe ian e lec ion (in he case o adiosi y
p og ams) [40,41], and as a esul hei abili y o ende he eal beha io o ligh is limi ed.
Mo eo e , mos o he s udies on p edic i e me hods men ioned and suppo ed by building moni o ing do no desc ibe he
luminance condi ions o he eal sky [25,38]. This is con i med by he esea ch on his p ocedu e based on scale models
[19,42]. As deduced om p e ious s a emen s, he e is no sole alid way o es ablish a p edic i e me hod o calcula e dayligh
4
ac o s gi en he inaccu acy o he indi idual analysis o he p ocedu es men ioned. The e o e, a solid p edic i e me hod mus
be based on he esul s ob ained om he compa ison o di e en p ocedu es o da a collec ion.
1.2. Aim and objec i es
The aim o his esea ch is o de e mine a p edic i e me hod o he calcula ion o dayligh ac o s o di e en poin s o a
cou ya d o a cen al space o an a ium, based on he geome y o he a chi ec u e and on he e lec ance o he in e io
su aces. As a esul , he p ope design o hese a chi ec u al esou ces could be de ined acco ding o he dayligh ac o s
ob ained, which ep esen he ligh ing com o and ene gy e iciency p oduced by dayligh .
This s udy aims o de ine he p edic i e me hod using he cu e i ing p ocess and he esul s ob ained by means o scale
models in an a i icial sky and eal models unde a eal o e cas sky. Acco dingly, unlike p e ious esea ch, his me hod is
easoned on wo di e en p ocedu es o da a collec ion in o de o es ablish a eliable o mula ion.
Following p e ious pape s on his esea ch [32,39], he me hod desc ibed de e mines he dayligh ac o s o di e en gi en
poin s on a cou ya d o a ium and calcula es he sky and e lec ed componen s independen ly, de ining he con ibu ion o
each componen a each s udy poin . One o he no el aspec s o his me hod is ha he quan i ica ion o he di e en
componen s is ca ied ou sepa a ely, p o iding in o ma ion abou he in luence o he geome y o he a chi ec u e and he
e lec ance o he inne su aces. In addi ion, his new me hod allows he calcula ion o dayligh ac o s a nine di e en poin s
o he loo and walls o he cou ya d o a ium, helping o de e mine he illuminance dis ibu ion inside hese a chi ec u al
esou ces.
As al eady s a ed, unlike p e ious s udies, his new me hod is based on eal measu emen s o achie e mo e accu a e
calcula ions. Acco ding o he me hodology desc ibed below, he sky condi ions we e de e mined using luminance aw iles
calib a ed wi h a luminance me e , achie ing highly p ecise measu emen s o dayligh ac o s unde eal condi ions.
2. Desc ip ion o Me hodology o Calcula ion
2.1. Scale model p ocedu e
The i s p ocedu e o da a collec ion consis s in measu ing he dayligh ac o s on he loo o a cou ya d scale model in an
a i icial sky. The scale model was made o medium-densi y ibe boa d using a lase cu e and 3D p in e ollowing he
ecommenda ions o Thanacha eonki e al. [42] in o de o minimize any impe ec ions a ec ing he measu emen s aken. The
loo o he cou ya d is a squa e o 30 cm by 30 cm. The s ackable scale model allows he assessmen o dayligh ac o s on
he loo o he cou ya d conside ing a a iable heigh om 30 o 120 cm, ha is o say, a a iable heigh o leng h a io o 1:4,
as seen in Figu e 1.

5
Figu e 1: S ackable scale model o a cou ya d made using lase cu e and 3D p in e in an a i icial sky.
The base o he scale model has small ga es on he co ne s and midpoin s o he pe ime e o he cou ya d, so ha he posi ion
o he illuminance me e in he co esponding s udy poin s (Fig. 2) can be inco po a ed sui ably. Fo all p ocedu es, h ee s udy
poin s on he loo plan o he cou ya d we e conside ed: cen e o he loo plan (A), middle o he wall (B), and co ne (C),
calcula ing maximum, in e media e, and minimum illuminance alues. All ga es we e closed o using black ca dboa d o
p e en incoming ligh om he a i icial sky om en e ing he base o he scale model (Fig. 1).
Figu e 2: S udy poin s in he cou ya d scale model, showing di e en wall e lec ances.
6
As seen in Figu e 2, he inne walls o he scale model we e co e ed wi h opaque ca dboa d ep esen ing di e en e lec ance
alues. The ca dboa d p oduces a Lambe ian e lec ion and e lec ances we e measu ed using a PCE-RGB 2 colo ime e ,
which shows a maximum a ia ion o ±3 RGB o 10 measu es. The e lec ance o he walls o he scale model is de ined in
Table 1.
Table 1: Re lec ance o he walls o he cou ya d scale model.
Wall Re lec ance Accu acy
Black 15.00 % -0.62%<R<+1.44%
G ey 32.00 % -4.80%<R<+2.42%
Whi e 78.00 % -6.16 %<R<+3.54%
The illuminance me e used o measu e he dayligh ac o s is a PCE-174 lux me e , which has an accu acy o ±5% o
illuminance alues lowe han 10,000 lux. Since he dayligh ac o s co espond o he quo ien o he inne and he ou e
illuminances, i is deduced ha his ma gin o e o is educed o measu es o illuminance lowe han he h eshold ci ed.
The a i icial sky co esponds o a pa allelepiped model, con as ed and calib a ed ollowing he s udy by Na a o e al. [43]
and subsequen esea ch [40]. Howe e , an accu acy analysis is ca ied ou o de e mine he alida ion o he a i icial sky in
o de o p o ide a solid assessmen o his p ocedu e. This accu acy analysis is based on wo s a emen s ela ing o he
de ini ion o he o e cas sky [26].
The i s s a emen is a gued in he de ini ion by Moon-Spence [44] which es ablishes ha he luminance o he o e cas sky
a ies acco ding o he ollowing law (1):
𝐿=𝐿·(1+2𝑠𝑖𝑛𝜃)
3 (1)
whe e LZ is he luminance a he zeni h o he sky aul and
θ
he p ojec ion angle. The e o e, he luminance measu ed a an
ele a ion o 60° co esponds o (2):
𝐿 =𝐿·(1+√3)
3 (2)
Mo eo e , he luminance measu ed conside ing an ele a ion o 30° co esponds o (3):
𝐿 =2𝐿
3 (3)
The second s a emen is based on he ela ionship be ween he ex e io illuminance and he luminance a he zeni h o he sky
aul (4), as ollows:
𝐸=1
3𝜋𝐿 2𝑠𝑖𝑛𝜃𝑐𝑜𝑠𝜃(1+2𝑠𝑖𝑛𝜃)𝑑𝜃=7
9𝜋𝐿 (4)



7
Acco ding o he p e ious s a emen s, nine measu es o luminance we e made in he a i icial sky: one o he zeni h and eigh
o he ca dinal poin s conside ing ou measu es o an ele a ion o 60° and ou mo e o 30°. The luminance me e model is
a Ma o-Spo 2, which has a measu emen angle o 1° and an accu acy o ±2%. The illuminance on he ho izon al plane was
measu ed using he PCE-174 lux me e desc ibed abo e. Acco ding o hese ools, he luminance in he zeni h is 2,120 cd/m2
while he illuminance measu e on he ho izon al plane shows 5,065 lx. The accu acy o he a i icial sky is shown in Table 2.
Table 2: Accu acy pa ame e s o he a i icial sky.
Analy ical esul s Measu emen s Luminance
Accu acy
a 30°
Luminance
Accu acy
a 60°
Illuminance
Accu acy
Luminance
a 30°
Luminance
a 60°
Ex e io
Illuminance
Luminance
a 30°
Luminance
a 60°
Ex e io
Illuminance
1,413 cd/m2 1,930 cd/m2 5,180 lx 1,264 cd/m2 1,812 cd/m2 5,065 lx -11.78% -6.51% -2.27%
As seen in Table 2, he co espondence be ween he analy ical esul s and he measu es aken wi h he luminance me e shows
a maximum di e gence o -6.51% conside ing an ele a ion o 60°. In addi ion, he ma gin o e o inc eases up o -11.78% in
he case o an ele a ion o 30°. This ma gin o e o is no mal o pa allelepiped a i icial skies, due o he limi ed e lec ance
o he mi o walls. Fo una ely, since he sky componen assessed in he cou ya d comes mainly om he zeni h, his ma gin
o e o ba ely a ec s he esul s ob ained. Mo eo e , as he ela ionship be ween ex e io illuminance and zeni h luminance
shows an accu acy o -2.27%, i is concluded ha he a i icial sky is sui able o his p ocedu e.
Acco ding o he me hodology desc ibed abo e, his p ocedu e shows a maximum ma gin o e o o 8.43% conside ing whi e
walls o he cou ya d scale model and he a i icial sky accu acy es ablished.
2.2. Real model p ocedu e
The second p ocedu e co esponds o he assessmen o dayligh ac o s measu ed on eal cou ya ds unde eal o e cas skies
whe e luminance dis ibu ion can be i ed o he Moon-Spence de ini ion [26,44].
All measu emen s we e conduc ed in Se ille, Spain, loca ed a la i ude 37° no h and longi ude 6° wes . This p ocedu e is
clea ly he mos complica ed, gi en he di icul y o conduc ing ligh ing measu emen s in a loca ion whe e he ideal cloudy sky
is ha d o ind. In ac , o he 16 ials ca ied ou , 4 we e disca ded due o di icul ies in assessing wall e lec ances and a
u he 7 es s we e uled ou due o he misma ch o he luminance dis ibu ion o he o e cas sky. The e o e, 5 ials we e
accep ed o his p ocedu e, desc ibed b ie ly in Figu e 3.
8
Figu e 3: Real cou ya d samples used o he eal model p ocedu e.
The cou ya ds selec ed ha e a wid h o leng h a io ha is almos squa e, wi h a uni o m heigh o all walls. The e lec ance
o loo and walls o each cou ya d was measu ed using he colo ime e desc ibed abo e, measu ing colo samples o
indi idual walls and windows. A Leica Dis o X310 lase me e was used o de e mine he heigh and loo dimensions o each
cou ya d.
As in he p e ious p ocedu e, h ee s udy poin s we e conside ed: cen e o he loo plan (A), middle o he wall (B), and
co ne (C). In his case, he ou middle poin s o he wall and co ne s we e measu ed in o de o minimize he ma gin o e o
o he measu emen s. In o de o ex end he measu emen s o dayligh ac o s o eal cou ya ds, he measu emen s aken
conside ed a heigh o 2 me e s abo e loo le el.
In o de o cha ac e ize he sky dis ibu ion o each ial, he Ma o-Spo 2 luminance me e was used o con as he luminance
maps ob ained om he Raw iles o a Canon Eos 70D. Th ee luminance measu emen s we e aken o each sky and ial:
zeni h, 45° ele a ion and ho izon. Figu e 4 shows h ee sky luminance dis ibu ions, calcula ed ollowing he me hod
men ioned abo e and co esponding o ials 1, 3, and 4.
15
The e o e, he IRC can be de ined as a unc ion o he sky componen measu ed a he middle poin o he wall (SCB)
acco ding o equa ion (8) and mul iplied by he a e age coe icien o e lec ance (R).
4.2.2. Quan i ying he e lec ed componen
In acco dance wi h he scale model p ocedu e, he in e nally e lec ed componen (IRC) is quan i ied o he cen e poin o he
loo plan, aking in o conside a ion he di e ence be ween he measu ed dayligh ac o s (DF) shown in Figu e 6, and he sky
componen (SC) de ined in equa ion (7) by Acos a e al. [32]. The esul s ob ained a e shown in Table 4, depending on he
heigh o leng h a io and he e lec ance o walls.
Table 4: Quan i ica ion o IRC in he cen e o he loo plan o he scale model.
Ra io H/L Wall
Re lec ance
A e age
Re lec ance DFA Cen e SCA Cen e IRCA Cen e SCB·R SCB·R / IRC
1/1 15.00% 12.50% 38.89% 29.41% 9.48% 2.84% 3.34
2/1 15.00% 13.50% 14.81% 9.43% 5.37% 1.16% 4.62
3/1 15.00% 13.93% 7.90% 4.42% 3.47% 0.59% 5.88
4/1 15.00% 14.17% 4.74% 2.54% 2.20% 0.35% 6.27
1/1 32.00% 23.83% 43.83% 29.41% 14.42% 5.42% 2.66
2/1 32.00% 27.10% 18.76% 9.43% 9.32% 2.34% 3.99
3/1 32.00% 28.50% 10.46% 4.42% 6.04% 1.21% 5.00
4/1 32.00% 29.28% 7.01% 2.54% 4.47% 0.72% 6.17
1/1 78.00% 54.50% 59.43% 29.41% 30.02% 12.39% 2.42
2/1 78.00% 63.90% 35.34% 9.43% 25.91% 5.51% 4.70
3/1 78.00% 67.93% 21.52% 4.42% 17.10% 2.88% 5.94
4/1 78.00% 70.17% 14.51% 2.54% 11.97% 1.74% 6.89
As seen in Table 4, he a e age e lec ance (R) is ha o he mean alue conside ing he e lec ance o walls, loo and opening
o he cou ya d o a ium. As ou lined in he calcula ion assump ions, he a iable SCB·R is de ined o each scale model,
acco ding o he heo y o he in eg a ing sphe e [36]. These a iables will help o de e mine he p edic i e me hod o he IRC.
In o de o conclude a scala which de ines he me hod, he a io o SCB·R o IRC is also shown in Table 4.
4.2.3. Cu e i ing o he e lec ed componen
As can be deduced om he dayligh ac o esul s obse ed in he scale models, he e is a co ela ion be ween he IRC and he
heigh o leng h a io o he cou ya d. The IRC speci ically ends o ise p opo ionally o he SC as he heigh o leng h a io
inc eases. The e o e, his a io will ac as a a iable o he p edic i e me hod equa ion. In o de o quan i y he weigh o his
a iable, a scala and an exponen o he heigh o leng h a io a iable a e de ined acco ding o a cu e i ing p ocess, shown
in Table 5.

16
Table 5: Fi ing o he SCB·R / IRC unc ion acco ding o he heigh o leng h a io.
Ra io H/L SCB·R / IRC
· (H/L)1.0
SCB·R / IRC
· (H/L)0.9
SCB·R / IRC
· (H/L)0.8
SCB·R / IRC
· (H/L)0.7
SCB·R / IRC
· (H/L)0.6
SCB·R / IRC
· (H/L)0.5
SCB·R / IRC
· (H/L)0.4
1/1 3.34 3.34 3.34 3.34 3.34 3.34 3.34
2/1 2.31 2.47 2.65 2.84 3.05 3.26 3.50
3/1 1.96 2.19 2.44 2.73 3.04 3.40 3.79
4/1 1.57 1.80 2.07 2.38 2.73 3.14 3.60
1/1 2.66 2.66 2.66 2.66 2.66 2.66 2.66
2/1 2.00 2.14 2.29 2.46 2.63 2.82 3.02
3/1 1.67 1.86 2.08 2.32 2.59 2.89 3.22
4/1 1.54 1.77 2.04 2.34 2.69 3.08 3.54
1/1 2.42 2.42 2.42 2.42 2.42 2.42 2.42
2/1 2.35 2.52 2.70 2.89 3.10 3.33 3.56
3/1 1.98 2.21 2.47 2.75 3.07 3.43 3.83
4/1 1.72 1.98 2.27 2.61 3.00 3.45 3.96
A i hme ic
mean 2.13 2.28 2.45 2.65 2.86 3.10 3.37
S anda d
de ia ion 1.29 1.06 0.84 0.70 0.77 1.07 1.55
As seen in Table 5, he lowes s anda d de ia ion co esponds o an exponen o 0.7, wi h an a i hme ic mean o 2.65.
The e o e, i can be concluded ha he IRC a he cen e poin o he cou ya d loo can be de ined as ollows (12):
𝐼𝑅𝐶≅𝑓(𝑆𝐶·𝑅,𝐻/𝐿)≅2.6·𝑆𝐶·𝑅·(𝐻/𝐿). =2.6𝐿𝑅
2𝐿+2.4𝐻·𝐻
𝐿. =2.6𝐿.𝐻.𝑅
2𝐿+2.4𝐻(12)
whe e 2.6 co esponds o he scala equi alen o he a i hme ic mean, L is he mean leng h o he cou ya d, H he heigh o he
cen e poin o he loo plan and R he a e age e lec ance o he inne su aces.
Acco ding o equa ions (7) and (12), he dayligh ac o o he cen e o he cou ya d loo co esponds o (13):
𝐷𝐹=𝑆𝐶+𝐼𝑅𝐶≅𝐿
𝐿+2.4𝐻+2.6𝐿.𝐻.𝑅
2𝐿+2.4𝐻 (13)
whe e L is he mean leng h o he cou ya d, H he heigh o he cen e poin o he loo plan and R he a e age e lec ance o
he inne su aces.
Following he same cu e i ing p ocess o he es o he s udy poin s, i can be concluded ha he scala chosen a ies
acco ding o he loca ion o he measu emen . In ac , conside ing an exponen o 0.7 o he heigh o leng h a io a iable, he
a i hme ic mean o he middle poin o he wall is 2.29 o a s anda d de ia ion o 0.61, whe eas he mean alue o he co ne
is equi alen o 2.07 o a s anda d de ia ion o 0.59. The e o e, he dayligh ac o s o he midpoin o he wall and he co ne
a e equi alen o equa ions (14) and (15) espec i ely:
𝐷𝐹=𝑆𝐶+𝐼𝑅𝐶≅𝐿
2𝐿+2.4𝐻+2.3𝐿.𝐻.𝑅
2𝐿+2.4𝐻 (14)
17
𝐷𝐹=𝑆𝐶+𝐼𝑅𝐶≅𝐿
4𝐿+2.4𝐻+2𝐿.𝐻.𝑅
2𝐿+2.4𝐻 (15)
whe e L is he mean leng h o he cou ya d, H he heigh o he cen e poin o he loo plan and R he a e age e lec ance o
he inne su aces.
5. Con as ing he p edic i e me hod
5.1. Con as ing wi h scale models
Once he p edic i e me hod is de ined, i s accu acy is de e mined acco ding o he p ocedu es p oposed. As desc ibed in he
me hodology, he i s p ocedu e o con as ing he me hod is o measu e dayligh ac o s in scale models in an a i icial sky,
which ep oduces he ideal condi ions o an o e cas sky.
As deduced om he cu e i ing p ocess shown in he me hod de ini ion, he IRC was de ined ollowing he scale model
p ocedu e, he e o e, high accu acy is expec ed in he con as ing o he me hod in his p ocedu e.
The ela i e di e ence o he dayligh ac o s ob ained by he p edic i e me hod wi h espec o hose measu ed in he scale
model is shown in Figu e 9. The heigh o leng h a io is ep esen ed in he X-axis, acco ding o he wall e lec ance o each
scale model, whe eas he Y-axis shows he ela i e di e ence be ween he me hod and he measu emen s o dayligh ac o s
in he cen e o he loo plan (DFA), middle poin o he wall (DFB) and co ne o he cou ya d (DFC).
Figu e 9: Rela i e di e ence o he p edic i e me hod o dayligh ac o s wi h espec o he measu emen s in he scale model
p ocedu e.
18
As Figu e 9 shows, he a e age di e ence be ween he p edic i e me hod and he dayligh ac o s measu ed in he scale model
is 4.18%, while he s anda d de ia ion is 2.19%. Fu he mo e, he maximum di e gence be ween bo h app oaches is equal o
9.96%. I is he e o e concluded ha he p edic i e me hod is p ope ly i ed o he measu emen s o he scale model.
5.2. Con as ing wi h eal models
As can be deduced, con as ing he p edic i e me hod wi h he measu emen s o dayligh ac o s in eal models is less accu a e
han he p e ious p ocedu e gi en he di e gence o he eal cloudy sky wi h ega d o he Moon-Spence de ini ion [44].
Howe e , su icien accu acy is p edic ed, as deduced om Figu e 10, which shows he ela i e di e ence o he dayligh
ac o s de ined by he p edic i e me hod wi h espec o he alues measu ed in eal cou ya ds. Each ial is ep esen ed in he
X-axis, om 1 o 5, ollowed by a le e A, in he case o measu emen s a 0 m abo e loo le el, o B, in he case o
assessmen s a 2 m abo e loo le el. As in he p e ious compa ison, he Y-axis shows he ela i e di e ence be ween he
me hod and he measu emen s o dayligh ac o s in he cen e o he loo plan (DFA), middle poin o he wall (DFB) and
co ne o he cou ya d (DFC).
Figu e 10: Rela i e di e ence o he p edic i e me hod o dayligh ac o s wi h espec o he measu emen s in he eal model
p ocedu e.
As obse ed in Figu e 10, he a e age di e ence be ween he p edic i e me hod and he esul s ob ained in he measu emen s
in eal cou ya ds is equal o 6.75%, sligh ly highe han in he p ocedu e abo e. Fu he mo e, he s anda d de ia ion o he
ela i e di e ence is de ined as 4.27%, conside ing he en i e sample o eal cou ya ds and measu emen s, so i can be
19
deduced ha he me hod is p ope ly i ed o he esul s ob ained. Conside ing he p e ious s a emen s, i is concluded ha he
p edic i e me hod is sui able o de ine he dayligh ac o s based on he measu emen de eloped in eal cou ya ds.
6. Analysis o ene gy e iciency
6.1. Calcula ion p ocedu e
In o de o quan i y he ene gy sa ing in elec ic ligh ing achie ed by cou ya ds and a iums, he dayligh au onomy (DA)
mus be de e mined. As shown in he s a e o he a , his me ic is de ined as he pe cen age o he yea when a minimum
illuminance h eshold is me by dayligh alone. The e o e, he highe he dayligh au onomy, he lowe he ene gy consump ion
in elec ic ligh ing. Acco dingly, his me ic can be de ined as equa ion (16):
𝐷𝐴𝑚=∑𝑤𝑓 ·𝑇
∑𝑇 ∈󰇟0,1󰇠; 𝑤𝑓=1 𝑖𝑓 𝐸≥𝐸
0 𝑖𝑓 𝐸<𝐸 (16)
whe e Ti is he occupancy du ing he yea , w i is he weigh ing ac o which depends on he illuminance h eshold, ED is he
dayligh illuminance measu ed a a gi en poin , and EL is he illuminance h eshold.
The dayligh au onomy alues can be deduced om he dayligh ac o s ob ained by using he p edic i e me hod, conside ing a
con inuous o e cas sky, which ep esen s he wo s case scena io o he assessmen o he ene gy e iciency. The hou s o
occupancy de e mine he sola al i ude h oughou he yea , allowing he calcula ion o he ex e io illuminance unde o e cas
sky condi ions. Subsequen ly, he dayligh ac o s de ined by he p edic i e me hod can se e o de e mine he in e io
illuminance o each ime pe iod. Finally, he in e io illuminance is compa ed wi h he illuminance h eshold and he dayligh
au onomy unde o e cas sky condi ions is quan i ied.
The quan i ica ion o ene gy consump ion no only depends on he geome y and quali ies o he cou ya d o a ium, bu he
size o he window and he inne su aces o he oom also a ec he esul s ob ained. Following p e ious esea ch on dayligh
au onomy alues measu ed h ough windows [45], he ene gy consump ion has been calcula ed conside ing he ollowing
assump ions:
• The oom and he window a e cen e ed in he middle poin o he wall o he a ium o cou ya d.
• The window o acade a io co esponds o 60%. The window is squa e.
• The a e age e lec ance o he inne su aces o he oom is 70%, o a g ey loo (60%) and ligh g ey walls and
ceiling (80%). The op ical ansmi ance o he glass co esponds o 70%.
• The measu emen a ea co esponds o he a ea nea he window, om he acade o a dis ance o 3 me e s.
20
As can be deduced, he al e a ion o hese a iables would p o ide di e en esul s in he quan i ica ion o he ene gy
consump ion. The e o e, he esul s ob ained only se e o a speci ic scena io, al hough hey would be use ul in es ima ing he
impac o cou ya d and a ium design in he ene gy pe o mance o buildings.
Since he sola al i ude a ies acco ding o he la i ude o he loca ion, he dayligh au onomy is assessed acco ding o his
a iable.
6.2. Ene gy e iciency in b igh cou ya ds
Following he calcula ion p ocedu e shown abo e, he dayligh au onomy unde o e cas sky condi ions is quan i ied,
conside ing an illuminance h eshold o 500 lx and occupancy hou s om 8 am o 5 pm. Table 6 shows he dayligh au onomy
alues measu ed a he middle poin o he wall o b igh cou ya ds, acco ding o an a e age e lec ance o he inne su aces
o 70% and a glass ansmi ance o 70%.
Table 6: Dayligh au onomy in b igh cou ya ds, conside ing o e cas sky condi ions, an illuminance h eshold o 500 lx and
occupancy hou s om 8 am o 5 pm.
Ra io H/L La i ude
0 º 10 º 20 º 30 º 40 º 50 º 60 º
1/1 94% 94% 92% 92% 90% 85% 72%
4/3 94% 93% 91% 91% 88% 83% 69%
5/3 94% 92% 91% 90% 87% 81% 65%
2/1 92% 91% 90% 86% 85% 77% 62%
7/3 88% 90% 89% 84% 81% 73% 58%
8/3 86% 87% 87% 83% 78% 68% 55%
3/1 84% 84% 83% 82% 76% 62% 51%
10/3 84% 84% 81% 80% 73% 58% 47%
11/3 84% 81% 78% 75% 68% 54% 44%
4/1 83% 80% 78% 72% 65% 50% 41%
As can be seen in Table 6, he dayligh au onomy is no iceably highe o low la i udes, dec easing o high a ios. Acco ding
o hese esul s, he minimum ene gy sa ing in elec ic ligh ing is quan i ied in Table 7, conside ing a ypical ene gy e iciency
alue o LED lamps o 1.8 W/m2/100 lx.

21
Table 7: Minimum ene gy sa ings in elec ic ligh ing o b igh cou ya ds, acco ding o an illuminance h eshold o 500 lx
and occupancy hou s om 8 am o 5 pm. Measu ed in kWh/m2.
Ra io H/L La i ude
0 º 10 º 20 º 30 º 40 º 50 º 60 º
1/1 178.17 178.17 174.38 174.38 170.59 161.11 136.47
4/3 178.17 176.27 172.48 172.48 166.80 157.32 130.78
5/3 178.17 174.38 172.48 170.59 164.90 153.53 123.20
2/1 174.38 172.48 170.59 163.00 161.11 145.95 117.51
7/3 166.80 170.59 168.69 159.21 153.53 138.36 109.93
8/3 163.00 164.90 164.90 157.32 147.84 128.89 104.25
3/1 159.21 159.21 157.32 155.42 144.05 117.51 96.67
10/3 159.21 159.21 153.53 151.63 138.36 109.93 89.08
11/3 159.21 153.53 147.84 142.16 128.89 102.35 83.40
4/1 157.32 151.63 147.84 136.47 123.20 94.77 77.71
As deduced om Table 7, he minimum ene gy sa ing a ies om 13% o 75% acco ding o he heigh o wid h a io. This
a ia ion is mo e no able in high la i udes.
6.3. Ene gy e iciency in da k cou ya ds and a iums
The minimum ene gy sa ing in da k cou ya ds and a iums is assessed ollowing he p ocedu e explained abo e and
conside ing he same illuminance h eshold and occupancy hou s. Table 8 shows he dayligh au onomy alues o he
midpoin o he wall o da k cou ya ds o a iums, assuming an a e age e lec ance o he inne su aces o 30% and a glass
ansmi ance o 70%.
Table 8: Dayligh au onomy in da k cou ya ds and a iums, conside ing o e cas sky condi ions, an illuminance h eshold o
500 lx and occupancy hou s om 8 am o 5 pm.
Ra io H/L La i ude
0 º 10 º 20 º 30 º 40 º 50 º 60 º
1/1 93% 92% 91% 91% 87% 82% 66%
4/3 92% 91% 90% 86% 85% 77% 62%
5/3 87% 89% 88% 84% 79% 71% 57%
2/1 84% 84% 83% 81% 76% 62% 51%
7/3 84% 82% 79% 77% 70% 56% 45%
8/3 83% 79% 77% 71% 63% 50% 40%
3/1 77% 77% 73% 68% 54% 44% 34%
10/3 72% 70% 67% 61% 48% 39% 29%
11/3 70% 66% 63% 52% 42% 32% 23%
4/1 64% 63% 57% 45% 35% 27% 17%
As in he p e ious ial, he dayligh au onomy shown in Table 8 is highe o low la i udes, dec easing o na ow cou ya ds
o a iums. Conside ing he alue o ene gy e iciency o LED lamps de ined be o e, he minimum ene gy sa ing is shown in
Table 9.
22
Table 9: A e age ene gy sa ings in elec ic ligh ing o da k cou ya ds and a iums, acco ding o an illuminance h eshold o
500 lx and occupancy hou s om 8 am o 5 pm. Measu ed in kWh/m2.
Ra io H/L La i ude
0 º 10 º 20 º 30 º 40 º 50 º 60 º
1/1 176.27 174.38 172.48 172.48 164.90 155.42 125.10
4/3 174.38 172.48 170.59 163.00 161.11 145.95 117.51
5/3 164.90 168.69 166.80 159.21 149.74 134.57 108.04
2/1 159.21 159.21 157.32 153.53 144.05 117.51 96.67
7/3 159.21 155.42 149.74 145.95 132.68 106.14 85.29
8/3 157.32 149.74 145.95 134.57 119.41 94.77 75.82
3/1 145.95 145.95 138.36 128.89 102.35 83.40 64.44
10/3 136.47 132.68 126.99 115.62 90.98 73.92 54.97
11/3 132.68 125.10 119.41 98.56 79.61 60.65 43.59
4/1 121.31 119.41 108.04 85.29 66.34 51.18 32.22
As in he abo e case, he minimum ene gy sa ing a ies acco ding o he heigh o wid h a io. Howe e , o da k cou ya ds
o a iums, his a ia ion is no iceably highe han in he p e ious ials, a ying om 45% o low la i udes o 288% o high
la i udes.
7. Conclusions
The p edic i e me hod de ined in his esea ch, exp essed in equa ions DFA (13), DFB (14) and DFC (15), p o ides an accu a e
p ocedu e o de e mine he dayligh ac o s o speci ic poin s in a cou ya d o a cen al space o an a ium. In ac , as
obse ed in Figu e 9, he compa ison o he p oposed me hod wi h scale models in an a i icial sky shows an a e age
di e ence o 4.18% and a s anda d de ia ion o 2.19%, demons a ing p ope beha io o he o mula ion de ined h ough
compa ison wi h p e ious esea ch [35,37,39] whe e he ma gin o e o is no iceably highe . Fu he mo e, as seen in Figu e
10, he compa ison o he me hod de eloped wi h ega d o he measu emen s in eal cou ya ds unde eal o e cas sky
condi ions shows a sligh inc ease o he a e age di e ence and a s anda d de ia ion o 4.27%. I is he e o e concluded ha
he equa ions p oposed help de e mine dayligh ac o s wi h sui able accu acy.
Unlike p e ious app oaches, he p oposed me hod de e mines bo h he sky and he e lec ed componen o each s udy poin ,
so ha he e ec o he geome y and he e lec ance o he inne su aces can be quan i ied sepa a ely. Fu he mo e, he
equa ions o he cou ya d o a ium pe ime e , which co espond o DFB (14) and DFC (15), allow dayligh ac o s on e ical
planes o be measu ed, concluding he illuminance caused by he sky dome on di e en poin s o he loo plan and walls.
As deduced om he analysis o ene gy e iciency, his me hod can quan i y he minimum ene gy sa ing in elec ic ligh ing,
acco ding o an illuminance h eshold and occupancy hou s.
The p ac ical applica ion o he p oposed me hod can be e y b oad. I can be used in building in o ma ion modeling (BIM)
p og ams o he simple quan i ica ion o he ene gy pe o mance o cou ya ds and a iums wi hou he need o complex
23
calcula ion. The simple o mulae can se e as a ool o he p e-design s age o hese a chi ec u al esou ces, de e mining he
dimensions needed o ensu e sui able illuminance p o ided by dayligh ing. Mo eo e , his me hod can be implemen ed in
u u e u banism s anda ds o es ablish a simple o mula o de e mining he minimum heigh o wid h a io o cou ya ds and
a iums.
Acknowledgemen s
The au ho s would like o hank José Luis He nández and An onio Pue as o hei collabo a ion in he measu emen o
dayligh ac o s and he cha ac e iza ion o se e al cou ya ds used in he eal model p ocedu e.
Re e ences
[1] A. Das, S.K. Paul, A i icial illumina ion du ing day ime in esiden ial buildings: Fac o s, ene gy implica ions and u u e
p edic ions, Applied Ene gy 158 (2015) 65-85.
[2] M. Vujoše ić, A. K s ić-Fu undžić, The in luence o a ium on ene gy pe o mance o ho el building, Ene gy and
Buildings 156 (2017) 140-150.
[3] W. Lan, H. Qiong, Z. Qi, X. Hong, R.K.K. Yuen, Role o a ium geome y in building ene gy consump ion: The case o a
ully ai -condi ioned enclosed a ium in cold clima es, China, Ene gy and Buildings 151 (2017) 228-241.
[4] M. Sudan , R.G. Mis ick, G.N. Tiwa i, Clima e-Based Dayligh Modeling (CBDM) o an a ium: An expe imen ally
alida ed no el dayligh pe o mance, Sola Ene gy 158 (2017) 559-571.
[5] R.P. Leslie, L.C. Rade sky, A.M. Smi h, Concep ual design me ics o dayligh ing, Ligh ing Resea ch and Technologies
44 (2012) 277-290.
[6] M.G. Figuei o, J.A. B ons, B. Pli nick, B. Donlan, R.P. Leslie, M.S. Rea, Measu ing ci cadian ligh and i s impac on
adolescen s, Ligh ing Resea ch and Technology 43 (2011) 201-215.
[7] I. Acos a, R.P. Leslie, M.G. Figuei o, Analysis o ci cadian s imulus allowed by dayligh ing in hospi al ooms, Ligh ing
Resea ch and Technology (2015), doi: 10.1177/1477153515592948.
[8] D.H.W. Li, A e iew o dayligh illuminance de e mina ions and ene gy implica ions, Applied Ene gy 87 (2010) 2109-
2118.
[9] A. Gha a ianhoseini, U. Be a di, A. Gha a ianhoseini, The mal pe o mance cha ac e is ics o unshaded cou ya ds in ho
and humid clima es, Building and En i onmen 87 (2015) 154-168.
[10] A. Aldawoud, R. Cla k, Compa a i e analysis o ene gy pe o mance be ween cou ya d and a ium in buildings, Ene gy
and Buildings 40 (2008) 209-214.
[11] R.G. Hopkinson, P. Pe he b idge, J. Longmo e, Dayligh ing, London: Heinemann (1966).
[12] A. Tsang assoulis, V. Bou dakis, Compa ison o adiosi y and ay- acing echniques wi h a p ac ical design p ocedu e o
he p edic ion o dayligh le els in a ia, Renewable Ene gy 28 (2003) 2157-2162.
24
[13] M. Mohsenin, J. Hu, Assessing dayligh pe o mance in a ium buildings by using Clima e Based Dayligh Modeling,
Sola Ene gy 119 (2015) 553-560.
[14] M.A. Mohsen, Sola adia ion and cou ya d house o ms - I. A ma hema ical model, Building and En i onmen 14 (1979)
89-106.
[15] B. Bouche , M. Fon oynon , Day-ligh ing o unde g ound spaces: design ules, Ene gy and Buildings 23 (1996) 293-298.
[16] E. Yas, V. Ok, E alua ion o he e ec s o cou ya d building shapes on sola hea gains and ene gy e iciency acco ding
o di e en clima ic egions, Ene gy and Buildings 73 (2014) 192-199.
[17] M. Taleghani, M. Tenpie ik, A. Dobbels een, Ene gy pe o mance and he mal com o o cou ya d/a ium dwellings in
he Ne he lands in he ligh o clima e change, Renewable Ene gy 63 (2014) 486-497.
[18] B. Calcagni, M. Pa oncini, Dayligh ac o p edic ion in a ia building designs, Sola Ene gy 76 (2004) 669-682.
[19] J. Du, S. Sha ples, Assessing and p edic ing a e age dayligh ac o s o adjoining spaces in a ium buildings unde
o e cas sky, Building and En i onmen 46 (2011) 2142-2152.
[20] J. Du, S. Sha ples, The a ia ion o dayligh le els ac oss a ium walls: Re lec ance dis ibu ion and well geome y e ec s
unde o e cas sky condi ions, Sola Ene gy 85 (2011) 2085-2100.
[21] J.C. W igh , K.M. Le he man, Illuminance in a ia: e iew o p edic ion me hods, Ligh ing Resea ch and Technology
30(1) (1998) 1-11.
[22] CIE, In e na ional ligh ing ocabula y, Commission In e na ionale de l’Éclai age (2011), CIE S 017:2011.
[23] A. Chel, G.N. Tiwa i, H.N. Singh, A modi ied model o es ima ion o dayligh ac o o skyligh in eg a ed wi h dome
oo s uc u e o mud-house in New Delhi (India), Applied Ene gy 87 (2010) 3037-3050.
[24] I. Acos a, J. Na a o, J.J. Send a, P. Esqui ias, Dayligh ing design wi h ligh scoop skyligh s: Towa ds an op imiza ion o
p opo ion and spacing unde o e cas sky condi ions, Ene gy and Buildings 49 (2012) 394-401.
[25] S.K.H. Chow, D.H.W. Li, E.W.M. Lee, J.C. Lam, Analysis and p edic ion o dayligh ing and ene gy pe o mance in
a ium spaces using dayligh -linked ligh ing con ols, Applied Ene gy 112 (2013) 1016-1024.
[26] CIE, Spa ial Dis ibu ion o Dayligh - CIE S anda d Gene al Sky, Commission In e na ionale de l’Éclai age (2003). CIE
S 011/E: 2003.
[27] Associa ion Suisse des Elec iciens, Éclai age in é ieu pa la lumiè e du jou , Associa ion Suisse Des Elec iciens, Swiss
No m SN 418911 (1989).
[28] C.F. Reinha , J. Ma dalje ic, Z. Roge s, Dynamic Dayligh Pe o mance Me ics o Sus ainable Building Design,
Leukos 3(1) (2006) 7-31.
[29] P.R. Boyce, K.A.G. Sme , LRT symposium “Be e me ics o be e ligh ing” – a summa y, Ligh ing Resea ch and
Technology, 46 (2013) 619-636.
[30] P. T egenza, Dayligh ing algo i hms. ETSU S 1350, U.K. Depa men o T ade and Indus y on behal o he Ene gy
Technology Suppo Uni (1993) 43.
[31] CIE, Tes cases o assess he accu acy o ligh ing compu e p og ams, Commission In e na ionale de l’Éclai age (2006).
CIE 171:2006.