PLEA 2003 - The 20 h Con e ence on Passi e and Low Ene gy A chi ec u e, San iago – CHILE, 9 - 12 No embe 2003
The A chi ec Robe o Ri e o and Dayligh ing
Resea ch
Jose M. Cabeza and Jose M. Almodo a
Escuela Tecnica Supe io de A qui ec u a. Uni e sidad de Se illa
A da. Reina Me cedes 2, 41012, Se illa. Spain
Tel.: 34-95 455 6556 / Fax: 34-95 455 6972
Email: c owley@a akis.es
[email p o ec ed]
ABSTRACT: By he end o he 1950’s decade, a chi ec Robe o Osca Ri e o, who had been
s udying in England, e u ned o his na i e U uguay and p oduced a e olu iona y app oach o
dayligh ing echniques: he was able o ela e ligh ing in ensi ies wi h posi ions o poin s loca ed
unde nea h ec angula windows, plo ing he esul in a simple able. He could do so wi h he help
o pains aking g aphs ha he d ew manually.
To in oduce he alue o he ansmi ance in his me hods he had o de ine an exp ession widely
quo ed by scien is s a ound he wo ld, he Ri e o T ansmi ance Fo mula, which shows he
ele ance o di ec ionali y in a ac o usually aken as scala in mos calcula ions.
This p ocedu e also pe mi ed he s udy o skies like he CIE o e cas sky, which we e s ongly
dependen on he angle o al i ude and hence he pe o mance o uni o m and o e cas skies could
be compa ed.
Wi h so many o una e ad ances he was on he e ge o inding a mo e gene al solu ion o
adia i e exchange p oblems, which in iguingly enough, he was no able o p oduce e en ually.
Robe o Ri e o has passed away ecen ly, and his o iginal ex s ha e almos disappea ed as he e
was no e-edi ion o his ma e ial. Since he manusc ip s we e con eyed in Spanish, we ha e el
he necessi y o explain his disco e ies o an English-speaking audience. In o de o do his, we
will use a con empo a y poin o iew, and we will discuss how a he could ha e eached and wha
he achie ed in he dayligh ing ield.
Con e ence Topic: Me hods and ools o design assis ance
Keywo ds: Dayligh ing. Ri e o. Sky calcula ion. Con igu a ion ac o s.
1. BACKGROUND OF THE RESEARCH
F om he beginning o he 20 h cen u y, he
science o ligh ing was slowly bu su ely es ablished.
The indings o J. H. Lambe and especially hose
con ained in his ea ise on Pho ome y o 1758, we e
edisco e ed, dis o ed and inally applied. This
p ocess was mainly encou aged by he p omo e s o
he new p oduc s ha became a ailable in he ield o
a i icial de ices and luminai es.
Then, among he many in e es ing e o s ha ook
place, we could quo e hose o Pleijel, D. Spence , P.
H. Moon, Hopkinson and H. H. Higbie.
Howe e , hey did no seem o know each o he ’s
wo k, especially in wha ega ds o he excellen
pape s by Higbie and Randall.
Ri e o was amilia wi h wha we could desc ibe
as he No dic school o dayligh ing, which included
English, Scandina ian and occasionally F ench
s udies, bu no Ge many o he Uni ed S a es, whe e
a di e en app oach migh ha e p e ailed as we will
show.
Thus, Ri e o was conce ned wi h he p oblems
posed by he uni o m sky, which had been a main
issue in Pleijel’s wo k, and also wi h he new and
mo e complex app oach p esen ed by cloudy skies as
seen in he heo ies o Spence -Moon, la e adop ed
by he CIE (In e na ional Commission o Ligh ing).
We would say now ha he CIE o e cas sky, wi h
i s unequal luminance dis ibu ion is he a che ypal
case o non-di use emi e s.
In his ca ego y o sky, he luminous dis ibu ion
on he hemisphe e is go e ned by he ollowing
physical conside a ions.
LLL
≠
=
)(),(
θ
ϕ
θ
( )
3
21
*)( θ
θsen
LL +
=
PLEA 2003 - The 20 h Con e ence on Passi e and Low Ene gy A chi ec u e, San iago – CHILE, 9 - 12 No embe 2003
2. THE CONTRIBUTION OF RIVERO
To in eg a e he quan i y o illuminance ecei ed
om a sky o uni o m luminance, Ri e o p o ed ha
his was equal in alue o geome ical p ojec ions
o e a sphe e, wha is oday mo e known as he
p ojec ed solid angle p inciple ( igu e 3).
He de eloped an ex ao dina y sphe ical
igonome y o ind accu a e exp essions o
ho izon al and e ical ligh ac o s, he was able o
achie e his by means o applica ion o he p ojec ed
solid angle p inciple, a solu ion which a oided hea y
in eg al calculus, pa adoxically, such calculus had
been p o ided by Higbie a a much ea lie da e and
was appa en ly known in Ge many, a leas by hose
wo king wi h he a chi ec Hannes Meye , as we can
see in igu es 1 and 2.
Figu e 1: Unbuil p ojec o a School in Basel
(Swi ze land) by he a chi ec Hannes Meye , showing
dayligh ing g aphs in he igh -bo om co ne , o be
compa ed wi h he g aphs in igu e 2.
Figu e 2: The g aphs p oduced by Higbie, o
calcula e he ligh coming om il ed skyligh s,
de eloped only wo yea s be o e Meye ’s p ojec .
(1926)
As expec ed, his solu ion coincided wi h he so-
called su ace- o-poin con igu a ion ac o , which can
be compu ed now in a much mo e gene al way han
wi h he o me a emp s. Ri e o was no awa e o his
inding, he hough ha he was able o in eg a e a
po ion o he sky ligh , which in ac yields he same
alue bu wi h a di e en meaning.
Figu e 3: The p ojec ed solid angle p inciple
Higbie in u n, belie ed ha he had ound only he
exchange o di use ene gy om ec angula windows
o de ined poin s, and admi ed openly ha his
me hod could no be used wi h eal skies o
anspa en windows, while in ac his is a pe ec ly
possible hing o do. Bo h esea che s had come o
he same solu ion h ough di e se pa hs and
wi hou ealising o i !
PLEA 2003 - The 20 h Con e ence on Passi e and Low Ene gy A chi ec u e, San iago – CHILE, 9 - 12 No embe 2003
Figu e 4: Display o he con igu a ion ac o s as
in eg a ed by Higbie.
A e ha , Ri e o conside ed ha he could educe
leng hy compu a ional wo k on ei he o mulas o
p ojec ions, which, a he ime we e deemed e y
di icul o ca y ou o a chi ec s and designe s, by
ep esen ing he ligh emi e as a ec angula g id
o m (spaced e e y 5 deg ees in sphe ical
coo dina es) and hen adding he p ojec ions o he
so-di ided agmen s o he sky ha we e seen om
he calcula ion poin and h ough he window, in a
kind o app oach ha eminds us o ini e-elemen
me hod.
In ac , a ew “ligh ing p o ac o s” p oduced in he
ollowing yea s a he B i ish Resea ch S a ion,
wo ked in a simila manne . Once he speci ic
dimensions o a window a e known, hey a e
a e aged by dis ances o he s udy poin , o
de e mine hei angles. Then hose angula quan i ies
we e e e ed o clus e s o ac ions om he sky-
aul , p e iously plo ed in ables.
As he ables bo e a homological ela ionship wi h
he windows unde s udy -a consequence o he
a o emen ioned, hey allowed o g aphical as well as
nume ical use.
Figu e 5: Example o ou pu om Ri e o’s Tables
Wi h a single nomog am he had esol ed he main
p oblems o he ligh ing science o he ime, he ool
was able o calcula e he e ec o windows wi hou
need o o mulas, ee om cu ed o complex
p ojec ions, bu s ill app op ia e o d awing and isual
access. And wi h ano he impo an ea u e, he ables,
acco ding o Ri e o’s iew we e o ally independen
om clima ic da a, i.e. hey only displayed ac ions o
ex e nal illuminance ega dless o i s alue.
Mo eo e , in he same s uc u e, he wo ked o
include he e ec o he newly ound CIE o e cas sky.
In o de o do his, he inc eased -in p opo ion o he
zeni h, he alues o he clus e s p e iously ob ained
o he uni o m sky. This is a nume ical way o sol ing
an o he wise complex in eg al.
None heless, i he windows we e glazed he
p oblem o ansmi ance appea ed o be a se ious
one, and he e is whe e his wo ld-wide quo ed o mula
comes in.
He had o de ise an exp ession o he
ansmi ance ha could be ela ed o he angle
θ
in ol ed in he edious calcula ions al eady o ganized.
A single scala quan i y was no adequa e as hey
we e many igo ous s udies on he alue o
ansmi ance and he whole p ocedu e ha had been
ollowed, insis ed on he di e en ial quali y o sund y
egions o he sky. A e compa ing some o he
a ailable o mulas he came up wi h he ollowing
equa ion.
)cos*(cos*3
0θθθ
θsenTT +=
Which p oduces a g aphical esul as abo e.
Figu e 6: Ca esian plo o Ri e o’s ansmi ance
equa ion.
I is ema kable ha in such a simple bu e icien
way he could ake in o accoun all he impo an
a iables unde he same abula s uc u e.
PLEA 2003 - The 20 h Con e ence on Passi e and Low Ene gy A chi ec u e, San iago – CHILE, 9 - 12 No embe 2003
3. CONCLUSIONS
Rega ding o he aspec s o bo h Higbie’s and
Ri e o’s wo k, we could add ha hey g asped he
concep o ec o analysis in ligh ing, bu no in a
s aigh way. Higbie, o ins ance, s udied he
con igu a ion ac o o inclined su aces, whose
nume ical alue could ha e been ob ained in ano he
way, making use o he al eady in eg a ed alues o
e ical and ho izon al ac o s. In he case o Ri e o,
o make commen s on a g aphical example, he
desc ibes he e ec o a o a ed ec angula window
on a e ical plane.
Bo h esea che s discussed o some ex en he
p oblems o skyligh s, he ypical saw oo h sec ion in
Higbie’s case was e en ea ed in a a he de ailed
manne . Ri e o composed a signi ican pa o his
ables o “ho izon al windows”. Howe e , none o
hem a gued on he pa icula i ies o sunligh ing o
di ec ligh .
We could conclude by saying ha hei main lack
i we could speak so, is ha hey did no da e o
con on eali y, hey we e no con iden abou he eal
a ailabili y o me eo ological da a o in he e o o
p edic dayligh ing hey pu sued sa e assump ions,
pe haps now we will ne e be su e.
Only we would ha e liked o pay homage o
Ri e o and he people who i s discussed hese
p oblems in Ame ica. Thei app oach was p obably
he bes possible and we can only wonde wha
cou se would ha e aken en i onmen al design i all
he a o emen ioned cons ain s would ha e been
sol ed o en isaged by hem.
Like o he U uguayan-bo n a chi ec s as Eladio
Dies e o Gilbe o Ga o-Sob al, Ri e o is an
ou s anding ep esen a i e o Sou h-Ame ican genius
in he espec o A chi ec u al and En i onmen al
Science .
Figu e 7: The A lan ida Chu ch, nea Mon e ideo.
Eladio Dies e. (1960). Dies e was ex emely sensi i e
wi h he ma e ials employed in his s uc u al design,
ha can be desc ibed as ecologically-o ien ed.
Figu e 8: The Public School “Ma iscal Suc e” in Qui o
(Ecuado ) designed by he U uguayan G. Ga o
Sob al o ake in o accoun en ila ion, ligh ing and
seismic e ec s, almos he same p eocupa ions o
Hannes Meye ‘s school p ojec some 30 yea s be o e.
ACKNOWLEDGMENTS
The au ho s would like o app ecia e he kindness
and help o P o esso Lucia Masca o who p o ided us
many yea s ago, wi h a copy o Ri e o o iginal ex ,
p ese ed a Rio G ande do Sul Uni e si y in B azil,
whe e i ecei ed ample a en ion o some ime.
REFERENCES
[1] Ri e o, Robe o. Tablas pa a el calculo del
Fac o de Iluminacion Na u al pa a en anas con
id ios y sin id ios. Mon e ideo. Facul ad de
A qui ec u a. 1958.
[2] Higbie H, and Randall W. A me hod o
p edic ing he ligh emi ed om windows.
T ansac ions om he Elec ical Enginee ing
Socie y. Ann A bo . Michigan. 1926.
[3] Cabeza Lainez, Jose M. Edi icios in eligen es
e sus sis emas pasi os: la e ige acion pasi a
en A qui ec u a. Ph. D. Thesis. 1994. Uni e si y
o Se ille. Spain.
[4] Almodo a Melendo, Jose M. Desa ollo de
me odos de simulacion: Aplicacion al analisis
ambien al del pa imonio. Colegio de A qui ec os
Se illa. FIDAS. 2003.
PLEA 2003 - The 20 h Con e ence on Passi e and Low Ene gy A chi ec u e, San iago – CHILE, 9 - 12 No embe 2003