Environmental Controls I/IG
Lecture 13
Solar Geometry
Shading Strategies
Sun Position
Can be described by
two angles:
Altitude
Azimuth
S: p. 1514, T.C.12
Solar Angles
Describe the
sun position
relative to a
vertical
surface
Solar Altitude: β (beta)
Vertical angle to
sun position
Solar Azimuth: Φ (phi)
Horizontal
bearing angle
from south
Surface Azimuth: Ψ (psi)
Surface horizontal
bearing angle
from south
Surface Solar Azimuth: γ (gamma)
Angle between
solar and
surface
azimuths
γ=Φ-Ψ
Sign Conventions
Angles east of
south are negative
Angles west of
south are positive
90º
-90º
45º
+
-45º
S0º
Calculating Surface Solar Azimuth
γ=Φ–Ψ
For example:
Building façade is oriented
south east (Ψ =-45º)
Solar azimuth (ϕ) is 30º
west of south
γ = 30º – (-45º) = 75º
Note: |γ|≥ 90º, façade in
shade
30º
-45º
Profile Angle: Ω (omega)
Defines limits of shade conditions
For horizontal
projections:
TAN(Ω)=TAN(β) / COS(Y)
Profile Angle: Ω (omega)
For horizontal projections:
SH=PH TAN(Ω)
where,
PH: width of enclosing side of
horizontal projection
SH: height of shadow below
horizontal projection
Profile Angle: Ω (omega)
Defines limits of shade conditions
For vertical projections:
TAN(Ω)=TAN(Y)
Profile Angle: Ω (omega)
For vertical projections:
Sw=Pv TAN(Y)
where,
Pv: width of enclosing side of
vertical projection
Sw: width of shadow beyond
vertical projection
Sizing Horizontal Projections
Establish fenestration
pattern and determine
size of openings
Sizing Horizontal Projections
Determine cut off date and time for
solar penetration
Mar 21 @10 AM solar time
Determine surface azimuth
Due south, Ψ=0º
Determine required shadow height
SH=6’
?
Sizing Horizontal Projections
Establish profile (Ω) angles for the solstices at solar
noon using surface solar azimuth (Y = Φ –Ψ).
At solar noon (Φ=0º) and for L=40º, Ψ=0º:
12/21
6/21
β=90-23.5-L=26.5º
TAN(Ωw)=TAN(β)/COS(Y)
Ωw=26.5º
β=90+23.5-L=73.5º
TAN(Ωs)=TAN(β)/COS(Y)
Ωs=73.5º
Sizing Horizontal Projections
Establish profile (Ω) angles for cut off
date and time using surface solar azimuth
(Y = Φ –Ψ).
At 10 AM solar time and for L=40º, Ψ=0º:
Sizing Horizontal
Projections
Mar 21 @10 AM Solar
Time
β= 41.6º
Φ= -41.9º
Y=Φ-Ψ
Y=-41.9º-0º=-41.9º
S: p. 1514, T.C.12
Sizing Horizontal Projections
Establish profile (Ω) angles for cut off date and
time using surface solar azimuth (Y = Φ –Ψ).
At 10 AM solar time and for L=40º, Ψ=0º:
3/21
β=41.6º Y=-41.9º
TAN(Ω)=TAN(β)/COS(Y)
TAN(Ω)= 0.888/0.744= 1.19
Ω=50º
Sizing Horizontal Projections
Given SH = 6’ and
SH=PH Tan(Ω)
Solve for PH
PH=SH/TAN(Ω)
PH=6/1.19=5.04’ ~ 5’-0 ½”
say 5’-0”
Solar Envelope
Reduce horizontal projections by
adding horizontal louvers in a
vertical screen
Louver
Spacing
Ω
Ph
Sh
Sizing Horizontal Projections
Use the summer solstice profile angle
(ΩS) to determine spacing of vertical
louvers
S
H
ΩS
Spacing (S)= H/TAN(ΩS)
If H=12’’, then S=12/TAN(ΩS)=3.55” say 3½”
Note: method does not include louver thickness
Sizing Horizontal Projections
Use the summer solstice profile angle
(ΩS) to determine spacing of reverse
inclined louvers
H
ΩS
S
2S
Spacing (S)= H/TAN(ΩS)
If H=12’’, then S=12/TAN(ΩS)=3.55” say 3½”
Note: method does not include louver thickness
Lateral Penetration
Mar 21 at 10 AM solar time
β
When Y≠0º, lateral penetration occurs at an angle = β
Lateral Penetration Solutions
Extend projection bilaterally
β
Lateral Penetration Solutions
Install vertical component bilaterally
Critical Angle Analysis
Critical angles define solar aperture
height (SAH)
ΩW
SAH
Ω
ΩS
Sizing Vertical Projections
SW=|PVTAN(Y)|
or
PV=|SW/TAN(Y)|
Sizing Vertical Projections
On Mar 21 @ 10 AM
(Y=-41.9º), if SW=6’
what should PV be to shade
window
PV=|SW/TAN(Y)|
PV=|6/-1.115|=5.4’ ~5’-5”
Shading
Strategies
Shading Devices – Overview
South Façade:
Horizontal overhang
or
Brise-soleil
San Cristobal Stables
The Capital (Chandigarh)
Shading Devices –Overview
East/West Façade:
Vertical fins angled to
the north
and/or
Brise-soleil
Keio University Graduate School Research Center
Monastery of Ste Marie de La Tourette
Shading Devices –Overview
North Façade:
Vertical fins (used in
hot climates only)
Phoenix Central Library
L: p. 559 fig. 17.10b
Shading Devices – Tectonics

Vertical
Louvers or Screens
John Deere Headquarters, Moline IL
Jewett Art Center, Wellesley, MA
Shading Devices – Tectonics

Horizontal
Solid and louvered
planes, projections
or recesses
Paimio Sanatorium, Finland
Getty Center Los Angeles, CA
Shading Devices –Tectonics

Sculptural Form
Thickness
Projections
Screens
Reynolds Aluminum
Building, Detroit, MI
Unity Temple, Oak Park, IL
Beach House, Lido Shores, FL
Obayashi Tokyo Design Center