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Environmental Controls I/IGEnvironmental Controls I/IG
Lecture 13Solar Geometry
Shading Strategies
Sun PositionSun Position
Can be described by two angles:
Altitude
Azimuth
S: p. 1514, T.C.12
Solar AnglesSolar Angles
Describe the sun position relative to a vertical surface
Solar Altitude: Solar Altitude: ββ (beta) (beta)
Vertical angle to sun position
Solar Azimuth: Solar Azimuth: ΦΦ (phi) (phi)
Horizontal bearing angle from south
Surface Azimuth: Surface Azimuth: ΨΨ (psi) (psi)
Surface horizontal bearing angle from south
Surface Solar Azimuth: Surface Solar Azimuth: γγ (gamma)(gamma)
Angle between solar and surface azimuths
γ = Φ - Ψ
Sign ConventionsSign Conventions
Angles east of south are negative
Angles west of south are positive
+ -
S
-90º90º
0º
-45º45º
Calculating Surface Solar Calculating Surface Solar AzimuthAzimuth
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
-45º30º
Profile Angle: Profile Angle: ΩΩ (omega) (omega)
Defines limits of shade conditions
For horizontal projections:
TAN(Ω)=TAN(β) / COS(Y)
Profile Angle: Profile Angle: ΩΩ (omega) (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: Profile Angle: ΩΩ (omega) (omega)
Defines limits of shade conditions
For vertical projections:
TAN(Ω)=TAN(Y)
Profile Angle: Profile Angle: ΩΩ (omega) (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 ProjectionsSizing Horizontal ProjectionsEstablish fenestration pattern and determine size of openings
Sizing Horizontal ProjectionsSizing 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 ProjectionsSizing Horizontal ProjectionsEstablish 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 β=90-23.5-L=26.5ºTAN(Ωw)=TAN(β)/COS(Y)
Ωw=26.5º
6/21 β=90+23.5-L=73.5ºTAN(Ωs)=TAN(β)/COS(Y)
Ωs=73.5º
Sizing Horizontal ProjectionsSizing Horizontal ProjectionsEstablish 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 Sizing Horizontal ProjectionsProjections
Mar 21 @10 AM Solar Timeβ= 41.6º Φ= -41.9º
Y=Φ-ΨY=-41.9º-0º=-41.9º
S: p. 1514, T.C.12
Sizing Horizontal ProjectionsSizing Horizontal ProjectionsEstablish 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=-41.9ºTAN(Ω)=TAN(β)/COS(Y)
TAN(Ω)= 0.888/0.744= 1.19
Ω=50º
Sizing Horizontal ProjectionsSizing 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 EnvelopeSolar EnvelopeReduce horizontal projections by adding horizontal louvers in a vertical screen
Ω
LouverSpacing
Ph
Sh
Sizing Horizontal ProjectionsSizing Horizontal Projections
ΩS
H
S
Spacing (S)= H/TAN(ΩS)
If H=12’’, then S=12/TAN(ΩS)=3.55” say 3½”
Note: method does not include louver thickness
Use the summer solstice profile angle (ΩS) to determine spacing of vertical louvers
Sizing Horizontal ProjectionsSizing Horizontal Projections
ΩS
H
S
Spacing (S)= H/TAN(ΩS)
If H=12’’, then S=12/TAN(ΩS)=3.55” say 3½”
Note: method does not include louver thickness
Use the summer solstice profile angle (ΩS) to determine spacing of reverse inclined louvers
2S
Lateral PenetrationLateral Penetration
Mar 21 at 10 AM solar time
β
When Y≠0º, lateral penetration occurs at an angle = β
Lateral Penetration Lateral Penetration SolutionsSolutions
Extend projection bilaterally
β
Lateral Penetration Lateral Penetration SolutionsSolutions
Install vertical component bilaterally
ΩS
Ω
ΩW
Critical Angle AnalysisCritical Angle Analysis
Critical angles define solar aperture height (SAH)
SAH
Sizing Vertical ProjectionsSizing Vertical Projections
SW=|PVTAN(Y)|
or
PV=|SW/TAN(Y)|
Sizing Vertical ProjectionsSizing 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 Shading StrategiesStrategies
Shading Devices – OverviewShading Devices – Overview
South Façade: Horizontal overhang or Brise-soleil
San Cristobal Stables
The Capital (Chandigarh)
Shading Devices –OverviewShading 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 –OverviewShading Devices –Overview
North Façade: Vertical fins (used in hot climates only)
L: p. 559 fig. 17.10b
Phoenix Central Library
Shading Devices – TectonicsShading Devices – Tectonics
VerticalLouvers or Screens
John Deere Headquarters, Moline IL Jewett Art Center, Wellesley, MA
Shading Devices – TectonicsShading Devices – Tectonics
HorizontalSolid and louvered planes, projections or recesses
Paimio Sanatorium, Finland
Getty Center Los Angeles, CA
Shading Devices –Shading Devices –TectonicsTectonics
Sculptural FormThickness Projections Screens
Beach House, Lido Shores, FL
Unity Temple, Oak Park, IL
Obayashi Tokyo Design Center
Reynolds Aluminum Building, Detroit, MI