Environmental Controls I/IG Lecture 9 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 + - S 45º -45º 0º

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 -45º 30º

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 β=90-23.5-L=26.5º TAN(Ωw)=TAN(β)/COS(Y) Ωw=26.5º 6/21 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 Ω Louver Spacing Ph Sh Reduce horizontal projections by adding horizontal louvers in a vertical screen

Sizing Horizontal Projections Use the summer solstice profile angle (ΩS) to determine spacing of vertical louvers 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

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

Solar Aperture Sizing Insolation desired: 2600 Btuh Determine initial size Insolation desired: 2600 Btuh Available insolation* : 269Btuh/sf Initial area(AI)= 2600 Btuh/269 Btuh/sf= 9.7 sf *(S: p. 1649, T B.12; South Facing at solar noon on 12/21) Percent sunshine(SS%) 45% or 0.45 (L: p. 89) Solar Heat Gain Coefficient (SHGC) Single glazed clear=0.79 (S: p. 171 T 4.13)

Solar Aperture Sizing Interior filters (IF) Drapes full open= 1.00 (S: p. 179, T 4.21) Exterior filters (EF) Cottonwood Trees= 0.68 (S: p. 111, T 3.5) Determine final Aperture Area(AAF) AAF=AAI/(SS% x SHGC x IF x EF) AAF=9.7/(0.45x0.79x1.00x0.68)=40.1 say 40 sf

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