SolarGeometry

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)


For horizontal projections:

SH=PH TAN(Ω)

where,PH: width of enclosing side of

horizontal projection

SH: height of shadow below horizontal projection


Defines limits of shade conditions

For vertical projections:

TAN(Ω)=TAN(Y)


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


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


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


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

SolarGeometry

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