Solar Geometry, Solar Radiation and Solar Control
An introductory lecture

Andrew Bairstow

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Grouping broadly, the major influences on the comfort within a building are defined by:

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Solar radiation is a dominant influence on all climatic factors. We can consider these as

An understanding of the nature of this primary relationship can help us to design better buildings: ones which respond positively rather than negatively to the environment.

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Solar Geometry describes the relationship between the sun and earth
or more importantly
The relationship of solar radiation, the product of the sun with any location on the earth
Solar Radiation is heading this way

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The earth orbits the sun in an approximate circle (radius 150 000 000 km) with the sun at its centre.
The plane of the earths revolution is called the ecliptic and includes the sun.
ecliptic

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The earth rotates about an axis tilted 23.45o from the normal to the ecliptic (ie a line at right angles to the plane) Tilt of Axis

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The earth does NOT rotate in its orbit but is translated (ie slides) rotationtranslation

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If the earth rotated about the sun then the angle between a line joining the earth and sun would never change. However the sliding motion of the earth results in this angle varying from 66.55o (90-23.45) to 113.45o (90+23.45). topupdownBottom





































December Solstice

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June Solstice

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This change is represented by the term DECLINATION. The declination angle is the angle between the ecliptic and the equatorial plane. positive declinationnegative declination

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The declination changes throughout the year Yearly variation in Declination

December March June September topupdownBottom





































The latitude of a location is defined as the angle between a line joining the location to the earth's centre and the equatorial plane. definition of latitude

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The equator is a convenient reference from which to measure latitude: the earths axis is the normal to this plane. Locations above this plane (ie northern hemisphere) are generally considered to be positive whilst those below (southern hemisphere) are negative. sign of latitude

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A location needs to be specified horizontally. A reference for this is less obvious but is taken as a semicircular plane, perpendicular to the equatorial plane and passing through Greenwich. Longitude is defined as the angle between this reference and a similar semicircle passing through the location. No consistent convention of positive and negative longitude exists. definition of longitude

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All locations at the same latitude experience the same geometrical relationship with the sun. Any differences are acountable by local climate and differences in atmospheric composition.

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At a local level we can think of the earth as being flat. tangent to earth surface

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It is usual to describe the relationship between solar radiation at any location in solar time. This is a time scale in which 12 noon is the time at which the radiation arrives perpendicular to the earths surface (ie from the South or North depending on latitude and time of year). Solar noon occurs at the same time for any location with the same longitude.
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Solar noon will occur 1 hour earlier for every 15 degrees east and 1 hour later for every 15 degrees west. Solar Time shift due to longitude

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Time Zones are based on the MEAN Solar Time at a specific longitude. For example UK time is based on the MEAN Solar Time at 0o.The Equation of Time takes account of seasonal differences. The Equation of Time

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For Example: Solar Time for

Swansea(4oW) = Local Time - 4x4 + EOT minutes

Great Yarmouth(2oE) = Local Time + 2x4 + EOT minutes

note this is correct only for Winter/Spring when local time is Greenwich Mean Time. Subtract a further hour in Summer/Autumn. topupdownBottom





































An office building in Swansea is in use from 8am until 6pm. When is the earliest and latest in Solar Time at which it will be used?

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Earliest Solar Time will occur in the summer.

Daylight Savings

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Earliest occupation will occur at:

08.00 - 0.16 - 0.07 - 1.00
i.e 06.37 Solar Time at end of July
Daylight Savings

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Latest occupation will occur at:

18.00 - 0.16 + 0.17
i.e 18.01Solar Time at beginning of November
Daylight Savings

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We can easily derive the angle at which solar radiation reaches the earths surface at solar noon.

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When declination is zero (March/September Equinox), this is simple: Max Altitude for zero declination

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More generally: Max Altitude for any declination

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Thus for Oxford (51.7oN), solar radiation will arrive at a vertical angle of approximately 15o in the middle of winter up to approximately 62o in the middle of summer. Max Altitude range for Oxford

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The sun appears hotter in the 'summer than in the 'winter'. There are two reasons for this:1. Solar radiation has to pass through more atmosphere in the winter than the summer. Air Mass in WinterAir Mass in Summer

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2. The solar radiation is spread over a larger area in winter than in summer. Area Concentration in WinterArea Concentration in Summer

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However, radiation on a vertical surface may be more concentrated in the winter and captured within a building by being transmitted through the windows Radiation on Vertical Surface

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The vertical angle at which radiation approaches is referred to as the altitude. This varies throughout the day as does the direction from which it arrives (azimuth). Definition of Altitude and Azimuth

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These may be plotted on a set of Cartesian Axes for different days of the year. altitude and azimuth on cartesian axes

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However, it is more useful to plot these on special axes with lines of constant altitude as concentric circles and lines of constant azimuth as radial lines SunPath Axes

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This is the Stereopathic SunPath Diagram. This example is for 52oNorth Stereopathic SunPath Diagram

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The Stereopathic SunPath Diagram can be used to assess the performance of shading devices and to assess the extent of overshadowing caused by other buildings. The shadow Angle Protractor is a useful additional tool. shadow angle protractor

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Here a building with South-East facing window has an overhanging roof to shade it from high sun angles and adjacent wall to shade from the east Simple Building with shading device

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To assess a vertical shading device then the vertical shadow angle is determined. Vertical Shadow Angle

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This may be marked on the Shadow Angle Protractor Vertical Shadow Mask

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Similarly, a side fin provides shading in azimuth. The corresponding Horizontal Shadow Angle may be determined using the protractor Horizontal Shadow Angle

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This may be marked on the Shadow Angle Protractor Horizontal Shadow Mask

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The Orientation should be noted when transferring the protractors to the SunPath diagram Orientation

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The Vertical Shadow Mask may be transferred to the SunPath diagram. SunPath plus VSA

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The Horizontal Shadow Mask may be transferred to the SunPath diagram. SunPath plus HSA

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And the combination SunPath plus VSA and HSA

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Many Building Simulation Tools negate the need for the use of SunPath diagrams for the assessment of shading devices.
They are however still useful design tools.
Computer Programs do exist to take the tedium out their use for example SolRpath Some simple solar geometry software is available online, for example SunAngle
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Solar Radiation The solar radiation which arrives just outside the earths atmosphere is called "extraterrestrial radiation". Not all of this radiation will reach the earths surface. During its travel through the atmosphere:

Atmosphere

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Seasonal Variation in Irradiance Kew Irradiance

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Power and Energy The rate at which solar energy is received is called Irradiance (W/m2)
The total energy received over a given time is called Irradiation or Insolation (kWh/m2)
Irradiance and Irradiation

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Bibliography
Szokolay SEnvironmental Science Handbook1980Construction Press
Olgyay A & Olgyay VSolar Control and Shading devices1957Princeton University Press
Szokolay S Solar Geometry PLEA Notes 1996
Muneer T Solar Radiation and Daylight Models for the energy efficient design of buildings 1997 Butterworth-Heinemann
Harkness EL & Mehta ML Solar Radiation Control in Buildings 1978 Applied Science
Duffie JA & Beckman WA Solar Engineering of Thermal Processes 1991 Wiley
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page location
comfort influences
Solar Radiation as Primary and Secondary influence on
Solar Geometry: a definition
Ecliptic
Angle of axis of rotation
Earth does not rotate about the sun
Why is 'sliding' relevent?
December Solstice in 3D
June Solstice in 3D
Declination: a definition
Declination: yearly variation
Latitude: a definition
Latitude: sign convention
Longitude
Latitude and Geometrical Relationship
Flat Earth
Solar Time
15 deg = 1 hour
EOT
UK time differences
Solar Time: Calculation Example
GMT and BST
Answer: Earliest Time
Answer: Latest Time
Altitude at solar noon
Altitude: max at declination zero
Altitude: max for any declination
Declination Range in Oxford
Seasonal solar intensity: air mass
Seasonal solar intensity: intensity
Solar intensity on wall in winter
Altitude and Azimuth
Altitude and Azimuth: cartesian coordinates
Stereopathic sun path diagram: axes
Stereopathic sun path diagram: 52degN
Shadow Angle Protractor
Simple Building with shading device
VSA
VSA on Shadow Angle Protractor
HSA
HSA on Shadow Angle Protractor
Protractors and Sun Path: Orientation
Vertical Shadow Mask: Transferring
Horizontal Shadow Mask: Transferring
Both Masks
SolRPath
Radiation Components
Seasonal Variation
Energy and Power
Bibliography
Other Tutorials