Recommendations for calculation of solar radiation on buildings

IS 11907: Introduction & Need for Design Data Summary

Context & Need:

• Solar radiation estimates using standard atmosphere assumptions (300 dust particles/cm³, 2.5 mm ozone, 15 mm water vapor) overestimate by ~20% for India (Clause 2.1).
• Design solar radiation data is essential for building orientation, glass selection, and HVAC sizing (Clause 0.2).
• Measured data is scarce; hence, theoretical computations are used.
• Design values represent 95% exceedance values under clear sky, close to max solar radiation (Clause 0.2).

Key Tables & Specifications

• Note: Interpolate for other solar altitudes (Clause 2.2.1.1).

Design Solar Radiation Calculation Principles

• Use Tables 3 & 4 for design values on horizontal and vertical surfaces (8 cardinal directions) for latitudes ≥ 9°N at 4° intervals (Clause 3.1).
• Summer values correspond

IS 11907: Scope - Key Formulas, Tables & Specifications

Scope:
IS 11907 provides guidelines for calculating design solar radiation on building surfaces, important for thermal and structural design.

Key Tables:

Interpolate values for other altitudes.

Reflectivity of Common Ground Surfaces (rg):

Example: Total Solar Radiation on Building Surfaces

Formula for Total Solar Radiation on a Surface:

[ Q = I \times A ]

• (Q) = Total solar radiation (W)
• (I) = Design solar radiation on surface (W/m²)
• (A) = Area of the surface (m²)

This helps in designing building envelopes considering solar

General Principle of Design — IS 11907 Key Points

1. Design Solar Radiation Concept:

• Design values represent near-maximum solar radiation under clear sky, covering 95% of time.
• Used for building orientation, glass area/type, and HVAC load calculations.
• Based on theoretical computations due to limited measured data.

2. Solar Radiation Components (Clause 2.2.1.1):

Values for other altitudes can be interpolated.

3. Ground Reflectivity (Clause 2.2.3.1):

4. Practical Application:

• Use design solar radiation values for sizing cooling loads.
• Calculate solar radiation on building facades using altitude-based direct and diffused components.
• Consider ground reflectivity to estimate reflected radiation.

Formula for Total Solar Radiation on a Surface

[ I = I_b \times \cos \theta + I_d + I_r ]

Where:

• (I_b) = Direct beam radiation (W/m²)
• (\theta) = Angle of incidence on the surface
• (I_d) = Diffused radiation on the surface (W/m²)
• (I_r = r_g \times (I_b \times \sin \alpha + I_d)) = Reflected radiation from ground
• (r_g) = Ground reflectivity
• (\alpha) = Solar altitude angle

flowchart LR
    A[Sun's Position] --> B[Calculate Solar Alt

IS 11907: Components of Solar Radiation — Key Formulas & Specifications

Components of Solar Radiation (Clause 2.2)

Total solar radiation on a surface under clear sky =
I = ID + Ia + IGR

• ID: Direct radiation (augmented direct radiation at normal incidence, Table 1)
• Ia: Uniform diffuse sky radiation
• IGR: Ground reflected radiation (for non-horizontal surfaces)

Design Values (Clause 3.1)

• Use Tables 3 & 4 for design solar radiation on surfaces (horizontal & vertical) at latitudes ≥ 9°N.
• Values consider summer (max solar altitude) & winter (min solar altitude) conditions.
• Ground reflected radiation for vertical surfaces is excluded in tables; calculate separately using ground reflectivity.

Calculation Notes

• Design values correspond to 95% clearness (near max solar radiation).
• For sloping surfaces, adjust based on surface tilt and orientation.
• Refer to Appendices A & B for worked examples.

Formula for Ground Reflected Radiation (approximate)

[ IGR = \rho_g \times I_h \times \frac{1 - \cos \beta}{2} ]

• (\rho_g): Ground reflectivity (albedo)
• (I_h): Solar radiation on horizontal surface
• (\beta): Surface tilt angle from horizontal

Summary Table (Conceptual)

flowchart LR
    A[Total Solar Radiation (I)] --> B[Direct Radiation (ID)]
    A --> C[Diffuse Sky Radiation (Ia)]
    A --> D[Ground Reflected Radiation (IGR)]

Use IS 11907 Tables and Appendices for precise values and design calculations.

IS 11907: Direct Solar Radiation Key Formulas & Specs

1. Direct Radiation (ID) Calculation

• General formula: [ I_D = I_N \times \cos i ] where:

  • (I_N) = Direct radiation at normal incidence (W/m²)
  • (i) = Angle of incidence of sun’s rays on the surface

• For horizontal surfaces: [ \cos i = \sin \delta \quad \Rightarrow \quad I_{DH} = I_N \times \sin \delta ] (\delta) = Solar altitude angle

• For vertical surfaces: [ \cos i = \cos \delta \times \cos \beta ] [ I_{DV} = I_N \times \cos \delta \times \cos \beta ] (\beta) = Angle between sun direction and wall in horizontal plane

2. Design Values (Table 1)

• Use Table 1 for augmented direct radiation (I_N) under clear sky for different latitudes.
• Tables 3 & 4 provide combined direct + diffuse radiation for horizontal & vertical surfaces at 8 cardinal orientations.
• Design values are based on:
  • Summer solstice (June 22) for latitudes up to 29°N
  • Winter solstice (Dec 22) for winter values

3. Components of Total Solar Radiation (Clause 2.2)

• (I = I_D + I_a + I_{GR})
  • (I_D) = Direct radiation
  • (I_a) = Uniform diffuse sky radiation
  • (I_{GR}) = Ground reflected radiation (not included in Tables, calculate separately based on ground reflectivity)

Summary Table of Formulas

IS 11907: Diffuse Radiation from the Sky

Key Formulas & Specifications

• Diffuse radiation on horizontal surface:
  ( I_{dH} ) (from Table 1, depends on solar altitude angle)

• Diffuse radiation on vertical surface:
  [ I_{dV} = \frac{1}{2} I_{dH} ]

• Total solar radiation components (clear sky):
  [ I_{total} = I_D + I_a + I_{GR} ] where

  • ( I_D ) = Direct radiation
  • ( I_a ) = Uniform diffuse sky radiation
  • ( I_{GR} ) = Ground reflected radiation

Table 1: Solar Radiation Values (Excerpt)

For intermediate altitudes, interpolate values linearly.

Table 2: Ground Reflectivity (Typical Values)

Summary Diagram

flowchart LR
    A[Direct Radiation (ID)] --> C[Total Solar Radiation]
    B[Diffuse Radiation (Ia)] --> C
    D[Ground Reflected Radiation (IGR)] --> C

Note: Use Table 1 values for (I_{dH}), halve for vertical surfaces. Include ground reflectivity from Table 2 for (I_{GR}). For total design radiation, refer Appendix A of IS 11907.

Ground Reflected Radiation (IS 11907)

Key Formula:

[ I_{GRV} = r_g \times I_{TH} ]

• (I_{GRV}) = Ground reflected radiation on a vertical surface (W/m²)
• (r_g) = Reflectivity of the ground (dimensionless)
• (I_{TH}) = Total solar radiation on a horizontal surface (W/m²), where: [ I_{TH} = I_{DH} + I_{dH} ] (I_{DH}) = Direct horizontal solar radiation
  (I_{dH}) = Diffuse horizontal solar radiation

Typical Ground Reflectivity Values (Clause 2.2.3.1):

Example:

If (I_{TH} = 606 , W/m^2) and ground reflectivity (r_g = 0.20), [ I_{GRV} = 0.20 \times 606 = 121.2 , W/m^2 ]

This component is added to direct and diffuse radiation to estimate total solar radiation on vertical surfaces for design purposes.

flowchart LR
    A[Total Solar Radiation on Horizontal Surface \(I_{TH}\)] --> B[Multiply by Ground Reflectivity \(r_g\)]
    B --> C[Ground Reflected Radiation on Vertical Surface \(I_{GRV}\)]

IS 11907: Design Solar Radiation on Buildings

Key Points from Clause 3.1:

• Design solar radiation values (Direct + Diffuse) for horizontal and vertical surfaces (8 cardinal directions) are tabulated in Tables 3 and 4.
• Applicable for latitudes ≥ 9°N, at 4° intervals.
• Values cover both summer (around June 22, summer solstice) and winter (December 22, winter solstice).
• Ground reflected radiation on vertical surfaces is not included but can be calculated based on ground reflectivity.

Calculation Overview:

• Use Table 3 for summer solar radiation values.
• Use Table 4 for winter solar radiation values.
• For sloping surfaces, interpolate between horizontal and vertical values or use Appendix B example.

Typical Formula for Design Solar Radiation (S):

[ S = S_d + S_{diff} + S_{ref} ]

Where:

• ( S_d ) = Direct solar radiation on the surface (from tables)
• ( S_{diff} ) = Diffuse solar radiation (from tables)
• ( S_{ref} ) = Reflected solar radiation (calculated as ( \rho \times S_h ), where ( \rho ) = ground reflectivity, ( S_h ) = horizontal solar radiation)

Simplified Steps:

1. Identify latitude and surface orientation.
2. Select design radiation values from Tables 3 & 4.
3. For sloping surfaces, interpolate between horizontal and vertical values.
4. Add reflected component if required.

Example Table Snippet (Indicative):

(Values are illustrative; refer IS 11907 Tables 3 & 4 for actual data)

flowchart LR
    A[Identify Latitude & Orientation] --> B[Select Solar Radiation from Tables]
    B --> C{Surface Type}
    C -->|Horizontal| D[Use Horizontal

Key Formulas for Design Solar Radiation on Sloping Surfaces (IS 11907)

1. Direct Solar Radiation on Sloping Surface:

[ I_{DS} = I_N (\cos e \cos \phi \cos \theta + \sin \theta \sin \delta) ]

• (I_N): Solar radiation at normal incidence (from Table 1)
• (\theta): Angle of inclination with the vertical (0° for vertical, 90° for horizontal)
• (e, \phi, \delta): Solar angles as per solar geometry

2. Diffuse Radiation on Sloping Surface:

[ I_{DS} = I_{dH} \times \frac{1 + \sin \theta}{2} ]

• (I_{dH}): Diffuse radiation on horizontal surface

3. Ground Reflected Radiation on Sloping Surface:

[ I_{GRS} = I_g \times I_{TH} \times \frac{1 - \sin \theta}{2} ]

• (I_g): Ground reflectivity
• (I_{TH}): Total horizontal solar radiation

Table Extract: Design Solar Radiation (W/m²) for Latitude 29ºN (New Delhi)

Notes:

• Use Tables 3 and 4 for design values of solar radiation for various latitudes and orientations.
• Appendix C of IS 11907 provides detailed calculation examples.
• Ground reflected radiation for vertical surfaces is usually excluded unless site-specific reflectivity is known.

flowchart LR
    A[Solar Radiation on Sloping Surface] --> B[Direct Radiation]
    A

IS 11907: Determination of Total Design Solar Radiation

Key Points:

• Design solar radiation values are given in Tables 3 and 4 for latitudes from 9ºN upwards at 4º intervals.
• Values include Direct + Diffuse radiation for horizontal and vertical surfaces in 8 cardinal directions.
• Summer values correspond to June 22 (summer solstice); winter values correspond to December 22 (winter solstice).
• Ground reflected radiation on vertical surfaces is not included but can be added based on ground reflectivity.
• Design values represent near-maximum clear sky conditions for 95% of the time.

Example Calculation (Latitude 29ºN - New Delhi):

Formula for Total Solar Radiation on Building:

[ Q = \sum (I_i \times A_i) ] Where:

• (Q) = Total solar radiation on building (W)
• (I_i) = Design solar radiation on surface (i) (W/m²)
• (A_i) = Area of surface (i) (m²)

Summary:

• Use Tables 3 & 4 for design radiation values based on latitude and orientation.
• Multiply radiation by surface area to get incident radiation per surface.
• Sum all surfaces for total building solar load.

flowchart TD
    A[Select Latitude & Orientation] --> B[Obtain Design Solar Radiation (W/m²) from Tables]
    B --> C[Measure Surface Areas (m²)]
    C --> D[Calculate Radiation per Surface: I × A]
    D --> E[Sum Radiation for all Surfaces]
    E

IS 11907: Design Solar Radiation on Buildings

Key Points from IS 11907:

• Design Solar Radiation Values (Direct + Diffuse) are given in Tables 3 and 4 for horizontal and vertical surfaces at latitudes from 9ºN upwards at 4° intervals.
• Values correspond to summer (June 22) and winter (December 22) solstices.
• Ground reflected radiation for vertical surfaces is not included but can be added based on site reflectivity.
• Appendix B & C provide illustrative examples for flat and sloping surfaces.

Example Calculation (Latitude 29ºN - New Delhi):

Formula for Total Radiation on Surface:

[ Q = I \times A ]

Where:

• (Q) = Total solar radiation on surface (W)
• (I) = Design solar radiation (W/m²) from Table 3 or 4
• (A) = Area of the surface (m²)

Notes:

• Use values from Table 3 for horizontal and vertical surfaces based on latitude and orientation.
• For sloping surfaces, refer to Appendix C for detailed calculations.
• Adjust for ground reflectivity if needed.

flowchart TD
    A[Select Latitude & Orientation] --> B[Get Design Solar Radiation (W/m²) from Table 3/4]
    B --> C[Measure Surface Area (m²)]
    C --> D[Calculate Total Radiation: Q = I × A]
    D --> E[Sum for all surfaces to get building total]

This approach ensures accurate estimation of solar loads

IS 11907: Calculation of Solar Radiation on Sloping Surfaces

Key Formulas (Clause 4.1)

1. Direct Solar Radiation on Sloping Surface:

[ I_{DS} = I_N \left( \cos e \cos \phi \cos \theta + \sin \theta \sin \delta \right) ]

• (I_N) = Solar radiation at normal incidence (from Table 1)
• (\theta) = Inclination angle of surface from vertical (0° vertical, 90° horizontal)
• (e, \phi, \delta) = Solar angles as per solar geometry

2. Diffuse Radiation on Sloping Surface:

[ I_{DS} = I_{dH} \times \frac{(1 + \sin \phi)}{2} ]

• (I_{dH}) = Diffuse radiation on horizontal surface
• (\phi) = Surface slope angle from horizontal

3. Ground Reflected Radiation on Sloping Surface:

[ I_{GRS} = I_g \times I_{TH} \times \frac{(1 - \sin \phi)}{2} ]

• (I_g) = Ground reflectivity (albedo)
• (I_{TH}) = Total horizontal radiation

Tables Reference

• Table 1: Solar radiation at normal incidence for various latitudes and dates.
• Table 3: Design total solar radiation (direct + diffuse) on horizontal and vertical surfaces (W/m²).
• Table 4: Solar radiation values for different orientations and latitudes.

Notes

• Use Appendix C for a detailed example of sloping surface radiation calculation.
• Design values consider summer solstice (June 22) and winter solstice (December 22).
• Ground reflected component is excluded for vertical surfaces unless adjusted by ground reflectivity.

flowchart TD
    A[Start] --> B[Obtain Solar Radiation at Normal Incidence (I_N)]
    B --> C[Calculate Direct Radiation on Sloping Surface (I_DS)]
    C --> D[Calculate Diffuse Radiation on Sloping Surface (I_DS)]
    D --> E[Calculate Ground Reflected Radiation (I_GRS)]
    E --> F[Sum Total Radiation: I_Total = I_DS + I_DS