BR 187¶
Chitty, R. (2014) External fire spread: building separation and boundary distances (BR 187, 2nd edn). Watford: BRE Trust
BR 187 provides guidance on external fire spread calculations for building design.
This module provides calculations for external fire spread to buildings as specified in BR 187, the UK guidance document for external fire spread.
- Available modules:
chapter_1: Chapter 1 calculations appendix_a: Appendix A thermal radiation calculations
Example
>>> import ofire
>>> ofire.br_187.chapter_1
>>> ofire.br_187.appendix_a
Chapter 1 - External Fire Spread Fundamentals¶
This chapter provides fundamental calculations for external fire spread assessment including ventilation factors and building geometry considerations.
Equation 1 - Ventilation Factor¶
This module provides functions for calculating ventilation factors used in external fire spread assessments.
- ofire.br_187.chapter_1.equation_1.calculate_ventilation_factor(a_s, a, h)¶
Calculate ventilation factor for external fire spread assessment (Equation 1).
This function calculates the ventilation factor used in BR 187 methodologies for assessing external fire spread between buildings.
\[O = \frac{A_s}{A \cdot \sqrt{H}}\]where:
\(O\) is the ventilation factor (m⁻¹/²)
\(A_s\) is the area of external wall surface (m²)
\(A\) is the area of openings in the external wall (m²)
\(H\) is the height of openings (m)
- Parameters:
- Returns:
Ventilation factor (m⁻¹/²)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> factor = ofire.br_187.chapter_1.equation_1.calculate_ventilation_factor(100.0, 20.0, 2.5)
Appendix A - Thermal Radiation Calculations¶
This appendix provides comprehensive calculations for thermal radiation from fire sources, including radiation intensity calculations and view factor determinations for various geometric configurations.
These calculations are essential for assessing thermal radiation exposure in external fire spread scenarios between buildings.
Equation A1 - Radiation Intensity from Fire Sources¶
Calculates thermal radiation intensity from fire sources using the Stefan-Boltzmann law.
- ofire.br_187.appendix_a.equation_a1.radiation_intensity(sigma, emissivity, temperature)¶
Calculate radiation intensity from a fire source (Equation A1).
The radiation intensity is calculated using the Stefan-Boltzmann law:
\[I_s = \sigma \cdot \varepsilon \cdot T^4\]where:
\(I_s\) is the radiation intensity (kW/m²)
\(\sigma\) is the Stefan-Boltzmann constant (5.67 × 10⁻¹¹ kW/m²K⁴)
\(\varepsilon\) is the surface emissivity (dimensionless, 0-1)
\(T\) is the absolute temperature (K)
- Parameters:
- Returns:
Radiation intensity (kW/m²)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Equation A2 - Radiation Intensity at Receiver¶
Calculates the thermal radiation intensity received at a target location considering geometric view factors and source intensity.
- ofire.br_187.appendix_a.equation_a2.radiation_intensity_at_receiver(phi, i_s)¶
Calculate radiation intensity at receiver location (Equation A2).
Calculates the thermal radiation intensity received at a target location considering geometric view factors.
\[I_R = \phi \cdot I_s\]where:
\(I_R\) is the radiation intensity at receiver (W/m²)
\(\phi\) is the view factor (dimensionless)
\(I_s\) is the source radiation intensity (W/m²)
- Parameters:
- Returns:
Radiation intensity at receiver (W/m²)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Example
>>> import ofire >>> received = ofire.br_187.appendix_a.equation_a2.radiation_intensity_at_receiver(0.15, 50000.0)
Equation A3 - Parallel Source and Receiver Centre Aligned¶
Provides view factor calculations for parallel source and receiver surfaces that are centre aligned.
- ofire.br_187.appendix_a.equation_a3.x(w, s)¶
Calculate dimensionless width parameter.
\[X = \frac{W}{2 \cdot S}\]where:
\(X\) is the dimensionless width parameter
\(W\) is the width of radiation source (m)
\(S\) is the distance from source to receiver (m)
- Parameters:
- Returns:
Dimensionless width parameter
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
- ofire.br_187.appendix_a.equation_a3.y(h, s)¶
Calculate dimensionless height parameter.
\[Y = \frac{H}{2 \cdot S}\]where:
\(Y\) is the dimensionless height parameter
\(H\) is the height of radiation source (m)
\(S\) is the distance from source to receiver (m)
- Parameters:
- Returns:
Dimensionless height parameter
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
- ofire.br_187.appendix_a.equation_a3.phi(x, y, additive)¶
Calculate view factor using dimensionless parameters.
Calculates the view factor for parallel source and receiver surfaces that are centre aligned using dimensionless parameters X and Y calculated by
ofire.br_187.appendix_a.equation_a3.x()andofire.br_187.appendix_a.equation_a3.y().\[\phi = \frac{2}{\pi}\left(\frac{X}{\sqrt{1+X^2}}\tan^{-1}\left(\frac{Y}{\sqrt{1+X^2}}\right)+\frac{Y}{\sqrt{1+Y^2}}\tan^{-1}\left(\frac{X}{\sqrt{1+Y^2}}\right)\right)\]where:
\(\phi\) is the view factor (dimensionless)
\(X\) is the dimensionless width parameter (see
x())\(Y\) is the dimensionless height parameter (see
y())
- Parameters:
- Returns:
View factor (dimensionless)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Equation A4 - Parallel Source and Receiver Corner Aligned¶
Provides view factor calculations for parallel source and receiver surfaces that are corner aligned.
- ofire.br_187.appendix_a.equation_a4.x(w, s)¶
Calculate dimensionless width parameter.
\[X = \frac{W}{S}\]where:
\(X\) is the dimensionless width parameter
\(W\) is the width of radiation source (m)
\(S\) is the distance from source to receiver (m)
- Parameters:
- Returns:
Dimensionless width parameter
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
- ofire.br_187.appendix_a.equation_a4.y(h, s)¶
Calculate dimensionless height parameter.
\[Y = \frac{H}{S}\]where:
\(Y\) is the dimensionless height parameter
\(H\) is the height of radiation source (m)
\(S\) is the distance from source to receiver (m)
- Parameters:
- Returns:
Dimensionless height parameter
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
- ofire.br_187.appendix_a.equation_a4.phi(x, y, additive)¶
Calculate view factor using alternative method.
Calculates the view factor for parallel source and receiver surfaces that are corner aligned.
\[\phi = \frac{1}{2\pi}\left(\frac{X}{\sqrt{1+X^2}}\tan^{-1}\left(\frac{Y}{\sqrt{1+X^2}}\right)+\frac{Y}{\sqrt{1+Y^2}}\tan^{-1}\left(\frac{X}{\sqrt{1+Y^2}}\right)\right)\]where:
\(\phi\) is the view factor (dimensionless)
\(X\) is the dimensionless width parameter
\(Y\) is the dimensionless height parameter
- Parameters:
- Returns:
View factor (dimensionless)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
Equation A5 - Perpendicular Source and Receiver Corner Aligned¶
Provides view factor calculations for perpendicular source and receiver surfaces that are corner aligned.
- ofire.br_187.appendix_a.equation_a5.x(w, s)¶
Calculate dimensionless width parameter.
\[X = \frac{W}{S}\]where:
\(X\) is the dimensionless width parameter
\(W\) is the width of radiation source (m)
\(S\) is the distance from source to receiver (m)
- Parameters:
- Returns:
Dimensionless width parameter
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
- ofire.br_187.appendix_a.equation_a5.y(h, s)¶
Calculate dimensionless height parameter.
\[Y = \frac{H}{S}\]where:
\(Y\) is the dimensionless height parameter
\(H\) is the height of radiation source (m)
\(S\) is the distance from source to receiver (m)
- Parameters:
- Returns:
Dimensionless height parameter
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed
- ofire.br_187.appendix_a.equation_a5.phi(x, y, additive)¶
Calculate view factor for specific geometric configuration.
Calculates the view factor for perpendicular source and receiver surfaces that are corner aligned.
\[\phi = \frac{1}{2\pi}\left(\tan^{-1}(X) - \frac{1}{\sqrt{Y^2 + 1}}\tan^{-1}\left(\frac{X}{\sqrt{Y^2 + 1}}\right)\right)\]where:
\(\phi\) is the view factor (dimensionless)
\(X\) is the dimensionless width parameter
\(Y\) is the dimensionless height parameter
- Parameters:
- Returns:
View factor (dimensionless)
- Return type:
- Assumptions:
To be completed
- Limitations:
To be completed