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:
  • a_s (float) – Area of external wall surface (m²)

  • a (float) – Area of openings in the external wall (m²)

  • h (float) – Height of openings (m)

Returns:

Ventilation factor (m⁻¹/²)

Return type:

float

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:
  • sigma (float) – Stefan-Boltzmann constant (kW/m²K⁴)

  • emissivity (float) – Surface emissivity (dimensionless, 0-1)

  • temperature (float) – Absolute temperature (K)

Returns:

Radiation intensity (kW/m²)

Return type:

float

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:
  • phi (float) – View factor (dimensionless)

  • i_s (float) – Source radiation intensity (W/m²)

Returns:

Radiation intensity at receiver (W/m²)

Return type:

float

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:
  • w (float) – Width of radiation source (m)

  • s (float) – Distance from source to receiver (m)

Returns:

Dimensionless width parameter

Return type:

float

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:
  • h (float) – Height of radiation source (m)

  • s (float) – Distance from source to receiver (m)

Returns:

Dimensionless height parameter

Return type:

float

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() and ofire.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:
  • x (float) – Dimensionless width parameter

  • y (float) – Dimensionless height parameter

  • additive (bool) – Whether this view factor is positive or negative

Returns:

View factor (dimensionless)

Return type:

float

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:
  • w (float) – Width of radiation source (m)

  • s (float) – Distance from source to receiver (m)

Returns:

Dimensionless width parameter

Return type:

float

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:
  • h (float) – Height of radiation source (m)

  • s (float) – Distance from source to receiver (m)

Returns:

Dimensionless height parameter

Return type:

float

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:
  • x (float) – Dimensionless width parameter

  • y (float) – Dimensionless height parameter

  • additive (bool) – Whether this view factor is positive or negative

Returns:

View factor (dimensionless)

Return type:

float

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:
  • w (float) – Width of radiation source (m)

  • s (float) – Distance from source to receiver (m)

Returns:

Dimensionless width parameter

Return type:

float

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:
  • h (float) – Height of radiation source (m)

  • s (float) – Distance from source to receiver (m)

Returns:

Dimensionless height parameter

Return type:

float

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:
  • x (float) – Dimensionless width parameter

  • y (float) – Dimensionless height parameter

  • additive (bool) – Whether this view factor is positive or negative

Returns:

View factor (dimensionless)

Return type:

float

Assumptions:

To be completed

Limitations:

To be completed