Calculation of the Phases of Fire Using the Fire Tetrahedron

 Calculation of the Phases of Fire Using the Fire Tetrahedron

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Introduction

Understanding the phases of fire is essential for firefighters, safety engineers, and building managers. The Fire Tetrahedron—a model representing the four essentials of combustion—helps professionals not only describe how a fire behaves but also estimate its development mathematically.

This article provides:

• A deep explanation of the Fire Tetrahedron.

• A scientific breakdown of the phases of fire (ignition, growth, fully developed, decay).

• Calculation methods and formulas used by safety engineers.

• International fire safety standards India refers to.

• Practical insights for creating fast-response fire teams.

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 The Fire Tetrahedron: A Quick Recap

Traditionally, the Fire Triangle represented three elements—fuel, heat, and oxygen. The Fire Tetrahedron adds a fourth component: the chemical chain reaction.

• Fuel: Anything combustible (wood, paper, gas).

• Heat: The energy to start and sustain combustion.

• Oxygen: Usually from air (21%).

• Chain Reaction: The ongoing free radical reactions that keep fire burning.

Mathematical Model:
If we assign variables:

• F = Fuel mass

• H = Heat energy

• O₂ = Oxygen concentration

• C = Chain reaction efficiency

Then the combustion potential (CP) can be simplified as:

CP = F × H × O₂ × C

Any variable reduced below a critical threshold → fire cannot sustain.

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Phases of Fire

Fires progress through four main phases, and each phase can be described numerically:

1. Ignition Phase

2. Growth Phase

3. Fully Developed Phase

4. Decay Phase

Each phase’s intensity can be graphed as Heat Release Rate (HRR) vs. Time.

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Ignition Phase

• Description: Initial heating of fuel to ignition temperature.

• Key Variables:

  • Ignition Temperature (Ti)

  • Heat Flux (q″)

  • Fuel Mass (m)

Calculation Example:
Time to ignition (tᵢ) can be estimated using:

tᵢ = (ρ × c × (Tᵢ – T₀) × d²) / (2 × k × q″)

Where:

• ρ = density of fuel

• c = specific heat

• k = thermal conductivity

• d = thickness

• T₀ = initial temperature

This equation helps fire safety engineers predict how quickly a material will ignite.

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Growth Phase

• Description: Fire spreads; flames increase.

• Mathematical View:
  Heat Release Rate (HRR) = α × t² (NFPA 72 model)

Where α is the fire growth coefficient:

• Slow growth: α = 0.00293 kW/s²

• Medium: α = 0.01172 kW/s²

• Fast: α = 0.0469 kW/s²

This equation allows you to predict HRR at time t.

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Fully Developed Phase

• Description: Peak burning; all fuel involved.

• Key Variables:

  • Maximum HRR (HRRmax)

  • Total Fuel Load (FL)

  • Ventilation Factor (V)

Calculation:

HRRmax = (ṁf × ΔHc)

Where:

• ṁf = fuel mass loss rate (kg/s)

• ΔHc = heat of combustion (kJ/kg)

This is critical for structural design, sprinkler systems, and evacuation planning.

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Decay Phase

• Description: Fuel is consumed, HRR drops.

• Mathematical Estimation:
  You can model the decay as an exponential decrease:

HRR(t) = HRRmax × e^(–βt)

Where β is the decay coefficient depending on ventilation and fuel depletion.

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International Fire Safety Standards India Refers To

India’s National Building Code (NBC 2016) draws from:

• NFPA (USA) – National Fire Protection Association standards.

• BS EN (UK & EU) – British and European fire codes.

• ISO 834 – Standard fire curve for testing materials.

• Australian Standards AS 3959 – For bushfire prone areas.

Indian Fire Services follow a hybrid approach: NBC + NFPA guidelines for high-rise and industrial buildings.

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Applying the Fire Tetrahedron to Calculations

The Fire Tetrahedron isn’t just conceptual; it feeds into equations:

• Fuel Mass (F): Controls duration.

• Heat (H): Controls ignition & spread.

• Oxygen (O₂): Controls ventilation.

• Chain Reaction (C): Efficiency factor.

Combined, these variables form a predictive matrix for each phase.

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Practical Example: Warehouse Fire

• Fuel load: 400 MJ/m²

• Ignition flux: 25 kW/m²

• Ventilation: 2 openings

By plugging into the equations above, safety engineers can predict:

• Ignition time: ~60 s

• HRR growth to 5 MW within 4 min

• HRRmax at 15 MW after 8 min

• Decay phase starts at 25 min

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Conclusion

Understanding and calculating the phases of fire using the Fire Tetrahedron allows:

• Better fire safety design.

• Faster emergency response.

• Compliance with Indian and international standards.

This knowledge transforms fire science from a reactive approach to a predictive, data-driven strategy.