T-Squared Fire Growth
Definition
A model in which heat release rate increases as the square of time from established burning (HRR = alpha × t²). The alpha coefficient classifies growth rate as slow, medium, fast, or ultra-fast, corresponding to different fuel types and arrangements.
- Formula
- HRR = alpha x t^2
- Coefficient
- Alpha classifies growth as slow, medium, fast, or ultra-fast
- Applies from
- Established/growing fire, not incipient ignition
- Field
- Compartment fire behaviour and plume modelling
Common questions
How does the alpha coefficient help a fire investigator reconstruct a timeline?+
By matching observed fuel packages, such as furniture type and arrangement, to a known alpha classification, an investigator can estimate how quickly heat release rate would have grown after established burning began, which supports modelling when flashover or detector activation likely occurred relative to ignition.
Why doesn't the t-squared model apply to the very earliest stage of a fire?+
The t-squared curve describes growth once a fire has moved past incipient smouldering or slow initial flaming into an established, growing phase; the ignition and very early growth period follows different, less predictable dynamics driven by the specific ignition source and immediate fuel, so the model is not applied to that stage.
What limits the reliability of using t-squared modelling as forensic evidence?+
The model assumes an idealised, unconfined, well-ventilated growth curve for a chosen fuel package, but real compartment fires are affected by ventilation limits, fuel package variability, and interruptions, so alpha-based estimates are typically presented as a modelled scenario supporting other physical evidence, not a standalone determination.
Related terms
- Alpert Correlation
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- CFAST
- Consolidated Fire and Smoke Transport model from NIST; a multi-room two-zone fire model used for evacuation time analysis, detector performance prediction, and...
- Fractional Effective Dose (FED)
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- Heskestad Correlation
- An analytical expression derived by Gunnar Heskestad at FM Global relating fire plume centreline temperature to heat release rate and height above...
- McCaffrey Plume Model
- A three-zone empirical model for fire plume centreline temperature and velocity developed by Brian McCaffrey at NIST, with separate power-law relationships for...
- NIST FDS (Fire Dynamics Simulator)
- A freely available large-eddy simulation CFD code from NIST that models coupled fire, smoke, and heat transfer in three-dimensional geometries. Validated against...
- Soot Horizon
- The visible line on vertical surfaces marking the lowest height reached by the smoke layer during the early fire growth phase, representing...
- Two-Zone Model
- A compartment fire model that divides the room into an upper hot gas zone and a lower cool ambient zone, computing their...
- Virtual Origin
- In plume correlation models, the effective point source location below the actual fuel surface from which the plume behaves as if it...