A t-squared fire in FDS: TAU_Q, RAMP_Q and checking the HRR

fdsrun editorial team · 6 November 2026 · 5 min read

How to write a t-squared design fire in FDS: a negative TAU_Q or RAMP_Q with points, α coefficients, time to peak and checking CHID_hrr.csv.

A design fire is most often described by a "t-squared" curve: the heat release rate grows with the square of time, Q(t) = α · t², up to a peak value. FDS offers two ways to write it — a single parameter or a table of points. Both work, but each has a trap.

The coefficient α and the time to peak

Typical fire growth classes and the time to reach 1 MW:

The time to the peak is t = √(Qmax / α). For a fast-growth 2.5 MW fire: √(2500 / 0.0469) ≈ 231 s.

Option 1: a negative TAU_Q

On the &SURF line a negative TAU_Q means t-squared growth: the heat release reaches the full HRRPUA after |TAU_Q| seconds and stays constant afterwards (FDS User Guide, section 11.1).

&SURF ID='FIRE', HRRPUA=500., TAU_Q=-231. /
&VENT XB=10.0,12.0,4.0,6.5,0.0,0.0, SURF_ID='FIRE' /   ← 2.0 × 2.5 m = 5 m² × 500 kW/m² = 2.5 MW

The trap: if the run does not start at zero (T_BEGIN ≠ 0), the TAU_Q curve starts at T_BEGIN, not at zero.

Option 2: RAMP_Q with points

When the fire also has a steady phase and a decay, a table is more convenient: T is time, F the fraction of HRRPUA. FDS interpolates linearly between points, so the parabola needs several points, not two.

&SURF ID='FIRE', HRRPUA=500., RAMP_Q='t2_fast' /
&RAMP ID='t2_fast', T=  0., F=0.00 /
&RAMP ID='t2_fast', T= 60., F=0.07 /
&RAMP ID='t2_fast', T=120., F=0.27 /
&RAMP ID='t2_fast', T=180., F=0.61 /
&RAMP ID='t2_fast', T=231., F=1.00 /
&RAMP ID='t2_fast', T=900., F=1.00 /

TAU_Q and RAMP_Q are mutually exclusive — give only one of them for a surface.

Check what actually burns

• Area after snapping to the mesh. Obstructions and vents snap to cell faces. A 2.0 × 2.5 m burner stays unchanged with 20 cm cells, but with 30 cm cells its area changes, and so does the heat release.
• The CHID_hrr.csv file. After a few minutes of the run compare the HRR column with the intended curve — the quickest way to catch a mistake in the area or the ramp.
• Resolution. A growing fire means a growing D*; check D*/δx for the heat release that matters for the assessment (cell size and D*/δx).

The file check below catches references to undefined RAMP_ID and SURF_ID and shows the forecast run time for the whole scenario.

Sources: FDS User Guide (NIST SP 1019), sections 9.2, 11.1; α values from the t-squared fire classification used in NFPA 72 and the SFPE Handbook. FDS and Smokeview are software of the National Institute of Standards and Technology; NIST is not affiliated with fdsrun.