Thermal Radiation and Separation Distance

Direction of the calculation

Separation distance for a target fluxRadiant flux at a given distance

The fire

Q̇ — heat release rate (kW)

This can be taken from the pool fire calculator or the t² fire growth calculator.

D — fire base diameter (m)

Needed to test the validity range: the model holds approximately above R = 2.5·D.

χ_r — the radiative fraction of the heat release rate

Fuel-dependent. A typical range is 0.15–0.35, but the tool does not choose a value for you and does not reject one outside that range.

Source of the value

Required. The tool does not supply this value, and a result resting on a value with no source is marked as undocumented.

Target flux

Choosing the criterion is an engineering judgement. The tool neither chooses nor recommends — beside each value is what it describes and what is known about where it came from.

1.6 kW/m²Prolonged human exposure without harm — the low threshold in common use.Equivalent to 507 BTU/hr·ft², within 1.4% of 500. At that magnitude such closeness is not a coincidence, so this is most likely a rounding of an imperial value.4.7 kW/m²Pain within a few seconds of exposure; used as a threshold for a human escape route.Equivalent to 1,490 BTU/hr·ft², within 0.7% of 1,500. Here too the closeness is not a coincidence at that magnitude.12.5 kW/m²Piloted ignition of wood and melting of thermoplastic materials.Equivalent to 3,962 BTU/hr·ft², close to 4,000 — but at that magnitude such closeness is common by chance, and is not evidence of an imperial origin.37.5 kW/m²Damage to equipment and structures under prolonged exposure.Equivalent to 11,887 BTU/hr·ft², close to 12,000 — but at that magnitude almost any value is close to a multiple of 500, so this is no evidence of an origin.Another value, from a document you hold

Validity range

The conditions that determine whether the correlation applies. Crossing them changes the state of the result.

The point source model concentrates all the radiation at a single point, and holds in the far field only — approximately R above 2.5·D. In the near field the flame is not a point, and the model does not describe it.
In the reverse calculation the distance is the output, so falling outside the validity range is not visible in the input at all: every figure can be sound and the answer still land in the near field. In that case the result must not be treated as a safe separation distance, and a solid flame calculation is required.

Model limits

What the model does not describe, even within its validity range. These always hold.

The direction of the error in the near field is not fixed and is not determined by the model: as R tends to zero the 1/R² term diverges while a real flame's emissive power is bounded, and at intermediate ranges the geometry can reverse the relationship. The tool states no direction, because an unknown direction presented as known is exactly what makes a result get used as a safe distance.
The model describes radiation only. It does not account for absorption in humid air, wind, shielding or obstruction, and it does not replace a near-field calculation where one is needed.

What the tool does not supply

χ_r is fuel-dependent and does not ship with the tool. The equation is publishable science; the material property sits in a table that is not ours, so it is entered by you together with the document it came from.

The equation

q̇" = (χ_r · Q̇) / (4π · R²)

q̇" [kW/m²]: Radiant flux
χ_r: The radiative fraction of the heat release rate
Q̇ [kW]: Heat release rate
R [m]: Distance from the fire to the target

Values required for the calculation that do not vary within the equation:

The fire base diameter is not a variable in the equation. It is required in order to test R against 2.5·D — the validity range of the point source model.

The point source model — SFPE Handbook 5th ed.

Result

Missing data

A value is missing that you can supply here and now.

No result was calculated. The details are below.

To complete the calculation the following are missing:

χ_r — the radiative fraction
q̇" — target flux

Source of the equation

The point source model — SFPE Handbook of Fire Protection Engineering, 5th ed.

The flux thresholds are not taken from a single document. The document the chosen threshold came from must be recorded in the report.

Your data is stored in this browser alone and is never sent to Hoshen or to anyone else.

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