Virtual origin - Revision history

Jan: Add 4 watermarked SVG illustrations from the Expert visual plan

2026-11-02T16:18:47Z

Add 4 watermarked SVG illustrations from the Expert visual plan

← Older revision		Revision as of 17:18, 2 November 2026
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	The virtual origin is thus the equivalent point source height of a fire with a finite area.<ref name="Hesk-2-6" /><ref name="IS-9-5" /> Cadorin and co-workers describe it as the position where a virtual point source would produce the same effects as the real fire.<ref name="Cadorin-443">Cadorin et al. (2003), p. 443.</ref> In practice, the plume temperature, velocity and mass flow at a given height are calculated as if the fire were a point at this level.<ref name="IS-9-5" /> The ''Introduction to Fire Safety Engineering'' calls it a computational point on the axis of the plume.<ref name="VR-6.7" />		The virtual origin is thus the equivalent point source height of a fire with a finite area.<ref name="Hesk-2-6" /><ref name="IS-9-5" /> Cadorin and co-workers describe it as the position where a virtual point source would produce the same effects as the real fire.<ref name="Cadorin-443">Cadorin et al. (2003), p. 443.</ref> In practice, the plume temperature, velocity and mass flow at a given height are calculated as if the fire were a point at this level.<ref name="IS-9-5" /> The ''Introduction to Fire Safety Engineering'' calls it a computational point on the axis of the plume.<ref name="VR-6.7" />
			[[File:fse-virtual-origin-v1.svg\|thumb\|upright=1.5\|alt=Two fire plumes: dashed plume edges extended downwards meet at a point below the fuel of a wide fire and above the fuel of a tall fire.\|The virtual origin is the point from which the plume above the flames appears to originate: below the fuel surface for a wide, low fire (left) and above it for a tall, intense fire (right). Based on Heskestad (2002), pp. 2-6 and 2-11.]]

	Near the fire, this correction is significant, and Heskestad stresses that the location of the virtual origin must then be known for accurate predictions.<ref name="Hesk-2-6" /> For a pool fire, it usually lies near the fuel surface.<ref name="Hesk-2-6" /> At great heights above the fire, the difference between z and z − z<sub>0</sub> becomes small. In the NFPA 92B plume equations for atria, the virtual origin is set to zero, which Milke justifies by its being small compared with the height.<ref name="Milke-4-299">Milke (2002b), p. 4-299.</ref> Heskestad does the same in an example with a 20 m high atrium, where deviations of the virtual origin from the fire level are inconsequential.<ref name="Hesk-2-9" /> Because the fire is treated as a point source, the shape of the fuel is then of secondary importance.<ref name="Milke-4-299" />		Near the fire, this correction is significant, and Heskestad stresses that the location of the virtual origin must then be known for accurate predictions.<ref name="Hesk-2-6" /> For a pool fire, it usually lies near the fuel surface.<ref name="Hesk-2-6" /> At great heights above the fire, the difference between z and z − z<sub>0</sub> becomes small. In the NFPA 92B plume equations for atria, the virtual origin is set to zero, which Milke justifies by its being small compared with the height.<ref name="Milke-4-299">Milke (2002b), p. 4-299.</ref> Heskestad does the same in an example with a 20 m high atrium, where deviations of the virtual origin from the fire level are inconsequential.<ref name="Hesk-2-9" /> Because the fire is treated as a point source, the shape of the fuel is then of secondary importance.<ref name="Milke-4-299" />
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	Heskestad illustrates this with a methyl alcohol pool fire of 1.5 m diameter, which releases 884 kW.<ref name="Hesk-2-10" /> Its virtual origin lies 0.29 m below the fuel surface. The same pool burning heptane releases about 4,420 kW, and its virtual origin lies 0.85 m above the surface.<ref name="Hesk-2-11" />		Heskestad illustrates this with a methyl alcohol pool fire of 1.5 m diameter, which releases 884 kW.<ref name="Hesk-2-10" /> Its virtual origin lies 0.29 m below the fuel surface. The same pool burning heptane releases about 4,420 kW, and its virtual origin lies 0.85 m above the surface.<ref name="Hesk-2-11" />
			[[File:fse-virtual-origin-v2.svg\|thumb\|upright=1.5\|alt=Line chart of four correlations for the virtual origin divided by fire diameter, rising from below zero to above zero as heat release rate increases.\|Virtual origin divided by fire diameter against Q^2/5/D for four correlations, with the methyl alcohol, heptane and lubricating oil examples. Based on Heskestad (2002), pp. 2-10 to 2-11, and Iqbal and Salley (2004), p. 9-11.]]

	For storage fires, the virtual origin follows from the flame height. In one of Heskestad's examples, a 3 m deep storage burns at 1,500 kW with flames 3.67 m above its base, which places the virtual origin 0.84 m above the base.<ref name="Hesk-2-11" /> For a wide range of typical fuel packages, Milke reports virtual origins between 0.5 m and −5 m.<ref name="Milke-4-299" /> Negative values arise when modest heat release rates are spread over a large area, so that the second term of the equation exceeds the first.<ref name="Milke-4-299" />		For storage fires, the virtual origin follows from the flame height. In one of Heskestad's examples, a 3 m deep storage burns at 1,500 kW with flames 3.67 m above its base, which places the virtual origin 0.84 m above the base.<ref name="Hesk-2-11" /> For a wide range of typical fuel packages, Milke reports virtual origins between 0.5 m and −5 m.<ref name="Milke-4-299" /> Negative values arise when modest heat release rates are spread over a large area, so that the second term of the equation exceeds the first.<ref name="Milke-4-299" />
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	Without the virtual origin, the same equation gives about 224 °C at the beam. Ignoring the correction would therefore underestimate the temperature rise by about 21 K, or 10%. The effect fades with height: at 15 m above the fire, the difference in temperature rise is about 5%, and at 30 m about 2.5%. This agrees with Heskestad's statement that the virtual origin matters mainly near the fire.<ref name="Hesk-2-6" />		Without the virtual origin, the same equation gives about 224 °C at the beam. Ignoring the correction would therefore underestimate the temperature rise by about 21 K, or 10%. The effect fades with height: at 15 m above the fire, the difference in temperature rise is about 5%, and at 30 m about 2.5%. This agrees with Heskestad's statement that the virtual origin matters mainly near the fire.<ref name="Hesk-2-6" />
			[[File:fse-virtual-origin-v3.svg\|thumb\|upright=1.5\|alt=Line chart: plume centreline temperature falls with height; the curve with the virtual origin lies above the one without it, mostly near the fire.\|Plume centreline temperature above a 5,000 kW lubricating oil pool fire with the virtual origin (0.44 m) and with the virtual origin set to zero. Based on Iqbal and Salley (2004), pp. 9-10 to 9-11, and Heskestad (2002), p. 2-6.]]

	== Use in fire engineering ==		== Use in fire engineering ==
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	Cetegen and co-workers based their correlation on entrainment measurements above gas burners of 0.10 to 0.50 m, with and without a floor flush with the burner.<ref name="Hesk-2-10" /> Their constant is −0.80 without such a floor and −0.50 with one, so a surrounding floor raises the virtual origin by 0.3 times the diameter.<ref name="Hesk-2-10" /> Sign conventions also differ. Heskestad counts the virtual origin as positive above the fire surface, while in the Hasemi model used by OZone the virtual source is drawn below it.<ref name="Hesk-2-6" /><ref name="Cadorin-444" />		Cetegen and co-workers based their correlation on entrainment measurements above gas burners of 0.10 to 0.50 m, with and without a floor flush with the burner.<ref name="Hesk-2-10" /> Their constant is −0.80 without such a floor and −0.50 with one, so a surrounding floor raises the virtual origin by 0.3 times the diameter.<ref name="Hesk-2-10" /> Sign conventions also differ. Heskestad counts the virtual origin as positive above the fire surface, while in the Hasemi model used by OZone the virtual source is drawn below it.<ref name="Hesk-2-6" /><ref name="Cadorin-444" />
			[[File:fse-virtual-origin-v4.svg\|thumb\|upright=1.5\|alt=Two sketches of a fire: on the left z0 is measured upwards from the fuel, on the right the Hasemi virtual source distance is measured downwards.\|Two sign conventions: in Heskestad's correlations z0 is positive above the fuel surface; in the Hasemi model used by OZone the virtual source distance is drawn below it. Based on Heskestad (2002), p. 2-6, and Cadorin et al. (2003), pp. 443 to 444.]]

	The plume equations that use the virtual origin have their own limits. They are not valid at or below the mean flame height.<ref name="Hesk-2-7">Heskestad (2002), p. 2-7.</ref> For a fire with very low flames, a 2.44 m silicone fluid pool with a virtual origin of −1.5 m, Heskestad predicted a centreline temperature rise near the surface of 580 K.<ref name="Hesk-2-7" /> The rise of roughly 440 K derived from the measurements was fairly close to this prediction. It is not yet clear, however, whether such predictions are generally valid for fires with very low flames.<ref name="Hesk-2-7" />		The plume equations that use the virtual origin have their own limits. They are not valid at or below the mean flame height.<ref name="Hesk-2-7">Heskestad (2002), p. 2-7.</ref> For a fire with very low flames, a 2.44 m silicone fluid pool with a virtual origin of −1.5 m, Heskestad predicted a centreline temperature rise near the surface of 580 K.<ref name="Hesk-2-7" /> The rise of roughly 440 K derived from the measurements was fairly close to this prediction. It is not yet clear, however, whether such predictions are generally valid for fires with very low flames.<ref name="Hesk-2-7" />

Mark: FSE wiki: corrections after independent fact-check (written by Claude Opus 5.5)

2026-11-01T23:23:14Z

FSE wiki: corrections after independent fact-check (written by Claude Opus 5.5)

Mark: New FSE wiki article: Virtual origin (written by Claude Opus 5.5)

2026-11-01T22:33:07Z

New FSE wiki article: Virtual origin (written by Claude Opus 5.5)

New page

The '''virtual origin''' of a fire plume is the height of an imaginary point source from which the plume above the flames of a real fire appears to originate.<ref name="Hesk-2-9">Heskestad (2002), p. 2-9.</ref> Plume equations are derived for heat released at a single point, while real fires burn over an area, such as a pool of liquid or the top of a cabinet.<ref name="IS-9-5">Iqbal and Salley (2004), p. 9-5.</ref> By measuring heights from the virtual origin instead of from the fuel surface, the point-source equations can describe these real fires.<ref name="Hesk-2-6">Heskestad (2002), p. 2-6.</ref>

The virtual origin is usually written as z0, its height above the base of the fire. It can lie below the fuel surface, which is typical for fires with a modest heat release rate spread over a large area.<ref name="Hesk-2-11">Heskestad (2002), p. 2-11.</ref> For fires with a high heat release rate it often lies above the fuel surface.<ref name="Hesk-2-11" /><ref name="VR-6.7">Van Rossum (2027), §6.7.</ref> For pool fires, Heskestad's correlation calculates it from the heat release rate and the diameter of the fire.<ref name="Hesk-2-9" /> The location matters for predictions close to the fire. High above it, the virtual origin may simply be placed at the fuel surface.<ref name="Hesk-2-6" />

== Point sources and real fires ==
A [[fire plume]] is the buoyant flow of hot gases, including any flames, that rises above a burning fuel into the surrounding air.<ref name="Hesk-2-1">Heskestad (2002), p. 2-1.</ref> The classic plume theory describes a plume that rises from a point source of heat.<ref name="Hesk-2-6" /> Real fires are area sources, such as pool fires, burning cabinets and cable trays, and their plume near the fire does not behave like a point-source plume.<ref name="IS-9-5" /> Heskestad's solution is to keep the point-source equations but to replace the height above the fire, z, by the height above a virtual source, z − z0.<ref name="Hesk-2-6" />

The virtual origin is thus the equivalent point source height of a fire with a finite area.<ref name="Hesk-2-6" /><ref name="IS-9-5" /> Cadorin and co-workers describe it as the position where a virtual point source would produce the same effects as the real fire.<ref name="Cadorin-443">Cadorin et al. (2003), p. 443.</ref> In practice, the plume temperature, velocity and mass flow at a given height are calculated as if the fire were a point at this level.<ref name="IS-9-5" /> The ''Introduction to Fire Safety Engineering'' calls it a computational point on the axis of the plume.<ref name="VR-6.7" />

Near the fire, this correction is significant, and Heskestad stresses that the location of the virtual origin must then be known for accurate predictions.<ref name="Hesk-2-6" /> For a pool fire, it usually lies near the fuel surface.<ref name="Hesk-2-6" /> At great heights above the fire, the difference between z and z − z0 becomes small. In the NFPA 92B plume equations for atria, the virtual origin is set to zero, which Milke justifies by its being small compared with the height.<ref name="Milke-4-299">Milke (2002b), p. 4-299.</ref> Heskestad does the same in an example with a 20 m high atrium, where deviations of the virtual origin from the fire level are inconsequential.<ref name="Hesk-2-9" /> Because the fire is treated as a point source, the shape of the fuel is then of secondary importance.<ref name="Milke-4-299" />

== Calculating the virtual origin ==
Heskestad derived his correlation from a theoretical model that relies on his [[flame height]] correlation. He checked it against virtual origins measured in pool fires with diameters from 0.16 to 2.4 m.<ref name="Hesk-2-9" /> Such measurements use the plume temperature law: the temperature rise on the axis, raised to the power −3/5, varies linearly with height above the flames. A straight line through the data crosses the height axis at the virtual origin.<ref name="Hesk-2-9" />

The available data did not show a dependence on the type of fuel within their scatter. Large differences in heat of combustion or convective fraction might still affect the result.<ref name="Hesk-2-9" /> In words, the virtual origin rises with the heat release rate to the power 2/5 and falls with the diameter of the fire:<ref name="Hesk-2-9" /><ref name="IS-9-6">Iqbal and Salley (2004), p. 9-6.</ref>
<math display="block">z_0 = 0.083\,\dot{Q}^{2/5} - 1.02\,D</math>
The mean flame height has the same structure, but with a larger coefficient:<ref name="Hesk-2-4">Heskestad (2002), p. 2-4.</ref><ref name="VR-6.7" />
<math display="block">L = 0.235\,\dot{Q}^{2/5} - 1.02\,D</math>
For other fire types, such as deep storage fires, Heskestad gives the virtual origin directly from the flame height and the convective heat release rate:<ref name="Hesk-2-10">Heskestad (2002), p. 2-10.</ref>
<math display="block">z_0 = L - 0.175\,\dot{Q}_\mathrm{c}^{2/5}</math>

{| class="wikitable"
! Symbol !! Description !! Unit
|-
| <math>z_0</math> || height of the virtual origin above the base of the fire (negative below it) || m
|-
| <math>L</math> || mean flame height above the base of the fire || m
|-
| <math>\dot{Q}</math> || total heat release rate || kW
|-
| <math>\dot{Q}_\mathrm{c}</math> || convective heat release rate || kW
|-
| <math>D</math> || diameter of the fire, or effective diameter of a non-circular fire || m
|-
| <math>z</math> || height above the base of the fire || m
|}

The total heat release rate is used for the flame height and the virtual origin. The convective part, which drives the buoyancy, is used for the other plume properties.<ref name="IS-9-6" /> Radiation typically takes 20 to 40% of the total, so the convective heat release rate is often 0.6 to 0.8 times the total.<ref name="IS-9-6" /> For a fire that is not circular, D is the diameter of a circle with the same area as the fire.<ref name="IS-9-6" /> The two flame height and virtual origin equations imply that the virtual origin lies about 0.152 times the total heat release rate to the power 2/5 below the flame tip. With a convective fraction of 0.7, this is almost exactly the 0.175 times the convective rate to the power 2/5 in the storage equation.<ref name="Hesk-2-10" />

Once the virtual origin is known, the plume equations of the [[Heskestad plume]] use z − z0 in place of z.<ref name="Hesk-2-6" /> The temperature rise on the plume axis above the flames then falls with (z − z0) to the power −5/3.<ref name="Hesk-2-6" /> The mass flow in the plume, which consists almost entirely of air drawn in by [[entrainment]], grows with (z − z0) to the power 5/3.<ref name="Hesk-2-11" /><ref name="Milke-4-298">Milke (2002b), p. 4-298.</ref> The plume radius grows, and the axial velocity falls, with the same distance from the virtual origin.<ref name="Hesk-2-6" /> Inside the flames these relations do not apply, and the mass flow is instead taken in proportion to the height divided by the flame height.<ref name="VR-6.7" /><ref name="Peacock-14">Peacock et al. (2026), p. 14.</ref> For normal atmospheric conditions, the temperature rise on the axis above the flames is:<ref name="Hesk-2-6" />
<math display="block">\Delta T_0 = 25.0\,\dot{Q}_\mathrm{c}^{2/3}\,(z - z_0)^{-5/3}</math>
Here ΔT0 is the temperature rise on the plume axis in kelvin. The constant 25.0 holds for air at 293 K with a density of 1.2 kg/m³.<ref name="Hesk-2-6" />

== Sign and size ==
Negative values of the virtual origin are often found for fires with a low heat release rate and a large diameter. Positive values are common for fires with a high heat release rate.<ref name="Hesk-2-11" /> The storage equation shows why: the virtual origin lies a fixed distance, 0.175 times the convective heat release rate to the power 2/5, below the mean flame tip.<ref name="Hesk-2-10" /> Short flames over a wide fire therefore place it below the fuel surface, and tall flames above it.

Heskestad illustrates this with a methyl alcohol pool fire of 1.5 m diameter, which releases 884 kW.<ref name="Hesk-2-10" /> Its virtual origin lies 0.29 m below the fuel surface. The same pool burning heptane releases about 4,420 kW, and its virtual origin lies 0.85 m above the surface.<ref name="Hesk-2-11" />

For storage fires, the virtual origin follows from the flame height. In one of Heskestad's examples, a 3 m deep storage burns at 1,500 kW with flames 3.67 m above its base, which places the virtual origin 0.84 m above the base.<ref name="Hesk-2-11" /> For a wide range of typical fuel packages, Milke reports virtual origins between 0.5 m and −5 m.<ref name="Milke-4-299" /> Negative values arise when modest heat release rates are spread over a large area, so that the second term of the equation exceeds the first.<ref name="Milke-4-299" />

The virtual origin of a growing fire need not stay in one place. In tests with rack storage of plastic goods, flames spread upwards and sideways while the fire grew.<ref name="Alpert-2-25">Alpert (2002), p. 2-25.</ref> Yu and Stavrianidis therefore used a virtual origin that moves with the convective heat release rate, from 2.4 m below the base of the fire at the start.<ref name="Alpert-2-25" /> Their ceiling jet correlations use the effective ceiling height above this moving point.<ref name="Alpert-2-25" />

== Worked example ==
NUREG-1805 calculates the plume temperature at a steel beam 7.62 m above a pool fire of lubricating oil.<ref name="IS-9-10">Iqbal and Salley (2004), p. 9-10.</ref> The pool covers 3.21 m², and the fire releases 5,000 kW, of which 70% is convective.<ref name="IS-9-11">Iqbal and Salley (2004), p. 9-11.</ref> The ambient temperature is 25 °C and the air density 1.18 kg/m³.<ref name="IS-9-11" /> The effective diameter is that of a circle with the same area:
<math display="block">D = \sqrt{\frac{4 \times 3.21}{\pi}} = 2.02\ \mathrm{m}, \qquad z_0 = 0.083 \times 5000^{2/5} - 1.02 \times 2.02 = 0.44\ \mathrm{m}</math>
The virtual origin thus lies 0.44 m above the fuel surface, and the beam is 7.18 m above it.<ref name="IS-9-11" /> With the convective heat release rate of 3,500 kW, the plume temperature at the beam becomes 244 °C.<ref name="IS-9-10" />

Without the virtual origin, the same equation gives about 224 °C at the beam. Ignoring the correction would therefore underestimate the temperature rise by about 21 K, or 10%. The effect fades with height: at 15 m above the fire, the difference in temperature rise is about 5%, and at 30 m about 2.5%. This agrees with Heskestad's statement that the virtual origin matters mainly near the fire.<ref name="Hesk-2-6" />

== Use in fire engineering ==
The virtual origin appears in most methods that use the Heskestad plume. The International Fire Engineering Guidelines (2005) use it in the equation for the centreline temperature of flames and plumes.<ref name="IFEG-2.4-7">National Research Council of Canada et al. (2005), p. 2.4-7.</ref> The same guidelines use it in the mass entrainment equations for smoke filling.<ref name="IFEG-2.5-3">National Research Council of Canada et al. (2005), p. 2.5-3.</ref> NUREG-1805 lists its calculation as the second of four steps in estimating the centreline temperature of a plume.<ref name="IS-9-8">Iqbal and Salley (2004), p. 9-8.</ref>

The zone model CFAST uses the same correlation in dimensionless form, also based on the total heat release rate.<ref name="Peacock-14" /> For a fire against a wall or in a corner, CFAST mirrors the fire in the wall faces. It doubles or quadruples the convective heat release rate, enlarges the fire diameter and divides the resulting entrainment by two or four.<ref name="Peacock-14" /> The virtual origin then changes as well, because it depends on the effective diameter.<ref name="Peacock-14" />

The concept also appears in ceiling jet and structural calculations. Alpert recommends correcting the ceiling height for the location of the virtual point source when ceiling jet heat transfer correlations are applied.<ref name="Alpert-2-22">Alpert (2002), p. 2-22.</ref> For steel members near a localised fire, the OZone tool uses Hasemi's model, in which a virtual heat source is placed relative to the fire surface.<ref name="Cadorin-443" /> The heat flux to a beam then depends on distances measured from this virtual source.<ref name="Cadorin-444">Cadorin et al. (2003), p. 444.</ref>

The same idea can be applied to sources that are not points. In a balcony spill example, Cooper places an imaginary line source 1.7 m below the balcony edge, so that a line plume equation can describe the smoke that spills over the edge.<ref name="Cooper-3-232">Cooper (2002b), p. 3-232.</ref> As with a point source, the imaginary source is chosen so that the equation reproduces the known mass flow at a reference height.<ref name="Cooper-3-232" />

== Limits and uncertainty ==
The virtual origin is hard to measure. It is found by extrapolating temperatures measured along the plume axis, and small errors in these temperatures have a large effect on the result.<ref name="Hesk-2-9" /> Such errors can come from sensors placed off the axis, from radiation affecting the readings or from too little averaging of the signal.<ref name="Hesk-2-9" /> Heskestad's correlation rests on pool fires of 0.16 to 2.4 m diameter.<ref name="Hesk-2-9" />

Different correlations exist, and they do not always agree. Heskestad's chapter compares his correlation with those of Hasemi and Tokunaga and of Cetegen and co-workers, finds them surprisingly similar and recommends his own for its simplicity, theoretical basis and central position.<ref name="Hesk-2-10" /> For the lubricating oil fire of the worked example, however, the correlation of Hasemi and Tokunaga places the virtual origin about 0.28 m below the fuel surface instead of 0.44 m above it.<ref name="Hesk-2-10" />

Cetegen and co-workers based their correlation on entrainment measurements above gas burners of 0.10 to 0.50 m, with and without a floor flush with the burner.<ref name="Hesk-2-10" /> Their constant is −0.80 without such a floor and −0.50 with one, so a surrounding floor raises the virtual origin by 0.3 times the diameter.<ref name="Hesk-2-10" /> Sign conventions also differ. Heskestad counts the virtual origin as positive above the fire surface, while in the Hasemi model used by OZone the virtual source is drawn below it.<ref name="Hesk-2-6" /><ref name="Cadorin-444" />

The plume equations that use the virtual origin have their own limits. They are not valid at or below the mean flame height.<ref name="Hesk-2-7">Heskestad (2002), p. 2-7.</ref> For a fire with very low flames, a 2.44 m silicone fluid pool with a virtual origin of −1.5 m, the predicted temperature near the surface was 580 K against about 440 K measured.<ref name="Hesk-2-7" /> According to the International Fire Engineering Guidelines, the centreline temperature equation is accurate up to a temperature rise of 500 K and overestimates it between 500 and 900 K.<ref name="IFEG-2.4-7" /> NUREG-1805 adds that it does not apply to jet fires and underestimates temperatures when the surrounding air is already hot.<ref name="IS-9-7">Iqbal and Salley (2004), p. 9-7.</ref>

Care is also needed with the constants in some guidance documents. In the International Fire Engineering Guidelines, the flame height and virtual origin equations reuse the symbols C1 and C2 of the entrainment equation above them.<ref name="IFEG-2.5-3" /> The values listed for these symbols, 0.071 and 0.027, differ from the coefficients 0.235 and 0.083 in Heskestad's chapter.<ref name="IFEG-2.5-3" /><ref name="Hesk-2-4" /><ref name="Hesk-2-9" />

== See also ==
* [[Thomas plume]]
* [[Dimensionless heat release rate]]
* [[Alpert correlations]]
* [[Line plume]]

== Notes ==
<references />

== References ==
* Alpert, R. L. (2002). Ceiling jet flows. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-18–2-31). National Fire Protection Association; Society of Fire Protection Engineers.
* Cadorin, J.-F., Pintea, D., Dotreppe, J.-C., & Franssen, J.-M. (2003). A tool to design steel elements submitted to compartment fires–OZone V2. Part 2: Methodology and application. ''Fire Safety Journal'', ''38'', 429–451. https://doi.org/10.1016/S0379-7112(03)00015-8
* Cooper, L. Y. (2002b). Smoke and heat venting. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 3-219–3-242). National Fire Protection Association; Society of Fire Protection Engineers.
* Heskestad, G. (2002). Fire plumes, flame height, and air entrainment. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 2-1–2-17). National Fire Protection Association; Society of Fire Protection Engineers.
* Iqbal, N., & Salley, M. H. (2004). ''Fire Dynamics Tools (FDTs): Quantitative fire hazard analysis methods for the U.S. Nuclear Regulatory Commission Fire Protection Inspection Program'' (NUREG-1805). U.S. Nuclear Regulatory Commission, Office of Nuclear Reactor Regulation.
* Milke, J. A. (2002b). Smoke management in covered malls and atria. In P. J. DiNenno, D. Drysdale, C. L. Beyler, W. D. Walton, R. L. P. Custer, J. R. Hall Jr., & J. M. Watts Jr. (Eds.), ''SFPE handbook of fire protection engineering'' (3rd ed., pp. 4-292–4-310). National Fire Protection Association; Society of Fire Protection Engineers.
* National Research Council of Canada, International Code Council, Department of Building and Housing, & Australian Building Codes Board. (2005). ''International fire engineering guidelines'' (2005 ed.). Australian Building Codes Board.
* Peacock, R. D., McGrattan, K. B., Forney, G. P., & Reneke, P. A. (2026). ''CFAST – Consolidated Fire and Smoke Transport: Vol. 1. Technical reference guide'' (Version 7, NIST Technical Note 1889v1). National Institute of Standards and Technology. https://doi.org/10.6028/NIST.TN.1889v1
* Van Rossum, E. (2027). ''Introduction to Fire Safety Engineering''. Fire Safety Academy.

[[Category:Fire Dynamics]]

← Older revision		Revision as of 00:23, 2 November 2026
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	The available data did not show a dependence on the type of fuel within their scatter. Large differences in heat of combustion or convective fraction might still affect the result.<ref name="Hesk-2-9" /> In words, the virtual origin rises with the heat release rate to the power 2/5 and falls with the diameter of the fire:<ref name="Hesk-2-9" /><ref name="IS-9-6">Iqbal and Salley (2004), p. 9-6.</ref>		The available data did not show a dependence on the type of fuel within their scatter. Large differences in heat of combustion or convective fraction might still affect the result.<ref name="Hesk-2-9" /> In words, the virtual origin rises with the heat release rate to the power 2/5 and falls with the diameter of the fire:<ref name="Hesk-2-9" /><ref name="IS-9-6">Iqbal and Salley (2004), p. 9-6.</ref>
	<math display="block">z_0 = 0.083\,\dot{Q}^{2/5} - 1.02\,D</math>		<math display="block">z_0 = 0.083\,\dot{Q}^{2/5} - 1.02\,D</math>
	The mean flame height has the same structure, but with a larger coefficient:<ref name="Hesk-2-4">Heskestad (2002), p. 2-4.</ref><ref name="VR-6.7" />		The mean flame height has the same structure, but with a larger coefficient:<ref name="Hesk-2-3">Heskestad (2002), p. 2-3.</ref><ref name="VR-6.7" />
	<math display="block">L = 0.235\,\dot{Q}^{2/5} - 1.02\,D</math>		<math display="block">L = 0.235\,\dot{Q}^{2/5} - 1.02\,D</math>
	For other fire types, such as deep storage fires, Heskestad gives the virtual origin directly from the flame height and the convective heat release rate:<ref name="Hesk-2-10">Heskestad (2002), p. 2-10.</ref>		For other fire types, such as deep storage fires, Heskestad gives the virtual origin directly from the flame height and the convective heat release rate:<ref name="Hesk-2-10">Heskestad (2002), p. 2-10.</ref>
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	The virtual origin is hard to measure. It is found by extrapolating temperatures measured along the plume axis, and small errors in these temperatures have a large effect on the result.<ref name="Hesk-2-9" /> Such errors can come from sensors placed off the axis, from radiation affecting the readings or from too little averaging of the signal.<ref name="Hesk-2-9" /> Heskestad's correlation rests on pool fires of 0.16 to 2.4 m diameter.<ref name="Hesk-2-9" />		The virtual origin is hard to measure. It is found by extrapolating temperatures measured along the plume axis, and small errors in these temperatures have a large effect on the result.<ref name="Hesk-2-9" /> Such errors can come from sensors placed off the axis, from radiation affecting the readings or from too little averaging of the signal.<ref name="Hesk-2-9" /> Heskestad's correlation rests on pool fires of 0.16 to 2.4 m diameter.<ref name="Hesk-2-9" />

	Different correlations exist, and they do not always agree. Heskestad's chapter compares his correlation with those of Hasemi and Tokunaga and of Cetegen and co-workers, finds them surprisingly similar and recommends his own for its simplicity, theoretical basis and central position.<ref name="Hesk-2-10" /> ~~For~~ the lubricating oil fire of the worked example~~, however, the correlation of Hasemi and Tokunaga places the~~ virtual origin about 0.28 m below the fuel surface instead of 0.44 m above it.<ref name="Hesk-2-10" />		Different correlations exist, and they do not always agree. Heskestad's chapter compares his correlation with those of Hasemi and Tokunaga and of Cetegen and co-workers, finds them surprisingly similar and recommends his own for its simplicity, theoretical basis and central position.<ref name="Hesk-2-10" /> The correlation of Hasemi and Tokunaga, as given by Heskestad, can also be applied to the lubricating oil fire of the worked example. The calculated virtual origin then lies about 0.28 m below the fuel surface, instead of 0.44 m above it.<ref name="Hesk-2-10" />

	Cetegen and co-workers based their correlation on entrainment measurements above gas burners of 0.10 to 0.50 m, with and without a floor flush with the burner.<ref name="Hesk-2-10" /> Their constant is −0.80 without such a floor and −0.50 with one, so a surrounding floor raises the virtual origin by 0.3 times the diameter.<ref name="Hesk-2-10" /> Sign conventions also differ. Heskestad counts the virtual origin as positive above the fire surface, while in the Hasemi model used by OZone the virtual source is drawn below it.<ref name="Hesk-2-6" /><ref name="Cadorin-444" />		Cetegen and co-workers based their correlation on entrainment measurements above gas burners of 0.10 to 0.50 m, with and without a floor flush with the burner.<ref name="Hesk-2-10" /> Their constant is −0.80 without such a floor and −0.50 with one, so a surrounding floor raises the virtual origin by 0.3 times the diameter.<ref name="Hesk-2-10" /> Sign conventions also differ. Heskestad counts the virtual origin as positive above the fire surface, while in the Hasemi model used by OZone the virtual source is drawn below it.<ref name="Hesk-2-6" /><ref name="Cadorin-444" />

	The plume equations that use the virtual origin have their own limits. They are not valid at or below the mean flame height.<ref name="Hesk-2-7">Heskestad (2002), p. 2-7.</ref> For a fire with very low flames, a 2.44 m silicone fluid pool with a virtual origin of −1.5 m, ~~the~~ predicted temperature near the surface ~~was~~ 580 K ~~against about 440 K measured~~.<ref name="Hesk-2-7" /> ~~According to the International Fire Engineering Guidelines, the centreline temperature equation is accurate up to a temperature~~ rise of ~~500 K and overestimates it between 500 and 900~~ K.~~<ref name="IFEG-2.4-7" /> NUREG-1805 adds that it does~~ not ~~apply to jet~~ fires ~~and underestimates temperatures when the surrounding air is already hot~~.<ref name="IS-9-7"~~>Iqbal and Salley (2004), p. 9-7.<~~/~~ref~~>		The plume equations that use the virtual origin have their own limits. They are not valid at or below the mean flame height.<ref name="Hesk-2-7">Heskestad (2002), p. 2-7.</ref> For a fire with very low flames, a 2.44 m silicone fluid pool with a virtual origin of −1.5 m, Heskestad predicted a centreline temperature rise near the surface of 580 K.<ref name="Hesk-2-7" /> The rise of roughly 440 K derived from the measurements was fairly close to this prediction. It is not yet clear, however, whether such predictions are generally valid for fires with very low flames.<ref name="Hesk-2-7" />

	Care is also needed with the constants in some guidance documents. In the International Fire Engineering Guidelines, the flame height and virtual origin equations reuse the symbols C<sub>1</sub> and C<sub>2</sub> of the entrainment equation above them.<ref name="IFEG-2.5-3" /> The values listed for these symbols, 0.071 and 0.027, differ from the coefficients 0.235 and 0.083 in Heskestad's chapter.<ref name="IFEG-2.5-3" /><ref name="Hesk-2-4" /><ref name="Hesk-2-9" />		According to the International Fire Engineering Guidelines, the centreline temperature equation is accurate up to a temperature rise of 500 K and overestimates it between 500 and 900 K.<ref name="IFEG-2.4-7" /> NUREG-1805 adds that it does not apply to jet fires and underestimates temperatures when the surrounding air is already hot.<ref name="IS-9-7">Iqbal and Salley (2004), p. 9-7.</ref>

			Care is also needed with the constants in some guidance documents. In the International Fire Engineering Guidelines, the flame height and virtual origin equations reuse the symbols C<sub>1</sub> and C<sub>2</sub> of the entrainment equation above them.<ref name="IFEG-2.5-3" /> The values listed for these symbols, 0.071 and 0.027, differ from the coefficients 0.235 and 0.083 in Heskestad's chapter.<ref name="IFEG-2.5-3" /><ref name="Hesk-2-3" /><ref name="Hesk-2-9" />

	== See also ==		== See also ==