Response time index - Revision history

Jan: Remove links to pages that do not exist; retain displayed text (wiki-wide link audit).

2026-11-02T21:34:41Z

Remove links to pages that do not exist; retain displayed text (wiki-wide link audit).

← Older revision		Revision as of 22:34, 2 November 2026
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	== Interpretation in sprinkler design ==		== Interpretation in sprinkler design ==

	Fast thermal response is one feature of an [[ESFR sprinkler~~\|ESFR sprinkler]]~~, but it does not establish the complete suppression performance of that sprinkler. NUREG-1805 also identifies droplet size and discharge velocity, together with strict design and installation requirements. A suitable RTI value cannot replace evidence that the sprinkler and its water supply suit the protected hazard.<ref name="N-10-3">Iqbal and Salley (2004), p. 10-3.</ref>		Fast thermal response is one feature of an ESFR sprinkler, but it does not establish the complete suppression performance of that sprinkler. NUREG-1805 also identifies droplet size and discharge velocity, together with strict design and installation requirements. A suitable RTI value cannot replace evidence that the sprinkler and its water supply suit the protected hazard.<ref name="N-10-3">Iqbal and Salley (2004), p. 10-3.</ref>

	Operation of a thermal element is also distinct from water arrival. In a dry pipe system, valve operation and movement of water through the piping introduce additional delay after a sprinkler opens. Fleming separates this water-delivery time into trip and transit components. These delays do not become part of RTI merely because they influence the eventual application of water.<ref name="F-85" />		Operation of a thermal element is also distinct from water arrival. In a dry pipe system, valve operation and movement of water through the piping introduce additional delay after a sprinkler opens. Fleming separates this water-delivery time into trip and transit components. These delays do not become part of RTI merely because they influence the eventual application of water.<ref name="F-85" />

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2026-11-02T16:06:18Z

Add 3 watermarked SVG illustrations from the Advanced visual plan

← Older revision		Revision as of 17:06, 2 November 2026
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	The basic heat balance compares convective heat input with energy stored in the sensing element. Increasing the element's mass or heat capacity increases the energy required for a given temperature rise. Increasing exposed area or the heat-transfer coefficient increases the rate at which that energy can enter. The thermal time constant combines these influences into one quantity for the assumed exposure.<ref name="S-5">Schifiliti et al. (2002), p. 4-5.</ref>		The basic heat balance compares convective heat input with energy stored in the sensing element. Increasing the element's mass or heat capacity increases the energy required for a given temperature rise. Increasing exposed area or the heat-transfer coefficient increases the rate at which that energy can enter. The thermal time constant combines these influences into one quantity for the assumed exposure.<ref name="S-5">Schifiliti et al. (2002), p. 4-5.</ref>
			[[File:fse-response-time-index-v1.svg\|thumb\|upright=1.5\|alt=Hot gas flows over a sensing element while arrows distinguish convective heating from heat lost to its mounting.\|RTI relates convective exposure to the heating response of a sensing element. Based on Schifiliti et al. (2002), pp. 4-5–4-6.]]

	<div class="fse-equation">τ = mc / (hA);   RTI = τ√u</div>		<div class="fse-equation">τ = mc / (hA);   RTI = τ√u</div>
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	Doubling RTI to 100 (m·s)<sup>1/2</sup>, with every other input unchanged, doubles the calculated time to approximately 46.1 s. Alternatively, retaining RTI at 50 while increasing gas speed to 4 m/s halves the time to approximately 11.5 s. The square root of speed explains why a fourfold velocity increase produces a twofold change in this particular response calculation.<ref name="S-5-6" />		Doubling RTI to 100 (m·s)<sup>1/2</sup>, with every other input unchanged, doubles the calculated time to approximately 46.1 s. Alternatively, retaining RTI at 50 while increasing gas speed to 4 m/s halves the time to approximately 11.5 s. The square root of speed explains why a fourfold velocity increase produces a twofold change in this particular response calculation.<ref name="S-5-6" />
			[[File:fse-response-time-index-v2.svg\|thumb\|upright=1.5\|alt=Three exponential temperature curves cross 68 °C after about 11.5, 23.0 and 46.1 seconds.\|Illustrative RTI responses to a constant 150 °C gas stream. Based on Schifiliti et al. (2002), p. 4-6, Equations 11–15; article calculation.]]

	The comparison isolates thermal sensitivity because the exposure remains fixed. It does not say that a real sprinkler with half the RTI always operates in half the time after ignition. In a growing fire, the earlier and later devices encounter different portions of the changing gas history. The response equation must then be integrated over that history.<ref name="S-8-9">Schifiliti et al. (2002), pp. 4-8–4-9.</ref>		The comparison isolates thermal sensitivity because the exposure remains fixed. It does not say that a real sprinkler with half the RTI always operates in half the time after ignition. In a growing fire, the earlier and later devices encounter different portions of the changing gas history. The response equation must then be integrated over that history.<ref name="S-8-9">Schifiliti et al. (2002), pp. 4-8–4-9.</ref>
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	Operation of a thermal element is also distinct from water arrival. In a dry pipe system, valve operation and movement of water through the piping introduce additional delay after a sprinkler opens. Fleming separates this water-delivery time into trip and transit components. These delays do not become part of RTI merely because they influence the eventual application of water.<ref name="F-85" />		Operation of a thermal element is also distinct from water arrival. In a dry pipe system, valve operation and movement of water through the piping introduce additional delay after a sprinkler opens. Fleming separates this water-delivery time into trip and transit components. These delays do not become part of RTI merely because they influence the eventual application of water.<ref name="F-85" />
			[[File:fse-response-time-index-v3.svg\|thumb\|upright=1.5\|alt=An unscaled timeline separates heating to operation from dry-valve trip and water transit.\|RTI governs thermal response, while dry pipe water delivery introduces additional delays. Based on Fleming (2002), p. 4-85; Schifiliti et al. (2002), pp. 4-6–4-7.]]

	An RTI result is most useful when the analysis states the operating temperature, local exposure model and included heat-transfer mechanisms. Sensitivity to uncertain gas conditions can then be examined alongside sensitivity to the device parameter. Reporting excessive numerical precision would obscure uncertainties that the handbook identifies in activation temperature, ambient conditions and ceiling-jet predictions.<ref name="S-9-10" />		An RTI result is most useful when the analysis states the operating temperature, local exposure model and included heat-transfer mechanisms. Sensitivity to uncertain gas conditions can then be examined alongside sensitivity to the device parameter. Reporting excessive numerical precision would obscure uncertainties that the handbook identifies in activation temperature, ambient conditions and ceiling-jet predictions.<ref name="S-9-10" />

Peter: New FSE wiki article: Response time index (written by GPT-6)

2026-11-01T22:39:37Z

New FSE wiki article: Response time index (written by GPT-6)

New page

'''Response time index''' ('''RTI''') is a measure of the thermal sensitivity of a sprinkler or heat detector sensing element. In the conventional convective model, it equals the element's thermal time constant multiplied by the square root of the surrounding gas speed. A lower RTI produces faster heating under otherwise identical conditions. Its SI unit is (m·s)1/2.<ref name="S-5-6">Schifiliti et al. (2002), pp. 4-5–4-6.</ref>

RTI connects a measured device characteristic with a model of the local fire environment. Calculating operation also requires the gas temperature and velocity history, the initial element temperature and the operating criterion. The resulting time belongs to that combination of device and exposure. RTI itself is neither a number of seconds nor the temperature at which the element operates.<ref name="S-6-7">Schifiliti et al. (2002), pp. 4-6–4-7.</ref><ref name="I-3">Australian Building Codes Board et al. (2005), p. 2.7-3.</ref>

The usual model treats the element as a small body with one representative temperature. More detailed treatments can account for heat conducted into the sprinkler mounting and cooling by discharged water. The usefulness of an RTI calculation consequently depends on both the thermal model and the accuracy of the gas conditions supplied to it.<ref name="S-6">Schifiliti et al. (2002), p. 4-6.</ref><ref name="FDS-107">McGrattan et al. (2026), p. 107.</ref>

== Physical meaning of thermal sensitivity ==

An automatic [[Sprinkler head|sprinkler head]] combines a heat-sensitive operating mechanism with a water-discharge function. RTI characterises the heating response of that mechanism. It does not describe the amount of water passing through an opened sprinkler or the distribution of its spray. Those functions require additional hydraulic and discharge information.<ref name="F-85">Fleming (2002), p. 4-85.</ref><ref name="F-75">Fleming (2002), p. 4-75.</ref>

The basic heat balance compares convective heat input with energy stored in the sensing element. Increasing the element's mass or heat capacity increases the energy required for a given temperature rise. Increasing exposed area or the heat-transfer coefficient increases the rate at which that energy can enter. The thermal time constant combines these influences into one quantity for the assumed exposure.<ref name="S-5">Schifiliti et al. (2002), p. 4-5.</ref>

<div class="fse-equation">τ = mc / (hA);   RTI = τ√u</div>

{| class="wikitable"
! Symbol !! Meaning !! SI unit
|-
| τ || Thermal time constant at gas speed u || s
|-
| m || Effective mass of the heated element || kg
|-
| c || Specific heat of the element || J/(kg·K)
|-
| h || Convective heat-transfer coefficient || W/(m²·K)
|-
| A || Effective area exposed to convective heating || m²
|-
| u || Gas speed at the element || m/s
|-
| RTI || Response time index || (m·s)1/2
|}

The characteristic time changes with gas speed because convective heat transfer changes. With RTI held constant, the expression gives τ = RTI/√u. Faster gas flow therefore produces a smaller time constant in this model. RTI is used to transfer information between different flow conditions without assigning a new time constant at every velocity.<ref name="S-5-6" />

That transfer is approximate. Real elements have complex shapes, and their heat transfer does not follow an exact square-root relationship across every flow regime. The handbook discusses variation with Reynolds number and differences observed during testing. A quoted RTI should therefore be understood as an experimentally based model parameter with an applicable range.<ref name="S-6" />

== Measuring RTI in a plunge test ==

In a plunge test, the sprinkler or detector is suddenly introduced into a stream of hot gas. Gas temperature and velocity are known and remain approximately constant during the exposure. The elapsed time to operation is measured. The convective response equation can then be rearranged to determine the RTI associated with that test.<ref name="S-6" />

The test also requires the initial temperature and the temperature associated with operation. If these quantities are omitted, a measured response time cannot uniquely determine RTI. A short time in a very hot, fast stream is not directly comparable with the same time in a cooler, slower stream. The calculation separates those exposure conditions from the inferred sensitivity.<ref name="S-6" />

The test arrangement can affect how well the result transfers to a fire environment. The handbook notes that high test velocities can make conductive heat loss relatively small compared with convective heating. At a different velocity, heat conducted into the mounting may have greater influence. An RTI derived under one condition does not establish that neglected heat losses remain negligible elsewhere.<ref name="S-6" />

Device geometry can also direct gas towards or away from the sensing element. Orientation and nearby mounting components therefore matter when relating a laboratory result to installation conditions. Fleming identifies sprinkler orientation, flow deflection, frame conduction and position below the ceiling among the influences on predicted response. An appropriate device input cannot compensate for an incorrectly represented local environment.<ref name="S-6" /><ref name="F-85" />

The inverse calculation also provides a useful interpretation of the measurement. For a specified test stream, the logarithmic temperature ratio converts the measured operating time into a thermal time constant. Multiplication by the square root of test velocity then gives RTI. A reported result should retain the temperature and velocity conditions so that the inferred parameter can be interpreted correctly.<ref name="S-6" />

Repeating a test at different velocities can reveal whether one RTI adequately describes the observed response. The handbook discusses measurements showing variation and considers reporting more than one time constant. Such variation need not mean that a stopwatch measurement was wrong. It can indicate that a single simplified heat-transfer parameter does not capture the device equally well across the tested conditions.<ref name="S-6" />

== Convective response and operating temperature ==

For a [[Heat detector|heat detector]] or sprinkler represented by a single thermal mass, the simplest response equation is:<ref name="S-6" /><ref name="I-3" />

<div class="fse-equation">dTl/dt = (√u / RTI)(Tg − Tl)</div>

{| class="wikitable"
! Symbol !! Meaning !! Unit
|-
| Tl || Temperature of the link or sensing element || °C
|-
| Tg || Local gas temperature || °C
|-
| t || Time after the specified exposure begins || s
|-
| u || Local gas speed || m/s
|-
| RTI || Response time index || (m·s)1/2
|}

The temperature difference drives heating, while RTI and gas speed determine the rate of response. If the element and gas have the same temperature, this model predicts no net convective heating. When the gas becomes hotter, the element approaches the gas temperature progressively. It does not instantaneously acquire the temperature predicted by a fire model.<ref name="S-5-6" />

For a fixed-temperature device, [[Detector activation time|detector activation time]] is found when the calculated element temperature reaches the operating temperature. RTI and operating temperature are separate inputs to that calculation. Changing either can alter the result, but they do so in different ways. A lower operating temperature changes the threshold; a lower RTI changes the speed of heating towards it.<ref name="S-6-7" />

This interpretation does not transfer unchanged to every heat detector mechanism. Rate-of-rise devices can depend on air expansion within a chamber, while rate-compensated devices involve differential heating of several components. The handbook explains why a single lumped element may not represent those mechanisms adequately. Their operation requires a model appropriate to the device rather than an assumed universal RTI threshold.<ref name="S-7">Schifiliti et al. (2002), p. 4-7.</ref>

== Worked example under constant conditions ==

If gas temperature and velocity remain constant, the convective equation has an exponential solution. Let the element initially be at the ambient temperature Ta. For an operating temperature Tr between Ta and Tg, rearrangement gives the following response time.<ref name="S-6" />

<div class="fse-equation">Tl(t) = Ta + (Tg − Ta)[1 − exp(−t√u / RTI)]</div>
<div class="fse-equation">tr = (RTI / √u) ln[(Tg − Ta) / (Tg − Tr)]</div>

Here Ta is the initial element temperature, Tr is the operating temperature and tr is the calculated response time in seconds. The logarithm uses a dimensionless ratio of temperature differences. The stated condition Tg > Tr > Ta ensures a finite positive heating time in this example.<ref name="S-6" />

Consider hypothetical gas at 150 °C moving at 1 m/s, with the element initially at 20 °C and operating at 68 °C. For RTI = 50 (m·s)1/2, the time constant is 50 s. Substitution gives approximately 23.0 s to operation. These are illustrative inputs selected to demonstrate the equation, rather than the declared characteristics of a particular product.<ref name="S-6" />

Doubling RTI to 100 (m·s)1/2, with every other input unchanged, doubles the calculated time to approximately 46.1 s. Alternatively, retaining RTI at 50 while increasing gas speed to 4 m/s halves the time to approximately 11.5 s. The square root of speed explains why a fourfold velocity increase produces a twofold change in this particular response calculation.<ref name="S-5-6" />

The comparison isolates thermal sensitivity because the exposure remains fixed. It does not say that a real sprinkler with half the RTI always operates in half the time after ignition. In a growing fire, the earlier and later devices encounter different portions of the changing gas history. The response equation must then be integrated over that history.<ref name="S-8-9">Schifiliti et al. (2002), pp. 4-8–4-9.</ref>

The time origin also matters. The example begins when the constant hot stream reaches the element. It includes neither the time for a fire to develop nor the transport time before hot gases arrive. Treating its 23.0 s result as a prediction from ignition would therefore introduce a delay assumption absent from the calculation.<ref name="S-8-9" />

The logarithmic expression also shows why the temperature margin above the operating threshold matters. As the constant gas temperature approaches the operating temperature from above, the predicted heating time increases strongly. If the gas remains below the required operating temperature, the convection-only model cannot heat an initially cooler element to that threshold. A low RTI does not remove this limit.<ref name="S-6" />

The constant-exposure solution provides a check on a numerical implementation. With the same fixed inputs, numerical integration should approach the exponential temperature history as numerical error decreases. Agreement checks the calculation under those assumptions. It does not validate the assumed gas conditions or establish that conduction and radiation are negligible in a particular installation.<ref name="S-6" /><ref name="S-8-9" />

== Obtaining the local fire environment ==

A fire plume and [[Ceiling jet|ceiling jet]] transport heat towards a ceiling-mounted device. Predicting the element response requires conditions at that device, rather than only the fire's total heat release rate. Ceiling height, radial position and the fire's development influence the local temperature and velocity. These environmental inputs are independent of the device RTI.<ref name="S-7" /><ref name="I-3" />

The [[Alpert correlations|Alpert correlations]] provide one approach to estimating ceiling-jet conditions under their assumptions. The handbook describes a quasi-steady method that divides a changing fire into short intervals. Within each interval, gas conditions are calculated and the element temperature is advanced from its previous value. The thermal history is therefore carried forward rather than restarted at ambient temperature.<ref name="S-8-9" />

A small numerical time step cannot correct an unsuitable environmental model. The handbook discusses errors associated with ignoring gas transport and treating the ceiling as effectively unbounded. Walls and an accumulated hot layer can alter the conditions surrounding a detector. Position below the ceiling also matters because a sensing element may lie outside the region represented by a correlation.<ref name="S-7" /><ref name="S-9-10">Schifiliti et al. (2002), pp. 4-9–4-10.</ref>

The supplied CFAST technical guide illustrates another implementation. It obtains device conditions from plume, ceiling-jet or compartment-layer calculations according to location. For some locations it uses an estimated gas speed. Thus, even when two models contain the same RTI response equation, different representations of local gas conditions can give different operating times.<ref name="CFAST-35">Peacock et al. (2026), p. 35.</ref>

== Heat losses and interaction with water ==

Heat conducted from the element into its mounting can delay its temperature rise. The supplied FDS technical guide represents this influence with an experimentally determined conduction parameter, usually called the C-factor. RTI describes the convective sensitivity, while the C-factor describes a separate heat-loss pathway. Setting the latter to zero is a modelling choice with a physical consequence.<ref name="FDS-107" />

The same FDS formulation includes an empirical term for cooling by water droplets from previously operating sprinklers. This recognises that operation of one sprinkler can change the exposure of another sensing element. The handbook also cautions that activation calculations omitting spray cooling can misrepresent subsequent sprinkler operation. A first-operation calculation and a sequence of operating sprinklers therefore require different consideration of their surroundings.<ref name="FDS-107" /><ref name="S-7" />

Radiation is another distinct heat-transfer mechanism. The simple handbook treatment neglects it when convective heating dominates the early fire conditions being considered. The supplied FDS guide states that its sprinkler and heat-detector activation models do not account for thermal radiation. Model output consequently remains subject to that limitation even when a detailed gas-flow calculation supplies the temperature and velocity.<ref name="S-5" /><ref name="FDS-107" />

== Interpretation in sprinkler design ==

Fast thermal response is one feature of an [[ESFR sprinkler|ESFR sprinkler]], but it does not establish the complete suppression performance of that sprinkler. NUREG-1805 also identifies droplet size and discharge velocity, together with strict design and installation requirements. A suitable RTI value cannot replace evidence that the sprinkler and its water supply suit the protected hazard.<ref name="N-10-3">Iqbal and Salley (2004), p. 10-3.</ref>

Operation of a thermal element is also distinct from water arrival. In a dry pipe system, valve operation and movement of water through the piping introduce additional delay after a sprinkler opens. Fleming separates this water-delivery time into trip and transit components. These delays do not become part of RTI merely because they influence the eventual application of water.<ref name="F-85" />

An RTI result is most useful when the analysis states the operating temperature, local exposure model and included heat-transfer mechanisms. Sensitivity to uncertain gas conditions can then be examined alongside sensitivity to the device parameter. Reporting excessive numerical precision would obscure uncertainties that the handbook identifies in activation temperature, ambient conditions and ceiling-jet predictions.<ref name="S-9-10" />

The overall response objective can extend beyond operation of the device. The detection-system chapter separates detection, signal processing and subsequent actions needed to meet a safety objective. An RTI calculation addresses only the thermal part of that sequence. This separation preserves the distinction between device sensitivity and complete system response. Any assumed processing or response delay must be accounted for separately when comparing a predicted operation time with the required outcome.<ref name="S-2-3">Schifiliti et al. (2002), pp. 4-2–4-3.</ref>

== See also ==
* [[Sprinkler skipping]]

== Notes ==
<references />

== References ==
* Australian Building Codes Board, National Research Council of Canada, International Code Council, & Department of Building and Housing. (2005). ''International fire engineering guidelines''.
* Fleming, R. P. (2002). Automatic sprinkler system calculations. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., Chapter 4-3, pp. 4-72–4-87). National Fire Protection Association.
* 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.
* McGrattan, K., Hostikka, S., Floyd, J., McDermott, R., Vanella, M., Mueller, E., & Paul, C. (2026). ''Fire Dynamics Simulator technical reference guide: Volume 1, Mathematical model'' (6th ed., NIST SP 1018-1; supplied revision FDS-6.11.1). National Institute of Standards and Technology.
* Peacock, R. D., McGrattan, K. B., Forney, G. P., & Reneke, P. A. (2026). ''CFAST: Consolidated Fire and Smoke Transport (Version 7), Volume 1: Technical reference guide'' (NIST TN 1889v1; supplied revision CFAST-7.7.7). National Institute of Standards and Technology.
* Schifiliti, R. P., Meacham, B. J., & Custer, R. L. P. (2002). Design of detection systems. In P. J. DiNenno (Ed.), ''SFPE handbook of fire protection engineering'' (3rd ed., Chapter 4-1). National Fire Protection Association.

[[Category:Fire Suppression]]