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Contents
  1. 1What hand calculations are
  2. 2Common fire calculations
  3. 3Example: flame height
  4. 4Example: evacuation time
  5. 5Use in design and regulation
  6. 6Accuracy and limits
  7. 7See also
  8. 8Notes
  9. 9References

Hand calculations in fire safety engineering are simple calculation models in which a few formulas give an estimate of a fire effect or an evacuation time. The work can be done literally by hand, in a spreadsheet or with a modest computer application.[1] Typical examples are the height of a flame, the temperature of a smoke layer, the response time of a detector and the time needed to evacuate a room.[2][3] They form the simplest level of fire modelling, below the zone model and computational fluid dynamics.[4]

Hand calculations give quick insight and can be used to check a more complex calculation with many variables.[3] They rest on correlations that were mostly derived from experiments, so each one is valid only within the conditions of those experiments.[5] Walton notes that manual methods give good estimates of specific effects, such as the time to flashover. They are, however, poorly suited to analyses in which many processes interact over time.[6] A well-known example is Heskestad's flame height correlation. It predicts a mean flame height of about 4.2 m for a stack of wood pallets burning at 2.6 MW.[7]

What hand calculations are

Introduction to Fire Safety Engineering distinguishes three forms of model: real tests, simple calculation models and complex computer simulations. The simple models are those in which a hand calculation can be made with a few formulas.[1] The International Fire Engineering Guidelines (IFEG, 2005) list "formulas, equations and hand calculations" as the first of several forms of analysis. The others include spreadsheet calculations, statistical studies and experiments with physical scale models.[8]

Most hand calculations are closed-form algebraic expressions. They give a result directly from the inputs, without step-by-step numerical solution.[9] The US Nuclear Regulatory Commission (NRC) describes its library of such methods as "first-order" methods. These include traditional approaches, correlations, closed-form approximations, exact solutions and hazard models.[10] Many of the correlations come from the SFPE Handbook of Fire Protection Engineering and the NFPA Fire Protection Handbook.[2]

Spreadsheets make such calculations faster and reduce errors. In the NRC spreadsheets, users enter data in marked input cells, and they can pick a material from a list so that its properties are filled in automatically. This avoids errors in typing property values by hand.[10] Each spreadsheet shows the calculation step by step, so that the user can follow the method.[10]

A hand calculation is only as good as its input data. The NRC tools, for example, need thermal properties of walls and ceilings, such as thermal inertia, conductivity, specific heat and density. They also need fuel properties, such as the mass burning rate and the effective heat of combustion, and target properties, such as the ignition temperature and the critical heat flux for ignition.[11] For this reason, each spreadsheet contains a table of properties of materials commonly found in nuclear power plants.[2]

The term covers both fire and people. On the fire side, the IFEG name hand calculations for smoke layer height, smoke production and the response time of heat detectors.[12][13] On the people side, Introduction to Fire Safety Engineering gives an eight-step hand calculation of evacuation time.[3] The Australian FSVM handbook notes that evacuation models can be either simple hand calculations or more advanced simulation software.[14]

Common fire calculations

The library of Fire Dynamics Tools (FDTs) published by the NRC in 2004 shows the range of fire hand calculations. It was written for inspectors of nuclear power plants, and its chapters cover the main topics.[15] These include the hot gas layer temperature and smoke layer height in a room, the burning of liquid pool fires and flame heights. Further chapters treat radiant heat flux and ignition of a target, plume temperature, sprinkler and detector response, flashover and the fire resistance of steel members.[15] The spreadsheets need only a working knowledge of algebra.[16]

Several hand calculations have their own articles in this wiki. The Heskestad plume correlations come from the SFPE Handbook chapter on fire plumes, flame height and air entrainment, and include the flame height formula shown below.[17] The Alpert correlations underlie hand calculations of the time at which heat detectors respond.[13] The MQH correlation, named after McCaffrey, Quintiere and Harkleroad, approximates the temperature of the hot upper layer in a room from an energy balance and a fit to test data.[18] Walton and Thomas collect such simplified techniques because compartment temperatures are used to predict the onset of hazardous conditions, damage, ignition of objects and flashover.[19]

Walton and Thomas also explain why such methods exist. The energy equations of a room fire have no general explicit solution, so they are either solved approximately by hand, using a limiting set of assumptions, or more completely by a computer program.[18] Their hand methods predict average temperatures. They should not be used for local temperatures, such as at a detector or sprinkler or where flames touch a surface.[18]

Introduction to Fire Safety Engineering uses hand calculations throughout. Its heat transfer chapter assumes steady conditions, because changes over time are very hard to include in a hand calculation. The results are therefore mainly suited to finding the order of magnitude of a heat flow.[20] Visibility in smoke can be predicted reasonably well with CFD, and to a lesser extent with hand calculations and zone models.[21] For large malls and atria without smoke venting, the IFEG point to simple empirical correlations for the height of the smoke layer as it descends over time, for a given heat release rate.[12]

Example: flame height

Heskestad's correlation for the mean height of a flame shows how a hand calculation works. The flame height grows with the heat release rate of the fire, but a wider fire has a relatively lower flame. In its simplest form, for normal atmospheric conditions, the correlation reads:[17]

L=0.235Q˙2/5−1.02D

Symbol Description Unit
L mean flame height above the base of the fire m
Q˙ total heat release rate of the fire kW
D diameter of the fire, or the diameter of a circle with the same area m

For a small heat release rate, the formula gives a negative flame height. This is physically impossible, so the correlation is not valid there.[17] The coefficient 0.235 is a typical value. For many gaseous and liquid fuels it lies between 0.226 and 0.240, but it is lower for some fuels, such as 0.200 for gasoline.[17]

The coefficient also depends on the state of the air. Heskestad shows this with a methyl alcohol pool fire 1.5 m across. Its mean flame height rises from 1.83 m under normal conditions to 2.23 m on a hot day at high altitude.[7]

Worked example. Heskestad gives the example of a 1.2 m high stack of wood pallets, 1.07 m by 1.07 m, burning at 2,600 kW.[7] A circle with the same area has a diameter of 1.21 m. The flame height is then 0.235 × 26000.4 − 1.02 × 1.21 = 4.22 m above the base of the stack.[7][22]

The flame is thus about 3.5 times as high as the fire is wide.[22] In Introduction to Fire Safety Engineering, the same comparison of flame length and fire diameter decides which plume model is more reliable. When the flame is longer than the diameter, the Heskestad plume model applies; when it is shorter, the Thomas plume model is preferred.[23]

Example: evacuation time

Introduction to Fire Safety Engineering sets out a hand calculation of evacuation time in eight steps.[3] The steps are: count the people per room, find the flow capacity of each door or stair, and divide the people over the exits. Next, find the governing exit and the walking time of the first person to it. Then add the time for everyone to pass that exit and the walking time of the last person to a safe place.[3] The method assumes a homogeneous group of people and a simple geometry.[3]

In the book's example, 300 people are divided equally over four stairs, two of 2.4 m and two of 1.6 m width. The narrower stairs, with a capacity of 1.2 persons per second each, govern.[3] The first person walks 5 m at 1 m/s, the 75 people assigned to a narrow stair need 63 s to pass, and the last person walks a further 10 m.

The total is 5 + 63 + 10 = 78 s.[3] The book notes that even an equal division over the exits is a very optimistic assumption, because it is not known which exits people will actually choose.[3] Methods that treat people as a flow through doors and stairs in this way are known as hydraulic flow models; the IFEG describe them by the relation flow = speed × density × width.[24] The hydraulic evacuation model article describes this approach in more detail.

Use in design and regulation

Hand calculations are accepted in several regulatory frameworks, usually as one option among others. In Australia, the FSVM handbook asks the design team to agree, as part of the performance-based design brief, whether hand calculations, zone models or CFD models will be used. The choice is made for each enclosure where the time to untenable conditions must be found.[4] In New Zealand, C/VM2 (second edition, 2025) prescribes simple equations for travel time and door flow, which are themselves hand calculations.[25] It adds that it does not give a complete guide to egress analysis.[25]

Hand calculations also serve as a check on complex models. Introduction to Fire Safety Engineering notes that a simple approach can act as a check on a more complex one.[3] In the NIST investigation of the World Trade Center towers, the structural computer models were checked against hand calculations for typical floor sections. The steel stresses agreed within 4 % for the long-span trusses and 3 % for the short-span trusses. Deflections agreed within 5 to 15 %.[26]

In the same investigation, the failure loads of floor components, such as truss seats and shear connectors, were found either by hand calculations or by finite element analyses. Simplified models built on these results were then placed in the model of the whole floor.[27] Agreement between methods still has limits. Walton notes that similar results from several models increase confidence but do not guarantee accuracy, because the models may share the same basic assumptions.[28]

There are limits to this use. For complex buildings with large populations, the FSVM data sheets consider hand calculations of evacuation impractical, so computer models are needed. These may simply be automated hand calculations.[29] The IFEG note that hand calculations of smoke spread beyond the room of fire origin are more difficult and are rarely used. Their results also carry greater uncertainty.[30]

Accuracy and limits

The NRC verified and validated its library of hand calculations against experiments as part of the NUREG-1824 study.[31] The study found that the libraries of engineering calculations had limited capabilities for the scenarios tested and lacked methods for many of the quantities of interest.[5] The correlations they do contain are based on conservation laws and widely accepted in fire protection engineering. Because they are empirical, they are subject to many limiting assumptions, and users must be cautious.[5] In the same study, the two-zone models and the CFD model reproduced most measured quantities within the experimental uncertainty.[5] The verification work also identified a number of corrections to the five models studied, ranging from inconsequential changes to errors that could lead to incorrect results.[5]

The FDT spreadsheets need little or no computing time and give first-order results, either as a single value or as a series of values with a plot.[11] Validation for one application does not mean validation for a different scenario.[31] Iqbal and Salley therefore stress that the tools must be applied within the limits of their validity.[10]

Precision is easily overstated. Iqbal and Salley advise users to focus on the magnitude of a result rather than its decimals. A component that is damaged at 700 °F (371 °C) is likely to be damaged at a calculated 699.99 °F as well.[32] They encourage bounding calculations, for example with doors open and closed or ventilation on and off, to find the range of credible results.[32] The IFEG ask for similar sensitivity studies, such as repeating a calculation with a fire that grows several times faster or with significantly lower walking speeds.[33]

Introduction to Fire Safety Engineering gives similar advice on rounding. Only the final result should be rounded, inputs such as fire loads and walking speeds are often uncertain by tens of per cent, and two or at most three significant figures are realistic.[34] When results are compared with limits, required times are rounded up and available times down.[34]

See also

Notes

  1. ↑ 1.0 1.1 Van Rossum (2027), §8.2.
  2. ↑ 2.0 2.1 2.2 Iqbal and Salley (2004), p. iii.
  3. ↑ 3.00 3.01 3.02 3.03 3.04 3.05 3.06 3.07 3.08 3.09 Van Rossum (2027), §7.5.
  4. ↑ 4.0 4.1 Australian Building Codes Board (2020b), p. 21.
  5. ↑ 5.0 5.1 5.2 5.3 5.4 Najafi et al. (2007), p. 3-4.
  6. ↑ Walton (2002), p. 3-189.
  7. ↑ 7.0 7.1 7.2 7.3 Heskestad (2002), p. 2-4.
  8. ↑ National Research Council of Canada et al. (2005), p. 1.2-23.
  9. ↑ Najafi et al. (2007), p. 2-13.
  10. ↑ 10.0 10.1 10.2 10.3 Iqbal and Salley (2004), p. xxxix.
  11. ↑ 11.0 11.1 Dreisbach and Hill (2007), p. 2-2.
  12. ↑ 12.0 12.1 National Research Council of Canada et al. (2005), p. 2.5-4.
  13. ↑ 13.0 13.1 National Research Council of Canada et al. (2005), p. 2.7-2.
  14. ↑ Australian Building Codes Board (2020b), p. 109.
  15. ↑ 15.0 15.1 Iqbal and Salley (2004), pp. v–viii.
  16. ↑ Iqbal and Salley (2004), p. xxxvii.
  17. ↑ 17.0 17.1 17.2 17.3 Heskestad (2002), p. 2-3.
  18. ↑ 18.0 18.1 18.2 Walton and Thomas (2002), p. 3-175.
  19. ↑ Walton and Thomas (2002), p. 3-171.
  20. ↑ Van Rossum (2027), §5.1.
  21. ↑ Van Rossum (2027), §6.1.
  22. ↑ 22.0 22.1 Heskestad (2002), p. 2-4; recalculated with Equation 8 on p. 2-3.
  23. ↑ Van Rossum (2027), §6.7.
  24. ↑ National Research Council of Canada et al. (2005), p. 2.8-3.
  25. ↑ 25.0 25.1 Ministry of Business, Innovation and Employment (2025b), pp. 32–33.
  26. ↑ Faschan and Garlock (2005), p. 53.
  27. ↑ Gross and McAllister (2005), p. 66.
  28. ↑ Walton (2002), p. 3-190.
  29. ↑ Australian Building Codes Board (2020a), p. 283.
  30. ↑ National Research Council of Canada et al. (2005), p. 2.5-6.
  31. ↑ 31.0 31.1 Dreisbach and Hill (2007), p. 1-2.
  32. ↑ 32.0 32.1 Iqbal and Salley (2004), p. xl.
  33. ↑ National Research Council of Canada et al. (2005), p. 1.2-24.
  34. ↑ 34.0 34.1 Van Rossum (2027), §1.7.

References

  • Australian Building Codes Board. (2020a). Data sheets: Fire Safety Verification Method (Handbook annex, Print version 1.1).
  • Australian Building Codes Board. (2020b). Handbook: Fire Safety Verification Method (Print version 1.1).
  • Dreisbach, J., & Hill, K. (2007). Verification and validation of selected fire models for nuclear power plant applications: Vol. 3. Fire Dynamics Tools (FDTs) (NUREG-1824; EPRI 1011999). U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research; Electric Power Research Institute.
  • Faschan, W. J., & Garlock, R. B. (2005). Reference structural models and baseline performance analysis of the World Trade Center towers (NIST NCSTAR 1-2A). National Institute of Standards and Technology.
  • Gross, J. L., & McAllister, T. P. (2005). Structural fire response and probable collapse sequence of the World Trade Center towers (NIST NCSTAR 1-6). National Institute of Standards and Technology.
  • 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.
  • Ministry of Business, Innovation and Employment. (2025b). Verification Method C/VM2: Framework for fire safety design (2nd ed.).
  • Najafi, B., Joglar, F., & Dreisbach, J. (2007). Verification and validation of selected fire models for nuclear power plant applications: Vol. 1. Main report (NUREG-1824; EPRI 1011999). U.S. Nuclear Regulatory Commission, Office of Nuclear Regulatory Research; Electric Power Research Institute.
  • 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.
  • Van Rossum, E. (2027). Introduction to Fire Safety Engineering. Fire Safety Academy.
  • Walton, W. D. (2002). Zone computer fire models for enclosures. 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. 3-189–3-193). National Fire Protection Association; Society of Fire Protection Engineers.
  • Walton, W. D., & Thomas, P. H. (2002). Estimating temperatures in compartment fires. 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. 3-171–3-188). National Fire Protection Association; Society of Fire Protection Engineers.
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