Appendix D - Bushfire Risk Assessment and Management Plan

Equation (1) and Equation (2) can be used in two different ways. Firstly, it can be used
to predict the rate of fire spread at a given time and the resultant fire run distance up to
this point of time. Secondly, they can be used to estimate the maximum rate of fire
spread which can be reached for a given fire run distance. As shown in Equation (1)
and (2), the use of them requires the constant a. This constant value depends on the
time which a fire requires to develop to a quasi-steady state. The required time for a
point ignition fire under fairly stable fuel moisture and wind conditions is in 20 – 30
minutes (Luke and McArthur 1978). According to Cheney and Gould (1997), the more
frequently the direction of wind switches the shorter a fire will take to reach its quasi-
steady state. With respect to the magnitude of wind, the opposite is true. In addition,
fire intensity also influences how soon a fire can reach its quasi-steady state. Low
intensity fires tend to reach its quasi-steady state faster than high intensity fires
(McAlpine and Wakimoto 1991). Cheney and Gould (1995) found that low intensity
grass and woodland fires lit from point sources reached their maximum rate of spread
in 5-10 minutes while medium to high intensity fires in winds above 4m/s took 12 -45
minutes. In some circumstances, it may take many hours for high intensity forest fires
to reach a quasi-steady state.
Considering the time which a fire reaches a quasi-steady state is highly variable, the
value of constant a in Equation (1) and (2) also varies within a certain range. In order to
obtain meaningful predictions with these equations, a proper value of constant a needs
to be used according to the expected fire scenarios such as fast growth fires, medium
fast growth fires and slow growth fires. If the times for fast growth fires, medium fast
growth fires and slow growth fires develop to 90% of their quasi-steady rate of spread
are assumed to be 10 minutes, 30 minutes and 60 minutes respectively, then the
corresponding values of constant a can be determined by using Equation (1) being
1.05, 3.16 and 6.32 respectively. Therefore, the variants of Equations (1) and (2) for
the three different fire scenarios are:
(1) Fast growth fires
   R = Rss e-1.05/t                                                       ……(3)
              t
            e
                          -1.05/t
   S=Rss                            dt                                     ……(4)
            0

(2) Medium fast growth fires
      R = Rss e-3.16/t                                                    ……(5)
                      t
                   e
                              -3.16/t
      S=Rss                              dt                                ……(6)
                  0

(3) Slow growth fires
    R = Rss e-6.32/t                                                      ……(7)
                  t
                 e
                             - 6.32/t
    S = Rss                              dt                                ……(8)
                  0

The relative rate of spread for a given time for a given fire scenario can then be directly
predicted by utilising the analytical equations or the graphic forms of these equations
shown in Figure 1. For instance, the relative rate of spread at time = 30 minutes for
fast, medium and slow growth fires are determined to be 0.96, 0.90 and 0.81
respectively in accordance with Figure 1.