Self defense sprinklers have been fitted on an individual basis to a
number of bushfire appliances. System designs vary greatly, with
outputs varying from as little as 15 litres per minute to over 1000
litres per minute. The following discussion uses known values for the
physical properties of water and *assumed values* for the
efficiency of present sprinkler systems in an attempt to calculate,
from first principles, the amount of water required to protect a
typical Australian heavy bushfire tanker from a typical burnover.

Given that the Specific Heat Capacity of 1 kg of water = 4.18kJ ^{
(5)}, it follows that the heating of 1kg (hereafter regarded as 1
litre) of water by one degree Kelvin (hereafter regarded as 1 degree
C) will absorb 4.18 kJ. If it is assumed that a sprinkler system
delivers water at 20 degrees C, it then follows that heating each
litre of water delivered to 100 degrees C will absorb (80 x 4.18kJ) =
335kJ. But conversion of water at 100 degrees C to steam at 100
degrees C involves a change of state and absorbs a much greater amount
of energy, some 2.26MJ per litre ^{(5)}. It follows then, that
each litre of water which is delivered at 20 degrees C, and then
converted to steam at 100 degrees C, will absorb a total of (2.26 +
0.335) = 2.6MJ of energy.

*Hence, each litre of water which is delivered by a defensive
sprinkler system, and subsequently converted to steam, will absorb
2.6MJ of energy.*

Whilst fire intensity is traditionally expressed in terms of kW per
linear metre of the fire edge, it may be more helpful to know the
radiant heat loading impinging on each square metre of the fire
appliance which is exposed to the fire. Mangan ^{(6)} reported
heat fluxes of 15-70 kW/m2 in 2 moderately severe experimental
grassfires of around 2500kW/m. He similarly recorded fluxes of 130-160
kW/m2 in a more intense pine forest burn. Cheney ^{(7)}
reported that experimental loads of 40 kW/m2 ignited vehicle door
liners within 4 minutes, and that flame envelopment could involve heat
fluxes exceeding 100kW/m2. Examination of the video records of the
above experimental burnovers, and of the real life burnover of the
Bridgewater Tanker at Longwood in 1980 showed that each involved a
period of 15-30 seconds of direct flame contact, preceded by a period
of radiant heat exposure.

Suppose, then, that we desire to protect the 7 x 3 m side of a typical Australian heavy bushfire tanker from a hypothetical severe grassfire burnover involving 30 seconds of radiant heat exposure at 50 kW/m2 followed by 30 seconds of direct flame contact at 100kW/m2, We can calculate that the radiant heat exposure will involve a heat loading of (50 x 7 x 3) = 1050kW for 30 seconds. The period of direct flame contact will then involve a further loading of (100 x 7 x 3) = 2100kW for another 30 seconds.

But 1 watt = 1 Joule/second, so 1050 kW = 1050 kJ per second, which = 1.05 MJ/sec and is sufficient to convert (1.05/2.6) = 0.4 litres of water into steam per second. Hence, absorbing all of the energy of the above 30 second radiant heat exposure will require the vaporisation of 0.4 litres of water per second, or approximately 25 litres per minute (lpm).

It should be realised, however, that no sprinkler system will be
100% efficient. Indeed, if we assume that the system projects 40%
of its output to each side of the vehicle, and only 10% to the
front and the rear, then a typical burnover from the side will
result in only 40% of the sprinkler output being directed in the
direction of the threat. If we also assume that, of that 40%, 1/3
falls to the ground, 1/3 is blown away and only the final 1/3 is
actually available to absorb heat energy, we can calculate that the
efficiency of a sprinkler system can scarcely exceed 10%. If we
accept that the sprinkler system is 10% efficient, it follows then
that a minimum output of 250 litres per minute will be required to
absorb all of the radiant heat energy of the above severe
(2500kW/m) grassfire. By similar reasoning, protection from actual
flame immersion will require double the output, or 500 litres per
minute. Hence, if one then accepts that the typical duration of a
grassfire burnover is 1 minute ^{(7)}, it can be concluded
that, with current ‘all over’ systems:

*full sprinkler protection of a typical Australian Heavy
Bushfire Tanker from a severe grassfire burnover will require a
minimum of 500 litres of water per minute for 1 minute.*

But a typical Australian burnover takes place in on narrow track in Eucalyptus forest and is probably of greater intensity and duration than this. Hence, with current sprinkler systems:

*the water output required for full tanker protection during a
typical Australian burnover is probably twice as great, or at least
1000 litres per minute for 1-2 minutes.*

Last updated 4 November 2014