Philip ClarksonThursday 4pm

Jessica Jensen-Schmidt: S00127413Scott Williams: S00071140

Country Fire Brigade

(Country Fire Authority, 2012)

The Country Fire Brigade (CFA)The Country Fire Authority (CFA) is a community-based organisation that deliver services to ensure the safest and best possible outcomes for the community (Country Fire Authority, 2012). The CFA has stations all across regional Victoria, as well some in the outer metropolitan area. The CFA serve over 3.3 million Victorians and help to protect more than one million homes and properties across the state (Country Fire Authority, 2012).

The CFA is a very large organisation, and as such they have a huge amount of equipment. Across Victoria. The CFA has and coordinates more than 1,200 community stations, – more than 2,100 tanker and pumper fire trucks – a range of all-terrain and rescue vehicles and access to aircraft – over 50,000 sets of protective clothing – over 50,000 communication tools including radios and pagers (Country Fire Authority, 2012).

CFA members respond to a wide range of emergency incidents at any time of the day or night. These incidents include bush and structure fires, road accidents, chemical spills, rescue, floods and other natural disasters (storm damage etc). CFA also work together with Victorian communities, emergency services (including Police, MFB, DEPI and SES) the Fire Services Commissioner, municipalities, and government departments to deliver these essential services. The CFA are also developing a safer community through prevention management, such as vegetation management, and also deliver community education and safety programs (Country Fire Authority, 2012).

Interviewee:

Allan Kosmer

Allan started in CFS (South Australian Fire Authority) on Kangaroo Island in 1994 when he was working in forestry department, some fires burnt for over a month when he was there.

He has been with the CFA since 1994 in several different stations, currently at Wallan. He did a course in geographic mapping systems and is one of only several qualified in the state. Allan was awarded a medal in March 2014 for his services in the black Saturday fires for over 7 days’ work in a national significant event.

Initial Thoughts

Initial Mathematical Thoughts/Ideas

• When determining the number of crews to attend a fire, consideration would have to be given to the size (area) and location of the fire. The CFA would also have to consider other factors such as, weather, wind, available units, topography, location of water sources and other craft/support available (such as helicopters).

• When finding the most efficient and effective route to a call out, there would be utilisation and consideration of the following- maps (including grid maps, road maps and topography maps), size of the vehicle, weight of the vehicles (considering its performance capabilities), weather patterns (reading isobar maps), timing, preparing staff and vehicle/s, travelling time (max average speed by distance).

• Considering the vehicle load when attending a fire- the maximum amount of water that a vehicle can carry, estimating the amount of water required, the impact on of load weight on travel time and ability to access certain areas (such as hilly or off road areas), tipping factors.

• Speed of the fire across certain terrains, that it would increase or decrease depending on the type of fuel (such as bush , grass etc), factors such as heat, wind and the incline, decline in the land, creeks and roads.

Initial Mathematical Thoughts/Ideas

• Prioritising call outs- distance from the barracks, estimation of time needed for the call out, consideration to the size and nature of the fire (speed of fire and the area that it consumes), the density of population within an area (people per square kilometer).

• Crew per call out: minimum required for safety purposes, leaving a certain number at a barracks, size and nature of the fire.

• When attending a bush fire, pre-planning regarding the distance/time from a water supply and also ensuring that there is a safe and viable exit. In this situation a number of influencing factors, such at the size of the fire, the direction that it travelling, type of fire, distances etc would all need to be mathematically considered to ensure the safety of all CFA members.

• The capacity of the truck and the hose flow rates, this would have an impact on how long the truck/unit can stay out before refilling. We then thought consideration would have to be made to the distance to a water supply and duration that it would take to refill.

Truck and Hose Capacities

Image 1: MFB Barracks (Architectus, 2012)

Duration: 3 minutes 4 seconds

Image 1: Fire Crew ‘Blacking Out’ (Sydney Morning Herald, 2014)

Mathematics Discovered

The fire truck pictured has a maximum water capacity of 3,000 litres, with an additional 750 litres in reserve. It has the capacity to pump out/dispense 900 litres of water per minute or 15 litres per second (900 litres per minute divided by 60 seconds = 15 litres per second). If this truck pumped at its maximum capacity, it would exhaust its useable water supply (3,000 litres) in 200 seconds (3,000 litres divided by 15 litres per seconds = 200 seconds) or 3 minutes 20 seconds (200 seconds divided by 60 seconds = 3 (which is minutes) with 20 left over (which is seconds).

When the CFA is ‘blacking out’ (as per the picture) they utilise a 25mm hose, which has a maximum pumping capacity of 20 litres of water per minute. A truck would be able to ‘black out’ for 2 hours 30 minutes (3,000 litres divided by 20 litres per minute = 150 minutes; 150 converted into hours is 2 hours (120 minutes) 30 minutes (taking the total to 150 minutes) before its water supply was depleted.

When actively fighting a fire, one truck would last a maximum of 30 minutes. This would mean the truck would be pumping water at a rate of 100 litres per minute (3,000 litres divided by 30 minutes = 100 litres being expelled per minute).

Refilling 3,000 litre fire truck with water from a refill site/facility takes on average about 5 minutes, which is at a rate of 600 litres per minute (3,000 litres divided by 5 minutes – 600 litres per minute).

• Volume (litres cubed)• Capacity (Litres) • Duration/time (seconds, minutes)• Rate of flow (litres per minute or litres per second)• Length and width• Statistics (average)• Comparison

Key Mathematical Concepts Identified

Refilling Trucks

Image 2: MFB Attending to a Call out in Melbourne CBD (Australian Transprot Discussion Board, n.d)

Duration: 2 minutes 18 seconds

Image 2: Fire Crew Refilling a Fire Truck from a Dam(Sydney Morning Herald, 2014)

Mathematics DiscoveredWhen the CFA is deploying crew members to a fire emergency it is critical that they consider water availability. The CFA have to consider variables, such as the quantity of water, the distance the water is from the ‘strike area’, the type of water source (i.e. dam, hydrant etc) as this effects the time it takes to refill the vehicle, planning and attack strategies.

When the CFA is pumping from a dam there are several factors that will impact on how long it will take to pump 3,000 litres (as per the capacity of the truck in the picture) in to the fire truck. A water pump has a maximum pump capacity of 900 litres per minute, however there are other variables that cause resistance.

The head (length of the hose) is a negative pressure and impacts on how long it takes to pump water from the water source in to the truck. The slope or incline of the bank also has a negative pressure and decreases the rate in which water can be pumped into the truck.

As a result of these variables, CFA crew members allow 7-8 minutes to fill up a truck (such as the one pictured) from dam. This means on average the truck is being filled at a rate of 375 litres per minute (3000 litres divided by 8 minutes= 375 litres per minute), or 6.25 litres per second (375 litre divided by 60 total litres per second= 6.25 litre per second).

• Volume (litres cubed)•Duration/time• Rate of flow (litres per minute) • Negative space/resisting force• Statistics- the use of mean time for planning purposes• Estimation• Distance (kilometers) • Slopes, angles and incline • Length and width

Key Mathematical Concepts Identified

Helicopter Capacity

Image 2: MFB Attending to a Call out in Melbourne CBD (Australian Transprot Discussion Board, n.d)

Duration: 7 minutes 46 seconds

Image 3: Sky Crane Fighting a Fire(Sydney Morning Herald, 2014)

Mathematics DiscoveredThe helicopter pictured- a sky crane- has a carrying capacity of 9,000 litres, which is three times great than that carrying capacity a standard fire truck.

It’s refilling hose is about 450mm in diameter and can refill the sky crane to its maximum water capacity in 45 seconds, which is at a rate of 200 litres per second (9,000 litres divided by 45 seconds= 200 litres per second. This is 32 times faster than the average pump rate to fill a truck from a dam (200 liters per second divided by 6.25 litres per second= 32 times faster).

Helicopter can dump it’s water load in various spray patterns and quantities depending on purpose and crew safety. There are several variables that impact this, such as flame height, vicinity of ground crew etc.

Fuel capacity of a sky crane is about 3,000 litres. On average, it uses about 1,000 litres of fuel an hour. Due to it’s very high fuel consumption it is accompanied by a fuel tanker with a fuel capacity of 44,000 litres. This will allow the sky crane, on average, an additional 44 hours of flying time (44,000 litres divided by 1,000 litres (which is litres used per hour) = 44 hours)

They sky crane has a running cost of between $2000 -$3000 per trip.

• Volume (litres cubed)• Capacity (Litres) • Duration/time (seconds, minutes)• Rate of flow (litres per minute or litres per second)• Spray patterns• Comparison• Length and width• Statistics (average)• Cost and budgeting

The sky crane has a wing span of 27 meters and height of 3 storey’s.

The sky cranes are sent from the USA during Australia's fire season, transported in a large cargo plane and takes 48 hours to assemble once unloaded. Travel periods and cost associated (not to mention running costs) need to be considered when planning and budgeting for and during the fire season.

Key Mathematical Concepts Identified

Rate of Fire Spread and Area

Duration: 6 minutes 24 seconds

Image 4 and 5: CSIRO Grassland Fire Spread Meter(Commonwealth Scientific and Industrial Research Organisation, 2014)

DocumentNOTE: To view larger copies of images 4 and 5, please click the document link

Mathematics Discovered‘The rate of fire spread’ indicates how far (kilometers) a fire will travel in a certain amount of time (hours).

The rate at which a fire will spread is impacted on by a number of variables, These variable include, the air temperature, humidity, fuel moisture content (how much moisture in the grass, leaves etc- this is calculated by taking the weight of the fuel initially, oven drying it and then subtracting the new weight from the original rate), wind direction and mean speed and the density of the pasture (which has number rating attached).

Fuel stocks will not ignite/burn if it has a fuel moisture content over 22%.

A fires rate of speed will double with every 10 degree increase in burning surface incline.

Once the rate of spread is determined, the CFA can then map where the fire will be in certain time periods. This gives them the opportunity to plan and allocate the appropriate number of resources.

• Speed (kilometers per hour)• Duration/time• Moisture content (percentage)• Density• Area• Inclines and Degrees• Distance (kilometers)• Generalised formula (algebra)• Cartography

Key Mathematical Concepts Identified

Strike Teams and Resources

Image 2: MFB Attending to a Call out in Melbourne CBD (Australian Transprot Discussion Board, n.d)

Duration: 5 minutes 57 seconds

Image 6: Burning Fire (Sydney Morning Herald, 2014)

Mathematics DiscoveredDetermining the number of crew members that are required to attend a fire is a critical role within the CFA. The number of crew required depends on the location, size, vicinity etc of the fire emergency.

In many cases crew members are arranged in ‘strike teams’. One ‘strike team’ consists of 5 fire trucks, with 5 crew members per truck (totaling 25 crew members). With an additional 3 crew members, who act as the strike leaders.

For example, if a fire emergency requires 5 strike teams, this will equate to 25 trucks, and 140 crew members (5 trucks by 5 crew members each multiplied by 5 strike teams= 125 (or number of strike teams squared) and then adding 3 multiplied by 5 strike teams = 140.

Logistical factors need to be considered and as a result more mathematical calculations have to be made. Strike teams work in 12 hour shifts (either 7am to 7pm or vice versa). Each crew member needs to be provided with adequate food, for which quantities based on number of crew member in attendance to a fire emergency need to be calculated. Each member also needs appropriate bedding, sleeping quarter (tents) etc. Each of these items has to be ordered based on the number of crew members.

• Generalised formulas (algebra)• Operations• Mathematical reasoning• Time• Duration • Space (geometry)

Key Mathematical Concepts Identified

Mathematical Problem Associated with CFA

During the recent Macedon District Fires 23 strike teams were required. We wanted to work out how much water (in total) would be required for a 12 hour shift to actively suppress a fire in ideal circumstances. This would be calculated to ensure that there is an adequate supply of water at the planned source.

In one strike team there is 5 fire trucks (each with a water capacity of 3,000 litres, plus 750 litres in reserve) and each truck requires 5 crew members. An additional 3 crew members are required to per strike team- these are the strike leaders.

Total crew members required per strike team:Number of trucks per strike team multiplied by the number of crew members per truck.5 truck x 5 crew members = 25 crew members in total

Add 3 members to account for the strike leaders.25 crew members + 3 strike leaders = 28 crew members per 1 strike team.

Total number of crew members required for the 23 strike teams:28 members per strike team multiplied by 23 strike teams.28 crew members per strike team x 23 strike teams = 644 crew members in total

Total number of trucks required for 23 strike teams:23 strike teams multiplied by 5 trucks per team23 strike teams x 5 trucks = 115 trucks in total

Facts for the purpose of this calculation:- Each truck has a capacity to hold 3,000 litres of water, with 750 litre in reserve (based on

information provided by Allan).

- Whilst fighting the fire the truck is expending water at a rate of 100 litres per minute, which is the maximum time that a truck will stay out before refilling (based on information from Allan).

- The water source is 15 minutes in each direction from the active ‘fire site’. It will take the each truck 8 minutes (based on information provided by Allan). This equates to a 38 minute round trip.

Time the the truck can fight the fire before refilling:Truck capacity divided by flow rate = minutes truck takes to expend all its water3,000 litres of water / 100 litre per minute = 30 minutes

Time per ‘round trip’:Therefore, it takes 68 minutes for the truck to expend its water, refill and return to the fire front (30 minutes to expend all the water + 15 minutes to travel to the water source + 8 minutes to refill + 15 minutes to travel back to the fire front)- 68 minute per round trip

Total number number of ‘round trips’ the truck can complete in 12 hours:Total number of minutes divided by the minutes per ‘round trip’ = number of trips

Find the total minutes in 12 hours:Total hours multiplied minutes per hours = total number of minutes12 hours x 60 minutes per hour = 720 minutes

Total minutes divided by the total round trip:720 minutes / 68 minutes = 10 trips totals 680 minutes or 11 hours 20 minutes. The truck would then be full and at the fire front, enabling it to expend another load (totaling 30 minutes) before heading home. This would take the total duration up to 11 hours and 50 minutes and it would have unloaded 11 full tanks of water.

Total water expended:Number of tanks expended multiplied by the truck capacity = total water expended11 water tank ‘unloads’ x 3,000 litres per load = 33,000 litres used per truck per 12 hours (which is one shift).

The total amount of water used by the 23 strike teams over one shift:Total trucks multiplied by total water expended per truck (over one shift)115 truck x 33,000 litres per truck per 12 hour shift= 3,795,000 litres of water would be needed in a 12 hour period.

If we also considered the reserve tank, we would require an additional 750 litres per truck:Total number of trucks multiplied the capacity of the reserve tank115 trucks x 750 litres per truck = 86,250 litres of water

Total water required per 12 hour shift for 23 strike teams would be:3,795,000 litres + 86,250 litres = 3,881,250 litres

+68 +68 +68 +68 +68 +68 +68 +68 +68 +68 +30

68 136 204 272 340 408 476 544 612 680 710 720

We then compared a standard fire truck water expenditure in a 12 hour period to that of a sky crane.

Facts for the purpose of this calculation:- A sky crane has a total water capacity of 9,000 litres (based on information provided

by Allan). - If the sky cranes flight time is 4 minutes each way to water source and we allow 2

minutes for it to lower/retract and refill with water. It has the capacity to disperse 9,000 litres every 10 minutes.

- The sky crane needs to refuel after 3 hours of flying (based on information provided by Allan).

Total number of litres expended in a 1 hour period:9,000 litres per 10 minutes by 6 (there are 6, 10 minute lots in 1 hour) = 54, 000 litres per hour

Total number of litres expended in a 3 hour period:54,000 litres per hour multiplied by 3 hours = 162, 000 litres of water in 3 hours.

Water deposited over 12 hours deducting the refuelling time:10.5 hours (removing refuel time) by 54,000 litres per hour = 567,000 litres in 12 hour period.

In contrast, one fire truck could expend a maximum of 33,000 litres per 12 hour shift. This is 94% less than the sky crane in the same period.

Percentage calculation:

33,000 litres divided by 567,000 litres= 5.8 % (which indicates the truck expended 6% of the amount that he sky crane did).

Therefore, if we consider the sky crane was expended 100% water, then the fire truck only expended 6% of this amount, meaning the truck expended 94% less than the sky crane (100%- 6% = 94%).

We need to further consider the amount of ground support compared to one sky craneIn the case above 567,000 litres to 3,881,250 litres, this equates to 13% of water from one sky crane compared to 87% from 23 strike ground crews.

Mathematical Understandings Post the

Investigation

ReflectionThere were a variety of mathematical concepts that we didn’t consider in our initial lists, such as the logistics of providing support to the crew members- i.e. food, accommodation, drinking water, bathroom facilities, space etc and also the generalised formula for calculating fire spread.

We found the CIRSO fire spread meters very surprising. We had considered some form of calculations and influencing factors, however we didn’t consider that there were generalised calculation meters that are readily available to calculate the speed of spread for a grass fire. We also discovered that there were similar calculation meters available for other types of fire terrains, such as forest fires. Unfortunately, we did not get to investigate the mathematics behind these calculation meters, however it would be an interesting avenue to research in the future- determining how these numbers are acted on mathematically to give an accurate answer (rate of fire spread).

As the CFA is such a broad organisation with huge amount of mathematics to consider over numerous areas and with a large number of variables. As a result, we had to narrow our focus to a smaller field within the CFA. There may have been a few areas that we have misrepresented in our initial concepts, however as we condensed our focus area we were not able to seek full clarification on some of our predicted mathematical ideas. We also found that some our questions were discussed/answered without prompting.

Mathematics plays a vital role and is utilised in almost every aspect of our everyday lives, whether we realise it or not. Our lives would be very difficult without basic mathematical knowledge; for example, how could you tell the time, organise your money, read a map or follow the measurements in a recipe? We need an understanding of the basic principles of mathematics, such as addition and subtraction, division and multiplication, units of measure and time and an ability to interpret data displays.

Every job within society requires employees to be able to understand and undertake some level of mathematical thinking in order to complete certain tasks. In some roles, such as a fire fighter, builder, architect, engineer and teacher, a deeper and more specialised understanding of mathematics is required. Allan Kosmer’s understanding of mathematics within his role (and field) has allowed him and his colleagues to successfully ‘fight’ fires, which in turn has saved lives, property, wildlife, natural resources and valuable infrastructure.

It is also important that as pre-service teachers we realise the full breadth and use of mathematics within society in order to highlight, to our students, the importance of gaining a comprehensive understanding of mathematics. In knowing the range of applications that mathematics has in our lives, we are able to to provide meaning and context to the mathematics that we teach. Through this, students will be able to connect the concepts they are learning with the world they live in, and recognise the purpose and relevance of their learning.

Acknowledgements

Scott and I would like to thank Allan Kosmer (interviewee) sincerely for the time he donated to participate in the interview. We would also like to thank him for allowing us to record and publish the interview.

References

Country Fire Authority . (2012). Country Fire Brigade, Who We Are. Retrieved 24 March, 2014, from http://www.cfa.vic.gov.au/about/who_we_are/

Sydney Morning Herald. (2014). Photo Gallery - Bushfires rage in Victoria - Free National images. Retrieved 15 March, 2014, from http://www.smh.com.au/photogallery/2009/02/07/1233423569062

Commonwealth Scientific and Industrial Research Organisation. (2014). CSIRO Grassland Fire Spread Meter. Retreived 15 March, 1014, from http://www.csiro.au/Outcomes/Safeguarding-Australia/GrassFireSpreadMeter.aspx