connect with maths ~ discovering sustainability & maths in a world heritage icon

Australian Association of Mathematics Teachers Webinar . 14 October 2015Wednesday 14 October 2015

Discovering Sustainability & Maths in

A World Heritage Icon

Naomi MartinManager, Environmental Sustainability

Source: Perception vs fact.com

Australian Association of Mathematics Teachers Webinar . 14 October 2015

Inspired by Nature


Sydney Opera HouseOpera House.Educationsustainability

Teachers.sustainability cross curriculum priorityEngage students in maths.

Students.Interest in sustainability

What we have in commonGive students motivation and tools to make their own changes towards a more sustainable future.

Excite students by showing maths that can make a difference.


SUMMARY OF TALK• 2 sustainability stories: Energy & Carbon

• Case study at Opera House• Applying the tools at school

• 3 Opera House maths in design stories.

Australian Association of Mathematics Teachers Webinar . 14 October 2015Sustainability Story #1Concert Hall Lights: Energy saving calculations


Version v3_NM review

Price $/Kwh1

Labour Rate/hr per

person

Current Operational

Hours

Proposed Operational

Hours Days NGA Factor2

Project Cost $3

0.17$ 47.00$ 14 14 364 1.06 2,000,000.00$

Type Fitting Qty

Watts Including

Ballast Lamp QtyLamp Life

(Hours)Relamping Period Yrs6

Cost per lamp6 Install Time Hrs

Crown Lights 64 575 1 300 0.06 35.00$ 2Low level 194 200 1 1,000 0.20 25.00$ 2High level 89 300 1 1,000 0.20 12.50$ 2Work Lights 16 575 1 300 0.06 35.00$ 2

Type Fitting Qty

Watts Including

Ballast Lamp QtyLamp Life

(Hours)Relamping Period Yrs

Cost per lamp3 Install Time Hrs

LED crown lights 72 160 1 50,000 9.81 3,745.00$ 2LED high level HS 89 100 1 50,000 9.81 2,445.00$ 2LED low level HS 194 35 1 50,000 9.81 1,763.00$ 2

INPUT PROPOSED LIGHTING VARIABLES3

Project Description: Concert Hall crown and high level house lights

Date: 29-June-2014

INPUT CONTROL VARIABLES

INPUT CURRENT LIGHTING VARIABLES6


5,096 Hrs 5,096 Hrs568,204 Kwh 138,662 Kwh

602 tCO2-e 147 tCO2-e96,594.68$ 23,572.57$ 77,947.57$ 84,518.89$

263,303.53$ 3,401.07$ 437,845.77$ 111,492.53$

429,542 kWh455 tCO2-e

73,022.11$ -$6,571.33

259,902.45$ 326,353.24$

6.13 Years76%

CURRENT LIGHTING PROJECTIONS PROPOSED LIGHTING PROJECTIONSTotal Hours used per year Total Hours used per yearEnergy Usage pa Energy Usage paCO2 pa CO2 paEnergy Cost pa Energy Cost paCost of lamps per year Cost of lamps per yearCost of labour for relamping per year Cost of labour for relamping per yearTotal Annual Operational Costs Total Annual Costs

PROJECTED PROJECT RESULTSAnnual Energy Savings Annual CO2 SavingsAnnual cost savings energyAnnual cost saving on lampsAnnual labour costs savings for relampingTotal annual cost savings over life of new lampPayback period including energy & relamping cost savings% Reduction in energy use


At School

You can choose energy efficient appliances to reduce power use. Maths gives you the tools to calculate energy and cost savings.


At School

• Total Power (watt)• One classroom has 2

fluorescent tubes in each fixture, in 8 fixtures that draw 45W each tube.

• What is the total power?


At School

• Total Power (watt)• One classroom has 2

fluorescent tubes in each fixture, in 8 fixtures that draw 45W each tube.

• What is the total power?

• = 2 x 8 x 45W • = 720W


At School

• Hours used• The lights are on 12 hrs

per day, 5 days per week, 40 weeks per year.

• What is the total time they are on?


At School

• Hours used• The lights are on 12 hrs

per day, 5 days per week, 40 weeks per year.

• What is the total time they are on?

• = 12 x 5 x 40• = 2400hrs


At School

• Energy = Power (W) x time (hr)• Power (W) = 720• Hours (hr) = 2400. • What is the Energy used per

year in kWhs?• = 720 x 2400• = 1,728,000 Wh (/1000)• = 1728 kWh


Current: T8 LED tube & motion sensors

Power (Watts) 45 W 20 WBulbs 2 2Number of fixtures 8 8Total Power multiply above 720 W 320 W

Hours/Day 12 hr 8 hrDays/week 5 days 5 daysWeeks 40 weeks 40 weeks

Total Hours hrs x days x wks 2,400 hrs 1,600 hrs

Energy use (Wh) W x hrs 1,728,000 Wh 512,000 WhEnergy use kWh W / 1000 1,728 kWh 512 kWhCost per kWh 0.3 $/KWh 0.3 $/KWh

Annual costcost x energy use (kWh) 518.4 153.6

Energy saving compared to T8 (%) ((old -new )/old) x 100 70%Cost Saving compared to T8($) annual cost T8 - annual cost LED 364.80$


At School

You can choose energy efficient appliances to reduce power use. Maths gives you the tools to calculate energy and cost savings. Tools• Spreadsheets, forumulas• Units of measurement • Equations for energy/power.


• Sustainability - Cross Curriculum Priority• OH Education –beyond arts students

Sustainability Story #2: Carbon and Events


Carbon & Events


VIVID15_Party_Slides_23


Carbon 101


1) Concentration of CO2 increasing. http://www.csiro.au/greenhouse-gases/

2015-1976 = 39 years



Rise in CO2 (ppm)= 395.569-329.653=65.91 ppm

2015-1976 = 39 years

Rise in CO2 (ppm)= 398-330= 68ppm

http://www.csiro.au/greenhouse-gases/



Rise in CO2 (ppm)= 395.569-329.653=65.91 ppm

2015-1976 = 39 years

Rise in CO2 (ppm)= 398-330= 68ppm

Rate of change = 68ppm/39yr = = 1.75ppm/yr

http://www.csiro.au/greenhouse-gases/


• CO2 is 0.039% of the atmosphere

• 0.05% alcohol blood limit

2) Increase in CO2 has big impacts


http://www.theguardian.com/environment/interactive/2013/sep/27/climate-change-how-hot-lifetime-interactive

2) Increased CO2 has big impacts - Temperature


2) Increased CO2 has big impacts - Temperature


2) Increased CO2 has impacts - Sydney


Why - impacts

400ppm


2) Increased CO2 has impacts - Sydney Opera House


Kids

• What has STEM got to do with me.

http://www.environment.gov.au/system/files/resources/b24f8db4-e55a-4deb-a0b3-32cf763a5dab/files/national-greenhouse-accounts-factors-2014.pdf

3) We can make a difference by understanding carbon emissions




Case Studies (content).3) We can make a difference by understanding carbon emissions

• Carbon emitted = volume of fuel or activity x emission factor.

ActivityEmissions Factor Unit Reference

Electricity (NSW) 0.99 kg CO2-e / kWh NGA Factors

Unleaded Petrol 2.80 T CO2-e / kL NGA Factors

Flight - medium haul 0.18 kg CO2-e/km/personEPA Victoria

Meat and meat products 5.83 kg CO2-e/$ EPA Victoria

Vegetable and fruit growing, hay, plant nurseries, flowers 0.92 kg CO2-e/$ EPA Victoria


3) We can make a difference by understanding carbon emissions

• Carbon Calculators http://www.epa.vic.gov.au/agc/home.html


CARBON 101 SUMMARY 1) CO2 is increasing2) Continuing to increase CO2 in atmosphere has impacts we would like to avoid3) By understanding carbon emissions, you can make a difference


Back to the case study..


Case Studies (content).

Electr

icity

Natural

gas &

liquid fu

elsFlig

hts

Caterin

gWast

e

Accommodati

on

Paper

used in

mark

eting

Ground tran

sport

Ticket

s0.00

200.00

400.00

600.00

800.00

1000.00

1200.00

1400.00

Vivid 2011 1609 T CO2-e

Vivid 2012 1067 T CO2-e

Sources of GreenhouseGas Emissions

Tonn

es C

O2

equi

vale

nt

Sustainability Story #2: Vivid Live Carbon Footprint


Insert carbon counter

Band 1 - Rider

= more than one car over a year

Carbon

STEM Academy, University of Sydney. Wednesday 25 November 2014

Band 2 - Rider

= half a scooter over one year

STEM Academy, University of Sydney. Wednesday 25 November 2014


At SchoolHere are some eg. calculationsWhat would you do to reduce your carbon?

Activity UnitEmissions Factor Unit

Tonnes CO2-e

Electricity for a 4 person home in Sydney for one year 7492 kWh 0.99

kg CO2-e / kWh 7.42

Car for 1 year with 12L/100km, driving 15,000km 1.80 kL 2.80 T CO2-e / kL 5.04Return flight to Melbourne (713km 1 way) 1426 km 0.18

kg CO2-e/km/person 0.26

Cutting out one serve of red meat per week for 1 year (assume $10 steak) 520.00$ 4.44 kg CO2-e/$ 2.31


At School

You can choose to reduce the carbon you emit.

Maths gives you the toolsTools• Graphs, rates of change• Interpret pictograms• Units of measurement.• Formulas• Extrapolate


Sydney Opera House.Mathematics of Design


Spherical Solution


Case Studies (content).Spherical Solution

After three years of intensive search for a basic geometry for the shell complex I arrived in October 1961 at the spherical solution shown here.

I call this my ‘key to the shells’ because it solves all the problems of construction by opening up to mass production, precision in manufacture and simple erection and with this geometrical system I attain full harmony between all the shapes in this

fantastic complex.Joern Utzon


• The geometry used in the Opera House isn’t hard, but it is so practical.

• You can apply geometry in so many ways


• Terracycle• Green Lane Green Cross• Bookend Trust• Environmental Educators

22m

8m

23.4m

9m12m

How long does it take sound to travel?

(2 x 23.4m)/340.29 m/s = 0.14 sec

(2 x 12m)/340.29m/s = 0.07 sec

Concert Hall Acoustics

Spherical Solution

Spherical solution


Case Studies (content).


• Terracycle• Green Lane Green Cross• Bookend Trust• Environmental Educators


• The maths used in many designs isn’t hard, but it is so practical.

• Understanding geometry helps you build things.

Collaborate with partners

Feedback

• How could this presentation and case studies be further developed to help you?

• Format – online case studies? Digital tours? Onsite tours with tour guide or ‘do it yourself’ tours, activities around a show

• What would Sydney Opera House need to provide you as materials?

• Partnership Opportunities – how far we get depends on our resources

Cool Australiahttp://www.coolaustralia.org/

http://www.coolaustralia.org/