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 Martin
Manager, Environmental Sustainability

Source: Perception vs fact.com

Australian Association of Mathematics Teachers Webinar . 14 October 2015
Inspired by Nature

Sydney Opera House
Opera
House.
Education
sustainability
Teachers.
sustainability
cross curriculum
priority
Engage students in
maths.
Students.
Interest in
sustainability
What we have in common
Give 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.

Sustainability Story #1
Concert 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 Qty
Lamp Life
(Hours)
Relamping
Period Yrs6
Cost per
lamp6
Install Time Hrs
Crown Lights 64 575 1 300 0.06 35.00$ 2
Low level 194 200 1 1,000 0.20 25.00$ 2
High level 89 300 1 1,000 0.20 12.50$ 2
Work Lights 16 575 1 300 0.06 35.00$ 2
Type Fitting Qty
Watts
Including
Ballast Lamp Qty
Lamp Life
(Hours)
Relamping
Period Yrs
Cost per
lamp3
Install Time Hrs
LED crown lights 72 160 1 50,000 9.81 3,745.00$ 2
LED high level HS 89 100 1 50,000 9.81 2,445.00$ 2
LED 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 Hrs
568,204 Kwh 138,662 Kwh
602 tCO2-e 147 tCO2-e
96,594.68$ 23,572.57$
77,947.57$ 84,518.89$
263,303.53$ 3,401.07$
437,845.77$ 111,492.53$
429,542 kWh
455 tCO2-e
73,022.11$
-$6,571.33
259,902.45$
326,353.24$
6.13 Years
76%
CURRENT LIGHTING PROJECTIONS PROPOSED LIGHTING PROJECTIONS
Total Hours used per year Total Hours used per year
Energy Usage pa Energy Usage pa
CO2 pa CO2 pa
Energy Cost pa Energy Cost pa
Cost of lamps per year Cost of lamps per year
Cost of labour for relamping per year Cost of labour for relamping per year
Total Annual Operational Costs Total Annual Costs
PROJECTED PROJECT RESULTS
Annual Energy Savings
Annual CO2 Savings
Annual cost savings energy
Annual cost saving on lamps
Annual labour costs savings for relamping
Total annual cost savings over life of new lamp
Payback 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 W
Bulbs 2 2
Number of fixtures 8 8
Total Power multiply above 720 W 320 W
Hours/Day 12 hr 8 hr
Days/week 5 days 5 days
Weeks 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 Wh
Energy use kWh W / 1000 1,728 kWh 512 kWh
Cost per kWh 0.3 $/KWh 0.3 $/KWh
Annual cost
cost x energy
use (kWh) 518.4 153.6
Energy saving
compared to T8 (%) ((old -new )/old) x 100 70%
Cost Saving
compared to T8($) 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

1) Concentration of
CO2 increasing.
Rise in CO2 (ppm)
= 395.569-329.653
=65.91 ppm
2015-1976 = 39 years
Rise in CO2 (ppm)
= 398-330
= 68ppm

1) Concentration of
CO2 increasing.
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

• 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.
Activity
Emissions
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 increasing
2) Continuing to increase CO2 in atmosphere has impacts we would like to avoid
3) By understanding carbon emissions, you can make a difference

Back to the case study..

Case Studies (content).
0.00
200.00
400.00
600.00
800.00
1000.00
1200.00
1400.00
TonnesCO2equivalent
Sources of Greenhouse
Gas Emissions
Vivid 2011 1609 T CO2-e
Vivid 2012 1067 T CO2-e
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 School
Here are some eg. calculations
What would you do to reduce
your carbon?
Activity Unit
Emissions
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 5.04
Return 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 tools
Tools
• 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
9m
12m
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 Australia
http://www.coolaustralia.org/

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