 # Arriving at Calculations

1. How does NRCan arrive at the fuel, CO2 and dollar amounts quoted in the messages for three minutes of idling?

## Per Vehicle Calculation:

### Idle time per day = 3 min per day = 0.050 hours per day

 Idle fuel flow (L/hr) = (idle fuel flow factor 12 ) × (engine displacement in litres 13 ) = (0.6 litres/hr per litre of engine displacement) × (3 litres) = 1.8 litres per hour Idle fuel use (L/year) = (idle fuel flow) × (idle time per day) × (days in year) = 1.8 L/hr × 0.050 hr/day × 365 days/year = 32.85 litres per year Idle CO2 emissions (kg/year) = (idle fuel use) × (CO2 emission factor) 14 = 32.85 L/yr) × 2.3 kg/L = 75.56 kg per year Idle fuel cost (\$/year) = (idle fuel use) × (cost of fuel) = 32.85 L/yr × \$1 per litre (assumed) = \$32.85 per year Canada-Wide Savings – Per Year based on the year 2007: Fuel savings (litres/year) = (fuel use per vehicle) × (number of vehicles) = 32.85 L/year × 19,198,960 vehicles 15 = 630,685,836 L/year = 630 million litres per year CO2 savings (tonnes) = (CO2 emissions per vehicle) × (number of vehicles) = 75.56 kg/year × 19,198,960 vehicles 16 = 1,450,577,423 kg/year = 1,450,577 tonnes/year = 1.4 million tonnes per year Cost savings (\$/year) = (fuel cost per vehicle) × (number of vehicles) = \$ 32.85 × 19,198,960 vehicles 17 = \$ 630,685,836 per year = \$ 630 million per year Number of vehicles off road = (fuel savings) ÷ (annual fuel use per vehicle) = 630,685,836 l/year ÷ 1,950 L/year = 323,429 vehicles = 320,000 vehicles

### Canada-Wide Savings - Per Day:

The following values were calculated using the Canada-wide savings per year and dividing by 365 days:

• Daily fuel savings: 1.7 million litres per day
• Daily CO2 savings: 3,974 tonnes per day
• Daily cost savings: \$1.7 million per day

2. My vehicle's engine size and idle times are different than the examples in question 1. Can you tell me what my fuel use and CO2 emissions are per year?

Idle Time Fuel Use (litres per year) CO2 Emissions (kg per year)
(minutes per day) 1 litre Engine 3 litre Engine 5 litre Engine 1 litre Engine 3 litre Engine 5 litre Engine
1 4 11 18 9 25 41
2 7 22 37 16 51 85
3 11 33 55 25 76 126
4 15 44 73 34 101 168
5 18 55 91 41 126 209
6 22 66 110 51 152 253
7 26 77 128 60 177 294
8 29 88 146 67 202 336
9 33 99 164 76 228 377
10 37 110 183 85 253 421

3. How can a vehicle produce about three times its own weight in CO2 each year?

 Ratio = (annual fuel use per vehicle × CO2 emission factor) ÷ (average vehicle weight) = (1,950 L × 2.3 kg CO2/l) ÷ 1,450 kg = 4,485 kg ÷ 1,450 kg = 3.093 = 3 times its own weight

4. How does idling for just 10 minutes use over 1 cup of fuel for a vehicle with a 3 litre engine and over 2 cups of fuel for a vehicle with a 5 litre engine?

Idle time = 10 minutes = 0.166 hours

For a 3 litre engine:

 Fuel use = (idle time) × (idle fuel flow factor 18 ) × (engine displacement) = (0.166 hr) × (0.6 L/hr per litre of engine displacement) × (3.0 litres) = (0.166 hr) × (1.8 L/hour) = 300 ml = 300 ml ÷ 236 ml per cup = 1.3 cups

For a 5 litre engine

 Fuel use = (idle time) × (idle fuel flow factor 19 ) × (engine displacement) = (0.166 hr) × (0.6 L/hr per litre of engine displacement) × (5.0 litres) = (0.166 hr) × (3.0 L/hour) = 500 ml = 500 ml ÷ 236 ml per cup = 2.1 cups

Note: 1 cup = 8 fluid ounces = 236 millilitres

12 Review of the Incidence, Energy Use and Costs of Passenger Vehicle Idling; Gordon W. Taylor, P.Eng. Prepared for the Office of Energy Efficiency, Natural Resources Canada, 2003
13 In 2005 the average engine displacement for light-duty vehicles was 3.0 litres
14 Actual value: 2.289 kg CO2/L – National Inventory Report 1990-2006, Table A12-7, April 2008
15 For the year 2007 from Statistics Canada