1. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Lecture Notes Transportation Energy Use in Cars 3: Rolling Resistance

2. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Question Why would the pressure in our car tires affect gasoline consumption? Rolling resistance accounts for all the small bits of friction within the car, and more significantly, the friction within the tires and the road Rolling resistance affects the motion of a car Underinflated tires affect the fuel consumption of a car Rolling Resistance

3. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Background 1.Accelerating the car up to its cruising speed 2.Overcoming air resistance 3.Overcoming rolling resistance 4.Heat (partly converted to motion, flowing to the environment with exhaust gases and by convection cooling of the engine) Energy from the fuel in a car goes to 4 main Places: Rolling Resistance

4. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Background Rolling Resistance Rolling resistance is commonly approximated a constant frictional force, dependent on the weight of the car (similar to any other kind of friction)

5. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Background Rolling Resistance The coefficient of rolling resistance is usually written as. It has different values for different vehicle types: Tire TypeCoefficient of Rolling Friction Low rolling resistance car tire0.006 – 0.01 Ordinary car tire0.015 Truck tire0.006 – 0.01 Train wheel0.001

6. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Approach Rolling Resistance To figure out how the resistance force impacts fuel economy, we need to figure out how much energy is required to overcome it. For this, use the Work-Energy principle (shows how much energy a force will add to the system)

7. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Approach Rolling Resistance Rolling friction opposes vehicular motion; it thus subtracts energy from the car which is made up by burning more fuel For a typical sedan (1200kg) plus driver (70kg), the rolling resistance will be:

8. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Approach Rolling Resistance Over the course of driving one kilometre, this will require extra energy given by:

9. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Approach Rolling Resistance We can calculate the fuel requirement using the efficiency formula: Calculating the Fuel Requirement, Per km

10. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Approach Calculating the Fuel Requirement, Per km And to provide this amount of energy, we need to use: Rolling Resistance

11. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Interpretation We need 0.023 L of fuel per km to overcome frictional rolling resistance (at 100 km/h) Added to the 0.064 L/km to overcome air resistance, the total energy needed to overcome resistive forces is 0.087 L/km (at 100 km/h) This is slightly higher than the reported average of 0.076 L/km, but is reasonable since we calculated it at a high speed of 100 km/h Rolling Resistance

12. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Impact of Low Tire Pressure Change in Gas Consumption Fuel consumption increases to 0.024 L/km Fuel consumption is an extra 0.01L/km or 1% of fuel mileage Change in Coefficient of Rolling Friction, µRR µRR increases 5%New µRR = 0.01575 Change in Pressure 5% decrease in pressurePressure drops by 5% to 38 psi* * Model of a car with 40 psi tires Rolling Resistance

13. Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Bibliography 1.a. b. Natural Resources Canada. Tire Inflation (online). http://oee.nrcan.gc.ca/transportation/personal/driving/autosmart- maintenance.cfm#h [25 August 2009].a.b. http://oee.nrcan.gc.ca/transportation/personal/driving/autosmart- maintenance.cfm#h 2.MacKay DJC. Sustainable Energy - Without the Hot Air (Online). UIT Cambridge. p.262. http://www.inference.phy.cam.ac.uk/sustainable/book/tex/ps/253.326. pdf [25 August 2009]. http://www.inference.phy.cam.ac.uk/sustainable/book/tex/ps/253.326. pdf 3.Wikimedia Foundation Inc. Gasoline (Online). http://en.wikipedia.org/wiki/Gasoline [25 August 2009]. http://en.wikipedia.org/wiki/Gasoline 4.A Discovery Company. How Tires Work (online). http://auto.howstuffworks.com/tire4.htm [25 August 2009]. http://auto.howstuffworks.com/tire4.htm 5.MacKay DJC. Sustainable Energy - Without the Hot Air (Online). UIT Cambridge. p.31. http://www.inference.phy.cam.ac.uk/sustainable/book/tex/ps/1.112.pdf [25 August 2009]. http://www.inference.phy.cam.ac.uk/sustainable/book/tex/ps/1.112.pdf Rolling Resistance