Transportation Energy Use in Cars 3: Lecture Notes
Question Why would the pressure in our car tires affect gasoline consumption? resistance accounts for all the small bits of friction within the car, and more significantly, the friction within the tires and the road resistance affects the motion of a car Underinflated tires affect the fuel consumption of a car
Background Energy from the fuel in a car goes to 4 main Places: 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)
Background resistance is commonly approximated a constant frictional force, dependent on the weight of the car (similar to any other kind of friction) Where : F m g RR RR Force due to rolling resistance coefficient mass of F RR of the vehicle rolling resistance acceleration due to gravity ( )( m)( g) RR
Background The coefficient of rolling resistance is usually written as RR. It has different values for different vehicle types: Tire Type Coefficient of Friction Low rolling resistance car tire 0.006 0.01 Ordinary car tire 0.015 Truck tire 0.006 0.01 Train wheel 0.001
Approach 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) Work (Force)(Distance)
Approach 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: F mg RR RR (0.015)(1270 kg)(9.8 m/s 187 Newtons 2 )
Approach Over the course of driving one kilometre, this will require extra energy given by: W ( F RR )(Distance) (187N)(1000 m) 187000 N m 187 kj for each kilometre driven
Approach Calculating the Fuel Requirement, Per km We can calculate the fuel requirement using the efficiency formula: Work Output Work Output Efficiency Work Input Fuel Energy Input Fuel Energy Input Work Output Efficiency 748 kj 187 kj 25%
Approach Calculating the Fuel Requirement, Per km And to provide this amount of energy, we need to use: # of Joules Energy per litre # of litres # of Joules # of litres Energy per litre 748 kj 32 MJL 0.023 L to drive 1 km
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
* Model of a car with 40 psi tires Impact of Low Tire Pressure Change in Pressure 5% decrease in pressure Pressure drops by 5% to 38 psi* Change in Coefficient of Friction, µ RR µ RR increases 5% New µ RR = 0.01575 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
Bibliography 1. a. b. Natural Resources Canada. Tire Inflation (online). http://oee.nrcan.gc.ca/transportation/personal/driving/autosmartmaintenance.cfm#h [25 August 2009]. 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]. 3. Wikimedia Foundation Inc. Gasoline (Online). http://en.wikipedia.org/wiki/gasoline [25 August 2009]. 4. A Discovery Company. How Tires Work (online). http://auto.howstuffworks.com/tire4.htm [25 August 2009]. 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].