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 2: Constant Speed Cruising

Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Question If we don’t burn gas, eventually the car would stop Friction and air resistance tend to oppose motion. We thus need energy to keep an object moving to over come these forces Constant Speed Cruising If a body in motion tends to stay in motion, why do we need to burn gas to travel at highway speeds?

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: Constant Speed Cruising

Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Background As a car moves, it leaves behind a tube of swirling air (as in the figure below). The engine needs to provide the energy for all that swirling. We want to make a reasonably accurate estimate of how much energy we need for all the swirling air left behind. Constant Speed Cruising

Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Background Constant Speed Cruising

Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Model Imagine the swirling air is confined to a long tube region near the path of the car. Cross sectional area of tube = A tube Frontal area of car = A car A car < A tube A tube /A car = Drag Coefficient, C D. C D = 0.33 for a typical family sedan C D = 0.9 for a cyclist Constant Speed Cruising

Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Approach Determine how much energy the car loses to the air To do this, figure out the kinetic energy (K.E) of moving air. Constant Speed Cruising

Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Approach To figure out the K.E, we need: m (kg), the mass of the car V (m 3 ), the volume of the tube of air. v (m/s), the velocity of car = velocity of air Figuring out the K.E Constant Speed Cruising

Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Approach d = distance traveled by the car = length of the tube of air that the car encounters The total volume of the tube will be: And the mass of the tube will be: Constant Speed Cruising

Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Approach So now the kinetic energy will be: Constant Speed Cruising

Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Approach Given that the area of a typical family sedan is: We calculate the work done against resistance, for each km a typical car driving at 50km/h travels Calculating the Work Done Against Air Resistance Constant Speed Cruising

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 Work Done Against Air Resistance So for each km travelled, 126kJ of work is done against air resistance Constant Speed Cruising

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 We can calculate the fuel requirement using the efficiency formula: Constant Speed Cruising

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: Constant Speed Cruising

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 L of fuel per km to overcome rolling resistance at 50km/h This is only 21% of the total energy cost of a car (0.076 L/km) Thus at this speed, air resistance is a very small part of the fuel requirement of the car. Since resistance changes with v 2, it becomes a larger part of the fuel requirement at higher speeds ~0.064 L/km at 100 km/h Constant Speed Cruising

Physics and Astronomy Outreach Program at the University of British Columbia Physics and Astronomy Outreach Program at the University of British Columbia Bibliography 1.MacKay DJC. Sustainable Energy - Without the Hot Air (Online). UIT Cambridge. p pdf [25 August 2009]. pdf 2.Wikimedia Foundation Inc. Gasoline (Online). [25 August 2009]. 3.MacKay DJC. Sustainable Energy - Without the Hot Air (Online). UIT Cambridge. p pdf [25 August 2009]. pdf 4.MacKay DJC. Sustainable Energy - Without the Hot Air (Online). UIT Cambridge. p [25 August 2009]. Constant Speed Cruising