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Physics and Astronomy Outreach Program at the University of British Columbia

Transportation Energy Use in Cars 2: Constant Speed Cruising. Lecture Notes. Physics and Astronomy Outreach Program at the University of British Columbia. Constant Speed Cruising. Question. If a body in motion tends to stay in motion, why do we need to burn gas to

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Physics and Astronomy Outreach Program at the University of British Columbia

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  1. Transportation Energy Use in Cars 2: Constant Speed Cruising Lecture Notes Physics and Astronomy Outreach Program at the University of British Columbia

  2. Constant Speed Cruising Question If a body in motion tends to stay in motion, why do we need to burn gas to travel at highway speeds? • 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 Physics and Astronomy Outreach Program at the University of British Columbia

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

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

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

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

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

  8. Constant Speed Cruising Approach Figuring out the K.E • To figure out the K.E, we need: • m (kg), the mass of the car • V (m3), the volume of the tube of air. • v (m/s), the velocity of car = velocity of air Physics and Astronomy Outreach Program at the University of British Columbia

  9. Constant Speed Cruising 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: Physics and Astronomy Outreach Program at the University of British Columbia

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

  11. Constant Speed Cruising Approach Calculating the Work Done Against Air Resistance 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 Physics and Astronomy Outreach Program at the University of British Columbia

  12. Constant Speed Cruising Approach Calculating the Work Done Against Air Resistance So for each km travelled, 126kJ of work is done against air resistance Physics and Astronomy Outreach Program at the University of British Columbia

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

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

  15. Constant Speed Cruising Interpretation • We need 0.016 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 v2, it becomes a larger part of the fuel requirement at higher speeds ~0.064 L/km at 100 km/h Physics and Astronomy Outreach Program at the University of British Columbia

  16. Constant Speed Cruising Bibliography • 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]. • Wikimedia Foundation Inc. Gasoline (Online). http://en.wikipedia.org/wiki/Gasoline [25 August 2009]. • MacKay DJC. Sustainable Energy - Without the Hot Air (Online). UIT Cambridge. p.257. http://www.inference.phy.cam.ac.uk/sustainable/book/tex/ps/253.326.pdf [25 August 2009]. • 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]. Physics and Astronomy Outreach Program at the University of British Columbia

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