Transportation Energy Use in Cars 2: Constant Speed Cruising

Lecture Notes

Physics and Astronomy Outreach Program at the University of British Columbia

Question

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?

• 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

Background

Constant Speed Cruising

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) Physics and Astronomy Outreach Program at the University of British Columbia

Background

Constant Speed Cruising • 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

Background

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

Model

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

Approach

Constant Speed Cruising • 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

Approach

Constant Speed Cruising

Figuring out the K.E

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 Physics and Astronomy Outreach Program at the University of British Columbia

Approach

Constant Speed Cruising • d = distance traveled by the car = length of the tube of air that the car encounters

Length



d

The total volume of the tube will be:

Volume



(Area)(Len gth)



A tube d

And the mass of the tube will be:

Mass



(Density)( Volume)

 

A tube d

Physics and Astronomy Outreach Program at the University of British Columbia

Approach

Constant Speed Cruising So now the kinetic energy will be: K.E

 1 2 mv 2 

1 2

A tube dv

2 

1 2



A car C D dv

2 Physics and Astronomy Outreach Program at the University of British Columbia

Approach

Constant Speed Cruising

Calculating the Work Done Against Air Resistance

Given that the area of a typical family sedan is:

A

 ( 2 m )( 1 .

5 m )  3 m 2 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

Approach

Constant Speed Cruising

Calculating the Work Done Against Air Resistance

Work done against  air resistance  1 

Acar C D dv

2 2 1 2 ( 1 .

3 kg/m 3 )( 3 m 2 )( 0 .

33 )( 1000 m )( 14 m/s ) 2  126 , 12 6 kg  m 2 /s 2  1 26 kJ So for each km travelled, 126kJ of work is done against air resistance Physics and Astronomy Outreach Program at the University of British Columbia

Approach

Constant Speed Cruising

Calculating the Fuel Requirement, Per km

We can calculate the fuel requirement using the efficiency formula: Efficiency  Work Output Work Input  Work Output Fuel Energy Input Fuel Energy Input  Work Output Efficiency 

5 0 5 kJ

 126 kJ 25% Physics and Astronomy Outreach Program at the University of British Columbia

Approach

Constant Speed Cruising

Calculating the Fuel Requirement, Per km

And to provide this amount of energy, we need to use: Energy per litre  # of Joules

# of litres

 # of litres

# of Joules Energy per litre

 505 kJ 32 MJL  0 .

01 6 L to drive 1 km Physics and Astronomy Outreach Program at the University of British Columbia

Interpretation

Constant Speed Cruising • 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 v 2 , 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

Bibliography

Constant Speed Cruising 1. 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].

2. Wikimedia Foundation Inc.

Gasoline

http://en.wikipedia.org/wiki/Gasoline (Online). [25 August 2009].

3. 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].

4. 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