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

Lecture Notes

Transportation

Energy Use in Cars 3: Rolling Resistance

Physics and Astronomy Outreach Program at the University of British ColumbiaPhysics 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

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

Background

1. Accelerating the car up to its cruising speed

2. Overcoming air resistance3. Overcoming rolling resistance4. 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 mainPlaces:

Rolling Resistance

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

BackgroundRolling

Resistance

Rolling resistance is commonly approximated a constant frictional force, dependent on the weight of the car (similar to any other kind of friction)

gravity todueon accelerati

vehicle theof mass

resistance rolling oft coefficien

resistance rolling todue Force F

:Where

RR

RR

g

m

))()(( gmF RRRR

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

BackgroundRolling

Resistance

The coefficient of rolling resistance is usually written as . It has different values for different vehicle types:

RR

Tire Type Coefficient of Rolling 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

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

ApproachRolling

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)

stance)(Force)(DiWork

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

ApproachRolling

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:

mgF RRRR

Newtons 718

)m/s 8.9(kg) 0127)(015.0( 2

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

ApproachRolling

Resistance

Over the course of driving one kilometre, this will require extra energy given by:

)Distance)(( RRFW

driven kilometreeach for kJ 718

mN 018700

)m 0100)(N187(

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

ApproachRolling

Resistance

We can calculate the fuel requirement using the efficiency formula:

InputEnergy Fuel

OutputWork

Input Work

OutputWork Efficiency

%25

kJ 718

Efficiency

OutputWork InputEnergy Fuel

kJ 748

Calculating the Fuel Requirement, Per km

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

ApproachCalculating the Fuel Requirement, Per kmAnd to provide this amount of energy, we need to use:

litres of #

Joules of #litreper Energy

litreper Energy

Joules of #litres of #

MJL 32

kJ 748

km 1 drive toL 023.0

Rolling Resistance

Physics and Astronomy Outreach Program at the University of British ColumbiaPhysics 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

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

Impact of Low Tire Pressure

* Model of a car with 40 psi tires

Rolling Resistance

Physics and Astronomy Outreach Program at the University of British ColumbiaPhysics 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].

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].

Rolling Resistance