Transcript Where do you think most of the energy from the fuel ends

Transportation
Energy Use in Cars
3: Rolling
Resistance
Lecture Notes
Physics and Astronomy Outreach Program at the University of British Columbia
Question
Rolling
Resistance
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
Physics and Astronomy Outreach Program at the University of British Columbia
Background
Rolling
Resistance
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
Rolling
Resistance
Rolling resistance is commonly approximated
a constant frictional force, dependent on the
weight of the car (similar to any other kind of
friction)
FRR  (RR )(m)(g )
Where:
FRR  Forcedue to rollingresistance
RR  coefficient of rollingresistance
m  mass of the vehicle
g  acceleration due to gravity
Physics and Astronomy Outreach Program at the University of British Columbia
Background
Rolling
Resistance
The coefficient of rolling resistance is usually
written as RR. It has different values for
different vehicle types:
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 Columbia
Approach
Rolling
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)
Work (Force)(Distance)
Physics and Astronomy Outreach Program at the University of British Columbia
Rolling
Resistance
Approach
• 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:
FRR   RR mg
 (0.015)(1270 kg)(9.8 m/s2 )
 187 Newtons
Physics and Astronomy Outreach Program at the University of British Columbia
Rolling
Resistance
Approach
Over the course of driving one kilometre, this
will require extra energy given by:
W  ( FRR )(Distance)
 (187N)(1000 m)
 187000 N  m
 187 kJ for each kilometredriven
Physics and Astronomy Outreach Program at the University of British Columbia
Rolling
Resistance
Approach
Calculating the Fuel Requirement,
Per km
We can calculate the fuel requirement using
the efficiency formula:
WorkOutput
WorkOutput
Efficiency

WorkInput
Fuel EnergyInput
WorkOutput 187 kJ
Fuel EnergyInput 

Efficiency
25%
 748 kJ
Physics and Astronomy Outreach Program at the University of British Columbia
Approach
Rolling
Resistance
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
Energyper litre
748 kJ

32 MJL
 0.023 L to drive 1 km
Physics and Astronomy Outreach Program at the University of British Columbia
Interpretation
Rolling
Resistance
• 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
Physics and Astronomy Outreach Program at the University of British Columbia
* Model of a car with 40 psi tires
Rolling
Resistance
Impact of Low Tire
Pressure
Change in Pressure
5% decrease in pressure
Pressure drops by 5% to 38 psi*
Change in Coefficient of Rolling Friction, µRR
µRR increases 5%
New µRR = 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
Physics and Astronomy Outreach Program at the University of British Columbia
Bibliography
Rolling
Resistance
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].
Physics and Astronomy Outreach Program at the University of British Columbia