Transportation
Energy Use and Cars 2 and 3: Constant Speed Cruising and Rolling Resistance
Take-Home Experiment
Purpose
To measure the mechanical power required to maintain the vehicle of your choice at a constant speed,
on a flat road, on a windless day. You may choose a car or a bicycle (pedal or motor).
Introduction
The force Fcar required to keep a vehicle moving at a constant speed v is equal to the combined drag
force at the speed.
1
Fcar f r D r mg CD Av 2
2
(1)
Where r is the coefficient of rolling friction, m is the mass of the vehicle (and occupant(s)), g is
acceleration due to gravity, CD is the coefficient of drag, is the density of air displaced, A is the cross
sectional area of the
cylinder of air the vehicle displaces and v is the constant speed. You can measure
Fcar as a function of v by measuring the combined drag. This can be done simply by taking your foot off
the gas, or by stopping pedalling, and noting the rate at which the speed is reduced. This acceleration a
can be multiplied by the vehicle’s mass (don’t forget the occupant(s)!) and velocity at that instant to give
the mechanical power Pcar.
Pcar Fcar v mav
(2)
Note: Only magnitude is being taken into account, which is why there are no minus signs anywhere. We
may safely assume that Pcar is positive.
The following equation can then be used to analyze the velocity dependence and extract the coefficient
of drag and rolling friction.
1
Pcar ( f r D)v r mg v C D Av 3
2
(3)
The Challenge
Design a procedure for measuring the speed as a function of time of a car or a bicycle. [See suggested
methods outlined below.] Pick a flat, quiet road, on as calm a day as possible. Take data several times in
both directions to account for any slight slope or wind. Using principles of drag force and rolling friction
determine the amount of power required to keep the vehicle at a constant speed. Using a spread sheet
and graph fitting functions extract the coefficient of rolling friction and drag for your vehicle.
Key Concepts
Drag force
Physics and Astronomy Outreach Program at the University of British Columbia
Rolling friction
Skills
Data collection and experimental design.
Calculate the power required to keep a vehicle moving at a constant speed.
Graphical analysis and curve fitting.
Materials
Vehicle (car, bicycle)
Tools for measuring speed and time
Method
1. Measure the speed as a function of time for your vehicle. For a car, this is straightforward if
there are two of you. It is unsafe to attempt this alone! For bicycles suggestions include buying
a speedometer, timing along a marked path, or using a small digital camera that shoots video.
2. Pick a flat, quiet road on a calm day.
3. Accelerate to as high a speed as is safe and coast to a standstill.
4. Using a spreadsheet to calculate acceleration and force from velocity and time.
5. Calculate the power as a function of velocity. (Eq. 2)
6. Plot speed vs. time and power vs. velocity.
7. Using a function (Eq. 3) and by manually inputting values until you get a fit, extract the
coefficients of rolling resistance (r) and drag (CD).
SAFETY NOTE:
It is not necessary to drive more than 50 km/h to get good results.
Do not try this when other vehicles are around.
Any experimental procedure that is dangerous will receive a mark of zero.
Suggested assigned time: 2 weeks
Questions to think about:
1.
2.
3.
4.
5.
How will you measure and/or take into account wind speed and direction?
What graphs will you plot?
What are the limitations (errors) of your measurements?
For cars, does your data depend on whether or not you are in gear or in neutral?
Are your results reasonable?
Rachel Moll and Chris Waltham (2009-12-08)
Physics and Astronomy Outreach Program at the University of British Columbia
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