Transportation
Energy Use and Cars 2 and 3: Constant Speed Cruising and Rolling Resistance
Take-Home Experiment Write-Up
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 occupants!) and velocity at that instant to give
the mechanical power Pcar.
Pcar  Fcar v  mav
(2)
Note: I am talking magnitudes only here, 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)
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.
Physics and Astronomy Outreach Program at the University of British Columbia

Any experimental procedure that is dangerous will receive a mark of zero.
Some things to make note of:




Type of vehicle, mass (usually given inside driver’s door; use scales for you and bicycle) and
frontal area.
Date, time and place where data was taken. Note local wind direction and estimate speed –
drop a piece of tissue paper.
If the car is an automatic, coast in neutral.
Take data several times in both directions to account for any slight slope or wind.
Sample Results: A bicycle
The graph below shows the motive force required to maintain a bicycle at a constant velocity. Data were
taken in two directions (east and west) and the coefficients of the fitting curve (fit to Equation 1) were
extracted and found to be: CD ~ 1 and R ~ 0.0012.
Force (N)
Velocity (m/s)
Physics and Astronomy Outreach Program at the University of British Columbia
Sample Results: Comparison of two cars
Data below was collected with two different vehicles (an SUV and a compact car). The drag coefficient
CD ~ 0.2 and the coefficient of rolling resistance is R ~ 0.1. This difference in the curves is accounted for
by the mass of the vehicles.
Summary
The coefficient of drag and of rolling resistance for a car or a bicycle can be found by plotting power vs.
velocity. The coefficients of drag and rolling resistance for most vehicles are similar but the power
required to maintain a constant speed vary largely because of the mass of the vehicles.
Physics and Astronomy Outreach Program at the University of British Columbia
References
Waltham, C.E., & Copeland, B. (1999). Power requirements for rollerblading and bicycling. The Physics
Teacher, 37(6), 379-382.
Rachel Moll and Chris Waltham (2009-12-08)
Physics and Astronomy Outreach Program at the University of British Columbia