Road Vehicle Performance:
Introduction and Resistance
TTE 4004
Transportation Engineering
Dr. Scott Washburn
Introduction

Roadway design is governed by two
main factors:

Vehicle capabilities




acceleration/deceleration
braking
cornering (chap. 3)
Human capabilities


(late chap. 2, chap. 3)
perception/reaction times
eyesight (peripheral range, height above
roadway)
TTE 4004: Transportation Engineering
Introduction

Performance of road vehicles forms the
basis for roadway design guidelines
such as:






length of acceleration / deceleration lanes
maximum grades
stopping-sight distances
passing-sight distances
setting speed limits
timing of signalized intersections
TTE 4004: Transportation Engineering
Introduction

Studying vehicle performance serves
two important purposes:
1.
2.
provides insight into roadway design and
traffic operations and the compromises
that are necessary to accommodate the
wide variety of vehicles that use
roadways
it forms a basis on which to assess the
impact of advancing vehicle technologies
on existing roadway design guidelines
TTE 4004: Transportation Engineering
Tractive Effort and Resistance



These are the opposing forces that
determine straight-line performance of
road vehicles
Tractive effort is simply the force
available at the roadway surface to
perform work (expressed in lbs [N])
Resistance (expressed in lbs [N]) is
defined as the force impeding vehicle
motion
TTE 4004: Transportation Engineering
Tractive Effort and Resistance

Three major sources of vehicle
resistance are:



Aerodynamic
Rolling (originates from the roadway
surface/tire interface)
Grade or gravitational
TTE 4004: Transportation Engineering
Tractive Effort and Resistance

Illustration of forces with vehicle force diagram
Fig. 2.1
Ff + Fr = ma + Ra + Rrlf + Rrlr + Rg
F = ma + Ra + Rrl + Rg
TTE 4004: Transportation Engineering
Aerodynamic Resistance


Can have significant impacts on vehicle
performance, particularly at high speeds.
Aerodynamic resistance originates from a
number of sources:

Turbulent flow of air around the vehicle body
(≈ 85%)



Function of shape of vehicle, particularly the rear
Friction of air passing over vehicle body (≈ 12%)
Air flow through vehicle components such as
radiators and air vents (≈ 3%)
TTE 4004: Transportation Engineering
Aerodynamic Resistance

Based on these sources, equation for
determining aerodynamic resistance is:
Ra 

2
CD Af V 2
(Eq. 2.3)
Ra = aerodynamic resistance in lb (N)
ρ (rho) = air density in slugs/ft3 (kg/m3)
CD = coefficient of drag (unitless)
Af = frontal area of vehicle (projected area
of vehicle in direction of travel) in ft2 (m2)
V = vehicle speed* in ft/s (m/s)
* V is speed of vehicle relative to prevailing wind speed (we
will assume wind speed of zero for purposes of this class)
TTE 4004: Transportation Engineering
Aerodynamic Resistance

Air density is a function of both
elevation and temperature (see text
Table 2.1).


 altitude,  density
 temperature,  density
TTE 4004: Transportation Engineering
Aerodynamic Resistance


The drag coefficient is a term that implicitly
accounts for all three of the aerodynamic
resistance sources previously discussed
The drag coefficient is measured from
empirical data, either from wind tunnel
experiments or actual field tests in which a
vehicle is allowed to decelerate from a known
speed with other sources of resistance (rolling
and grade) accounted for
TTE 4004: Transportation Engineering
Aerodynamic Resistance


Table 2.2 gives an approximate range of the
drag coefficients for different types of road
vehicles
Table 2.3 gives some drag coefficients for
various automobiles over the last 35+ years


Has dropped from about 0.5 to mid 0.2’s for sedan
type vehicles
Still in 0.4 – 0.5 range for SUVs and trucks
TTE 4004: Transportation Engineering
Aerodynamic Resistance


As seen in equation 2.3, Ra is
proportional to V 2. Thus, this
resistance will increase rapidly with
increasing speed.
We can develop an expression for
determining the power needed to
overcome aerodynamic resistance
TTE 4004: Transportation Engineering
Aerodynamic Resistance

Power is the product of force and speed, so
multiplying Eq. 2.3 by speed gives:
PRa 

2
CD Af V 3
(Eq. 2.4)
or, since 1 horsepower = 550 ft-lb/sec,
hpRa 
C D A f V 3
1100
Thus, the power required to overcome aerodynamic
resistance increases with the cube of speed.
TTE 4004: Transportation Engineering
Rolling Resistance

Refers to the resistance generated from a
vehicle’s internal mechanical friction, and
pneumatic tires and their interaction with the
roadway surface.



Primary source (about 90%) of this resistance is
the deformation of the tire as it passes over the
roadway surface.
Tire penetration/roadway surface compression
(about 4%)
Tire slippage and air circulation around tire &
wheel (about 6%)
TTE 4004: Transportation Engineering
Rolling Resistance

Factors affecting Rrl


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Rigidity of tire and roadway surface
Tire inflation pressure and temperature
Vehicle speed
TTE 4004: Transportation Engineering
Rolling Resistance


Due to wide range of factors that affect
rolling resistance, a simplifying approximation
is used.
Studies have shown that rolling resistance
can be approximated as the product of a
friction term (coefficient of rolling resistance)
and the weight of the vehicle acting normal
to the roadway surface.
TTE 4004: Transportation Engineering
Rolling Resistance

Coefficient of rolling resistance (frl) for
road vehicles operating on paved
surfaces is approximated as:
V 

f rl  0.011 

 147 
V 

f rl  0.011 

 44.73 
TTE 4004: Transportation Engineering
(Eq. 2.5)
with V in ft/s
with V in m/s
Rolling Resistance

Thus, rolling resistance is approximated by:
Rrl  f rlW cos  g

However, since grades are often small, the
equation is further simplified by assuming
cos g = 1 (giving a slightly more
conservative estimate), yielding:
Rrl  f rlW
TTE 4004: Transportation Engineering
(Eq. 2.6)
Rolling Resistance

To determine power required to
overcome rolling resistance, multiply
the previous equation by speed, which
yields:
hpRrl
f rlWV

550
PRrl  f rlWV
TTE 4004: Transportation Engineering
(Eq. 2.7)
horsepower
N-m/s
Grade Resistance


Gravity, of course, can offer significant
resistance on inclines
The grade resistance is determined
simply as the component of the vehicle
weight acting parallel to the roadway
surface
TTE 4004: Transportation Engineering
Grade Resistance
Rg  W sin  g

sin  g  tan  g

Rg  WG
(Eq. 2.9)
TTE 4004: Transportation Engineering