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Introduction to Road Vehicle
Performance
Road Vehicle Performance:
Introduction and Resistance

Roadway design is governed by:
Vehicle capabilities
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
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
CE 322
Transportation Engineering
Dr. Ahmed Abdel-Rahim
Introduction to Road Vehicle
Performance

Basis for roadway design guidelines:
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length of acceleration / deceleration lanes
maximum grades
stopping-sight distances
passing-sight distances
setting speed limits
timing of signalized intersections
How does performance affect max
grades?
acceleration/deceleration
braking
cornering (chap. 3)
Human capabilities
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(late chap. 2, chap. 3)
perception/reaction times
eyesight (peripheral range, height above
roadway)
Introduction

Studying vehicle performance serves
two important purposes:
insight into
1.
1.
2.
3.
2.
roadway design
traffic operations and
compromises
basis to assess impact of advancing
vehicle technologies on design guidelines
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Tractive Effort and Resistance
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Opposing forces determining straightline performance
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Major sources of vehicle resistance:
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Tractive effort = force available to
perform work
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Resistance = force impeding vehicle
motion
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Tractive Effort and Resistance
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Tractive Effort and Resistance
Illustration of forces with vehicle force diagram
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Fig. 2.1
Gravity, Rg
Grade or gravitational
Effect of speed?
Sources:
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Turbulent air flow around vehicle body (≈ 85%)
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Friction of air passing over vehicle body (≈ 12%)
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Air flow through vehicle components (≈ 3%)
Rolling
Tractive
Rolling (originates from the roadway
surface/tire interface)
Aerodynamic Resistance
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Air
Aerodynamic
Ff + Fr = ma + Ra + Rrlf + Rrlr + Rg
F = ma + Ra + Rrl + Rg
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Aerodynamic Resistance
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Aerodynamic resistance force equation:
Aerodynamic Resistance
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Air density properties (Table 2.1).

Ra 

2
CD Af V
2
(Eq. 2.3)

 altitude,  density
 temperature,  density
Ra = aerodynamic resistance in lb (N)
ρ (rho) = air density in slugs/ft3 (kg/m3)
CD = coefficient of drag (unitless)
Af = frontal projected area of vehicle in ft2 (m2)
V = vehicle speed* in ft/s (m/s)
Aerodynamic Resistance
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Drag coefficient accounts for all 3 sources
Road vehicle drag coefficients Table 2.2
(for different types)
Drag coefficients trend  Table 2.3
(past 35 years)
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Aerodynamic Resistance
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How sensitive is Ra to speed?.
Let’s develop a relationship for how
much power is needed to overcome Ra.
What is the trend?
What impact could this have on roadway design?
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Aerodynamic Resistance
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Power is the product of force and speed, so
multiplying Eq. 2.3 by speed gives:
PRa 

2
CD Af V 3
Rolling Resistance (Rrl)
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(Eq. 2.4)
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or, since 1 horsepower = 550 ft-lb/sec,
hpRa 
Source
CD Af V 3
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vehicle’s internal mechanical friction
Pneumatic tires and interaction with the roadway.
Tire deformation (≈90%)
Tire slippage and air circulation around tire &
wheel (about 6%)
Tire penetration/surface compression (about 4%)
1100
Sensitivity of power to speed…
Rolling Resistance (Rrl)
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Factors affecting Rrl
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Rigidity of tire and roadway surface
Tire inflation pressure and temperature
Vehicle speed
Rolling Resistance (Rrl)
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Approximated as product of a friction term
(coefficient of rolling resistance) and vehicle weight.
Coefficient of rolling resistance (frl) on paved surfaces
V 

f rl  0.011 

147


V 

f rl  0.011 

 44.73 
(Eq. 2.5)
with V in ft/s
with V in m/s
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Rolling Resistance (Rrl)
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Rolling Resistance (Rrl)
Rolling resistance approximation:
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Rrl  f rlW cos  g
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For a 10% grade, what is the cosine term?
Rrl  f rlW
Power required to overcome rolling
resistance:
hp Rrl
f WV
 rl
550
PRrl  f rlWV
(Eq. 2.7)
horsepower
N-m/s
(Eq. 2.6)
Grade Resistance (Rg)

What is the grade resistance to vehicle
motion?
Grade Resistance (Rg)
Rg  W sin  g

sin  g  tan  g

Rg  WG
(Eq. 2.9)
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