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Vehicle Dynamics. CEE 320 Steve Muench. Outline. Resistance Aerodynamic Rolling Grade Tractive Effort Acceleration Braking Force Stopping Sight Distance (SSD). Main Concepts. Resistance Tractive effort Vehicle acceleration Braking Stopping distance. Resistance.

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vehicle dynamics

Vehicle Dynamics

CEE 320Steve Muench

outline
Outline
  • Resistance
    • Aerodynamic
    • Rolling
    • Grade
  • Tractive Effort
  • Acceleration
  • Braking Force
  • Stopping Sight Distance (SSD)
main concepts
Main Concepts
  • Resistance
  • Tractive effort
  • Vehicle acceleration
  • Braking
  • Stopping distance
resistance
Resistance

Resistance is defined as the force impeding vehicle motion

  • What is this force?
  • Aerodynamic resistance
  • Rolling resistance
  • Grade resistance
aerodynamic resistance r a
Aerodynamic Resistance Ra

Composed of:

  • Turbulent air flow around vehicle body (85%)
  • Friction of air over vehicle body (12%)
  • Vehicle component resistance, from radiators and air vents (3%)

from National Research Council Canada

rolling resistance r rl
Rolling Resistance Rrl

Composed primarily of

  • Resistance from tire deformation (90%)
  • Tire penetration and surface compression ( 4%)
  • Tire slippage and air circulation around wheel ( 6%)
  • Wide range of factors affect total rolling resistance
  • Simplifying approximation:
grade resistance r g
Grade Resistance Rg

Composed of

  • Gravitational force acting on the vehicle

θg

For small angles,

Rg

θg

W

available tractive effort
Available Tractive Effort

The minimum of:

  • Force generated by the engine, Fe
  • Maximum value that is a function of the vehicle’s weight distribution and road-tire interaction, Fmax
maximum tractive effort
Maximum Tractive Effort
  • Front Wheel Drive Vehicle
  • Rear Wheel Drive Vehicle
  • What about 4WD?
diagram
Diagram

Ra

h

ma

Rrlf

h

Wf

W

Fbf

θg

lf

Rrlr

lr

Wr

L

Fbr

θg

vehicle acceleration
Vehicle Acceleration
  • Governing Equation
  • Mass Factor

(accounts for inertia of vehicle’s rotating parts)

example
Example

A 1989 Ford 5.0L Mustang Convertible starts on a flat grade from a dead stop as fast as possible. What’s the maximum acceleration it can achieve before spinning its wheels? μ = 0.40 (wet, bad pavement)

1989 Ford 5.0L Mustang Convertible

braking force
Braking Force
  • Front axle
  • Rear axle
braking force18
Braking Force
  • Ratio
  • Efficiency
braking distance
Braking Distance
  • Theoretical
    • ignoring air resistance
  • Practical
  • Perception
  • Total

For grade = 0

stopping sight distance ssd
Stopping Sight Distance (SSD)
  • Worst-case conditions
    • Poor driver skills
    • Low braking efficiency
    • Wet pavement
  • Perception-reaction time = 2.5 seconds
  • Equation
stopping sight distance ssd21
Stopping Sight Distance (SSD)

from ASSHTO APolicy on Geometric Design of Highways and Streets, 2001

Note: this table assumes level grade (G = 0)

ssd quick and dirty
SSD – Quick and Dirty
  • Acceleration due to gravity, g = 32.2 ft/sec2
  • There are 1.47 ft/sec per mph
  • Assume G = 0 (flat grade)

V = V1 in mph

a = deceleration, 11.2 ft/s2 in US customary units

tp = Conservative perception / reaction time = 2.5 seconds

primary references
Primary References
  • Mannering, F.L.; Kilareski, W.P. and Washburn, S.S. (2005). Principles of Highway Engineering and Traffic Analysis, Third Edition). Chapter 2
  • American Association of State Highway and Transportation Officals (AASHTO). (2001). A Policy on Geometric Design of Highways and Streets, Fourth Edition. Washington, D.C.