Vehicle Dynamics

5/20/2018 Vehicle Dynamics

1/24

CEE320

Winter

2006

Vehicle Dynamics

CEE 320Steve Muench


2/24

CEE320

Winter2006

Outline

1. Resistancea. Aerodynamic

b. Rollingc. Grade

2. Tractive Effort

3. Acceleration

4. Braking Force5. Stopping Sight Distance (SSD)


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Winter2006

Main Concepts

Resistance

Tractive effort

Vehicle acceleration

Braking

Stopping distance

grla RRRmaF


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Resistance

Resistance is defined as the force impeding

vehicle motion

1. What is this force?2. Aerodynamic resistance

3. Rolling resistance

4. Grade resistance

grla RRRmaF


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CEE320

Winter2006

Aerodynamic Resistance Ra

Composed of:

1. Turbulent air flow around vehicle body (85%)

2. Friction of air over vehicle body (12%)3. Vehicle component resistance, from radiators

and air vents (3%)2

2

VACR fDa

3

2VACP fDRa

sec5501 lbfthp

from National Research Council Canada


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CEE320

Winter2006

Rolling Resistance Rrl

Composed primarily of

1. Resistance from tire deformation (

90%)

2. Tire penetration and surface compression (

4%)

3. Tire slippage and air circulation around wheel ( 6%)

4. Wide range of factors affect total rolling resistance

5. Simplifying approximation:

WfR rlrl

147

101.0 V

frlWVfP rlrlR

sec5501 lbfthp


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Grade Resistance Rg

Composed of

Gravitational force acting on the vehicle

gg WR sin

gg tansin

gg

WR tan

Ggtan

WGRg

For small angles,

g W

g

Rg


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Winter2006

Available Tractive Effort

The minimum of:

1. Force generated by the engine, Fe

2. Maximum value that is a function of thevehicles weight distribution and road-tire

interaction, Fmax

max,minefforttractiveAvailable FFe


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Tractive Effort Relationships


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Winter2006

Engine-Generated Tractive Effort

Force

Power

r

MF dee

0

2

min

sec60

rpmengine

550

lbfttorque

sec

lbft550hp

Fe = Engine generated tractive effort

reaching wheels (lb)

Me = Engine torque (ft-lb)

0 = Gear reduction ratio

d = Driveline efficiencyr = Wheel radius (ft)


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Vehicle Speed vs. Engine Speed

0

12

irnV e

V = velocity (ft/s)

r = wheel radius (ft)

ne = crankshaft rpsi = driveline slippage

0 = gear reduction ratio


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Typical Torque-Power Curves


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Maximum Tractive Effort

Front Wheel Drive Vehicle

Rear Wheel Drive Vehicle

What about 4WD?

L

hL

hflW

F

rlf

1

max

L

hL

hflW

F

rlr

1

max


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Winter2006

Diagram

g


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Winter2006

Vehicle Acceleration

Governing Equation

Mass Factor

(accounts for inertia of vehicles rotating parts)

maRF m

2

00025.004.1 m


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Example

A 1989 Ford 5.0L Mustang Convertible starts on a flat grade from a dead

stop as fast as possible. Whats the maximum acceleration it can achieve

before spinning its wheels? = 0.40 (wet, bad pavement)

1989 Ford 5.0L Mustang Convertible

Torque 300 @ 3200 rpm

Curb Weight 3640

Weight Distribution Front 57% Rear 43%

Wheelbase 100.5 in

Tire Size P225/60R15

Gear Reduction Ratio 3.8

Driveline efficiency 90%

Center of Gravity 20 inches high


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Braking Force

Front axle

Rear axle

L

fhlWF rlrbf

max

L

fhlWF

rlf

br

max


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r2006

Braking Force

Ratio

Efficiency

rear

front

fhl

fhlBFR

rlf

rlr

maxg

b


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r2006

Braking Distance

Theoretical ignoring air resistance

Practical

Perception

Total

grlb

b

fg

VVS

sin2

22

21

Gg

ag

VVd

2

22

21

pp tVd 1

ps ddd

a

VVd

2

2

2

2

1

For grade = 0


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Stopping Sight Distance (SSD)

Worst-case conditions

Poor driver skills

Low braking efficiency Wet pavement

Perception-reaction time = 2.5 seconds

Equation

rtV

Gg

ag

VSSD 1

21

2


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Stopping Sight Distance (SSD)

from ASSHTOAPolicy on Geometric Design of Highways and Streets, 2001

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


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SSDQuick and Dirty

aVV

VV

Ggag

VVd

222

22

1

2

2

2

1 075.12.11

075.12.11

1

2

47.1

02.322.112.322

047.1

2

1. Acceleration due to gravity, g = 32.2 ft/sec2

2. There are 1.47 ft/sec per mph

3. Assume G = 0 (flat grade)

ppp VttVd 47.147.1 1

V= V1in mph

a = deceleration, 11.2 ft/s2in US customary units

tp= Conservative perception / reaction time = 2.5 seconds

ps Vta

Vd 47.1075.1

2


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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.

Documents

Vehicle Dynamics