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Road Vehicle Performance

CEE 320Anne Goodchild

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Outline

1. Resistancea. Aerodynamicb. Rollingc. Grade

2. Tractive Effort1. Maximum Tractive Effort2. Engine Generated Tractive Effort

3. Acceleration4. Braking

1. Stopping Sight Distance

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Review

• Force (N): – influence that tends to change motion– mass (kg) * acceleration (m/s2)

• Torque (Nm):– infleunce that tends to change rotational motion– Force * lever arm

• Work (Nm):– Force * distance

• Power (Nm/s):– Rate of doing work (work/time)

Units matter!

CE

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Primary Opposing Forces

• Resistance (N): Force impeding vehicle motion• Tractive Effort (N): Force available at the roadway

surface to perform work

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Primary Opposing Forces

• Resistance (N): Force impeding vehicle motion• Tractive Effort (N): Force available at the roadway

surface to perform work

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Sum forces on the vehicle

grla RRRmaF

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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

2VACR fDa

from National Research Council Canada

CE

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Power required to overcome Ra

• Power– work/time – force*distance/time

– Ra*V

3

2VACP fDRa

sec5501

lbfthp

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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

147101.0

Vfrl

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Power required to overcome rolling resistance

• On a level surface at maximum speed we could identify available hp

WVfP rlrlR

sec5501

lbfthp

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Grade Resistance Rg

Composed of – Gravitational force acting on the vehicle– The component parallel to the roadway

gg WR sin

gg tansin

gg WR tanGg tan

WGRg

For small angles,

θg W

θg

Rg

G=grade, vertical rise per horizontal distance (generally specified as %)

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Available Tractive Effort

The minimum of:1. Force generated by the engine, Fe2. Maximum value that is a function of the

vehicle’s weight distribution and road-tire interaction, Fmax

max,mineffort tractiveAvailable FFe

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Engine-Generated Tractive Effort

• Force

r

MF de

e

0

Fe = Engine generated tractive effort reaching wheels (lb)

Me = Engine torque (ft-lb)

ε0 = Gear reduction ratio

ηd = Driveline efficiency

r = Wheel radius (ft)

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Engine Generated Tractive Effort: Power

1000

2

2speed engine torquetime

torquepower

eee

nMP

Pe in kW

550

2 eee

nMhP

hPe in hp

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Vehicle Speed vs. Engine Speed

0

12

irn

V e

V = velocity (ft/s)

r = wheel radius (ft)

ne = crankshaft rps

i = driveline slippage

ε0 = gear reduction ratio

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Diagram

Ra

Rrlf

Rrlr

ma

Wθg

Fbf

Fbr

h

h

lf

lr

L

θg

Wf

Wr

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Maximum Tractive Effort

• Front Wheel Drive Vehicle

• Rear Wheel Drive Vehicle

= coefficient of road adhesion

LhL

hflW

F

rlf

1

max

LhL

hflW

F

rlr

1

max

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Tractive Effort Relationships

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Typical Torque-Power Curves

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Vehicle Acceleration

• Governing Equation

• Mass Factor (accounts for inertia of vehicle’s rotating parts)

maRF m

200025.004.1 m

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Braking

• Maximum braking force occurs when the tires are at a point of impending slide.– Function of roadway condition– Function of tire characteristics

• Maximum vehicle braking force (Fb max) is– coefficient of road adhesion () multiplied by

the vehicle weights normal to the roadway surface

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Braking Force

• Front axle

• Rear axle

L

fhlWF rlr

bf

max

L

fhlWF rlf

br

max

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Braking Force

• Maximum attainable vehicle deceleration is g

• Maximum obtained when force distributed as per weight distribution

• Brake force ratio is this ratio that acheives maximum braking forces

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Braking Force

• Ratio

• Efficiency

rear

front

fhl

fhlBFR

rlf

rlrrf

max

maxg

b

We develop this to calculate braking distance – necessary for roadway design

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Braking Distance

• Theoretical

– Assumes effect of speed on coefficient of rolling resistance is constant and calculated for average of initial and ending speed

– Ignores air resistance

– Minimum stopping distance given braking efficiency• For population of vehicles, what do you assume about rolling

resistance, coefficient of adhesion, and braking efficiency?

grlb

b

fg

VVS

sin2

22

21

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Braking Distance

• Practical

• For 0 grade

Gga

g

VVd

2

22

21

a

VVd

2

22

21

typically assume a = 11.2 ft/sec2

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Response time

• Perception time

• Total stopping distance

pp tVd 1

ps ddd

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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

Gga

g

VSSD 1

21

2

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Stopping Sight Distance (SSD)

from ASSHTO A Policy on Geometric Design of Highways and Streets, 2004

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