NAZARIN B. NORDIN nazarin@icam.edu.my. What you will learn: Tractive effort, tractive resistance, braking efficiency Tractive resistance components: rolling

BTE 1013ENGINEERING SCIENCES

12. TRACTIVE EFFORT AND TRACTIVE RESISTANCE

NAZARIN B. NORDINnazarin@icam.edu.my

What you will learn:

• Tractive effort, tractive resistance, braking efficiency

• Tractive resistance components: rolling/ gradient/ air resistance

• Energy dissipated/ power required at constant velocity on level plane, accelerating/ braking forces applied on level plane, braking efficiency

Vehicle Dynamics

CEE 320Steve Muench

Outline

1. Resistancea. Aerodynamicb. Rollingc. Grade

2. Tractive Effort3. Acceleration4. Braking Force5. Stopping Sight Distance (SSD)

Main Concepts

• Resistance• Tractive effort• Vehicle acceleration• Braking• Stopping distance

grla RRRmaF

Resistance

Resistance is defined as the force impeding vehicle motionWhat is this force? 1. Aerodynamic resistance2. Rolling resistance3. Grade resistance

grla RRRmaF

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

3

2VACP fDRa

sec5501

lbfthp

from National Research Council Canada

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 resistance5. Simplifying approximation:

WfR rlrl

147101.0

VfrlWVfP rlrlR

sec5501

lbfthp

Grade Resistance Rg

Composed of – Gravitational force acting on the vehicle

gg WR sin

gg tansin

gg WR tanGg tan

WGRg

For small angles,

θg W

θg

Rg

Available Tractive Effort

The minimum of:1. Force generated by the engine, Fe

2. Maximum value that is a function of the vehicle’s weight distribution and road-tire interaction, Fmax

max,mineffort tractiveAvailable FFe

Tractive Effort Relationships

Engine-Generated Tractive Effort

• Force

• Power

r

MF de

e

0

2

minsec

60

rpm engine

550

lbft torque

sec

lbft550 hp

Fe = Engine generated tractive effort reaching wheels (lb)

Me = Engine torque (ft-lb)

ε0 = Gear reduction ratio

ηd = Driveline efficiency

r = Wheel radius (ft)

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

Typical Torque-Power Curves

Maximum Tractive Effort

• Front Wheel Drive Vehicle

• Rear Wheel Drive Vehicle

• What about 4WD?

LhL

hflW

F

rlf

1

max

LhL

hflW

F

rlr

1

max

DiagramR

a

Rrlf

Rrlr

ma

Wθ

g

Fbf

Fbr

h

h

lf

lr

L

θg

Wf

Wr

Vehicle Acceleration

• Governing Equation

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

maRF m

200025.004.1 m

ExampleA 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

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

Braking Force

• Front axle

• Rear axle

L

fhlWF rlr

bf

max

L

fhlWF rlf

br

max

Braking Force

• Ratio

• Efficiency

rear

front

fhl

fhlBFR

rlf

rlr

maxg

b

Braking Distance

• Theoretical– ignoring air resistance

• Practical

• Perception

• Total

grlb

b

fg

VVS

sin2

22

21

Gga

g

VVd

2

22

21

pp tVd 1

ps ddd

a

VVd

2

22

21

For grade = 0

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

Stopping Sight Distance (SSD)

from ASSHTO A Policy on Geometric Design of Highways and Streets, 2001

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

SSD – Quick and Dirty

a

VVV

V

Ggag

VVd

222

221

22

21 075.1

2.11075.1

2.11

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 = V1 in mpha = deceleration, 11.2 ft/s2 in US customary unitstp = Conservative perception / reaction time = 2.5 seconds

ps Vta

Vd 47.1075.1

2

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.

THANK YOU