bte 1013 engineering sciences

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BTE 1013 ENGINEERING SCIENCES 12. TRACTIVE EFFORT AND TRACTIVE RESISTANCE NAZARIN B. NORDIN [email protected]

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BTE 1013 ENGINEERING SCIENCES. 12. TRACTIVE EFFORT AND TRACTIVE RESISTANCE. NAZARIN B. NORDIN [email protected]. What you will learn:. Tractive effort, tractive resistance, braking efficiency Tractive resistance components: rolling/ gradient/ air resistance - PowerPoint PPT Presentation

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Page 1: BTE 1013 ENGINEERING  SCIENCES

BTE 1013ENGINEERING SCIENCES

12. TRACTIVE EFFORT AND TRACTIVE RESISTANCE

NAZARIN B. [email protected]

Page 2: BTE 1013 ENGINEERING  SCIENCES

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

Page 3: BTE 1013 ENGINEERING  SCIENCES

Vehicle Dynamics

CEE 320Steve Muench

Page 4: BTE 1013 ENGINEERING  SCIENCES

Outline

1. Resistancea. Aerodynamicb. Rollingc. Grade

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

Page 5: BTE 1013 ENGINEERING  SCIENCES

Main Concepts

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

grla RRRmaF

Page 6: BTE 1013 ENGINEERING  SCIENCES

Resistance

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

grla RRRmaF

Page 7: BTE 1013 ENGINEERING  SCIENCES

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

Page 8: BTE 1013 ENGINEERING  SCIENCES

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

Page 9: BTE 1013 ENGINEERING  SCIENCES

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

Page 10: BTE 1013 ENGINEERING  SCIENCES

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

Page 11: BTE 1013 ENGINEERING  SCIENCES

Tractive Effort Relationships

Page 12: BTE 1013 ENGINEERING  SCIENCES

Engine-Generated Tractive Effort

• Force

• Power

rMF de

e 0

2

minsec60

rpm engine550

lbft torquesec

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)

Page 13: BTE 1013 ENGINEERING  SCIENCES

Vehicle Speed vs. Engine Speed

0

12

irnV e

V = velocity (ft/s)r = wheel radius (ft)ne = crankshaft rps

i = driveline slippageε0 = gear reduction ratio

Page 14: BTE 1013 ENGINEERING  SCIENCES

Typical Torque-Power Curves

Page 15: BTE 1013 ENGINEERING  SCIENCES

Maximum Tractive Effort

• Front Wheel Drive Vehicle

• Rear Wheel Drive Vehicle

• What about 4WD?

LhL

hflW

F

rlf

1

max

LhL

hflWF

rlr

1

max

Page 16: BTE 1013 ENGINEERING  SCIENCES

DiagramR

a

Rrlf

Rrlr

ma

g

Fbf

Fbr

h

h

lf

lrL

θg

Wf

Wr

Page 17: BTE 1013 ENGINEERING  SCIENCES

Vehicle Acceleration

• Governing Equation

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

maRF m

200025.004.1 m

Page 18: BTE 1013 ENGINEERING  SCIENCES

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 rpmCurb 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

Page 19: BTE 1013 ENGINEERING  SCIENCES

Braking Force

• Front axle

• Rear axle

L

fhlWF rlrbf

max

L

fhlWF rlf

br

max

Page 20: BTE 1013 ENGINEERING  SCIENCES

Braking Force

• Ratio

• Efficiency

rear

frontfhlfhl

BFRrlf

rlr

maxg

b

Page 21: BTE 1013 ENGINEERING  SCIENCES

Braking Distance

• Theoretical– ignoring air resistance

• Practical

• Perception

• Total

grlb

b

fgVVS

sin2

22

21

Ggag

VVd2

22

21

pp tVd 1

ps ddd

aVVd

2

22

21

For grade = 0

Page 22: BTE 1013 ENGINEERING  SCIENCES

Stopping Sight Distance (SSD)

• Worst-case conditions– Poor driver skills– Low braking efficiency– Wet pavement

• Perception-reaction time = 2.5 seconds• Equation

rtVG

gag

VSSD 1

21

2

Page 23: BTE 1013 ENGINEERING  SCIENCES

Stopping Sight Distance (SSD)

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

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

Page 24: BTE 1013 ENGINEERING  SCIENCES

SSD – Quick and Dirty

aVVVV

GgagVVd

222

221

22

21 075.1

2.11075.1

2.111

247.1

02.322.112.322047.1

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 VtaVd 47.1075.1

2

Page 25: BTE 1013 ENGINEERING  SCIENCES
Page 26: BTE 1013 ENGINEERING  SCIENCES

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.

Page 27: BTE 1013 ENGINEERING  SCIENCES

THANK YOU