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CEE 320 Winter 2006 Vehicle Dynamics CEE 320 Steve Muench

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CEE 320 Winter 2006 Outline 1.Resistance a.Aerodynamic b.Rolling c.Grade 2.Tractive Effort 3.Acceleration 4.Braking Force 5.Stopping Sight Distance (SSD)

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CEE 320 Winter 2006 Main Concepts Resistance Tractive effort Vehicle acceleration Braking Stopping distance

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CEE 320 Winter 2006 Resistance Resistance is defined as the force impeding vehicle motion 1.What is this force? 2.Aerodynamic resistance 3.Rolling resistance 4.Grade resistance

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CEE 320 Winter 2006 Aerodynamic Resistance R a 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%) from National Research Council Canada

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CEE 320 Winter 2006 Rolling Resistance R rl 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:

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CEE 320 Winter 2006 Grade Resistance R g Composed of –Gravitational force acting on the vehicle For small angles, θgθg W θgθg RgRg

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CEE 320 Winter 2006 Available Tractive Effort The minimum of: 1.Force generated by the engine, F e 2.Maximum value that is a function of the vehicle’s weight distribution and road-tire interaction, F max

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CEE 320 Winter 2006 Tractive Effort Relationships

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CEE 320 Winter 2006 Engine-Generated Tractive Effort Force Power FeFe =Engine generated tractive effort reaching wheels (lb) MeMe =Engine torque (ft-lb) ε0ε0 =Gear reduction ratio ηdηd =Driveline efficiency r=Wheel radius (ft)

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CEE 320 Winter 2006 Vehicle Speed vs. Engine Speed V =velocity (ft/s) r =wheel radius (ft) nene =crankshaft rps i =driveline slippage ε0ε0 =gear reduction ratio

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CEE 320 Winter 2006 Typical Torque-Power Curves

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CEE 320 Winter 2006 Maximum Tractive Effort Front Wheel Drive Vehicle Rear Wheel Drive Vehicle What about 4WD?

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CEE 320 Winter 2006 Diagram RaRa R rlf R rlr ma W θgθg F bf F br h h lflf lrlr L θgθg WfWf WrWr

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CEE 320 Winter 2006 Vehicle Acceleration Governing Equation Mass Factor (accounts for inertia of vehicle’s rotating parts)

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CEE 320 Winter 2006 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 Torque300 @ 3200 rpm Curb Weight3640 Weight DistributionFront 57% Rear 43% Wheelbase100.5 in Tire SizeP225/60R15 Gear Reduction Ratio3.8 Driveline efficiency90% Center of Gravity20 inches high

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CEE 320 Winter 2006 Braking Force Front axle Rear axle

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CEE 320 Winter 2006 Braking Force Ratio Efficiency

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CEE 320 Winter 2006 Braking Distance Theoretical –ignoring air resistance Practical Perception Total For grade = 0

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CEE 320 Winter 2006 Stopping Sight Distance (SSD) Worst-case conditions –Poor driver skills –Low braking efficiency –Wet pavement Perception-reaction time = 2.5 seconds Equation

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CEE 320 Winter 2006 Stopping Sight Distance (SSD) from ASSHTO A Policy on Geometric Design of Highways and Streets, 2001 Note: this table assumes level grade (G = 0)

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CEE 320 Winter 2006 SSD – Quick and Dirty 1.Acceleration due to gravity, g = 32.2 ft/sec 2 2.There are 1.47 ft/sec per mph 3.Assume G = 0 (flat grade) V = V 1 in mph a = deceleration, 11.2 ft/s 2 in US customary units t p = Conservative perception / reaction time = 2.5 seconds

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CEE 320 Winter 2006

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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.

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