1. CEE 320 Fall 2008 Road Vehicle Performance CEE 320 Anne Goodchild

2. CEE 320 Fall 2008 Outline 1.Resistance a.Aerodynamic b.Rolling c.Grade 2.Tractive Effort 1.Maximum Tractive Effort 2.Engine Generated Tractive Effort 3.Acceleration 4.Braking 1.Stopping Sight Distance

3. CEE 320 Fall 2008 Review Force (N): –influence that tends to change motion –mass (kg) * acceleration (m/s 2 ) 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) UnitsUnits matter!matter

4. CEE 320 Fall 2008 Primary Opposing Forces Resistance (N): Force impeding vehicle motion Tractive Effort (N): Force available at the roadway surface to perform work

5. CEE 320 Fall 2008 Primary Opposing Forces Resistance (N): Force impeding vehicle motion Tractive Effort (N): Force available at the roadway surface to perform work

6. CEE 320 Fall 2008 Sum forces on the vehicle

7. CEE 320 Fall 2008 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

8. CEE 320 Fall 2008

9. Power required to overcome R a Power –work/time –force*distance/time –R a *V

10. CEE 320 Fall 2008 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:

11. CEE 320 Fall 2008 Power required to overcome rolling resistance On a level surface at maximum speed we could identify available hp

12. CEE 320 Fall 2008 Grade Resistance R g Composed of –Gravitational force acting on the vehicle –The component parallel to the roadway For small angles, θgθg W θgθg RgRg G=grade, vertical rise per horizontal distance (generally specified as %)

13. CEE 320 Fall 2008 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

14. CEE 320 Fall 2008 Engine-Generated Tractive Effort Force FeFe =Engine generated tractive effort reaching wheels (lb) MeMe =Engine torque (ft-lb) ε0ε0 =Gear reduction ratio ηdηd =Driveline efficiency r=Wheel radius (ft)

15. CEE 320 Fall 2008 Engine Generated Tractive Effort: Power P e in kW hP e in hp

16. CEE 320 Fall 2008 Vehicle Speed vs. Engine Speed V =velocity (ft/s) r =wheel radius (ft) nene =crankshaft rps i =driveline slippage ε0ε0 =gear reduction ratio

17. CEE 320 Fall 2008 Diagram RaRa R rlf R rlr ma W θgθg F bf F br h h lflf lrlr L θgθg WfWf WrWr

18. CEE 320 Fall 2008 Maximum Tractive Effort Front Wheel Drive Vehicle Rear Wheel Drive Vehicle  = coefficient of road adhesion

19. CEE 320 Fall 2008 Tractive Effort Relationships

20. CEE 320 Fall 2008

21. Typical Torque-Power Curves

22. CEE 320 Fall 2008 Vehicle Acceleration Governing Equation Mass Factor (accounts for inertia of vehicle’s rotating parts)

23. CEE 320 Fall 2008 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 (F b max ) is –coefficient of road adhesion (  ) multiplied by the vehicle weights normal to the roadway surface

24. CEE 320 Fall 2008 Braking Force Front axle Rear axle

25. CEE 320 Fall 2008 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

26. CEE 320 Fall 2008 Braking Force Ratio Efficiency We develop this to calculate braking distance – necessary for roadway design

27. CEE 320 Fall 2008 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?

28. CEE 320 Fall 2008 Braking Distance Practical For 0 grade typically assume a = 11.2 ft/sec 2

29. CEE 320 Fall 2008 Response time Perception time Total stopping distance

30. CEE 320 Fall 2008 Stopping Sight Distance (SSD) Worst-case conditions –Poor driver skills –Low braking efficiency –Wet pavement Perception-reaction time = 2.5 seconds Equation

31. CEE 320 Fall 2008 Stopping Sight Distance (SSD) from ASSHTO A Policy on Geometric Design of Highways and Streets, 2004 Note: this table assumes level grade (G = 0)