Vehicle Types and Dynamics Milos N. Mladenovic Assistant Professor Department of Built Environment

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1 Vehicle Types and Dynamics Milos N. Mladenovic Assistant Professor Department of Built Environment

2 Outline Transport modes Vehicle and road design relationship Resistance forces Acceleration Braking Turning 2

3 Technical, Operational, and System Ch. 3

4 Two Major Design Factors Vehicle capabilities acceleration/deceleration braking cornering Human capabilities perception/reaction times eyesight (peripheral range, height above roadway) 4

5 Road Vehicles Design length of acceleration / deceleration lanes maximum grades stopping-sight distances passing-sight distances setting speed limits minimum height clearance minimum corner radius timing of signalized intersections 5

6 Road Vehicles Design Studying vehicle performance serves two important purposes: provides insight into roadway design and traffic operations requirements for accommodating a wide variety of vehicles it forms a basis for understanding the impact of advancing vehicle technologies on existing roadway design guidelines 6

7 Road Vehicles Design Main components of road vehicle performance 1. Tractive effort 2. Resistance 3. Acceleration 4. Braking 5. Turning 7

8 Tractive Effort and Resistance These are the opposing forces that determine straight-line performance of road vehicles Tractive effort is simply the force available at the roadway surface to perform work (expressed in [N]) Resistance (expressed in [N]) is defined as the force impeding vehicle motion 8

9 3 Major Sources of Resistance 1. Aerodynamic 2. Rolling (originates from the roadway surface and tire interaction) 3. Grade / gravitational 9

10 Vehicle Force Diagram F f(r) = available tractive effort on the front (rear) tires [N] m = vehicle mass [kg] a = acceleration [m/s^2] R a = aerodynamic resistance [N] R rlf(r) = rolling resistance on the front (rear) tires [N] R g = grade resistance [N] W = weight [N] F f + F r = ma + R a + R rlf + R rlr + R g F = ma + R a + R rl + R g 10

11 Aerodynamic Resistance - R a Can have significant impacts on vehicle performance, particularly at high speeds. Aerodynamic resistance originates from a number of sources: Turbulent flow of air around the vehicle body ( 85%) Function of shape of vehicle, particularly the rear Friction of air passing over vehicle body ( 12%) Air flow through vehicle components such as radiators and air vents ( 3%) 11

12 Aerodynamic Resistance - R a R a C 2 A V R a = aerodynamic resistance in (N) ρ (rho) = air density in (kg/m 3 ) C D = coefficient of drag (unitless) A f = frontal area of vehicle (projected area of vehicle in direction of travel) in (m 2 ) V = vehicle speed* in (m/s) V is speed of vehicle relative to prevailing wind speed (we will assume wind speed of zero for purposes of this class) Resistance will increase rapidly with increasing vehicle speed D f 2 12

13 Aerodynamic Resistance - R a Air density is a function of both elevation and temperature. altitude, density temperature, density 13

14 Aerodynamic Resistance - R a The drag coefficient (C D ) is a term that implicitly accounts for all three of the aerodynamic resistance sources. The drag coefficient is measured from empirical data, such as wind tunnel experiments or actual field tests. 14

15 Aerodynamic Resistance - R a 15

16 Resistance R a and Power P P R a RaV C 2 D A V f 3 N-m/s Power is the product of force and speed Power required to overcome aerodynamic resistance increases with the cube of speed 16

17 Rolling Resistance - R rl Refers to the resistance generated from a vehicle s internal mechanical friction, and pneumatic tires and their interaction with the roadway surface. Primary source (about 90%) of this resistance is the deformation of the tire as it passes over the roadway surface. Tire penetration/roadway surface compression (about 4%) Tire slippage and air circulation around tire & wheel (about 6%) 17

18 Rolling Resistance - R rl Factors affecting Rrl Rigidity of tire and roadway surface Tire inflation pressure and temperature Vehicle speed Due to wide range of factors that affect rolling resistance, a simplifying approximation is used. Studies have shown that rolling resistance can be approximated as the product of a friction term (coefficient of rolling resistance) and the weight of the vehicle acting normal to the roadway surface. 18

19 Rolling Resistance - R rl Coefficient of rolling resistance (f rl ) for road vehicles operating on paved surfaces is approximated as: f rl V with V in m/s Rolling resistance is approximated by: R rl f rl W cos g Assume cos g = 1 for small grades R rl f rl W 19

20 Resistance R rl and Power P P f WV R rl rl N-m/s Power is the product of force and speed Power required to overcome rolling resistance directly depends on coefficient of rolling resistance and vehicle s weight 20

21 Grade Resistance - R g The grade resistance is determined simply as the component of the vehicle weight acting parallel to the roadway surface R g W sin sin R g WG g g tan g 21

22 Vehicle Dynamics 22

23 Available Tractive Effort Tractive effort available to overcome resistance forces and/or to accelerate the vehicle is determined as min from: 1. Some maximum value that is a function of the vehicle s weight distribution and the characteristics of the pavement/tire interface maximum tractive effort (F max ) F W max r coefficient of road adhesion x normal force (rear) 2. The force generated by the vehicle s engine enginegenerated tractive effort (F e ) 23

24 Engine-generated Tractive Effort F e M e 0 d r F e = engine-generated tractive effort (N) M e = engine torque (N-m) 0 = overall gear reduction ratio (unitless) d = mechanical efficiency term (unitless) r = radius of the drive wheels (m) 24

25 Typical Energy Use for a ICE Car 25

26 Vehicle Acceleration The available tractive effort to accelerate is reduced by the resistance forces F = m ma + R a + R rl + R g m is the mass factor, and accounts for the inertia of the vehicle s rotating parts that must be overcome during acceleration γ m F R γ m ma = ε

27 Vehicle Acceleration The force available to accelerate is given by: F net F R if F - R > 0, then the vehicle accelerates. if F - R = 0, then the vehicle stays at the same speed. if F - R < 0, then the vehicle decelerates. 27

28 Vehicle Acceleration Time to accelerate F net = γ m m dv dt i.e. dt = γ mm dv F net V 2 t = γ m m න V 1 dv f(v) Distance to accelerate V 2 VdV d a = γ m m න V 1 f(v) 28

29 Vehicle Dynamics 29

30 Vehicle Dynamics 30

31 Vehicle Dynamics 31

32 Vehicle Braking Distance required to accelerate vs. distance required to decelerate Braking performance is key factor for design of horizontal and vertical curves Minimum stopping distance: Theoretical conditions Practical conditions 32

33 Force-Moment Generating Diagram Braking forces F bf(r) have replaced the tractive forces and are in the opposite direction Also, ma points in opposite direction (because this force is counteracting braking force) 33

Braking Force Ratio and Efficiency Designing vehicle s braking system usually focuses on good on average, because the optimal brake-force proportioning changes with both vehicle and

34 Braking Force Ratio and Efficiency Designing vehicle s braking system usually focuses on good on average, because the optimal brake-force proportioning changes with both vehicle and road conditions Passenger and cargo loading conditions, especially for trucks, is a major factor Changes in road conditions produce different coefficients of road adhesion ( ) ABS? 34

35 Theoretical Stopping Distance Forces on one vehicle, under one road condition Assuming final speed V 2 = 0 S W b 2gK a ln1 bw K f rl a V W 2 1 W sin g Where: - b is the mass factor accounting for moments of inertia during braking, given value of 1.04 for automobiles - grade resistance term is + for uphill, - for downhill gmax - breaking efficiency b - Aerodynamic resistance factor K a CD Af 2 35

36 Practical Stopping Distance Estimation of ALL driver skill levels, vehicle types, and weather conditions Where: a = acceleration (negative for deceleration) in m/s^2 Db = deceleration distance in m V1, V2 = initial and final vehicle speed (m/s) Acceptable deceleration rate by AASHTO is 3.4 m/s^2 36

37 Practical Stopping Distance To account for the effect of the grade Where: g = gravitational acceleration (9.81 m/s^2) G = roadway grade in percent/100 (+ for uphill, - for downhill) 37

38 Perception/Reaction Time-Distance d r = V 1 t r d r = distance traveled during PRT (m) t r = time required to perceive and react to the need to stop (sec) 2.5 sec by AASHTO d s = d + d r d s = total stopping distance (m) d = distance traveled during braking (m) d r = distance traveled during perception/reaction (m) 38

39 Selective vs. Full Deceleration Feels Moderate Comfortable Uncomfortable Stopping Probability Deceleration Rate (m/s^2)

40 Vehicle Dimensions Finland 40

41 Vehicle Dimensions Finland 41

42 Regular 12-meter Bus - Los Angeles Standard propulsion: diesel motor 42

43 25 m Double-Articulated Bus - Aachen Not legal in the vast majority of cities Copyright: Felix Schmidt 43

44 Different Bus Vehicle Types 44

45 Technical Data for Selected Bus Models 45

46 Vehicle Turning Low-speed turning characteristics (<= 15 km/h) vs. High-speed turning characteristics (> 15 km/h) 46

47 Critical Body Points 47

48 Critical Body Points 48

49 Key Turning Dimensions 49 Width of vehicle wheel path is: Inner wheel path radius: When the outside body path radius, R bo, is known, R bi is : W l l R R f a o b i b 2 2 ) ( t a o w o w w w l R R W 2 2 t a o w i w w l R R 2 2

50 Semi-Trailer Turning Radius Trucks Image Library 50

51 Electric Street Car - Portland Typically 4 to 6 axles Copyright: Ed Beimborn 51

52 100% Low-floor Car LRT - Paris High floor: m Low floor: m 52

53 Technical Data for Rail Transit Vehicles 53

54 Turning Geometry of a Four-Axle Rail Vehicle General observations: - Profile widening on the inside of the curve depends on the distance between truck swivels, l t ; - Profile widening on the outside depends mostly on the overhang length, l o. 54

55 Turning Geometry of a Four-Axle Rail Vehicle For given vehicle dimensions l i, l o, and W and track centerline radius R the positions of these points are expressed by the following equations: o b R ' R ' R W lt 2 The inner and outer body radii are, respectively, and R R i b R ' W 2 2 lt l 2 o 2 55

56 Turning Geometry of a Four-Axle Rail Vehicle The widening of the free profile on the inner and outer sides are, respectively: and R i b R ' R R o b R ' W 2 2 lt 2 l o 2 W R 2 The total width of the free profile is: W b W R i b R O b or W b R ' W 2 2 lt 2 l o 2 R ' W 2 56

JCE4600 Fundamentals of Traffic Engineering

JCE4600 Fundamentals of Traffic Engineering Introduction to Geometric Design Agenda Kinematics Human Factors Stopping Sight Distance Cornering Intersection Design Cross Sections 1 AASHTO Green Book Kinematics