Vehicle Dynamics & Control - Capsule Course

Explore basic vehicle geometry of a four-wheeled vehicle, including front and rear axles, wheelbase L, track widths w_f, w_r, center of gravity positions l_f, l_r, and typical sedan values.

Learn how vertical forces, weight, and normal reactions act at the front and rear axles, while longitudinal forces include traction, drag, lift, rolling resistance, and braking.

Analyze external forces on a vehicle around a circular road, highlighting center of gravity, outer and inner normal forces, centripetal and centrifugal effects on lateral and vertical directions.

Classify mechanics by statics and dynamics. Then split dynamics into kinematics and kinetics, exploring tire load, circular motion, and traction force, and introducing kinematic and kinetic bicycle models.

Apply Newton's second law to longitudinal forces, showing that net force equals mass times acceleration. Knowing mass and acceleration lets you compute the other.

Explore the center of rotation and instantaneous center in turning vehicles, showing how wheel velocities are perpendicular to the radius and how the center shifts with steering.

Explain moment of a force and moment of a couple by transferring forces to the center of gravity, using line-of-action distance to define anticlockwise moments.

Explore how a moment of force and a couple affect a vehicle, transferring forces to the center of gravity and producing anticlockwise moments, informing oversteer, understeer control, and torque vectoring.

Define the right handed coordinate system used in this course, with x toward the driving direction, y to the driver's left, and z upward, where i cross j equals k.

Learn the force notation F with directional subscripts (x, y, z) and location subscripts (front/rear axle, left/right wheel). Understand moment notation m and its axis subscript (x, y, z).

Explore the vertical coordinate system for vehicles, with origin at the center of gravity, in ISO W5, covering x (longitudinal), y (lateral), z (vertical) and translations: surge, sway, heave.

Analyze static reaction forces on a standing vehicle, linking front and rear axle loads to weight and CG position via wheelbase and lr/lf; forward CG increases front axle load.

Explore dynamic load transfer during acceleration and braking. Front and rear axle normal forces depend on weight, wheelbase, and height of center of gravity.

Analyze dynamic load transfer during cornering and how center of gravity height, track width, and CG-to-wheel distances shape inner and outer wheel normal forces and rollover risk.

Explore pitch motion caused by longitudinal dynamic load transfer and suspension flexibility, including squat and dive, and how springs respond during acceleration and braking.

Lateral dynamic load transfer drives roll motion during a turn, as centrifugal force outward shifts load to the outer wheels and compresses their suspension while the inner suspension relaxes.

Steering input on front wheels generates a yaw motion by creating different lateral force moments at the front and rear wheels, causing the vehicle to change direction on curves.

Relate wheel rotation to tangential speed via v = omega R and contrast translation, where the center moves without rotation, and compare traction with sliding on the road.

Explore rolling as a blend of rotation and translation, shown by a wheel moving on a surface. See how pure rotation, pure translation, and blends define rolling.

Explore the rolling case where vehicle speed exceeds the wheel's tangential speed, causing center speed to surpass omega and slip between wheel and road surface during braking.

Examine the rolling case when wheel tangential speed exceeds vehicle center speed, showing how center speed remains lower than omega times radius and how slip occurs between wheel and road.

Explain braking sleep ratio and traction sleep ratio, defining braking as (v - r omega)/v times 100 and traction as (r omega - v)/(r omega) times 100, with normalization and fallbacks.

Explore braking force coefficient and traction force coefficient mu_x as ratios of force to normal force in longitudinal vehicle dynamics, highlighting their slip-ratio dependence and separate braking and driving cases.

Analyze the braking and traction force coefficient versus slip ratio, 0% slip pure rolling, 100% slip wheel lock. Note mu x peak near 0.9 on asphalt.

Demonstrates generating a mu-slip curve from a flat belt test rig, by varying omega and computing slip from (v − r omega)/v while measuring braking force.

Explain braking and traction forces on a tire, showing braking torque opposite to velocity and forward traction, both governed by mu_x times the normal force and affected by slip.

Explore how viscoelastic tire material causes rolling resistance on hard surfaces through hysteresis during contact patch deflection, with compression yielding higher front-side forces than rear-side decompression.

Show how the vertical load eccentricity creates a moment balanced by rolling resistance at the contact patch, leading to FR = mu_r FZ.

Estimate typical values of the coefficient of rolling resistance for ordinary car tires on concrete, ranging from 0.01 to 0.015, yielding about 15 N at a 1000 N load.

Explore dynamic rolling radius, or effective radius, and its link between vehicle speed and wheel rotation. Compute it as velocity divided by angular velocity for use in brake systems.

Explore the dynamic rolling radius concept, its theoretical relation and empirical links: Ari relates to RG and RL in theory, and to RC for radial tear.

Explore tire slip angle alpha and how the wheel's velocity vector relative to a flat belt creates positive or negative slip angles using a right-handed coordinate system.

When a tire has slip angle, a lateral force acts perpendicular to the tire plane and grows with the slip angle, F = -C_alpha * alpha, indicating cornering stiffness.

Explore lateral force versus tire slip angle, noting a linear region up to 6-8 degrees before nonlinear behavior, with about 702,000 N per degree stiffness and alpha conversion considerations.

Define the lateral force coefficient as the ratio of lateral force to normal force, mu_y, as a function of slip angle alpha, and relate it to braking and traction coefficients.

Learn how the wheel side slip angle beta relates to steering angle delta, and the slip angle alpha, with alpha = beta minus delta, and why this matters for simulations.