ABS (anti-lock braking system)

Senses wheel slip under braking and trims the brake pressure to hold each tire just below its peak slip ratio, so the wheels never lock. Many racing series ban it. See also threshold braking.

Adhesion

One of the two sources of rubber grip: the tread rubber gripping the road surface itself. Compare hysteresis.

Anti-roll bar

A torsion spring linking the left and right wheels of an axle. It adds roll stiffness to that axle, so a stiffer bar moves more of the lateral load transfer to that end of the car. It cannot change the total.

Balance

Which axle reaches its grip limit first. If the front saturates first the car runs wide (understeer); if the rear does, it rotates (oversteer).

Brake bias (brake balance)

The share of the total braking force made by the front brakes, written \(\beta\) in Lesson 3.3 (not to be confused with sideslip). Set by piston and disc sizes and a bias knob in the cockpit. See also ideal brake distribution.

Brake-force diagram

A plot of front against rear braking force, both as fractions of the car's weight, with lines of constant deceleration, the front- and rear-lock lines and the ideal curve. A fixed brake bias is a straight line from the origin.

Camber (\(\gamma\))

The tilt of a wheel from vertical, seen from the front of the car. Negative camber means the top of the wheel leans in toward the car's centerline. Race cars set negative static camber so that, after body roll, the heavily loaded outside tire ends up near its best angle.

Camber thrust

The lateral force a tilted, rolling tire makes even at zero slip angle, pushing toward the side it leans: \(F_y \approx C_\alpha\alpha + C_\gamma\gamma\), with the camber stiffness \(C_\gamma\) much smaller than \(C_\alpha\).

Center of gravity (CG)

The point where the car's weight acts and where its mass can be treated as concentrated. The body axes have their origin there, and its height \(h\) drives every load-transfer formula.

Centrifugal force

Not a real force, and never drawn on a free-body diagram. In a ground-fixed frame nothing pushes a cornering car outward: the tires pull it inward. The outward “push” you feel is your body trying to keep going straight.

Closed loop

The car with the driver in the loop: its motion is fed back to the driver, who keeps correcting. Closed-loop tests show how car and driver perform together. Compare open loop.

Combined slip

A tire working at a slip angle and a slip ratio at the same time, as when braking or accelerating in a corner. Longitudinal and lateral force then share one grip budget, described by the friction ellipse.

Compound

The tread rubber recipe. A softer compound usually grips more and works at lower temperatures but wears faster; a harder one needs more heat but lasts longer.

Contact patch

The small area where a tire touches the road. Every tire force reaches the car through it.

Control (controllability)

How readily and predictably the car follows the path the driver intends. Compare stability.

Cornering stiffness (\(C_\alpha\))

The slope of a tire's lateral-force curve at zero slip angle, usually in N/deg: how much lateral force each degree of slip angle buys in the linear range.

Course angle

The car's direction of travel on the track: heading plus sideslip, \(\psi + \beta\).

Critical speed (\(U_{\text{crit}}\))

The speed above which an oversteering car becomes unstable, \(U_{\text{crit}} = \sqrt{L/|K|}\). An understeering car has no critical speed.

Delay (driver)

The roughly 0.15–0.3 s a human needs to notice an error and start correcting it. Delay combined with too much gain causes overcorrection.

Earth-fixed axes (\(X, Y, Z\))

Axes attached to the ground, used to describe where the car is on the track. Compare vehicle-fixed axes.

Effective rolling radius (\(r_e\))

The radius that links a free-rolling wheel's spin rate to the ground speed: \(\Omega r_e = V\).

Elastic load transfer

The part of lateral load transfer that passes through the springs and anti-roll bars as the body rolls. It comes from the roll moment and is shared between the axles by their roll stiffness.

Equilibrium

A condition the car can hold steadily, such as driving straight at constant speed. Stability asks what happens after a small disturbance from it.

Free-body diagram (FBD)

A sketch of one isolated body with every external force on it. For a car: gravity, the forces at the four contact patches, and aerodynamic forces. Engine, brake and steering torques are internal.

Friction circle

The limit \(\sqrt{F_x^2 + F_y^2} \le \mu F_z\): a tire's total horizontal force is capped, so grip used for braking or driving is not available for cornering.

Friction ellipse

The friction circle stretched to allow different longitudinal and lateral limits: \((F_x/F_{x,\max})^2 + (F_y/F_{y,\max})^2 \le 1\). The same shape bounds a car's g-g diagram.

Front weight distribution

The fraction of the car's weight carried by the front axle, \(b/L\), usually quoted as a percentage.

g-g diagram

A plot of a car's longitudinal against lateral acceleration, in g, recorded through a lap. Its boundary is the performance envelope.

Gain (driver)

How strongly the driver corrects an error. Too little and the car drifts off line; too much and the driver overcorrects.

Geometric load transfer

The part of lateral load transfer that passes through the suspension links, set by roll-center height. It acts immediately, with no body roll needed.

Heading (yaw angle, \(\psi\))

The angle between the car's \(x\) axis and the earth's \(X\) axis: where the car is pointing on the track.

Hysteresis

One of the two sources of rubber grip: the rubber deforming around the road's texture and losing energy as it does. Compare adhesion.

Ideal brake distribution

The front brake share that makes both axles reach their limit together: \(\beta_{\text{ideal}} = b/L + a_{CG}\,h/L\). It moves rearward when grip falls, for example in the rain.

Inertial load (\(m\mathbf{a}\))

The \(m\mathbf{a}\) term of Newton's second law. On this course's free-body diagrams it is drawn dashed at the CG as the result of the real forces. Moving it to the force side (d'Alembert's trick) is legitimate only if you don't also write \(m\mathbf{a}\); that is where “centrifugal force” comes from.

Instant center (IC)

The point a wheel momentarily pivots about relative to the body. For a double-wishbone suspension it is where the extended upper and lower wishbones meet. Used to find the roll center.

ISO 8855

The international vehicle axis standard: \(x\) forward, \(y\) left, \(z\) up. Used by many modern textbooks and simulation tools. Compare SAE vehicle axes.

Jacking

The upward push on the body from lateral tire forces acting through the suspension links when the roll center is above the ground. It raises the CG just when the car needs it low, which is why race cars use fairly low roll centers.

Lateral load transfer

Load moving from the inside wheels to the outside wheels in a corner. The total, \(m a_y h / t\), is fixed by mass, lateral acceleration, CG height and track width; springs and bars only change how it is split between the axles.

Load sensitivity (tire)

A tire's friction coefficient falls as its vertical load rises, so doubling the load less than doubles the peak force. It is why load transfer costs grip.

Load transfer

The change in the tires' vertical loads caused by accelerating a CG that sits above the ground. See longitudinal and lateral load transfer.

Lock lines (front and rear)

On the brake-force diagram, the lines where the front or rear axle's brake force reaches \(\mu N\). Beyond a line, those wheels lock; beyond both, all four do.

Lock-up

A braked wheel that has stopped turning while the car still moves (slip ratio \(-1\)). The tire slides: braking force drops and lateral grip almost disappears.

Longitudinal load transfer

Load moving onto the front axle under braking (and onto the rear under acceleration): \(\Delta F_z = m a_x h / L\).

Longitudinal stiffness (\(C_\kappa\))

The slope of the longitudinal-force curve at zero slip ratio, in N per unit slip. It is much higher than the cornering stiffness, so working slip ratios are only a few percent.

Magic Formula

Pacejka's empirical tire model, \(F_y = D\sin(C\arctan[\ldots])\), the most widely used way to fit measured tire curves. \(D\) is the peak force and \(BCD\) the cornering stiffness.

Normalization

Dividing tire force by load (\(F_y/F_z\)) to compare curves measured at different loads. How far the curves fail to collapse onto one shows the load sensitivity.

Open loop

The car's response with the driver's inputs held fixed, such as hands off the wheel after a bump. Open-loop tests reveal properties of the car alone. Compare closed loop.

Operating window

The combination of camber, pressure and temperature in which a tire grips best. Getting the tires “in the window”, and keeping them there, is a big part of every test day.

Oversteer

The tendency of a car to rotate more than the driver asked, because the front tires win over the rears. Above its critical speed an oversteering car is unstable. Module 5 makes the definition precise.

Performance envelope

The boundary of the accelerations a car can reach, drawn on the g-g diagram. An expert driver keeps the car on it; every moment inside it is time left on the table.

Pitch (\(\theta\))

Rotation about the car's \(y\) axis, with rate \(q\). SAE positive: nose up. ISO positive: nose down.

Preview (driver)

Looking ahead, typically about a second down the road, and aiming the car at a point there.

Roll (\(\phi\))

Rotation about the car's \(x\) axis, with rate \(p\). Positive in both SAE and ISO: right side down.

Roll axis

The line joining the front and rear roll centers. Its height under the sprung CG, \(h_{ra}\), sets the roll moment arm.

Roll center (RC)

A point on each axle, set by the suspension links, about which the body rolls (for small motions) and through which lateral forces pass into the body without rolling it. Found by drawing lines from each contact patch through its instant center.

Roll gradient

Body roll per g of lateral acceleration, in deg/g.

Roll moment (\(M_\phi\))

The sprung mass's lateral force acting about the roll axis, \(M_\phi = m_s a_y (h_s - h_{ra})\). The springs and anti-roll bars resist it, so the body rolls through \(\phi = M_\phi / K_\phi\).

Roll moment arm

The height of the sprung CG above the roll axis, \(h_s - h_{ra}\).

Roll stiffness (\(K_\phi\))

How strongly an axle's springs and anti-roll bar resist body roll, in N·m/deg.

Roll stiffness distribution

The front axle's share of the total roll stiffness, \(K_{\phi f}/(K_{\phi f} + K_{\phi r})\). In the simple model it is also the front share of lateral load transfer, so it is the main tool for tuning balance.

SAE vehicle axis system

The axes used in RCVD and this course (SAE J670): \(x\) forward, \(y\) right, \(z\) down, right-handed, origin at the CG. Compare ISO 8855.

Saturation

An axle is saturated when its tires reach the peak of their force curve, so more slip gives no more force. Whichever axle saturates first sets the car's limit and its balance.

Sideslip angle (\(\beta\))

The angle between the car's \(x\) axis and the velocity of its CG: how much the car is moving sideways relative to where it points. (In Lesson 3.3, \(\beta\) is the brake bias instead.)

Slip angle (\(\alpha\))

The angle between a wheel's heading and the direction its contact patch is moving. A tire needs a slip angle to make lateral force. In SAE axes, \(\alpha_f = \beta + a r/V - \delta\) and \(\alpha_r = \beta - b r/V\).

Slip ratio (\(\kappa\))

The mismatch between wheel speed and ground speed, \(\kappa = (\Omega r_e - V)/V\). Positive when driving, negative when braking, \(-1\) for a locked wheel. A tire needs slip ratio to make longitudinal force.

Sprung mass (\(m_s\))

Everything carried on the springs: chassis, engine, driver and fuel. Compare unsprung mass.

Stability

Whether a small disturbance dies out (stable) or grows (unstable) with the driver's inputs held fixed. Compare control.

Steady state

A condition in which speed, yaw rate and accelerations are all constant, such as a steady turn. The yaw moments then balance: \(\Sigma M_z = 0\).

Steer angle (\(\delta\))

The angle between the car's \(x\) axis and the front wheels' heading: how far the front wheels are turned.

Threshold braking

Holding the brake pedal right at the edge of lock-up, near the tires' peak slip ratio. A core racing skill in series that ban ABS.

Tire curve regions (linear, transitional, frictional)

The three parts of a force–slip curve. Linear: almost all of the patch grips and force rises in proportion to slip. Transitional: sliding spreads forward from the back of the patch and the steering goes light. Frictional: most of the patch slides and more slip gives no more grip.

Traction control

The driving-side counterpart of ABS: it trims engine torque to stop wheelspin and hold the driven tires below their peak slip ratio.

Trail braking

Keeping some braking while turning in to a corner, so the car blends braking into cornering and stays on the edge of the performance envelope.

Understeer

The tendency of a car to turn less than the driver asked, because the rear tires win over the fronts. An understeering car has no critical speed. Module 5 makes the definition precise.

Understeer gradient (\(K\))

A single number summarizing a car's balance, in rad/(m/s²): positive for understeer, negative for oversteer. Derived in Module 5.

Unsprung load transfer

The part of lateral load transfer caused by the unsprung mass's own lateral force, \(m_{us} a_y h_{us} / t\) per axle. Set by wheel, brake and upright mass; not adjustable at the track.

Unsprung mass (\(m_{us}\))

Everything that moves with the wheel: tire, wheel, upright, brakes, and part of the links and springs. Typically around a tenth of a race car's mass. Compare sprung mass.

Vehicle-fixed (body) axes (\(x, y, z\))

Axes with their origin at the car's CG that move and rotate with it. Used to describe what the car is doing: accelerations, rotation rates and tire forces. An accelerometer bolted to the chassis measures along them.

Viscoelastic

Behaving partly like a spring and partly like a damper. Tread rubber is viscoelastic, and its properties change strongly with temperature.

Wheelspin

A driven wheel turning much faster than the ground speed after passing its peak slip ratio. It is the driving-side version of lock-up: the force falls, so the wheel runs away.

Yaw

Rotation about the car's vertical \(z\) axis. SAE positive: nose right. ISO positive: nose left. See also heading and yaw rate.

Yaw moment of inertia (\(I_z\))

The car's resistance to changes in yaw rate, in \(\Sigma M_z = I_z\ddot\psi\).

Yaw rate (\(r\))

How fast the car's heading changes, in rad/s or deg/s. In a steady turn \(r = V/R\).