Car_suspension - Wikiparency

# Car suspension A **car suspension** is the system of springs, dampers, linkages and [[Tire|tyres]] that carries a vehicle's body on its wheels and allows the two to move relative to each other. Everything the road does to the car arrives through the tyre contact patches and leaves through the suspension, so the same components decide two things that pull against each other: how much of the road reaches the occupants, and how firmly the tyres are held against the ground. Tuning a suspension is choosing where between those two to sit. The engineering vocabulary follows that split. The [[Sprung_mass|sprung mass]] is everything the springs hold up; the [[Unsprung_mass|unsprung mass]] is the wheel, hub, brake and part of the linkage that must follow the road. The spring rate, the wheel rate and the roll rate say how hard the suspension pushes back in bounce and in roll; [[Damping|damping]] says how quickly the motion dies; travel says how far the wheel can move before it runs out of room; and [[Weight_transfer|weight transfer]] says how the load moves between wheels when the car brakes, accelerates or turns. A suspension that is comfortable is soft and lightly damped, which lets the body wallow and the wheel skip; one that holds the road is stiff and firmly damped, which passes the road straight through to the seat. The framework microsim *Car suspension: the quarter car, one corner at a time* models one corner as two masses, two springs and a damper. The reader drives that corner over a hump, a long wave, a short wave or a washboard, moves the damper and the two masses, and watches the body acceleration, the wheel travel and the two natural frequencies — the body bounce near 1 Hz and the wheel hop near 11 Hz — separate out of the same road. ## History Road vehicles were sprung long before they were driven. Carriage bodies hung on leather braces, then on steel leaf springs laid along or across the frame, and the first motor cars inherited both the beam axles and the [[Leaf_spring|leaf springs]] of the carriages they replaced. The leaf spring was convenient because one component did three jobs at once: it carried the load, it located the axle fore and aft, and its interleaf [[Friction|friction]] damped the motion. It was also a poor spring, because that same friction made the rate depend on how hard the last bump had been, and because a spring stiff enough to locate an axle is stiffer than a spring chosen for ride would be. The pressure to do better came from speed. A carriage suspension only has to work at the pace of a horse; an engine-driven car meets the same bump several times faster, and the forces and frequencies rise with it. Every later development in the field — separating springing from location, adding a hydraulic damper, giving each wheel its own linkage, and finally making the damper adjustable — is a response to that one change, and each is a subject of [[Vehicle_dynamics|vehicle dynamics]] rather than of carriage building. ### Modern suspension The move to modern suspension was a move to separate those jobs. Springing passed to [[Coil_spring|coil springs]], [[Torsion_bar_suspension|torsion bars]] and gas springs; damping passed to a dedicated hydraulic [[Shock_absorber|damper]]; and location passed to linkages designed for the wheel path they produce rather than for the load they carry. The most widely built result is the strut, patented as a "vehicle wheel suspension system" by Earle S. MacPherson: a telescopic strut standing on the wheel mount, with the road spring around it and a transverse arm and a longitudinal rod locating the wheel below.[^macpherson] The patent was filed on March 21, 1947 and granted on January 6, 1953, assigned to the General Motors Corporation.[^macpherson] Its advantage is the one every packaging engineer cares about: it puts the spring, the damper and the upper pivot in one tall, narrow column at the corner of the car, leaving the space between the wheels for a transverse engine. The alternative that survives where space and cost allow is the [[Double_wishbone_suspension|double wishbone]], which buys control of [[Camber_angle|camber]] and roll centre with an extra arm. ## Difference between rear suspension and front suspension The two ends of a car are asked to do different jobs, so they are rarely the same design. The front wheels steer, which means the suspension must carry the [[Steering|steering]] axis and keep its geometry sane through travel and roll; they also take most of the [[Brake|braking]] load, because braking pitches the car forward. The rear wheels may have to carry drive torque and its reaction, or nothing at all. That is why the drive layout decides the rear suspension more than any other choice. On a [[Front-wheel_drive|front-wheel-drive]] car the rear axle carries no drive torque and no steering, so a simple [[Beam_axle|beam]] or a twist beam does the whole job cheaply and well. On a [[Rear-wheel_drive|rear-wheel-drive]] car the rear suspension has to react drive and braking torque as well as locate the wheels, which is what a live axle's linkage — a [[Panhard_rod|Panhard rod]] or a [[Watt's_linkage|Watt's linkage]] across the car, trailing links along it — is for, and why [[Independent_suspension|independent]] rear suspension with a body-mounted final drive costs more.[^gillespie] The asymmetry continues into the geometry: anti-dive is designed into a front suspension and anti-squat into a rear one, because dive and squat are what braking and acceleration respectively do to the two ends. ## Spring, wheel, and roll rates Three different stiffnesses are all called "rate", and confusing them is the commonest error in suspension arithmetic. The spring rate is the property of the spring itself, the force it gains per unit of compression, `k = F/x` — [[Hooke's_law|Hooke's law]] applied to a coil. The wheel rate is the stiffness measured at the tyre contact patch, which is what the car actually rides on. The roll rate is the torque an axle generates per degree of body roll. ### Spring rate A [[Spring_(device)|coil spring]] is linear over its working range, so its rate is a single number: a spring that shortens 10 mm under 200 N has a rate of 20 kN/m. The rate a car needs follows from the ride frequency the designer wants, not the other way round, because what an occupant feels is the frequency of the body bounce, and that frequency is set by the rate divided by the mass it carries. In the microsim's default corner, a sprung mass of 300 kg on a 20 kN/m spring in series with a 180 kN/m tyre gives a body bounce at 1.23 Hz and a wheel hop at 11.3 Hz.[^sim-spec] Halving the spring to 10 kN/m drops the bounce to 0.89 Hz and leaves the hop at 11.0 Hz; doubling it to 40 kN/m raises the bounce to 1.66 Hz and the hop only to 11.8 Hz, because the wheel mode is governed by the tyre, which the designer did not touch. Rate also has to survive load. A car that carries four passengers and luggage adds a large fraction of its sprung mass, which on a constant-rate spring lowers both the ride height and the [[Natural_frequency|natural frequency]]; vehicles expected to carry heavy loads are therefore given stiffer springs than ride alone would suggest, or a progressive rate — variable-pitch coils, tapered leaves, a gas volume — that is soft near the static position and stiff near the end of travel, or a levelling system that restores the height instead of the rate. ### Wheel rate The spring almost never sits on the wheel. It bears on a control arm somewhere between the pivot and the wheel, so the wheel moves further than the spring does, and the wheel rate is the spring rate reduced by the square of the motion ratio: `k_w = k_s · (MR)²`, where the motion ratio is the spring's travel divided by the wheel's. The square appears because the ratio costs displacement once and force once. A 40 kN/m spring at a motion ratio of 0.7 gives a wheel rate of `40 × 0.49` = 19.6 kN/m — half of what the spring's own number suggests, so a designer who wants 20 kN/m at the wheel must order a spring of about 41 kN/m. The tyre is then a second spring in series, stiffer than the suspension by an order of magnitude, and the combination is the ride rate that the body actually bounces on: `k_r = k_w k_t/(k_w + k_t)`, which for 20 kN/m on 180 kN/m is 18 kN/m.[^gillespie] Because the two are in series, the softer one dominates: the tyre's 180 kN/m costs the ride rate only 10 percent. The motion ratio is not a constant either — it changes through travel as the linkage swings, which is one of the things a suspension geometry is designed to control, and it is why a [[Four-bar_linkage|linkage]] drawing and a rate calculation belong to the same exercise. ### Roll rate In roll, the two wheels of an axle move in opposite directions, so each spring works against half the track. The axle's roll stiffness is `K_φ = k_w t²/2` for a track `t`, which for a 20 kN/m wheel rate on a 1.5 m track is 22.5 kN·m/rad, or 393 N·m per degree of roll. An [[Anti-roll_bar|anti-roll bar]] adds roll stiffness without adding ride stiffness, because it resists only the opposed motion of the two wheels; that is why it is the tuning device of choice. The front and rear roll rates need not be equal, and their ratio — the roll couple distribution — sets how the lateral load transfer is split between the axles, and with it the balance between [[Understeer_and_oversteer|understeer and oversteer]].[^gillespie] *Try: put the corner on the speed hump at 72 km/h, then walk the damper from 0.5 to 6 kN·s/m — at the soft end the body keeps bouncing for several passes and the acceleration trace stays low and slow, at the stiff end the same hump throws the trace past 1 g and the wheel starts to hop; then switch the road to the 0.75 m washboard at 30 km/h and watch the tyre load fall to zero with the wheel-hop caption.*[^sim-spec] ## Weight transfer When a car accelerates in any direction, load moves between its wheels. The total is fixed by four things only: the mass, the acceleration, the height of the centre of gravity, and the distance between the wheel centres taken in the direction of the acceleration — the wheelbase for braking and acceleration, the track for cornering. In longitudinal form, `ΔW = m a h / L`.[^gillespie] Nothing in that expression mentions springs: the springs decide how quickly the transfer arrives and how far the body moves while it happens, not how much of it there is. The transfer splits into three paths. Unsprung weight transfer acts through the wheels and hubs directly and is present whether the car has springs or not. Sprung weight transfer acts through the springs and through the suspension links, and reaches the axle in two ways: as a moment about the roll axis carried by the springs and bar, and as a direct force through the links themselves. The link path has a vertical component, the jacking force, which lifts the sprung mass when the roll centre is above ground and pulls it down when the roll centre is below. The arithmetic is quick and unforgiving. A 1500 kg car with its centre of gravity 0.55 m above the road and 2.7 m between its axles, braking at 0.6 g, moves `1500 × 5.88 × 0.55 / 2.7` = 1.80 kN forward: the front axle goes from about 8.1 kN to 9.9 kN and the rear from 6.6 kN to 4.8 kN.[^sim-spec] The rear brakes must be sized for the axle load they will actually have, not the one the car has standing still, which is the reason for brake proportioning valves and, later, electronic brake-force distribution. *Try: in the weight-transfer variant set the braking to 0.6 g on the 1500 kg car with its centre of gravity at 0.55 m and 2.7 m of wheelbase — the bars move 1.80 kN from the rear axle to the front, the load arrows at the two ends grow and shrink together, and the drawn brake dive (exaggerated fourfold) shows what the springs do about it.*[^sim-spec] ## Other properties Beyond rates and load transfer, a suspension is judged on a dozen properties that rarely appear in one equation. Travel is the distance the wheel can move between full droop and full compression; running out of it means striking the bump stop, which in a passenger car is typically near 100 mm of compression from the static position, and which turns the spring's gentle curve into a wall.[^sim-spec] Damping controls how fast the motion decays, and it is a compromise in its own right: light damping is comfortable and lets the body oscillate, heavy damping controls the body and passes every sharp edge in the road straight into it. In the microsim's default corner the damper gives a damping ratio of 0.245 on the body mode, which is inside the 0.2–0.4 band that production cars use and well below the critical value that would stop overshoot entirely.[^sim-spec][^hallauer] Camber control, roll centre height and instant centre are all statements about the path the wheel takes through travel, which the linkage geometry sets. A tyre makes its best lateral force at a small negative camber, so a linkage that lets the outer wheel go positive in roll throws away grip exactly when it is needed, and [[Automobile_handling|handling]] is lost to geometry rather than to rates. Anti-dive and anti-squat are the same idea in the longitudinal plane: by inclining the links in side view, part of the braking or driving load is carried as a direct thrust through the links rather than through the springs, and the body's pitch is reduced by that percentage. The remaining properties decide production cars as much as any of the above: the flexibility of bushings, which both isolates high-frequency shock and adds compliance the designer must account for; the space the layout occupies; aerodynamic drag, which is why racing cars hide their springs and dampers inboard; and cost. Unsprung mass deserves its own line, because it does not merely add weight — it sets the wheel-hop frequency `f₂ ≈ √((k_s + k_t)/m_u)/2π` and therefore decides how well the tyre can follow a rough road. *Try: in the unsprung-mass variant raise the wheel mass from 40 to 70 kg and run the 2 m waves at 62 km/h — the 8.6 Hz the road now feeds in lands on the wheel-hop mode, which the heavier wheel has dragged down to 8.5 Hz, and both panels fill with a resonance that lifts the tyre clear of the road.*[^sim-spec] ## Springs and dampers Whatever the linkage, two functions have to be provided at every corner: something to store the energy of a bump and give it back, and something to turn that energy into heat before it is given back too many times. The spring and the damper do those jobs, and the pair can be built as separate parts, as a combined coilover unit, or as one [[Hydropneumatic_suspension|hydropneumatic]] sphere in which a trapped gas volume is the spring and a valve in the fluid path is the damper. A suspension is classified by how much outside help those two elements get: none at all, a control signal that changes the damper, or a power supply that can drive the corner directly. ### Passive suspensions A passive suspension stores energy in a spring and dissipates it in a damper, with no external power and no signal path. The spring can be a leaf, a coil, a torsion bar, a rubber cone, a gas volume in an [[Air_suspension|air spring]], or a combination, as in the hydropneumatic layouts where a gas volume is the spring and a valved orifice between the fluid and the sphere is the damper. The damper is a piston pushing oil through valves, and the force it produces is roughly proportional to velocity, which is what makes the quarter car linear enough to be worth solving in closed form; real dampers are deliberately asymmetric, softer in rebound than in compression or the reverse, and blow off at high velocity so that a sharp edge does not become a hammer blow. ### Semi-active and active suspensions A semi-active suspension keeps the passive spring but makes the damper adjustable, either by a valve that changes orifice area or by a [[Magnetorheological_fluid|magnetorheological]] fluid whose viscosity follows an applied field. It can only dissipate energy, never add it, so it cannot lift a wheel — but because it can change its dissipation within a millisecond, it can approach the performance of a much more expensive active system. The classic result of the field is that a semi-active damper switched by the sign of the relative and absolute velocities recovers most of the benefit of an ideal "skyhook" damper attached to an imaginary fixed sky, at a small fraction of the power.[^karnopp1974] An [[Active_suspension|active suspension]] goes further and replaces or supplements the spring with a powered actuator, so that the body can be held level through a corner and the corner's response is set by a control law rather than by a rate; the price is hydraulic or electric power, extra mass, and a failure mode a passive spring does not have. ### Interconnected suspensions Interconnecting the corners lets a passive system treat the vehicle's motions differently. An anti-roll bar is the simplest case: it stiffens the roll mode and leaves the bounce mode alone. Hydraulic and pneumatic interconnections extend the idea to all four corners, so that bounce, pitch, roll and warp can each be given their own stiffness and damping — a soft warp mode keeps all four wheels loaded on uneven ground, while a stiff roll mode keeps the body flat, a combination no set of four independent units can produce. ## Types Suspensions divide into two families by one question: whether the vertical motion of one wheel forces motion at the wheel on the other side. The answer decides the unsprung mass, the camber behaviour, the cost, and whether the quarter-car model used here is a fair description of the corner at all. A third, intermediate family gets its own name because it answers "partly". ### Dependent suspensions A dependent suspension joins the two wheels of an axle with a beam or a live axle, so that a camber change on one side produces an equal and opposite change on the other. The beam keeps the wheels parallel and upright relative to each other, which suits heavy vehicles and off-road use, and it needs only a linkage to locate it: trailing links or leaf springs along the car, a Panhard rod or a Watt's linkage across it. Its disadvantages are unsprung mass — a live axle carries the final drive with it — and the fact that a single wheel bump tilts the whole axle and with it the body. ### Independent suspensions An independent suspension gives each wheel its own linkage to the body, so that in principle one wheel's motion leaves the other alone. The family includes the [[MacPherson_strut|MacPherson strut]], the double wishbone, the [[Multi-link_suspension|multi-link]], the [[Swing_axle|swing axle]], the [[Semi-trailing_arm_suspension|semi-trailing arm]] and, as a way of keeping a driven axle's final drive on the body while the wheels stay upright, the [[De_Dion_tube|de Dion tube]]. Independence lowers unsprung mass, frees the designer to choose a wheel path, and makes it possible to keep the outer wheel's camber under control in roll; the multi-link's several short links exist precisely so that camber, toe and the longitudinal path can be specified separately instead of falling out of one arm's geometry. The quarter-car model is exactly a statement about an independent suspension: it is only honest to model one corner alone if the other corner is not attached to it. On a beam axle the same road input reaches both wheels through the beam, and the vehicle has to be modelled as a half car at least. ### Semi-independent suspension The twist beam sits between the two families. Its trailing arms are joined by a crossmember stiff in bending and deliberately soft in torsion, so the two wheels are partly independent — one wheel's motion twists the beam rather than tilting the other wheel bodily, and the beam's torsional stiffness acts as a built-in anti-roll bar. It is the cheapest way to give a light front-wheel-drive car acceptable rear geometry, and it is on tens of millions of cars for that reason. *Try: in the independent-suspension variant drop the corner's unsprung mass to 30 kg and take the speed hump again — this corner alone responds, and the model contains no second wheel to be disturbed by it, which is exactly what independence means and exactly the assumption the quarter car makes.*[^sim-spec] ## Other instances The principles travel well beyond cars. A tilting suspension adds a lean mechanism to an otherwise conventional independent layout, so that a narrow vehicle can bank into a corner and keep its tyres loaded, the same trick a [[Tilting_train|tilting train]] uses for passenger comfort rather than grip. The rocker-bogie mechanism used on the Mars rovers dispenses with springs entirely. NASA's Perseverance carries six wheels 52.5 cm in diameter on a centre differential with left and right rockers and bogies; the linkage is arranged so that all six wheels stay loaded while the body pitches only half as much as the terrain, letting the rover roll over obstacles as large as a wheel and climb rocks up to 40 cm, and the vehicle is designed to withstand a 45-degree tilt in any direction, although operators keep it below 30 degrees.[^nasa-perseverance] With a top speed measured in centimetres per second, there is no dynamic ride problem to solve — only a static distribution one — so the [[Rocker-bogie|rocker-bogie]] optimises load sharing instead of frequency. Tracked vehicles distribute the load over many road wheels and a [[Continuous_track|continuous track]], and the suspension problem becomes one of keeping each road wheel loaded while the hull stays stable enough to shoot from. [[Armoured_fighting_vehicle|Armoured fighting vehicles]] weighing tens of tonnes have used torsion bars, [[Christie_suspension|Christie-type]] coil springs and hydropneumatic units for this, with the springing medium chosen as much for its resistance to mine blast and shell fragments as for its rate. ## Minnesota *This section is specific to Wikitube.* The quarter-car model is not only a teaching device: it is the international definition of road roughness. The [[International_roughness_index|International Roughness Index]] is computed by running a standard quarter car — the "golden car" — over a measured [[Road_surface|road profile]] at 80 km/h and accumulating the suspension stroke per distance travelled. Its parameters are defined per unit sprung mass: `k_t/m_s` = 653 s⁻², `k_s/m_s` = 63.3 s⁻², `m_u/m_s` = 0.15 and `c_s/m_s` = 6.0 s⁻¹.[^sayers1995] Those numbers describe the same vehicle the microsim does, and they produce the same two modes: a body bounce at `√(63.3 × 653/(63.3 + 653))/2π` = 1.21 Hz and a wheel hop at `√((63.3 + 653)/0.15)/2π` = 11.0 Hz, against the sim's 1.23 Hz and 11.3 Hz.[^sim-spec] | Quantity | Microsim default | IRI golden car (scaled to 300 kg) | |---|---|---| | Sprung mass `m_s` | 300 kg | 300 kg | | Unsprung mass `m_u` | 40 kg | 45 kg | | Suspension rate `k_s` | 20 kN/m | 19.0 kN/m | | Tyre rate `k_t` | 180 kN/m | 196 kN/m | | Damping `c_s` | 1.2 kN·s/m | 1.8 kN·s/m | | Body bounce | 1.23 Hz | 1.21 Hz | | Wheel hop | 11.3 Hz | 11.0 Hz | [[Minnesota]] measures those strokes for a living. MnROAD, near Albertville, is "a pavement test track made up of various research materials and pavements owned and operated by the Minnesota Department of Transportation," with more than fifty instrumented test sections on two 3.5-mile segments of [[Interstate_94|Interstate 94]] and a 2.5-mile low-volume road.[^mnroad] A test section's roughness index is, in the end, a statement about how much a 300 kg quarter car would have moved on its springs while driving over it — which is why a pavement engineer in Albertville and a ride engineer on a four-post shaker rig are, in this one respect, solving the same two-degree-of-freedom problem. The model has limits the reader should carry out of the sim. Its road profiles — a 30 mm hump 3 m long every 25 m, 20 m waves 20 mm high, 2 m waves 8 mm high and a 0.75 m washboard of 10 mm — are ILLUSTRATIVE shapes chosen to show the two modes, not measured Minnesota profiles, and the drawn heights are exaggerated twelvefold so that the motion is visible.[^sim-spec] The quarter car itself is linearised about its equilibrium with the tyre always attached to the ground: it flags wheel hop and draws the gap when the computed tyre load reaches zero, but it does not model the wheel actually leaving the road, which is precisely what happens on a real washboard.[^sim-spec] ## See also - [[Sprung_mass]] - [[Unsprung_mass]] - [[Weight_transfer]] - [[Independent_suspension]] - [[MacPherson_strut]] - [[Multi-link_suspension]] - [[Anti-roll_bar]] - [[Shock_absorber]] - [[Ackermann_steering_geometry]] - [[Vibration_isolation]] - [[International_roughness_index]] ## References [^macpherson]: MacPherson, Earle S. "Vehicle wheel suspension system." U.S. Patent 2,624,592, filed March 21, 1947, granted January 6, 1953; assignee General Motors Corporation. https://patents.google.com/patent/US2624592A/en [^gillespie]: Gillespie, Thomas D. (1992). *Fundamentals of Vehicle Dynamics*. Warrendale, Pennsylvania: Society of Automotive Engineers. The ride and cornering relations used here are this book's standard forms (chapter 5, "Ride"; chapter 6, "Steady-State Cornering"); the Engineering portal's section plan cites it the same way. Page numbers are not pinned for this article. [^hallauer]: Hallauer, William L., Jr. *Introduction to Linear, Time-Invariant, Dynamic Systems for Students of Engineering*. Blacksburg, Virginia: Virginia Tech Libraries (VTechWorks). Second-order systems, pp. 185–201: damping ratio `ζ = c/(2√(km))`, undamped and damped natural frequencies, and the underdamped, critical and overdamped responses. Portal Book 021. https://vtechworks.lib.vt.edu/items/02fcc86a-3a2f-4df0-9b4c-a58e1a90a234 [^karnopp1974]: Karnopp, Dean; Crosby, Michael J.; Harwood, R. A. (1974). "Vibration control using semi-active force generators." *Journal of Engineering for Industry* 96 (2): 619–626. https://asmedigitalcollection.asme.org/manufacturingscience/article/96/2/619/427773/Vibration-Control-Using-Semi-Active-Force (DOI not re-checked for this article.) [^sim-spec]: Engineering portal pack, sim spec `specs/sims/Car_suspension.json` and its hooks: `design.vehicle.quarterCar` integrated by `robot.dyn.rk4` in four 1/240 s sub-steps per frame with the travelled distance carried as a fifth state, `design.vehicle.naturalFrequencies` for `f₁` and `f₂`, and `mech.oscillation.damped` for `ζ`. Build report, engineering run job E-G, September 18, 2026: defaults `m_s` 300 kg, `m_u` 40 kg, `k_s` 20 kN/m, `k_t` 180 kN/m, `c_s` 1.2 kN·s/m, giving `f₁` = 1.232 Hz, `f₂` = 11.26 Hz and `ζ` = 0.245, with a static tyre load of 3.34 kN. The four road profiles and the ×12 vertical exaggeration are marked ILLUSTRATIVE on the sim's picture sheet and in its sources; the 100 mm bump-stop threshold is named there as a typical limit; the model is linear about equilibrium with the tyre always attached and therefore cannot represent lift-off. The braking numbers are the Weight_transfer variant's (`design.vehicle.loadTransfer` and `staticAxleLoads`, brake dive drawn ×4). [^nasa-perseverance]: NASA. "Rover Components" (Mars 2020 Perseverance mission): six wheels of 20.7 in (52.5 cm) diameter, the rocker-bogie suspension of a centre differential with left and right rockers and bogies, obstacles and depressions "as large as the rover's wheel (20.7 inches, or 52.5 centimeters)", "knee-high rocks up to 15.75 inches (40 centimeters)", and a design tilt limit of 45 degrees with operations kept under 30 degrees. https://science.nasa.gov/mission/mars-2020-perseverance/rover-components/ [^sayers1995]: Sayers, Michael W. (1995). "On the calculation of International Roughness Index from longitudinal road profile." *Transportation Research Record* 1501: 1–12. Golden-car parameters `k_t/m_s` = 653 s⁻², `k_s/m_s` = 63.3 s⁻², `m_u/m_s` = 0.15, `c_s/m_s` = 6.0 s⁻¹, simulated at 80 km/h (49.7 mph). https://onlinepubs.trb.org/Onlinepubs/trr/1995/1501/1501-001.pdf [^mnroad]: Minnesota Department of Transportation, Materials and Road Research. "MnROAD": "MnROAD is a pavement test track made up of various research materials and pavements owned and operated by the Minnesota Department of Transportation," located near Albertville, Minnesota, comprising over 50 unique test sections across a 3.5-mile original westbound I-94 segment, a 3.5-mile I-94 mainline segment and a 2.5-mile low-volume road. https://www.dot.state.mn.us/mnroad/  **Microsim — three.js (Wikitube framework):** *Car suspension* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/engineering/Car_suspension.html" data-title="Car suspension"></div> *Built from `MICROSIM_GUIDE/specs/sims/Car_suspension.json`; part of the [[PORTAL_Engineering|Engineering portal]] spine (section sims and See-also variants).*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Car_suspension) : [Wikitube](https://en.wikitube.io/wiki/Car_suspension) - skeleton pinned to revision 1371744752 (2026-09-18).