CarKinematiX Academy
Suspension design, explained properly — then handed to you to try.
Every chapter ends up in the same place: a link that opens the simulator with a car already loaded, and instructions naming exactly what to drag and which number to watch. Read them in order or start where it hurts.
How a wheel actually moves
Linkage geometry from first principles: the two views, the points that aren't there, and every angle that changes while you aren't looking.
- Your suspension has exactly one job (and it isn't comfort)Ride quality is a side effect. The actual job is keeping four contact patches loaded and square to the road — and your linkage is quietly changing the angles the whole time you're driving.
- The instant center: the pivot that isn't thereYour wheel pivots around a point that has no bearing, no bracket and no bolt — and is often several meters outside the car. Find it and most of suspension geometry stops being mysterious.
- Camber curve: how much lean, and where it comes fromCamber gain is one divide away from the swing-arm length you found last chapter. Here's the equation, why it lands within a few percent of the solver, and how to work out how much you actually need.
- Roll center: the most abused point in vehicle dynamicsIt has no bearing, it moves constantly, and half of what's said about it on forums is wrong. It also decides how hard your springs have to work — so here's what it actually is, and the one number you get from it.
- Roll center migration: the number that won't sit stillYour roll center is a design value at exactly one ride height. Drive the car and it moves — on one Mini, by 186 mm across travel, straight through ground level. Here's how to measure the envelope and how much is too much.
- Bump steer: your suspension is steering without youThe tie rod swings on a different arc than the control arms, so the wheel steers itself over every bump. Here's the construction that kills it at the front — and why the rear deliberately keeps some.
- Kingpin axis, part 1: KPI, scrub radius, and why your steering fights backThe wheel steers about a line through two joints — not through the middle of the tire. Where that line hits the ground decides steering weight, kickback, and what happens when one front tire finds ice.
- Kingpin axis, part 2: caster, trail, and free camberCaster is why the wheel comes back to center, why steering loads up, and — the part people miss — how the outside front tire gets negative camber exactly when it needs it, without any camber gain at all.
- Anti-dive and anti-squat: side-view geometry earns its keepYou can stop a car diving under braking without a single extra newton of spring — by tilting the arms in side view. Here's where the percentage comes from, and why 100% is almost always the wrong answer.
- Motion ratio: the lever between the spring and the roadYour spring rate is not your wheel rate. The linkage sits in between as a lever, and because the effect goes as the square, a small ratio change makes a big difference — 400 lb/in can arrive as 196.
- Ackermann, and whether you actually want itThe inside wheel is on a tighter circle, so it should turn more. That's been the textbook answer since 1817 — and most race cars deliberately ignore it. Here's the geometry, and the slip-angle argument that overrules it.
Springs, dampers and the road
What a spring rate really buys you, why one damping number is a lie, and what a road actually looks like to a wheel.
- Spring rate, wheel rate, ride frequency: the only three numbersA spring rate on its own tells you almost nothing — it depends on the car's mass and the linkage in between. Ride frequency is the number that lets you compare a Miata to a Dakar truck and have the comparison mean something.
- Flat ride: why the rear should be stiffer than the frontMatching front and rear ride frequencies is the tidy, symmetrical, obvious thing to do — and it makes the car pitch. The fix is a 1920s idea that still decides how modern cars are sprung.
- Damping ratio: the number nobody prints on the shockShock manufacturers sell you clicks. What actually matters is ζ — how much damping you have relative to the amount that would stop the car oscillating entirely. Here's how to compute it, and what happens when it's wrong.
- Digressive dampers: four numbers and a kneeOne damping coefficient can't serve both body control and ride, because those happen at different velocities. A digressive damper solves it by changing slope partway up — and the place it changes is the tuning knob that matters.
- Bump stops are springs, and they're doing more than you thinkMost people treat the bump stop as a crash pad — the thing that stops metal hitting metal. On a modern car it's a second, progressive spring that's carrying load long before you'd call it 'bottoming out'.
- Unsprung mass and wheel hop: the second resonanceYour car has two natural frequencies, not one. The body bounces around 1.3 Hz; the wheel bounces around 13 Hz on the tire's own stiffness — and that second one decides whether the tire is touching the road.
The whole car in a corner
Weight transfer, roll stiffness, tires that get worse as you lean on them, and the one number that describes balance.
- Weight transfer: the master equationHow much load moves to the outside wheels in a corner depends on four things, and springs are not one of them. This single fact kills more suspension misconceptions than anything else in the course.
- Roll stiffness distribution: the balance knobThe total load transfer is fixed. How it splits between the axles is not — and that split is the most powerful understeer/oversteer adjustment on the car. It's also why the anti-roll bar is the cheapest tuning part you own.
- Tires: load sensitivity, and why grip isn't a coefficientPress a tire harder and it grips harder — but not proportionally. That single non-linearity is why load transfer costs lap time, why balance tuning works at all, and why four evenly loaded tires beat two heavily loaded ones.
- Understeer gradient and the skidpadOne number describes a car's steady-state balance: how much extra steering it needs as lateral acceleration rises. And a car can be perfectly neutral at 0.3 g while oversteering at the limit — which is the setup in this app.
Braking
The multiplication chain from your foot to the pad, and why the front usually locks first.
- From pedal to pad: the hydraulic chainYour foot makes 300 N. The tire needs 15 000. In between is a chain of five multiplications, and knowing where the gain comes from is how you diagnose a brake system instead of guessing at it.
- Brake bias, lock-up, and why the front usually goes firstThe ideal front/rear brake split changes with how hard you're braking — from 70% at gentle deceleration to 83% at the limit. A fixed hydraulic system can only be right at one point, so which point you choose is the whole design.
Case studies
Everything above, applied to two jobs: lowering a road car without wrecking it, and drawing a front corner from nothing.
- Lowering a car, and the four things it quietly breaksLowering is the most popular modification there is, and it changes five geometry numbers at once — none of which appear on the box the springs came in. Here is each one, measured, on the same suspension.
- Designing a front corner from a blank sheetEvery chapter in this course, applied in the order a real designer works — from packaging constraints and a target camber curve to hardpoints you could hand to a fabricator.