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Car setup
An invented open-wheel car; wings change downforce and drag together.
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Model checks
The science
Downforce and drag
Fdown = ½ ρ CL A v2, Fdrag = ½ ρ CD A v2 + Crr m gWings raise the lift coefficient CL and the drag coefficient CD together. Top speed is where engine power equals (Fdrag + rolling resistance) v.
Corner speed with aerodynamic grip
A car on a circle of radius R needs m v2/R = μ(Fz) Fz, with Fz = m g + ½ ρ CL A v2. For constant μ this has the closed form v2 = μ g R / (1 − μ ρ CL A R / 2m). Tyre grip also falls with load: μ = μ0 (1 − 0.10 (Fz/4/4000 − 1)).
Quasi-steady-state lap
The lap is solved in three steps: the speed each corner allows, a forward pass limited by power and the friction ellipse (ax2 + ay2 ≤ agrip2), and a backward braking pass capped at 5.5 g. The g-g diagram plots the acceleration used at every metre of the lap against the grip circle.
Honest simplifications
- Invented car, not any real team's; power, mass, areas and aero maps are plausible round numbers.
- Quasi-steady state: no weight transfer, suspension, tyre temperature or slip dynamics; a single friction ellipse for all four tyres.
- The ghost lap follows the computed speed profile exactly, whereas a driver in the 3D page is slower than this ideal.
- The circuit is the one used by the 3D page; grip is the same on every surface, with no kerbs or gradient.
What to try
- Load Low drag and Maximum downforce and compare top speed with the minimum corner speed on the speed trace.
- In the g-g diagram the points hug the dashed grip circle: the car is always using all its grip when braking or cornering.
- Raise the fuel load to 100 kg: lap time grows by roughly a few hundredths of a second per kilogram.
- In the wing sweep, notice that on this circuit more wing keeps paying off; a long-straight circuit would show an optimum.