| Lap | S1 | S2 | Time | Delta |
|---|
Delta is against the quasi-steady-state ghost lap for the same setup (flying lap, ideal driver at the grip limit). The player starts 150 m before the line at 45 m/s.
This is a point-mass (single-track) model of an invented open-wheel car on an invented 3 km circuit. It is educational, not a team-grade simulator.
Downforce F = ½ ρ CL A v² and drag D = ½ ρ CD A v² with ρ = 1.2 kg/m³, A = 1.3 m². Wing angle sets CL linearly with a crude stall roll-off above 22°; CD follows a drag polar CD = CD0 + k CL² (0.52 + 0.032 CL²). No ride-height, yaw or wake effects are modelled.
Vertical load Fz = m g + Fdown. Peak friction falls with load per tyre (load sensitivity): μ(Fz) = μ0 [1 − 0.10 (Fz/4 / 2800 N − 1)]. Grip force μFz is shared between cornering and acceleration/braking with a friction circle (ax/ax,max)² + (ay/ay,max)² ≤ 1. Tyre temperature, wear and slip angle are not modelled; compounds only change μ0.
Maximum steady corner speed solves m v²/R = μ(Fz) Fz. For constant μ it has the closed form v = √(μ m g / (m/R − μ · ½ρCLA)): when the denominator is ≤ 0 aerodynamic grip outgrows the centripetal demand and the corner is flat out. The lap is solved quasi-steadily on the track spline: corner speed limits, then a forward pass (power- and traction-limited acceleration, 520 kW at the wheels) and a backward pass (brake-limited deceleration including drag), lap time = ∑ 2Δs/(vi+vi+1). The ghost drives exactly that profile.
Single point mass, flat track (no gradients or banking), no weight transfer or yaw dynamics, no gearbox, constant power, instantaneous brake balance, no slipstream or tyre degradation. The player car uses the same grip, power and drag equations in a time-stepped 2D integrator; steering assist is a pure-pursuit controller. The car and circuit are generic inventions and not affiliated with any team, series or manufacturer.