Vehicle Dynamics Lab

ERS: the Lap Energy Budget

Vehicle Dynamics · Demo

Harvest under braking, spend on the straights — find the biggest deployment the lap can actually pay for.

one lap · 90 s▮ straight▮ braking▮ cornerbattery full · 4 MJemptybattery charge around the lapbattery → wheels · 60 kW

The strategy

The trace shows the steady lap your strategy actually delivers — find the biggest deployment with no red derate zones.

Per lap, at steady state

Deployed3.60 MJ
Harvested (MGU-K)1.13 MJ
Recovered (MGU-H)2.47 MJ
Thrown away0.20 MJ
Derated0.0 s/lap

2014 rules: 120 kW MGU-K, 4 MJ battery, 2 MJ/lap harvest cap, 4 MJ/lap deployment cap — the MGU-H answers to none of them.

In plain terms

A hybrid Formula 1 car carries a battery the size of a lap: about 4 MJ, roughly one second of engine-power worth of energy for every ten seconds of racing. It refills two ways — the MGU-K turns the rear axle’s braking into charge instead of brake heat, and the MGU-H milks the exhaust whenever the engine is working — and it empties one way: extra shove down the straights. The strategy question is brutally simple: what is the biggest spend the lap can pay back? Overspend and the battery runs dry mid-straight — the derate — and the car is suddenly 160 horsepower poorer at the worst possible moment.

How this is computed

The lap is a fixed 90 s sequence of straights (60 s), braking zones (11 s) and corners (19 s), integrated at 0.1 s steps under the 2014 power-unit rules: MGU-K 120 kW120\ \text{kW}, energy store 4 MJ4\ \text{MJ}, harvest capped at 2 MJ per lap, deployment capped at 4 MJ per lap, MGU-H uncapped at a representative 40 kW on throttle (half in corners). The readouts come from the steady-state lap — the model re-runs the lap until the final charge equals the starting charge, which is the only lap a race strategy can repeat. Energy is conserved exactly:

ΔEstore=Eharvest+EHEdeploy\Delta E_{store} = E_{harvest} + E_{H} - E_{deploy}

What the model leaves out: a lap-time figure (energy is reported in MJ, not tenths), thermal limits and charge windows, and circuit-to-circuit lap shapes — and the MGU-H’s 40 kW is a representative figure, because the teams guard the real numbers. The Mercedes W05 page in the Formula 1 timeline shows the same machine from the hardware side.