KERS: Braking Energy Recovery on a Race Circuit

Energy Recovery System

Harvest power limit 120 kW

Deploy power limit 120 kW

Energy store capacity 4.0 MJ

Energy Store

Stored energy

2.00 MJ

State of charge

50%

Power flow

0.0 kW

Speed

0 km/h

Lap time

0.0 s

Best lap

—

Harvested / lap

0.00 MJ

How it works

Every time the car brakes it must shed kinetic energy KE = ½mv². Normally that energy becomes brake-disc heat and is lost. A kinetic energy recovery system (KERS / MGU-K, as used in Formula 1 since 2009) instead routes part of that braking force through a motor-generator into a battery or flywheel store, then feeds it back through the motor as extra thrust on the next straight.

Braking:  P_dissipated = F_brake · v          (F_brake = m·a_brake, fixed by grip)
          P_harvest = min(P_limit, P_dissipated, store headroom)
Cornering: v_corner = √(μ·g·R)                 (centripetal grip limit)
Deploying: P_traction = P_engine + P_deploy
          a = (P_traction / v − F_drag − F_roll) / m
Energy:    E_stored(t) = ∫ P_harvest dt − ∫ P_deploy dt   (clamped 0 ≤ E ≤ capacity)

Harvest power limit — the motor's regenerative braking power ceiling; the total deceleration into a corner never changes (grip sets that), only how much of the dissipated energy is captured versus lost as brake heat.
Deploy power limit — the extra propulsion power available from the store on top of the engine while accelerating out of a corner and down the straight.
Store capacity — the energy ceiling of the battery/flywheel; once full, further harvest power is wasted as heat, and once empty, deploy stops.
The green sparks are energy flowing into the store under braking; the orange sparks are stored energy being deployed as thrust.

Real-world relevance: this is the same power-flow logic behind F1's ERS, hybrid road-car regenerative braking, and KERS flywheel buses — capture what grip forces you to shed, spend it where power actually helps.

Harvesting (braking) Deploying (accelerating)

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