Lap-Time Optimization and Hybrid Energy Allocation in Formula One: Power-Unit Scenarios for 2026-2028, Attack-Recovery Strategies, and Track Geometry

Under the 2026 Formula One regulations, which pair a near-equal combustion--electric power split with active aerodynamics, lap performance is circuit-location-dependent and energy-allocation, and the announced 2027--2028 shift toward a larger combustion share raises the question of how this spatial allocation must change to minimize lap time. We answer this question by establishing a spatial-domain minimum-time optimal-control model that jointly optimizes vehicle speed, battery energy, combustion and electrical power, mechanical braking, and active-aerodynamic scheduling. On the Albert Park reference, the 2026 baseline is optimized, and we map how each resource is used around the lap. Re-parameterizing the same model with the announced 58/42 and 60/40 power-unit proxies in 2027 and 2028, we find the latter reduces mean lap time by 2.226 s at Albert Park. To examine whether this benefit is consistent across terrains, we construct five synthetic track archetypes with controlled geometry and optimize the same profiles on each. The improvement ranges from 0.977 to 4.540 s/lap, and the ranking of lap-time gains across the five archetypes is the same in every profile comparison. On this model we further introduce a two-lap formulation with a prescribed intermediate battery state, simulating an attack--recovery tactic. Sweeping the intermediate state shows that the total two-lap time cost grows approximately with the net battery depletion at the intermediate lap boundary. Combining the experiments, the paper summarizes more than twenty findings of direct value to F1 engineers and drivers, including, among others, where and when electrical assistance is most valuable and how attack-lap gains affect subsequent recovery. Overall, this paper offers a quantitative way to evaluate announced rule changes and their driving and engineering implications.