  The sustainable mobility trend touches the racing world as well, from the
hybridization of Formula 1 (F1) and Le Mans Hypercars to the fully electric
Formula E racing class. In this scenario, the research community is studying
how to push electric racing vehicles to their limit, combining vehicle dynamics
and energy management, to successfully solve the minimum lap time problem.
Recently, this class of problems has been enlarged towards optimal sizing, with
a particular interest in batteries, which represent the main bottleneck for
electric vehicle performance. In this work, starting from a thorough review of
literature approaches, we define a general optimization framework of minimum
lap and race time problems for electric vehicles, suitable to figure out the
impact of different modeling choices on both problem structure and optimal
variables profiles. Exploiting a case study on Generation 3 (Gen 3) of Formula
E cars, we delve into the impact of battery models' complexity on both optimal
sizing and optimal battery usage. We show how highly detailed models are
necessary to study the evolution of both battery and vehicle control variables
during the race, while, simple models are more than sufficient to address the
battery sizing problem.
