  This paper presents a convex optimization framework to compute the
minimum-lap-time control strategies of all-wheel drive (AWD) battery electric
race cars, accounting for the grip limitations of the individual tyres.
Specifically, we first derive the equations of motion (EOM) of the race car and
simplify them to a convex form. Second, we leverage convex models of the
electric motors (EMs) and battery, and frame the time-optimal final-drives
design and EMs control problem in space domain. The resulting optimization
problem is fully convex and can be efficiently solved with global optimality
guarantees using second-order conic programming algorithms. Finally, we
validate our modeling assumptions via the original non-convex EOM, and simulate
our framework on the Formula Student Netherlands endurance race track. Thereby,
we compare a torque vectoring with a fixed power split configuration, showing
that via torque vectoring we can make a better use of the individual tyre grip,
and significantly improve the achievable lap time by more than 4%. Finally, we
present a design study investigating the respective impact of the front and
rear EM size on lap time, revealing that the rear motor sizing is predominant
due to the higher vertical rear tyre load caused by the center of pressure
position and rearwards load transfer under acceleration.
