"Bumper car" amusement rides are disclosed. An exemplary bumper car comprises a frame, a seat, a portable source of electrical power for propelling the car, multiple drive wheels, a motor controller, and at least one rider control. The seat is configured to hold and position at least one rider of the bumper car. The source is a portable source, mounted to the frame, of electrical power for propelling the bumper car. Each drive wheel comprises a respective hub motor that, when supplied with the electrical power from the source, rotates the respective drive wheel relative to the frame and propels the bumper car. The controller is connected to the source and to the hub motors. The controller is configured: (a) to limit a maximal current supplied by the source to the hub motors during a surge-current situation to a preset maximum, and (b) to ramp down the maximal current over a preset time interval during the surge-current situation. The at least one rider control is interconnected with the source and the hub motors and is configured to be manipulated by a rider for maneuvering the bumper car.