>Why hasn't anyone made a hybrid car that uses a gasoline-powered turbine generator to charge its batteries instead of a piston engine?
The current engine formula (2014-) in Formula 1 racing might be of interest to you.
> During acceleration of a Formula 1-car, the turbo charger is performing at its peak and is spinning at about 100,000 rpm. The MGU-H (Heat) functions at that moment as a generator. This is connected to the turbo charger and converts the energy, generated by the turbo, into electricity; that, in turn, is stored in a battery or sent directly to the MGU-K.
> This MGU-K (Kinetic), connected straight to the crankshaft of the turbo engine, acts as an electric motor that supplies extra power to said engine. This MGU changes into a dynamo, which stores the energy that is released during braking in the battery. This stored energy, can later be used to support the turbo engine during acceleration or overtaking.
The current engine formula (2014-) in Formula 1 racing might be of interest to you.
> During acceleration of a Formula 1-car, the turbo charger is performing at its peak and is spinning at about 100,000 rpm. The MGU-H (Heat) functions at that moment as a generator. This is connected to the turbo charger and converts the energy, generated by the turbo, into electricity; that, in turn, is stored in a battery or sent directly to the MGU-K.
> This MGU-K (Kinetic), connected straight to the crankshaft of the turbo engine, acts as an electric motor that supplies extra power to said engine. This MGU changes into a dynamo, which stores the energy that is released during braking in the battery. This stored energy, can later be used to support the turbo engine during acceleration or overtaking.