Hi I am an engineering student.

I have a question about oblique shock and expansion fans. In my understanding, oblique shock and expansion fans could happen on supersonic airplane foil. But how often are they happening?

Lets say if there is an airplane moving at constant speed at 3 times sound speed, how do we know how much energy is lost due to expansion fans and oblique shocks if this airplane travels for 3 km? How many shocks should we consider?