Tuning 2 stroke exhausts is fundamentally mathematics of applied fluid dynamics. There are several good books about it. But Villiers were used in tuned form on a variety of machines, so there already exists a store of information. The modern era has modified designs, as better feed back information could be obtained. So from the baffled megaphone giving a simple shockwave timed to aid the extraction of burned gas from the cylinder we have moved to a system that has a stinger on the end. A more complex result. Bonds with stingers seems a bit extreme, but its all good fun.
For my sins I now hold the tooling, and am making, the tuned exhausts designed and tested on the rolling road by Church/Frankland. These offer instant extra power and torque to the Sachs 200 and are designed for the Messerschmitt. It fits in the same place, with the same mounts. Best used with a high compression head, and a better carb, the performance is increased by a proven 25%, but it is the torque and full power available over so much more of the rev range that makes the real difference. Those using this system in action all report positively.
For those confused. Having more power and torque is not always to go faster out right, but to improve drivability within the design perimeters of the car. Done well, and in balance, it often finds increased economy, should the driver choose to drive in that way.