The Mach-Effect thruster is a propellantless propulsion concept that has been in development by J.F. Woodward for more than two decades. It consists of a piezo stack that produces mass fluctuations, which in turn can lead to net time-averaged thrusts. So far, thrust predictions had to use an efficiency factor to explain some two orders of magnitude discrepancy between model and observations. Here, a detailed 1D analytical model is presented that takes piezo material parameters and geometry dimensions into account leading to correct thrust predictions in line with experimental measurements. Scaling laws can now be derived to improve thrust range and efficiency. An important difference in this study is that only the mechanical power developed by the piezo stack is considered to be responsible for the mass fluctuations, whereas prior works focused on the electrical energy into the system. This may explain why some previous designs did not work as expected. The good match between this new mathematical formulation and experiments should boost confidence in the Mach effect thruster concept to stimulate further developments.