The importance of equation η = μn 2 in dimensional analysis and scaled vehicle experiments in vehicle dynamics

Dimensional analysis has been very helpful in experimentation of very large or small-scale engineering systems. A good example would be experimentation on the aircrafts and ships, which was made cost-effective and simple by dimensional analysis. The history of dimensional analysis mentioned in the introduction section of the present document includes many of such applications. Automotive industry, however, never felt the need as the price or the size of land vehicles did not make experimentation so far-fetched; therefore, there are many crash tests which every new vehicle has to go through before mass production This changed with the imminent introduction of autonomous vehicles, which brought all the risks involved in experimenting with them. Many cost-effective experimental platforms are introduced, such as QCar https://www.quanser.com/products/qcar/ or laboratories, such as Scaled Autonomous Vehicles Indoor (SAVI) https://cast.tamu.edu/research/technology-demonstrator-platforms/scaled-autonomous-vehicles-indoor-tdp/. The present study will enable the results taken from such platforms to be translated to real-sized vehicles, enabling researchers to study dynamics of various vehicles. Classical vehicle equations of motion including constant velocity, accelerating bicycle model and roll model have been made dimensionless. The case of steady-state responses is also calculated in a dimensionless form. Some practical numerical examples are also mentioned as a proof of theory.