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The introduction of parallel post transmission hybrid electric vehicles has demonstrated a limitation of previous mathematical models of the hydraulic torque converter. Earlier models developed by Hrovat and Tobler (2) and Kotwicki (4) in the 1980's only covered the cases of the below coupled and coupled states without anticipating the need to analyze the converter in the overrunning case. This study develops the relations for the overrunning case, allowing the reader to establish accurate predictions or computer simulations of the flow, torque, and speeds that will be result in the case of a post transmission hybrid system. Without additional measures, these post transmission hybrid systems will generate large fluid losses in the torque converter.

The hybrid electric vehicle is currently changing the automotive market at an impressive rate. While not as highly publicized, the transit bus market is being transformed at an equal rate. As these markets move forward, the school bus market remains largely unchanged. As an unchanged market, there is still the opportunity to optimize a hybrid vehicle platform for school buses. This study begins the modeling process of an existing class C school bus and investigates the potential that both series and parallel hybrids hold to reduce fuel consumption and emissions for a school bus. The primary focus of this study is to investigate the potential benefits of adding an electricity grid interconnection to hybrid electric school buses, allowing them to add to the hybrid potential with a pre-charged battery pack from the electric utility grid. These vehicles are known as plug-in hybrids.