This paper describes a novel method for extended expansion in a rotary combustion engine running ordinary gasoline to analyze the effects on fuel efficiency and emissions. The engine consists of a toroidal-shaped piston that rotates around a drum to expand and evacuate the hot gas. There are several problems with today's internal combustion engines or IC engines. The current IC engines do not always have the necessary internal volume to expand the hot gases to near atmospheric pressure, and since the whole process of compression, combustion, and expansion happen within the same space, excess heat builds up and increases emissions of nitric oxides and nitrogen dioxide. The proposed solution is to redesign the IC engine as to supply greater expansion volume and to separate the combustion and exhaust areas. With the concept rotary engine, it is hoped that these issues will be minimized in ways that traditional IC engines are unable. This thesis is a work in five parts. Chapter one covers a strong literature review on fuel injection, fuel air mixing, the combustion process and IC engine emissions. Comparative review is done with previous work and engine dimensions are based off of existing designs. Chapter two serves as a data review for fuel injection along with a preliminary thermodynamic review on the concept engine and the effects extended expansion has on combustion rates and emissions. Iteration is done by choosing different combustion temperatures and compression ratios as to best design the concept engine. Chapter three covers the written code to simulate both fuel injection and the resulting combustion process. The fuel injection includes fuel atomization, spray penetration, evaporation rate and average droplet diameter within the combustion chamber. After injection has been modeled and validated with literature, combustion can be studied. The combustion analysis focuses on the temperature, pressure and emissions during the engine cycle. Collected data is compared to a traditional IC engine using similar air fuel ratios. Chapter four validates the code written for chapter three using a simulation software called KIV A-3. Using this program, data for fuel injection, combustion and emissions are generated and plotted, which is used to compare to the code written in MATLAB. Finally chapter five is the conclusions, where recommendations and future work is discussed.