A four cylinder, 3.6 liter CI engine operates with a compression ratio of 18 and an air fuel ratio of 17. The engine operates on a dual cycle. The maximum pressure is limited to 12 MPa and the maximum temperature is limited to 3600 K. Assume that at the start of compression the temperature is 50 C and the pressure is 100 kPa. The fuel heating value is 43,000 kJ/kg. The fuel injection timing is to be optimized for peak indicated efficiency. Designers must develop the fuel injection sequence to control how much of the heat is released at constant volume and how much at constant pressure. Determine the optimum fraction of heat release at constant volume conditions and the fraction of heat release at constant pressure conditions. Support all conclusions with calculations.