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Propulsive Efficiency

Propulsive efficiency can be defined as the useful power output over the rate of change in energy of the airflow through the engine. If useful power is thrust x velocity, and the rate of change of KE is expressed in terms of air mass flow rate, provide an expression for ηP in these terms. If the efflux pressure is brought back to ambient conditions, the thrust term is simplified to the rate of momentum change through the engine. Substituting for thrust, ηP can be expressed in terms of the forward speed parameter v = V1 / V4 . Sketch the variation of propulsive efficiency versus forward speed parameter for (i) a turbojet, (ii) a turboprop and (iii) a turbofan of typical BPR of 5. What do these (T and ηP) plots suggest about the selection of engine type (ie: turbojet/prop/fan) for application on aircraft designed for short sectors and for long haul flights?