How does compressor RPM affect the power of a turbofan engine?

The relationship between compressor RPM and the power output of a turbofan engine is indeed nonlinear. As the compressor RPM increases, the airflow through the engine and the associated pressure ratios also increase, leading to a rise in power. However, this increase isn't solely proportional; it varies depending on the design and operational limits of the engine.

At lower RPMs, a slight increase can produce a more pronounced effect on power, while at higher RPMs, the efficiency and performance characteristics may change, contributing to a different rate of power increase. This nonlinear response is due to factors like airflow compression, thermodynamic efficiency, and the turbofan's geometry impacting how effectively the engine can convert airflow into thrust.

Thus, understanding this nonlinear relationship is critical for optimizing engine performance and ensuring safe operation across a range of speeds. This concept emphasizes the complexity of engine behavior rather than a straightforward linear power increase with RPM.