What happens to the low-pressure rotor speed in two-spool engines at high altitudes?

In two-spool engines, the behavior of the low-pressure rotor speed at high altitudes can be attributed to changes in compressor load. At higher altitudes, the air density decreases, resulting in less mass flow through the engine. This reduction in air density means that the compressor has to work less hard to achieve a certain thrust output.

As the compressor load decreases, the low-pressure rotor can spin faster because there is less drag from the airflow being processed. This increase in speed is a result of the engine's design and the relationship between the compressor and rotor speeds in a two-spool configuration, where one spool (the high-pressure side) drives the other (the low-pressure side).

In summary, at high altitudes, the decrease in compressor load allows the low-pressure rotor speed to increase, enabling efficient engine performance despite the lower air density. This is a key feature that is designed into modern turbofan engines to optimize performance across a range of operating conditions.