There was much for a pilot to learn in the transition from propeller-driven airplanes to jets and much to like about the new propulsion technology. One was power management. Jets had a throttle lever. Prop planes with powerful altitude-compensating engines had a throttle and also controls for the propeller rpm, mixture, cowl flaps, carburetor heat, alternate air, oil cooler and intercooler shutters, and the supercharger. Not to mention magneto, oil dilution, ADI (Anti-Detonant Injection) pump, and other switches. There were a few more gauges to monitor as well, each associated with one of the controls, whereas the jet pilot dealt with any engine issues with only the throttle.
This is the throttle quadrant of a Grumman F6F-5N Hellcat.
Although reciprocating engine power management was basically accomplished with the throttle and propeller controls, fighter pilots also had to control the supercharging of the engine based on altitude. Supercharging was necessary to offset the loss of power due to thinner air as the airplane climbed. Basically, the supercharger thickened the air by pressurizing it.
The following is from the F6F Hellcat pilot's manual.
The notches in the performance lines indicate the transition between the supercharger (also known as blower or boost) settings, which were neutral, low ratio, and high ratio. Takeoff was accomplished at the neutral setting, meaning the air going into the cylinders was not being pressurized. Depending on the power setting (roughly normal, maximum cruising, military, and war emergency), the pilot would shift into low ratio at 7,000 to 13,000 feet and into high ratio at 22,000 to 25,000 feet.
To shift up to a higher ratio, the pilot had to reduce throttle to avoid exceeding manifold pressure at the increased boost. Shifting down was unrestricted although the pilot was cautioned, except in an emergency, not to shift less than five minutes after the last one to allow the dissipation of heat from the clutches. He was also warned to "never close the throttle even momentarily (and avoid any abrupt movement of the throttle) while operating in low or high blower." In addition, the use of supercharging at lower altitudes than necessary might result in surging in the induction ducting; the pilot was cautioned not to reduce throttle in that event but to immediately shift to the next lower blower speed "unless the tactical situation makes this undesirable"; open the throttle and reduce RPM; or shift to alternate air. Although the pilots of early jets had to avoid abrupt throttle movements in certain conditions to avoid the risk of flame out or compressor stall, their workload and attention to power settings was notably less in a combat situation.
But there was still more for the pilot of a propeller-driven fighter to keep in mind. War emergency power (WEP) was predicated on the availability of anti-detonate fluid (essentially a water and methanol mix) of which there was a 12-minute supply. All the pilot had to do was advance the throttle beyond the limit stop (at one point, this was a break wire) to close a limit switch that activated the ADI system. However, before that, he was advised to check the ADI fluid quantity gauge to insure there was water available and activate the ADI pump to clear the lines of air and build up pressure in the system (the tank was behind him, a long way from the engine). Continuous operation was not to exceed five minutes. If he was operating in low or high blower when the ADI fluid ran out, the auxiliary stage pressure regulator would control the manifold pressure to military power limits. However, this protection was not provided in neutral blower. If he did not pull the throttle back immediately, the result would be "serious engine damage, or total failure, within a few seconds." He also had to remember to turn off the ADI pump because it was not designed to run dry.
War emergency power shortened engine life but at low altitudes it provided about 500 feet per minute more rate of climb and 25 mph more speed. It doesn't sound like much, but in a well-known World War II incident, Ira Kepford used it to get out of serious trouble. He was alone, just above the water so he couldn't dive away, headed away from home and help, and had three pursuing Japanese fighters in position to shoot at him if he turned either left or right. Using WEP, he was able to open the distance between his F4U Corsair and the Japanese fighters enough to be able to turn back safely.
Automatic control of cowl flaps and supercharging was introduced with the Vought F4U-5 Corsair. However, it received mixed reviews because of the uncertainty when or if the system would actuate the cowl flaps or do a blower shift. In any event, by that time propeller-driven fighters were obsolete.