Due to longitudinal stability, aircraft tends to maintain constant angle of attack. In straight flight the wing loading is constant, so speed remains the only significant factor and the aircraft tends to maintain constant speed (or rather oscillate around it in phugoid oscillation). If you increase the power and speed is maintained, law of conservation of energy dictates that the aircraft has to climb and when power is reduced it has to descend. So in theory you control speed with elevator (trim) and vertical speed with power. See How It Flies, chapter 2 for a detailed discusson.

In practice changing power affects pitch trim too, so you need to always adjust both. And you have to arrest the phugoid oscillation.

It might be interesting to note that Airbus control laws change the rules so that attitude controls climb/descent and power controls speed by automatically adjusting the trim.

Due to longitudinal stability, aircraft tends to maintain constant angle of attack. In straight flight the wing loading is constant, so speed remains the only significant factor and the aircraft tends to maintain constant speed (or rather oscillate around it in phugoid oscillation). If you increase the power and speed is maintained, law of conservation of energy dictates that the aircraft has to climb and when power is reduced it has to descend. So in theory you control speed with elevator (and trim so it is maintained without pressure on the controls) and vertical speed with power. See How It Flies, chapter 2 for a detailed discusson.

In practice changing power affects pitch trim too, so you need to always adjust both. And you have to arrest the phugoid oscillation.

It might be interesting to note that Airbus control laws change the rules so that attitude controls climb/descent and power controls speed by automatically adjusting the trim.