It's the oldest debate in aviation: does elevator control airspeed or does it control altitude? Does power control altitude or does it control airspeed?
Come to think of it, "Who gets left seat?" may be an older debate. But this one is more fun.
Every flight instructor struggles with it. The student asks, and the instructor hems and haws and says things that start "Well, sometimes ...," or draws out a long list of conditionals ("If you're high and the airplane is slow and it's a Tuesday in the northern hemisphere, then you should ..."). Is there a simple answer?
I used to use a flip answer: "Power and pitch control airspeed and altitude; you have to stay coordinated." Well, it's not really flip, but it's not really useful, either. So, it there a useful simple answer?
I believe that I have stumbled on one, in a roundabout way. Let's back up a little bit to another classic instructor - student dialog. The instructor asks how to recover from a stall. The student is confused, because the FAA's publications, followed by the commercial publications, use a lot of flowery folderol about turbulent flow and burbling air to talk about why an airplane stalls rather than saying what a stall is. The thing is, when you give a student the correct definition of stall, it includes the recovery:
Students who have been exposed to this have a dangerous attitude about stall recovery, because they do not have a clear idea that it's pitch, not power, that will save the day. So here's a typical dialog:
Me: How do you recover from a stall?
Student: Add power and ...
Me, interrupting: What do we do in gliders?.
Power has almost nothing to do with stall recovery; stall recovery means reducing the angle of attack. You need power to pull your scared bellybutton away from the ground. (Admittedly, power slightly reduces the stall speed of many light aircraft, so it may in fact aid stall recovery, but that is a secondary effect.)
So now let us return to the original debate. The solution to the conundrum is to examine the nature of power. Power becomes one of the four forces, namely thrust, although it also involves a small amount of lift at higher deck angles. A force means that there is a change in energy.
Energy is the key.
There are two kinds of energy, potential energy, which is proportional to height, and kinetic energy, which is proportional to the square of speed. Energy is conserved, so if you lose one you have to gain the other. "Trading airspeed for altitude" is how gliders go around; "trading altitude for airspeed" is a favorite chant of airshow announcers, watching some tiny 9G biplane in a screaming dive toward the bottom of the box.
But energy changes. The only way to change the energy is to exert a force. Two of the four forces are important here. Drag tends to reduce energy: it slows you down. That's why gliders are so small and sleek. The reduced drag means that the glider retains more energy. How reduced is the drag? A Cessna 172's lift over drag ratio is about 10:1. My glider's lift over drag is 39:1. At the same weight, the glider has 1/4 of the drag!
The other force is thrust, which tends to increase energy. Thrust speeds you up. No, wait, thrust makes you go up. It's both! Thrust adds energy, which can be in the form of speed (kinetic energy) or altitude (potential energy).
Gliders don't have thrust, and depend on rising air to gain energy. Airplanes can gain a little energy this way, but usually depend on stored chemical energy (in other words, fuel that is converted to kinetic or potential energy.
But you knew this already: "An airplane climbs because of excess thrust." A climb increases the airplane's energy.
And so we come to the definitive (pardon my hubris) answer on power management during approaches.
In practical terms:
Add power when you are low and slow; you need a lot of energy.
Reduce power if the PAPI is all white; you are high, so you have too much energy.
Leave the power alone if you are low and fast. Raise the nose to convert airspeed into altitude. Just don't let the speed get too low.
Leave the power alone if you are high and slow. Lower the nose to gain speed, and you will lose altitude.
If we could only find a simple rule for the price of oil.