Most of my habits were formed analog and I taught that way even in digital aircraft. Some of it gets lost in slower GA planes, but the principles apply. Energy management isn't as critical around the turn in a Cessna, but if you understand it and apply it, it allows you to be precise. Those habit patterns translate well as you move up to larger a/c.
Quick example, earlier in the discussion someone was saying that a dive results in more airspeed. That is true when starting your descent from abeam, around the base turn, when turning final, or on final approach. You may be able to hit a certain altitude at a certain point, but how you get there matters. And it affects your energy state upon reaching that point. Your energy state is going to influence where you end up afterwards, so if you dump the nose to get to a reference point, you may hit it. But, you do so with more energy.
In the spirit of
@nauga;
Cooter,
Who used to shout, "Keep'em safe Paddles!"
Thankfully my primary instructor wasn't a fan completely of the "rules of thumb" about "pitch for airspeed, power for altitude" or vice-versa. He used those early on but always with the admonition that any pitch and power are inexorably intertwined.
Like you say, if you pitch (let's say down) to hit an altitude, you also sped up if you didn't remove the appropriate amount of power. So the two must be used in concert.
In another forum today, in fact, a pile of CFIs discussed the pitch/power thing and most agreed they teach starting with the "pitch for airspeed, power for altitude" mantra early on because they're trying to instill in pilots that if they're stalled or headed for a stall they want the pilot to pitch down NOW if that's all they remember to do.
But in reality you might also need more power in that scenario. Like you said, depends on what the energy trend was that got them there.
Disconnecting pitch and power into either speed or altitude, is a simplification technique, but the physics reality is that they're inexorably linked.
Most pilots really figure this out at the Instrument rating, I think. Pitching to chase a glideslope they start to realize they can't do that and hold an airspeed. To settle the whole thing down they learn to work both in concert more than they probably have before. Often because the only time they've really attempted any precision with it was on final and on the back side of the power curve.
Try this-- next time you are up in wind, try flying the pattern with a higher rpm setting than usual. I know pitch for airspeed power for altitude but it's ok to cheat a bit and use the extra power to better plow through the wind.
Plow through the wind? Are you trying to describe that as groundspeed goes down (more headwind) if the same descent rate per minute is held, you'll come up short, because it takes longer to get there? There's two fixes for that, fly faster (which is what you're suggesting by adding power) or turn in closer to the runway on base and accept that the approach is steeper. Both have challenges, but flying faster means at some point in the approach you have to dissipate more energy to slow to a proper landing speed.
For the church-goers for the "stabilized approach" methodology, you'll have to "destabilize" significantly to get slowed over the fence. Technically the steeper approach is more stable than flying faster to counteract the headwind's effect on landing point out of a consistent rate of descent.
You may feel like you need more elevator control( more yoke input) but the extra power will accomplish a bit more speed up until you pull it out and will avoid the dive to the deck technique which is causing you to struggle with the landing touchdown.
Flying with more power in most singles means the tail has more authority, not less. You'd need less control input pressure for the same effect as a lower speed. Also if trim is being used properly, the average control input pressure should be near zero. I honestly have no idea what you're attempting to get across here, but it makes no sense.
The hardest part of gusty landings I think, is the touchdown and keeping the nose straight in the gusts. If you are getting blown off the center line you need to put the wing down into the wind and kick the opposite rudder. Getting blown off center has nothing to do with airspeed-- it has everything to do with not using proper technique to remain on the center line.
Actually as you slow, the rudder is less effective and airspeed can have a VERY significant impact on directional control. Again, this makes no sense. "Proper technique" means adding more rudder as the aircraft slows and to a lesser extent, more aileron all the way through the landing until the ailerons hit the stops and you're rolling on the ground below flying airspeed.
In fact, with a cross wind, "running out of rudder" to maintain directional alignment is often the cause of a go-around, since you've now exceeded the maximum crosswind capability of the aircraft in today's conditions. If the rudder pedal that was holding the aircraft aligned with the runway bottoms out as the aircraft slows down, directional control only can get worse from there.