Forget flat and vertical....that's 2D thinking.
There are only two maneuvers...rolls and pulls.
There are only two kinds of turns...those that trade energy for altitude and those that trade altitude for energy.
Roll. Pull. Altitude going up, airspeed going down. Trading energy for altitude. Your relationship to the horizon is of little importance. Only your relationship to the target has relevance. Your target is hard breaking and you don't want to try to match his turn so you trade energy for altitude and then trade that altitude back in for energy. High Yo Yo
Roll. Pull. Altitude going down. Airspeed going up (or steady if you are pulling really hard). Trading altitude for energy. Why would I do that? Again it revolves around the relationship to the bandit. In a merge situation where the bandit gives you some separation horizontally and pulls the standard nose high pull for an attempt at a vertical merge an energy building or energy conserving nose low turn into the nose high bandit will give you position on his 6 with energy to spare.
All Basic Fighter Maneuvers are performed in relation to the target aircraft. If you ask someone to describe any BFM and they give you precise instruction like " For the high yo yo pull the nose 45 degrees above the horizon then roll to 135 degrees and pull the nose 45 degrees below the horizon" then you know they are feeding you a line of BS.
The answer on how to do any BFM is always "depends on what the target is doing".
It can be described in general terms.
For example the High Yo Yo would be described in this manner.
"When the bandit enters his break pull the nose high enough to stay above the bandit turn circle, roll the lift vector to a position of lead pursuit on the bandit and then pull bringing the nose to lead, pure or lag pursuit as the situation dictates."
If you do High Yo Yo's using that description they are right every time. Of course you have to understand the concepts of turn circle, lift vector placement and pursuit curves or the description doesn't make much sense.
Sigh....where to start....
First off,
"forget flat or vertical...that's 2D thinking?" I know we're not flying F14's here but bear with me a moment. Tomcat's fought in the flats and verticals for their entire time in service as have many other fighters and none of them were "2D" fighters. Its strengths were a very efficient turn (not the highest rate but very efficient), excellent pitch rate, acceleration, and speed. The simplest F14 fight was to force a level two-circle fight at corner, and when the bandit sold E for angles or spiral climbed for a nose-low lead turn conversion at the next merge you'd take him close aboard and pull straight up in a pure vertical extension. In the vertical, you'd roll to put the lift vector behind him, pitch over, and dive in for the kill. Nothing but flat and vertical moves with the exception that at the end, the dive in for the kill was an oblique and yes, it's an NRG fight. If the bandit went up at the first merge then you'd extend, reverse, come in underneath and again take it straight up into a pure vertical fight. Again, nothing but horizontal and vertical moves with the addition of a high yo-yo for the reversal and yes this is still an NRG fight. The idea that "flat" and "vertical" can be dismissed is sort of blowing smoke of folks tailpipes. Again, I realize that we're not flying F14's here but I'm illustrating that even in the modern fighter world of NRG fights flat and vertical still matter. Also, while not identical, similar fights happen in AH all the time but we usually call them ropes.
Second,
"only two maneuvers...rolls and pulls?" Great, if these are the only "maneuvers" there are then BFManeuvers just got really, really easy and Topgun has been wasting everyone's time. The reality is that they are the actions taken that result in a maneuver, they are not maneuvers in and of themselves. The roll positions the lift vector and the pull creates the turn and the results are BFManeuvers. BFManeuvers are turns, rolling scissors, flat scissors, extensions, reversals, yo-yo's, displacement rolls, lag rolls, etc.
Third,
"there are only two kinds of turns...those that trade energy for altitude and those that trade altitude for energy." That's an NRG concept and, generally speaking it's true but unfortunately incomplete. There are turns that trade NRG for angles and there are maximum sustained turns in which the airplane is on its P
s=0 line. In neither of these is the fighter required to either trade NRG for altitude or altitude for NRG yet, by golly, they're still turns. These would generally be considered part of an angles vice NRG fight but even an NRG fighter usually needs to convert at least some stored NRG into angles for the kill unless they're going strickly for snaps.
Fourth,
"and they give you precise instruction like " For the high yo yo pull the nose 45 degrees above the horizon then roll to 135 degrees and pull the nose 45 degrees below the horizon" then you know they are feeding you a line of BS." There's a difference between basic and advanced instruction that you apparently are choosing to ignore. This is sort of like explaining racing techniques in a Ferrari when the new driver can hardly coordinate his clutch and gearshift yet. Learning the mechanics of a high yo-yo, i.e., the required hand/eye coordination and the capabilities of your aircraft WRT to turn radius, NRG addition or loss, unusual attitudes, etc., is the start of BFM instruction, it's hardly "a line of BS." Those are fundamental skills and knowledge that must be learned first. The mechanics of a maneuver like a high yo-yo is taught in the very beginning of BFM instruction; the how and why it's used in relation to the bandit, the bandit's turn radius, and closure, and tactics follows once the mechanics and concept are learned. It's not that the relationship between the fighter and bandit is irrelevant that would be a huge mistake, it's that you've got to understand how to do one before you learn how to employ one. There's a difference.
Fifth,
"your relationship to the horizon is of little importance." Really? It's of little importance??? You yourself just spent that entire paragraph and the next explaining explicitly why it
is important. The whole NRG fight concept is intrinsically tied to the horizon and your relative nose position, those elements can not be divorced from each other. Since an NRG fight is about trading airspeed and altitude and back it's sorta important to know where the darned horizon is. Saying everything is in relation to the bandit is misleading and you prove that in your own discussion. You are oversimplifying this.
Much of what you say is good and useful knowledge and you're certainly entitled to your opinion but you undermine your credibility by making grandiose and condescending comments that just aren't supportable. As you saw fit to caution others about BS, I'll do the same.
When people make such sweeping and apparently bold statements keep your tailpipe away from them...you may get smoke blown up it.