The mistake here is assuming that because an airplane is at a high pitch angle relative to the Earth, it is at a high AoA. In point of fact, an aircraft zooming *straight* vertically is in an unloaded state-the wings must be producing zero lift, otherwise it would be looping. Assuming the aircraft has sufficient airspeed for vertical maneuvering, an Immelman will always be more energy efficient way to reverse than a flat turn, whether fast or slow.
Not entirely. I get what you're saying, but think that, to achieve vertical, an aircraft must pull through the horizon up to vertical.
Q: How does it achieve this?
A: By changing the AoA.
The angle of attack must be increased to move the center of lift (CL), which increases the lift vector. This is the only way an aircraft can achieve a nose-high configuration. Even though the relative wind is mostly head-on, there is some relative wind that comes from a non-head-on angle as the pilot pulls back on the stick, due to the change in aircraft attitude. The wind can't "adjust" fast enough to the wing as it pulls through it as the aircraft is pulling upward. This is a change in AoA (remember that AoA is the angle between the relative wind and the wing, regardless of control input configuration). The lift produced by this change in AoA produces drag, specifically induced drag.
Now, let's examine the Immelman vs. flat turn. There's a common misconception that flat turns bleed a ton of energy. In reality, flat turns don't inherently bleed any more energy than Immelmans. What bleeds energy is the G-load combined with the lift vector.
When an aircraft is an a very slight turn, such as a standard-rate or one-half standard-rate turn, the longitudinal axis is pointed just slightly off from vertical. Functionally, this means that the lift produced by the wings is almost straight vertical (measured against the longitudinal axis), but not quite. This produces just enough lift vector in the horizontal that the aircraft will turn horizontally with very, very little loss in forward airspeed, very little G-loading (1.1G's or less if executed properly). In essence, there is virtually no loss of energy state of the aircraft, save for the induced drag and miniscule G-load from the 1.1 load factor.
Now, enter the Immelman. The Immelman is a half-loop, followed by an aileron roll at the top of the loop. How does it conserve energy, exactly? The Immelman works by keeping the lift vector directly opposing gravity on the first half of the maneuver, and then uses the 1G pull of the Earth ("God's G") to assist in the second portion of the half-loop. This is very energy efficient as there's no change in lift vector in relation to gravity, as there is with a standard-rate turn.
So Immelman's always conserve energy over flat-turns, right? The correct answer: no, not always.
What many pilots take forgranted is that, in air combat, we aren't interested in minimizing loads on the aircraft or flying in the most efficient way; instead, we're interested in shooting that other mother f'er down as quickly and efficiently as possible. This means that standard and half-rate turns, as described above, are all but worthless in a combat environment. If we need to turn horizontally, we need to typically bank and yank on the stick, and we need to do it hard. This introduces violent changes to the lift vector and wing loading, which drains a ton of energy.
The Immelman is subjected to the same limitations. We can't do gentle Immelmans - we do them quick to get around on the enemy. Guess what? The faster you perform an Immelman, the harder you pull back on that stick, the more energy you're going to drain. It's simple physics. However, because of the vertical lift vector and God's G, it's a lot more efficient than turning horizontally. This is where the assumption that performing an Immelman
saves energy comes from, when it reality it doesn't; it simply
burns less energy.
So, back to the flat turn vs the Immelman in a non-combat environment. We know that we can perform a flat turn very gently and burn very, very little energy, so what about an Immelman? The problem here is that in almost every propeller-driven aircraft, you're limited by thrust. All WWII aircraft had thrust-to-weight ratios of less than 1.0, which means that the second you pull past the critical AoA, you're counting down to the time you stall. Unfortunately, we can't perform an Immelman with a G-load of less than 1.1 - for that matter, we can barely perform them with a G-load of 2.0 in many aircraft. We have to perform them quickly to ensure we roll out wings level at the top without dropping below corner speed (remember that below corner speed, we're increasing our induced drag as it requires a higher AoA to maintain straight and level). If we buffet at all, or if we come out below corner speed, we're introducing additional drag and losing energy efficiency compared to a flat turn. This means we need to pull several G's (and therefore have a higher AoA) to maximize our efficiency, which bleeds more energy than our half-rate turn at 1.1G's.
It's counter-intuitive to most air combat enthusiasts, but Immelman's and vertical maneuvering burn energy - all maneuevering burns energy - using the vertical just burns less energy.
Remember that energy fighting is not about absolute energy levels, but rather the relative energy levels of the pilot against his opponent.
