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The Immelmann turn refers to two different aircraft maneuvers:
After making a high-speed diving attack on an enemy, the attacker would then climb back up past the enemy aircraft, and just short of the stall, apply full rudder to yaw his aircraft around. This put his aircraft facing down at the enemy aircraft, making another high-speed diving pass possible. This is a difficult maneuver to perform properly, as it involves precise control of the aircraft at low speed. With practice and proper use of all of the fighter's controls, the maneuver could be used to reposition the attacking aircraft to dive back down in any direction desired.
In modern aerobatics, an Immelmann turn (also known as a roll-off-the-top, or simply an Immelmann) is an aerobatic maneuver. Essentially, the aerobatic Immelmann comprises an ascending half-loop followed by a half-roll, resulting in level flight in the exact opposite direction at a higher altitude.
To successfully execute the aerobatic Immelmann turn, the pilot accelerates to sufficient airspeed to perform a loop in the aircraft. The pilot then pulls the aircraft into a climb, and continues to pull back on the controls as the aircraft climbs. Rudder and ailerons must be used to keep the half-loop straight when viewed from the ground. As the aircraft passes over the point at which the climb was commenced, it should be inverted and a half loop will have been executed. Sufficient airspeed must be maintained to recover without losing altitude, and at the top of the loop the pilot then executes a half-roll to regain normal, upright aircraft orientation. As a result, the aircraft is now at a higher altitude and has changed course 180 degrees.
Not all aircraft are capable of (or certified for) this maneuver, due to insufficient engine power, or engine design that precludes flying inverted (usually piston engines that have an open oil pan, however, when properly flown the aircraft will maintain positive "G" throughout the maneuver eliminating the requirement for an inverted oil system). In fact, few early aircraft had sufficiently precise roll control to have performed this maneuver properly.