Phugoids are often demonstrated to student pilots as an example of the speed stability of the aircraft and the importance of proper trimming. When it occurs, it is considered a nuisance, and in lighter aeroplanes (typically showing a shorter period) it can be a cause of pilot-induced oscillation.
The phugoid, for moderate amplitude, occurs at an effectively constant angle of attack, although in practice AoA actually varies by a few tenths of a degree. This means that the stalling AoA is never exceeded, and it is possible (in the <1g section of the cycle) to fly at speeds below the known stalling speed. Free flight models with badly unstable phugoid typically stall or loop, depending on thrust.
An unstable or divergent phugoid is caused, mainly, by a large difference between the incidence angles of the wing and tail. A stable, decreasing phugoid can be attained by building a smaller stabilizer on a longer tail, or, at the expense of pitch and yaw "static" stability, by shifting the center of gravity to the rear.
The name apparently is an example of poor Greek translation by Lanchester, a British aerodynamicist who first predicted it. The English word was mistakenly derived from the Greek word for "fleeing, flight" (phuge) instead of the Greek word for "flying, flight".
United Airlines Flight 232 suffered an engine failure which caused total hydraulic system failure. The crew flew the aircraft with throttle only. Suppressing the phugoid tendency was particularly difficult. The pilots were able to reach Sioux City Gateway Airport but crashed during the landing attempt. The pilots and a majority of the passengers survived.
Another aircraft that lost all hydraulics was a DHL operated Airbus A300B4 that was hit by an surface-to-air missile fired by Iraqi insurgents in the 2003 Baghdad DHL attempted shootdown incident. This was the first time that a crew was able to land an air transport aircraft safely only adjusting engine thrust.
The crash of the Helios solar powered aircraft was precipitated by reacting to an inappropriately diagnosed phugoid oscillation the results of which ultimately resulted in the aircraft structure exceeding design loads.