A phugoid or fugoid // is an aircraft motion where the vehicle pitches up and climbs, and then pitches down and descends, accompanied by speeding up and slowing down as it goes "uphill" and "downhill." This is one of the basic flight dynamics modes of an aircraft (others include short period, dutch roll, and spiral divergence), and a classic example of a negative feedback system.
The phugoid has a nearly constant angle of attack but varying pitch, caused by a repeated exchange of airspeed and altitude. It can be excited by an elevator singlet (a short, sharp deflection followed by a return to the centered position) resulting in a pitch increase with no change in trim from the cruise condition. As speed decays, the nose will drop below the horizon. Speed will increase, and the nose will climb above the horizon. Periods can vary from under 30 seconds for light aircraft to minutes for larger aircraft. Microlight aircraft typically show a phugoid period of 15–25 seconds, and it has been suggested that birds and model airplanes show convergence between the phugoid and short period modes. A classical model for the phugoid period can be simplified to about (0.85 × speed in knots) seconds, but this only really works for larger aircraft.
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 airplanes (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 the angle of attack actually varies by a few tenths of a degree. This means that the stalling angle of attack 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 term "phugoid" was coined by Frederick W. Lanchester, the British aerodynamicist who first characterized the phenomenon. He derived the word from the Greek words φυγή and εἶδος to mean "flight-like" but recognized the diminished appropriateness of the derivation given that φυγή meant flight in the sense of "escape" rather than vehicle flight.
In the 1975 Tan Son Nhut C-5 accident, USAF C-5 68-0218 with flight controls damaged by failure of the rear cargo/pressure door, encountered phugoid oscillations while the crew was attempting a return to base, and crash-landed in a rice paddy adjacent to the airport. Of the 328 people on board, 153 died, making it the deadliest accident involving a US military aircraft.
In 1985, Japan Airlines Flight 123 lost all hydraulic controls and its vertical stabiliser, and went into a phugoid before crashing into a mountain. With 520 deaths it remains the deadliest single-aircraft disaster in history.
In 1989, 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 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 a surface-to-air missile fired by the Iraqi resistance 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 by only adjusting engine thrust.
The 2003 crash of the Helios solar powered aircraft was precipitated by reacting to an inappropriately diagnosed phugoid oscillation which ultimately resulted in the aircraft structure exceeding design loads.
Captain Chelsey (Sully) Sullenberger of US Airways Flight 1549 that water landed in the Hudson said in a Google talk that the automatic protection from phugoid mode implemented in the Airbus A320 prevented him from manually getting all possible lift from the wings at four seconds before water impact, causing the crash to be more violent. 
- Charles Hampson Grant, Model Airplane Design and Theory of Flight, Jay, New York, 1941
- Keith Laumer, How to Design and Build Flying Models, Harper, New York, 1960
- Frederick William Lanchester, Aerodonetics: constituting the second volume of a complete work on aerial flight, D. Van Nostrand Company, New York, 1909
- ASN Aircraft accident description McDonnell Douglas DC-10-10 N1819U - Sioux Gateway Airport, IA (SUX)
- 'Investigation of the Helios Prototype Aircraft Mishap Volume I Mishap Report', Thomas E. Noll, NASA Langley Research Center, 2004, http://www.nasa.gov/pdf/64317main_helios.pdf
- Sully Sullenberger: "Making a Difference" Talks at Google, 2012, (40:23) https://www.youtube.com/watch?v=cKuw49KBywA