Energy–maneuverability theory

Energy–maneuverability theory is a model of aircraft performance. It was developed by Col. John Boyd, a fighter pilot, and Thomas P. Christie, a mathematician with the Air Force,[1] and is useful in describing an aircraft's performance as the total of kinetic and potential energies or aircraft specific energy. It relates the thrust, weight, aerodynamic drag, wing area, and other flight characteristics of an aircraft into a quantitative model. This allows combat capabilities of various aircraft or prospective design trade-offs to be predicted and compared.

All of these aspects of airplane performance are compressed into a single value by the following formula:

${\displaystyle {\begin{array}{rcl}P_{S}&=&V\left({\frac {T-D}{W}}\right)\\\\V&=&{\text{Speed}}\\T&=&{\text{Thrust}}\\D&=&{\text{Drag}}\\W&=&{\text{Weight}}\end{array}}}$

In words, the specific excess energy is proportional to the ratio of net motive forces compared to the weight of the plane and proportional to speed. (Note that dimensionally, ${\displaystyle P_{S}}$ has units of "speed," not "specific energy" (energy per unit mass).)

The net motive force is found by calculating the engine's ability to move the plane after accounting for friction and other aerodynamic issues that slow down the plane. The ratio (T-D)/W is similar to T/W, the Thrust-to-weight ratio, which is also used as a figure of merit for airplanes and rockets. By normalizing the motive forces to the weight of the plane, it is clear how efficient the plane is. A very large engine may be able to generate a huge thrust but could be so heavy that it would not even lift itself. The ratio is unity (T-D)/W = 1 when the engine is powerful enough to keep the plane at constant speed in a 90 degree ascending trajectory. Fighter jets, such as the F-16 have a T/W ratio close to 1, depending on fuel weight and armament.

The difference between T/W and (T-D)/W is that T/W does not include the effects of friction and other aerodynamic losses. When a plane is moving very slowly, these losses are small and can be ignored. However, T/W does not accurately describe the performance of the plane at its normal operating conditions. By including drag in the formula, the aerodynamics of the plane are also summarized in the ${\displaystyle P_{S}}$ value.

The specific excess energy model is proportional to the speed of the plane. This means that the faster the plane is capable of flying, the better its score. The other parts of this model (thrust, drag, and weight) may say that a plane is excellent but a good fighter must also go fast.

Boyd, a U.S. jet fighter pilot in the Korean War, began developing the theory in the early 1960s. He teamed with mathematician Thomas Christie at Eglin Air Force Base to use the base's high-speed computer to compare the performance envelopes of U.S. and Soviet aircraft from the Korean and Vietnam Wars. They completed a two-volume report on their studies in 1964. Energy Maneuverability came to be accepted within the U.S. Air Force and brought about improvements in the requirements for the F-15 Eagle and later the F-16 Fighting Falcon fighters.[2]

Notes

1. Neufeld, Jacob; Watson, George M. (Jr.); Chenoweth, David, eds. (1997), Technology and the Air Force: A Retrospective Assessment (PDF), Air Force History and Museums Program, United States Air Force, p. 204
2. Jenkins, Dennis R. McDonnell Douglas F-15 Eagle, Supreme Heavy-Weight Fighter, p. 7. Aerofax, 1998.

See also

• Lagrangian mechanics

References

• Hammond, Grant T. The Mind of War: John Boyd and American Security. Washington, D.C.: Smithsonian Institution Press, 2001. ISBN 1-56098-941-6 and ISBN 1-58834-178-X.
• Coram, Robert. Boyd: The Fighter Pilot Who Changed the Art of War. New York: Back Bay Books, 2002. ISBN 0-316-88146-5 and ISBN 0-316-79688-3.
• Wendl, M.J., G.G. Grose, J.L. Porter, and V.R. Pruitt. Flight/Propulsion Control Integration Aspects of Energy Management. Society of Automotive Engineers, 1974, p. 740480.