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 United States Air Force, 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 enables the combat capabilities of various aircraft or prospective design trade-offs to be predicted and compared.

Formula

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

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

This represents an aircraft's specific excess power and is directly proportional to the potential climb rate (or sink rate) of the aircraft or equivalently its net energy generation (or loss).

Note however that this can apply during any kind of maneuver. Not simply a constant speed climb. Often this is expressed in the form of an energy-maneuverability contour plot with speed on the X axis and turn rate on the Y axis. The idea being that if at some point on the diagram an aircraft has greater specific excess power (or less negative specific excess power, or simply can occupy that point on the diagram while the other cannot) it will be gaining an energy advantage in that maneuver relative to what that other plane would do in the same maneuver. Thus, in a symmetrical situation, one plane will run out of energy first, being lower and slower than the other, and become limited to sustained maneuvers, while the other will be in a higher energy state with remaining speed and altitude, able to use a much broader range of its maneuver envelope.

Note however that certain maneuvers actively benefit an aircraft's capabilities from low or negative specific excess power. Particularly bleeding speed using airbrakes, reducing or reversing thrust, or post-stall maneuvers in order to make tighter turns or improve nose authority.

History

John 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.

See also

• Index of aviation articles
• 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.