# Energy Maneuverability Theory Explained

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The energy maneuverability theory provides a model that describes the performance of an aircraft. It was originally developed by Thomas Christie, who was a mathematician, and Colonel John Boyd, who was a fighter pilot. The duo completed their theory in 1964 with the publication of a two-volume report of their studies. An update was completed in 1966.

When the energy maneuverability theory was first introduced, it was given a confidential security status. A scan of the updated 1966 document which discusses this theory is available through archives.gov.

This theory is one of the first to be developed by using high-speed computer processes. Christie and Boyd used the computer at Eglin Air Force Base to compare the performance envelopes of U.S.-based and Soviet-based aircraft that were flown during the conflicts in Korea and Vietnam.

The theory is useful in its description of an aircraft’s performance by providing a total of kinetic and potential energies. It can also describe aircraft specific energy.

By analyzing the mathematics of the energy maneuverability theory, it becomes possible to predict the combat capabilities of an aircraft. It can also allow designers and engineers to compare possible designs when creating a new aircraft as it can predict different trade-offs that may occur.

The aspects of airplane performance within the energy maneuverability theory can be described in one basic formula: Ps – V (T-D/W).

In this equation, V represents velocity; T represents thrust; D represents drag; and W represents weight. That allows the specific excess energy to be proportional to the ratio of net motive forces when they are compared to the weight of the aircraft and its proportion to velocity.

### What Is the Thrust-to-Weight Ratio?

The thrust-to-weight ratio is used for any craft that is capable of flight. That allows the performance of the engine or the vehicle, such as a rocket or a jet engine, to be analyzed. This provides information regarding the overall maneuverability of the aircraft in question.

Various controls are available to pilots that allow them to manage throttle settings, altitude, airspeed, and even the air temperature within the cabin or cockpit. The weight of the aircraft will change as fuel is burned and this must also be taken into account. For that reason, the thrust-to-weight ratio is usually determined by the maximum level of static thrust at sea level, which is then divided by the maximum takeoff weight.

In the energy maneuverability theory, the principle is still the same as the thrust-to-weight ratio, but with a slight twist. Drag is subtracted from thrust and this normalizes the motive forces to the aircraft’s weight. That normalization process creates an efficiency equation that analyzes aircraft performance.

The normalization is required because the traditional thrust-to-weight ratio calculation does not describe the performance of an aircraft accurately while it is flying under normal operating conditions. By incorporating drag into the equation, the aerodynamic design of the aircraft can then be summarized.

Think of it like this: the engine of an aircraft might be able to provide an enormous amount of thrust. Its shape might create some extra drag. The weight of the engine, however, might be so great that it is virtually impossible for the aircraft to achieve enough speed for taking off. By using the (T-D)/W ratio, a unity efficiency value can be created, which is expressed as a “1.”

A perfectly efficient aircraft would receive a “1” rating if the engine can keep the plane at a constant speed while gaining altitude at a 90-degree angle. Most aircraft that come close to this perfect efficiency rating are fighter jets, such as the F-series from the U.S. military. The energy maneuverability theory, in fact, helped to bring about the improvements in the design of the F-15 and F-16 aircraft.

### How Did the Energy Maneuverability Theory Change Aircraft Dynamics?

Colonel Boyd was likely the only person on the planet who could have contributed knowledge of aircraft performance for the energy maneuverability theory. His skills in the cockpit were legendary. During his pilot training responsibilities, he offered to pay any pilot \$40 if they could defeat him within 40 seconds, even with Boyd at a disadvantaged position.

He never had to pay the bounty.

What Boyd was able to accomplish with this theory was to encourage the U.S. government to build lighter aircraft that would have added maneuverability. Even the F-18 Hornet is based off information that came from Boyd’s implementation of the theory.

Modern military aircraft benefit the most from this theory, but all aircraft can benefit from its principles. That allows us, in turn, to create safer aircraft that perform as efficiently as possible.