At Nellis Air Force Base in the late 1950s, an instructor kept a standing bet with anyone who wanted it. Take up a position on his tail, the classic winning position in air combat. He would be reversed and behind you inside forty seconds, or he would pay you forty dollars.

The accounts differ on how quickly he usually managed it. What nobody disputes is that he did not appear to lose, and that the money stayed in his pocket.

John Boyd was not an ace. He flew 22 combat missions in Korea, always as a wingman, and never fired his guns in anger. His contribution to air combat was not a kill tally. It was a piece of arithmetic that made it possible, for the first time, to say which of two aircraft would win a fight and why.

The problem nobody could put a number on

Before Boyd, comparing two fighters meant comparing specifications. Top speed, service ceiling, rate of climb, turn radius. Each number described the aircraft doing one thing perfectly, in isolation, and none of them described a fight.

Pilots knew the specification sheet lied. An aircraft that turned tightly might bleed so much speed doing it that the turn was suicide. An aircraft that climbed well at sea level might be helpless at altitude. Everyone understood this in their hands. Nobody could write it down.

Boyd’s insight came, of all places, from a thermodynamics course at Georgia Tech: treat the aeroplane as a system trading energy. Altitude is stored energy. Speed is stored energy. You can exchange one for the other, and manoeuvring spends the total.

One equation

The result is specific excess power, written Ps and pronounced P-sub-s.

Ps = V(T − D)/W, where V is true airspeed, T is thrust available, D is drag and W is weight. Thrust minus drag is the force you have spare. Multiply by speed and divide by weight and you get, in units of velocity, the rate at which the aircraft can add energy to itself.

Positive Ps means you are gaining energy and can climb or accelerate. Negative means you are spending it. The contour where Ps equals zero is the most important line on the chart: it is the boundary of sustained manoeuvre, the hardest you can turn indefinitely without slowing down or descending.

Pull harder than that boundary and you get a better instantaneous turn at the cost of energy you will need in about four seconds. That trade, instantaneous against sustained, is the whole of air combat manoeuvring reduced to a readable graph.

The diagrams themselves are explained above, in the terms a fighter pilot would use.

The trick that made it useful

Calculating Ps for one aircraft is an engineering exercise. Boyd’s actual contribution was to plot two aircraft on the same axes.

Overlay the charts and the answer stops being a matter of opinion. Wherever your contour sits outside the other aircraft’s, you have an advantage and should fight there. Wherever it sits inside, you are losing and should leave. Air combat tactics became, in principle, a map-reading problem.

The March 1966 report is online and declassified, and its language is more measured than the legend suggests. On the F-4C against the MiG-21 it states that at a glance the diagrams indicate the MiG-21 has an enormous instantaneous manoeuvrability advantage, and that the MiG-21 can out-turn the F-4C. Then it adds the other half: the F-4C has the ability to gain energy more rapidly than the MiG-21 throughout most of the envelope.

That is not a verdict. It is a set of instructions. Do not turn with it; use your energy advantage, fight in the vertical, and force the engagement into the region where the numbers favour you. Which is what American aircrew were eventually trained to do.

Two footnotes worth having, because they are usually left out. The report names two co-authors alongside Boyd, Thomas Christie and Lieutenant James Gibson. And it credits its own method to someone else, noting that an approximate method for finding a best flight path was discovered by E. Rutowski, who had published the same energy concept at Douglas in 1954 for range calculations.

The stolen computer time

The work was unsanctioned. Boyd had no funding and no tasking, and the calculations needed a mainframe he was not authorised to use, so he took the time anyway with a project number supplied by Christie.

Here the story bifurcates and it is worth being careful. The widely repeated version has Boyd stealing something like a million dollars of computer time. The best-sourced contemporary account, by an analyst who worked alongside him for 23 years, says something rather different: that Boyd intended to take thousands of hours, and that investigators in the end found only four hours of stolen time. Either way the Air Force’s response was the same, which tells you what it thought of the result. Boyd received a scientific achievement award and the Legion of Merit.

The Fighter Mafia, and the limits of the legend

By 1969 Boyd was a lieutenant colonel in the Pentagon, in the company of Pierre Sprey and Colonel Everest Riccioni, who coined the name Fighter Mafia and styled himself its godfather.

Riccioni found $149,000 in 1969 for a lightweight fighter study, split between Northrop and General Dynamics. A request for proposals followed in January 1971 for a 20,000-pound fighter. The 1974 flyoff selected the YF-16, which became the F-16.

Boyd and Sprey were both reportedly disgusted by what the production F-16 became once a proper radar and multirole capability were added. The design-to-cost ceiling of three million dollars per aircraft, so often quoted, was never made contractual.

The legend has grown in the retelling, and parts of it do not survive contact with the record. Boyd’s involvement in the A-10 was minimal; by one well-sourced account he was not very interested in close air support at all. Nor was he universally admired.

The man

Boyd was, by every account including admiring ones, difficult.

He was also, deliberately, poor. Colleagues called him the Ghetto Colonel, and his own explanation of why is the clearest statement of his method that exists.

The choice he put to younger officers, in Spinney’s traceable formulation, was between being somebody and doing something. Boyd chose the second and paid for it in rank and comfort.

Past the aeroplanes

After retiring in 1975 Boyd stopped thinking about fighters and started thinking about conflict itself. The energy work had already taught him that speed of transition mattered more than any single performance figure; what he added was the observation that the same is true of decision-making.

The result was the OODA loop, observe, orient, decide, act, and the enormous briefing called Patterns of Conflict that he first delivered in 1976 and refined for the rest of his life. It was never published as a book. He gave it as a lecture, at length, to anyone who would sit through it.

The Fighter Mafia’s reputation is itself contested, and the video above puts the sceptical case alongside the admiring one.

Boyd died of cancer on 9 March 1997, aged 70, and is buried at Arlington. Within days the Commandant of the Marine Corps wrote a letter about him.

It is a remarkable thing to say about an officer who never commanded in combat and never shot anyone down. It is also, on the evidence, defensible.

Boyd’s real legacy is not the F-16, or the OODA loop, or the arguments he won in the Pentagon. It is that a question pilots had answered by instinct for fifty years became a question you could answer with a graph, and then check.

Sources: Boyd, Christie and Gibson, Energy-Maneuverability (U), APGC-TR-66-4, Eglin AFB, March 1966; Franklin C. Spinney, Genghis John, US Naval Institute Proceedings, July 1997; Grant T. Hammond, The Essential Boyd, 1997; Marshall L. Michel III, The Revolt of the Majors, Auburn University, 2006; John T. Correll, The Reformers, Air Force Magazine, 2008; Michael Hankins, From Balloons to Drones, 2018; US Navy CNATRA P-821.