GM Article: The Physics of Flight

THE PHYSICS OF FLIGHT

BGen (Ret’d) Gregory C.P. Matte, CD, PhD

VFC General Manager

Admittedly, this article is nearly two years overdue, and was inspired by a brief yet enlightening discussion with Dr. Geoff Steeves as it pertained to providing his undergraduate students with a guest lecture on practical applications of the laws of physics. As fellow aviators, Geoff was intrigued with my brief yet visceral explanation of the application of energy management in “dog fighting”, as it pertained to aerial fighter tactics. As for myself, I was interested in the performance metrics of the Cessna 172S. My military experience infused an interest in exploring the outer performance limits of the CF-5 Freedom Fighter, and more specifically, the CF-18 Hornet, so as to establish my own baseline of the ultimate limits of performance. This knowledge and experience served to provide me with the confidence to take the CF-18 to its established limits (and beyond), while enjoying the ability to fully exploit the entire spectrum of the Hornet’s performance envelope in mock dogfighting training sessions.

Underlying this discussion with Geoff was a narrative that I would loosely describe as the “physics of flight”. As a starting point, lets agree that everyone who takes flying lessons becomes acquatinted with and learns to trust Bernoulli’s equation and the theory of lift. This theory is witnessed every time we take-off from terra firma as a result of the lift created by the low-pressure environment on the top surface an asymmetrically designed wing such as we find on the Cessna. However, the theory of lift and the physics of flight can quickly expand beyond the basics, as I came to appreciate when I progressed from flying the CT-134A Beechcraft Musketeer, through to the CT-114 Tutor and onto the CF-5 Freedom Fighter. The CF-5 was the “lead-in” conversion trainer that was required before advancing onto the CF-18 Hornet.

My introduction to basic fighter maneuvers (aka “dog fighting”) was preceded by an academic introduction to energy management theory as well as the dynamics of 3-dimensional maneuvering that were part of the basic fighter pilot training curriculum. The primary objective of dogfighting is to maneuver one’s aircraft into a weapons engagement zone (WEZ) against the opponent in which either a missile can be successfully fired, or the gun can be applied. However, unless the opponent is caught completely off guard, one must balance the efforts to maneuver into a WEZ with that of avoiding becoming the target due to an error in maneuvering tactics or an excessive loss of airspeed. Airspeed dictates maneuvering performance, with the sweet spot commonly referred to as “corner speed”. It is also why fighter pilots often state that “speed is life” when it comes to dogfighting. Corner speed equates to the lowest airspeed in which the maximum permissible G-forces can be applied. In the CF-18, corner speed was situated between 310 to 325 KIAS depending on the weight and configuration (external stores) of the aircraft. A primary factor in dogfighting is gaining “angles” on the opponent, particularly when the duel starts with a neutral advantage (e.g., the aircraft meet head on). As such, when one considers the(simplified) formula relating to turn radius, namely r=v2/g2,the importance of corner speed becomes apparent. If your airspeed is well in excess of corner speed, say 500 KIAS, then the turn radius will be approximately 12,350 feet despite being able to pull 7.5 G, whereas at a speed of 315 KIAS and 7.5 G, the turn radius would be considerably tighter at approximately 4,900 feet. Conversely, as airspeed decreases below corner speed, the amount of G that can be pulled decreases as well. Thus, at an airspeed of say 200 KIAS, the CF-18 can only pull about 2.5 G, thereby leading to a turn radius of approximately 17,800, so getting slow in a dogfight can quickly become a fatal disadvantage, further reinforcing the adage that “speed is life”!

While the solution to quickly regaining airspeed is to push the aircraft over into a zero-G environment (thereby minimizing lift-induced drag), doing so results in sacrificing angles while giving the opponent an opportunity to close into their own weapon solution on you. Consequently, corner speed is the ideal airspeed for dogfighting and to score an aerial victory. However, the ability to maintain corner speed is where energy management theory factors in. Although aerodynamic performance is affected by density altitude (e.g., temperature and humidity), the dominant factor is altitude, with the best performance being achieved at sea level. As such, at higher altitudes, one must exchange altitude to maintain airspeed while pulling G; essentially converting potential energy into kinetic energy. The other benefit of a turning descent is that the aircraft benefits from the earth’s gravitational pull in addition to the G-forces that the aircraft can generate. It is for this reason that even if the same G is pulled doing a loop, the resulting loop is never symmetric but egg-shaped over the top.

However, when dogfighting an aircraft of a different design, then other factors come into play such as wing loading, thrust, G-limits, weight, and parasite drag (external stores), which all factor into the equation as well as weapon system capabilities. As such, different aircraft types perform differently, and understanding the strengths and weaknesses of an opponent is crucial to gaining the upper hand. The unification of these competing factors into dog fighting tactics was first achieved by Colonel John Boyd with the assistance of Thomas Christie, a mathematician with the United States Air Force, and became known as energy management theory. By studying aircraft designs and power plants on different aircraft, they were able to create energymanagement (E-M) diagrams that showed performance limits at different altitudes above sea level in 5000-foot increments. By overlaying a transparency of your own fighter aircraft with that of an opponent’s, at any given altitude, one could immediately determine areas of advantage and disadvantage in performance.

This knowledge could then be combined with 3-dimensional maneuvering to achieve the most effective performance and the quickest achievement of a WEZ solution. In some cases, this meant consciously bringing the opponent below corner speed to gain the advantage. For instance, the F-16 has a similar corner speed with the CF-18, yet it can pull up to 9 G, while the CF-18 is limited to 7.5 G. However, given the leading edge extension on the CF-18 (that gives a cobra appearance) and the superior vertical stabilator authority of its twin tail, the CF-18 had an advantage over the F-16 in a slower speed regime wherein 3-dimensional maneuvering could be augmented by un-loaded (zero-g rolls) to further intimidate F-16 pilots thereby causing them to lose airspeed and/or altitude to avoid falling into the CF-18’s WEZ. This form of dogfighting was affectionately known as a “knife fight in a phone booth”.

Given that Boyd was a pioneer in developing E-M theory and a fighter weapons instructor, he was able to combine his knowledge and skills with consistently winning results and earned the call sign “Forty Second Boyd” given his ability to achieve a weapons solution against his colleagues in about 40 seconds despite starting the dual from a neutral position. Although E-M theory originated in the world of fighter aviation, understanding the underlying principles is useful in civil aviation, such as for aerobatics, but also simply to better understand aircraft performance in a variety of flight regimes.