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The Vortex—A Journey into Beauty and Mystery

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Vorticity is everywhere. We cannot live without it and we cannot fly without it. The vortex as a construct of fluid motion is necessary for the wing to lift. The propulsion system, be it a propeller or a jet engine, also needs a vorticity to provide the force needed to overcome the resistance of motion through air. This chapter is a road map of how we will proceed on a journey of exploration that will take us from abstract ideas to the observation of beauty and the realization of great flight performance.


  • Flight
  • Jet propulsion

Air museums around the world are displays of the manifestations of the many ideas that went into making it possible for a person to take to the air. The earliest desires to do so are recorded in mythology, the human imagination, and envy of what birds can do. Icarus and Leonardo da Vinci dreamed of flying but, alas, their efforts were not successful. Balloons lifted people into the air using the buoyancy of warm air in the eighteenth century. Just going up was not enough. We want to go somewhere! Serious thoughts about flying using air-moving (aerodynamic) forces also date back a couple of centuries with great minds addressing the possibility.

The intent of this writing is to tell the interesting story of the science of flight and, in part, to dispel some misunderstandings about the topic. The reader is assumed to be interested in aviation generally without formal training in the subject. The story centers on two main topics: the generation of lift by a wing and the generation of thrust by a modern jet engine. Both are the result of the successful development of a wing for controlled flight and the internal combustion engine. While many labored to be first to fly, the Wright brothers succeeded as history witnessed. The contributions made by others should not be underestimated. The history of how we got to our time when non-stop flight half-way around the world is possible is told by many others. One such story told by the author may be of interest.Footnote 1

The curious observer of airplanes would surely enjoy having the mysteries of flight explained in simple terms that do not rely on mathematics so the beauty inherent in successfully doing so can be better appreciated. Placards or descriptive scale models in a museum are limited to explain the function of the artifact in view. Words by personnel available may also not be adequate in clarifying the matter. To answer questions like the above and more detailed ones like: Why is this airplane built like this? or What does this feature accomplish? requires a little study and this narrative is meant to shed some light on such questions.

The endeavor of flight is a technical one and there is no way around that fact. There was physics to be exploited to the point where it could be utilized even if detailed understanding was not yet in hand. Structures had to be invented to allow for light-weight “wings” to be built. That necessarily involved understanding the limitations of materials with which to build a wing and a body of something that would fly. Ideas to do this came from observation of nature and a keen pursuit of “let’s try this!” It finally came together with the efforts of the Wright brothers who, above all, realized and addressed the importance of control so that flight was possible and relatively safe.

A lesson learned by all who attempted to fly is that the human body cannot exert sufficient power to fly to the degree that a bird can. A solution required an extension of the understanding ushered in by the Industrial Revolution. The steam engine developed then as a means to produce more power than a horse had to be improved upon. It was too heavy. A flight capable engine had to be a small and light-weight package. That step was realized with the invention of the gasoline, and later, the gas turbine engine.

All the basic challenges to flight were met successfully in the first half of the twentieth century. The necessary engine made flight practical. Materials, structures, controllability, and aerodynamics were mastered to the point where the airplanes we use today to travel to all corners of the world are a reality. Aviation was eagerly embraced by the military as well as individuals who can use aircraft of various kinds for commerce, business, pleasure, or sport. The typical air museum will have on exhibit many such craft to amaze us with the ingenuity that was built into them.

To people who are not versed in the sciences of flight, there are many questions that may want answers or, at least, plausibility of understanding. Two such questions stand out and these are addressed by many attempts at explanation: How, or better why, does a wing generate lift? and How does the jet engine work to provide the thrust?

The ability to design, build, and operate an airplane safely is a firmly rooted in technical understanding of the physics of the motion of our invisible air. The functionality of an airplane is not based on magic. In connection with the generation of lift, we will conclude that the vortex is a central feature of fluid motion and is necessary for a wing to function. Another conclusion is that fluid friction, while it may be detrimental to performance, is also necessary. With friction always present, sufficient power has to be provided to overcome the drag associated with flight. An important aspect of our story is that it is challenging to force fluid to flow “nicely” into a region of higher pressure. This is what we ask air flowing over a wing to do after it has provided a region of low pressure on the upper surface of the wing for lift. That aspect imposes a serious limit to what airplanes can do for it involves drag and even the possibility of stall, i.e., a failure to provide lift.

Not only does friction enable lift, it also plays a role in drag associated with air rubbing along an airplane’s surfaces. It also plays a critical role in determining the pressures we might have thought we designed into a wing. Both friction and pressure forces on an airplane surface are important components of resistance to motion that has to be overcome with an engine. Hence it is important to understand their nature. We extend that exploration to look at the heating of airplane surfaces experienced by flight at very high speeds. Spoiler alert: it is not friction that causes the body of the Concorde or the SR-71 to be hot when landing.

Understanding the geometric aspects of flow is one thing. Turning that to a knowledge of forces experienced by a wing requires the ability to relate velocities to pressure. We consequently delve into the intricacies of the relationship of fluid motion on the pressure that may be experienced by a surface that tries to coerce the air to follow a prescribed path. The Bernoulli principle,Footnote 2 a common way expressing changes in velocity to changes in pressure, has limitations that are “easily” overcome with a better understanding of fluid motion physics.

Use of the word “fluid” here is to alert the reader that we deal primarily with air as a medium because flight takes place in our atmosphere. Water is also a fluid medium. It has the advantage of providing us with many observable situations, a luxury that air provides less readily because it is invisible and transparent. Thus, thinking about water can be very helpful because these two media share a number of similarities in the way they behave.

This discussion will largely be limited to subsonic aerodynamics, the kind we experience stepping in a small sport airplane or a modern airliner. In subsonic flight shock waves will be involved in regions of locally supersonic flow. These waves play a role in placing limits on the performance of wings.

In the second part of this writing, we will extend our understanding of wing performance to gain insight on propulsion and, specifically, how a jet engine works. There are lots of little wings in that engine and they work well to deliver amazing performance in many of the airplanes we fly. Our understanding of lift on the wing is applicable to what happens or can happen in a jet engine.

To be honest and unapologetic, I will use words related to the physical phenomena that have specific and precise meanings. These can be investigated further in the technical literature. To the best of my ability, I will minimize the use of mathematical statements called equations. They can intimidate the lay reader, but for the engineer, they are visually and intellectually powerful ways to express relationships. In order to allow for further investigations by the reader, I will describe simply and accurately the various concepts necessary for the discussion. Hopefully these words will help.

To describe properties of air and other fluids, I will occasionally use symbols. Such use will be limited in the text, but more complete in an appendix. Symbols are very convenient shorthand. The subject of this story covers aspects of two separate disciplines that necessarily merge for our look at flight: aerodynamics and thermodynamics. Each carries its own language and symbols. On several occasions, a specific symbol may be used to describe different quantities to be introduced in the proper place of our story. Examples are: (1) Velocity V and its components in various directions u, v, and w share their symbol use with u also used to describe internal energy and v also used for specific volume, (2) The symbol Cp is applied to a non-dimensional pressure coefficient and the air specific heat at constant pressure, (3) q may be used to denote dynamic pressure or heat transferred per unit mass, and (4) w is used for downward velocity (see (1) above) and work in the thermodynamic sense. These possible sources of confusion should not be a problem for the reader because the context is usually clear. In practice, these quantities are seldom (here, never) used in the same context.

Finally, the need for quantitative description of the physical world, has led to the use of two systems of measurement, the so-called English System and the S-I (metric) system. Historically, the English system has been and still is in use in the United States and in the aviation world even as the world uses a much more practical and much more widely accepted metric system for most other purposes. I, having grown up with the English system, will describe quantities in that fashion and hereby extend sincere apologies to readers whose familiarity with the metric system might force them to think a little longer about the quantities described.


  1. 1.

    See “Powering the World’s Airliners” in the bibliography.

  2. 2.

    After the Swiss mathematician and physicist Daniel Bernoulli (1700–1782).

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Decher, R. (2022). The Vortex—A Journey into Beauty and Mystery. In: The Vortex and The Jet. Springer, Singapore.

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