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Basics

1.1 Introduction

Aerodynamics is the study of forces and the resulting motion of objects through the air. This word is coined with the two Greek words: aerios, concerning the air, and dynamis, meaning force. Judging from the story of Daedalus and Icarus,1 humans have been interested in aerodynamics and flying for thousands of years, although flying in a heavier-than-air machine has been possible only in the last century. Aerodynamics affects the motion of high-speed flying machines, such as aircraft and rockets, and low-speed machines, such as cars, trains, and so on. Therefore, aerodynamics may be described as a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a solid object. Aerodynamics is a subfield of fluid dynamics and gas dynamics. It is often used synonymously with gas dynamics, with the difference being that gas dynamics applies to all gases.

Understanding the flow field around an object is essential for calculating the forces and moments acting on the object. Typical properties calculated for a flow field include velocity, pressure, density, and temperature as a function of spatial position and time. Aerodynamics allows the definition and solution of equations for the conservation of mass, momentum, and energy in air. The use of aerodynamics through mathematical analysis, empirical approximations, wind tunnel experimentation, and computer simulations forms the scientific basis for heavier-than-air flight and a number of other technologies.

Aerodynamic problems can be classified according to the flow environment. External aerodynamics is the study of flow around solid objects of various shapes. Evaluating the lift and drag on an airplane or the shock waves that form in front of the nose of a rocket are examples of external aerodynamics. Internal aerodynamics is the study of flow through passages in solid objects. For instance, internal aerodynamics encompasses the study of the airflow through a jet engine.

Aerodynamic problems can also be classified according to whether the flow speed is below, near or above the speed of sound. A problem is called subsonic if all the speeds in the problem are less than the speed of sound, transonic if speeds both below and above the speed of sound are present, supersonic if the flow speed is greater than the speed of sound, and hypersonic if the flow speed is more than five times the speed of sound.

The influence of viscosity in the flow dictates a third classification. Some problems may encounter only very small viscous effects on the solution; therefore the viscosity can be considered to be negligible. The approximations made in solving these problems is the viscous effect that can be regarded as negligible. These are called inviscid flows. Flows for which viscosity cannot be neglected are called viscous flows.

1.2 Overview

Humans have been harnessing aerodynamic forces for thousands of years with sailboats and windmills [1]. Images and stories of flight have appeared throughout recorded history [2], such as the legendary story of Icarus and Daedalus [3]. Although observations of some aerodynamic effects such as wind resistance (for example, drag) were recorded by Aristotle, Leonardo da Vinci, and Galileo Galilei, very little effort was made to develop a rigorous quantitative theory of airflow prior to the seventeenth century.

In 1505, Leonardo da Vinci wrote the Codex (an ancient manuscript text in book form) on the Flight of Birds, one of the earliest treatises on aerodynamics. He was the first to note that the centre of gravity of a flying bird does not coincide with its centre of pressure, and he describes the construction of an ornithopter with flapping wings similar to birds.

Sir Isaac Newton was the first to develop a theory of air resistance [4], making him one of the first aerodynamicists. As a part of that theory, Newton considered that drag was due to the dimensions of the body, the density of the fluid, and the velocity raised to the second power. These all turned out to be correct for low-speed flow. Newton also developed a law for the drag force on a flat plate inclined towards the direction of the fluid flow. Using for the drag force, for the density, for the area of the flat plate, for the flow velocity, and for the inclination angle, his law was expressed as

This equation is incorrect for the calculation of drag in most cases. Drag on a flat plate is closer to being linear with the angle of inclination as opposed to acting quadratically at low angles. The Newton formula can lead one to believe that flight is more difficult than it actually is, due to this overprediction of drag, and thus required thrust, which might have contributed to a delay in human flight. However, it is more correct for a very slender plate when the angle becomes large and flow separation occurs or if the flow speed is supersonic [5].

1.3 Modern Era

In 1738, the Dutch-Swiss mathematician Daniel Bernoulli published Hydrodynamica. In this book Bernoulli described the fundamental relationship among pressure, density, and velocity, in particular Bernoulli's principle, which is one method to calculate aerodynamic lift [6]. More general equations of fluid flow - the Euler equations - were published by Leonhard Euler in 1757. The Euler equations were extended to incorporate the effects of viscosity in the first half of the eighteenth century, resulting in the Navier-Stokes equations.

Sir George Cayley is credited as the first person to identify the four aerodynamic forces of flight - weight, lift, drag, and thrust - and the relationships between them [7,8]. Cayley believed that the drag on a flying machine must be counteracted to enable level flight to occur. He also looked into the nature of aerodynamic shapes with low drag. Among the shapes he investigated were the cross sections of trout. This may appear counterintuitive; however, the bodies of fish are shaped to produce very low resistance as they travel through water. Their cross sections are sometimes very close to that of modern low-drag aerofoils.

Air resistance experiments were carried out by investigators throughout the eighteenth and nineteenth centuries. Drag theories were developed by Jean le Rond d'Alembert [9], Gustav Kirchhoff [10], and Lord Rayleigh [11]. Equations for fluid flow with friction were developed by Claude-Louis Navier [12] and George Gabriel Stokes [13]. To simulate fluid flow, many experiments involved immersing objects in streams of water or simply dropping them off the top of a tall building. Towards the end of this time period, Gustave Eiffel used his Eiffel Tower to assist in the drop testing of flat plates.

A more precise way to measure resistance is to place an object within an artificial, uniform stream of air where the velocity is known. The first person to experiment in this fashion was Francis Herbert Wenham, who in doing so constructed the first wind tunnel in 1871. Wenham was also a member of the first professional organisation dedicated to aeronautics, the Royal Aeronautical Society of the United Kingdom. Objects placed in wind tunnel as models are almost always smaller than in practice, so a method was needed to relate small-scale models to their real-life counterparts. This was achieved with the invention of the dimensionless Reynolds number by Osborne Reynolds [14]. In 1883, Reynolds also experimentally studied laminar to turbulent flow transition.

By the late nineteenth century, two problems were identified before heavier-than-air flight could be realised. The first was the creation of low-drag, high-lift aerodynamic wings. The second problem was how to determine the power needed for sustained flight. During this time, the groundwork was laid down for modern-day fluid dynamics and aerodynamics, with other less scientifically inclined enthusiasts testing various flying machines with little success.

In 1889, Charles Renard, a French aeronautical engineer, became the first person to reasonably predict the power needed for sustained flight [15]. Renard and German physicist Hermann von Helmholtz explored the wing loading (weight-to-wing-area ratio) of birds, eventually concluding that humans could not fly under their own power by attaching wings onto their arms. Otto Lilienthal, following the work of Sir George Cayley, was the first person to become highly successful with glider flights. Lilienthal believed that thin, curved aerofoils would produce high lift and low drag.

Octave Chanute provided a great service to those interested in aerodynamics and flying machines by publishing a book outlining all of the research conducted around the world up to 1997 [16].

1.3.1 Actual Flights

With the information contained in Chanute's book, the personal assistance of Chanute himself, and research carried out in their own wind tunnel, the Wright brothers gained enough knowledge of aerodynamics to fly the first powered aircraft on 17 December 1903. The Wright brothers' flight confirmed or disproved a number of aerodynamic theories. Newton's drag force theory was finally proved incorrect. This first widely publicised flight led to a more organised effort between aviators and scientists, leading the way to modern aerodynamics.

During the...