# Category Fundamentals of Modern Unsteady Aerodynamics

## Center of Pressure (xcp)

The location at which the resultant aerodynamic moment is zero. If we consider the profile (the wing section) as a free body, this point can be assumed as the center of gravity for the pressure distribution along the surface of the profile.

1.1.3 Aerodynamic Center (xac)

This is the point where the aerodynamic moment acting on the wing is independent of the angle of attack. The aerodynamic center is essential for the stability pur­poses. For a finite wing it is the line connecting the aerodynamic centers of each section along the span.

If the flow field around a flying body does not change with respect to time, the aerodynamic forces and moments acting on the body remain the same all the time. This type of aerodynamics is called steady aerodynamics.

## Definitions

1.1.1 Aerodynamics

It is the branch of science which studies the forces and moments necessary to have a controlled and sustainable flight in air. These forces are named the lift in the direction normal to the flight and the drag or the propulsive force in the direction of the flight. In addition, it studies the effect of the velocity fields induced by the motion during flight. On the other hand, the study of the forces created by the motion of an arbitrarily shaped body in any fluid is the concern of the Fluid Mechanics in general. It is necessary to make this distinction at this stage.

1.1.2 Aerodynamic Coefficients

These are the non-dimensional values of pressure, force and moment which affect the flying object. In non-dimensionalization, the free stream density p and the free stream velocity U are used as characteristic values. One half of the dynamic pressure, VipU2 is utilized in obtaining pressure coefficient, cp. As the character­istic length, half of the chord length and as the characteristic area the wing surface area are considered. Hence, the product of dynamic pressure with the half chord is used to obtain the sectional lift coefficient q, the drag coefficient cd, and the moment coefficient cm, wherein the square of the half chord is used. For the finite wing, however, the coefficient of lift reads as CL, the drag CD and the moment coefficient CM.

## Flights in Earth’s

Flights in Earth’s atmosphere existed long before the presence of mankind. 300 million years ago it was performed by insects with wings, 60 million years ago by birds and 50 million years ago by bats as flying mammals (Hitching 1982). Man, on the other hand, being the most recently emerged species among the living things first realized the concept of flight by depicting the flying animals in his creative works related to mythology or real life (Gibbs-Smith 1954). Needles to say, as a discipline, the science of Aerodynamics provides the most systematic and fundamental approach to the concept of flight.

The Aerodynamics discipline which determines the basic conditions of flying made great progress during the past hundred years, which is slightly longer than the average life span of a modern man (Anderson 2001). The reason of this progress is mainly the existence of wide range of aerospace applications in mili­tary and civilian industries. In the civilian aerospace industries, the demand for development of fast, quiet and more economical passenger planes with long ran­ges, and in the military the need for fast and agile fighter planes made this progress possible. The space race, on the other hand, had an accelerating effect on the progress during the last 50 years.

Naturally, the faster the planes get the more complicated the related aerody­namics become. As a result of this fast cruising, the lifting surfaces like wings and the tail planes start to oscillate with higher frequencies to cause in turn a phase lag between the motion and the aerodynamic response. In order to predict this phase lag, the concept of unsteady aerodynamics and its underlying principles were introduced. In addition, at higher speeds the compressibility of the air plays an important role, which in turn caused the emergence of a new branch of aerody­namics called compressible aerodynamics. At cruising speeds higher than the speed of sound, completely different aerodynamic behavior of lifting surfaces is observed. All these aerodynamical phenomena were first analyzed with mathe­matical models, and then observed experimentally in wind tunnels before they were tested on prototypes undergoing real flight conditions. Nature, needless to say, inspired many aerodynamicists as well. In recent years, the leading edge

U. Gulfat, Fundamentals of Modern Unsteady Aerodynamics, 1

DOI: 10.1007/978-3-642-14761-6_1, © Springer-Verlag Berlin Heidelberg 2010

vortex formation which gives extra lift for highly swept wings at high angles of attack has been studied extensively. During the last decade, the man made flight has no longer been based on a fixed wing. The flapping wing aerodynamics which utilizes the unsteady aerodynamic concepts is used in designing and building micro air vehicles to serve mankind in various fields.

First, let us introduce various pertinent definitions in order to establish a firm convention in studying the topics of unsteady aerodynamics in general.

## Fundamentals of Modern Unsteady Aerodynamics

The flying animate objects were present in earth’s atmosphere about hundreds of million years before the existance of human kind on earth. Only at the beginning of twentieth century, the proper analysis of the lifting force was made to provide the possibility of powered and manned flight. Prior to that, one of the pioneers of mechanics, Sir Isaac Newton had used ‘his impact theory’ in an attempt to for­mulate the lifting force created on a body immersed in a free stream. In late seventeenth century, his theory was a failure due to calculation of insufficient lift generation and made him come to the conclusion that ‘flying is a property of heavenly bodies’. In a similar manner, almost after two centuries, William Thomson (Lord Kelvin) whose contributions to thermo and gas dynamics are well known, then proved that ‘only objects lighter than air’ can fly!

Perhaps it was the adverse influence of these two pioneers of mechanics on Western Europe, where contributions to the discipline of hydrodynamics is unquestionable, that delayed the true analysis of the lift generation. The proper analysis of lifting force, on the other hand, was independently made at the onset of twentieth century by the theoretical aerodynamicists Martin Kutta and Nicolai Joukowski of Central and Eastern Europe respectively. At about the same years, the Wright brothers, whose efforts on powered flight were ridiculed by authorities of their time, were able to fly a short distance. Thereafter, in a time interval little more than a century, which is a considerably short span compared to the dawn of civilization, we see not only tens of thousands of aircrafts flying in earth’s atmosphere at a given moment but we also witnessed unmanned or manned missions to the moon, missions to almost every planet in our solar system and to deeper space to let the existence of life on earth be known by the other possible intelligent life forms.