Aerodynamics (like hydrodynamics) is a branch of fluid dynamics, which is the study of fluids in motion. The fundamental laws governing the movements of gases, such as air, and liquids, such as water, are identical. The equations representing these natural laws are, however, so complex that, although formulated more than 100 years ago, they cannot be easily solved to account for all systems and conditions.
Even today, it takes the most powerful computers to solve the complex equations that govern the flow of fluids around irregularly shaped objects. It is a sobering thought to realize that we may be able to design craft that can enter space and glide back to Earth, but the detailed description of the way a river erodes its banks and changes course still relies a great deal on experiment rather than calculation.
Aerodynamics is of crucial importance in the design of jet engines, the turbines that drive electricity generators, and even the family automobile. Reducing aerodynamic drag on anything that moves through the atmosphere, be it a car, an airplane, or a train, means greater efficiency and less fuel consumption. The study of aerodynamics in the modern world has received a huge boost from the need to conserve energy.
Air is by no means as insubstantial as it might at first appear. At sea level on a mild day, the density of air is about 0.077 lbs. per cu. ft. (1.23 kg/m2). A large sedan car of about 20 sq. ft. (1.9 m2) cross section moving at 30 mph (50 km/h) must displace about 71 lbs. (32 kg) of air every second. Good aerodynamic design helps the air flow over and around a car in a smooth controlled sweep, minimizing the distance each molecule of air must be moved and thus minimizing drag forces.
The equations that describe in a general fashion the motion of fluids were first developed by C. L. M. H. Navier in 1820 and subsequently perfected by the Irish physicist George Stokes in 1845. These equations, now called the Navier–Stokes equations, relate velocity, density, pressure, compressibility, viscosity, and spatial dimensions of fluid. Because of the number of variables involved, the subject of fluid dynamics has been broken down into a number of subdivisions where certain conditions predominate and others can be ignored. The result is a whole series of solutions—each applying in a limited range of circumstances. Historically, hydrodynamics came first and includes the greater number of assumptions. Water is, however, almost incompressible, that is, the density of water does not change with the pressure applied to it. This property of water and other liquids simplifies the original Navier–Stokes equations.
Aerodynamic principles
At the beginning of the present century, aerodynamics, with the possibility of flight in air, began to attract more attention than hydrodynamics. Because of the concentration of effort, aerodynamics, based on the same assumptions as hydrodynamics, soon outstripped its parent. The German physicist Ludwig Prandtl showed that the effect of viscosity for flow around streamlined (smooth) bodies was confined to a thin layer immediately adjacent to the body. This region is called the boundary layer. Outside the boundary layer, viscous forces are negligible, and consequently, potential flow theories apply. The analysis of streamlined bodies enabled airfoil design to advance rapidly.
Whereas smooth, streamlined bodies have an unbroken and stable boundary layer, bluff (unstreamlined) bodies do not. The flow starts to separate because of misbehavior of the boundary layer, and potential flow solutions, even away from the body, become inaccurate. Even today, no complete theory for low-speed flow around bluff bodies exists, but an understanding of what happens physically has been built up over the years. As aircraft speeds increased, it was found that the assumption of incompressibility introduced errors. The reason for this phenomenon can be explained by Bernoulli’s equation.
Bernoulli’s equation (derived by the Swiss physicist Daniel Bernoulli, who did much early work in hydrodynamics) is a statement of energy conservation in a fluid. A fluid, like any moving body, has kinetic energy through its motion and potential energy because of its potential to move under the influence of Earth’s gravitation. At all points in a fluid, there is a static pressure proportional to the height of fluid above that point—this pressure is a measure of the potential energy of the fluid at that point. The kinetic energy of the fluid is proportional to the square of the velocity and gives rise to a dynamic pressure. If no energy is added to or taken away from the fluid stream, total energy will be conserved even if there is an interchange between kinetic energy (dynamic pressure) and potential energy (static pressure)—this is the principle behind Bernoulli’s equation.
Because dynamic pressure is proportional to the square of the fluid velocity, the rate at which pressure changes with increasing velocity will depend on the absolute velocity as well as its rate of change. Consequently, the higher the speeds involved, the larger will be the pressure changes and the greater the density changes because of compressibility. Below 126 mph (210 km/h), the density changes can be ignored and air can be treated as incompressible, but above this airspeed, the assumption becomes increasingly inaccurate.
