# Aerodynamic drag

In aerodynamics, aerodynamic drag is the fluid drag force that acts on any moving solid body in the direction of the fluid freestream flow.[1] From the body's perspective (near-field approach), the drag results from forces due to pressure distributions over the body surface, symbolized ${\displaystyle D_{pr}}$, and forces due to skin friction, which is a result of viscosity, denoted ${\displaystyle D_{f}}$. Alternatively, calculated from the flowfield perspective (far-field approach), the drag force results from three natural phenomena: shock waves, vortex sheet, and viscosity.

## Introduction

The pressure distribution acting on a body's surface exerts normal forces on the body. Those forces can be summed and the component of that force that acts downstream represents the drag force, ${\displaystyle D_{pr}}$, due to pressure distribution acting on the body. The nature of these normal forces combines shock wave effects, vortex system generation effects, and wake viscous mechanisms.

The viscosity of the fluid has a major effect on drag. In the absence of viscosity, the pressure forces acting to retard the vehicle are canceled by a pressure force further aft that acts to push the vehicle forward; this is called pressure recovery and the result is that the drag is zero. That is to say, the work the body does on the airflow, is reversible and is recovered as there are no frictional effects to convert the flow energy into heat. Pressure recovery acts even in the case of viscous flow. Viscosity, however results in pressure drag and it is the dominant component of drag in the case of vehicles with regions of separated flow, in which the pressure recovery is fairly ineffective.

The friction drag force, which is a tangential force on the aircraft surface, depends substantially on boundary layer configuration and viscosity. The net friction drag, ${\displaystyle D_{f}}$, is calculated as the downstream projection of the viscous forces evaluated over the body's surface.

The sum of friction drag and pressure (form) drag is called viscous drag. This drag component is due to viscosity. In a thermodynamic perspective, viscous effects represent irreversible phenomena and, therefore, they create entropy. The calculated viscous drag ${\displaystyle D_{v}}$ use entropy changes to accurately predict the drag force.

When the airplane produces lift, another drag component results. Induced drag, symbolized ${\displaystyle D_{i}}$, is due to a modification of the pressure distribution due to the trailing vortex system that accompanies the lift production. An alternative perspective on lift and drag is gained from considering the change of momentum of the airflow. The wing intercepts the airflow and forces the flow to move downward. This results in an equal and opposite force acting upward on the wing which is the lift force. The change of momentum of the airflow downward results in a reduction of the rearward momentum of the flow which is the result of a force acting forward on the airflow and applied by the wing to the air flow; an equal but opposite force acts on the wing rearward which is the induced drag. Induced drag tends to be the most important component for airplanes during take-off or landing flight. Another drag component, namely wave drag, ${\displaystyle D_{w}}$, results from shock waves in transonic and supersonic flight speeds. The shock waves induce changes in the boundary layer and pressure distribution over the body surface.

## History

The idea that a moving body passing through air or another fluid encounters resistance had been known since the time of Aristotle. Louis Charles Breguet's paper of 1922 began efforts to reduce drag by streamlining.[2] Breguet went on to put his ideas into practice by designing several record-breaking aircraft in 1920s and 1930s. Ludwig Prandtl's boundary layer theory in the 1920s provided the impetus to minimise skin friction. A further major call for streamlining was made by Sir Melvill Jones who provided the theoretical concepts to demonstrate emphatically the importance of streamlining in aircraft design.[3] [4][5] In 1929 his paper ‘The Streamline Airplane’ presented to the Royal Aeronautical Society was seminal. He proposed an ideal aircraft that would have minimal drag which led to the concepts of a 'clean' monoplane and retractable undercarriage. The aspect of Jones’s paper that most shocked the designers of the time was his plot of the horse power required versus velocity, for an actual and an ideal plane. By looking at a data point for a given aircraft and extrapolating it horizontally to the ideal curve, the velocity gain for the same power can be seen. When Jones finished his presentation, a member of the audience described the results as being of the same level of importance as the Carnot cycle in thermodynamics.[2][3]