Drag (physics)

In fluid dynamics, drag, sometimes referred to as fluid resistance, also known as viscous force, is a force acting opposite to the direction of motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers, or between a fluid and a solid surface. Drag forces tend to decrease fluid velocity relative to the solid object in the fluid's path.
Unlike other resistive forces, drag force depends on velocity. Drag force is proportional to the relative velocity for low-speed flow and is proportional to the velocity squared for high-speed flow. This distinction between low and high-speed flow is measured by the Reynolds number.

Examples

Examples of drag include:

Net aerodynamic or hydrodynamic force: Drag acting opposite to the direction of movement of a solid object such as cars, aircraft, and boat hulls.
Viscous drag of fluid in a pipe: Drag force on the immobile pipe restricts the velocity of the fluid through the pipe.
In the physics of sports, drag force is necessary to explain the motion of balls, javelins, arrows, and frisbees and the performance of runners and swimmers. For a top sprinter, overcoming drag can require 5% of their energy output.
Types

There are many distinct types of drag caused by different physical interactions between the object and fluid. Two types of drag are relevant for all objects:

Form drag, which is caused by the pressure exerted on the object as the fluid flow goes around the object. Form drag is determined by the cross-sectional shape and area of the body.
Skin friction drag, which is caused by friction between the fluid and the surface of the object. The surface may be the outside of an object, such as a boat hull, or the inside of an object, such as the bore of a pipe.

There are two types of which are primarily relevant for aircraft:

Lift-induced drag appears with wings or a lifting body in aviation and with semi-planing or planing hulls for watercraft
Wave drag is caused by the presence of shockwaves and first appears at subsonic aircraft speeds when local flow velocities become supersonic. The wave drag of the supersonic Concorde prototype aircraft was reduced at Mach 2 by 1.8% by applying the area rule which extended the rear fuselage on the production aircraft.

Wave resistance affects watercraft:

Wave resistance occurs when a solid object is moving along a fluid boundary and making surface waves.

Last, in aerodynamics the term "parasitic drag" is often used. Parasitic drag is the sum of form drag and skin friction drag and is entirely negative to an aircraft, in contrast with lift-induced drag which is a consequence of generating lift.

Comparison of form drag and skin friction

The effect of streamlining on the relative proportions of skin friction and form drag is shown in the table at right for an airfoil, which is a streamlined body, and a cylinder, which is a bluff body. Also shown is a flat plate in two different orientations, illustrating the effect of orientation on the relative proportions of skin friction and form drag, and showing the pressure difference between front and back.
A body is known as bluff or blunt when the source of drag is dominated by pressure forces, and streamlined if the drag is dominated by viscous forces. For example, road vehicles are bluff bodies. For aircraft, pressure and friction drag are included in the definition of parasitic drag. Parasite drag is often expressed in terms of a hypothetical.

Lift-induced drag

Lift-induced drag is drag which occurs as the result of the creation of lift on a three-dimensional lifting body, such as the wing or propeller of an airplane. Induced drag consists primarily of two components: drag due to the creation of trailing vortices ; and the presence of additional viscous drag that is not present when lift is zero. The trailing vortices in the flow-field, present in the wake of a lifting body, derive from the turbulent mixing of air from above and below the body which flows in slightly different directions as a consequence of creation of lift.
With other parameters remaining the same, as the lift generated by a body increases, so does the lift-induced drag. This means that as the wing's angle of attack increases, the lift coefficient also increases, and so too does the lift-induced drag. At the onset of stall, lift is abruptly decreased, as is lift-induced drag, but viscous pressure drag, a component of parasite drag, increases due to the formation of turbulent unattached flow in the wake behind the body.

Parasitic drag

Parasitic drag, or profile drag, is the sum of viscous pressure drag and drag due to surface roughness. Additionally, the presence of multiple bodies in relative proximity may incur so called interference drag, which is sometimes described as a component of parasitic drag. In aeronautics the parasitic drag and lift-induced drag are often given separately.
For an aircraft at low speed, induced drag tends to be relatively greater than parasitic drag because a high angle of attack is required to maintain lift, increasing induced drag. As speed increases, the angle of attack is reduced and the induced drag decreases. Parasitic drag, however, increases because the fluid is flowing more quickly around protruding objects increasing friction or drag. At even higher speeds, wave drag enters the picture. Each of these forms of drag changes in proportion to the others based on speed. The combined overall drag curve therefore shows a minimum at some airspeed - an aircraft flying at this speed will be at or close to its optimal efficiency. Pilots will use this speed to maximize endurance, or maximize gliding range in the event of an engine failure.
The equivalent parasite area is the area which a flat plate perpendicular to the flow would have to match the parasite drag of an aircraft. It is a measure used when comparing the drag of different aircraft. For example, the Douglas DC-3 has an equivalent parasite area of and the McDonnell Douglas DC-9, with 30 years of advancement in aircraft design, an area of although it carried five times as many passengers.

The drag equation

Drag depends on the properties of the fluid and on the size, shape, and speed of the object. One way to express this is by means of the drag equation:
where

is the drag force,
is the density of the fluid,
is the speed of the object relative to the fluid,
is the cross sectional area, and
is the drag coefficient – a dimensionless number.

The drag coefficient depends on the shape of the object and on the Reynolds number
where

is some characteristic diameter or linear dimension. Actually, is the equivalent diameter of the object. For a sphere, is the D of the sphere itself.
For a rectangular shape cross-section in the motion direction,, where a and b are the rectangle edges.
is the kinematic viscosity of the fluid.

At low, is asymptotically proportional to, which means that the drag is linearly proportional to the speed, i.e. the drag force on a small sphere moving through a viscous fluid is given by Stokes’ Law:
At high, is more or less constant, but drag will vary as the square of the speed varies. The graph to the right shows how varies with for the case of a sphere. Since the power needed to overcome the drag force is the product of the force times speed, the power needed to overcome drag will vary as the square of the speed at low Reynolds numbers, and as the cube of the speed at high numbers.
It can be demonstrated that drag force can be expressed as a function of a dimensionless number, which is dimensionally identical to the Bejan number. Consequently, drag force and drag coefficient can be a function of Bejan number. In fact, from the expression of drag force it has been obtained:
and consequently allows expressing the drag coefficient as a function of Bejan number and the ratio between wet area and front area :
where is the Reynolds number related to fluid path length L.

At high velocity

As mentioned, the drag equation with a constant drag coefficient gives the force moving through a fluid at a relatively large velocity, i.e. high Reynolds number, Re > ~1000. This is also called quadratic drag.
The derivation of this equation is presented at.
The reference area A is often the orthographic projection of the object, or the frontal area, on a plane perpendicular to the direction of motion. For objects with a simple shape, such as a sphere, this is the cross sectional area. Sometimes a body is a composite of different parts, each with a different reference area.
In the case of a wing, the reference areas are the same, and the drag force is in the same ratio as the lift force. Therefore, the reference for a wing is often the lifting area, sometimes referred to as "wing area" rather than the frontal area.
For an object with a smooth surface, and non-fixed separation points, the drag coefficient may vary with Reynolds number Re, up to extremely high values.
For an object with well-defined fixed separation points, like a circular disk with its plane normal to the flow direction, the drag coefficient is constant for Re > 3,500.
The further the drag coefficient C_d is, in general, a function of the orientation of the flow with respect to the object.

Power

Under the assumption that the fluid is not moving relative to the currently used reference system, the power required to overcome the aerodynamic drag is given by:
The power needed to push an object through a fluid increases as the cube of the velocity increases. For example, a car cruising on a highway at may require only to overcome aerodynamic drag, but that same car at requires. With a doubling of speeds, the drag/force quadruples per the formula. Exerting 4 times the force over a fixed distance produces 4 times as much work. At twice the speed, the work is done twice as fast. Since power is the rate of doing work, 4 times the work done in half the time requires 8 times the power.
When the fluid is moving relative to the reference system, for example, a car driving into headwind, the power required to overcome the aerodynamic drag is given by the following formula:
Where is the wind speed and is the object speed.