Parasitic drag

Parasitic drag is drag that acts on an object when the object is moving through a fluid. In the case of aerodynamic drag, the fluid is the atmosphere. Parasitic drag is a combination of form drag and skin friction drag.[1] Parasitic drag does not result from the generation of lift on the object, and hence it is considered parasitic.

Drag curve for a lifting body in steady flight

The other components of total drag, lift–induced drag, wave drag, and ram drag (see ram pressure), are separate types of drag, and are not components of parasitic drag.

Description

In flight, lift–induced drag results from the lift force that must be produced so that the craft can maintain level flight. Induced drag is greater at lower speeds where a high angle of attack is required. As speed increases, the induced drag decreases, but parasitic drag increases because the fluid is striking the object with greater force, and is moving across the object's surfaces at higher speed. As speed continues to increase into the transonic and supersonic regimes, wave drag grows in importance. Each of these drag components 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 close to its optimal efficiency. Pilots will use this speed to maximize the gliding range in case of an engine failure. However, to maximize the gliding endurance (minimum sink), the aircraft's speed would have to be at the point of minimum drag power, which occurs at lower speeds than minimum drag.

At the point of minimum drag, C_D,o (drag coefficient of the aircraft when lift equals zero) is equal to C_D,i (induced drag coefficient, or coefficient of drag created by lift). At the point of minimum power, C_D,o is equal to one third times C_D,i. This can be proven by deriving the following equations:

${\displaystyle F_{drag}=qA_{s}C_{D}}$

where:

${\displaystyle q={\frac {1}{2}}\rho u^{2}}$

is the dynamic pressure and

${\displaystyle C_{D}=C_{D,o}+C_{D,i}}$

where

${\displaystyle C_{D,{\text{i}}}={\frac {C_{L}^{2}}{\pi A\!\!{\text{R}}}}}$,

${\displaystyle A\!\!{\text{R}}={\frac {b^{2}}{S}}\,}$ is the aspect ratio,

Form drag

Form drag or pressure drag arises because of the shape of the object. The general size and shape of the body are the most important factors in form drag; bodies with a larger presented cross-section will have a higher drag than thinner bodies; sleek ("streamlined") objects have lower form drag. Form drag follows the drag equation, meaning that it increases with velocity, and thus becomes more important for high-speed aircraft.

Form drag depends on the longitudinal section of the body. A prudent choice of body profile is essential for a low drag coefficient. Streamlines should be continuous, and separation of the boundary layer with its attendant vortices should be avoided.

Skin friction drag

Skin friction drag arises from the friction of the fluid against the "skin" of the object that is moving through it. Skin friction arises from the interaction between the fluid and the skin of the body, and is directly related to the wetted surface, the area of the surface of the body that is in contact with the fluid. Air in contact with a body will stick to the body's surface and that layer will tend to stick to the next layer of air and that in turn to further layers, hence the body is dragging some amount of air with it. The force required to drag an "attached" layer of air with the body is called skin friction drag. Skin friction drag imparts some momentum to a mass of air as it passes through it and that air applies a retarding force on the body. As with other components of parasitic drag, skin friction follows the drag equation and rises with the square of the velocity.

Skin friction is caused by viscous drag in the boundary layer around the object. The boundary layer at the front of the object is usually laminar and relatively thin, but becomes turbulent and thicker towards the rear. The position of the transition point from laminar to turbulent flow depends on the shape of the object. There are two ways to decrease friction drag: the first is to shape the moving body so that laminar flow is possible. The second method is to increase the length and decrease the cross-section of the moving object as much as practicable. To do so, a designer can consider the fineness ratio, which is the length of the aircraft divided by its diameter at the widest point (L/D). It is mostly kept 6:1 for subsonic flows. Increase in length increases Reynolds number. With Reynolds no. in the denominator for skin friction coefficient's relation, as its value is increased (in laminar range), total friction drag is reduced. While decrease in cross-sectional area decreases drag force on the body as the disturbance in air flow is less. For wings of an aircraft, a decrease in length (chord) of the wings will reduce "induced" drag though, if not the friction drag.

The skin friction coefficient, ${\displaystyle C_{f}}$, is defined by

${\displaystyle C_{f}\equiv {\frac {\tau _{w}}{q}},}$

where ${\displaystyle \tau _{w}}$ is the local wall shear stress, and q is the free-stream dynamic pressure.[2] For boundary layers without a pressure gradient in the x direction, it is related to the momentum thickness as

${\displaystyle C_{f}=2{\frac {d\theta }{dx}}.}$

For comparison, the turbulent empirical relation known as the One-seventh Power Law (derived by Theodore von Kármán) is:

${\displaystyle C_{f,tur}={\frac {0.074}{Re^{0.2}}},}$

where ${\displaystyle Re}$ is the Reynolds number.[3]

For a laminar flow over a plate, the skin friction coefficient can be determined using the following formula:[4]

${\displaystyle C_{f,lam}={\frac {1.328}{\sqrt {Re}}}}$

Profile drag

Profile drag is a term usually applied to the parasitic drag acting on a wing. With a two-dimensional wing there is no lift-induced drag so the whole of the drag is profile drag. With a three-dimensional wing the total drag minus the lift-induced drag is the profile drag[5] - it is defined as the sum of form drag and skin friction.[6]

See also

• NACA duct
• Skin friction line

References

1. Clancy, L.J. (1975). Aerodynamics, Sub-section 5.9. Pitman Publishing. ISBN 0 273 01120 0
2. "Skin friction coefficient -- CFD-Wiki, the free CFD reference". www.cfd-online.com. Retrieved 22 April 2018.
3. Introduction to Flight, John Anderson Jr., 7th edition
4. tec-science (2020-05-31). "Drag coefficient (friction and pressure drag)". tec-science. Retrieved 2020-06-25.
5. Anderson, John D. (1984). Fundamentals of Aerodynamics, p.192, 233. McGraw-Hill Book Company ISBN 0-07-001656-9
6. "Profile drag definition and meaning - Collins English Dictionary". www.collinsdictionary.com. Retrieved 22 April 2018.