Parasitic drag

File:Drag Curve 2.jpg

Parasitic drag (also called skin friction drag) is drag caused by moving a solid object through a fluid medium (in the case of aerodynamics, more specifically, a gaseous medium). Parasitic drag is made up of many components, the most prominent being form drag. Skin friction and interference drag are also major components of parasitic drag.

In aviation, induced drag tends to be greater at lower speeds because a high angle of attack is required to maintain lift, creating more drag. However, as speed increases the induced drag becomes much less, but parasitic drag increases because the fluid is flowing faster around protruding objects increasing friction or drag. At even higher transonic and supersonic 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 the gliding range in case of an engine failure. However, to maximize the gliding endurance, the aircraft's speed would have to be at the point of minimum power, which occurs at lower speeds than minimum drag. At the point of minimum drag, C_D,o (drag coefficient of 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:

\[F_{drag} = \frac{1}{2} \rho V^2 A_s C_D \] and \[C_{D} = C_{D,o} + C_{D,i}\] where \[C_{D,i} = K C_L^2\]

Form drag

Form drag, profile drag, or pressure drag, arises because of the form of the object. The general size and shape of the body is the most important factor in form drag - bodies with a larger apparent cross-section will have a higher drag than thinner bodies. Sleek designs, or designs that are streamlined and change cross-sectional area gradually are also critical for achieving minimum form drag. Form drag follows the drag equation, meaning that it rises with the square of speed, and thus becomes more important for high speed aircraft.

Profile drag (Pxp): depends on the longitudinal section of the body. A diligent choice of body profile is more than essential for low drag coefficient. Streamlines should be continuous and separation of the boundary layer with its attendant vortices should be avoided.

Interference drag

A characteristic that is dominant in bodies in transonic flow is the concept of interference drag. One can imagine two bodies of the aircraft (e.g. horizontal and vertical tail) that intersect at a particular point. Both bodies generate high supervelocities, possibly even supersonic. However, at the intersection there is less physical space for the flow to go and even higher supervelocities are generated resulting in much stronger local shock waves than would be expected if either one of the two bodies would be considered by itself. The stronger shock wave induces an increase in wave drag that is termed interference drag. Interference drag plays a role throughout the entire aircraft (e.g. nacelles, pylons, empennage) and its detrimental effect is always kept in mind by designers. Ideally, the pressure distributions on the intersecting bodies should complement each other’s pressure distribution. If one body locally displays a negative pressure coefficient, the intersecting body should have positive pressure coefficient. In reality, however, this is not always possible. Particular geometric characteristics on aircraft often show how designers have dealt with the issue of interference drag. A prime example is the wing-body fairing which smooths the sharp angle between the wing and the fuselage. Another example is the junction between the horizontal and vertical tail plain in a T-tail . Often, an additional fairing (acorn) is positioned to reduce the added supervelocities. The position of the nacelle with respect to the wing is a third example of how interference-drag considerations dominate this geometric feature. For nacelles that are positioned beneath the wing, the lateral and longitudinal distance from the wing is dominated by interference-drag considerations. If there is little lateral space available between the wing and the nacelle (because of ground clearance) the nacelle is usually positioned much more in front of the wing.

Skin friction

Skin friction 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. As with other components of parasitic drag, skin friction follows the drag equation and rises with the square of the velocity.

The skin friction coefficient, \(C_f\), is defined by:

\[C_f \equiv \frac{\tau_w}{\frac{1}{2} \, \rho \, U_\infty^2}\]

Where \(\tau_w\) is the local wall shear stress, \(\rho\) is the fluid density and \(U_\infty\) is the free-stream velocity (usually taken outside of the boundary layer or at the inlet).

It is related to the momentum thickness as follows\[C_f = 2 \frac{d \theta}{d x}\]

For comparison, the turbulent empirical relation known as the 1/7 Power Law (derived by Theodore von Kármán) is\[C_f = \frac{0.0583}{Re^{0.2} }\]

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 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, like an airfoil. The second method is to decrease the length and cross-section of the moving object as much as is 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).

See also

• NACA duct

References

nl:Parasitaire weerstand