Lift-induced drag

A body which is exposed to a flow of a fluid, is resisted. This resistance can be broken down into individual components that have different causes.

One of these components is the induced drag (also: induced air resistance). It is caused by not flowing in river or direction of motion compensation flows caused by flow-induced pressure differences. The induced resistance is additive with a surface resistance (friction ) and the form drag ( face ) in the total resistance.

Induced resistance in a plane

In the wing of an aircraft, the induced drag can be illustrated particularly well. The aircraft produces dynamic lift by moving a support surface with a given pitch through the air. The result is above the wing relative vacuum and below the wing relative overpressure. At the ends of the blades pierce the regions with the different pressure conditions along, and there is a compensating flow of the area of higher pressure to the lower pressure zone rather than, that of the bottom to the top. It created at the wingtips, two opposite edge vortices, which do not contribute to lift. However, the continuous generation of these vortices requires energy and is called " induced drag ." The resistance is at optimal lift distribution (see below) depends only on the aspect ratio and the lift coefficient using the formula:

The induced resistance can be specified ( with Λ = ∞) in the form of the additional angle of attack compared with the pure profile data:

The induced resistance has in aircraft in slow flight accounted for over 50 % of the total resistance.

Stretching

The air flow at the outermost portion of the blade is affected by the balance flow most. Therefore wing with a large aspect ratio produce inversely proportional to the stretching induced a lower resistance than low wing with small aspect ratio with the same area and the same buoyancy.

Reduction of the profile lift coefficient

Profile Polar are always listed as a wing with infinite extension. The induced resistance may also be in the form of a reduction in buoyancy, and are thus given a power reduction. The formula is:

Influence of speed

With increasing speed of the aircraft in horizontal flight, the angle is smaller, since the lift force always has to compensate for the weight of the aircraft and therefore remains the same. Due to the lower angle of the induced drag will be less. Conversely, at low speeds, for example, during takeoff and landing, the induced drag is greatest.

Lift distribution, Oswald factor

The optimal distribution of the lift along the span is elliptical. The corresponding optimal wing plan form is only about elliptical, since the buoyancy is only approximately proportional to the chord (Re- number change with the chord ). This can be derived mathematically from the Prandtl lifting line theory (after Ludwig Prandtl ). In this theory, the flow around the wing is modeled as a potential flow, and there are some assumptions that allow an analytical solution of the problem.

Once the wing has a different floor plan, such as a rectangular or pointed, the induced drag increases. This is detected by the Oswald factor. This factor is defined as the ratio to the theoretical optimum, and therefore always less than one. The higher the Oswald factor, the more favorable is the geometry of the wing. Ideally ( ellipse ) is the Oswald factor equal to one. Typically, the Oswald factor is in the range of 0.6 to 0.9. For resistance optimization using structural variants such as Twist, escalation, reduced camber and thickness or winglets.

For description of the influence of any lift distribution on the induced resistance of the Oswald factor and the K- factor was introduced. With these factors, the deviation of the induced resistance between the optimal and the actual lift distribution is summarized in a single value. In older publications can be found mainly the Oswald factor, while publications of recent times prefer the k- factor.

Or

Both points of view are equivalent. The k- factor is defined as follows:

Oswald factor is also referred to as a wing span efficiency or efficiency.