Sweep theory

Sweep theory is an aeronautical engineering description of the behavior of airflow over a wing when the wing's leading edge encounters the airflow at an oblique angle. The development of sweep theory resulted in the swept wing design used by most modern jet aircraft, as this design performs more effectively at transonic and supersonic speeds. In its advanced form, sweep theory led to the experimental oblique wing concept.

Overview

Adolf Busemann introduced the concept of the swept wing and presented this 1935 at the 5. Volta-Congress in Rom.Sweep theory in general was a subject of development and investigation throughout the 1930s and 1940s, but the breakthrough mathematical definition of sweep theory is generally credited to NACA's Robert T. Jones in 1945. Sweep theory builds on other wing lift theories. Lifting line theory describes lift generated by a straight wing (a wing inwhich the leading edge is perpendicular to the airflow). Weissinger theory describes the distribution of lift for a swept wing, but does not have the capability to include chordwise pressure distribution. There are other methods that do describe chordwise distributions, but they have other limitations. Jones' sweep theory provides a simple, comprehensive analysis of swept wing performance.

Description

To visualize the basic concept of simple sweep theory, consider a straight, non-swept wing of infinite length, which meets the airflow at a perpendicular angle. The resulting air pressure distribution is equivalent to the length of the wing's chord (the distance from the leading edge to the trailing edge). If we were to begin to slide the wing sideways (spanwise), the sideways motion of the wing relative to the air would be added to the previously perpendicular airflow, resulting in an airflow over the wing at an angle to the leading edge. This angle results in airflow traveling a greater distance from leading edge to trailing edge, and thus the air pressure is distributed over a greater distance (and consequently lessened at any particular point on the surface).

This scenario is identical to the airflow experienced by a swept wing as it travels through the air. The airflow over a swept wing encounters the wing at an angle. That angle can be broken down into two vectors, one perpendicular to the wing, and one parallel to the wing. The flow parallel to the wing has no effect on it, and since the perpendicular vector is shorter (meaning slower) than the actual airflow, it consequently exerts less pressure on the wing. In other words, the wing experiences airflow that is slower - and at lower pressures - than the actual speed of the aircraft.

One of the factors that must be taken into account when designing a high-speed wing is compressibility, which is the effect that acts upon a wing as it approaches and passes through the speed of sound. The significant negative effects of compressibility made it a prime issue with aeronautical engineers. Sweep theory helps mitigate the effects of compressibility in transonic and supersonic aircraft because of the reduced pressures. This allows the mach number of an aircraft to be higher than that actually experienced by the wing.

There is also a negative aspect to sweep theory. The lift produced by a wing (called the coefficient of lift, or C_L), is directly related to the speed of the air over the wing. Since the airflow speed experienced by a swept wing is lower than what the actual aircraft speed is, this becomes a problem during slow-flight phases, such as takeoff and landing. There have been various ways of addressing the problem, including the variable-incidence wing design on the F-8 Crusader and swing-wings on the F-14, F-111, and the Panavia Tornado.

References

* [http://www.desktopaero.com/appliedaero/potential3d/sweeptheory.html Simple sweep theory math]
* [http://www.desktopaero.com/obliquewing/library/whitepaper/OFW_WP_Ch2_v0711.html Advanced math of swept and oblique wings]
* [http://adg.stanford.edu/aa241/drag/sweepncdc.html Sweep theory in a 3D environment]