Area rule

The Whitcomb area rule, also called the transonic area rule, is a design technique used to reduce an aircraft's drag at transonic and supersonic speeds, particularly between Mach 0.75 and 1.2.

This is one of the most important operating speed ranges for commercial and military fixed-wing aircraft today, with transonic acceleration being considered an important performance metric for combat aircraft and necessarily dependent upon transonic drag.

At high-subsonic flight speeds, the local speed of the airflow can reach the speed of sound where the flow accelerates around the aircraft body and wings. The speed at which this development occurs varies from aircraft to aircraft and is known as the critical Mach number. The resulting shock waves formed at these points of sonic flow can greatly reduce power, which is experienced by the aircraft as a sudden and very powerful drag, called wave drag. To reduce the number and power of these shock waves, an aerodynamic shape should change in cross sectional area as smoothly as possible.

The area rule says that two airplanes with the same longitudinal cross-sectional area distribution have the same wave drag, independent of how the area is distributed laterally (i.e. in the fuselage or in the wing). Furthermore, to avoid the formation of strong shock waves, this total area distribution must be smooth. As a result, aircraft have to be carefully arranged so that at the location of the wing, the fuselage is narrowed or "waisted", so that the total area does not change much. Similar but less pronounced fuselage waisting is used at the location of a bubble canopy and perhaps the tail surfaces.

The area rule also holds true at speeds exceeding the speed of sound, but in this case the body arrangement is in respect to the Mach line for the design speed. For example, consider that at Mach 1.3 the angle of the Mach cone formed off the body of the aircraft will be at about μ = arcsin(1/M) = 50.3° (μ is the angle of the Mach cone, or simply Mach angle). In this case the "perfect shape" is biased rearward; therefore, aircraft designed for high speed cruise usually have wings towards the rear. A classic example of such a design is the Concorde. When applying the transonic area rule, the condition that the plane defining the cross-section meets the longitudinal axis at the Mach angle μ no longer prescribes a unique plane for μ other than the 90° given by M = 1. The correct procedure is to average over all possible orientations of the intersecting plane.

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