Area rule

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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, necessarily dependent upon transonic drag.



At high-subsonic flight speeds, supersonic airflow can develop in areas where the flow accelerates around the aircraft body and wings. The speed at which this occurs varies from aircraft to aircraft, and is known as the critical Mach number. The resulting shock waves formed at these points of supersonic flow can bleed away a considerable amount of power, which is experienced by the aircraft as a sudden and very powerful form of 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. This leads to a "perfect" aerodynamic shape known as the Sears-Haack body, roughly shaped like a cigar but pointed at both ends.

The area rule says that an airplane designed with the same cross-sectional area distribution in the longitudinal direction as the Sears-Haack body generates the same wave drag as this body, largely independent of the actual shape. As a result, aircraft have to be carefully arranged so that large volumes like wings are positioned at the widest area of the equivalent Sears-Haack body, and that the cockpit, tailplane, intakes and other "bumps" are spread out along the fuselage and or that the rest of the fuselage along these "bumps" is correspondingly thinned.

The area rule also holds true at speeds higher than the speed of sound, but in this case the body arrangement is in respect to the Mach line for the design speed. For instance, 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 deg (μ is the angle of the Mach cone, or simply Mach angle). In this case the "perfect shape" is biased rearward, which is why aircraft designed for high speed cruise tend to be arranged with the wings at the rear.[1] A classic example of such a design is Concorde. When applying the supersonic area rule, the condition that the plane defining the cross-section meet the longitudinal axis at the Mach angle μ no longer prescribes a unique plane for μ other than the 90 degrees given by M=1. The correct procedure is to average over all possible orientations of the intersecting plane.

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