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# Rectangular Wings

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In random reading about matters aeronautical I have twice come across essays in defense of rectangular wings. Not coincidentally, perhaps, both were by men who had taken part in the design of the Piper Cherokee, the airplane whose thick rectangular wing gave a new application to the name "Hershey Bar." The first essay was by the late John Thorp, best known as the designer of the T-18 homebuilt. The second was by Karl Bergey, who is, among other things, emeritus professor of aerospace engineering at the University of Oklahoma.

Bergey is building a fast, high-performance homebuilt that happens to use a Cherokee wing?the original stubby rectangular one, before they added the tapered outer panels. So many people found the combination of "fast" and "rectangular wing" incongruous that Bergey felt obliged to put his case in writing.

Both Thorp and Bergey begin by laying out the case for tapered wings, which offer three apparent advantages over rectangular ones. The first is structural. By carrying more of the airplane's weight farther inboard, a tapered wing reduces the bending moment?the force tending to break the wing-at the root. At the same time, the root airfoil, having the longest chord, provides more space for retractable landing gear and greater depth for its structural members which, being deeper, can be at once stiffer and lighter.

The second apparent advantage is aerodynamic, and has to do with the drag penalty associated with lift?the so-called induced drag. Induced drag cannot be eliminated, but it is at its minimum when the spanwise distribution of lift is elliptical. Equating area distribution with lift distribution (a big conceptual leap, but let's make it for the time being), the argument goes on to assert that a rectangular wing deviates greatly from the elliptical ideal, especially near the tips, whereas a moderately tapered wing?or a double-tapered one, with a straight inner section and a tapered outer section?approximates the ellipse much more closely.

The third argument in favor of tapered wings is aesthetic. They just look nice. Few would gainsay this claim, but it is scientifically weightless. Still, looks are important in the selling of airplanes, and even Thorp and Bergey would probably concede that when the design of wings is viewed as a commercial rather than a technological enterprise, the aesthetic argument, however insubstantial or misguided, may turn out to be the most compelling one of all.