Busemann's Biplane
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Busemann's Biplane is a conceptual airframe design that inherently prohibits the formation of N-type shock waves and thus does not create a sonic boom. It was invented by Adolf Busemann.
It consists of two triangular cross-section plates a certain distance apart, with flat sides top and bottom parallel to the fluid flow. The spacing is sufficiently large that the flow does not choke and supersonic flow is maintained between the plates.
Usually with supersonic flow a positive pressure shock wave is generated at the front and a negative pressure shock wave at the rear.
With the biplane, the high pressure shock wave created is only on the inside between the two plates and reflects between the two plates until it cancels/fills in the negative pressure shock wave forming at the rear, leaving no external shock waves to propagate to infinity. The flat sides top and bottom generate no shock waves as the flow is parallel.
The lack of external shock waves means that the Busemann Biplane does not suffer from any wave drag.
Although it has been shown to otherwise work in wind tunnel testing, unfortunately, no way of using the biplane to generate aerodynamic lift has been found, and it remains a curiosity.