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The Sears–Haack body is the shape with the lowest theoretical wave drag in supersonic flow, for a slender solid body of revolution with a given body length and volume. The mathematical derivation assumes small-disturbance (linearized) supersonic flow, which is governed by the Prandtl–Glauert equation .
However, the Sears–Haack body shape is derived starting with the Prandtl–Glauert equation which approximately governs small-disturbance subsonic flows, as well as Ackeret Theory, which closely describes supersonic flow. Both methods lose validity for transonic flows where the area rule applies, due to assumptions made in their derivations.
For a fuselage the resulting shape was the Sears–Haack body, which suggested a perfect cross-sectional shape for any given internal volume. The von Kármán ogive was a similar shape for bodies with a blunt end, like a missile. Both were based on long narrow shapes with pointed ends, the main difference being that the ogive was pointed on ...
The Haack series nose cones are not perfectly tangent to the body at their base except for the case where C = 2/3. However, the discontinuity is usually so slight as to be imperceptible. For C > 2/3, Haack nose cones bulge to a maximum diameter greater than the base diameter. Haack nose tips do not come to a sharp point, but are slightly rounded.
Sears-Haack body. During World War II, Haack was involved in Nazi military research.His work on an analytical formula for projectile nose cone shapes that exhibit the lowest air resistance depending on caliber or diameter and length or volume and length of the profile was published in 1941 by the Lilienthal society [2] but was kept secret during World War II.
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The closed form solution for the minimum wave drag of a body of revolution with a fixed length was found by Sears and Haack, and is known as the Sears-Haack Distribution. Similarly, for a fixed volume, the shape for minimum wave drag is the Von Karman Ogive .
Transonic (or transsonic) flow is air flowing around an object at a speed that generates regions of both subsonic and supersonic airflow around that object. [1] The exact range of speeds depends on the object's critical Mach number, but transonic flow is seen at flight speeds close to the speed of sound (343 m/s at sea level), typically between Mach 0.8 and 1.2.