Wolfgang Haack - Haack Minimum Drag Shapes

Haack Minimum Drag Shapes

During World War II, the patriotic-minded Haack was involved in 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 but was kept secret during World war II.

Haack shapes or Sears–Haack bodies are not ogives or constructed from any other geometric figures. The shapes are instead mathematically derived streamlined bodies of revolution for the purpose of minimizing drag. Minimal projectile-shape variations can change the air-resistance and hence the effective range of high powered gun projectiles considerably, especially when they change velocity from the supersonic to the transonic and eventually to subsonic air flow regimes or vice versa during flight. For this kind of applications the Haack shape offers significantly improved characteristics compared to the tangent ogive or even the secant ogive often used for very-low-drag bullets and artillery shells. Only after the end of World War II have Haack shaped projectiles for artillery guns and sniper rifles been produced. Besides that Haack shapes are also applied in modern fast flying aircraft. Fighter aircraft are probably good examples of nose shapes optimized for the transonic region, although their nose shapes are often distorted by other considerations of avionics and inlets. For example, an F-16 nose appears to be a very close match to a Haack shape.