Wolfgang Haack
Encyclopedia
Wolfgang Siegfried Haack (born April 24, 1902 in Gotha; November 28, 1994 in Berlin) was a German
mathematician and aerodynamicist. He and William Sears
independently discovered the Sears–Haack body in 1947.
in Hanover
and mathematics
in Jena
. He earned his doctorate in 1926 at the Friedrich Schiller University. He habilitated in 1929 at the TH Danzig after a short research visit to Hamburg
and a job as an assistant at the Technical University of Stuttgart
. After his short-term change to the 1935 TH Berlin in 1937, he followed the call to the TH Karlsruhe. During the Second World War he worked on projectile design. After the war he became the successor to Georg Hamel
at the TU Berlin Department of Mathematics and Mechanics. On his initiative a new Department of Computational Mathematics was founded in 1964, which he held until his retirement in 1968. In 1992 Haack was appointed as an honorary member of the Society for Applied Mathematics and Mechanics.
s to numerical mathematics. In particular, he dealt with both elliptical and with hyperbolic partial differential equations of the first order. Coming from differential geometry, Pfaff's differential forms were always of special concern to him. As an engineer, he was always focussed on applied research
, such as gas dynamics in supersonic flows. During his time in Berlin, he supervised over a dozen dissertations.
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 ogive
s 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 tangential ogive or even the secant ogive often used for very-low-drag bullet
s and artillery shells
. Only after the end of World War II have Haack shaped projectiles for artillery
guns and sniper rifle
s 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.
with the aim that an electronic calculator would be acquired for the Technische Universität Berlin. The Deutsche Forschungsgemeinschaft
assumed that the existing computing machines at Darmstadt
, Göttingen
and Munich
were sufficient for the time being. It was due to his solicitation of donations from the private industry that in 1958 the first computer at the TU Berlin was set up.
Germans
The Germans are a Germanic ethnic group native to Central Europe. The English term Germans has referred to the German-speaking population of the Holy Roman Empire since the Late Middle Ages....
mathematician and aerodynamicist. He and William Sears
William R. Sears
William Rees Sears was a notable aeronautical engineer and educator.-Career:William R. Sears was born in Minneapolis, Minnesota, the son of William and Gertrude Sears. He earned his BS degree from the University of Minnesota in 1934...
independently discovered the Sears–Haack body in 1947.
Life
Wolfgang Haack studied mechanical engineeringMechanical engineering
Mechanical engineering is a discipline of engineering that applies the principles of physics and materials science for analysis, design, manufacturing, and maintenance of mechanical systems. It is the branch of engineering that involves the production and usage of heat and mechanical power for the...
in Hanover
Hanover
Hanover or Hannover, on the river Leine, is the capital of the federal state of Lower Saxony , Germany and was once by personal union the family seat of the Hanoverian Kings of Great Britain, under their title as the dukes of Brunswick-Lüneburg...
and mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
in Jena
Jena
Jena is a university city in central Germany on the river Saale. It has a population of approx. 103,000 and is the second largest city in the federal state of Thuringia, after Erfurt.-History:Jena was first mentioned in an 1182 document...
. He earned his doctorate in 1926 at the Friedrich Schiller University. He habilitated in 1929 at the TH Danzig after a short research visit to Hamburg
Hamburg
-History:The first historic name for the city was, according to Claudius Ptolemy's reports, Treva.But the city takes its modern name, Hamburg, from the first permanent building on the site, a castle whose construction was ordered by the Emperor Charlemagne in AD 808...
and a job as an assistant at the Technical University of Stuttgart
University of Stuttgart
The University of Stuttgart is a university located in Stuttgart, Germany. It was founded in 1829 and is organized in 10 faculties....
. After his short-term change to the 1935 TH Berlin in 1937, he followed the call to the TH Karlsruhe. During the Second World War he worked on projectile design. After the war he became the successor to Georg Hamel
Georg Hamel
Georg Karl Wilhelm Hamel was a German mathematician with interests in mechanics, the foundations of mathematics and function theory....
at the TU Berlin Department of Mathematics and Mechanics. On his initiative a new Department of Computational Mathematics was founded in 1964, which he held until his retirement in 1968. In 1992 Haack was appointed as an honorary member of the Society for Applied Mathematics and Mechanics.
Applied mathematics
The interaction of Wolfgang Haack is at the interface between mathematics and mechanics. His research areas ranging from the mechanics of differential geometry and partial differential equationPartial differential equation
In mathematics, partial differential equations are a type of differential equation, i.e., a relation involving an unknown function of several independent variables and their partial derivatives with respect to those variables...
s to numerical mathematics. In particular, he dealt with both elliptical and with hyperbolic partial differential equations of the first order. Coming from differential geometry, Pfaff's differential forms were always of special concern to him. As an engineer, he was always focussed on applied research
Applied research
Applied research is a form of systematic inquiry involving the practical application of science. It accesses and uses some part of the research communities' accumulated theories, knowledge, methods, and techniques, for a specific, often state, business, or client driven purpose...
, such as gas dynamics in supersonic flows. During his time in Berlin, he supervised over a dozen dissertations.
Haack minimum drag shapes
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
, the patriotic-minded Haack was involved in military research. His work on an analytical formula for projectile nose cone shapes
Nose cone design
Given the problem of the aerodynamic design of the nose cone section of any vehicle or body meant to travel through a compressible fluid medium , an important problem is the determination of the nose cone geometrical shape for optimum performance...
that exhibit the lowest air resistance depending on caliber
Caliber
In guns including firearms, caliber or calibre is the approximate internal diameter of the barrel in relation to the diameter of the projectile used in it....
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
Sears-Haack body
The Sears–Haack body is the aerodynamic body shape with the lowest theoretical wave drag. Aircraft designed to operate at high subsonic or supersonic speeds have their cross-sectional areas designed to match as closely as possible the proportions of Sears-Haack body.By Whitcomb's area rule, the...
are not ogive
Ogive
An ogive is the roundly tapered end of a two-dimensional or three-dimensional object.-Applied physical science and engineering:In ballistics or aerodynamics, an ogive is a pointed, curved surface mainly used to form the approximately streamlined nose of a bullet or other projectile.The traditional...
s or constructed from any other geometric figures. The shapes are instead mathematically derived streamlined bodies of revolution
Solid of revolution
In mathematics, engineering, and manufacturing, a solid of revolution is a solid figure obtained by rotating a plane curve around some straight line that lies on the same plane....
for the purpose of minimizing drag
Drag (physics)
In fluid dynamics, drag refers to forces which act on a solid object in the direction of the relative fluid flow velocity...
. 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
Supersonic
Supersonic speed is a rate of travel of an object that exceeds the speed of sound . For objects traveling in dry air of a temperature of 20 °C this speed is approximately 343 m/s, 1,125 ft/s, 768 mph or 1,235 km/h. Speeds greater than five times the speed of sound are often...
to the transonic
Transonic
Transonic speed is an aeronautics term referring to the condition of flight in which a range of velocities of airflow exist surrounding and flowing past an air vehicle or an airfoil that are concurrently below, at, and above the speed of sound in the range of Mach 0.8 to 1.2, i.e. 600–900 mph...
and eventually to subsonic
Speed of sound
The speed of sound is the distance travelled during a unit of time by a sound wave propagating through an elastic medium. In dry air at , the speed of sound is . This is , or about one kilometer in three seconds or approximately one mile in five seconds....
air flow regimes or vice versa during flight. For this kind of applications the Haack shape offers significantly improved characteristics compared to the tangential ogive or even the secant ogive often used for very-low-drag bullet
Very-low-drag bullet
Very-low-drag bullets are primarily a small arms ballistics development of the 1980s–1990s, driven by shooters' desire for bullets that will give a higher degree of accuracy and kinetic efficiency, especially at extended ranges. To achieve this the projectile must minimize air resistance in flight...
s and artillery shells
Shell (projectile)
A shell is a payload-carrying projectile, which, as opposed to shot, contains an explosive or other filling, though modern usage sometimes includes large solid projectiles properly termed shot . Solid shot may contain a pyrotechnic compound if a tracer or spotting charge is used...
. Only after the end of World War II have Haack shaped projectiles for artillery
Artillery
Originally applied to any group of infantry primarily armed with projectile weapons, artillery has over time become limited in meaning to refer only to those engines of war that operate by projection of munitions far beyond the range of effect of personal weapons...
guns and sniper rifle
Sniper rifle
In military and law enforcement terminology, a sniper rifle is a precision-rifle used to ensure more accurate placement of bullets at longer ranges than other small arms. A typical sniper rifle is built for optimal levels of accuracy, fitted with a telescopic sight and chambered for a military...
s 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
Transonic
Transonic speed is an aeronautics term referring to the condition of flight in which a range of velocities of airflow exist surrounding and flowing past an air vehicle or an airfoil that are concurrently below, at, and above the speed of sound in the range of Mach 0.8 to 1.2, i.e. 600–900 mph...
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.
Pioneer of numerical mathematics
Haack recognized early on the potential of computers for scientific and industrial research. As early as 1950 he established a working group on electronic calculating machines. He contacted Konrad ZuseKonrad Zuse
Konrad Zuse was a German civil engineer and computer pioneer. His greatest achievement was the world's first functional program-controlled Turing-complete computer, the Z3, which became operational in May 1941....
with the aim that an electronic calculator would be acquired for the Technische Universität Berlin. The Deutsche Forschungsgemeinschaft
Deutsche Forschungsgemeinschaft
The Deutsche Forschungsgemeinschaft is an important German research funding organization and the largest such organization in Europe.-Function:...
assumed that the existing computing machines at Darmstadt
Darmstadt
Darmstadt is a city in the Bundesland of Hesse in Germany, located in the southern part of the Rhine Main Area.The sandy soils in the Darmstadt area, ill-suited for agriculture in times before industrial fertilisation, prevented any larger settlement from developing, until the city became the seat...
, Göttingen
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...
and Munich
Munich
Munich The city's motto is "" . Before 2006, it was "Weltstadt mit Herz" . Its native name, , is derived from the Old High German Munichen, meaning "by the monks' place". The city's name derives from the monks of the Benedictine order who founded the city; hence the monk depicted on the city's coat...
were sufficient for the time being. It was due to his solicitation of donations from the private industry that in 1958 the first computer at the TU Berlin was set up.
External links
- Biografie in der Festschrift 125 Jahre Technische Universität Berlin (biography in German)