*David Bloor*

- Published in print:
- 2011
- Published Online:
- September 2013
- ISBN:
- 9780226060941
- eISBN:
- 9780226060934
- Item type:
- chapter

- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226060934.003.0007
- Subject:
- History, History of Science, Technology, and Medicine

This chapter addresses the “infinite wing” paradigm with an analysis deliberately confined to a two-dimensional cross section of the flow in which the wingtips are ignored. It was Wilhelm Kutta in ...
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This chapter addresses the “infinite wing” paradigm with an analysis deliberately confined to a two-dimensional cross section of the flow in which the wingtips are ignored. It was Wilhelm Kutta in Munich who triggered the striking progress in the field of two-dimensional flow that was made in Germany before and during the Great War. His work is the starting point of this chapter. Where Rayleigh used a simple, flat plane as a model of a wing, Kutta used a shallow, circular arc. Both men treated the air as an inviscid fluid, but where Rayleigh postulated a flow with surfaces of discontinuity, Kutta postulated an irrotational flow with circulation. Joukowsky, a Russian who published in German, then showed how to simplify and generalize Kutta's reasoning. A variety of other workers in Gottingen, Aachen, and Berlin, starting from Kutta's and Joukowsky's publications, carried the experimental and theoretical analysis yet further.Less

This chapter addresses the “infinite wing” paradigm with an analysis deliberately confined to a two-dimensional cross section of the flow in which the wingtips are ignored. It was Wilhelm Kutta in Munich who triggered the striking progress in the field of two-dimensional flow that was made in Germany before and during the Great War. His work is the starting point of this chapter. Where Rayleigh used a simple, flat plane as a model of a wing, Kutta used a shallow, circular arc. Both men treated the air as an inviscid fluid, but where Rayleigh postulated a flow with surfaces of discontinuity, Kutta postulated an irrotational flow with circulation. Joukowsky, a Russian who published in German, then showed how to simplify and generalize Kutta's reasoning. A variety of other workers in Gottingen, Aachen, and Berlin, starting from Kutta's and Joukowsky's publications, carried the experimental and theoretical analysis yet further.

*David Bloor*

- Published in print:
- 2011
- Published Online:
- September 2013
- ISBN:
- 9780226060941
- eISBN:
- 9780226060934
- Item type:
- chapter

- Publisher:
- University of Chicago Press
- DOI:
- 10.7208/chicago/9780226060934.003.0008
- Subject:
- History, History of Science, Technology, and Medicine

This chapter divides the theory of lift into two parts: the theory of the wing profile, that is, the wing sections of the kind studied by Kutta and Joukowsky, and the theory of the planform of the ...
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This chapter divides the theory of lift into two parts: the theory of the wing profile, that is, the wing sections of the kind studied by Kutta and Joukowsky, and the theory of the planform of the wing, the shape of the wing when seen from above. The designer may choose a simple, rectangular shape or give the wing a more aesthetically pleasing curved leading or trailing edge. The wingtips may be rounded or square, and, most important of all, the wing may be made long and narrow, referred to as high aspect ratio, or short and stubby, referred to as low aspect ratio. The discussion here concerns the distribution of the lift along the span of the wing and the properties that a wing possesses in virtue of its finite length and the flow around the wingtips.Less

This chapter divides the theory of lift into two parts: the theory of the wing profile, that is, the wing sections of the kind studied by Kutta and Joukowsky, and the theory of the planform of the wing, the shape of the wing when seen from above. The designer may choose a simple, rectangular shape or give the wing a more aesthetically pleasing curved leading or trailing edge. The wingtips may be rounded or square, and, most important of all, the wing may be made long and narrow, referred to as high aspect ratio, or short and stubby, referred to as low aspect ratio. The discussion here concerns the distribution of the lift along the span of the wing and the properties that a wing possesses in virtue of its finite length and the flow around the wingtips.

*David R. Steward*

- Published in print:
- 2020
- Published Online:
- November 2020
- ISBN:
- 9780198856788
- eISBN:
- 9780191890031
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/oso/9780198856788.003.0003
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

The mathematical functions associated with analytic elements may be formulated using a complex function $\Omega$ of a complex variable ${\zcomplex}$. Complex formulation of analytic elements is ...
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The mathematical functions associated with analytic elements may be formulated using a complex function $\Omega$ of a complex variable ${\zcomplex}$. Complex formulation of analytic elements is introduced in Section 3.1 for exact solutions obtained by embedding point elements that generate divergence, circulation, or velocity within a uniform vector field. Influence functions for analytic elements with circular geometry are obtained using Taylor and Laurent series expansions in Section 3.2, and conformal mapping extends this formulation to analytic elements with the geometry of ellipses (Section 3.3). The Courant's Sewing Theorem is employed in Section 3.4 to develop solutions for interface conditions across straight line segments, and the Joukowsky transformation extends methods to circular arcs and wings (Section 3.5), which satisfy a Kutta condition of non-singular vector field at their trailing edges. Vector fields with spatially distributed divergence and curl are formulated using the complex variable ${\zcomplex}$ with its complex conjugate $\overline{\zcomplex}$ in Section 3.6, and the complex conjugate is further employed in the Kolosov formulas (Section 3.7) to solve force deformation problems for analytic elements with traction or displacement specified boundary conditions.Less

The mathematical functions associated with analytic elements may be formulated using a complex function $\Omega$ of a complex variable ${\zcomplex}$. Complex formulation of analytic elements is introduced in Section 3.1 for exact solutions obtained by embedding point elements that generate divergence, circulation, or velocity within a uniform vector field. Influence functions for analytic elements with circular geometry are obtained using Taylor and Laurent series expansions in Section 3.2, and conformal mapping extends this formulation to analytic elements with the geometry of ellipses (Section 3.3). The Courant's Sewing Theorem is employed in Section 3.4 to develop solutions for interface conditions across straight line segments, and the Joukowsky transformation extends methods to circular arcs and wings (Section 3.5), which satisfy a Kutta condition of non-singular vector field at their trailing edges. Vector fields with spatially distributed divergence and curl are formulated using the complex variable ${\zcomplex}$ with its complex conjugate $\overline{\zcomplex}$ in Section 3.6, and the complex conjugate is further employed in the Kolosov formulas (Section 3.7) to solve force deformation problems for analytic elements with traction or displacement specified boundary conditions.