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Theory of Lifting Surfaces, Part 2

Description: A mathematical model is presented towards a theory of lifting and resistance on wings. It consists of a theory of multiplanes, conditions of flow at a great distance from the wing, lifting systems of minimum resistance, and free stream and stream limited by walls.
Date: August 1, 1920
Creator: Prandtl, L.
Partner: UNT Libraries Government Documents Department

Tasks of air flow research

Description: The researches at the Gottingen Institute are discussed especially in regards to the physical properties of fluids. The three main properties of fluids examined concern density, viscosity, and compressibility.
Date: June 1, 1926
Creator: Prandtl, L
Partner: UNT Libraries Government Documents Department

Recent results of turbulence research

Description: The first sections of this report deal with two prominent questions, namely the origin of turbulence and the characteristics of turbulent currents. In the third section conclusions are drawn for the flow along a rough wall, whereby an important relation for the velocity distribution is revealed. The principles are also applied to straight rough and smooth tubes.
Date: August 1, 1933
Creator: Prandtl, L
Partner: UNT Libraries Government Documents Department

The New Interpretation of the Laws of Air Resistance

Description: A closer examination of Newton's formula for air resistance shows that it is well to consider the air as an ordinary fluid, and, indeed for most of the velocities considered, as a non-compressible fluid, so long as the dimensions of the moving body are large in comparison with the mean free path of the particles of air.
Date: April 1, 1923
Creator: Prandtl, L
Partner: UNT Libraries Government Documents Department

First experiences with the rotating laboratory

Description: This report describes experiences with a rotating cylinder to explore the effects of motion and flow upon human sensory organs. One observation was that the variation of the resultant line of gravity (from gravity and centrifugal force) was not felt so strongly as might be expected. The impressions produced by the physical effects on the members of the body, especially the ones caused by the deflecting force (Coriolis force), are exactly what the laws of physics would lead us to expect, although somewhat surprising when observed in one's own body.
Date: July 1, 1926
Creator: Prandtl, L
Partner: UNT Libraries Government Documents Department

Note on the calculation of boundary layers

Description: The properties of the solutions of the hydrodynamic equations of viscous fluid by "boundary-layer omission" are discussed. A method is indicated for the numerical determination of the solution for a known initial profile u(x(sub o),y) and pressure distribution p(x) within the region.
Date: November 1, 1940
Creator: Prandtl, L
Partner: UNT Libraries Government Documents Department

Recent work on airfoil theory

Description: The basic ideas of a new method for treating the problem of the airfoil are presented, and a review is given of the problems thus far computed for incompressible and supersonic flows. Test results are reported for the airfoil of circular plan form and the results are shown to agree well with the theory. As a supplement, a theory based on the older methods is presented for the rectangular of small aspect ratio.
Date: December 1, 1940
Creator: Prandtl, L
Partner: UNT Libraries Government Documents Department

Report on Investigation of Developed Turbulence

Description: The recent experiments by Jakob and Erk, on the resistance of flowing water in smooth pipes, which are in good agreement with earlier measurements by Stenton and Pannell, have caused me to change my opinion that the empirical Blasius law (resistance proportional to the 7/4 power of the mean velocity) was applicable up to arbitrarily high Reynolds numbers. According to the new tests the exponent approaches 2 with increasing Reynolds number, where it remains an open question whether or not a specific finite limiting value of the resistance factor lambda is obtained at R = infinity. With the collapse of Blasius' law the requirements which produced the relation that the velocity in the proximity of the wall varied in proportion to the 7th root of the wall distance must also become void. However, it is found that the fundamental assumption that led to this relationship can be generalized so as to furnish a velocity distribution for any empirical resistance law. These fundamental assumptions can be so expressed that for the law of velocity distribution in proximity of the wall as well as for that of friction at the wall, a form can be found in which the pipe diameter no longer occurs, or in other words, that the processes in proximity of a wall are not dependent upon the distance of the opposite wall.
Date: January 18, 1949
Creator: Prandtl, L.
Partner: UNT Libraries Government Documents Department

Motion of fluids with very little viscosity

Description: I have set myself the task to investigate systematically the laws of motion of a fluid whose viscosity is assumed to be very small. The viscosity is supposed to be so small that it can be disregarded wherever there are no great velocity differences nor accumulative effects.
Date: March 1, 1928
Creator: Prandtl, L
Partner: UNT Libraries Government Documents Department

Attaining a steady air stream in wind tunnels

Description: Many experimental arrangements of varying kind involve the problems of assuring a large, steady air stream both as to volume and to time. For this reason a separate discussion of the methods by which this is achieved should prove of particular interest. Motors and blades receive special attention and a review of existent wind tunnels is also provided.
Date: October 1933
Creator: Prandtl, L
Partner: UNT Libraries Government Documents Department

Effect of stabilizing forces on turbulence

Description: The appearance of expressed discontinuity layers in the free atmosphere, where a warm air mass flows over a cold mass without perceptible intermingling forms the basis of the present report. In these experiments an air stream is to be blown between a water-cooled and a vapor-heated plate. According to what preceded it is anticipated that the exchange will be enhanced. Because these experiments had to be made at relatively low air speeds so as to let the lifting forces become effective, it first required a study of the test methods, and so we have not yet proceeded beyond the preliminary tests on the most suitable hot-wire connections and thermocouples for recording speed and temperature.
Date: June 1, 1931
Creator: PRANDTL L
Partner: UNT Libraries Government Documents Department

Induced drag of multiplanes

Description: The most important part of the resistance or drag of a wing system,the induced drag, can be calculated theoretically, when the distribution of lift on the individual wings is known. The calculation is based upon the assumption that the lift on the wings is distributed along the wing in proportion to the ordinates of a semi-ellipse. Formulas and numerical tables are given for calculating the drag. In this connection, the most favorable arrangements of biplanes and triplanes are discussed and the results are further elucidated by means of numerical examples.
Date: February 1, 1924
Creator: Prandtl, L
Partner: UNT Libraries Government Documents Department

Applications of Modern Hydrodynamics to Aeronautics

Description: The report gives, rather briefly, in part one an introduction to hydrodynamics which is designed to give those who have not yet been actively concerned with this science such a grasp of the theoretical underlying principles that they can follow the subsequent developments. In part two there follows a separate discussion of the different questions to be considered, in which the theory of aerofoils claims the greatest portion of the space. The last part is devoted to the application of the aerofoil theory to screw propellers. A table giving the most important quantities is at the end of the report. A short reference list of the literature on the subject and also a table of contents are added.
Date: 1923?~
Creator: Prandtl, L
Partner: UNT Libraries Government Documents Department

Applications of Modern Hydrodynamics to Aeronautics. Part 1: Fundamental Concepts and the Most Important Theorems. Part 2: Applications

Description: A discussion of the principles of hydrodynamics of nonviscous fluids in the case of motion of solid bodies in a fluid is presented. Formulae are derived to demonstrate the transition from the fluid surface to a corresponding 'control surface'. The external forces are compounded of the fluid pressures on the control surface and the forces which are exercised on the fluid by any solid bodies which may be inside of the control surfaces. Illustrations of these formulae as applied to the acquisition of transformations from a known simple flow to new types of flow for other boundaries are given. Theoretical and experimental investigations of models of airship bodies are presented.
Date: 1979?~
Creator: Prandtl, L.
Partner: UNT Libraries Government Documents Department

Theory of lifting surfaces

Description: The general basis of the theory of lifting surfaces is discussed. The problem of the flow of a fluid about a lifting surface of infinite span is examined in terms of the existence of vortexes in the current. A general theory of permanent flow is discussed. Formulas for determining the influence of aspect ratio that may be applied to all wings, whatever their plane form, are given.
Date: July 1920
Creator: Prandtl , L.
Partner: UNT Libraries Government Documents Department