Drag and Lift

Abstract

Abstract The problem of the forces that a fluid exerts on a solid body challenged hydrodynamics since d’Alembert’s foundational Essaiof 1752. It only found a quantitative, wide-ranging solution in the first third of the twentieth century, after a few partial successes in the nineteenth century and earlier. The first section of this chapter is devoted to these older attempts, including Newton’s molecular-impact theory, Rayleigh’s dead-water theory, and eddy-resistance theories by Poncelet and Saint-Venant. None of these theories truly succeeded in making quantitative predictions, and they all lacked a solid conceptual basis. Newton’s theory artificially neglected the mutual action of fluid molecules, Rayleigh’s implied an absurdly large wake, and Saint-Venant’s required some observational input. Yet they all contained important elements of the modern understanding of fluid resistance. Newton understood how a similitude argument constrained inertial resistance to be quadratic. Rayleigh’s theory foreshadowed the separation process now admitted for non-streamlined flow. Saint-Venant correctly described the eddy resistance resulting from the instability of separated flow. Section 7.2 is devoted to ship resistance. The development of steam navigation in the Victorian empire motivated the efforts of a few learned engineers to reflect on the optimal shape of ship hulls. John Scott Russell saw how to minimize wave resistance. William Rankine clearly distinguished skin friction, large-eddy resistance, and wave resistance. Lastly, and most importantly, William Froude expressed the conditions for a rational use of models and developed the relevant experimental techniques. In his analysis of skin friction, he finely described what Prandtl later called a turbulent boundary layer. His and Rankine’s insights into the mechanisms of high-Reynolds-number resistance nevertheless remained qualitative. The means were still lacking to turn them into efficient computational schemes.