Poul La Cour - Experiments in Aerodynamics 1896-1900

Experiments in Aerodynamics 1896-1900

The classical windmills should be able to rotate in a gentle breeze, but the traditional miller was not able to utilize the huge amount of energy in a storm. For la Cour the windmill was a power plant, which should produce a maximum of energy. Therefore the traditional windmill had to be changed, and that was the background for his experiments in aerodynamics starting in 1896. Traditional wisdom considered the action of wind on the wings as an impulse of particles, which made Newtonian calculations possible. Although Daniel Bernoulli and Leonhard Euler had laid the foundation of modern fluid dynamics a hundred years earlier this had had no consequence for such complicated practical problems as that of the action of wind on wings; and in the cases where a computation was possible, theory did not match experience (Paradox of d’Alembert). The union of theory and experiment came mainly through careful wind tunnel experiments. The Danish tradition in this area was started by H. C. Vogt and Johan Irminger in the early 1890s. La Cour continued in 1896 when he started to test small models of windmills in a wind tunnel, probably the first such experiments in the world focusing on windmills. After only a few weeks of experiments la Cour came to the general conclusions that are still accepted: to produce a maximum of energy with a given wing area, the number of wings should be small, their bevel small and the speed of rotation fast. A few years later he presented his results to an audience of engineers: working with the a standard size wing he found that under optimal conditions 8 wings would absorb 28% of the total energy passing swept area, and 16 wings only slightly better (29%), and even 4 wings were fairly good (21%). In a calculation based on the particle conception of wind, he found that the four wings could absorb 144% of the energy which struck them. He concluded that, in general all former theories and formulae concerning wings seemed to be incorrect; and to the extent they were correct, gave no information of any practical importance to the millwright. A closer examination of the quality of la Cour’s wind tunnel shows that the wind speed varies with a factor 2 form the centre line to the edge, thus putting some inaccuracy to his results. He was probably aware of this defect, for throughout 1899 he is very careful in the experimental setup. He now works with small wing sections, flat and curved plates, in the middle of the wind tunnel, and measures both size and direction of the resulting force, thereby discovering the advantages of curved profiles. His curved wing could produce a factor 3 better than the flat wing if there was not to much air resistance to take into account. Based on these experiment he suggested an ideal mill with four times the effect (per m2 wing area) of the average of five existing mills, which he had measured. When he actually in 1899 built a new mill in Askov it was only twice as effective, because of a 7% resistance area. Only twenty years after la Cour’s death a new Askov mill was built in 1929 directly according to la Cour’s “ideal” and this time the factor 4 was obtained. For comparison windmills today are about 3 times as effective as the 1929 mill. Needles to say that there are some assumptions and problems with all these comparisons, but they do indicate that an important step forward was made by la Cour.