Читать книгу The Rise of the Flying Machine - Hugo Byttebier - Страница 9

Giovanni Borelli and Isaac Newton

Leonardo’s designs inspired none of his contemporaries and two more centuries were to elapse before the problems were again approached scientifically. In 1680 an important book was published posthumously. It was written by Giovanni Alphonso Borelli, a learned Neapolitan doctor who had devoted himself to studying all forms of animal locomotion, including an analysis of the flight of birds, and had been struck by the strength and size of the musculature that moved the birds’ wings.

As a result of these studies, Borelli, like Leonardo two centuries earlier, concluded that man would never be capable of flying with the use of his muscles. This time, however, the problems were not shelved as in Leonardo’s time because the second half of the 17th century saw a major development in western thought based on the study of the surrounding material world.

A few years after the publication of Borelli’s book, and inspired by it, the great English physicist Isaac Newton, took up the problems again and he very carefully studied the movements of elongated shapes through fluids and gases to try to obtain a universal formula governing these movements and the resistance they created.

Newton arrived at a very interesting conclusion, that the resistance of a surface moving through a fluid was dependent on the density of that fluid (moving through air is easier than through water). It was also dependent on the surface of the moving shape and on the square of its speed because great speeds create very great resistance and a great deal of power is needed to overcome them.

The most interesting conclusion Newton reached was that the reaction resulting from the resistance induced by the horizontal movement of a flat body through a fluid at a small angle of incidence was that the moving object was pushed upwards with a force dependent on its surface and the square of its speed.

Newton thus arrived at the formula for calculating the resistance as:

R=KdSV2 sin2 θ.

He defined the resistance, R as a force acting in a direction perpendicular to the surface, and dependent on the density of the fluid (d), the square of the velocity of the incoming fluid stream (V2), the surface area (S), and the angle that the surface makes relative to the initial flow direction (called the angle of attack and represented by θ). K is a constant which could only be found by experimentation.

This formula, except for the square of sinus θ proved to be correct and indicates that the resistance that generates lift increases with the square of the speed, so that, given adequate power to overcome the resistance, any winged object can be made to fly. The emphasis is here on “adequate power” because this was the big hitch that kept the aeroplane enthusiasts from flying for nearly two more centuries.

In stating that the resistance of a moving wing was also dependent on the square of sinus θ. Newton made an error of far-reaching significance because it caused stagnation in aeronautical research, at least in France. Although Newton’s use of the term resistance to describe this force survived until the early twentieth century, it will be less confusing if we substitute it by the modern term reaction force.

In 1780, two French scholars, Condorcet and Monge, in a “rapport” to L’Académie des Sciences arrived at the same conclusions as Borelli whilst Coulomb at about the same time calculated that man, in order to fly, would need wings with a surface area of 12,000 square feet.

Early in the nineteenth century, a group of scientists, among whom were Gay-Lussac, Flourens and Navier, studied Newton’s formula and adapted it to bird flight. Navier, who made the calculations, came to the startling conclusion that seventeen swallows in flight developed a force equivalent to 1 hp.

There were opposing voices, from Bobinet and others, but Navier’s calculations were accepted and presented to L’Académie des Sciences in 1829. So, for about 40 years this brought interest in dynamic flight in France to a standstill.