Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/30

§ 8 or jet propulsion be employed) is taken as operating on a certain mass of fluid per second, to which it imparts a certain sternward velocity. It is assumed that the momentum per second so imparted constitutes and accounts for the whole propulsive force, an assumption that under practical conditions is doubtless very close to the truth. In the case of the screw propeller the mass of fluid per second is calculated from the volume of the cylindrical body of water defined by the track of an imaginary circle drawn through the tips of the blades; in other forms of propulsion similar approximate methods of assessment are adopted.

The sternward velocity imparted to the fluid by the propeller is, under proper conditions, small in comparison with the velocity of travel, so that the lines of flow are not radically altered, and instead of a circulation such as arises in the case of a normal plane, there is merely a slight contraction of the stream at the region in which the propeller operates, and a trifling readjustment of the surrounding lines of flow to suit.

In general it would appear that the Newtonian method is applicable in cases where the volume of the fluid handled is great, but where the impressed velocity is small in comparison with the velocity of motion, and where there are well-defined conditions on which to compute the amount of fluid dealt with per second, it is found to be entirely deficient in dealing with the resistance of bodies of smooth contour, or "streamline form," such as may now be discussed.

§ 9. On Streamline Form.—When a body of fish-shaped or ichthyoid form travels in the direction of its axis through a frictionless fluid there is no disturbance left in its wake. Now we have seen that in any case the fluid as a whole receives no momentum, so that it is perhaps scarcely legitimate to argue that there is no resistance because there is no communication of momentum, although this is a common statement. It is clear,