If the angle so formed be about 19° (19·45),[28] i.e., 1 in 3, and the point 5 in. from the centre, then every revolution this point will travel a distance
2 π r = 2 × 22/7 × 5 = 31·34.
Now since the inclination is 1 in 3,[29] the propeller will travel forward theoretically one-third of this distance, or
31·43/3 = 10·48 = 10½ in. approx.
Similarly any other case may be dealt with. If the propeller have a uniform constant angle instead of a uniform pitch, then the pitch may be calculated at a point about one-third the length of the blade from the tip.
§ 13. Hollow-Faced Blades.[30]—It must always be carefully borne in mind that a propeller is nothing more nor less than a particular form of aeroplane specially designed to travel a helical path. It should, therefore, be hollow faced and partake of the "stream line" form, a condition not fulfilled if the face of the blade be flat—such a surface cutting into the air with considerable shock, and by no means creating as little undesirable motion in the surrounding medium as possible.
It must not be forgotten that a curved face blade has of necessity an increasing pitch from the cutting to the trailing edge (considering, of course, any particular section). In such a case the pitch is the mean effective pitch.
§ 14. Blade Area.—We have already referred to the fact that the function of a propeller is to produce dynamic thrust—to drive the aeroplane forward by driving the air backwards. At the same time it is most desirable for efficiency that the air should be set in motion as little as possible, this being so much power wasted; to obtain the greatest reaction or thrust the greatest possible volume of air should be accelerated to the smallest velocity.
In marine engineering in slow-speed propellers (where cavitation[31] does not come in) narrow blades are usually used. In high-speed marine propellers (where cavitation is liable to occur) the projected area of the blades is sometimes as much as 0·6 of the total disk area. In the case of aerial propellers, where cavitation does not occur, or not unless the velocity be a very high one (1500 or more a minute), narrow blades are the best. Experiments in marine propulsion also show that the thrust depends more on the disk area than on the width of the blades. All the facts tend to show that for efficiency the blades of the propeller should be narrow, in order that the air may not be acted on for too long a time, and so put too much in motion, and the blades be so separated that one blade does not disturb the molecules of air upon which the next following one must act. Both in the case of marine and aerial propellers multiplicity of blades (i.e. increased blade area) tends to inefficiency of action, apart altogether from the question of weight and constructional difficulties. The question of increasing pitch in the case of hollow-faced blades, considered in the last paragraph, has a very important bearing on the point we are considering. To make a wide blade under such circumstances would be to soon obtain an excessive angle.
In the case of a flat blade the same result holds, because the air has by the contact of its molecules with the "initial minimum width" been already accelerated up to its final velocity, and further area is not only wasted, but inimical to good flights, being our old bugbear "weight in excess."