§ 9. Diameter.—"The diameter (says Mr. T. W.K. Clarke) should be equal to one-quarter the span of the machine."
If we increase the diameter we shall decrease the pitch ratio. From experiments which the writer has made he prefers a lower pitch ratio and increased diameter, viz. a pitch ratio of 1·5, and a diameter of one-third to even one-half the span, or even more.[27] Certainly not less than one-third. Some model makers indulge in a large pitch ratio, angle, diameter, and blade area as well, but such a course is not to be recommended.
§ 10. Theoretical Pitch.—Theoretically the pitch (from boss to tip) should at all points be the same; the boss or centre of the blade at right angles to the plane of rotation, and the angle decreasing as one approaches the tips. This is obvious when one considers that the whole blade has to move forward the same amount. In the diagrams Figs. 23 and 24 the tip A of the propeller travels a distance = 2 π R every revolution. At a point D on the blade, distant r from the centre, the distance is 2 π r. In both instances the two points must advance a distance equal to the pitch, i.e. the distance represented by P O.
Fig. 23.
Fig. 24.
A O = 2πR; D O = 2πr.
A will move along A P, B along B P, and so on. The angles at the points A, B, C ... (Fig. 24), showing the angles at which the corresponding parts of the blade at A, B, C ... in Fig. 23 must be set in order that a uniform pitch may be obtained.
§ 11. If the pitch be not uniform then there will be some portions of the blade which will drag through the air instead of affording useful thrust, and others which will be doing more than they ought, putting air in motion which had better be left quiet. This uniform total pitch for all parts of the propeller is (as already stated) a decreasing rate of pitch from the centre to the edge. With a total pitch of 5 ft., and a radius of 4 ft., and an angle at the circumference of 6°, then the angle of pitch at a point midway between centre and circumference should be 12°, in order that the total pitch may be the same at all parts.
§ 12. To Ascertain the Pitch of a Propeller.—Take any point on one of the blades, and carefully measure the inclination of the blade at that point to the plane of rotation.