40 X 5,280 X 100 / 60 X 1,200 X 85 = 3.45
or in round numbers a pitch of 3 1/2 feet. 40 (the speed in miles per hour) times 5,280 (feet per mile) divided by 00 (minutes in an hour) gives the speed of the aeroplane in feet per minute. Dividing this by 1,200 (revolutions per minute) gives the number of feet the aeroplane is to advance per revolution of the propeller. The "100/85" part of the equation represents the efficiency of the propeller which can safely be figured on, i.e., 85 per cent, or an allowance for slip of 15 per cent. Forty miles an hour is the maximum speed to be expected, while the r.p.m. rate of the engine should be that at which it operates to the best advantage.
The merits of the true-screw and variable-pitch propellers have already been dwelt upon. The former is not only more simple to build, but experience has shown that, as generally employed, it gives better efficiency. Hence, the propeller under consideration will, be of the true-screw type. Its pitch has already been calculated as 3 1/2 feet. For a machine of this size and power, it should be 6 feet in diameter. Having worked out the pitch and decided upon the diameter, the next and most important thing is to calculate the pitch angle. It will be evident that no two points on the blade will travel through the air at the same speed. Obviously, a point near the tip of the propeller moves faster than one near the hub, just as in rounding a curve, the outer wheel of an automobile has to travel faster than the inner, because it has to travel farther to cover the same ground. For instance, taking the dimensions of the propeller in question it will be seen that its tips will be traveling through the air at close to 4.3 miles per minute, that is,
6 X π X 1200 / 5,280 = 4.28
in which 6, the diameter of the propeller in feet, times π gives the circumference of the circle which is traveled by the blade tips 1,200 times per minute; this divided by the number of feet per mile gives the miles per minute covered. On the other hand, a point on the blade but 6 inches from the hub will turn at only approximately 3,500 feet per minute. Therefore, if every part of the blade is to advance through the air equally, the inner part must be set at a greater angle than the outer part. Each part of the blade must be set at such an angle that at each revolution it will move forward through the air a distance equal to the pitch. This is known as the pitch angle. The pitch divided by the circumference of the circle described by any part of the blade, will give a quantity known as the tangent of an angle for that particular part. The angle corresponding to that tangent may most easily be found by referring to a book of trigonometric tables.
For example, take that part of the blade of a 3 1/2-foot pitch propeller which is 6 inches from the center of the hub. Then
3.5 X 12 / 6 X 2 π = 1.1141 tangent of 48 degrees 5 minutes
in which 3.5 X 12 reduces the pitch to inches, while 6 X 2π is the circumference of the circle described by the point 6 inches from the hub. However, in order to give the propeller blade a proper hold on the air, it must be set at a greater angle than these figures would indicate. That is, it must be given an angle of incidence similar to that given to every one of the supporting planes of the machine. This additional angle ranges from 2 degrees 30 minutes, to 4 degrees, depending upon the speed at which the particular part of the blade travels; the greater the speed, the less the angle. This does not apply to that part of the blade near the hub as the latter is depended upon solely for strength and is not expected to add to the effective thrust of the propeller.
Table II shows the complete set of figures for a blade of 3 1/2-foot pitch, the angles being worked out for sections of the blade 3 inches apart.