Aeroplane Construction and Operation

by John B. Rathbun

The efficiency of the average aeroplane propeller will vary from 0.70 to 0.80. If e = propeller efficiency expressed as a decimal, the motor horsepower becomes: H = RV/375e. To obtain the motor horsepower, divide the theoretical horsepower by the efficiency. Using the complete formula for the solution of an example in which the flight speed is 100 M. P. H., the resistance 225 pounds and the efficiency 0.75, we have:

H = RV/375e = 225 x 100/375 x 0.75 = 80 horsepower.

Power Distribution. Since power depends upon the total resistance to be overcome, part of the power will be used for driving the lifting surfaces and a part for overcoming the parasitic resistance. The power required for driving the wings depends upon the angle of incidence, since the drag varies with every angle. The wing power varies with every flight speed, owing to the changes in angle made necessary to support the constant load. The power for the wings will be least at the speed and angle that corresponds to the greatest lift-drag ratio. Owing to the low value of the L/D at very small and very large angles, the power requirements will be excessive at extremely low and high speeds.

As the parasitic resistance increases as the square of the speed, the power for overcoming this resistance will vary as the cube of the speed. It is the parasitic resistance that really limits the higher speeds of the aeroplane, since it increases very rapidly at velocities of over 60 miles per hour.

The total power at any speed is the sum of the wing power and power required for the parasitic resistance. Owing to variations in the wing drag and resistance at every point within the flight range, it is exceedingly difficult to directly calculate the total power at any particular speed. The wing drag and the resistance should be calculated for every speed, and then laid out by a graph or curve. The minimum propeller thrust, or the minimum total resistance, occurs approximately at the speed where the body resistance and wing drag are equal. The minimum horsepower occurs at a low speed, but not the lowest speed, and this will differ with every machine.

Fig. 1. Power Chart of Bleriot Monoplane, With Outline of Wing Section. The Results Were Taken From Full Size Tests Made by the English Government.

Fig. 1 is a set of performance curves drawn from the results of tests on a full size Bleriot monoplane. At the bottom the horizontal row of figures gives the horizontal speed in feet per second. The first column to the left is the horsepower, and the second column is the resistance or drag in pounds. The four curves represent respectively the body resistance, wing or "plane" resistance, horsepower, and total resistance. The horizontal line "AV" shows the available horsepower. It will be noted that the body resistance increases steadily from 9 pounds at 50 feet per second, to 180 pounds at 100 feet per second. The wing resistance, on the other hand, decreases from 350 pounds at 56 feet per second to a minimum of 130 pounds at 83 feet per second. It will be noted that the angles of incidence are marked along the wing-drag curve by small circles. The incidence is 6° at 75 feet per second, and 4° at a little less than 85 feet per second.

The available horsepower "AV" is 42. This is shown as a straight line, although in the majority of cases it is slightly curved owing to variations in power at the higher speeds, and to variations in the propeller efficiency. At 90 feet per second the actual horsepower curve crosses the line of available horsepower "AV." Beyond this point horizontal flight is no longer possible, as the power requirements would exceed the available horsepower. It will be noted that the lowest total resistance occurs near the point where the body and wing resistance curves intersect, or in other words, where the body and wing resistance are equal. The minimum horsepower takes place at 63 feet per second, or at a point nearly 1/3 between the lowest flight speed and the highest speed attained by the available horsepower in horizontal flight (90 ft/sec).

The actual range of flight speeds is limited to points between the intersection of the "Horsepower required" curve, and the "Available horsepower" curve. By increasing the propeller efficiency, or by increasing the power of the motor, the available horsepower line is raised and the flight range increased.