Building and Flying an Aeroplane / A practical handbook covering the design, construction, and operation of aeroplanes and gliders

by Charles B. Hayward

The centripetal force varies directly as the square of the velocity of flight and inversely as the instantaneous radius of the curvature of its path.

In applying the above equation to compute the stress in an aeroplane of given mass m, we may assume a series of values for V and R, compute the corresponding values for Fn, and tabulate the results for reference. Table IV has been obtained in this manner. It may be noted that on substituting in the equation, V is taken as representing miles per hour, R as feet, and g as 22 miles an hour, in order to simplify the figuring, this being 32.1 feet per second. The table shows at a glance the centripetal force acting on an aeroplane to be a fractional part of the gravitational force, of weight of the machine and its load. For example, if the aviator is rounding a curve of 300 feet radius at 60 miles per hour, the centripetal force is 0.55 of the total weight. At the excessively high speed of 100 miles per hour and the extremely short radius of 100 feet, the centripetal force would be 4.55 times the weight of the moving mass. The pilot would then feel heavier on his seat than he would sitting still with a man of his own weight on either shoulder. For speeds below 60 miles per hour and radii of curvature above 500 feet, the centripetal force is less than one third of the weight. The table gives values for speeds of 30 to 100 miles per hour, by increments of 10 miles and for radii of curvature of 100 to 500 feet, by increments of 100 feet, so that intermediate speeds and radii may readily be calculated.

The entire stress on the aeroplane in horizontal flight, being substantially the resultant of the total weight and the centripetal force, can readily be figured by compounding them. Thus in horizontal wheeling, the resultant force as shown in the diagram, Fig. 50, is approximately

F = √(Fn²+W²)

In swooping, or undulating in a vertical plane, the resultant force at the bottom of the curve has its maximum value

F = (Fn+W)

and at any other part of the vertical path, it has a more complex though smaller value, which need not be given in detail.

It is obvious that the greatest stress on the machine occurs at the bottom of a swoop, if the machine be made to rebound on a sharp curve. The total force (Fn+W) sustained at this point may be found from the table, if V and R be known, simply by adding 1 to the figures given, then multiplying by the weight of the machine. For example, if the speed be 90 miles per hour and the radius of curvature 200 feet, the total force on the sustaining surface would be 2.84 times the total weight of the machine. In this case, the stress on all parts of the framing would be 2.84 times its value in level flight, when only the weight has to be sustained. The pilot would feel nearly three times his usual weight.