Aeroplane Construction and Operation

by John B. Rathbun

Complete Power Calculations. Knowing the total weight and the desired speed, we must determine the wing section and area before we start on the actual power calculations. This can either be determined by empirical rules in the case of a preliminary investigation, or by actual calculation by means of the lift coefficients after the approximate values are known. Sustaining a given weight, we can vary the angle, area, wing section, or the speed, the choice of these items being regulated principally by the power. Given a small area and a great angle of incidence, we can support the load, but the power consumption will be excessive because of the low value of the L/D ratio at high angles. If small area is desired, a large value of Ky due to a high lift-wing section is preferable to a low lift wing at high angles. In general, the area should be so arranged that the wing is at the angle of the maximum lift-drag ratio at the rated speed. A low angle means a smaller motor, less fuel, and hence a lighter machine. This selection involves considerable difficulty, and a number of wing sections and areas must be tried by the trial and error method until the most economical combination is discovered.

Graphical Gliding Diagrams of Several Aeroplanes Recorded in British Army Contest of 1912.

The first consideration being the total weight, we must first estimate this from the required live load. This can be estimated from previous examples of nearly the same type. Say that our required live load is 660 pounds, and that a live load factor of 0.30 is used. The total weight now becomes 660/0.30=2200 pounds. To make a preliminary estimate of the area we must find the load per square foot. An empirical formula for biplane loading reads: w = 0.065V - 0.25 where V = maximum speed in M. P. H., and w = load per square foot. If we assume a maximum speed of 90 M. P. H. for our machine, the unit loading is w = (0.065 x 90) - 0.25 = 5.6 pounds per square foot. The approximate area can now be found from 2200/5.6 = 393 square feet. (Call 390.) The minimum speed is about 48 per cent of the maximum, or 43 M. P. H. We can now choose one or more wing sections that will come approximately to our requirements by the use of the basic formula, Ky = w/V².

At high speed, Ky = 5.6/(90 x 90) = 0.000691. At low speed, Ky = 5.6/(40 x 40) = 0.003030. We must choose the most economical wing between these limits of lift, and on reference to our wing section tables we find:

It would seem from the above that the chosen area is a little too large, as the majority of the L/D ratios at high speed are poor, the best being 11.00 of the U.S.A.-1. The angles are small, being negative in most cases at high speed. While the lift-drag of the R.A.F-3 is very good at low speed, it is very poor at high, hence the area for this section should be reduced to increase the loading. The R.A.F.-6 and the U.S.A.-1 show up the best, for they are both near the maximum lift at low speed and have fair L/D ratios at high speed. It will be seen that for the best results there should be a series of power curves drawn for the various wings and areas. This method is too complicated and tedious to take up here, and so we will use U.S.A.-1, which does not really show up so bad at this stage. Both the R.A.F.-6 and the U.S.A.-1 have been used extensively on machines of the size and type under consideration. While we require Ky = 0.003030, and U.S.A-1 gives 0.003165, we will not attempt to utilize this excess, as it will be remembered that we should not assume the maximum lift for reasons of stability.

The wing-drag at high speed will be 2200/11.0 = 200 pounds, and at low speed it will be: 2200/10.4 = 211 pounds. Since the maximum L/D is 17.8 at 3°, where Ky is 0.00133, the least drag will be: 2200/17.8 = 124 pounds. This least drag will occur at V = V5.6/000133 = 65 M. P. H.

The wing drag for each speed must now be divided by the correction factor 0.85, which converts the monoplane values of drag into biplane values. Since this is practically constant it does not affect the relative values of Kx in comparing wings, but it should be used in final results. For this type of machine we will take the total parasitic resistance as r = 0.036V². At 90 M.P.H., r = 0.036 x 90 x 90 = 291.6 pounds. At 65 M. P. H., the resistance is: 0.036 x 65 x 65 = 152.1. At the extreme low speed of 43 M. P.H. we have r - 0.036x43 x 43 = 66.56 pounds. The total resistance (R) is equal to the sum of the wing-drag and the parasitic resistance. At 90 M. P. H. the total resistance becomes 200 + 291.6 = 491.6 pounds. At 65 M.P.H. the total is 124 + 152.1 = 176.1, and at 43 M.P.H. it is 211 + 66.56 = 277.56 pounds. The horsepower is computed from H = RV/375e, and at 90 M. P. H. this is : H = 491.6 x 90/375 x 0.80 = 147.5 H. P. where 0.80 is the assumed propeller efficiency. At 65 M. P. H. the horsepower drops to H = 176.1 x 65/375 x 0.8 = 38.1 H. P., assuming the same efficiency. In the same way the H. P. at 43 M. P. H. r is 39.8.

A table and power chart should be worked out for a number of sections and areas according to the following table. The calculations should be computed at intervals of 5 M. P. H., at least the lower speeds. Wing drag is not corrected for biplane interference: