Aeroplane Construction and Operation

by John B. Rathbun

Calculations for Lift and Area. Although the principles of surface calculations were described in the chapter on elementary aerodynamics, it will probably simplify matters to review these calculations at this point. The lift of a wing varies with the product of the area, and the velocity squared, this result being multiplied by the co-efficient of lift (Ky). The co-efficient varies with the wing section, and with the angle of incidence. Stated as a formula: L = KyAV² where A = area in square feet, and V = velocity of the wing in miles per hour. Assuming an area of 200 square feet, a velocity of 80 miles per hour, and with K = 0.0025, the total life (L) becomes: L= KyAV² =0.0025 x 200 x (80 × 80) = 3,200 pounds. Assuming a lift-drag ratio of 16, the "drag" of the wing, or its resistance to horizontal motion, will be expressed by D = L/r=3,200/16=200 pounds, where r = lift-drag ratio. It is this resistance of 200 pounds that the motor must overcome in driving the wings through the air. The total resistance offered by the aeroplane will be equal to the sum of the wing resistance and the head resistance of the body, struts, wiring and other structural parts. In the present instance we will consider only the resistance of the wings.

When the lift co-efficient, speed, and total lift are known, the area can be found from A = L/KyV², the lift, of course, being taken as the total weight of the machine. The area of the supporting surface for a speed of 60 miles per hour, total weight of 2,400 pounds, and a lift co-efficient of 0.002 is calculated as follows:

A = L/KyV² = 2,400/0.002 × (60 × 60) = 333 sq. ft.

A third variation in the formula is that used in finding the value of the lift co-efficient for a particular wing loading. From the weight, speed and area, we can find the co-efficient Ky, and with this value we can find a wing that will correspond to the required co-efficient. This method is particularly convenient when searching for the section with the greatest lift-drag ratio. Ky = L/AV², or when the loading per square foot is known, the co-efficient becomes Ky = L'/V². For example, let us find the co-efficient for a wing loading of 5 pounds per square foot at a velocity of 80 miles per hour. Inserting the numerical values into the equation we have, Ky = L'/V² =5/(80 × 80) = 0.00078. Any wing, at any angle that has a lift co-efficient equal to 0.00078 will support the load at the given speed, although many of the wings would not give a satisfactory lift-drag ratio with this co-efficient.

It should be noted in the above calculations that no correction has been made for "Scale," aspect ratio or biplane interference. In other words, we have assumed the figures as applying to model monoplanes. In the following tables the lift, lift-drag and drag must be corrected, since this data was obtained from model tests on monoplane sections. The effects of biplane interference will be described in the chapter on "Biplane and Triplane Arrangement," but it may be stated that superposing the planes reduces both the lift co-efficient and the liftdrag ratio, the amount of reduction depending upon the relative gap between the surfaces. Thus with a gap equal to the chord, the lift of the biplane surface will only be about 80 per cent of the lift of a monoplane surface of the same area and section.

Wing Test Data. The data given in this chapter is the result of wind tunnel tests made under standard conditions, the greater part of the results being published by the Massachusetts Institute of Technology. The tests were all made on the same size of model and at the same wind speed so that an accurate comparison can be made between the different sections. All values are for monoplane wings with an aspect ratio of 6, the laboratory models being 18x3 inches. The exception to the above test conditions will be found in the tables of the Eiffel 37 and 36 sections, these figures being taken from the results of Eiffel's laboratory. The Eiffel models were 35.4x5.9 inches and were tested at wind velocities of 22.4, 44.8, and 67.2 miles per hour. The tests made at M. I. T. were all made at a wind speed of 30 miles per hour. The lift co-efficient Ky is practically independent of the wing size and wind velocity, but the drag co-efficient Kx varies with both the size and wind velocity, and the variation is not the same for the different wings. The results of the M. I. T. tests were published in "Aviation and Aeronautical Engineering" by Alexander Klemin and G. M. Denkinger.

The R.A.F. Wing Sections. These wings are probably the best known of all wings, although they are inferior to the new U.S.A. sections. They are of English origin, being developed by the Royal Aircraft Factory (R.A.F.), with the tests performed by the National Physical Laboratory at Teddington, England. The R.A.F.-6 is the nearest approach to the all around wing, this section having a fairly high L/D ratio and a good value of Ky for nearly all angles. It is by no means a speed wing nor is it suitable for heavy machines, but it comprises well between these limits and has been extensively used on medium size machines, such as the Curtiss JN4–B, the London and Provincial, and others. The R.A.F-3 has a very high value for Ky, and a very good lift-drag ratio for the high-lift values. It is suitable for seaplanes, bomb droppers and other heavy machines of a like nature that fly at low or moderate speeds. The outlines of these wings are shown by Figs. 7 and 8, and the camber ordinates are marked as percentages of the chord. In laying out a wing rib from these diagrams, the ordinate at any point is obtained by multiplying the chord length in inches by the ordinate factor at that point. Referring to the R.A.F.-3 diagram, Fig. 8, it will be seen that the ordinate for the upper surface at the third station from the entering edge is 0.064. If the chord of the wing is 60 inches, the height of the upper curve measured above the datum line X-X at the third station will be, 0.064 × 60 = 3.84 inches. At the same station, the height of the lower curve will be, 0.016 × 60= 0.96 inch.

The chord is divided into 10 equal parts, and at the entering edge one of the ten parts is subdivided so as to obtain a more accurate curve at this point. In some wing sections it is absolutely necessary to subdivide the first chord division as the curve changes very rapidly in a short distance. The upper curve, especially at the entering edge, is by far the most active part of the section and for this reason particular care should be exercised in getting the correct outline at this point.

Figs. 7-8. R.A.F. Wing Sections. Ordinates as Decimals of the Chord.