Aeroplane Construction and Operation

by John B. Rathbun

Streamline Forms. When a body is of such form that it does not cause turbulence when moved through the air, the drag is entirely due to skin friction. Such a body is known as a "streamline form" and approximations are used for the exposed structural parts of aeroplanes in order to reduce the resistance. Streamline bodies are fishlike or torpedo-shaped, as shown by Fig. 2, and it will be noted that the air stream hangs closely to the outline through nearly its entire length. The drag is therefore entirely due to the friction of the air on the sides of the body since there is no turbulence or "discontinuity." In practical bodies it is impossible to prevent the small turbulence (I), but in well-designed forms its effect is almost negligible.

In poor attempts at streamline form, the flow discontinues its adherence to the body at a point near the tail. The poorer the streamline, and the higher the resistance, the sooner the stream starts to break away from the body and cause a turbulent region. The resistance now becomes partly turbulent and partly frictional, with the resistance increasing rapidly as the percentage of the turbulent region is increased.

The fact that the resistance is due to two factors, makes the resistance of an approximate streamline body very difficult to calculate, as the frictional drag and the turbulent drag do not increase at the same rate for different speeds. The drag due to turbulence varies as V squared while the frictional resistance only varies at the rate of V to the 1.86th power, hence the drag due to turbulence increases much faster with the velocity than the frictional component. If we could foretell the percentage of friction, it would be fairly easy to calculate the total effect, but this percentage is exactly what we do not know. The only sure method is to take the results of a full size test.

Fig. 2 gives the approximate section through a streamline strut such as used in the interplane bracing of a biplane. The length is (L) and the width is (d), the latter being measured at the widest point. The relation of the length to the width is known as the "fineness ratio" and in interplane struts this may vary from 2.5 to 4.5, that is, the length of the section ranges from 2.5 to 4.5 times the width. The ideal streamline form has a ratio of from 5. to 5.75. Such large ratios are difficult to obtain with economy on practical struts as the small width would result in a weak strut unless the weight were unduly increased. Interplane struts reach a maximum fineness ratio at about 3.5 to 4.5. Fig. 3 shows the result of a small fineness ratio, the short, stubby body causing the stream to break away near the front and form a large turbulent region in the rear.

An approximate formula showing the relation of fineness ratio and resistance (curvature equal) was developed by A. E. Berriman, and published in "Flight" Nov. 12, 1915. Let D = resistance of a flat plate at a given speed, and R = resistance of a strut at the same speed and of the same area, then the relation between the resistance of the flat plate, and the strut will be expressed by the formula R/D=4L/300d, where L = length of section and d = width as in Fig. 2. This can be transposed for convenience, by assuming the drag of a flat plate as D = 0.003AV², where A = area in square feet, and V = velocity in miles per hour. The ratio of the strut resistance to the flat plate resistance, given by Berriman's formula, can now be multiplied by the flat plate resistance, or strut resistance = R = 0.003AV² X 4L/300d. = 0.012LAV²/300d. It should be understood that the area mentioned above is the greatest area presented to the wind in square feet, and hence is equal to the length of the strut (not section) multiplied by the width (d).

Fig. 3. Imperfect Streamline Body with a Considerable Turbulence Due to the Short, Stubby Form. Fig. 4 Shows the Flow About a Circular Rod or Cylinder.

Assuming the length (L) of the section as 7.5 inches, and the width (d) as one inch, the fineness ratio will be 7.5. Using the Berriman formula in its original form, the relative resistance of the strut and flat plate of same area will be found as R/D=4L/3000 = 0.1, that is, the resistance of a streamline form strut of above fineness ratio will be about 0.1 of a flat plate of the same area. It should be understood that this is only an approximate formula since even struts of the same fineness vary among themselves according to the outline. Results published by the National Physical Laboratory show streamline sections giving 0.07 of the resistance of a flat plate of the same area, with fineness ratio = 6.5. In Fig. 4 the effects of flow about a circular rod is shown, a case where the fineness ratio is 1. The stream follows the body through less than one-half of its circumference, and the turbulent region is very large; almost as great as with the flat plate. A circular rod is far from being even an approach to a perfect form.

In all the cases shown, Figs. 1-2-3-4, it will be noticed that the air is affected for a considerable distance in front of the plane, as it rises to pass over the obstruction before it actually reaches it. The front compression may be perceptible for 6 diameters of the object. From the examination of several good low-resistance streamline forms it seems that the best results are obtained with the blunt nose forward and the thin end aft. The best position for the point of greatest thickness lies from 0.25 to 0.33 per cent of the length from the front end. From the thickest part it tapers out gradually to nothing at the rear end. That portion to the rear of the maximum width is the most important from the standpoint of resistance, for any irregularity in this region causes the stream to break away into a turbulent space. From experiments it has been found that as much as one-half of the entering nose can be cut away without materially increasing the resistance. The cut-off nose may be left flat, and still the loss is only in the neighborhood of 5 per cent.

Resistance Calculations (Turbulency). In any plate or body where the resistance is principally due to turbulent action, as in the flat plate, sphere, cone, etc., the resistance can be computed from the formula R = KAV², where R is the resistance in pounds and K, A, and V are as before. The resistance co-efficient (K) depends upon the shape of the object under standard air conditions, and differs greatly with flat plates, cones, sphere, etc. The area (A) is the area presented to the wind, or is the greatest area that faces the wind, and is taken at right angles to its direction. The following table gives the value of K for the more common forms of objects. See Figs. 4 to 12, inclusive: