Aeroplane Construction and Operation

by John B. Rathbun

With a given wing area, the span increases directly with an increase in the aspect ratio. The additional weight of the structural members due to an increased span tend to offset the aerodynamic advantages gained by a large aspect ratio, and the increased resistance due to the number and size of the exposed bracing still further reduces the advantage.

Effects of Aspect Ratio. Variations in the aspect ratio do not give the same results in all wing sections, and the lift co-efficient and L/D ratio change in a very irregular manner with the angle of incidence. The following tables give the results obtained by the N. P. L. on a Bleriot wing section, the aspect ratio being plotted against the angle of incidence. The figures are comparative, an aspect factor of unity (1,000) being taken for an aspect ratio of 6 at each angle of incidence. To obtain an approximation for any other wing section at any other aspect ratio, multiply the model test (Aspect=6) by the factor that corresponds to the given angle and aspect ratio. At the extreme right of the table is a column of rough averages, taken without regard to the angles.

The column of average values is not the average of the tabular values but is the average of the results obtained by a number of investigators on different wing sections. Through the small angles of 0° and 2° the low aspect ratios give a maximum Ky greater than with the larger aspects. The larger aspects increase the lift through a larger range of angles but have a lower maximum value for Ky at small angles. Beyond 2° the larger aspect ratios give a greater Ky.

Aspect for Flat Plates. For flat plates the results are different than with cambered sections. The lift-drag ratios are not much improved with an increase in aspect, but the highest maximum lift is obtained with a small aspect ratio. For this reason, a small aspect ratio should be used when a high lift is to be obtained at low speeds with a flat plate as in the case of control surfaces. An aspect ratio of unity is satisfactory for flat vertical rudders since a maximum effect is desirable when taxi-ing over the ground at low speeds. The flat plate effects are not important except for control surfaces, and even in this case the plates are being superseded by double cambered sections.

Reason for Aspect Improvement. The air flows laterally toward the wing tips causing a very decided drop in lift at the outer ends of the wings. The lift-drag ratio is also reduced at this point. The center of pressure moves back near the trailing edge as we approach the tips, the maximum zone of suction on the upper surface being also near the trailing edge. The lift-drag ratio at the center of the plane is between 4 or 5 times that at a point near the tips. All of the desirable characteristics of the wing are exhibited at a point near the center.

When the aspect ratio is increased, the inefficient tips form a smaller percentage of the total wing areas, and hence the losses at the tips are of less importance than would be the case with a small aspect. The end losses are not reduced by end shields or plates, and in attempts to prevent lateral flow by curtains, the losses are actually often increased. Proper design of the form of the wing tip, such as raking the tips, or washing out the camber and incidence, can be relied upon to increase the lift factor. This change in the tips causes the main wind stream to enter the wings in a direction opposite to the lateral leakage flow and therefore reduces the loss. Properly raked tips may increase the lift by 20 per cent.

Effects of Scale (Size and Velocity). In the chapter "Elementary Aerodynamics" it was pointed out that the lift of a surface was obtained by the motion of the air, or the "turbulence" caused by the entering of the plane. It was also explained that the effect of the lift due to turbulence varied as the square of the velocity and directly as the area of the wings. This would indicate that the lift of a small wing (Model) would be in a fixed proportion to a large wing of the same type. This holds true in practice since nearly all laboratories have found by experiment that the lift of a large wing could be computed directly from the results obtained with the model without the use of correction factors. That is to say, that the lift of a large wing with 40 times the area of the model, would give 40 times the lift of the model at the same air speed. In the same way, the lift would be proportional to the squares of the velocities. If the span of the model is taken at "1" feet, and the velocity as V feet per second, the product IV would represent both the model and the full size machine. The lift is due to aerodynamic forces strictly, and hence there should be no reason why the "V²" law should be interfered with in a change from the model to the full size machine.

In the case of drag the conditions are different, since the drag is produced by two factors that vary at different rates. Part of the drag is caused by turbulence or aerodynamic forces and part by skin friction, the former varying as V² while the skin friction varies as V¹.⁸⁸. The aerodynamic drag varies directly with the area or span while the skin friction part of the drag varies as 1⁰.⁹³, where 1 is the span. From considerations of the span and the speed, it will be seen that the frictional resistance increases much slower than the aerodynamic resistance, and consequently the large machine at high speed would give less drag and a higher value of L/D than the small model. In other words, the results of a model test must be corrected for drag and the lift-drag ratio when applied to a full size machine. Such a correction factor is sometimes known as the "Scale factor."

Eiffel gives the correction factor as 1.08, that is the liftdrag ratio of the full size machine will be approximately 1.08 times as great as the model.