A third class of chart is shown by Fig. 6. This single chart shows three of the factors by means of three curves; one for the lift-coefficient, one for the drag-coefficient, and one for the C. P. movement. Follow the solid curves only, for the dotted lines are for comparison with the results obtained by another laboratory in checking the characteristics of the wing. The curves refer to the R.A.F.-6 section described in the chapter on "Practical Wing Sections." The lift-coefficients Ky will be found at the right of the chart with the drag-coefficients Kx at the left and in the lower column of figures. The upper column at the left is for the C. P. movement and gives the C. P. location in terms of the chord length. The angles of incidence will be found at the bottom. Values are in terms of pounds per square foot, and miles per hour.
Fig. 6. Chart of R.A.F.-6 Wing Section with Three Independent Curves.
In using this chart, start with the angle of incidence at the bottom, and follow up vertically to the lift or drag curves. If the value of Ky is desired, proceed from the required incidence and up to the "Lift" curve, then horizontally to the right. To obtain the drag, follow up from the angle of incidence to the "drift" curve, and then horizontally to the left. For the position of the C. P., trace up from angle until the "Center of Pressure" curve is reached, and then across horizontally to the left. If the angle of 8 degrees is assumed, the lift-coefficient will be found as Ky = 0.0022, the drag Kx =0.00016, and the center of pressure will be located at 0.32 of the chord from the leading edge. This test was made with the air density at 0.07608 pounds per cubic foot, and at a speed of 29.85 miles per hour. The peak at the burble point is fairly flat, and gives a good range of angle before the lift drops to a serious extent. The aerofoil R.A.F.-6 is a practical wing form used in many machines, and this fact should make the chart of special interest.
Surface Calculations. The calculation of lift and drag for an aerofoil are the same as those for a flat plate, that is, the total lift is expressed by the formula: L = KyAV² where A is the area in square feet, and V is the velocity in miles per hour. From this primary equation, the values of the area and velocity may be found by transposition.
A = L/KyV² and V = L/KyA.
The drag can be found from the old equation, D = KxAV², or by dividing the lift by the lift-drag ratio as in the case of the flat plate.
Example: A wing of the R.A.F.-6 form has an area of 200 square feet, and the speed is 60 miles per hour. What is the lift at 6° incidence?
Solution. From Chart No. 6 the lift coefficient Ky is 000185 at 6°, hence the total lift is: L = KyAV² = 0.00185 x 200 x (60 x 60) = 1332 pounds. With an angle of 8 degrees, and with the same speed and area, the lift becomes,
L = 0.0022 x 200 x (60 x 60) = 1584 pounds. The drag coefficient Kx at an angle of 6° is 0.00012, and at 8° is 0.00016. The drag at 6° becomes D = KxAV² = 0.00012 x 200 x (60 x 60) = 86.4 pounds. The lift-drag ratio at this angle is L/D = 1332/864 = 15.4. The drag at 8° is D = KxAV² = 0.00016 x 200 x (60 x 60) = 115.2 pounds. The lift-drag at 8° is L/D = 1584/115.2 = 13.8.