Estimation of C^,, for a Complete Airplane Configuration

A Piper Cherokee PA-28 is pictured in Figure 3.62. Pertinent dimensions, areas, weights, and other data are tabulated on the figure. Extrapolating the

Figure 3.62 (Continued)

swept leading edge near the root into the fuselage centerline and accounting for the elliptically shaped tips gives a total wing area when the flaps are extended of 165.1ft2. The area of the wing within the fuselage is 25.3 ft2. Assuming beforehand, or by iteration, a reasonable value for the “stalling speed” of 60 mph leads to a Reynold’s number of approximately 3 x 106 for a wing section. For this Reynold’s number, Reference 3.1 shows a value for C(max of 1.45 for the plain 652-415 airfoil with a lift curve slope of 0.106 CJdeg.

Using an 18.5% chord, single-slotted flap deflected 40°, Figures 3.32, 3.33, and 3.34 predict а ДCt of 1.37 corresponding to an increase of 12.9° in the angle of attack of the zero lift line. ДС, тах is estimated at 1.33 giving a Cimax of 2.78 for the flapped wing sections. The derivative dCJdCi is estimated from Figure 3.31 to equal -0.20. Since CMac — —0.07 for the plain airfoil (Ref. 3.1), Смж— -0.34 for the flapped airfoil.

Accounting for the 2° of washout and the increment of айі caused by flaps leads to an aW(l value of 6.0° from Equation 3.76. This is the angle of attack of the zero lift line at midspan for a zero wing CL. Cta and C, h can then be calculated for the wing alone and are given in Table 3.3. The section Cimax

values are also included in the table. A small amount of trial and error will show that the wing stalls initially at 2ylb of around 0.3 at a wing Cl of 1.97. This estimated wing must next be corrected for the effect of the

fuselage.

However, since the cross section of the Cherokee’s fuselage is essentially rectangular, and with the low-wing configuration, the correction to for the fuselage is taken to be zero.

The aerodynamic moment of the wing is determined by integrating the section pitching moments from the wing-fuselage juncture to the wing tip.

fbl2

M = 2 I qc2Cm dy

J у fuse

Expressed as a moment coefficient,

M

qSc

■ f [IT (?) <-°-34) +L (?) (-oo7) *]

In this case be = S and c = 66 in., and CM becomes

Cm = -0.198

Assuming the increment in drag from the flaps to have a negligible effect on

the trim, Equation 3.82 becomes

= 1.86

In a similar manner, trim values were calculated for flap angles of 0, 10, and 25°. The resulting values were found to be 1.33, 1.42, and 1.70, respectively. These results are presented in Figure 3.63 together with experimental values. The points labeled “flight tests” were obtained by aerospace engineering students at The Pennsylvania State University as one of the experiments in a course on techniques of flight testing. The other two points were calculated from the stalling speeds quoted by the manufacturer in the airplane’s flight manual.