NACA-TN-1175

Abstract

INTRODUCTION <br>One of the problems for which lifting-line theory has proved inadequate (see reference 1) is that of estimating the hinge-moment parameters of finite-span control surfaces from section data. In reference 1 for which experimental data were available for three cases, satisfactory additional aspect-ratio corrections to the hinge moments of ailerons caused by chordwise loading due to angle of attack could be determined by means of lifting-surface theory. <br>Since the publication of reference 1, considerably more section and finite-span (tail surfaces and ailerons) hinge-moment data have become available, and In all eases the slope of the hinge-moment curve against angle of attack (measured at small angles of attack) could be predicted with satisfactory accuracy from the section data by means of the lifting-surface-theory aspect-ratio corrections. Although the lifting-surface-theory aspect-ratio corrections were determined from a linear theory and thus apply only to the range of angles or attack near zero, they are extremely valuable for differing the stick-force gradient for the important high-speed case and are necessary for estimating the stick-free stability characteristics. <br>No lifting-surface-theory solutions were available, however, for wings with chord wise loading due to flap deflection. In order to obtain at least one such solution, an electromagnetic-analogy model (reference 2) of an elliptic wing of aspect ratio 3, with the chord wise loading corresponding to that of a 0.5-chord plain flap in two-dimensional flow, was constricted and tested (reference 3). In order to check the aspect-ratio corrections, determined from the results of the tests on the electromagnetic-analogy model, a semispan wing of the same plan form, same flap-chord ratio, and of the NACA 0009 airfoil section was constructed and tested in the Langley 4,-by 6-foot vertical tunnel. The results of these tests are reported in reference 4. <br>As will be shown (see "Experimental Verification") the wind-tunnel tests provided a satisfactory check of the lifting-surface-theory aspect-ratio corrections both to the variation of hinge-moment coefficients with respect to angle of attack and to flap deflection. <br>Lifting-surface theory appeared to provide an accurate method of predicting finite-span characteristics from section data. It might, however, be many years before sufficient lifting-surface-theory results will be available to determine the corrections for any PIW form or flap-chord ratio because so many variables are involved. The lifting-surface-theory aspect-ratio corrections were determined for elliptic wings; however they apparently could also be applied to unswept wings of other plan forms (see reference 1), even to the rectangular wing as indicated by the data of reference 5. That is, the hinge-moment slopes near zero angle of attack and zero flap deflection were predicted satisfactorily for the rectangular wing of aspect ratio 3 by use of theoretical results for the elliptic wing of aspect ratio 3. <br>The effect of the chord of the flap on the lifting surfaceTheory aspect-ratio corrections was still to be determined; therefore, an electromagnetic-analogy model of an elliptic wing of aspect ratio 3 with elliptic chordwise as well as elliptic spanwise loading (approximately circular camber) (reference 3) and an elliptic wing of aspect- ratio 6 simulating a steady roll were also tested (reference 6). A study of lifting-surface-theory results available (elliptic wings of aspect ratio.3 with angle-of-attack loading, 0.5-chord-flap loading, and parabolic-arc camber and an elliptic wing of aspect ratio 6 with angle-of-attack loading and steady-roll loading) was made and certain consistencies in the results were observed. From these observations. the methods of extending the results so that they would provide lifting-surface-theory aspect-ratio corrections&#160;of satisfactory accuracy for engineering purposes were believed to be practical for horizontal tail surfaces of any flap-chord ratio, of aspect ratios from about 2 to 7,and with almost any plan form provided that the dihedral, taper, and sweep are not excessive. Insufficient lifting-surface-theory data are available, however, to predict the variation of hinge moments with elevator deflections for part-span elevators. <br>The actual method of determining lift and hinge-moment parameters from section data is presented herein in a fairly simple form in "Application of Method." The theoretical development of aspect-ratio corrections to lift and hinge-moment parameters for elliptic wings with constant-percentage-chord, full-span flaps and the methods used to extend these corrections to other plan forms are given in development of Method." <br>A comparison of the available experimental finite-span and section values and of the estimated values of lift and hinge-moment parameters is made for three horizontal tail surfaces and is presented in the section "Experimental Verification."