1、.) n NASA TECHNICAL NOTE AFWL TECHNlCl y e 5 BRY-KIRTLAND AF .-CALCULATIONS, AND COMPARISON WITH AN IDEAL MINIMUM, OF TRIMMED DRAG FOR CONVENTIONAL AND CANARD CONFIGURATIONS HAVING VARIOUS LEVELS OF STATIC STABILITY Milton D. McLuagblin /, , , . Lungley Reseurch Center Humpton, Vu. 23665 NATIONAL AE
2、RONAUTICS AND SPACE ADMINISTRATION WASHINGTON, 0. C. MAY 1977 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TECH LIBRARY KAFB. NM _ -1. Report No. 2. Government Accession No. 3. Recipients Catalog No. NASA TN D-8391 I I 4. Title and Subtitle 5. Rep
3、ort Date CALCULATIONS, AND COMPARISON WITH AN IDEALMINIMUM, OF TRIMMED DRAG FOR CONVENTIONAL AND 1 May 1977 CANARD CONFIGURATIONS HAVING VARIOUS LEVELS OF 6. Performing Organization Code STATIC STABILITY I 7. Author(s) Milton D. McLaughlin 9. Performing Organization Name and Address NASA Langley Res
4、earch Center Hampton, VA 23665 2. Sponsoring Agency Name and Address National Aeronautics and Space Administration Washington, DC 20546 5. Supplementary Notes 6. Abstract I 8. Performing Organization Report No.I L-11016 I 10. Work Unit No. I 512-53-01-12 I 11. Contract or Grant No. 13. Type of Repor
5、t and Period Covered Technical NoteI 14. Sponsoring Agency Code Classical drag equations have been used to calculate total and induced drag and ratios of stabilizer lift to wing lift for a variety of conventional and canard configurations. The study was conducted to compare the flight efficiencies o
6、f such configurations that are trimmed in pitch and have various values of static margin. Another purpose was to make comparisons of the classical calculation methods with more modern lifting-surface theory. 7. Key-Words (Suggested by Authoris) ) 18. Distribution Statement Aerodynamic drag Trim drag
7、 Unclassified - Unlimited Classical drag equations Tandem Static margin Canard Minimum drag Subject Category 02 19. Security Clanif. (of this report) I 20. Security Classif. (of this page) I 21. 1 $3.50 NO; Pages 22. Rice* Unclassified Unclassified For sale by the National Technical information Serv
8、ice, Springfield, Virginia 22161 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-CALCULATIONS, AND COMPARISON WITH AN IDEAL MINIMUM, OF TRIMMED DRAG FOR CONVENTIONAL AND CANARD CONFIGURATIONS HAVING VARIOUS LEVELS OF STATIC STABILITY Milton D. McLaug
9、hlin Langley Research Center SUMMARY Classical drag equations have been used to calculate total and induced drag and ratios of stabilizer lift to wing lift for a variety of conventional and canard configurations. The study was conducted to compare the flight efficiencies of such configurations that
10、are trimmed in pitch and have various values of static margin. Another purpose was to make comparisons of the classical calculation methods with more modern lifting-surface theory. Results from the calculations show that the conventional configurations generally had lower configuration drag coeffici
11、ents, and hence higher flight efficiencies, than canard con figurations with comparable values of gap, static margin, and ratio of stabilizer span to wing span. Also, in general, the canard configurations had larger variations of induced drag with static margin than the conventional configurations e
12、xcept for span ratios near zero, which are not usually employed. The minimum-induced-drag coefficient determined by the classical method was generally in agreement with that determined by lifting-surface theory for the canard configuration studied. This gives confidence in the accuracy of the classi
13、cal calculation method. INTRODUCTION Airplane designs may range from conventional designs, with stabilizer aft; to tandem designs, with wings of equal or nearly equal spans; to canard designs, with stabilizer for ward. With aircraft operating costs increasing, it is desirable to compare the perform
14、ance of these various configurations in order to determine more efficient configurations. The classical biplane theories of Munk and Prandtl (see refs. 1to 4) provide formulas for calculating the induced drag and minimum induced drag of wing and stabilizer configura tions. The total drag of these co
15、nfigurations may be determined by .adding profile drag. These calculations are quite simple and permit the evaluation of the performance of many configurations with little effort. In reference 5 Munks theory is used to show that the Provided by IHSNot for ResaleNo reproduction or networking permitte
16、d without license from IHS-,-,-induced drag of inplane versions of canard and conventional configurations is the same if the canard and tail are carrying equal but opposite trim loads. The purpose of this paper is to assess the performance of various wing and stabi lizer configurations by use of the
17、 classical biplane theory with constraints added to specify static margin and trim for each configuration. Drag and lift ratios are determined for many vertical-gap and span ratios on conventional, tandem; and canard configurations. The drag performance is compared for the different configurations a
18、nd related to an ideal minimum drag (Prandtls method). Also, results from Prandtls minimum-drag method are compared with some values of minimum induced drag calculated by the vortex-lattice method (ref. 6). SYMBOLS A aspect ratio, b2/S b surface span cD drag coefficient, D/qS, total profile -drag co
19、efficient, (cD,P)w(l + 9 cL lift coefficient, L/qSw CLa lift-curve slope C mCL static margin, fraction of Cw Cm,o zero-lift pitching-moment coefficient, MY ,o cmcY pitching -moment -curve slope -C D G K 2 mean aerodynamic chord drag vertical gap between stabilizer and wing ratio of wing lift to tota
20、l lift, individual surface lift when subscripted 4 s positive to rear1 distance from center of gravity to 1c 1- 1 distance from -c4w to 4 cs Mylo pitching moment at zero lift 4 dynamic pressure S surface area V free-stream velocity W normal induced velocity about a surface 4 w positive to rearX dist
21、ance from center of gravity to .i a! angle of attack . Ax distance from reference point to trim point in wing semispans w 2 h ratio of stabilizer aspect ratio to wing aspect ratio, hence, any variation with span ratio is dependent on the relative magnitudes of the profile-drag coefficient CD,P and t
22、he induced-drag param eter CL2/n-Aw. Thus at a higher lift coefficient or a lower profile-drag coefficient, the variation of total drag with 1-1 may show different trends from those of figure 3. The ratios of stabilizer lift to wing lift for canard configurations are higher than those for the conven
23、tional configurations of a given span ratio. (See fig. 3.) The higher lift ratios of the canard configuration result from the static-margin constraint. This “loading up“ of the canard results in a higher drag for the canard configuration than for the conventional configuration. At some points the li
24、ft ratio for the conventional configu ration is lower than the lift ratio for the minimum-drag configuration. In these instances the induced drag is essentially the same. (See figs. 3(b) and 3(c).) Effects of Static Margin The effects of variations in static margin on the induced-drag coefficients a
25、nd lift ratios of conventional and canard configurations with zero gap ratio are shown in figure 4. For a static margin of about zero and a span ratio of 0.6, the induced drag is about 15 per cent less for the conventional configuration than for the canard configuration. The canard configuration sho
26、ws larger variations of induced drag with static margin than the conven tional configuration except for span ratios near zero, which are not usually employed. The lift-ratio plots show that for large span ratios, the canard is loaded to a greater extent than is the tail on the conventional configura
27、tion. In reference 5, Munks theory is used to calculate the trim drag of a conventional and a canard configuration with respectively down and up stabilizer loads of 10 percent of the total lift for trim purposes. The calculations showed that the induced drag was the same for both configurations. The
28、se points are plotted in figure 4 so that the static margin can be seen. The static margin in these two instances is considerably different. The canard monoplane from reference 5 has a static margin of about 0.1, which is unstable; the con ventional monoplane from reference 5 has a static margin of
29、about -0.5, which is usually considered excessively stable. 11 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Effect of Zero-Lift Pitching-Moment Coefficient The zero-lift pitching-moment coefficient Cm,o can have a large effect on config uration dr
30、ag by changing the magnitude of the trim loads. To illustrate the effects of m,? a study was made of the lift ratios and drag coefficients for conventional and canard configurations having various static margins, two gap ratios, and two values of Cm,o. The configurations had a span ratio of 0.3 and
31、C values of 0 and 0.12. The results m,oof this study are presented in figure 5 as a function of static margin. The conventional configurations have lower drag values than the canard configura tions at the larger static margins. The effect of adding a positive Cm,o is to reduce the drag of the conven
32、tional configuration at the higher static margins and to reduce the drag of the canard configuration through nearly all of the static margin range. For Cm,o = 0.12, the canard configurations in the region of interest, near zero static margin, have lower drag values than conventional configurations.
33、The effect on the lift ratio of adding a positive Cm,o is to reduce stabilizer trim loads for both the conventional and canard configurations. This effect can be seen in fig ure 5 as an upward shift of the lift ratios for the conventional configurations and the down ward shift for the canard configu
34、rations. Comparison With Lifting-Surface Theory The results presented so far have been based on the assumption of elliptically loaded surfaces. In practice, the interference effects between the wing and the stabilizer will result in distortion of the lift distribution on the aft surface. This effect
35、 is likely to be most severe for a canard configuration. A comparison of the results of the present method with those obtained by a more accurate analysis is therefore of interest. Some calculations of induced drag by a vortex-lattice method given in reference 6 are used for this purpose. Induced-dr
36、ag coefficients for the canard configuration of reference 6 are given as a function of moment trim point in figure 6 for five values of gap to wing-span ratio GIbw. The configuration planform shown in figure 6 has a ratio of canard span to wing span 1-1 of 0.67. The value of the total lift coefficie
37、nt is 0.2. As indicated in reference 6, the span-wise lift distribution for each surface is almost elliptical. The different values of moment trim points (center-of-gravity locations) were obtained by varying the ratio of canard lift to wing lift. The induced-drag portion of equation (9) was used to
38、gether with interference factors from figure 1to calculate a minimum-induced-drag coefficient for each gap ratio of figure 6. These values are plotted at the proper value of Ax in figure 6. The min b,-/2,imum induced drag obtained by this method gives good results. The difference betweeh the induced
39、-drag coefficients calculated by the two methods is less than 2 counts (0.0002). The close fore-and-aft positions of the canard and wing m,ay contribute to the good agree 12 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-ment shown in figure 6. If t
40、he two surfaces were farther apart in the fore-and-aft direc tion, greater uncertainty would exist in the. relative positions of the wing and the vortex systems. CONCLUDING REMARKS Classical drag equations have been used to calculate total and induced drag and ratios of stabilizer lift to wing lift
41、for a variety of conventional and canard configurations. The study was conducted to compare the flight efficiencies of such configurations that are trimmed in pitch and have various values of static margin. Another purpose was to make comparisons of the classical calculation methods with more modern
42、 lifting-surface theory. The following observations are made on an analysis of this work: The conventional configurations generally had lower configuration drag coefficients, and hence higher flight efficiencies, than canard configurations with comparable values of gap, static margin, and ratio of s
43、tabilizer span to wing span. In general the canard configurations showed larger variations of induced drag with static margin than the conventional configurations except for span ratios near zero, which are not usually employed. For a zero-lift pitching-moment coefficient of 0.12 in the vicinity of
44、zero to small-negative static margins (stable), the canard configurations have lower drag characteristics than conventional configurations with similar values of gap and ratio of stabilizer span to wing span. The minimum induced-drag coefficient determined by the classical calculation method was gen
45、erally in agreement with that determined by the lifting-surface theory for the canard configuration studied. This gives confidence in the accuracy of the classical calculation method. Langley Research Center National Aeronautics and Space Administration Hampton, VA 23665 February 11, 1977 13 Provide
46、d by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-REFERENCES 1. Munk, Max M.: General Biplane Theory. NACA Rep. 151, 1922. 2. Prandtl, L.: Applications of Modern Hydrodynamics to Aeronautics. NACA Rep. 116, 1921. 3. Glauert, H.: The Elements of Aerofoil and A
47、irscrew Theory. Second ed., Cambridge Univ. Press, 1948. 4. Diehl, Walter Stuart: Engineering Aerodynamics. Rev. ed., Ronald Press Co., 1936. 5. Larrabee, E. E.: Trim Drag in the Light of Munks Stagger Theorem. Proceedings of the NASA, Industry, University General Aviation Drag Reduction Workshop, J
48、an Roskam, ed., Univ. of Kansas, July 1975, pp. 319-329. (Available as NASA CR- 145627.) 6. Lamar, John E. : A Vortex-Lattice Method for the Mean Camber Shapes of Trimmed Noncoplanar Planforms With Minimum Vortex Drag. NASA TN D-8090, 1976. 7. Decker, James L.: Prediction of Downwash at Various Angl
49、es of Attack for Arbitrary Tail Locations. Aeronaut. Eng. Rev., vol. 15, no. 8, Aug. 1956, pp. 22-27, 61. 14 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Span ratio, p Figure 1.- Prandtls drag interference factor for multiplane configurations with elliptical span loadings. 15 Provided by IHSNot for ResaleNo reproduction o
