CB No. L4L07 
 
 ' / 
 
 NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS 
 
 WARTIME REPORT 
 
 ORIGINALLY ISSUED 
 
 December I9UU as 
 Confidential Bulletin LUIXDJ 
 
 THE RELATION BETWEEN SPANWISE VARIATIONS IN THE CRITICAL 
 MACH NUMBER AND SPANWISE LOAD DISTRIBUTIONS 
 By Richard T. Whitconib 
 
 Langley Memorial Aeronautical Laboratoiy 
 Langley Field, Va. 
 
 UNIVERSITY OF FLORIDA 
 
 nnrUMENTS DEPARTMENT 
 ?20MARSTON SCIENCE LIBRARY 
 
 PO BOX 117011 ^^,,,«A 
 
 GAINESVILLE.FL 32611-7011 USA 
 
 HACA 
 
 WASHINGTON 
 
 NACA WARTIME REPORTS are reprints of papers originally issued to provide rapid distribution of 
 advance research results to an authorized group requiring them for the war effort. They were pre- 
 viously held under a security status but are now unclassified. Some of these reports were not tech- 
 nically edited. All have been reproduced without change in order to expedite general distribution. 
 
 L - 18b 
 
NAG A CB No. LI4.LO7 
 
 NATIONAL ADVISORY COMITTEE FOR AERONAUTICS 
 
 -•^ f 
 
 CONFIDENTIAL BULLETIN 
 
 THE xRSLATION BSTOEEN SPAN^VISE VARIATIONS IN THE CRITICAL 
 MACH NUMBER AND SPANWISE LOAD DISTRIBUTIONS 
 By Richard T. Whit comb 
 
 SUTvmARY 
 
 Data are presented to show the changes that occur in 
 the spanwise load distributions on wings when the critical 
 Mach number is exceeded. These data indicate that the 
 magnitude of the changes in spanwise load distribution 
 varies with the magnitude of the spanvi/ise variation in 
 the critical Mach numbers of the sections. Means of 
 reducing the magnitudes of such changes are considered. 
 
 INTRODUCTION 
 
 The results of tests of niomerous airfoils at high 
 speeds indicate that there may be considerable changes 
 in the spanwise load distributions on a wing when the 
 critical Mach number of the wing Is exceeded. After 
 the local Mach number on an airfoil section exceeds a 
 value of ujiity, a compression shock is formed that 
 results in a decrease in the lift coefficient on the 
 section for the same angle of attack (references 1 to 5)« 
 These decreases of lift coefficient generalljr occur at 
 different flight speeds on the various sections of a 
 v/ing. A change in the spanwise load distribution would 
 therefore usually be expected to occur on a wing 
 operating at a Mach n^omber above that at which a loss 
 of section lift coefficient first occurs since, at 
 this Mach niomber, some sections will have experienced 
 a greater loss in lift than other sections. Such changes 
 affect the wing bending moments, the airplane trim, and 
 the stability characteristics. 
 
 The possibility that such changes may occur has 
 been recognized for several years (reference l\.) . A 
 means is available for estimating the magnitude of 
 the changes through the use of the low-speed lifting- 
 line theory and two-dimensional high-speed wind-tunnel 
 data (reference 5)' 
 
CONFIDENTIAL NACA CB No. lJ|L07 
 
 An analysis of the results of wind-tunnel tests 
 in two-dimensional flow (references 1 to 3) indicates 
 that the magnitude of the loss in lift coefficient which 
 occurs at supercritical Mach numbers is a fixnction of 
 the amoimt by which the operating Mach number exceeds 
 the critical Mach number. The magnitudes of the changes 
 in the spanwise distribution of load on most airplane 
 wings shouTcPllierefore be expected to vary with the 
 magnitude of the spanwise variations of the section 
 critical Mach number. 
 
 The purpose of the -oresent paper is to illustrate 
 the relationship betvi/een the spanwise variations of 
 load distribution and the section critical Mach number. 
 In order to show this relationship, subcritical and 
 supercritical load distributions and variations of 
 critical Mach number, calculated from pressure measure- 
 ments made during high-speed wind-tunnel tests, are 
 shown for three tapered wings. Means of reducing the 
 indicated changes are considered. 
 
 EXPERIMENTAL RESULTS 
 
 Figure 1 shows the spanwise load distributions for 
 a wing (NACA 23015 root section and NACA ljJil2 tip 
 section) on which there is a large spanwise variation 
 in the section critical Mach number. Figure 2 shows the 
 spanwise load distributions for a wing (Boeing 117 sec- 
 tion, 22 percent thick at root and 12 percent thick at 
 tip) on which the spanwise variation in the section 
 critical Mach niimber is moderate. These two wings were 
 tested in the Langley 8-foot high-speed tunnel. Figure : 
 shows the sDanwise load distributions for a wing 
 (NACA 63 ( 1^2.0-) -1|2 2 root section and NACA 63(l4.20)-517 tip 
 section) on which there is only a slight spanwise 
 variation in the section critical Mach number. This 
 wing was tested in the Ames l6-foot high-speed tunnel. 
 The distributions have been deter^mined for a wing lift 
 coefficient of 0.2. The suoercritical span loadings 
 are for the Mach numbers at which the variations from 
 the subcritical loadings are most pronounced. The 
 loadings are presented in the conventional manner - 
 that is, as cnc plotted against the distance from 
 the center of the wing along the semispan, where Cn is 
 the section normal-force coefficient and c is the 
 section chord. The spanwise variations in the section 
 
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NACA CB JMo. L4LO7 CONFIDENTIAL 
 
 critical Mach number Iv'^-p are also shown in the figures, 
 
 These variations in critical 'fech number are determined 
 for the angles of attack corrisponding to a wing lift 
 coeffici.3nt Ct^ of 0.2 at lotf speeds. 
 
 The results shown were obtained from data recorded 
 during tests of wing models that spanned the throats of 
 the tunne?.s. The air flow over the wing sections near 
 the tips was therefore ai3"oroxlmately two dim.ensional as 
 compared with the flow that vi'ou.ld have been present 
 had the wing been tested with free tips. Unpublished 
 data obtained during vidnd-tunnel tests at high speeds 
 of a wing vi/ith a free tip indicate that the critical 
 Mach nuraber of a wing section is greater when the 
 section is operating in the air flovi near a free tip 
 than v;hen the section is operating in a tv/o-dimensional 
 flovY. If the wings had been tes-tsd with free tips at 
 the same angles of attack, the critical Mach numbers 
 of the tip sections v;ould therefore probably have been 
 greater than the critical Each niLmbers measured during 
 the present tests. 
 
 DISCUSSION 
 
 The results presented in figure 1 show the radical 
 changes that can occur in spanwise load distribution on 
 a wing with a large spanwise variation in the section 
 critical Mach mxmber. A considerable change in load 
 distribution on a wing with a moderate soanv/ise variation 
 in the critical Mach nranber is shown in figure 2, and 
 a negligible change on a wing with a small s-oanwise 
 variation in the critical Mxach n-umber is shown in 
 figure 5. These exnerimental results thus indicate 
 that the magnitude of the change in the spanwise load 
 distribution on a wing at supercritical Mach numbers 
 varies with th') magnitude of the spanwise variation 
 in the critical Mach number of the wirg sections. 
 
 The outboard m.ovement of the csntev of load on the 
 semispan of a wing at supercritical Mach numbers, as 
 shovni in figures 1 and 2, decreases tl'ie downwash in the 
 region of the tail for a given Vving lift coefficient 
 and decreases the change in downwash for a given change 
 in wing lift coefficient. These variations change the 
 elevator deflection required for trim and increase the 
 
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!^. CONFIDENTML NACA CB No. li|L07 
 
 stability of the airplane. Such an outboard movement 
 of the center of load also increases the bending 
 moments on a win-j structure , If the outboard movement 
 occurs v;hen the w'.ng Is supporcing its maximuiri design 
 load, the factor of safety for the wing structure is 
 decreased. The decrease in the lift coefficient on a 
 wing for a given angle of attack at supercritical Mach 
 numbers requires that the angle of attack of the air- 
 plane be increased in order to maintain a given lift 
 coefficient. This increase in angle of attack leads to 
 changes in the elevator deflection required for trim and 
 to increases in the stability at supercritical Mach 
 numbers, in addition to the clianges produced by a 
 spanwise movement of the center of load. 
 
 Because the outboard movement of the center of 
 load produces detrimental changes, this movement should 
 be held to a minimum. A comparison of results in 
 figures 1 to 3 indicates that, for a definite moderate 
 lift coefficient, the outboard movement can be reduced 
 by designing the wing-fuselage combination to give the 
 same critical Mach number for each of the wing sections. 
 The obvious method of obtaining this result is to design 
 the wing with the same section and the same section lift 
 coefficient at each station and to reduce to a minimum 
 the interference effects on the wing. The results 
 r)resented in figure 5 indicate that the same result may 
 be accomplished by using the proper combination of 
 various wing sections. The outboard movement of the 
 center of load may also be reduced by so deflecting 
 "dive-recover^"" flaps olaced inboard on the lower 
 surfaces of the wing that the lift increases on the 
 inboard sections where the greater losses in lift occur. 
 Dive-recovery flaos placed outboard would increase 
 rather than decrease the wing bending moments for a 
 given lift and would be less effective than inboard 
 flaps in reducing the total changes in the elevator 
 deflection required for trim and in reducing the 
 stability of an airplane. 
 
 C0NCLUDIN3 REMARKS 
 
 A comparison of the results of tests of three 
 different tapered wings indicates that the magnitude 
 of the spanwise movement of wing center of load at 
 supercritical Mach numbers varies with the magnitude 
 
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NACA CB No. Lli.L07 CONFIDENTIAL 
 
 of spanwise variation in critical Mach number; conse- 
 quently, it may prove desirable in the design of wings 
 for high-speed airplanes to choose sections, thickness- 
 to-chord ratios of sections, and section load distri- 
 butions to provide a constant value of the spanv/ise 
 critical Mach number. 
 
 Some of the effects of the spanwise shift of the 
 center of load may be overcome by the use of dive- 
 recovery flaps placed inboard. 
 
 Langley Memorial Aeronautical Laboratory 
 
 National Advisory Committee for Aeronautics 
 Langley Field, Va. 
 
 RSFSRENGES 
 
 1. Stack, John, Lindsey, V/. F., and Littell, Robert E. : 
 
 The Compressibility Burble and the Effect of 
 Compressibility on Pressures and Forces Acting 
 on an Airfoil. NAGA Rep, No. 6I4.6, I958. 
 
 2. Stack, John, and von Doenhoff, Albert E.: Tests of 
 
 16 Related Airfoils at Hifh Speeds. NAGA 
 Rep. No. k°2, l°3k' 
 
 3. Stack, John: The N.A.C.A. High-Speed Wind Bannel 
 
 and Tests of Six Propeller Sections. NACA Rep. 
 No. 1+65, 1^33. 
 
 II.. Sibert, H. W., and Lees, Lester: Compressibility 
 
 Phenomena as Related to Airplane Structural Design, 
 AGTR No. I|-52[t. (Revision I), Material Div., 
 Air Corps, July 7, 19[t.2. 
 
 5. Boshar, John: The Determination of Span Load 
 
 Distribution at High Speeds by Use of High-Speed 
 Wind-Tunnel Section Data, NACA ACR No. I4.B22, I9I44. 
 
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NACA CB No. L4L07 
 
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 fig. 1 
 
 Ce-^fer /fne 
 of tunne.1 
 
 Tunnel wall 
 
 Front vicvy of 
 wing 
 
 h 
 
 ?: 
 
 .e^r 
 
 .55 
 
 ftO 
 
 (0 
 
 o 
 
 y 
 
 O 
 
 A 
 
 /^^M=.7Z5 
 
 M=.300 
 
 Eefinnafzd 
 
 3e:nn/^pan 
 
 NATIONAL ADVISORY 
 COMMITTEE FOR AERONAUTICS 
 
 J I I 1 \ I I L. 
 
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 CONFIDENTIAL 
 
 Figure 1.- Measured spanwlse load distributions and spanwise 
 variation of section critical Uach number on tapered wing 
 with NACA 25015 root section and NACA 1+14.12 tip section at 
 Cl = 0.2. 
 
NACA CB No. L4L07 
 
 CONFIDENTIAL 
 
 Fig, 
 
 Ce,nter /ifne 
 /of -tunnel 
 
 Tunnel wall 
 
 Front view of 
 v/ing 
 
 .G5r 
 
 
 .55 
 
 -X— 
 
 I 
 
 C 
 
 o 
 
 (J 
 
 30 
 
 .20 
 
 .10- 
 
 M^JO 
 M=£2 
 
 J L. 
 
 o 
 
 ^ .6 
 
 3enn/spon 
 
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 COMMinEE FOR AERONAUTICS 
 
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 CONFIDENTIAL 
 
 Plgure 2.- Measured spanwise load distributions and spanwlse 
 variation of section critical Mach number on tapered wing 
 with root-section thickness ratio of 22 percent and tip- 
 section thickness ratio of 12 percent at C^ = 0.2. 
 
lACA CB No 
 
 AL07 
 
 CONF'IDENTIAL 
 
 Fig. 
 
 Center line 
 y of i-unn0/ 
 
 .60 
 
 X 
 
 .,55 L 
 
 -X — 
 
 Tunnel wall 
 
 Fhont vler)^ of 
 wing 
 
 — X- 
 
 40 
 
 0) 
 
 .10 - 
 
 o 
 
 M=30 
 f^=70 
 
 ^ .6 
 
 S<2mispan 
 
 NATIONAL ADVISORY 
 COMMin££ FOR AERONAUTICS 
 
 X 
 
 3 fO 
 
 CONFIDENTIAL 
 
 Plgvure 5.- Measured spanwlse load distributions and spanwlse 
 variation of section critical Mach number on tapered wing 
 with NACA 65(U20)-l4.22 root section and NACA 65 (420) -51? 
 tip section at C^ = 0,2. 
 
UNIVERSITY OF FLORIDA 
 
 262 08106 558 2 
 
 UNIVERSITY OF FLORIDA 
 
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