IVAC A- L'((?7 KB Ko. L5F15a NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIME REPORT ORIGINALLY ISSUED July 19U5 as Restricted Bulletin L5F15a TABLES MD CHARTS FOR THE EVALUATIOn OF PROFILE URAG FROM WAKE SDRVEYS AT HIGH SUBSONIC SPEETS ih.' * ■ By l>fcrron J. Block and S. Katzoff Langley Memorial Aeronautical Laboratory Langley Field, Va. NACA «^ I 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 - 107 DOCUMENTS DEPARTMh.Ni' NACA RB l^To. L5?15a NATIONAL ADVISORY COKMITTEE FOR AERONAUTICS 7/ J 000 9%- RESTRICTED BULLETIN TABLES AND CMRTS FOR THE EVALUATION OP PROFILE DRAG FROM WAKE SURVEYS AT IIIGPI SU:8S0NIC SPEEDS By Myron J. Block and S. Katzoff SUIvaiARY Tables and charts for the evaluation of profile drag from v/ake surveys at high subsonic speeds are presented. These tables and ch^arts are for use with ty/o methods of evaluation, an exact method that may be applied to wakes of any shape and a simple approximate method that may be applied when the variation of total-pressure loss across the wake has the typical form (resembling a cycle of a cosine-squared curve). IKTRODUCTION As an aid in the determination of profile drag from v;ake surveys at high subsonic speeds, tables and charts have been prepared to minimize the computational labor involved. These tables and charts are presented herein, together with a brief discussion of their application. The data are for both the approximate method of refer- ence 1, which simply applies a correction factor to the integral of the total-pressure loss across the v;ake, and the exact point-by-point method, for use when the distri- bution of total-pressure loss across the wake does not follow the tjrpical pattern. The data for both methods are for Mach numbers up to 1.0. SB!BOLS c chord d drag per unit span 2 NACa R3 No. L5P15^ c^ section iDrof ile-drag coefficient ^ _ F factor for evaluation of drag coefficient Dy aporoximate method H total pressure M Ivlach number p static oresoui'e V velocity w thickness of wake y distance across wake p density Subscripts: free stream 1 at plane of measurement max maximum THEORY AND METHOD The basic theory of the use of wake surveys for the measurement of v^ring profile drag has been largely dis- cussed in Drevious literature (for example, reference 2). No further discussion of the equations used will there- fore be given, except to note that the ratio of specific heats for air was taken as l-l^Oii,. Theoretical and experi- mental studies have confirmed thcit the basic assumptions - for example, that essentially streamline flow exists in the v/ake dovmstream of the measuring station and that the stagnation temperature in the wake is the same ds in the free stream - are accurate or are satisfactory aoproxi- mations to the actual conditions. Errors are more likely to arise from sources of a less fundairiental nature, such as from, cross flows of the wing boundary layer, which m.ay confuse the relation between the wake at a certain spanv/ise station and the profile drag of the wing at that NACA RB I'lo. L5?15a station, or from so high a degree of turbulence in the wake (as behind a flap) that both the method and the pressure readings are invalid. CHARTS AND TABLES FOR POINT -BY- POINT CaLCULATIONS The flight Mach number M^-, and the flight impact pressure Hq - pQ are assumed to be known, in addition to the values of total-pressure deficiency Hq - H]_ and of static-pressure rise p-|_ - Pq at r^oints in the wake. Table I and figure 1 give the factor ^(""^o) /Ho - Hi dy /Ho - ?o or Drag per unit span per unit thickness of wake / Hq ~ H^ IpoVo-^ / ''" ' '° Hq ~ -^^1 ^1 ~ P^ as a function of Mq, , and ^-^ ^. Multiplying Ho - Po Hq - p^ this factor by the fractional loss of impact pressure at Hq - Hi a point in the wake gives the value of cc^j , Ho - Po which corresponds to unit thickness of wake at that point. Integration of this value across the vvake gives cch for the section. The values given herein were com.puted in some detail for Mq = 0, 0.2, O.li, 0.6, 0.8, and 1.0, and for ^ •; Pt - P ^1 "• o Tz = -0.1, 0, 0.1, and 0.2. The- values for other ^o " Po Mach numbers and pressure ratios v^'ere found- by interpo- lation and numerous calculated checks were made. The factors are accurate within ±0.002. i|. NaCh RB No. L5?15a CHARTS FOR APPROXIMATE METHOD v'Vhen the distribution of total-pressure loss across the wake follows the typical pattern, profile drag can be obtained w;ith good accuracy by a relatively simple method (I'eference 1). In this method, the drag Is deter- mined directly from the product of the Integral of total- is Ho - Hi pressure loss across the wake / — ■ dy-. and a fac- I «o - P3 tor P, which is a function of the m-axlmum total-pressure loss in the wake, the average static pressure in the wake, and the flight Mach number; thus, t ^o - ^^1 /H., - il.\ Pn - P ■ where F is a function of ( — =• ) , ~ -, V"° - ■=%«. ''° - "- and Mq . In practice the Integral is obtained either by use of an integrating manometer or by actual integration of point-by- point measurements of Hq - H-, In the v;ake. Values of F are plotted in figure 2. The values were comouted by assuming that the total-pressure loss across the wake had a cosine- squared distribution ^ ^ -^ max and by dividing the value of cc^ , as computed by the f Ho - Hi point-by-point method, by the value of / — dy-i . 4 ^o " Pq Figure 2, which gives P directly for i.Iach numbers from to 1.0, Is considerably more convenient to use than the data of reference 1, which gives F directly only for Mq = and Includes a table of corrections for values of Mq other than zero. It should be pointed NACA R3 No. L5F15a out further that the correction table of reference 1 contains some systematic errors that are appreciable at high Mach numbers. The results presented herein are considered accurate (for an exact cosine-squared profile) to about ±0.2 percent. Although this simplified procedure can greatly expedite the commutation of wing profile drag, its appli- cation definitely requires that the wake profile bear a reasonable resemblance to the assumed cosine-squared profile, especially for wakes with large values of /Ho - HA [ r; 1 . Even v;lth an appreciable deformity from \^^ " Po/max the usual profile, however, the error in the use of this method will hardly exceed 2 percent. As in the case of a shock where the wake profile shov;s a relatively narro«v peak superimposed on a broad base (fig. 3)> the error, hov/ever, may easily become excessive. When point-by- point measurements in the wake are available, accuracy can be retained in such a case by considering the wake in two parts, as indicated in figure J; each part shows a satisfactory approximation to a cosine-squared profile but each has a different value of - V RELATED CHARTS Another paper (reference J) has been prepared that gives results related to those given in the present paper. In reference 5> charts are given of the ratio of P for compressible flow to P for incompressible flow for Mach numbers to 1.0, for values of — from -O.I4. to 0.1, Ho - Po and for values of ( -2 — , — i,) from to 0.7. A seoa,- \^ " ^o/max rate.chart is given of P for incompressible flow. I , Langley Memorial Aeronautical Laboratory National Advisory Committee for Aeronautics Langley Field, Va. NAG A R3 No. L5F15a REFERENCES 1. Silvsrstein, A., and Katzoff, S.; A Simplified Method for Deter-riinin.y ■■■ing Profile Drag in Plight, Jour. Aero. Sci., vol. 7", no. 7, May 19i^-0, pp. "295-501. 2. Davis, vVallace F.: Coraparison of Variovis L'ethods for Cor-.puting Drag from '.'/al^e Surveys. NACA AHR, Jan. 19if5. 3. Keaslet, Hax A.: Tlieoretical Investigation of Methods for CoLiputing Draf^ fi-on V/ake Surveys at Hish Sub- sonic Speeds. NACA ARR No. 5C21, 1945 . ADDENDUI/I The authors v;ish to call attention to the follov.'ing related papers Baals, Donald D., and Mourhess, Mary J.: Nuinerical Evalu- ation of the Jake -Survey Equations for Subsonic Flow Including the Effect of Energy Addition, NACa ARR No. L5H27, 191^5 which has appeared since publication of the present bulletin. The tables and charts of this related paper, ;mich is concerned only with the point-by-point method, are for use not onlj v;ith flows of constant total energy, as in ncrrrial wakes, but also v/ith flov/s of increased total energy, as in vvakes of propellers and jet-propulsion units. Total- pressure and static-pressure coefficients are based en 1 p S'Po^'o instead of on H - p as in the present bulletin. NACA RB No. L5Fl5a TABLE I.- VAWSS OP T^^/s^ ^ TOR EVALOATIOH or 7R07ZLE ERAO PRGM WAKZ auAVKy \^ Pi - Po -0.100 - ).075 - ).050 -0.025 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 ■h^^-'" ^ - Po \^^ 1.01*8 1 056 1 021i 1.012 1.000 0.988 0.975 0.962 0.949 0.956 0.925 0.909 0.895 .025 1.0U5 1 051 1 018 1.006 •994 .981 .968 ■955 .942 ■927 •915 .900 .886 .o;o 1.058 1 025 1 012 1.000 • 967 • 974 .961 • 948 ■ 954 .920 •907 .892 • 877 •075 1.052 1 019 1 006 ■993 .960 •967 • 954 • 940 .926 • 912 •899 .885 .868 .100 1.026 1 013 1 000 • 987 •975 .960 • 946 •932 .918 •904 • 890 .875 .859 .125 1.020 1 007 994 .980 .966 •955 • 938 ■924 .910 •895 .681 .865 • 849 .150 i.oiu 1 001 988 •975 ■959 • 945 • 950 .916 .901 .886 .671 .855 • 859 • 175 1.008 995 981 • 966 .952 • 957 .922 •908 .892 •877 .861 •845 .829 .200 1.002 988 97U • 959 ■944 • 929 .914 •699 .885 .867 .851 ■855 .816 .225 •995 981 967 •951 ■ 956 ■921 • 905 .890 .874 .858 .841 .825 .807 .250 .988 97U 959 •943 .926 ■ 912 .896 .880 .864 .847 • B50 • 613 .795 .275 .981 967 951 .955 .920 .903 .867 .870 ■854 • 857 .819 .801 .785 .JOO • 97U 959 9W •927 .911 •894 .878 .860 .644 • 626 .808 •789 ■770 .325 .967 951 955 .919 .902 .885 .868 .850 .835 .814 •796 ■777 • 757 •J50 •959 9W 927 .910 .893 ■875 .858 .859 .621 .805 •785 ■ 764 •745 -375 •951 955 9IB .901 .883 .865 .847 .828 .809 • 790 • 770 ■750 .728 .l»00 •91*5 926 909 .891 .873 •655 .836 .817 ■797 •777 • 756 ■735 .715 .lp25 •955 917 899 .881 .863 ■844 .824 .805 •784 • 764 •741 • 720 .697 •1*50 .926 908 889 .871 .852 .832 .811 • 792 .770 ■749 • 726 ■702 • 679 .W5 • 917 898 879 .860 .840 .820 • 79s •778 • 756 ■755 .710 • 685 .661 .500 .908 889 869 849 .828 .807 • 785 ■763 • 741 •718 .694 .669 .642 •525 .898 879 858 •657 .816 • 794 •771 ■ 748 •725 ■ 701 .675 .648 .620 • 550 .888 868 847 .825 .803 .781 • 756 ■755 .706 .685 .656 •627 • 597 • 575 .877 856 835 .612 ■789 .766 •741 .717 .691 .664 .636 .606 .575 • 600 • 866 6Uk 822 ■799 ■775 •750 • 725 • 699 •672 ■ 645 .614 .582 • 54s •625 • 855 832 809 .785 .760 • 754 .707 .681 •652 ■ 622 .590 • 557 .521 •650 • 8U5 819 795 • 770 .744 .717 .668 .660 .650 ■597 .564 •525 .488 • 675 .850 806 781 •754 ■ 726 .698 .667 .657 .606 .570 .554 •493 •451 .700 .817 792 766 • 757 .708 .676 .646 .613 .578 ■ 540 .500 •456 •409 ■725 .805 777 749 ■ 719 .686 .636 .622 • 587 • 548 .508 .462 .416 • 557 .750 • 789 760 751 .699 .667 • 654 •596 •558 .516 ■ 470 • 422 .565 .298 •775 •7-'5 71^ 712 .678 .644 .605 .568 • 524 .479 .429 • 572 • 303 .214 .600 • 757 724 690 •655 .618 • 579 ■556 .488 •437 ■ 579 .509 .218 .825 ■7kO 706 470 •651 .590 • 547 ■498 .446 .586 ■515 ■ 225 .850 • 721 685 6kt .604 ■ 558 • 509 •456 ■595 • 321 ■ 228 .875 .701 662 619 •572 • 522 •466 ■405 • 550 .234 .900 .679 6J5 587 • 536 .480 .416 • 540 .£1*0 .925 • 657 6O8 550 .496 .450 • 550 •246 .950 • 655 578 517 •446 • 565 .256 •975 .610 5W 475 .586 • 275 1.000 .6}2 5U8 U47 • 516 BATIOBAL ADVISORY COKIIITTZE TOR AERONAtTTICS Digitized by tine Internet Arclnive in 2011 witln funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/tableschartsforeOOIang NACA RB No. L5Fl5a 8 (J(cc,l^) /Ho - Bi TABLE I . - VAL0I3 .OP / POR IVAUIATIOI ij / Bo - Po OP PROPILB DIUO PROM «AKS SURVEY - Contlnutd "0 = 0.1 "^\, Pi - I>o -O.IOO -0 075 -0.050 -0.025 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 Ho-HJ-^" Bo - Po \^ 1.0lt2 1 029 1.018 1.005 0.993 0.981 0.968 0.956 0.945 0.951 0.917 0.901( 0.890 .025 1-057 1 024 1.015 •999 .987 ■97l( ■961 ■949 •956 ■925 .910 .896 .832 .050 1.031 1 018 1.007 ■99l( .980 .968 ■'955 ■ 942 .929 ■915 .902 .887 ■873 •075 1.025 1 013 1.001 .988 ■975 ■962 ■ 948 • 935 • 921 .908 •894 .879 .861( .100 1.019 I 007 ■ 99l( .981 •967 ■ 954 ■941 •927 •914 ■899 •885 .870 .855 .125 1.014 1 001 .988 .975 ■961 ■ 947 ■955 •919 .905 .890 .876 .860 • 81(5 150 1.008 996 .982 • 969 ■95l( ■ 940 ■925 •911 .896 .881 .867 .851 ■ 835 ■175 1.002 989 ■975 •962 ■ 91(7 • 932 .918 .903 .888 .875 .858 • 81(2 ■ 825 .200 .995 981 .9*8 ■ 95k ■ 939 ■ 925 .910 .894 ■879 .863 .848 .832 ■ 815 .225 •989 975 .961 • 9W • 931 .916 .901 .886 .871 .854 .858 .821 .804 .250 •985 969 ■951* •939 ■923 .908 893 .877 .862 .845 .826 .810 .792 ■ 275 .976 965 ■ JW ■ 932 •915 •899 .885 .867 .852 •835 .817 .799 .780 .300 ■969 955 ■ 938 •925 • 906 .890 •874 .857 .841 .823 .805 .787 ■768 •325 ■962 91(7 ■930 • 914 .898 .881 •86k. .847 .829 .812 .795 .774 ■755 •J50 ■955 939 .922 .905 .889 .871 • 855 .836 .818 ■799 .780 •761 ■ 741 .375 .9U7 930 ■913 .896 •879 .861 • 845 .824 .806 .786 .767 ■747 • 727 .1(00 •939 921 • 901* .887 .870 .850 .832 .812 .793 ■ 775 •755 •732 .712 .U25 .931 915 •895 • 877 .860 .840 .821 .801 .781 .760 • 759 .718 ■695 .1(50 •923 905 .886 .868 • 81(9 .829 .809 .789 .768 •747 .725 .702 ■679 ■m ■915 895 .876 • 857 .83a .818 .777 ■ 776 ■ 754 •752 •709 .685 .661 .500 .906 886 .666 .81(6 .Ba« .805 •784 ■762 .740 .71* .692 .666 .642 .525 .896 876 ■855 •835 .8ll( •792 .770 ■747 ■ 724 •699 ■ 674 .647 .620 •550 .886 866 •81(1» .82l( .801 ■779 .756 ■732 ■ 707 .680 .654 .627 ■ 598 ■575 .875 855 .B}2 .811 .788 ■764 • Y40 •715 .689 .661 • 633 .601( ■ 574 .600 .861; SItk .820 • 797 ■773 •749 .724 ■ 697 .671 .640 • 611 .580 .548 .625 .853 831 .807 .783 ■ 758 • 752 .706 ■ 677 .650 .619 • 586 • 556 •520 .650 .81(1 818 ■79k •769 ■ 7l|2 •715 .686 •657 .628 .595 • 5(.0 • 525 .1(88 .<75 .829 SOU •779 •752 ■725 ■ 696 .666 • 635 .601( •570 • 531 •495 •450 .700 .815 789 •763 •734 .706 • 676 .644 .612 .577 .540 .500 ■457 •409 •725 • 802 775 •7U7 .716 .686 •654 .620 .586 • 549 .508 .464 •415 •362 .750 .788 759 •729 • 697 .665 ■631 ■ 594 • 557 • 515 .472 .1(22 •567 .298 .775 .773 71(5 .710 .676 • 61(3 .604 ■ 565 • 525 •479 .430 •372 • 304 •21J .800 .757 725 .691 .655 .618 • 577 .534 •USS •437 .378 .310 • 218 .825 .739 70l( .669 .629 .590 • 544 •499 .446 .586 • 316 .223 .850 .720 683 • 61(1( .603 ■ 556 .510 •455 ■395 • 322 .228 .875 .700 659 • 617 ■ 57k ■ 521 •465 •405 .350 ■235 .900 .679 631( • 585 • 535 .1(76 .415 • 340 • 242 •925 .657 608 • 552 • 1(93 ■ 1*29 •351 •249 .950 .633 578 • 515 ■ kkk ■ 565 .260 •975 .610 5W .1(72 .381 • 274 1.000 .633 51(7 ■wr .316 NATIONAI, ADVISORY COMXITTEE POR AZRONAOTICS NACA RB No. L5Fl5a TABLE I.- VALUES OP /— POR EVALDATIOH "T /Ho - Po 07 PROFILE DRAG PROM WAKE 3DRTST - Contlnuad "o = 0.2 \ Pi - Po -0.100 -0.075 -0.050 -0.025 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 \. Ho - Do Ho - Hr\ Ho - Po \^ 1.02S 1.017 1.006 0.991* 0.982 0.970 0.958 0.91*6 0.935 0.921 0.908 0.895 0.881 .025 1.025 1.012 1.001 .988 .976 .961* .952 •939 .926 • 915 .900 .887 .875 .050 1.018 1.007 .995 •983 •970 958 ■91*5 •932 .919 .906 .892 .879 .865 .075 1.013 1. 001 •989 • 977 • 961* •952 ■939 ■925 .912 .898 .881* .870 .856 .100 1.007 .995 .983 • 971 • 958 •91*5 ■932 • 918 • 901* .890 .876 .862 .81*7 .125 1.002 .989 ■977 • 961* •952 • 958 ■921* .910 • 896 .882 .868 .855 •857 .150 .996 .985 ■ 971 .958 •91*5 ■ 931 •917 .902 .886 • 871* .859 • 8M* .827 • 175 .990 ■ 978 ■965 .951 •958 ■ 925 .909 .895 .880 .865 .850 •851* .817 .200 • 985 .972 ■ 958 • 9U* • 930 .917 .902 .887 .872 .656 .81*0 .821* .807 .225 ■979 .965 ■ 951 .937 • 925 • 909 .891* •879 .865 • 81*7 .850 .811* • 796 .250 • 975 ■959 •9U» • 930 •915 .901 .886 .870 .851* •837 .820 .803 • 786 • 275 .967 ■952 • 937 • 922 .908 • 895 •877 .860 .8U* .827 .810 .793 • 775 .JOO .960 ■9i;5 •950 •915 .900 .881* .868 .851 .851* .817 .799 .781 •765 •525 •953 ■ 938 • 923 .908 .892 .87« • 858 .81a .825 ■ 805 .788 •769 •750 •550 • 9W • 931 .915 .899 .865 .866 • 81*8 .830 .812 ■791* .771* .756 • 756 • 375 .939 • 923 •907 .890 .823 .855 .858 .819 .801 .782 .762 •71*2 .722 .ItOO • 931 .915 .898 .881 .865 •8U5 .827 .808 .789 .769 • 71*8 • 727 .707 .1(25 ■923 .907 .889 .872 ■ 85 J •856 .816 •797 • 777 •756 •731* .713 .691 ■450 •915 ■ 897 .880 .862 ■ 81*5 .821* .801* •785 • 761* • 71*2 .720 •699 .671* ■U75 .906 .888 .870 .851 .832 .812 .792 •771 •750 • 727 .705 .682 .656 .500 .897 ■ 879 .860 .Bia .820 .800 •779 • 758 •755 • 713 .689 .661* • 657 • 525 .888 ■ 869 .850 .850 .808 ■787 •765 • 71*3 .720 .697 .671 .61*6 • 616 • 550 .878 .859 •839 .819 • 795 ■773 •751 .728 .70U .678 .651 .621* • 59U • 575 .868 .8U8 .827 .806 • 782 •759 .736 .712 .685 • 659 .651 .60} .•570 .600 .858 ■ 837 .815 .792 •768 • 7W* •720 .691* .666 • 639 .609 • 578 .51*5 .625 .81*7 ■ 824 .802 .778 •753 ■ 728 •705 •675 .61*6 .616 .586 .552 .518 .650 ■835 .811 .788 .762 •737 •711 .685 .656 .621* .591* • 561 ■521* .1*87 •675 .823 .798 •771* .71*7 •721 • 695 .665 •635 .601 .568 •531 •t*93 .1*55 .700 .810 ■ 785 •759 •732 .705 • 671* .6U* • 6U .576 .538 ■1*98 •1*58 .1*08 •725 ■ 797 ■769 •7U2 •711* .681* •652 .620 .586 •51*9 • 507 .1*62 •1*15 .365 • 750 ■ 783 .751* ■72U • 691* .665 .629 • 595 • 557 •515 •1*69 .1*22 • 368 .298 ■775 .768 .758 .706 .671* .61*0 .601* • 566 .526 •1*77 .1*28 .571 .301* .215 .800 •752 .719 .686 .651 .615 ■576 .533 .1*86 •1*35 ■ .378 .310 .218 ■ 825 ■755 .699 .661* .628 .588 ■ 5U* .1*97 •1*1*2 .586 .516 .221* .850 .716 .679 .61*0 .602 •55I4 .50a .1*51* •395 .522 .230 .875 .696 .658 .615 •572 .521 .1*65 •1*05 • 328 .256 .900 .675 .631 ■ 585 •536 .1*80 • 1*15 .31*0 .21,2 .925 .651* .606 •551* .1*95 .1*29 ■352 • 21*9 .950 .632 •579 ■ 511* •1*1*3 •565 .260 ■ 975 .609 •51*5 ■1*72 .581 • 275 1.000 .633 • 5W ■M*7 .J16 HATIONAl ADVI30RI COMMITTEE P0.1 AER0KADTIC3 NACA RB No. L5Fl5a 10 ll(cca_) TABLS I.- VALtnS OP <17 ' / Hq - Hi "/ Ho - Po FOR IVALQUIOII OF P!!??ii.i mua man »axx ainvn - continuwi "0" O.J \^ Pi - Po -0.100 -0.075 -0.050 -0.025 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 Ho - H] Ho - Po Ho - Pi i.ooU 0.9914 0.985 0.972 0.962 0.949 0.958 0.926 0.914 0.902 0.890 0.878 0^865 .025 1.000 • 990 .979 .968 .957 .944 ■955 .920 .908 .S96 .885 .871 .858 050 •995 .986 .974 • 965 .951 •958 .926 .914 .902 .890 .876 .863 .850 075 .991 .980 .969 • 957 • 945 •932 .920 .908 •895 .882 • 869 .855 .842 100 .986 ■ 974 .964 •951 • 959 .927 .914 .901 .888 .875 • 862 .847 .853 125 .981 .969 .958 .945 •955 •921 .908 .394 .881 .867 .854 .838 .824 150 .976 .96U • 952 •959 •927 .914 .901 .887 .873 .859 .845 .830 .815 175 •971 ■958 • 946 •955 •921 ■907 • 894 .880 • 865 .851 •837 .822 .806 200 ■ 965 ■952 .940 .927 .914 .901 .887 .875 .857 .843 .828 .812 .796 225 .959 .9U6 • 954 921 .907 .894 .880 .966 .849 •855 •819 .802 .786 250 ■ 955 .91*0 .927 .914 .900 .886 .872 .857 .841 .826 .809 .795 .775 275 ■ 9W • 934 ■ 920 .907 .892 .878 .863 .848 .852 .816 .799 .785 •764 JOO .9lt2 • 927 .915 .899 .884 .B70 .854 .857 • 822 .804 .788 .771 •752 }25 .955 .920 .906 .892 • 876 .862 .845 .828 • 812 •794 •777 .758 .740 550 .928 .914 ■899 .885 .86a ■ 854 .836 .820 .802 .784 • 766 • 746 •727 575 .922 .907 .892 .877 ■859 .844 .826 .809 .791 • 772 •754 •755 .714 IlOO .915 .900 .884 .867 .850 .853 .816 .798 .779 •761 .741 .720 •699 l4i5 .908 .892 .875 .858 .840 .823 .805 .787 .767 • 748 ■727 • 706 .684 450 .900 .885 .1)67 .848 .850 .812 .794 .774 •754 •754 .715 .691 .668 U75 .892 • 874 .858 .859 .820 .801 .78* • 765 •741 • 720 • 698 • 674 .650 500 .88U .866 .848 .828 .809 .789 .769 •748 •727 ■ 704 .681 .657 .652 525 .875 .858 .858 .818 .798 .777 .756 .754 .712 • 688 .664 .639 .611 550 .866 .848 .827 .807 .786 .765 .745 .720 • 696 • 672 .645 .620 .590 575 .856 .8}8 .817 •797 .774 .752 .728 .704 .679 .652 .625 .598 .566 600 .eu6 .827 • 806 • 784 .760 .757 .715 .687 .661 .655 .604 .574 .542 625 .856 ■ 816 •795 •770 .7W .721 .696 .669 .641 .612 .581 .548 •515 650 .825 .803 .780 .756 ■750 .704 .677 • 649 .620 .588 .556 .522 •485 675 .814 .790 .766 .741 .7:4 .687 .658 •629 .597 .564 .528 .491 •449 700 .802 .777 .752 .725 .696 .667 .658 .606 •573 .556 .498 .455 .407 725 .789 .76J .756 .707 .677 .647 .615 .581 .545 .505 .461 .415 .358 750 ■776 ■ 748 .719 .688 .657 .626 .591 • 553 .512 •469 .420 .565 .297 775 762 ■ 752 .700 .668 .635 .599 •562 .521 • 477 .427 .569 ■ 502 ■ 213 800 .71*6 ■ 714 .681 • 647 .611 .572 .551 .485 •436 .577 .308 ■ 217 825 .750 .696 .660 .624 • 584 .542 .494 .445 •385 .514 .222 850 .711 .677 .657 .597 .555 .504 .453 • 594 ■ 321 .227 875 .692 .652 .612 .566 .518 .464 • 405 .328 • 234 900 .671 .628 • 582 • 531 •475 ■414 .340 .241 925 .650 .602 • 549 .492 .427 .552 .248 950 .629 ■ 572 • 511 •444 ■365 .26d ■975 .608 .544 .470 ■ 579 .274 1 .000 .652 ■ 546 .447 .316 DiTIOSAL ADVISORY COUaTTEE FOR ASiOHlUTICS NACA RB No. L5Fl5a 11 ^'"'lo' /Ho - H TABLE I.- VJlIDIS 0? /- FOR IV»LD1TI0» OP PROPILI SRia PROII HAEE 3DRVXT - Continued e.b \ Pi - Po -0.100 -0.075 -0.050 -0.025 0.025 0.050 0.075 0.100 0.125 a.150 ©•175 1 \. Bo - Po Ho - Hi\ 0.200 Ho - Po \^ 0.972 0.963 0.953 0.943 0.953 0.922 0.912 0.901 0.890 0.879 0.868 0.857 0.845 .025 .968 .959 .949 .939 .928 ■ 918 .907 .ejt .884 •873 .862 .850 837 .050 .9^ .956 ■ 91*5 .935 .923 ■ 913 .901 .890 .878 .866 .856 .843 831 .075 .960 •951 ■ 940 ■ 930 .919 ■ 908 .895 .884 .872 .859 .849 .835 825 .100 • 955 .947 ■ 935 .924 .915 ■ 901 .889 .877 .865 •853 .842 .827 814 .125 •952 • 942 ■ 930 .916 .910 • 895 .885 .871 .8^8 .847 • 834 .820 807 .150 .9W .937 • 925 • 914 .903 ■ 890 .877 .865 .852 .859 .826 .813 798 .175 ■9ki .931 ■ 920 • 908 .896 .883 .871 .858 .844 .832 .818 .805 789 .200 .938 .926 • 914 .902 .890 .876 .864 .851 .BJ8 .824 .810 .796 780 .225 .955 .921 .909 .897 .884 .871 •857 .844 .829 .816 .801 .786 770 .250 .928 •916 •90J .8J0 .877 .864 .850 .857 .822 .807 .792 .777 760 • 275 •923 ■ 909 •897 .884 .870 •857 .842 .828 .813 .798 .783 .767 750 .500 .917 •905 .890 .876 .863 .848 .834 .819 .805 .789 .773 •757 739 ■ 525 • 911 • 897 .884 .870 .856 .841 .826 .811 . ^794 •779 .765 •745 727 .550 .906 .891 .877 .863 .848 .834 .817 .802 ■784 •768 .752 .733 715 .375 .900 .884 .870 .855 .840 .825 .808 .792 .774 .757 .741 .721 702 .1(00 .89U .878 .862 .848 .832 .816 .798 .78J ■ 762 ■747 .728 .708 686 .U25 .887 .871 .854 .839 .823 .806 .788 .772 • 755 •735 • 716 .694 673 •WO .880 .863 .846 .831 .814 .797 .778 .7*0 .742 • 722 .702 .679 658 •U75 .875 .856 .838 .622 .804 .787 .767 .749 ■729 • 709 .688 • 664 641 .500 .865 .848 .830 .813 • 795 .776 .756 .737 ■715 • 694 .672 .648 623 .525 •857 .840 .821 .805 ■783 .764 .744 .72? .702 .679 .656 • 630 6O5 • 550 •81;9 .832 .812 • 793 • 772 •752 ■7J1 ■706 .686 .66; .637 .611 584 •575 .841 .823 .802 •783 .761 .740 ■717 ■ 695 .670 .646 ■617 .591 562 .600 .831 .813 • 792 • 771 ■748 .727 .701 .078 •652 .624 ■ 597 .568 536 .625 .821 .802 .781 • 758 •735 • 711 .686 •659 .632 .604 • 574 .542 509 .650 .811 •791 .768 •744 .721 ■ 695 .668 .641 .612 .582 ■ 549 •514 478 •<>75 .800 .779 ■755 •731 •705 .678 .650 .622 .590 .557 ■ 521 •484 444 .700 • 789 .766 .742 .716 ■ 688 .661 .651 ■599 .566 ■528 •491 •450 404 .725 •777 .753 .727 • 699 • 670 .640 .609 ■574 .559 .499 •456 •409 358 .750 •765 .728 .711 .681 •651 .619 • 584 • 547 .507 .465 •415 .360 295 .775 •752 •723 .694 .663 • 630 .595 • 557 •516 .472 .422 .566 .501 213 .800 • 737 .707 .676 .642 .606 •568 .526 ■ 481 .451 .574 .307 .216 .825 ■721 .689 .656 .618 • 580 •537 •491 ■441 .382 .313 • 220 .850 •705 .671 • 632 .594 •550 • 501 •451 ■392 .520 .226 .875 • 686 .648 .608 .564 •515 .465 .401 .329 .233 .900 .667 .625 • 579 •530 • 475 • 414 •358 ■ 240 •925 .647 ■599 • 548 ■491 ■ 426 .350 .247 .950 .625 .571 .510 ■443 565 .260 •975 .605 .542 •469 ■ 381 •274 1.000 .631 .547 .447 .317 HATIORAL ASViaoRY COIOilTTEE FOR AERONinTICS NACA RB No. L5F15a 12 TABLS I.- IkUHa OP dlccflj, J / "Jo - Po FOR KV&LIUTIOII OP ntOFILB ERAO FltOI fkEE SORVII - Continued »o = 0.5 Pi - Po -0.100 -0.075 -0 050 -0.025 0.025 0.050 0.075 0.100 0.125 0.150 0.175 0.200 \, Bo - Po Ho - Bi\ Bo - Po ^\ 0.952 0.925 915 0.906 0.898 0.888 0.878 0.870 0.860 0.850 0.81+0 0.829 0.817 .025 ■929 .921 912 .903 .891* .881+ .871+ .865 .855 .81+1* .851+ .825 .811 .050 .926 • 917 908 .899 .890 .880 .870 .860 .850 .858 .828 .817 .805 .075 •923 ■915 90I+ .895 .886 .875 .865 •851+ .81+1+ .852 .822 .809 •798 .100 .920 .909 900 .890 .882 .870 .860 .81+8 .838 .827 .816 .805 .791 .125 .916 .905 896 .885 ■ 877 .861+ .855 .81+2 .852 .820 .809 .797 .78U .150 •912 .902 892 .881 .872 .860 .850 .857 .826 .811+ .802 •790 .776 .175 .908 .898 888 •877 .867 .856 .81+U .832 .820 .809 •795 •783 •768 .200 • 901+ .895 881+ .873 .862 .851 .838 .827 .811+ .802 .788 •775 .760 .225 .900 .890 879 .868 ■ 857 .81+6 .852 .821 .807 .791+ .780 • 767 • 751 .250 .896 .886 871+ .863 .851 .839 .825 .811+ .799 .786 .772 ■ 757 ■ 71+2 • 275 .891 .880 869 .857 ■ 81+5 .832 .818 .806 .791 .T77 •765 • 71+7 •755 .300 .887 • 875 863 .850 .839 .821+ .811 •797 .783 .768 .751+ • 738 ■725 ■J25 .882 .870 857 .81+1+ .852 .818 .801+ •789 ■771* .761 • 7U+ •729 ■712 .350 .878 .865 851 ■639 .825 .811 .796 .782 •765 •752 • 751+ ■718 .700 ■375 .873 .859 81+5 .832 .818 .803 .788 ■773 ■756 • 71+1 .725 • 707 .688 .lt.00 .867 .855 839 .821+ .811 • 795 .780 ■ 761+ .71*6 •751 .712 .696 • 675 .U5 .861 .6U7 833 .818 .803 .787 .771 •753 ■735 .718 •699 .682 .662 ■kio .855 .81+1 826 .811 •795 •779 •762 •71+1 .721+ .706 .686 .667 .61+3 .U75 .81+9 .851+ 818 .801+ .786 .769 ■751 •752 .713 • 695 .673 ■652 .651 .500 .81+3 .827 810 .795 ■777 .759 • 71+0 .72a .701 .680 ■659 .657 .611+ •525 .836 .819 802 .786 .768 .71+8 •729 .709 .688 .667 ■ 61+1+ .621 .596 .550 .829 .812 791+ .776 •758 •738 .716 .696 .671+ •652 .628 .601+ .576 .575 .822 .801+ 785 .765 ■71+7 .726 •70I+ .682 .657 • 651+ .609 •581+ • 555 .600 .811+ .795 775 ■755 ■735 •712 .690 .667 .61+0 .616 .588 ■ 561 • 551 .625 .805 •781+ 761+ •7I+5 .722 .699 .671+ ■61+9 .623 • 596 .567 .556 • 505 .650 .796 -77I+ 753 .731 .708 .681+ .658 .633 .601+ ■ 576 • 51+5 .511 •U75 .675 .786 .763 71+1 .717 .692 .667 .61+0 ■ 615 .583 • 552 • 518 .1+82 •l+l+o .700 •775 ■751 72B .703 .676 .650 .622 .592 .560 ■525 ■1*87 •1+1+7 • 1+01 •725 • 761+ .758 715 .686 .659 ■ 631 .601 ■568 •535 .1+96 • 1+51+ •1+07 • 555 .750 .753 •725 699 .669 .61+1 .609 ■579 ■51+1 .502 .1+61 •1+15 .560 ■ 292 .775 •71+0 .712 683 .652 .621 • 587 •553 .512 .1+69 •1+19 .566 .298 .211 .800 •727 .698 666 ■63*1+ .599 ■562 •522 .1+77 .U8 ■ 572 .505 • 215 .825 •712 .681 61+7 .611 .571+ ■532 •1+87 .1+57 .580 .512 .220 .850 .696 .665 626 .587 • 51+6 .1+99 • U+B ■ 368 .319 •225 .875 • 679 .6ia 602 ■557 • 512 •1+59 • 397 .528 .252 .900 .662 •619 575 .521+ .1+72 .1+10 ■557 •259 .925 .61+2 .591+ 51+3 ■m •1.21+ •350 .21+7 .950 .620 .566 506 • 1+59 ■363 •259 •975 .600 ■ 539 1+68 • 376 •273 1.000 .6}0 .5U7 1+1+7 • 317 HillOSAL ADVISORY COKMITTES POR i£R0NADTIC3 NACA RB No. L5Fl5a 13 0(<=<=^ -~t ^~S-^ r-v ^^ K, k- --4- ■*K.'': - ""■[ -j- 1 " -~ E'BU" g t i ■ 1^ ^ k4,. ^<, -- [■ -S-. -^; 1-;^ ~ _: I--- ' ' ""^ k "-N k ^ ■-.:;. ■ ■ ^' ~^ 1 -: £^^- 1 '.- I- - ; ! ^"""" K ■^"^ ^ \ - '-:- ■; i . ■ ! '^ ■^ Vj fS -TV ^ ;.i:. ■■ N N,~: -^ 1 = 2v ": [ .- I 1 ■-X s .: Nv- K^ X 2S>__ ■n \" a. t . N • " i ■-■^^ X^ X ^ \ 1. o 1 — V ^- "s 1 ^>., 1 ■ . N V. i ; X > \ ■ IS. , ^ 1^ 1 - 1 N, n -', V- :-- x-^ 1. 1 -.; / " i [ \ -^:i \ H -^- n ■ %- : '-l-.-N ; "', N ■ ^ 1 tr , \ \ "-\ — ■-i ■ Ti £1^5 '■- A ■■■]--- ■-■ j - V ! I ''^ \ A, y^ -ik ;:_!-q - 1/ ,: i -:-: 1 ,. i -"- "T" \ ^ .\ \ :1 — ■ V .1 '■ ! " ' ' i ' ■\ , ;- 1 . I #- 1 i h " '!■ -1= i^i^^^an^ t^ i^ J-11^ ^t w ^ W4 Si- m ^ t^ »u -J:^ ^|,^ ^irf^ ^ iSf •mM iiti- td ,i^U tfn- t« ^it^ iinUit rf;i -rrn 44 NACA RB No. L5Fl5a Fig. Ic .' ■ ■ ■:■ '™, 12^ - 1 ■m. - " - - '■■- — — .... ..-J. 1 -1 :. ■ - — - - - - - - -■: ft ': _ ■ : 1 - ■ : ■ _;. ■•" : t{\ i"" — 1—, ^ i ■ ■ --i ' --^ — ^=^ '--~- ~~T— _ K _ i ■ "---T-_ ~" Pi - Po Q ■^^i --:^ i~~- -4. [~-- ^_ -~ Ho - Po - -. r^ -^^ -^ "^-- "~^--- ■~^ -^ ~A^ 'Tl "^^ --^ ^ ! ^S-.^ "^ S^ K r-^ -- _ -0 r ] --..^ ^■l \|^ "^ -^ -^ _B^ 1.^ ^■ , r- •^! ~-^ ■--- ■-- -^ ^ "^ -. " " ' ! ^--i^ 1^^ ■--- ■K -1 -< 1 " ^ 05 X 1 ■--, \i ^^ -i ■-^ -^i N X - \ i -- - N ■-. \ ■-^i -s s 'x -.° ' X -H,- - - o o 1 o 7 ■ \ 1 N \, N \ "< ~^l " ■ " 1 ; 1 " T= r ~ ^N K N N N ^ •X 05 X V K -" - X N \ \ K N^ \ --:; 1-: ' "; ■ ' v s" N (\ \ S ,, . \ A ^ 1- - "- ; -' r - V K" \ ^ "V^ ; ^ \ N > XV _ _r -: ^\ - ■~ \ \ ^ \ \ ■:■ s^ -\ >t ■ N >- , k N^ \ \ - " i- - - T N, \ \ i \ \ \ ! -_ :\V: " - s: \ \ \ s ^ - j 1 \-:- "" ^ ' ^■^ N ^ \ \, \ \ ~ -; -^ - ■' "'- " ^ .\, \ 1 \ \ "7 _-. . ■-_-' _ _ - _ '-- \ \ \ \ i~J:\ ,-f _ -- -; " \ \l '\ \ V "" *^ - --- '\ V; ^ y \ .- Z^ - :;-;: r' "^■' -A ^.: \ y _y \ :"3 .. -J _T." ---1- "^ \ \^ . -? ■ -- r ..- ' ..\ -. ■"- ■"- " \- ; ." ;■ " ; -7" T 1 "" -1 ~_ --■ -: -.;- " S -:; .\ \ 7 \ _ \ : r "": - NATIONAL ADVISORY \ y \ "-" " COMMITTEE FM ACnOHAUTICS L V \ --: -"- l-"-' " 1 1 T ■ r. -ii / \ 4 \ - ' -^;:' ---_ -- - -1 " \ J ^" " -" ^ 1 "" t ''^ - --; — : - (^ ! _ V' ;-; ^\ ) ^ ' r -i 1 ■_. ■_ --/ [ i "_ .< > -/ .i 1; ■i ! ": -/ "- -. - 4--^ - I - "l -.4 -_ - t - 1 -">--- - -_~- 7' ' = - > o - Po :-- : V7- -- - .'icl Mo . 0.2. ■' -_7 :-7 -T -j- - --jr -;- :- J - '- * '" - . ■ -- ^" Figure 1.- Continued.' " ^ ^ r r - --7' ■ X'-T -F- - p - - L-^ =F i 1 i f ;Z rX ■oT d'i ■«. 'r^ ir- ir '^'-r fi- ^ s ::^ :.'. M ■:. 'ji ;i-.- '^ rt 'Ji;. jft; i^ ^ 4li ^ rn f*H1 iSiT ••^1 NACA RB No. L5F15a Fig. Id s =5= s ss ~- .f:= :~: W- T-l w '.y-. --\:\ ^ -:^ : |..: : -r. .■:: .X r~ 2H .m ::: ;:•} ■ Ui -: ": rr- TT. *^: "" ':3 \ r i "■ , :i-.. Vi - U-'-- . " . ■ -\ firy . i' "■ 1 -^ ; ___r]^ ^ 1 ' -^ ~1 1 •~4_ \- ~~ ~^ -. . f— ,_^ -~-L^ r- -1 ^ 1 — u^ Pi - Po "o - Po i n -~-,^ — (^ ~4__ f~ -: ■"^ -~,^^ -J .^i ■^---. - ^--- ■T-, ^ ^ ■-- --^ --^ ... ■"""! 1 -i- T^ -^ >--^ ■-^ -C 1 1 ■.'^ i 1 :- - 1 . """%-, "~>^ "^ -^- i -^ ''- ^, '■;- C^' - "-4^ ^ --4 ---, ^ - '"'5 "- ^ kr ^ i ■ --X. ^ "~->. ■In i ; ■ xj ^■^ ->^ >V, n! V V X ^ - . i V. \ [■^ --. X, V ■^ ■V '1C \ N ■s 1 < o = -'i ■ - H k % X, 05 k \ s r-1 ■■ .- ■n ■n. V \ ^ H \ \ ^ V^ S I . '-: ■N ^ N - N V \ ^ \ N \ S N A - \ S ^ N 1 \ \ ^ \ J -y s= — N -\ \ ^ -- \ \ -_."■■' zrg 1 -a "O - K' \ \ \ k \ s \ s^.u \ s \ \ P 1 "O n , -I \, \ \ \ ' ! ■" ^ \ \ \ \ A £ ■\ \- \ \ r - I- \ 1 - _-■ -- -J -'■ -- ^"- \ \ \ \ f- - .- j l.-V ' - ^ \ \ '\ \ \ \ \ \ " ■ -J -^ .\ \" V ■\ ; . 1 --- ^ . ""- -■- -; V \ \ '^ '- : 1 i -- \ - 1 \ \ ' [ .... \" '- '" -" ["-- -'- -i \ \ \ \ *{ 1 1 1 ■ - 1 ■ --^ \ \ \ \ 1-"- __-: 1- -:. --- '-' - \ \ \ \ -"^ i i2' 1 . - : - 1" " - \ t\ \ I-. h- r-f:-: ■ 1 ■■ 1 . t - f-. \ \ - \] i i W' t4^ "1" " \ "_ i. -i- V \ '\ i ■ ■ _J__- - NATIONAL ADVISORY COHMITTEE FOt AEHONIUTIC \ \ ! - / ^ ^- S 1 - i " - \ 1 --- -_ ■] - : " '~' /% ■ i--" ;_ !- "^ ,~- ^ - '--- - -d ) _^^ -f- ^ <■ :-. r^ w ' 9 r. - ' """. ^':i 1 -.; .i f i 1 . /. :c --" 1 - "o - "l Lzi; T. _ L-i( - -, - t-.t^. :- 2^ 'C-i'r^ '^A r- -^ :z^ Ho - fo " - •-^r?^ ^=1^- Ul Mo • .s - '"~ - .-r_- i--t--- -I--- "-[-;-^ ^ ., -,. 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" ' - ' t-' ---' ' — _ ■H--' - - - 1- -- 1 - - -.. - ::■.' -J? - I \--- i. 7-1- - 7- ."' 1.- l^ ■ [ 1' -"" j i - L i (! ) ! "1-' '" ":^. .c ) } .^_ •' - ^ ' 1 ^^ ! .t 1 '■ •-' ' J- .t ! i- c 1 I 3 r tZ -'l--r ^I z-__ 1 / Ho-- Hi «o - Po - •- ■X- - - : -^- ~'- -- - -- --- ^ ' .L . -"T. "' ----- el Ho . 0.4. \ - _: . i - 7- 1 .-! ■ Figure 1.- Continued - - -' -- - ~ 1 -- ■-■ - " 1 1 ! - t M ' 1 ! 1 n 1 i I ! 1 1 1 1 NACA RB No. L5Fl5a Fig. If :r-:t- I ■ 1 ■ — 1 ~^ "^ ■ ;■ T. ,^ _:; H;: -■;- H- •■?; ;■; ■ L... i "■■ ffiayf. m^mai^m 1 1 1 i 1 . .. 1 ' 1 i ' 1 i , ffl j ■11 ■ 1 // ■ i • i . '■ i . 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( i 1 -1 \ -= - 1 - \ V i A' \ - f-^ . -J..- ~- 1 i 1 : \ 1 . f — 1 1 \ 1 J -• ', 1 - i- -, 1 - 1 : i ~- ■ \' \ I \ i - , i.l. \ 1 , -; - ■ 1- Vj - - 1 -: --- - ""t - I ■V H\ ll 1 " 1 "^? £- : I ■ , . , 1 V ' \ 33 r-j = - "■,--r ■-:;. ~t : z : NATIONAL ADVtSOBY COMMITTtE FOB AERONAUTICS -: ■ 1 \ 'tS -Z :' ""■ / :V-- -"-1 ■ ,( . )i J - '~-:-:^ ; \ ■^:\ -J-; - . - 4. t--- t 1 1 -- " ! -1.-- !-.l - i I - :;: .: ' ' " j^; i ^ !. - i- 1 -- ■ {■- _ Ut: ::-:i -, -:- » t t ^ — .:-^ * -t- " 1 1 . i 4- - ^-^ - rj. ./»^ ( : : -' - - {_ ■ ! , V:': ■ ]- ' - y :s^ -_ -'- - ,^ r -■ - J r .it 1 ,^ r ---- £ Ir-: - -l4 1 i ; r --- .i i- f- .< L f. r* C-ir ■ i -- ' !-> " (■ ^ ; .--t'-- ~ ' ;"-:-; : -~ z-: ~ ^ ^- >r - .- 1 ' "V zz "- - 1-=^ 7' -' .'- . : ; .- -i:= f^^ -: -.._ ^"- i ■t ' — ^^. "--- -_2_ - "- — _ ;^ - ' ! : i i_- "z _ _" Figure 1.- Continued. : - -/ --- : i '- - ■- -:- ^ -1 " -;- J- -■- " - •■^~ - ' ' " - ■ : ;^- :; - - 7: R.;.4- '--i-~- -- i-- : ■| - -n- NACA RB No. L5F15a Fig. Ig PTTTr , „.t-- ■ F^ F?= — •3: w f~. 'y -™ :it: "■■■■ w -; ^ ^ '-^ ^ ■=r ^ w- - [re ^ •T-; rrt? pP-rtr F^^ R='K: w rw =T: "^ RTT "f rr^ ™ ^HI ?K 1 ' . L_; i .■ -. ■' — — — — ._ — '. i \ \ \ \ • \ \ — 1 — -- — ~h i ! 1 : 1 1 , / / 1 ■ " ' ' - ^■ 1 ~T:" - .j "■. — : 1 — _ /A t 1 1 -r- ■ ■ i . 1 . i' 1 ■ i ' ■- ■■-"- - - n - 1 ; • . !-■ -_ -- -rr -- ~J-- —^ _- _^ — '• — --- 1 «o - f "i -— ^ , SC _j_r ■~1 :;^ ^-j._ ~^ --^ ;-- -r ~ ' p^ ■^'^^ ~s-~ ■-^l-- ,,^_ .-,4_^ ""-^ --4 '~~L_ -f1 [-- ~-l ==d ~- -^ ■-- -^ " ^ ^.-0.1 - ,;_ — - ..;. '•H i^ •— ■^ ^--., ■-^ "-- ' ~-^ L'' ^ H h-- -+- :■- :^ : — ■--- h-i -^ " ~^ --1 "" ' '^fc:s: ■ .'. o c° 7 ■-i. K-, f-- - -->- ■:^ ~-^ --, ^ ■ - " "■ -■<. 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Ih) Mo . 0.7. _ 7--- . 1 i=r- - ■ 1 IT .- " ■ '_ - 1 1 ..:: -_j ■=■: - - Figure 1.- continued L t . - 1 " g; . "" - - _ -_, ;: -. Y-\ ■-2. -^ .. :. n^ ._ ^r - g= ;- :^ -- - -il- ::-:■ ..:: x: 't. •^' ^; :::. .- - -. _ ~ '± '■z. rJ . NACA RB No. L5Fl5a Fig. li - -hn. 4z - WD ;ii:: B - rTijrHf Hi: Hi; n» ~ « :-i TK r -";k! -• rx ill i Fui ^ m -rn r^ :::i -1.- |-::tr;;: - - 1 1 1 ■ -.. r- - --: : 1- 1 ...1 1 : 1.. : - 1 ■•' ^ 1 ■ ' ' .;"." — . --: T- -r — - -- " i- fV - ; 1 • . - - _ ; - m :^ :; :; '-.'•.I ■, ! \ ' - -j-:- - - - - .... - ■■■'! : ..r| ■, a. r ■ ""|.-"- - 1 \— - n i ' ■■ :.,-. t . 1 •■ . . - ! ■ — ■ [ 1 - ■ ' i " - 1 1 J I !- j 1. - r. j fl , i : --- ] - 1 1 -" I i _j L ' ---- r - 1 - \ i " " - • ■ . [!___ :" 1 ^ i 1 ! : ^ ■ ~— — 1 h-f-H : I ■ i " ~~ ^-- ' — —, h—. — - i J t ■ 1 ■? ~^ — — i-^ ; 1 — 1 . t T- -~--_ -, - ] ■ ---, — ., -- -^ — :^1^ r.. :- =-| a. O H'*'"' ' -| k- -~ k- ^ t^. ' ^ ^' o :^ - i:: ^ " " -s ■^. ^ '^- ! ''--, -^ "'1 ■<. 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X l-^ ; : 3 ^° ^\ -; - - ' _ - '^ ~-^ -J,- X X N " ^; :t :-^- '"';f-. ^ - " X > \ fv \ V •N V :r -a ^ -- ' --" ^ H N N 15 k- -1n N S3 t--:=c •tj^-q i -'- ':~ :- -7 k^ \ \ \" \ \ s 3 sr? -J' " :J = ' -^ -.-- ^ \ \ \ V \ ^ - ' S eih;- ^;*7:: "^- i^ -' -■- --" -- \ 2- -\ k ^ N- " ;.- -' r"" - ^ ^ v: r. ■ := \ 'v " \, \ ~. ^^-" "" " ": ■ -; -; :- - "- X s \ \ 1 \ :iJ 7 -- --' -V \, V- \ \ 77 —_ 7:l ;. ■ - ul" , ---' ~ - 7- -;- --- -_- -'-- " v^ -- :-'- ^ \ \ A \ ■-..-. V " ~: ; ;■ 1-q t f- - -- — -" \ A \ \ -- _: *- - ^ - --- ---- 7~ 7 \ \ \ \ \ 7- :^: ■T r - -; 7 -^ 7 t^ \ \ :\ y 7 - ' ;.-l -_ I^ ----^ ^■ " -J — '-- - U--^ -' \ 1 \ '-- _T J ■--- -■a ■-■ ;: :'- 7" 7 . \ y ■ \ ~: "" " " ---- . ' NATIONAL ADVISORY COMMintt FM AEKOMiUTIC i ~ \ \ \ -\ -q '^ : ^ - _ ■3 -- --- V7 > "-"7 7 -7J= '' I \ \ " :7j ._: -'---:_ :..-. -y .-, y- -" _-, ------ \ -\ " "" -_:■ r ;" 7 :--- ^7 7 -- s ' 7 - : . •-- :_ -;- 7-- "J- - 7 77 -■' -- -^ " ' - -" '_'■ -:, - "^ ^1 -'7- - - , '7- b.r ~_" - ■^"^ -:-: 7 ^- -- >- ■"^ --- "" -- n -: ' _' - ~ _5 - °i I --/ f ■c > ^ ! ■i r i } '-:' t 1- 7 . :; a: ^ ..\ -T p- --" ' _d :l ■■■]- ;. ^^;. -- -■■- ---- - - 1 - I '. ■[ ! - "- -£l -' 1 . 1 : 1 1 .-■ 7: t"i 1 i ■ .- ..li ■■/ --- - -• - ■ i ■ ■ ap . " : -- - ; - i - !- ■ ^ :/ •- -.1 . " "- *^ . :-: D '' i V. - t - ■ f- : ■rJ\ 7- ;7 '" : 1- .; '"- :7. -T- - ^- -- -'- 1 ! 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' ; " t_v 1 ■ \ \- 1 r. ■r^ -l- - — .".-. _": _ ::- : " \ Ir ~- \ '~ / '- i hH ' " j 1 _ \ '-"^ t r "" 1 ' -" 1 - 5 1" -r"- i ■"^ n - |-' — " - ■-i^ ^ P- - -1 -. '. :k' 1 JL ; ! .d > 1 .t ) ■' i f 4 p / 7 "_ ^ . -. "o - "l rpr i: -7 '-: "]■■-- - "o - Po .... ''r 1 - - - - . " ^ u. ■ ^ \ - 1 1 1-1 (-1 .1 - 1-. ... J ..-.._ .^__. r ■ I- - - ' I 1 i ! ! 1 1 1 1 . ,- 1 - .._ z^ X r..- - -^l: NACA RB No. L5Fi5a Pig. 2a ' 1 - " >^ — cy . §2' It - _.., L-- (;> . _1 1 1 i I i 1 1 i 1 nts by approximate method. :'. '.' '," / / ■v: / .Z UJ . / 4 / u / / / 8 ^. / / / O (X o a 1 o X h / / 1 ^/ / -/ CM ' _ f ■°-v / '^) / / / 7 ^ 0) / / ' / / . 1 J / / / '" 3 CO «3 0) E >> > u _ w OJ - J*: n) - o GO u OJ - .-( ■H (-. o - o. - 'S c o --t - - 1 / / / ' - / / / '. ■ - - / / f / . ' :v- / / --- \n 1 / / / 7 / — ' E 1 / 1 7 ; In ^ o o o ~ X X "--: J - - *; j 1 - - - T - / / -- 1 N; f r--_. 1 •■" - 1 OTi ^. 4^ (d ( r.:- ■■ o :•-"; - j ^ w , :-; h t- 1 1 1 _1 - 1: 2.- Factor F 1 K O - ~ o - '_ - / / • 1 / V.' -; : 1 Li bo " [ / r> - 1 C i .« ). V< ). M : ^ J °d - °H Y/op . NACA RB No. L5F15a Fig. 2b - 1 .. . .1 m V) l':v .;.: 'iff ■j" ;' > K ':_! 1 ;"i ^ t!;:: *- S2 <; ) .■;| i'- / / '■-- P ** .^r : / / ' -■■^ :;? ^:fl / / / Z uj -', ", / ^^ (-1 ;■[: / / / ;/ 5i '< *'■* ^- / / / / B -'- - 1 [ / / 1- / '--;*- t O 1 o a 1 l-fc; - - ■: t -;- ^■ / . / '/ ;w kji. ::■ r - ■" i '"-," ■ . ■ oj o i ~ t r i o ,- ^J_/ fc. ^ ■ a 3= 3 / ^ / _ :: U :^^ r^- J ;-: / /_ k> ^1 / ; - / ' / : r-T ( ,y - / , "J .:. +-^- / ... / ■ ;- -; ^fi i:^--- "- j / / r- -I /^ f ■ ;^ y/ 1-: -— ^ -. -;t w r---- -J\ .- ;- '. t" -' -' ^ — - - ti:- 1 -". ^ L.^.,^.„ " - to--: - :. ■ / ' -.-_: -■._: ; e V jt" |5 ■■:":■ 7 j Vi 1 -1 o p. -^ ■ - 1 ."~L fe I- - ;i --;- t;: /- \i -";" -^ -:? ' i ^i ■.-_- t:- - "■ ..,. 1 t ,x,x '[- '- r_:..; : ": _ ' :^- ■-■^ -.. ■;-'."'j: S:!- -'-^^ .- - - '-^ ■^"; ' r ' — - ■ - - -■ --'",i ti; - j :- — ■ ~ -'..LI -- :. :1 Sf: :--- " I -■ 1 . ---- zi- - 'T ?^ I /{ / - s / ;£:; - :r 1 / - ■ -_- 1 fes K- - 1 ;V-: ■- fc- / -:-_-, - :--:^ r A 'i::-^. ±r^ ::-. "-:-;- / -'X i M 1 — , r-.± ^- ;.tJ . ■ -; -':"- ■ T-^ "■' I :-:t -^1 O h ■ - 1 ] — - ■« f- :- ; (U ; .-— J. - _-. ■:! : r:r: -": -;- f: -:-^ r^ ■'^":' tr- ;_:j --" --: v'r,^ Bi- .--- - 1 / ■ 1^" J :"?; = : ! . ■.t~^ 7": :z- ■ " 1 t- T^- ---: -: .: J - -^' ^v^.. ■ 1 -:-: --- Li 3 bo H j ~^- - \ / : *- s - "- _" ■ "S^. \ ■.~ . -K t a ?_ ^ r* - r: ■-- °d - °H "r/o„ J . - :--:- --- ;'7 :'^^r^.l 1 "== -n i " 1 ! ____ - -•---■ ■ . ■- -<^:-:- -^-• ti44 p._*j-p-,.-j^ ^r: -5- ■'V- "" v"^';^ A- -: 1 :: ■: i _" :-:::, ■ -1 _1 NACA RB No. L5F15a Fig. 2c m i'-' ',- h:t ■_: :- " t T— r:': - .... -■ ■■>: \.,.,. :-:/ J. ■i P m ^ ^ Mi - S5 , . o ^ ;:; 1 ,- j - ^ o p. '^-'__ ----: . -'-' 1 J ' - ± - : : i 1 - " o f~ ^ " ~^ \ -; ---,- ■"-:-7 :":;- 4 fi -' ■ r !'' :_: ^ - -;•-:-: --■-^ ;:::r: --;- A;;t / :-.: -^ " ' v; ' T " -: 1 -;1 F;- 1^ - : ;-.:/ :l ■■:; = :- - . ^-:" ) - -''\ -:;-; •--J 1 I- J ■ - -::- T" :--;- '^:i rL- =:; --:. I r: \- " -: ^- - ^< :-.; ;-- - .:- -^ - - ;; -: ;- - - -' . '} :"" -■' '^ '-■'-^i :•:;■ :; --= " ■ -■ --;■ '•\i o . o - 2.- Continued. [-1 1 1 1 ■ r T-J_ — -r - - .-_J :V^- ■-'i -;;; -"^ '-^ -:-- - - 1 'ri ■ CJ -^ :-: :^r; 4 V -1 - - \: -: ■ f ^- '-- - -^ ■ v::: -;- - i 01 L. _ be - " - 1 -_ «-> ' .| ; - ^ I - ^ ) :^ t: -;;■ ■- ;_s§ 5 ^M.;^ :; - n^ 1 X, i^ :-: : ! n . ^ >^ rl . "->-- -:. -, -- -;--;!: -"-:- - ::-_; •:; : - ■ 1- '--:- [- ■ K - ■ '.-- "r -:-} "-"■ " z ^-■. i--V If-- & 'r- Z.:-JX iTte ii*' ■■_X- ^ tctiS ■ :_: J m '•^t- ■^-' r. 1 ~r : ^h- tSr t+h ^^^ t4t % NACA RB No. L5Fl5a Fig. 2d I !'■- 1 1 1 , r -■- , -j- 10" . .1 i: f , ' ' ' ' ■ * ■ -OS. ?s ' \ i' - . v> ■ ; . ' ! ; vr~ 1 / j ■ ■ / ir 1 . / 1 -" ■ ^ i" 1 1 8 , » .-"" / : 1 '/ 1 ■ • '- / / / / 1 » -- ,' — '^ — ^. / 7 1 . ■ / 1 P. O ^ - - ■ W 1 - --' ?/ ,o/ - r-/ J r 1 / / / - -;» ■ ^ 1 / -v-^ / ■ ■ r , / : -: / j / ^ / ' j / " / .: r* — ^1 /: 1^ ''zA - 1 _. ^ /: /: I u ;:/; ^; -( '■! V j ■' - /. :"■;■ :-''i j -_ .1 ■ " :^ 1 - ir-: ■/. , 1 If o ' O :£;-; ^-3.; "--■ ] j --■j "--'-_ ^ X C 'r - 1 . -i o --. --- : " i 1 • \ V p li- ■ =1: : :-:- - / ■ , ,- / I ■ ' / (<^ w -^;- i >; ") '■ - 1 f ^:-: 1 ■Vv 'i~""," -" / -. ■ * ^- to o o ~ 1 / - T3 01 _ § - *J C o o 1 — -- - j ■ " ti - - -...- s ' " j- l .._... "■■ ;■ V ~ ■ I 1 "" ■ - . bo I / / "- r \ « i > y ) 1. .. k \ ^ : ^^ \ C ) Od °u "r/o ^ .p^f^ // P" "i" - .. ' / , . 1 NACA RB No. L5Fl5a Fig. 2e 1 - -i " 7 :l -■'\ T?^ 1- ' - >"^f ITri TTTT rrf ";; t^^ !'t' h-1- 'iy\m i^t U k\^m f^: iiii:ltHP ay P titiM '-tt#i ■■i{ ' gi t^i ! ' r .. -it ! -" ; / / ^ •s •4 / iS .■7 ...4 / / a? / / ^i / / / / ":-ri ^'i . . 1 ^^1 /. / / : y^ ■4 o O o. 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Lv r^ IVT ;!::-■. a >n.- 1 NACA RB No. L5F15a Fig. 2g ' i 1 - .'r >? -I t 1 § -O S - 9l ^ ' / / 2 3- S; '■ f •--t ;■ / / S i- . / / ^2 Z UJ . _ ' T^ / / 9!S ■"•' / / ^1 ^i. v.f y / 8 * o o a. 1 o X • / / ~" ■ ■; .-1 / / M c\i IV> } ^ oT ^ /. f " ■/ OCl ■, -I ■114 o. ■--■J 1 / T •i -; - / ■ y ■ . ^ ■--■-- . ~- f r 1 /, h'l . : ,-: '.■-: -■■: ■ -■-, / / / -£?f / / / "'- -;-c i'-"- r : /; --— - — " -; J / 1 ' - - - :■ T- : 4 " / -7: '^ ;r--i . 1 r'- T / 1 X al B - P-- .-..■:; :.; : f / ; ":' i.': : i_ /: / tn o l3= o a. 1 i ■ : ■.":' h--- 1 / - ^) .-. ■ ■:-. ~ -_::. . i / 1" '- " " -J; / / ^ L-: :- -■ / ' 3 "-:-'T^ - \ ^^ , \^ " "" " ~ .. ._ :f ' ^ / rv : -■ ^: ■^ \-''4 ['r-: - ■ . / :-- . ■ .i'i -■ ■ - ^^ jf rv^ :. r - : / "-", ■^\ - ..-:. -- - i -- - ■- - ^- ""- j 1 1 ..-rx ■^ ■'"- -i 1 -' - - ■ : ._.,. T '-:-- ID ^ O '■ E 1- : ■:■: 3 : -' ■ -^' : : f . - " ' -'■''' ; c ~-^ ■P c o o 1 cj OJ ^ : bo -:_ : . : r^. : i ;- .-. . :-.- /- - -"- ■ ■' - — r:.r z. :: J -:-7 -- _'■ ■Ji - 1 / 3- - " " (\ I c i a). --~ - H > s : (\ i "" ^ >^ - ! ■ ■ --,' -" - Ti^-ti-.; :^-.". r-\':'J.y .Lz:t :_r-- ^>i .] ^' 1^- ^ ■ - - " -- ._""^ r NACA RB No. L5F15a Fig. 2h ^ " -" —T\ 1-- -' 1 — ;:;| i* , ^l > — — -' -■ -- .r h . - l\ s b "1 / / i? V E ) / f- ■ / / ,t u -'tjI - / -1-;,-' ■■ J h 1 i,-: 1 'h r i /' o ^ ^^:[ 1 1 / .- ■ O a. 1 ex O a. I o X ■/ / ■ ;-f f; ^ ( / (^ 1 ;i- I ■ I." 1 f\ t X" " .-"V vl ■ Or 'C "> : i :' ■ [/■ ■■'■ :" ■ > "! '■ ■a ,.i-_ / '-- / ■ - ' ■— j -«- -/ ■_L v^: f . / / ' . 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