f^<^ 1^-20^ / NATIONAL ADVISORY COMMITTEE FOR AERONAUTICS WARTIMK REPORT ORIGINALLY ISSUED June 1943 as Memorandiun Report TEE LOCUS OF POSSIBLE POSITIONS OF A HKP.VY BOMBEE IN SPACE AFTEE A 12-SECOIfD TIME IIJTEEVAL ^ By Charles \J . Mathews and Clotaire Wood Langley Memorial Aeronautical Lahoratory Langley Fleld^ Va. NACA WASHINGTON NACA W.\ilTIME 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. 20h DOCUMENTS DEPARTMENT Digitized by tine Internet Arcliive in 2011 witli funding from University of Florida, George A. Smathers Libraries with support from LYRASIS and the Sloan Foundation http://www.archive.org/details/locusofpossiblepOOIang !.g^':ORA^IDlTj! REPOR T for the National Defense Research Council TEE LOCUS OF POSSIBLE POSITIONS OF A HEAVY 30M3ER IN SPACE AFTER A 12-SEC0I-:D TIME INTERVAL. .':3^" Charles "/. Mathews and Clot aire ■<7ood. INTRODUCTION At the request of the ITational Defense Research Council, calculations have been made to determine the loci of possible positions of 9 heavy bomber in space following a 12-second interval. The airplane fll£_,ht paths corresponding to various limiting ir.aneuvers v;ere calculated to deterrdne the position of the airplane at the end of the 12-second time interval. The calculations were made for a hypothetical airplane having characteristics siriilar to those of a 3-2l'. airplane. PROCEDURE AND ASSUJO'TIONS Flight paths v/ere determined by step-by-step integration for various extreme maneuvers entered from level flight at an altitude of 15,000 feet. Entrance speeds of 225 I'j-les per hour and 276 miles per houi' corresponding to 60 perc'.nt and 100 percent rated ooverj respect.1 vely, were investigated. Except where othervise specified, the D.iinit-ing positions of the airplane were determined for two power changes that were made at the start of the m.aneuvers. Thjso changes consisted of applying full throttle (109 percent rated engine power) and completely throttling the engines. Tne loci of _ osslble airplane positions were determined by calculating the airplane flight paths for the follov/ing extreme nianeiivers: 1. Abrupt climbing and diving maneuvers in the vei'tical plane limited by maxim.iom lift coefiicient or maximium permissible normal acceleration. 2. ClliTibing and diving m.aneuvers in the vertical piano at fixed flij^ht patli angles. 5. Level turns limited by maxlm.um lift coefficient or m.axim^um permissible normal acceleration. U' Level turns v;ith recovery after various tim.e incre- ments. 5. Full- throttle climbing turns v;i th a 60 angle of bank limited by maxim.um. lift coefficient or maximura permissible normal acceleration. 6. Full -throttle diving turns with a ^O'^ angle of bank limiited by miaxlm.um permissible negative norm.al acceleration. 7' Diving tui-ns consisting of straight dives for J seconds followed by turns i-vi th vertical bank limited b.y maximum permiisible normal scceleratlon. 8. Turns with vertical bank lim.lted by miaxiirrami lift coef- fici'"rnt or miaxim.u'ifi perm.issible norm.al acceleration. The RssiHued characteristics of the airplane investi- gated are listed below: (The wing area, engine power, gross weight, and limiting accelerations were tal^ren from speci- fications of the 3-2)4. airplane.) 1. "'ing area: 10l|.G sqviare feet 2. ■'>ross weight: jO ,0Q0 pounds 5. Power: four engines, normal rating 1100 horsepower each l\.. ''^aximujin lift cceffioient: power off 1.3 full throttle lo 5. ¥a.xir.iurn rolling velocity: For the maneuvers involving roll, the rates of roll v;ere deteriraned on the basis of a wing-tip helix angle of 0.0«:j radian at 223 miles per hour. For higher speeds, the rate of roll was assumed to drop off inversely with increase in speed because of increased stick forces. 6. Profile-drag coefficient: O.O525 7. '/laxirnum allowable normal acceleration: og, -Ig 0. Power absorbed by each windmilling propeller: 60 horsepower (reference 1) The variations of normal acceleration and rolling velocity with tir.ie used in calculating the rate of entry into the various maneuvers were 1 - a - estliTiated i'rom available flight test data showing response of airplanes to aorupt control manipulations. RESULTS hhJD DTSCUSSIOK Tha results of the celculations are presented as plots of the flight paths and as side views and horizontal sections of the loci. Figures 1 throUjZ;h -y shov/ the results obtained for the 60-percent power entrance condition. Figures 6 through 10 shov the results ootained for the 100-percent pcA'er entrance condition. Figures 1 through b. Paid 6 through 9 shov; plots of the calculated flight paths for all tlie maneuvers investigated. The points shown o'n these paths represent the posj.tions of the airplane at 1-second intervals. The locus of airplane positions for any period of tine less than Ic! seconds can be determined by fairing the points corresponding, to a given time. Figure 5 shows the side v1 ev; and horizontal sections of the calculated locus for the 60-nercent entrance power con- dition. Figure 10 sho\'-s the side view and horizontal sections of the calculated locus for the 100-percent entrance pov/or condition. It may be noted that the locus of airplane positions for either the 60-percent or 100-per-oent power entrance condition is bounded, by two curved surfaces v.'ith their concave sides facing the initial oosition of the airplane. The inner sur- face is determined by engine-throttled maneuvers and the outer surface bv full- throttle maneuvers- The distance betv/een these tv.'o surfaces is relat5_vely small and averages about 5'^0 feet for the 60-oeroent pov;er entrance condition and 250 feet for the 100-percent power entrance condition. The follow in^3, maximuni displacements from the initial position of the airplane at the end of the 12-second interval were obtained from the two assumed entrance pov;er condi tions: 1. ■f'aximiUTi gain in altitude - 60-percent power, 970 feet 100-percent power, 165O feet 2. ''axinura loss in altitude - 60-percent power, 2290 feet 100-percent pov/er, 225O feet 5. T.'aximumi lateral displacement - 60-percent pov;er, 26qO feet lOO-perc^nt power, 2c50 feet [|.. ^'axii.-ium dl solaceraent parallel to original line of flight - 60-perceat power, .li.55'--' feet 100-oercent TDower, 515O feet It should be remembered thst the loci calculated represent the limiting positions of the airplane that wo-old be obtained by flying the airplane at its structural and aerodynamic limits. The extent to which the extreme - 6 - boundaries of the loci v;ould be utilized would depend to some extent on the skill of the pilots and primarily on the incen- tive involved. Lanj.-;ley I'emorial Aeronautical Laboratory, National Advisory Comruttee for Aeronautics, Langley Field, Va. , June 8, 19U5' - 7 - REFERENCE 1. Hartinan, Edv/ln p., and ^1 e rir:.s.nn , David: The Negative Thrust and '-Lopque of Several iiill-Scale Propellers and Their Anplicatlon to Various rllght Problems. Rep. 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