AN INVESTIGATION OF THE POWER SPECTRAL DENSITY OF ATMOSPHERIC TURBULENCEbyGERHARDT C. CLEMENTSONB.S. U.S. Military Academy, 1942M.S. California Institute of Technology, 1945S.M. Massachusetts Institute of Technology, 1948SUBMITTED IN PARTIAL FULFILLMENT OF THEREQUIREMENTS FOR THE DEGREE OFDOCTOR OF SCIENCEatMASSACHUSETTS INSTITUTE OF TECHNOLOGY1950Signature of AuthorC r p m othesis SupervisorChairmar, Departmental Vommittee on Graduate Students6445-T-31May 12, 1950Prof. Joseph S. NewellSecretary of the FacultyMassachusetts Institute of TechnologyCambridge 39, MassachusettsDear Professor Newell:In accordance with the regulations of the faculty, I herebysubmit a thesis entitled, "An Investigation of the Power SpectralDensity of Atmospheric Turbulence," in partial fulfillment of therequirements for the degree of Doctor of Science.lespectfully yours,ACKNOWLEDGMENTThe author wishes to express his gratitude and appreciation to thefollowing persons and organizations who aided directly or indirectly inthe development of this thesis:To Dr. C. S. Draper, who in a large measure is directlyresponsible for the opportunity for carrying on this investi-gation.To the United States Air Forces for supplying the airplaneused in this investigation and for assigning the author to Mass-achusetts Institute of Technology for graduate training.To Professor R. C. Seamans, Jr., for his helpful and con-structive supervision and encouragement.To Dr. J. H. Laning, Jr. and Dr. Elmer Frey for many help-ful and practical suggestions.To the staff of the Tracking Control Project of the Instru-mentation Laboratory for invaluable technical assistance andsuggestions.To the personnel of the Bedford Flight Facility of the In-strumentation Laboratory, M.I.T., for wholehearted coopera-tion and assistance with the flight test phases of this investi-gation.To Miss Alice Woodand Miss MaryannHarris for the ardu-ous task of correlating and computing the flight test records.To Mr. L. E. Payne and his associates of Jackson & More-land for editing and reproducing the manuscript.This thesis was prepared while assigned as a graduate student fromU.S.A.F.I.T. under the auspices of D.I.C. Project-6445-T-31 and spon-sored by the Office of Air Research and the Armament Laboratory,Engineering Division, Air Materiel Command, through Contract No.W33-038-ac-13969, Project No. RR-3.TABLE OF CONTENTSPageABSTRACT viiChapter 1 INTRODUCTION 1A. Summary of Previous Work 1B. The Requirements for This Investigation 2Chapter 2 ELIMINATION OF INSTRUMENTATIONSYSTEM DYNAMICS FROM THE TEST DATA 4Chapter 3 THE PROBLEM OF ELIMINATING THE FORWARDVELOCITY OF THE INSTRUMENTATIONSYSTEM FROM THE REDUCED DATA 7Chapter 4 DISCUSSION OF RESULTS 9Chapter 5 CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCH 16A. Conclusions 16B. Recommendations and Suggestions for Further Research 16Appendix I GENERALIZED HARMONIC ANALYSIS 18A. Fourier Transform Pairs 18B. Mathematical Theorems Related to the Study ofAtmospheric Turbulence 20C. Statistical Analysis of Time Series 23D. The Harmonic Analysis of Random Functions 25Appendix II INPUT - OUTPUT STATISTICAL RELATIONSHIP 27Appendix I THE SAMPLING PROBLEMS INVOLVED IN THEAPPLICATION OF THE THEORY OF A GENERALIZEDHARMONIC ANALYSIS TO A FINITE NUMBER OFRECORDS OF FINITE LENGTH 31A. The General Problem of Estimating the Correlation Function 34B. The Sampling Problem of a Random Function of Time 35C. Sample Size Criteria 38D. Reasonable Estimate of the Correlation Function 41TABLE OF CONTENTS(continued)PageAppendix IAppendix[V METHODS OF APPROXIMATION USED INOBTAINING THE POWER SPECTRAL DENSITIESA. Method No. 2B. Method No. 3V AIRCRAFT PERFORMANCE FUNCTIONSA. GeneralB. Basic Assumptions and Definitions Used in theDevelopment of Performance FunctionsC. Assumptions for the Determination of theStatistical Properties of Rough AirD. Longitudinal Response EquationsE. Lateral Response EquationsF. The Test AirplaneG. Stability Derivatives Used in Computation of AirplanePerformance FunctionVI DESCRIPTION OF FLIGHT TEST INSTRUMENTATIONA. GeneralB. The Flight Test InstrumentationVII DESIGN OF A CORRELATION COMPUTERVIII BIBLIOGRAPHYX GLOSSARYK BIOGRAPHICAL SKETCHEST SUPPLEMENTAppendix IAppendix IAppendix IAppendix IAppendixFLIGHT TIABSTRACTIn this paper, a technique for determining the power spectral density of atmos-pheric turbulence based upon the Wiener - Lee theory of a system response to arandom forcing function is developed. The technique is then applied to therecords of measured airplane response to turbulent air.The flight test data consists of six flights representing four different meteoro-logical conditions. The results presented in Fig. 1 when reduced to an auto-correlation function in terms of distance through the air mass show no significantstatistical difference between the vertical velocity components of the turbulent airmass for the four meteorological conditions tested. The only significant differenceapparent is the mean power of the turbulence or the intensity of the gusts given inTable 1.To aid in reducing the flight test data, a correlation computer was designed andbuilt. This computer reduced the computation time by a factor of ten.The power spectral density of the rate of change of vertical velocity of the gustsspan-wise was also determined for one flight. This component of turbulence, which010~NOTE:-as Plotted points computed byCorrelation ComputerSolid curve drown from dotocomputed by I B. M puncho0 cord method. LEGEND:CONDITION # 1 o FLIGHT #85t86 (175 mph)CONDITION #2 B1 FLIGHT #87T89 (175ITSmph)CONDITION #3 - FLIGHT090 (175mph)04 CONDITION #4 A FLIGHT *91 11230mph)B 11 75 mph)Ja04L000 o 0 0 A 0 50 0A70 80 00 10A.B B00 nnA A--.....CORRELATION INTERVAL, d, In FeetFIG. 1 THE NORMALIZED REDUCED CORRELATION FUNCTION OF THE RESPONSE OF A B-25J AIRPLANE TO ATMOSPHERICTURBULENCE FOR FOUR DIFFERENT METEOROLOGICAL CONDITIONS.fvv u u 1 0TABLE 1Mean Power of TRoot-Mean SquareMeteorological 6E Response of 6 ResponseCondition [(C F) (0)] [(RMS) ()]Conditioin [degec]2 in [deg/sec]in [deg/sec] in [deg/sec]Unstable air massWater - land discon-tinuitiesThunderstormsMountainous terrain.0987.1672.1038.1224.3142.4089.3222.3499influences the airplane primarily in r o11, could not be determined with the degree ofcertainty possible for the longitudinal data due to the inadequate length of the records.However, on the basis of this limited data, a tentative conclusion can be made thatthe spectrum of this lateral component is not essentially different from the longitu-dinal component.viiiChapter 1INTRODUCTIONA. Summary of Previous WorkIn some respects, turbulence has been exhaustively investigated, and one mayjustifiably question the need or desire for an additional investigation. However, asis shown later, there is a great need for data on atmospheric turbulence of the typeherein presented. In order to appreciate this distinction, it is desirable that onereview the history of the study of turbulence that affects this problem.The most extensive program carried out by any agency within the UnitedStates for the study of atmospheric turbulence has been conducted by the NationalAdvisory Committee for Aeronautics. Unfortunately, this program was aimed pri-marily toward obtaining a statistical survey of air loads on airplanes in flight. Thisdata, in general, forms a statistical survey of the statics of extreme values (peakamplitudes only determined) of turbulent air, and in no way can be used to deter-mine a statistical survey of the dynamics of turbulent air. The correlation func-tion, which is introduced later, is a statistical parameter that measures the im-portance of the dynamics of a random process and is the basis of this investigation.The N.A.C.A. data cannot be used to obtain a correlation function for two reasons:1. The performance function or frequency response spectrum of theaircraft from which the data was measured are not known.2. Since only peak values of the output response were determined,nothing is known about the airplane response as a continuous func-tion between peaks. Consequently the dynamics of the output func-tion is completely unknown.In general, the present investigation is a practical application of Wiener's gen-eral theory.( 2 )* However, this work was not, until recently in an unrestrictedclassification; and the original idea and proposal for making this investigation is adirect result of the lectures of Dr. Yuk Wing Lee (2 2 ) of the Electrical EngineeringDepartment at the Massachusetts Institute of Technology.* See list of references in Appendix VIII for references in parentheses.In terms of the end result (the power spectral density of the turbulent air mass)this investigation is essentially the same as the correlation method of determiningboundary layer turbulence. An excellent report on this nodern statistical theory ofturbulence has been written by Monsieur Bass(13). The primary difference betweenthe study by Monsieur Bass and this investigation (other than the obvious differ-ence in scale) is that the turbulence he considers can be measured directly. Inthis investigation, it is necessary to measure the response of a sensing vehicle,the airplane, to the turbulence, and by the direct application of the Wiener - Leetheory, determine the input power spectral density.This work is an extension of a larger program in airplane dynamic research.The first and pioneering program was conducted by the Cornell Aeronautical Labo-ratory at Buffalo, New York. In this program, the frequency response of an air-plane was determined directly by sinusoidally oscillating the flight controls. Thesecond program, conducted at the Instrumentation Laboratory, M.I.T., determinedthe frequency response indirectly by making a harmonic analysis of the airplaneresponse to measured pulses. The present program leans heavily on the twoformer programs for the frequency response characteristics of the airplane andfrom this data conducts a generalized harmonic analysis of turbulent air.B. The Requirements for This InvestigationThe design of automatic control equipment for aircraft has, in the past, beenbased primarily on steady-state performance characteristics. In the preliminarydesign state, very little consideration was given to the fact that under certainmeteorological conditions, the aircraft and its control equipment would also besubjected to random inputs caused by the turbulence of the atmosphere. In general,the effect of turbulence was taken into consideration in the flight test stages of thedesign by modifications to the existing design. In some cases these modificationswere successful; and an excellent control system was obtained. However, in othercases, modifications were not so successful,The usual specifications were that the control equipment meet a certain re-quired steady-state performance, and be well-behaved in turbulent air. Thislatter requirement was not too important because the pilots were always availableto take over the controls.However, the day of the completely controlled aircraft in all types of weatheris not too far off. When this day arrives, the equipment must be properly designedto meet certain minimum requirements under all weather conditions. In addition,since the primary means of control will be automatic, it is highly desirable torealize the optimum designs for average weather conditions.The term "optimum design for the average condition" needs more careful defi-nition. Since the design is to be optimized for the average condition, it is evidentthat the design problem belongs in the general field of the statistics of dynamic ele-ments.Norbert Wiener (2 ) has solved this general problem for the case of a linearsystem subjected to random and controlled inputs. He has shown that for a givenstationary random process and a given class of controlled inputs, there exists aunique design of the mechanism which will minimize the integral squared error.However, in order to determine this optimum design, one must first determine thecorrelation functions of the controlled inputs and the random inputs.In addition to automatic control equipment, there is also the problem of sta-bilizing an airborne platform in turbulent air. In order to realize a good design,the spectrum of the turbulent air mass must be known. To meet this dual require-ment, this investigation was undertaken.The object of this investigation is to obtain the power spectral density of tur-bulent air for use in the design of control equipment and stabilized airborne plat-forms for aircraft.Chapter 2ELIMINATION OF INSTRUMENTATION SYSTEM DYNAMICSFROM THE TEST DATAThe problem of determining the power spectral density of the velocity compo-nents of a turbulent air mass is basically a general measurement problem, whereinthe output response of a sensing element is known and the input forcing function isdesired. In the usual measurement problem, the input is either periodic or of finiteduration, and consequently, is amenable to ordinary harmonic analysis. However,the velocity components of turbulent air are neither periodic nor of finite duration.In fact, they constitute a continuous infinite random set of functions. As is pointedout in Appendix I, it is not possible to obtain a harmonic analysis of such a randomfunction directly. Instead, one must make use of the auto-correlation function* andits Fourier transform, the power spectral density.In Appendix II, it is shown that the output response of a linear system to arandomly varying input is very sinmply related when the output and the input are de-scribed statistically by their auto-correlation function. In the time domain, the re-lation is given by a convolution integral as follows:0[(CF)oo (7)] = [(CF)(UIR)(t)][(CF)ii (t + r) ]dt (2-1)-00where T(C F) ()] colim 1 out (t) qout (t + r)dtT -P-oo 2T I-T* The auto-correlation function is defined as the correlation of a function oftime with itself when displaced along the time axis. The cross-correlation functionis defired ae the correlation of two different functions of time when displaced alongthe time axis.T[(CF)ii n 1 qin (t) in (t + r)dtT-. 2T i-T0[(CF)(UIR)(r)] = I [(UIR)(t)][(UIR)(t +r)]dt-00This expression can be reduced to a simpler form in the frequency domain bytaking the Fourier transform of Eq. (2-1) to give:(PSD)o()] = (PF)( )[qin qout] 1 2 [(PSD)li (w)J (2-2)where0[(PSD)oo (w)] = [(CF)oo () ] cos word-000[(PSD)ii(w)] = [(CF)ii ()] cos wdv-co CO(PF)()[qin qout] 2 = [(CF)(UIR)(r)] cos aTd-v-c00Equation (2-2) is the basis for eliminating the instrumentation system dynam-ics. The performance function used in this equation is the product of the aircraftinstrumentation performance function and the airplane performance function.In order to simplify as much as possible the data reduction problem, all air-plane response data was measured with the controls locked. If this were not done,the airplane would be simultaneously acted upon by two forcing functions and theproblem of data reduction and flight test instrumentation would be considerably inm-creased.The simplification, due to locked controls, is in itself a compromise betweenreliability of the correlation function obtained and ease of reducing the resultingdata. This compromise arises from the fact that the airplane differential equa-tions of motion are in general non-linear, but can be linearized in terms of smalloscillations about an equilibrium airspeed. With the controls locked, the air-plane eventually ends up in a tight spiral with the airspeed building up. Since theequilibrium point is now non-existent, the record must be terminated. In theflight test program, all records were terminated by a roll-off.In the case of the longitudinal response data, this compromise was quite satis-factory since record lengths of 20 to 30 response times* were obtained. In thelateral response data, these record lengths were only 4 to 5 response times and notof sufficient length to constitute reliable samples.In future programs, it will be highly desirable to consider the installation of anautopilot to maintain the equilibrium condition. This arrangement will give morereliable sampling, but has the disadvantage that the instrumentation system perform-ance function becomes a closed loop enclosing the airplane and autopilot, and con-sequently will be more difficult to determine. In this respect, a proposal has beenmade by the Flight Research Group of the Cornell Aeronautical Laboratory to cali-brate the airplane by flying over a concentrated thermal disturbance such as occursover an open hearth blast furnace. If this method of calibration proves successful,the addition of an autopilot to the instrumentation system constitutes no additionalproblem.* (RT), Response time is defined as the time required for the airplane responsetq decrease to and reriain less than 5 percent of its maximum output magnitude.Chapter 3THE PROBLEM OF ELIMINATING THE FORWARD VELOCITY OF THEINSTRUMENTATION SYSTEM FROM THE REDUCED DATAAt a fixed point in space, the instantaneous velocity of an air particle in a tur-bulent air mass can be described by a randomly varying vector. To describe thestate of turbulence at this fixed point in space, one must know both the time historyof the vector at the given point as well as the variation at a given instant of time ofthe velocity vectors with any three spatial coordinates. However, in this investiga-tion only the variation of the velocity vector in two directions at a given instant oftime is important in disturbing the airplane. These two variations are:1. The change of the normal component of the velocity vector as afunction of the distance along the flight path of the airplane.2. The change of the partial derivative.of the normal component ofthe velocity vector with respect to spanwise distance as a func-tion of the distance along the flight path of the airplane.The variation of the velocity vector with time at a fixed point in space is assumednegligible for the following reason:The lowest airplane velocity used in these tests was 299 ft/sec.The tail length of the airplane is 25.9 ft. Hence, at a fixed point inspace, the airplane can be influenced at the most by 0. 1 secondof the time history of the air mass velocity vector. It is as-sumed that no significant change in the velocity vector occurs inthis short an interval.Consequently, the random forcing function in the longitudinal case is assumed tobe given by the spatial distribution of the vertical component of the air mass velocityalong the flight path. This forcing function appears distributed in time due to themotion of the airplane through the air mass.The response of the airplane to the turbulent air mass is measured as a continu-ous function of time. This data is then reduced, by the method already presented inChapter 2, to a power spectral density of the vertical component of the air mass.This power spectral density represents the spectrum of the correlation function of theturbulent air mass as it appeared to an airplane flying at the test airspeed. To an-other airplane flying faster through the air mass, the turbulence would be compressedin time; and consequently the bandwidth of the power spectral density would be in-creased. This effect, however, can be compensated for.In Appendix I, a general relation is derived for the Fourier transform of afunction that is changed in scale, i.e.;[FT (w)][q (at)] _ 1 [FT (--)][q (t)]a aIn this particular case:*q(t) = [(CF)qq () ]A qqa = VA = True velocity of the airplane in feetper second.Applying this relation to the power spectral density of the air mass under thetest conditions, one obtains[(PSD)(w)][CF (VAr)] 1 [(PSD)( w )][CF (-)]VA VAHence, if the test power spectral density curve is scaled in both coordinatesby the true velocity of the airplane under the test conditions, a general curve isobtained that can be applied to any airplane for which the frequency response isknown at any applicable airspeed.* The symbol 4 means "equal by definition."Chapter 4DISCUSSION OF RESULTSIn the entire flight test program, more than one thousand feet of oscillographrecordings were taken. This program consisted of six flights that representedfour different meteorological conditions of the atmosphere, as follows:Condition No. 1Unstable Air Mass Flight #85Towering Cumulous Flight #86Hot Summer DayCondition No. 2Hot summer day, groundthermals obtained by fly- Flight #87ing over water-land dis- Flight #89continuities from Lowell,Mass. to Newburyport, Mass.Condition No. 3Low thunderstormsHigh ground winds Flight #90Cold front passageCondition No. 4High ground winds overmountainous terrain - Flight #91"White Mountains"Although this data cannot be assumed to be representative samples of atmos-pheric turbulence as a whole, it certainly is representative of a large group of tur-bulent air in which military and civilian flights must be conducted under normaloperations.4' ''' :'':'-' ''''I'' - '~ - -'~ ~'- -- '' :~ ~' -- T-- -- ___________________ ____ __ _I'Ttri of pitchil~I~~ II I i-----Rue I,-m.1.0 d " 9*rmcoaI I~ lIt(i V14:oI -,. y . . . .,. .. '" " ' " -' *'," -I." . -" '- -..... ~ ~ c call . . . . ,,,Nw .11le.No~mIa~I~aaIoI ~ ;FIG. 4-1 SAMPLE FLIGHT TEST DATA.0 .1 _I I:H-I--~---- ~I ~ I i I II1 ilil . L i i I iii I 1 . I i ii......... ..- ' ' ' ' ' '.1]i~;' ' ' ' r Igt No. 90Rm No. 1. N... .. Iv0Q0,. :i: .... ;i' ' i...... ' ': :Jill, : : ! , ; : I i : i !, i ! ' , i ;J1--~ ~~-~-------~~~~~~ ~-~ - - .: i ~~ L ..~' : 'i ' ' : ' ";r - ~L1.^..[ . .... IC: I , Jl LIJI[, LI J zJ .7 ..... I , ,,11 :acUmmmi liffidflli I. - . . ii . I , , 11 1IIIII*YLUIIBecause it was felt that, on the average, most persons would be interested pri-marily in the final results of this investigation, the entire group of flight test rec-ords were published in a supplement and only one sample record presented in Fig.4-1. For those persons who are interested in the entire group, the flight test datasupplements are available through the Instrumentation Laboratory, M.I.T., by re-quest.Although four output response variables of the airplane were measured, onlytwo were analyzed because of an unavoidable delay in construction of the corre-lation computer. The rate of pitch response, 6, of the airplane was analyzed com-pletely for all recorded data. The entire set of data is plotted in Fig. 4-2, which isz0U10NOTE.s Plotted points computed bygJ Correlotion ComputerSolid curve drown from dotocomputed by &B. M. punch0.6__ _ cord method. LEGENDCONDITION 0 1 FLIGHT *85186 (175mph)CONDITION *2 0 FLIGHT 687489 (175mphlCONDITION *3 - FLIGHT0 190 (5mph)CONDITION 04 A FLIGHT91 1250mph)la[(I175mph)J02 _o A A0 t 100 200 300 400 500 600 700 oo00 900 1000CORRELATION INTERVAL, d, in FeetFIG. 4-2 THE NORMALIZED REDUCED CORRELATION FUNCTION OF THE RESPONSE OF A B-25J AIRPLANE TO ATMOSPHERICTURBULENCE FOR FOUR DIFFERENT METEOROLOGICAL CONDITIONS.a normalized correlation function reduced to eliminate the true velocity of the air-plane. The plot is indeed remarkable when one recalls that it represents six flightson different days under four different meteorological conditions. This plot is thebasis for the conclusion drawn that, other than a difference of mean power (or in-tensity) of the gust, the atmospheric turbulence for the set of conditions tested is astationary random process, and can be adequately described by a single reducedpower spectral density curve. The mean power and root mean square of the outputresponse for each condition is given in Table 4-1.Figure 4-3 presents all three spectrums involved in computing the powerspectral density of the atmospheric turbulence. The three curves were plotted onthe same graph in order to graphically illustrate how the dynamics of the airplaneTABLE 4-1Mean Power Root-Mean-Squareof 8 Response of E RespqnseMeteorological [(CF) (0)] [(RMS)(e )]Condition in [deg/sec] 2 in [deg/sec]1. Unstable air mass .0987 .31422. Water-land discontinuities .1672 .40893. Thunderstorms .1038 .32224. Mountainous terrain .1224 .34992 4 6 8ANGULAR FREQUENCY, w, in Radians/sec0 .005 .01 D15 02 .025 03 .035Reduced Frequency, ( ), in (Rad per sec/Ft per sec)V AFIG. 4-4 REDUCED-NORMALIZED POWER SPECTRAL DENSITYOF VERTICAL VELOCITY COMPONENT OF ATMOSPHERICTURBULENCEFIG. 4-3 COMPARISON OF FREQUENCY SPECTRUM OFOF AVERAGE OF ALL FLIGHT TEST LONGITUDINAL DATAAT 175 m.p.h.~k.~I22~31>-p0awere eliminated from the response data. The power spectral density of the airplaneoutput response is the Fourier transform of Fig. 4-2 for a true airplane velocity of299 ft/sec and has already been corrected for the dynamics of the rate of pitch gyro.The power spectral density of the input turbulence is the output spectrum dividedby the square of the magnitude of the performance function of the airplane.Figure 4-4 is the reduced power spectral density of the vertical velocity com-ponent of atmospheric turbulence for the conditions tested. To use this curve for agiven true velocity and for one of the tested meteorological conditions,multiply theordinate by both the airplane true velocity in feet per second and the mean powergiven by Table 4-1; then, multiply the abscissa by the airplane true velocity in feetper second. This data can be used to optimize a given airplane control system.Since the airplane performance function has been linearized for an equilibriumairspeed, it is necessary to consider a number of optimum systems for the range ofairspeed desired, and then to choose a compromise design. This formidable task canbe made somewhat easier by an airplane control system simulator such as has beendeveloped by the Tracking Control Project of the Instrumentation Laboratory, M.I.T.This method would require the design of two filters and a "white noise" generator.( 2 6 )One filter must be designed to approximate the airplane performance function ratiogiven in Appendix V. The purpose of this filter is to modify the existing airplanesimulator to obtain the airplane frequency response function to atmospheric tur-bulence. The second filter must be designed so that the square of the magnitude ofits performance function approximates the atmospheric turbulence power spectraldensity curve. A preliminary check seems to indicate that a first-order networkgives a satisfactory approximation. If the "white noise" generator is then con-nected in chain with the two filters, this output signal can be added to the air-plane simulator control signal to simulate the statistical effect of atmosphericturbulence on the system.Figure 4-5 is the reduced rate of roll response correlation function of the air-plane for Condition No. 3. This curve was computed by I.B.M. methods and smoothedas indicated in Appendix IV.Figures 4-6 and 4-7 are the reduced data from Fig. 4-5. It is noticed that thepower spectral density curve of the lateral turbulence shows an apparent peak atthe "Dutch Roll" oscillation of the airplane. This peak is not considered charac-teristic of the atmospheric turbulence, but represents instead an indication of theuncertainty of the data in this case. This uncertainty arises from two main sources:1. The lateral airplane performance functions are not as reliablyknown as the longitudinal performance functions. This can beqit0 -FLIGHT #90Q8 CONDITION NO. 3175 mph0.6 --04 -020 200 00 600 800 1000 1200 ±400 600 ±800 2000CORRELATION INTERVAL, d, in Feet0.2-QO4Fig. 4-5 THE NORMALIZED REDUCED CORRELATION FUNCTION OF THE RATE OF ROLL RESPONSE OF AB-25J AIRPLANE TO ATMOSPHERIC TURBULENCE FOR METEOROLOGICAL CONDITION NO. 3attributed to the general difficulty of accurately measuring asystem performance function that has a large resonance peak.2. The sampling errors in the recorded data for the lateral re-sponse are much larger than for the longitudinal response dueto the fact that the average record length in this case is onlythree to four times the lateral response time, (RT)(lat), of theairplane. A dotted curve has been drawn on Fig. 4-7 to indi-cate the best estimate from this limited data of the lateralpower spectral density.The frequency spectrums in Figs. 4-3 and 4-6 are not shown for frequenciesbelow 1/2 radian per second because of lack of data as to their behavior in thisregion. No information was obtained in this region for two reasons:1. The airplane fixed control performance functions were notdetermined below 1/2 radian per second.142. The length of the airplane response records was not sufficient toinclude frequencies below 1/2 radian per second.This lack of data at the low frequencies is not a serious obstacle to the use of theover-all results because the major problems of stabilization of aircraft systemsarise for forcing frequencies above 1/2 radian per second.O 2 4 6. 8ANGULAR FREQUENCY, w, in Radians/secFIG. 4-8 COMPARISON OF FREQUENCY SPECTRUMOF LATERAL FLIGHT TEST DATA-k00 0.005 010 0015 0020REDUCED FREQUENCY, (-V-), in (Rad per sec/Ft per sec)VAFIG. 4-7 REDUCED POWER SPECTRAL DENSITY OF SPANWISERATE OF CHANGE OF VERTICAL VELOCITY COMPONENT OFATMOSPHERIC TURBULENCEChapter 5CONCLUSIONS AND SUGGESTIONS FOR FURTHER RESEARCHA. ConclusionsOn the basis of results obtained in this investigation, the following conclusionsare presented:1. Atmospheric turbulence is a stationary random process that can bestatistically described by a single reduced power spectral densitycurve.2. For the limited set of meteorological conditions tested, a singlepower spectral density curve reduced only by the airplane truevelocity has been determined.3. The power spectral density of the lateral forcing function velocitycomponents is apparently not significantly different from that ofthe longitudinal components.4. A correlation computer of the type designed for this thesis is aninvaluable aid for conducting this type of statistical study.B. Recommendations and Suggestions for Further Research1. This study should be expanded to include a much larger set ofmeteorological conditions. In case the turbulence appears to havea scale difference in correlation distance through the air mass, itis suggested that a characteristic length be determined for eachlarge meteorological condition that could be used to reduce thecorrelation function of the turbulence to a unique function in termsof a non-dimensional distance through the air mass. The non-dimensional distance could be obtained by dividing the correlationdistance by the characteristic length for each meteorological con-dition.2. The correlation computer should be re-designed to operate from amagnetic tape. This would be potentially faster, more accurate, andsimpler to operate.3. A compact, portable measuring system that records on a magnetictape should be designed so that it can be used to obtain future rec-ords of an airplane response to turbulent air.4. A method for obtaining the performance function for the airplaneresponse to turbulent air should be evolved that does not requirethe use of theoretical correction factors to the airplane fixed con-trol performance functions.5. An investigation should be made of the long period response andthe lateral response of the airplane by means of an airplane con-trolled by an auto-pilot.Appendix IGENERALIZED HARMONIC ANALYSISIntroductionThe theory of a generalized harmonic analysis was presented by Norbert Wiener in1930 (2) Since this investigation is primarily a practical application of thisgeneral theory, only so much of the theory as is directly connected to this effortwill be presented here. No attempt is made to present the rigorous theory, rathera conscious attempt has been made to present in a heuristic engineering manner thepractical application and usefullness of the theory. Any and all over-simplifica-tions in this respect are solely the responsibility of the author.As Norbert Wiener has pointed out (1), the theory of a generalized harmonic analysisis a natural and compatible union of two widely different fields of scientific en-deavor, statistical analysis of time series,and communication engineering. The pri-mary tools used from each field are the theory of correlation from the field ofstatistics and the theory of transient analysis of dynamic systems from the fieldof communication engineering. A short discussion is given on each of these toolsin order to lead to the general theory.A. Fourier Transform PairsIf q(t) is a periodic function of period T1, the following equations constitute theanalysis and synthesis of q(t) in terms of harmonics of the fundamental period T1 .T1 2n t2n=c 2n tj__n-q(t) = [FSC] [q(t)]e T1 (I - 2)n=-cowhere[MSC] Fourier series coefficient.If q(t) is non-periodic, it is possible to analyze and synthesize the function by acontinuous spectrum rather than discrete line spectra as in the case of a periodicfunction. The transform pair for the continuous spectrum can be developed as thelimiting case from Eqs. (I - 1) and (I - 2) as the fundamental period, TI, becomesinfinite. However, this limit must be taken properly to obtain a usable transformpair.From Eq. (I - 1) consider the following limit,Ti 2intlim2, q(t)e T' dt = L (I - 3)2but (7 )2rn tq(t)e- j TI dtIT1 TI2q(t) I dtIn order to ensure that the limit L1 of Eq. (I - 3) remain finite, it is necessaryto stipulate that11lim T2q(t) dt IHowever, when this condition is met,limT.- - TsTi 2tntq(t)e- TTo avoid this difficulty, the direct Fourier transform is defined as:{T [FSC] [q(t)]}or, in the limit:[PT] [q(t)] limPFT [q (t)] = o q(t)e-Jwt dtwherelim J 2nnTi -c -ITIn -cNow, substituting Eq. (I - 4) into Eq. (I - 2):n= =q(t) = lim -T ' n=_colim =T -c- T2nnt[FT] [q(t)I] Je T,TIlim - = lim Aw7-0 2n A -Oand in the limiting case,be finite.dt = 0 .(I - 4)(I - 5)but[FT] [q(t)]eJ- t d6with its Fourier transform pair already obtained as[Fr] (q(t)] =B. Mathematical Theorems Related to theco00q(t)e - j wt dtStudy of Atmospheric Turbulence1. The Shift Theorem(12)q(t+T)e-Ju t dt = eJWT q(t+t) e-w (t+-) d(t+u)= eJit [Fr] [q(t)]Hence:[FT] [q (t+t)] = eJ ' ' [FT] [q(t)]2. The Multiplication Theorem(10)Ifand[IFT][ql(t)][Fr] [q2 (t)]ccq±(t) = Jq2er) =2n,Ic:q 1 (t)e-jwt dtq2 (t)e-Jw dtThen, consider:ccq(t) =co(I - 6)[FT] [ql (t) ]eJ t dw[F] [q 2(t)]eJ' t dwcc'q J2 (FT] LqI(t)] [FT)lq2 (t)] eJw d (I - 7)2nf= ± o FT] [q!,(t)]e I) d J q,(t)eJwt dtwhere [FT] [q, (t) ] is the complex conjugate of [Fr] I[q, (t)].Since q (t) and q2 (t) both have transforms, the order of integration may be inter-changed so thatq() - q I(t)dt - IFTI1q2(t)]ew ) dw-- Corq() = J q(t)q 2 (t+ )d{ . (I - 8)Equating the right-hand sides of Eqs. (I - 7) and (I - 8):1-- CO [FT] [q.(t)I [F] [q2 (t)]e T d = c q1 (t)q2 (t+T) d4 (I - 9)Eq. (I - 9) is known as the multiplication theorem.For the special case that q,(t) = q2 (t) = q(t), one obtains,y- f [Fr][q(t)] 2 eJ 2 dw = q(t)q(t+t) dt . (I- 10)Eq. (I - 10) can be further specialized for r= 0 to obtain Parseval's theorem2 ][.Fr] [q (t) I d ( ---- q (t) dt3. The Convolution Integral (12)The output response of a linear mechanism to any input function beginning at "a"units in the past can be written in terms of a convolution integral by applying thethe principal of superposition, that isqo(t) = [qi(a)] [(UIR) (t-o)]da-awhere [(UIR)(t)] = Unit impulse response of the mechanism.Now let,t- a =thenqot) = - J [qi(t- )] [(UIR) (c)I]dt+aandt + aqo(t) =However, for a realizable physical system, [(UIR) (T)] = 0 for T < O, hencet+aqo(t) = fand for an infinite time processa- ,Henceqo(t) = / (UIR) (t)][qi(t-)]d .ccD4. Change of Scale(12)If q(t) has the Fourier transform [FT] [q(t)], and the symbol "a" is a constant, ora second variable which is independent of t and w, thenfC q()e-J d =[FT (u)] [q(t)](I - 11)[(UIR) (r)] [qi(t-r)]d .[(UIR) (c)] [qi(t-) ]duccJjq(a )e-ual() d(a ) = [FT(u)] q(t)Upon substitution ofTt = -aanda = uathis becomes:q(at)e-J w t dt = I[FT()] [q(t)]a aor[FT(w)] [q(at)] = -[FT()] [q(t)] . (I - 12)a aC. Statistical Analysis of Time Series1., The Correlation FunctionIn general, the functions that have been considered so far are either periodic orbounded, and converge at infinity at a sufficient rate for the integral of the ab-solute value of the function to be finite. However, there are a large class offunctions that are neither periodic nor converge at infinity. To handle this classof random functions, one must resort to a statistical analysis.A tool which the statistician often employs to measure the degree of dependence be-tween two sets of variables is the correlation coefficient (KC) defined as:N[L (xi - (av)xi) (Yi - (av)Yi)NN(KC) xy] N NN. [xi - (av) xi)]2 (aV) yi)121 1where (av)x i and (av)y i are average values of xi and yi, respectively.If the values of xi are all assumed to be discrete points of a continuous functionof time measured at equal time intervals; and if all the values of yi are assumed tobe the same set shifted by an integral number of intervals, one can define a serialcorrelation coefficient (SKC) as:[(SKC) xi+n(n)]N =NS (xi) (x i +n)NN[ (xi) 2 (xi+ n)where (av)xi and (av)xi+n have been assumed zero for convenience.Now let the number of variates, N, in the time series increase without limit. Letit be assumed that the statistical properties of the series approach definite limits,(or that the series is in statistical equilibrium). In this case,Nlim 1 (xi )N %.NCOlim 1N, NN1(xi+n) 2and consequently the numerator by itself is now a measure of correlation.has defined the auto-correlation function to be the following limit:i=N[(C0 )xx(n) 1 im 1 ixi+nN- - xixi+nN-- =2N 1i=-NWiener(I - 14)When the time interval between successive variates in the series is decreased inde-finitely, the auto-correlation function for the continuous case is defined as:[(CF)qq(r)I] = dt (I - 15)2. Properties of the Auto-Correlation Functiona.Consider: [q(t) + q(t+)] 2 0or:[q(t)] 2 + [q(t+t)] 2 2q(t)q(t+)and, averaging both sides:(I - 13)lim r 1a q(t) q (t+T)T-.- CO Tli aT-n -T [q(t)]2 dt + ,J22 lim +.-T--but, for a stationery random process:2Tbut, for a stationery random process:lim 1T -jo 2T[q(t)] 2 dt[q(t+) ] 2 dtq(t)q(t+) dt }(T= lim - /T 2TSr (CF)()] I[(CI (t)] = lmT---v-q(t)q(t+-T) dt .12T-TDefineS= t+t = s-anddt = ds .Then[(CF) (1)] =1 /lim -- q(s-r) q(s) ds = [(CF) (-)] .T---c 2T-T(I - 17)D. The Harmonic Analysis of Random FunctionsAlthough the Fourier transform of a stationary random function does not exist, itHence,(I - 16)[(CF) (0)] ~ +± [(CF) ()][(cF ()] >[q(t+)] 2 dt Idoes have a correlation function whose transform does exist. The Fourier transformof the correlation function is called the power spectral density, and is defined asfollows:[ (PSD) (W)] =and1(CF)(I - 18)[(CF) (t)]e-J dT[(PSD) (w)]eJ 'd .Since the auto-correlation function is an even function of time, this reduces to,(I -- 19)(PSD) ()I] = 2 (CM (r) ] cos Wr d00and1[(CF) (v)] =- [(PSD) (w)] cos Ct d .The following properties of the power spectral density, (PSD), are useful:1. [(PSD) (0)] = 2 f0 [(CF) (c)] dt2. [(PSD) (w)] = [(PSD) (-&)]3. From Eq. (I - 10),I2 q(t)q(t+)T2}('1dt = lim -S T1-. - TiS [FT [q(t)]eJ2n-lim siThen, taking the direct transform of each side,lim ITT--.I TI dW}dw(I - 20)[(PSD) ()][q(t)] = lim TI [FSClq(t)] .T, I[FSCIq (t)] 2 ej'Appendix IIINPUT - OUTPUT STATISTICAL RELATIONSHIPSSince the correlation function measures the statistical importance of the dynamicsin a random function of time, one may equally well develop the input-output statis-tical relationship from the point of view of applying the theory of correlation tothe convolution integral or one may choose to develop these relationships as anaveraging process of the system output as given by the convolution integral. Thelatter approach is used here because the author wishes to emphasize the importanceof thinking in terms of the dynamics of the system first, and the statistical ana-lysis of these dynamic relationships as a later specialization.In Appendix I, it was shown that the output response of a linear system can be writ-ten in terms of the convolution of the system unit impulse response and any knowninput forcing function, that is:qout(t) = / [(UIR) (a)] [qi,(t-a)] do (II - 1)where a is a dummy variable of integration.A similar equation for the output displaced in time by the interval, T, is:qout(t=) =J [(UIR) (v)] [qin(t-v+r)] dv (II - 2)where v is a dummy variable of integration.These two equations can be applied to any bounded input whether it is finite or in-finite. When the input is a random function, the output, although also random, willinclude the dynamics of the system. In the particular application of investigatingatmospheric turbulence, one cannot measure the input directly, but one can measurethe airplane response; consequently, the analysis starts from determining the auto-correlation function of the output. The auto-correlation function of the output isdefined as:T1 /(CF)lim qo(t)qo(t+t) dt . (II - 3)T-Substituting Eqs. (II - 1) and (II 2) into Eq. (II - 3) gives,Substituting Eqs. (II - 1) and (11 - 2) into Eq. (11 - 3) gives.,27TTim -T TTdt f [(UIR) (o)] [qi(t-a) ]do] La[(UIR) (v)] dv /[(UIR) (v)]dv J [[(PSD) 0oo (0 )] =[(UIR) (a)]da lirT-- m2T7-[(UIR)(v)] (qi(t-v+)]d I dv[qi (t-o) ] [qi (t-v+r) ]dt(UIR) (a) Ido [(CF) ii (+v-)]/[(CF)oo (T)] e-J" dT[(UIR) (v)] dvdT J a[(UIR) (a)]da[(CF)iiT + V- a = S .Then,[(PSD)oo (w)] =Tas /[(UIH) (v) ]dv/o[(UIR) (a) ]dao[ (CF) ii(s) ]e-J (s+o-v)[(UIR) (v)]eJ V dv I [ (C) ii(s)])e-J's ds[(PSD),oo ( ] = (PF) (O/cocoHowever,or,Now let,=occoObut:Hence,(T+v+o)]e-J[ (PSD)oo ()]I =rc[ (UIR) (c)]e-J do(PF ( ) [qinqout ] J [(UIl) (t)]e-jt dt)[qinqout] (PF ) ( )qinqout ] [(PSD)ii() ]PI ( ) [qinqoutll I [(PSD)ii()] .This equation is the mathematical basis for the calculation of the power spectraldensity of atmospheric turbulence from the airplane response power spectral density.In the discussion of the sampling problems involved in the determination of the out-put auto-correlation function, the statistical input-output relationship in the timedomain is useful. This relationship is obtained as follows:From Eq. (I - 10), since(PF) ( ) [qinout] :one obtains(J j P ] eJ d = IIf we defineL(CF) (UIR) (r)] [(UIR) (t)] [(UIR) (t+t)] dt1[(CF) (ur ) (1)] =and its direct transform is:I (w(Define:[Fr] [q,(t)] =] j=oI(PF)[(CF) (UIR) (t)]e-J dT2 (II - 6)(II - 7)(FT] [q2 (t)] [(PSD)iiIf Eqs. (II - 6) and (II - 7) are substituted in the multiplication theorem given byEq. (I - 9) in Appendix I, and in addition identify terms in the resulting equationwith the following relationships,thena(II - 5)IPF ]I eJwT do[(PSD)oo (W)]: (II - 4)j [(UIR) (t)]e- jP t dt[ (UIR) (t)] [(UIR) (t+T))]dt .[ (PSD) 0 0 (W) ] = 11 2I(PF)[(cF) oo() =[(CF) (UIR) (t) =[ (CF) ii (T) ]//cc2l[ (PSD) oo ( w) ] eJ " d2 ej't db[ (PSD) ii (M ) ] eJ ' d1Then, one obtains:[ (CF) (UIR) (t) [ (CF) ii (t+) ] dt . (II - 8)This relationship is used to estimate the interval of significant correlation of theairplane response data.[ (PSD) ii ][ (CF) oo () =Appendix IIITHE SAMPLING PROBLEMS INVOLVED IN THE APPLICATION OF THETHEORY OF A GENERALIZED HARMONIC ANALYSIS TO A FINITENUMBER OF RECORDS OF FINITE LENGTHIntroductionIn the practical application of the theory presented in Appendices I and II, rec-ords of finite length must always be used. From these records it is desired to ob-tain the best estimate of the correlation function and the power spectral density ofthe entire group of data from which a limited number of samples are available.There are two techniques for the solution of this sampling problem:1. A reasonable method of averaging the approximate correlationfunctions based on a finite sample which will be a consistent esti-mate of the correlation function of the entire group,2. A reasonable method of averaging the Fourier Series coefficientscomputed from the finite records to obtain a consistent estimateof the power spectral density of the entire group according toequation (1-20), i.e.,[(PSD)(w)][q(t)] = lim TiI [FSC] [q(t) 1Tf--9-0 IIBoth methods are theoretically valid approaches to the sampling problem butthe amount of work involved in the second approach is considerably greater than(6)that in the first method. For example (6), suppose one chooses to reduce a givenfinite record by measuring M data points at equal increments of time. Then, byemploying a straight line approximation to the time curve between each successivepoint, an approximate harmonic analysis (8 ) can be obtained as follows:[sin - At 1mn[FC] [q (t) ] - nnTiqn (mAt) cos - mAt-At Jm=OT,m=M- 3 qm(mAt) sin -- mAt (III - 1)T,To compute M harmonics, there are requiredM 2 multiplications and M2 ad-2ditions.If the length of the records is assumed to be at least 30 times a response time,(RT), of the dynamic element in the function of time being analyzed, thenMAt = 30 (RT)(The desirability of meeting this requirement on a record length is discussed fur-ther under the sampling problem of correlation functions.)The correlation function for a discrete time series is defined as:M-m[(CF) xx(m)] x- ixi + m0Figure III-1, which is a graphical illustration of convolution required to obtain theoutput correlation function, shows that the interval of significant correlation isapproximately equal to the response time of the mechanism plus the interval ofsignificant correlation of the input function. For an approximate criteria, one canassume the interval of significant correlation is not much greater than one response1 M211time (RT). Hence, there will be approximately -M2 multiplications and 1M230 30additions required to compute the correlation function. In addition, to compute thepower spectral density according to the equation*rsin -A 2 [ (PSD) (,) ] [q (t) ] AT A2 2CF(nAT) cos wnAt - CF(0) (III - 2)M 1 M2 1M2for frequencies, multiplications and - additions are necessary.22 30 2Y30Hence, to determine the power spectral density by first computing the correlation1function, the amount of work has been decreased by approximately 20. It is for* See Appendix IV.[(CF)iumft)]IT(cor) i t[(C F)00(n)](a)n[(CF)00 (r)(a)o0[(c F)oo0 0 ()] = [(c FuI(t)][(c F)ii(t + )]dt= [(CF)00()](a) + [(cF)OO()](b)+ [(CF)o0O()](c) + [(CF)00( )](d)where:[(c F)OO()](a) = [(C FIUIM(t) ]2 [(CF)ii(t + r) 2 dt-00[( F0 ()= I[(CF) UIR4t) 1 [(C F)i/( +) 1dt[(cF)00oo()](b) = J [(cFuII(t)] [(cF)ii(t +-r)] 2 dtI0000[(CF)00(-r)](c) = f [(C FkuR)(t) 12 [(C F)ii(t +r) ]2dt-0(RT~j~)[(CF)00( )](b)T(cor)i[(C F)oo(0rk)](d)'k[(C F)0 0 ( )](d)(RTUIR) T(cor) (RT UIR)+ T(cor)iFIG. m-1ILLUSTRATION OF A METHOD OF OBTAINING THE OUTPUT CORRELATIONFUNCTION BY GRAPHICAL CONVOLUTION.[(CF)ii(t)]2T(cor)[(C F)00( k) ](c)[(CF)00(o)1(c )(C F)H(t) ]1[(CF)oo(Tn)](b)this reason that the first method was used exclusively.A. The General Problem of Estimating the Correlation FunctionSince the correlation function is defined for the infinite sequence only, it isnecessary to consider methods of estimating the correlation function from finitesamples of the random function. In any sampling problem, the size of the sampleis of prime importance, and consequently a criteria for determining sample sizeis the first consideration.It has often been suggested that if one selects the sample lengths of the timeseries so that the total length is greater than 20 to 30 times the interval of sig-nificant correlation, then the correlation function can be estimated by an approxi-mate one based on the finite limits. This criteria is objectionable for two reasons.First, the interval of significant correlation cannot be determined until data hasbeen actually correlated, and hence this criteria cannot be used as a gauge in de-termining, a priori, the minimum length of the data record. Second, the question ofthe interval of apparent significant correlation is dependent upon the size of sampledue to sampling errors. Consequently, some criteria must be given for determin-ing what is a significant correlation and what is a sampling error. It is felt thatthese two objections must be resolved before one can discuss a reasonable esti-mate of the correlation function.If the sampling distribution of serial correlation coefficients were known,these sampling values could be used as in the case of random sampling to deter-mine the best estimate of the correlation function. Unfortunately, the theory ofsampling have not as yet been extended to the general case of time series. Thedifficulty lies in the fact that the individual members are stochastically dependenton time and the order of the individuals in each sample is important. This is nottrue in the case of random sampling. Special solutions of the sampling distributionof the serial correlation coefficient of a circular* time series, wherein the variatesare normally distributed, have been worked out (2 7 ) (2 8 ), but the general applicabilityof these solutions is highly questionable in the case of a continuous function of time,* The term "circular" means that the first and last terms of the series are identical.because no criteria are given for selecting the interval between data points to becorrelated. To be more specific, since a continuous function of time has within anyfinite record (no matter how short) an infinite set of points from which a timeseries can be selected to represent the continuous function, unless some criteria isgiven for the selection of these points, their number cannot be a measure of the sizeof the sample. This question of sample size is important since it gives an idea asto the proper method to weigh the sample serial correlation functions. The problemof determining a qualitative measure of the size of a time sample as well as thesignificant correlation can best be examined by means of an idealized theory.B. The Sampling Problem of a Random Function of TimeIt has been shown in Appendix II that for a linear system excited by any inputfor which a correlation function exists, the output correlation function can bewritten as:cc(CF)oo ( ) [ (CF) (UP) (t) ] [(CF) ii (t+T) ], dt (III - 3)where(Ci-F) (UIR (t)] =/ [(UIR) ()] [(UIR) (r + t)] dtFor the purpose of gaining an insight into the sampling problem of the outputserial correlation function, let the input be defined as a random sequence of deltafunctions where the delta function is defined as6 0(t) = O for (t < - e) or (t > + e)lrm 2 2e 0 1 e e6(t) =- for (- - < t < -)e 2 2then,n=+Nq(t) limr a n 6(t- tn)N--n=-NwheretAt-n = -tnThe coefficients a are independent random variables with zero mean and thensame probability distribution; and the time increments, (tn - tn-1) are independentrandom variables and have the same probability distribution. For these assump-tions it can be shown (2 2 ) that for the infinite process,(CF) ( ] [ (US) (an) 1 ] 6 (U)[tn - tn-11avwhere[N(MS) (an)I] - aHowever, the approximate correlation function of a finite sample of this infiniteset of delta functions is, i=NI[(CF) ii( WIT = >bi 6 (T - i )i=OHence, there exists spurious correlations of the input entirely due to sampling.This sample correlation function that consists of a finite set of delta functions re-duces to a single delta function at the origin when the sample length is infinite. Thelonger the sample the more dense becomes the set until in the limit the delta func-tions at all points different from the origin overlap and the average is zero. In thecase of the random set of delta functions the proper average to be used for thesample is not clear, but one can obtain an idea of the interval of significant corre-lation. This interval is useful to obtain an estimate of the errors in sampling for[(SKC)(r) ]T = 0.In this example, for the infinite sequence since[(CF)oo() = [(CF) (UIR) (t)][(CF)ii(t+T)] .dtthen,[ (CF) 0 1 () -[ (an )I [ (CF) (R () ][t n - tn-11avIf the response time (RT) of the system is defined as the time for the outputto decrease to and remain less than 5 percent of its peak magnitude, then:[(CF) (UIr) (RT)] r [(CO)oo(RT)]This is illustrated graphically in Fig. III-1.Hence, in the case for which the input consists of a random sequence of deltafunctions, any correlation greater than 5 percent at T = (RT) is largely an errordue to random sampling.For atmospheric turbulence the disturbances will not be delta functions. Inreference 24 it is shown from experimental data that the average gust is close to10 chord lengths. From this information, the average time duration of a gust forthe B-25 airplane is approximately:2(10C)[tdr]av 299 - .67 sec (175 mph, 10,000 ft)where[tdr ]av is the average gust duration timeC is the chord length of the airplane.On this basis, one can anticipate that the significant correlation interval of thegusts is about 1.0 second. Combining this knowledge with a knowledge of theresponse time of the system, the significant correlation interval of the airplaneresponse should be approximately:T(cor)o = (airplane + 1.0 secFor a B-25 t 175 mph and 26 percent M.A.C. and neglecting long periodeffects (see Appendix V):Wn = 2.4 rad/secDR = 0.7(RT)A(Long.) 3(CT)A(Long.) = 1.8 sec1(CT)A(Long.) (DR) Wn 0.6where (CT)A(Long.) is the characteristic time of the longitudinal response of theairplane. Consequently, there should be no significant correlation in the longi-tudinal case beyond 2.8 seconds.In the lateral response, for a first approximation, one can neglect the rollsubsidence and consider the correlation determined primarily by the "DutchRoll" mode. For a B-25J (4 ) at 175 mph and 26 percent M.A.C.:Wn = 1.4 rad/secDR = 0.15(RT)A(Lat.) 3(CT)A(Lat.) 15 secwhere (CT)A(Lat) is the characteristic time of the lateral response of the air-plane. Consequently, there should be no significant correlation beyond 16 seconds.C. Sample Size CriteriaIt has been previously pointed out that the length of the record cannot be a meas-ure of size of the sample. Rather, one must use a measure that includes the rela-tive importance of the dynamic time constants of the series. If the number of ran-dom disturbances can be spotted on the record, this could be used as a measureof size. However, in many cases these disturbances cannot be separately counted.In this case, the number of response times, (RT), in the total length will on theaverage accomplish the same purpose. The response time is a measure of theinterval in which the system dynamics are important. Hence, any choice of datapoints within this interval are on the average largely dependent upon each otherdue to the system dynamics. On the other hand if we assume that each disturb-ance is independent of each other, then data points selected at intervals greaterthan a response time are primarily related by the random nature of the disturbinginput and to a very small degree by the system dynamics. Hence, the number ofresponse times of the airplane included in the measured record is proposed as ameasure of sample size.By reasoning from the results of random sampling, one would expect that forlong records the distribution of serial correlation coefficients should be nearlysymmetrical and a mean based upon weighing each serial correlation coefficientby its length is a reasonable estimate. By the term "large" one should mean morethan 20 to 30 disturbances, and hence the length of records should be in general20 to 30 times the response time (RT) of the dynamic element relating the randomgenerating functions to the output functions. Since the length of the significant corre-lation interval will be closely related to the (RT) of the dynamic element, thiscriteria agrees very well with that given by Mr. Bubb(10) for an approximate cor-relation function. However, from a knowledge of the response time of the systemthis criteria can, a priori, be used as a rule for determining the length of recordwhich will on the average have a minimum sampling error (i.e., a large sample).As a guide to further research on turbulent air as well as a check on thereliability of this proposed sample length criteria, an actual check of the effect ofrecord length on the sample correlation function was made. The original record,which was 57 seconds long, was divided into four equal parts. The first quarter,the first half, the first three-quarters, and then the entire record were correlatedand the results plotted as shown in Fig. III-2. The first quarter, which is only 7response times of the rate of pitch response of a B-25J is extremely erratic andfails to converge properly. The first half, which is 14 response times, is im-proved somewhat but is still unreliable. However, the three-quarter length and thefull length indicate convergent correlation functions that are in reasonable agree-ment. These results experimentally verify the criteria that the record lengthshould be at least from 20 to 30 response times of the airplane. Contrast theseresults with that shown in Fig. 111I-3, which is the correlation function of the rate ofroll response of the airplane. In this case, the correlation function determinedfrom the entire record available is erratic and fails to converge. This is due tothe fact that the response time of the airplane in roll is 16 seconds and conse-quently, this record is only 4 response times. The roll data records are of in-sufficient length and therefore this data is not as reliable as the longitudinal re-sponse data.It might be pointed out here that if the "long period" response data of the air-plane, which has a response time of approximately 5 minutes were desired, oneshould obtain continuous records of from 100 to 150 minutes. This presents arather difficult instrumentation problem.CORRELATION INTERVAL, 7,in SecondsCORRELATION INTERVAL, , in Seconds CORRELATION INTERVAL,r , in SecondsFIG. III-2 ILLUSTRATION OF EFFECT OF SAMPLE LENGTH ON CONVERGENCE OF THE CORRELATION FUNCTIONcqa)1-U,tv(IDUCUCUU)co.aU)toaU-to-)Ca.)U)C138 -------0.8--"0-- -- - -0 L25I00/ 3 4 8CORRELATION INTERVAL, r, in Seconds-0.2FIG. m-3 ILLUSTRATION OF LACK OF CONVERGENCE OF SAMPLE CORRELATION FUNCTION FORRATE OF ROLL RESPONSE OF B-251 AIRPLANE DUE TO INSUFFICIENT LENGTH.D. Reasonable Estimate of the Correlation FunctionThe approximate correlation function (with finite limits) is a measure of co-variance of a time series with itself under shifts in time, and as such includes notonly a measure of the stochastic dependence but also the change in standard de-viation of each section of the time sequence as the sequence is shifted. It is onlyfor the infinite limit where the standard deviations are constant under shifts intime (stationary process) that the correlation function is a true measure of corre-lation. One can therefore define a large sample as one wherein the mean valueand the standard deviation does not change more than 5 percent at the largestsignificant value of the correlation interval. For large samples, the most reason-able estimate of the correlation function will be found by weighing each covarianceby the length of the interval and averaging over all samples.In case the standard deviation does change more than 5 percent, the bestmethod of averaging cannot be definitely specified because the sampling distribu-tion is not known. One might weigh each sample serial correlation coefficient byits length and average over all samples, but this would be equivalent to assuminga symmetrical distribution of the serial correlation coefficients. From the generalresults obtained in random sampling theory it seems that this might be a poorassumption. Another possibility would be to weigh and average the covarianceand the standard deviations for each sample separately and consider a reasonableestimate of the serial correlation coefficients for all samples to be the ratio ofthese averages. This method is easier to apply and in this investigation wasassumed to be the most reasonable estimate; i.e.,[ (Covar)q (t) q.(t+-) ]Tn[(CF)qq(T) ] [(Var) q (t) ] Tnn-_[__ _qMI_ _ )]Tn-where (Var) q (t+) ] T[(Var)q(t)]Tn is the weighted mean of the variance or mean power ofnq(t) over N records in a given flightN TSN Z / [q(t)] 2 dtTn 0[(Covar) q (t) q (t+ u ]Tn)_U is the weighted mean of the covariance of q(t)and q(t+r) over N records in a given flightN Tn-t(Tn q(t)qo(t+o) dt(Tn._r) 0 0[(Var)q(t)]TnT is the weighted mean of the variance of q(t) as a func-tion of the correlation interval TNZ (Tn-)oN Tn-7 f0 0 [q (t)] 2 dt[ (Var) q (t+T) ]Tn- is the weighted mean of the variance of q (t+r) as afunction of the correlation interval, TA 1(Tn )N TnTo o[q(t') ] 2 dtTh is the length of the n-th sampleN is the total number of samples.However, this presents increased computational work that may or may not bejustified depending upon the relative magnitude of the sampling errors involved.To check whether or not this refinement was justified, the data for Flight No. 90was reduced by three methods:1. Best estimate obtained by correcting for both the change of meansquare and mean with respect to an arbitrary base line as a functionof the correlation interval.2. Approximation to the best estimate based on correcting for only thechange in mean of each record with respect to the same arbitrarybase line as a function of the correlation interval.3. Approximation based on correcting the covariance of the entireset of records for the flight by the mean of the entire set withrespect to the same arbitrary base line at zero correlation in-terval.The results are presented in Figs. III-4 and III-5. From these figures it isseen that the difference is, at the most, no greater than 3 percent and consequently1.0 I 1 I I I6FLIGHT NO. 90TRANSIENT DATA AVERAGED BY I.B.M. METHODMETHOD No. 1 - Best estimate obtained by correct-ing for both the change of meansquare and mean with respect to anarbitrary base line as a function ofthe correlation interval.METHOD No. 2 - Approximation to best estimatebased on correcting for only thechange in mean of each record withrespect to the same arbitrary baseline as a function of the correlationinterval.METHOD No. 3 - Approximation based on correctingthe covariance of the entire set ofrecords for the flight by the meanof the entire set with respect to thesame arbitrary base line at zerocorrelation interval.No. 3o No. No.2CORRELATION INTERVAL, r, in SecondsFIG. III-4 COMPARISON OF THREE METHODS OF COMPUTINQ THE CORRELATIONFUNCTION FOR RATE OF PITCH RESPONSE, 0.OU 9-0.FLIGHT NO. 90TRANSIENT DATA AVERAGED BY I.B.M. METHODSMETHOD No. 1 - Best estimate obtained by correct-ing for both the change of meansquare and mean with respect to anarbitrary base line as a function ofthe correlation interval6 METHOD No. 2 -4 - -__ METHOD No. 3 -Approximation to best estimatebased on correcting for only thechange in mean of each record withrespect to the same arbitrary baseline as a function of the correlationinterval.Approximation based on correctingthe covariance of the entire set ofrecords for the flight by the meanof the entire set with respect to thesame arbitrary base line at zerocorrelation interval.No. 3"0.2 No. 2CORRELATION INTERVAL, ', in SecondsFIG. 111-5 COMPARISON OF THREE METHODS OF COMPUTING THE CORRELATIONFUNCTION FOR THE RATE OF ROLL RESPONSE,this refinement in the computation is not justified. All the remaining flights werecomputed by the simplest method indicated by Method 3.IIAppendix IVMETHODS OF APPROXIMATION USED IN OBTAINING THEPOWER SPECTRAL DENSITIESIt has been shown by Wiener(1) that the power spectral density and the corre-lation function in addition to being Fourier transforms of each other are also evenfunctions of frequency and the correlation time interval, respectively. Hence, thetransform pairs reduce to:[(PSD) ( 2)] = f [(CF) (r)] cos wor d (IV-1)0[ (CF) (1 [ (PSD) (W) ] cos t dw (IV-2)0There are three methods available for accomplishing these transforms on ex-perimental data:1. By approximation of the entire range of the experimental data with ananalytical equation and obtaining the transform in the closed form.2. By approximation of the experimental data by a series of analyticalsegments and obtaining the transform as the summation of the trans-forms of the segments.3. By appropriately combining methods 1 and 2 to obtain the best fit.For the data obtained in this investigation, Method 1 seems to be the least de-sirable since it was shown in Appendix III that the correlation function of the outputis, in general, a convolution and cannot be reasonably approximated throughout itsentire range by an analytical expression.In the longitudinal response, no correlation exists beyond 3.0 seconds exceptfor primarily sampling errors. Hence, in this case transforming the data by thesecond method is preferred.In the lateral response, correlation should exist to 16 seconds. However, it isnot advisable to attempt to correlate this data for the full time interval because thecorrelation function at 8 seconds is already becoming erratic. The lateral data canbe best approximated by the third method.A. Method No. 2In reference 8 a general method of approximating transforms that is based uponan isosceles triangle approximation to the true curve is presented. Although morerefined approximations are possible and may in some cases increase the degree ofapproximation by giving curved segments between the data points that more nearlyfit the experimental curve, this additional refinement is, in general, not justified.Therefore, the only method of transforming analytical line segments considered inthis thesis is the straight line segment system.The triangular pulse used for approximating the experimental curve is definedin Fig. IV-1. This triangular pulse leads to approximating the experimental curvecurve by a series of chords, as shown in Fig. IV-2.THE UNIT TRIANGULARPULSE HAS UNITAMPLITUDE(UT)(t) -- - - -(-TIMEt -I AMPLITUDE OFI I( I TRIANGULAR IPULSE TTIME -BY DEFINITION, THE UNIT AND GENERAL PULSES ARESYMMETRICAL AND HAVE A COMMON TIME DURATIONOF 2 ATCONSEQUENTLYT(t-t) T (UT)(t-T)]FIG.E-i. DEFINITION OF UNIT TRIANGULARPULSE AND GENERAL TRIANGULAR PULSE.-3At -2At - At 0 At 2At 3AtTime, tFIG. IV-2. THE TRIANGULAR PULSE METHOD OF APPROXIMATIONThen,n=Nq(t) - q(0) [ (UT) (t) ] +[Fr] [q(t)] -q(0) [Fr][(UT) (t)] +q (nt) [ (UT) (t - nAt) ]n=Nq (nAt)n=-N[Fr] [(UT) (t - nat)but, by the shift theorem:[Fr] [(UT) (t - nat)] I e-j n A t [Fr] [(UT) (t)]where w is measured in radians per second.and(IV-3)(IV-4)Since q(t) is an even function of time, Eq. IV-4 reduces to:sin(At n=N[FT] [q (t)I] At[IAt 2 ]2 2 q (ndt) cos (wnAt) - q (0) •- n=02This result can nowIV-2 to give:[(PSD) (W)] - At[ CF (r)] -be applied to the transform pair given by Eqs. IV-1 andsin[ 06..Z2 ]2r~s in -[ 2 ]22 CF(nAt) cos enAt - CF(0)n=02 (PSD) (nw) cos nA - (PSD) (0) (IV-7)n=0B. Method No. 3The correlation function of the lateral response has a damped sinusoidal re-sponse for all values of r >1.0 seconds. Hence, the lateral response correlationfunction can be approximated by:S(cF $$ () ] = [(CF) $$ (T ] (osc) + [(CF)$ ()1] (rem) (IV-8)The remainder component is transformed by the triangular approximationmethod the same as the correlation function for the longitudinal case. The oscil-latory component is transformed in the closed form from the following equationwhich is to be fitted to the experimental curve.[(CF)4$ (t)](osc) = A(osc) e-(DR) wat sin{n 1 - (DR) 2 t + (PA) (osc)}(IV-9)Then(IV-5)(IV-6)[A(osc) sin(PA) (osc) {1 + j (CT) (osc) "[FT] [(CF) 4 (t)] (osc) = 2 Re (CT) (osc) ( _ 2) + j 2(DR)n2A(osc) sin(PA) (osc) [n -2] ]+[2(DR)w n] (CT) (ose)w 2(CT) (osc) [ 2 _ 2]2 + [2(DR)n12 ( 2 Jwhere (IV-10)(CT) (OSCA sin (PA) (osc)(cT) (oc) -n[ V1- (DR)2 cos(PA)(osc) + (DR)sin(PA)(osC)(PA) (osc) td V1 - (DR)2 nFor the B-25J airplane flying at 175 mph and 8,000 feet altitude from data extractedfrom reference 4, the following parameters are determined to fit Eq. IV-9 to theexperimental data shown in Fig. IV-3.DR = 0.15W = 1.4 rad/secFrom Fig. IV-3 for td = 1.8 sec, the phase angle, (PA)(osc) = 143 degrees,(CT)(osc) = - .615 and the amplitude A(osc) = .269.When these values are substituted into Eq. IV-9, one obtains[(CF) 4 (t)] (osc)= .211 e- 2 1lt sin{ 79.5t + 1430} (IV-11)and, the Fourier Transform of Eq. IV-11 which is given by Eq. IV-10 is given by:] 1.2582 - 1.96 1[FT] ((C(j,() (S) = .43 [ 5,2 - 1.96 (IV-12)_ 1.96)2 + (. 1764) w21.0CORRELATION OF RATE OF0.8 ROLL RESPONSE, .FLIGHT NO. 90175 mph0.60.4/Approximate correlation function0.2-0.21 - 1 - - - - - - - - - - - - -0 2 3 4 5 6 7 8CORRELATION INTERVAL, r, in SecondsFIG. IV-3 COMPARISON OF BEST ESTIMATE OF EXPERIMENTAL NORMALIZEDCORRELATION FUNCTION WITH THE APPROXIMATION USED TO COMPUTETHE POWER SPECTRAL DENSITY FOR THE LATERAL RESPONSE DATAThe lateral response power spectral density can then be computed by:[ (PSD) (M) ] = [FT] [ (CF) (-1) ] (osc) + [FT] [ (CF) $ () ] (rem) •.8-C-)Appendix VAIRCRAFT PERFORMANCE FUNCTIONSA. GeneralIn Appendix II, the general input-output statistical relationship was developed as:(V-i)In this section the performance functions of the airplane are derived. Theseperformance functions are used to compute the power spectral density of the inputfrom the output power spectral density.aLNote:W=ZU=X IFIG.Y-i RIGHT-HAND AIRPLANE AXIS SYSTEM AS DEFINED BY N.A.C.A.ZA(PSD)()- =(PFI) 2 [(PS)i)[(PSD)oo0(w)] (PF) ( )[ I]I [(PSD)ii(Lo)]B. Basic Assumptions aid Definitions Used in the Development of Performance FunctionsIn this analysis,the N.A.C.A. Standard Airplane Axes and definitions of displace-ments are used. (See Fig. V-1).The derivation of the classical linearized equations of motion of an airplane forsmall oscillations about a point of equilibrium is not pertinent to this investigation,and consequently only the end results of this theory are presented here (1 1 )C. Assumptions for the Determination of the Statistical Properties of Rough AirThere are two principal types of rough air, namely, thermals and wind gusts.The rough air thermal is characterized by variations of the air mass principallyin the vertical direction. Gusts are characterized by variations ofwind in the horizontal direction. Each presents a problem to thecontrolled aircraft at different conditions. The thermals are encountered mostly be-tween 1,000 and 20, 000 feet, and gusts primarily close to the ground. However, asfar as the airplane is concerned they present similar problems. This analysis dealsprimarily with thermals, but can be extended easily to include considerations of gusts.A cross sectional view of the velocity distribution of a rough air thermal isassumed to be as shown in Fig. V-2.Rising AirFIG. V-2 CROSS-SECTIONAL VIEW OF A SIMPLIFIED THERMALThe rough air thermal makes itself apparent to the airplane in two principalways:1. There will be a change in the relative normal velocity of theairplane with respect to the air mass, i. e.,AW[A-P](norm) WA-I2. There will be a variation in the magnitude of the normal ve-locity of the air mass spanwise, i.e.,AP [A -P] = w[A-I](norm)ayRough air acts on the airplane like a load disturbance on a servo except thatthe summation points are in velocities instead of torques or forces. This is truebecause aerodynamic forces are generated by the relative velocities between thebody and the air mass.F(result)WA-IFIG.~-3 AIRPLANE FUNCTIONAL DIAGRAMFOR ANALYSIS OF RESPONSE TO ATMOSPHERIC TURBULENCEReferring to Fig. V-3, it is evident that by proper manipulation of the equationsof motion of the airplane, one can develop the following performance functions:(PF)A[Ey (V-2)(PF)A [wA-1, ] (V-3)(PF)A [ 6a' ](V-4)(PF)A ['7A-I (V-5)ayThe important point to note is that since Eqs. (V-1) and (V-2), and Eqs. (V-3)and (V-4) encompass the same loop respectively in their transfer functions, theyhave identical denominators. The first and third functions can be measured directlyon the airplane. The second and fourth can then be computed theoretically. Hence,the rough air performance functions can be determined within engineering tolerances.D. Longitudinal Response EquationsNeglecting non-steady airflow effects, the longitudinal response of an airplanefor fixed controls is composed of two damped oscillations. One is a lightly dampedlong period motion that is called the "Long Period Oscillation." The second, usuallynear critical damping and having a period of about two seconds, is called the "ShortPeriod Oscillation."It was pointed out in Appendix MI that in order to obtain a reliable estimate ofthe correlation function, which included the long period oscillation, one must have arecord length of from 100 to 150 minutes. A recording system designed to accommo-date a time interval of this length would lose completely the fine detail in the shortperiod oscillation. Hence, to obtain a correlation function that includes both longand short period effects would require two recorders with provisions for synchro-nizing the records. The total correlation function would then be obtained as follows:T[(CF)qq(r)]A(total) = lim - [q(SP) q(LP) (SP ) (LP)(t+ )dtT-- 2o -Twhere[(C F)qq() ]A(total) = Correlation function of the total airplane responseq(Sp) = Short period responseq(sP)Aq(SP)= Long period responseor[(CF)(T)]total = [(CF)(T)](Sp) + [(CF)(T)](Lp)+ [(CCF)(t)](SP)(Lp) + [(CCF)( )](LP)(SP)where[(CCF)(Q)] = Cross-correlation functionSince the undamped natural periods of these two oscillations are of the order of60 to 1, the long period oscillation will, from a practical standpoint, appear as aconstant when correlated with the short period oscillation. Hence, to a high degreeof approximation these two cross-correlation functions are negligible and one canwrite:[(CF)( )]A(total) " [(CF)(T)] (Sp) + [(CF)(T)](LP) (V-6)This equation permits the auto-correlation of the two oscillations separately.However, for the purpose for which this data is intended the long period effects canbe considered negligible. Consequently, the recording system was designed tomeasure short period effects only. Because the recording system accommodatedonly short period effects, the longitudinal equations of motion, which neglect thelong period oscillation, are presented.Neglecting long period effects, the longitudinal equations of motion reduce to: ( 1 1)- z - U + - wZ w = 6Z + WA-I Zw + A-I Z*6e" - -wM - wM = 6M + wAIMw + wAIMw W A - w6eA -IA= Equilibrium airspeed in feet per second= Equilibrium airspeed in feet per secondM 1 8MM() -I ()A 1 azZ( m a()IyyMoment of inertia of tl e airplane aboutthe Y axis in slug-feetAm = Mass of the airplane in slugs.wAA -I Vertical velocity of the air mass withrespect to inertial space.the dot over a variable represents the Newtonianderivative with respect to time.For zero initial conditions at a stable equilibrium flight, the Fourier transformof the above set of differential equations gives the following set of complex algebraicequations:[(jw)(1 - Zv) - Zw]w - [Uo] = 6 6 + [z(jIw) + Zw] WA I-[Mv(jm) + Mw]w -[(ju)- M] e = 6M6 + [M-(jW) + M] wA Iwhere the variables are now a function of the angular frequency, w .This set of equations can now be solved to obtain the following performancefunctions:(PF)A( 6 E) =(jw)M6 + (ZMw - ZwM6)AA(Long)(V-7)(PF)A(wA-Ie)where:AA(Long)(jw)[M(jw) + Mw]AA(Long)[(1 - Z)(jw) - Zw]- [(j m)M + Mw]- U0[(jW) - M ]where(V-8)(V-9)The performance function given by Eq. (V-2) can be measured experimentally.This experimental data can then be used in conjunction with Eqs. (V-2) and (V-3) tocompute the performance function corresponding to the theoretical Eq. (V-3). Forexample:(PF)A(WAx2)(PF)A(wA -) (T heor )(PF)A( 6 E6 )(Theor)(PF)A(6E(Exp) 2(PF)A(, 6E 4)(Exp)The longitudinal experimental performance functions weresented in reference 3 and multiplied by the following modifyinglongitudinal rough air performance function:taken from data pre-ratios to obtain the(PF)A(wA -I )(Theor)(PF)A( 6 E )(Theor) M 62M2 (w)2 +( ) 2M;)(W) 2 + __ _1(CT)2A(68)where(CT)A( 6 ) AM 6(M wZ 6 - M6 Zw )E. Lateral Response EquationsFor the assumptions already noted, the lateral equations of motion are:v+ U 0 - vY - qY = 0'WA -I9 -vLv -qL -4L =6 a L6a + L-vN -9)N -N = 6a N6a+ Naa Taking the Fourier transform for zero initial conditions, one obtains,Taking the Fourier transform for zero initial conditions, one obtains,(V-o)(V-11)(V-12)Y[-Lv]v + [-L ] 4+ [(jw) -L]p =6a L6a[-Nv]v + [(jw)'WA- LaySN aWA-IN +[-N] = 5aN6a + ayThis set of algebraic equations can now be solved to obtain the following per-formance functions:(PF)A(6& )a(jO) 2 [-L6a] - (jw)[N6a N j - Yv L6a - La N ]A (Lat)U0 [L N6 a - NvL6a] + Y [N 6 z L - L6a N]A A (L at)(PF) awA -Iay(jw)2 [-L ] - (jw) [N - L N - LYAA (Lat)Uo [NL v - L Nv] + Yv[N L - NL,]A (L at)A at)where:[Uol[- Li][(W)- N4 ]- ](jw)[(OW) -. I'P(V-13)(V-14)(V-15)AA(Lat)[ow) - Yv](V-16)[(jw) - Yv] v +and, as in the longitudinal case:(PF) aWA. 2(PF)A( -4 )(Theor)ay(PF)A(6 a )(Theor)N2N NN 2( W) +(w)_[Lj - N - Y] - Uo [L - Nv ] - Y [L -- -NV L;V L;IfI(V-17)( .)2 +(jw)[N -Y - [L N 6 a N N]-Y [L -N(iw) $ - Yv] -- oL N6a -5a[~j -L6a L6a L 6 aThis theoretical correction factor multiplied by experimental aileron responsedata gives the lateral rough air performance function. The experimental aileronresponse data was obtained from reference 4.F. The Test AirplaneThe airplane used in this investigation was a USAF B-25J, under bailment con-tract to the Instrumentation Laboratory, Massachusetts Institute of Technology. Theairplane was, prior to these tests, stripped of all its guns, turrets, and bombingequipment as shown in Fig. V-4.For these tests, the airplane was ballasted to 26 percent M.A. C. In addition,hydraulic shut-off valves were used between the front and rear main fuel tanks inorder to keep the change in longitudinal center of gravity and moment of inertia ofthe airplane with fuel consumption to a negligible amount.To simplify the data reduction and computation of the airplane performancefunctions, it was desirable to record the airplane response to the turbulent air with\V4j'4/iFIG. V-4 B-25J AIRPLANE U.S.A.F. No. 44-30328,c_-~#~the flight path controls locked. The control locks used are shown in Figs. V-5 andV-6. The elevator lock was previously designed by Mr. Clifford Muzzey for adouble stop used in determining the airplane performance function by the pulse tech-nique. The results of this investigation are presented in reference 3. The aileronand rudder locks were designed for use as control stops to determine the lateralperformance functions by the pulse technique. The results of this investigation aregiven in reference 4.ELEVATOR POSITION LOCKAILERON POSITION LOCKFIG. V-5 ELEVATOR AND AILERON CONTROL POSITION LOCKSFIG. V-6 THE RUDDER POSITION LOCKPhysical DataA2Areaw = s = 610 ftI = 64, 000 slug ft 2 (measured) (ig) 610 ftyy 2 Chord A 9.67 ftIxx = 63, 000 slug ft (estimated) Chrd(wing) w= 9.67 ftAIzz = 120, 000 slug ft 2 (estimated) Span(wing) = b = 67. 56 ftAWt. = 26,000 lbs. (measured) Area(tail) = st = 132.5 ft 2C. G. = 26 percent MAC (measured)Length(tail) = 1 = 25. 9 ftG. Stability Derivatives Used in Computation of Airplane Performance FunctionsCondition No. 1(175 mph, 26 percent M. A. C., 8, 000 ft., Press. Alt.)LongitudinaldCM swcw_2M6 ( ) o= -9.8(1/sec2)d6E IyyZ=(dCM s wc-w 32z d 6 M qo = -30.4 (ft/sec 2)d6 E mltM= dC M sc qo = -0.0128(1/ft-sec)da I Uyo0dCL) swqo_z = -(--da mU0S dCL n ddot-1.065 (1/sec)12 stqoyyg0= -0.00176 (1/ft)dCL stlt26 = -(1. 2 )(-_-) nt qdat IUo= -1.72 (1/sec)LateralL 6 a d a W = -3.7(1/sec2 )6a xxNa d= - q =d6 a IzzL = dC Iswb 2 qdC sb= (on) =d1 Ix U od Izz odC1d( )2U.148 (1/sec 2 )-. 0081 (1/ft-sec).0063 (1/ft-sec)2Uoi qo= -3.63(1/sec)2UOx I0dC sbN d ) o= -. 11 (1/sec)d( pb 2UoIzz2U0S dC 1 swb2L 2 %= . 53 (1/sec)d(pb ) 2Ixx2Uowhere dC sb 2qo = p U 2 N n qo=-.603(1/sec)U 4 rb 212 d (--U-)zz2Up = air mass densityCondition No. 2(230 mph, 26 percent M. A. C., 8,000 ft., Press. Alt.)LongitudinalM 6 = -16.95 (1/sec2 )Z = -52.6 (ft/sec2)M = -. 0218 (1/ft-sec)Z = -1.4 (1/sec)M = -0.00176 (1/ft)M; = -2.26 (1/sec)Appendix VIDESCRIPTION OF FLIGHT TEST INSTRUMENTATIONA. GeneralIn this investigation, the airplane served as the sensing instrument for deter-mining atmospheric turbulence. In order to record and interpret the data, however,it was necessary to, in turn, sense the response of the airplane and record this re-sponse as a continuous function of time. Consequently, the airplane and the flighttest instrumentation, as a unit, constitutes the measuring system. As with all prob-lems of measuring continuous functions of time, it is necessary not only to recordand compensate for all environmental changes, but also to apply dynamic correctionsto compensate for the dynamics introduced into the records by the measuring system.However, due to the random character of the input in this particular problem, it isnecessary to know only the attenuation characteristics of the frequency response ofthe measuring system. Since the airplane and the flight test instrumentation oper-ate in a chain, the frequency response of each unit may be determined separatelyand the over-all performance function determined as the product of the separate per-formance functions. The performance functions for the airplane are presented inAppendix V. The performance functions for the aircraft instrumentation are pre-sented in this appendix.B. The Flight Test InstrumentationWith the exception of the lateral accelerometer, the flight test recording equip-ment had been previously installed for the flight test programs in references 3 and4. The recording equipment consisted of four basic units:1. The Sensing Instruments2. The Recording Amplifiers3. The Recording Oscillograph4. In-flight static calibration equipment.RATE OF PITCH GYRO'RECORDING AMPLIFIERCONTROL PANELRECORDING OSCILLOGRAPHFIG. VI-1 VIEW OF INSTRUMENT RECORDING STATION FROMAFT HATCHIn this flight test program, the sensing instruments with their uncertainty levelswere as follows:a. Rate of Pitch Indicator (t 1 mil/sec) (A-1 gunsight single-degree-of-freedom gyro modified for test work).b. Rate of Roll Indicator (t 1 mil/sec) (Same type as 1).c. Normal accelerometer (+ .01 g) (Instrumentation Laboratory,M.I.T.) .d. Lateral accelerometer (+ . 001 g) (A -1 modified pendulousaccelerometer).Figures VI-1 and VI-2 show the location of these instruments in the aircraft.FIG. VI-2 VIEW OF BOMB-BAY ACCELEROMETER INSTALLATIONLOOKING FORWARD.~w ~FIG. VI-3 VIEW OF IN-FLIGHT CALIBRATION EQUIPMENTFigure VI-1 also shows the recording amplifiers and the recording oscillograph.Each amplifier performed three functions:1. Amplified the a-c pickoff signal.2. Demodulated the a-c signal.3. Amplified the resulting d-c signal for recordingon the oscillograph.The output of each amplifier is controlled by 12 attenuation settings that adjust theoscillograph trace sensitivity.The oscillograph is a 12-channel Consolidated Recording Oscillograph. The dy-namics of the amplifier and oscillograph are negligible for the frequencies involvedin the aircraftkresponse.The static calibration of each channel was accomplished in two steps. The firststep was the calibration of each sensing instrument in terms of divisions on a masterpickoff. This measurement was not subject to change and consequently was madeonly at the beginning and end of the program. The second step was the calibrationof the oscillograph trace for known displacements of the master pickoff for each at-tenuator setting of the amplifier. A view of the installation of the in-flight calibra-tion equipment is shown in Fig. VI-3. This measurement was made twice eachflight (when airborne before taking records, and at the conclusion of taking records).The instrument static calibrations are shown in Figs. VI-4, VI-7, VI-10, and VI-13.The over-all sensitivity indicated on each flight record was obtained from thesefigures and from the in-flight static calibrations.The dynamic calibration for each sensing instrument was obtained from a har-monic analysis of the response of each instrument to a step-function. The step-function records are shown for each instrument in Figs. VI-5, VI-8, VI-11, andVI-14. Their frequency functions squared follow each step-function record in Figs.VI-6, VI-9, VI-12, and VI-15.1w --I'0 - - I -120 -- -1001Aso Iso40 -2010-20 /-40-60-80100-120-140-160-180 /200-60 -50 -40 -3 0 -20 -10 0 +10 +20 430 +40 450 +6Angular velocity in miliradians per secondFIG. VI-4 STATIC CALIBRATION1'.IS*1Ni1- --.. -0.80.60.40.-00 2 4 6 8Angular frequency, 'w, in rad/secV I I I I Fig. VI-6 INSTRUMENT FREQUENCY FUNCTION SPECTRUM0 5 10 15 20 25Time, in units of A t = 0.02 secsFIG. VI-5 INSTRUMENT RESPONSE TO A STEP FUNCTIONRATE OF PITCH GYRO CALIBRATION DATA0160120400-40-80-120 e-160-12( -80 -40 0 40Angular velocity in miliradians per secondFIG. VI-7 STATIC CALIBRATION1.00806040.20 5 10 15 20 25Time, in units ofAt = 0.01 secFIG. VI-8 INSTRUMENT RESPONSE TO A STEP FUNCTION INPUT0 2 4 6 8Angular frequency, w , in rad/secFIG. VI-9 INSTRUMENT FREQUENCY FUNCTION SPECTRUMRATE OF ROLL GYRO CALIBRATION DATA7 - --Z-/0 80 120' " ' '6o50S40~300.0'-, 20Io00 .02/00--,.04 .06 .08 .10 .12 .14 .16 .18 .20 .22 .24 .26 28Normal acceleration in units of "g"FIG. VI-10 STATIC CALIBRATION1.00.80.6, 0.40.200 5 10 15 20 25Time, in units of At = 0.01 secFIG. VI-11 INSTRUMENT RESPONSE TO A STEP FUNCTION0 2 4 6 8Angular frequency, w, in rad/secFIG. VI-12 INSTRUMENT FREQUENCY FUNCTION SPECTRUMNORMAL ACCELEROMETER CALIBRATION DATA73- -.........--I _______ _______ -I_U___ 1i[___ ___ ___ ___I_______800~ 600400200002 004 .006 008 .01 .012Lateral acceleration in units of "g"FIG. VI-13 STATIC CALIBRATIONS5 10 15 20Time, in units of At = 0.05 secFIG. VI-14 INSTRUMENT RESPONSE TO A STEP FUNCTION.014 .016 .018 .021.00.80.6402o0 2 4 6 8 1Angular frequency, c, in rad/secFIG. VI-15 INSTRUMENT FREQUENCY FUNCTION SPECTRUMLATERAL ACCELEROMETER CALIBRATION DATAAppendix VIIDESIGN OF A CORRELATION COMPUTEROne of the greatestdeterrents to the application of the random function theory isthe tremendous amount of work involved in determining the correlation functionsupon which the optimum design is based. In an attempt to reduce somewhat the amountof work required in this computation, a correlation computer was designed jointlywith Mr. Hollander of the Instrumentation Laboratory, M. I. T.The computer consists of four primary components:1. The paper-drive system2. The tracking system3. The timing system4. The integrating systemFigure VII-1 is a functional diagram of the computer.The computer was designed as a general correlation computer for as many typesof data as might be submitted. In addition to integrating the cross-product of theoutput of the two tracking arms, it also integrates the value and the squared valueof the output of each arm.Mathematically, the computer gives the following data for each record:1. The time interval over which the integration was taken, with an uncer-tainty of t 0.02 seconds, i. e. (T- r).2. The integral of the cross product of the output of both tracking arms, i. e.T-,rf(t)f(t + r)dt = I03. The integral of the square of the output from each tracker, i. e.,T--r12 (PositionE 1 ) = f2(t)dt0T-12(Position 2) = i2(t + r)dt0INTEGRATORANDTIMER CONTROLSWITCHBUILDINGPOWERFIG. ' -1. FUNCTIONAL DIAGRAM OF CORRELATION COMPUTERf(t +T)I I ~-SWITCI-H oITION[fe L,olt t -tae, Ot *I WAS SMa)TGRATOPf13= T re,,t INT EGRATOP- 3K?=-&1121Fl81000 rl 50W.- ET AT (,OO nINTEGRATOR 2- 12 _,L CLtFIG. I-2 CO2ELATION COMPUTER W12ING DIAGRAMIlov4. The integral of the output from each tracker, i. e.13 (Position El) = ff(t)dt0T-'rI3(Position -2) = Jf(t + r)dt0The details of the switching arrangement for obtaining these integrals are shownin Fig. VII-2.Figures VII-3 and VII-4 are photographs of the computer in operation. FigureVII-5 shows the arrangement of the integrators and timer.The computer requires two operators. Each operator tracks the records as thepaper is driven at constant speed. The distance between tracking arms in indicatedtime determines the correlation interval. To each tracking arm a variac (voltagesource) and a potentiometer (current source) are mechanically coupled. In this waya current and a voltage are obtained that are directly proportional to the displace-ment of the tracking arm. The variac output is applied directly to the voltage sideof the integrator. However, in order to obtain the required sensitivity, it was foundnecessary to amplify the output of the potentiometers before applying the current tothe integrators.The integrators used are watt-second meters commercially obtainable. Theseinstruments are laboratory meters used to adjust and regulate the watt-hour metersused to totalize power consumption. The time constants of the meters are not ofconcern in this application since one is not interested in an instantaneous value ofthe integral, but rather in the steady-state value after integrating the entire lengthof the record.Integrator No. 1 integrates the product of the voltage from arm No. 2 of the cur-rent from arm No. 1. Integrator No. 2 integrates the product of the voltage and cur-rent from a given arm dependent upon the switch position. Integrator No. 3 integratesthe product of the voltage from a given arm, dependent upon the switch position, anda constant current taken from a separate source.Referring to Fig. VII-1 and Fig. VII-3, the operation of the computer can beexplained as follows:Operator No. 1 starts the paper drive by pressing foot switch No. 1. When thepaper drive has come up to constant speed as indicated by the paper speed indicator,Operator No. 2 presses switch No. 2, starting the integrators and the clock simul-taneously. The two operators then track the record until the end is reached at whichtime Operator No. 2 cuts the switch, stopping the integrators and the clock . While78RTRACKING ARM 1IWI4IPAPER SPEED INDICATORPAPER DRIVE MOTOR ASSEMBLY 1PAPER DRIVE REVERSINGFIG. VII-3LEFT-SIDE VIEW OF OPERATION OF CORRELATION COMPUTERSWITCHTRACKING ARM 42CORRELATION INTERVALZEROING TAPER PINTAKE-UP SPOOL AND TORQUE MOTORPAPER DRIVE FOOT SWITCHINTEGRATOR AND TIMER FOOT SWITCHFIG. VII-4 RIGHT-SIDE VIEW OF OPERATION OF CORRELATION COMPUTERiJ- NTTEGRATOR **l INrTEGRATOR 1 2 tJFRATR */TIMER (.02 sec)INTEGRATOR RESET BUTTONTRACKING ARM SELECTOR SWITCH CURRENT SENSITIVITY ADJUSTMENTFIG. VII-5 VIEW OF INTEGRATOR CONSOLE AND ELECTRIC TIMEROperator No. 2 records the totals from the integrators and the clock , OperatorNo. 1 stops the paper drive and reverses it for tracking in the opposite direction.To calibrate the computer, a plate was made with holes drilled + 1 inch fromthe zero point. The machine is calibrated in both directions by taking the integralof a 1-inch displacement of both arms over a measured time interval.In order to check on the over-all accuracy of the machine, a run that had pre-viously been totalized by I.B.M. machine methods was re-run on the computer.The first set of data, Flight No. 90, was computed by selecting discrete pointsat 0.1-second intervals from the oscillograph records. The set of discrete pointswere then correlated on I.B.M. equipment. One run of this data was used to checkthe overall accuracy of the correlation computer. The results of this check areshown in Fig. VII-6. The solid curve is theI.B.M. data and against this curve is plotted theRUNNO.1-3 results obtained from the correlation computer.reulsTomutrThese results indicate that the correlationfunction as computed by the correlation com-puter was obtained to within 5 percent of themean power of the record.This correlation computer can in additionbe used as a harmonic analyzer and a machineto compute the convolution integral. To usethis mechanism as a harmonic analyzer, theproduct of one tracking arm can be integratedagainst the output of a sine generator properlygeared to the paper drive mechanism. To usethis mechanism as a computer for the convolu-tion integral, first plot the system response to aunit impulse. Then plot the input forcing func-tion on a reversed time base. The convolutionCORRELATION INTERVAL, , In secordsFIG. VI-8 COMPARION OF CORRELATION FUNCTIONSOBTAINED BY I. B. M. AND CORRELATION COMPUTERREDUCTIONintegral can then be obtained by tracking these two curves for a given convolutioninterval.This machine was designed primarily to meet an existing need. That is, amethod of correlating 4000 feet of data already recorded on oscillograph paper.However, it is not felt that this machine, as set up, is the optimum solution. In-stead, it is believed that a faster and more accurate computer can be designed tocorrelate data recorded on a magnetic tape. In this case, the correlation intervalcan be established by using split pickups which can be displaced along the tape withrespect to each other. In order to use this scheme, however, it will be necessary toutilize a carrier frequency and demodulate the output from the pickup heads beforeintegrating. If this is not done, there will be only a limited number of points alongthe tape where the pickups can stop and still keep the carrier frequency between thetwo pickup signals in phase.Appendix VIIIBIBLIOGRAPHY1. Wiener, Norbert, "The Extrapolation, Interpolation and Smoothing of StationaryTime Series with Engineering Applications," John Wiley & Sons, Inc., New York,1949.2. Wiener, Norbert, "Generalized Harmonic Analysis," Acta Mathematica, Vol.55, 1930, p. 273.3. Muzzy, C.L., "Dynamic Response of a B-25J Airplane to Pulse Shape ElevatorDisturbances," Instrumentation Laboratory, Massachusetts Institute of Tech-nology, Engineering Memorandum No. 6445-E-27, July 1949.4. Bain, J.B., Michailis, F.H., and Wootton, J.C., "Investigation of AircraftLateral Motion Performance Function by Pulse Technique," Thesis for M.S.,M.I.T., 1949.5. Campbell, G.F., "Dynamic Lateral Stability Flight Tests of a B-25J Airplaneby the Forced Oscillation Method," Cornell Aeronautical Laboratory ReportNo. TB-405-F-7, 1947.6. James, Nichols and Phillips, "Theory of Servomechanisms," Vol. 25, Massa-chusetts Institute of Technology, Radiation Laboratory Series, McGraw-HillBook Company, Inc., New York, 1947.7. Clementson, G.C., "Investigation of the Response of an Aircraft to a FinitePulse Input," Thesis for M.S., 1948.8. Seamans, R.C., Jr., Blasingame, B.P., and Clementson, G.C., "The PulseMethod for the Determination of Aircraft Dynamic Performance," Journal ofthe Institute of Aeronautical Science, Vol. 17, No. 1, Jan. 1950.9. Loh, Yuan-Chiu, "Design of Linear Systems for Minimum Mean Integral SquareError," Thesis for Sc.D., 1949.10. Bubb, F.W., "Theory of Best Automatic Control Systems for Predicting andSmoothing," Technical Report No. WURF-MGE-26, Washington UniversityResearch Foundation, 1948.11. Durand, W.F., "Aerodynamic Theory," Vol. V, Div. N, Durand ReprintingCommittee, C.I.T., Calif., 1943.12. Gardner, M.F., and Barnes, J.L., "Transients in Linear Systems, Vol. 1,John Wiley & Sons, Inc., New York, 1945.13. Bass, J., "Les methodes modernes du calcul des probabilities et leur appli-cation au probleme de la turbulence," Rappart Technique No. 28, Groupementpour le development des recherches aeronautiques, Paris, 1946.14. Kenrick, G.W., "The Analysis of Irregular Motions with Applications to theEnergy Frequency Spectrum of Static and Telegraph Signals," Phil. Mag.,Ser. 7, Vol. 7, pgs. 176-196, January 1929.15. Alan E. Treloar, 1. "An Outline of Biometric Analysis" (1935), 2. "RandomSampling Distribution" (1940), Burgess Pub. Co., Minneapolis, Minn.16. Palmer O. Johnson, "Statistical Methods in Research," Prentice-Hall, NewYork, 1949.17. Dr. T. Koopmans, "Linear Regression Analysis of Economic Time Series,"Haarlen-De Erven F. Bohm, N.V., 1937.18. Tippett, L.H.C., M.Sc. (Lond.), "The Methods of Statistics," Williams andNorgats, Ltd., Great Russell Street.19. Kendall, M.G., "Contributions to the Study of Oscillatory Times-Series",Cambridge Univ. Press (1946).20. Davis, Harold T., "The Analysis of Economic Time Series," The PrincipiaPress Inc., Bloomington, Ind., 1941.21. Treloar, Alan E., "Elements of Statistical Reasoning," John Wiley & Sons,Inc., 1939.22. Lee, Y.W., Lecture Notes of "Optimum Linear Systems," Presented by Prof.Lee in the Department of Electrical Engineering, Massachusetts Institute ofTechnology, 1948.23. Rice, S.O., "Mathematical Analysis of Random Noise," Bell Telephone Tech-nical Journal, July 1944 and January 1945.24. Donely, Phillip, "Summary of Information Relating to Gust Loads on Air-planes," N.A.C.A. Tech. Note, 1976, dated Nov. 1949.25. Draper, C.S., "Generalized Concepts and Self-Defining Symbols for the De-sign and Specification of Instrument Systems," Instrumentation Laboratory,M.I.T., Cambridge, Mass., September 1949.26. Lee, Y.W., and Stutt, C.A., "Statistical Prediction of Noise," Technical Re-port No. 129, Research Laboratory of Electronics, Massachusetts Institute ofTechnology, July 12, 1949.27. Leipnitz, R.B., "Distribution of the Serial Correlation Coefficient in a Cir-cularly Correlated Universe," The Annals of Math. Statistics, Vol. XVII(1947) pp 80-87.28. Anderson, R.L., "Distribution of the Serial Correlation Coefficient," TheAnnals of Math. Statistics, Vol. XIII, (1942) pp 1-13.Appendix IXGLOSSARYThe system of notation used in this thesis was developed by Dr. C. S. Draper (2 5)However, in the development of the airplane performance functions it was felt thatthe standard N. A. C. A. notation was so firmly fixed in the aeronautical field that itwould not be desirable to attempt to transcribe it.The underlying philosophy of the Draper notation is to provide a set of symbolswhich in themselves will be a mnemonic tool which will define itself as well as desig-nate its application.SYMBOL DEFINITION[(CF)qq(O)][(CF)qq( r) ]o[(CF)xix (n)]oo1 xi+nC.G.(CT)(osc)(DR)(FF)( ) [qinqout][FSC][q(t)][FT(w)][q(t)]Mean power of a real function of time and is obtained as theaverage value of the function squared.Correlation function for an infinite continuous function of time.Correlation function for an infinite discrete time series.Center of gravity of the airplane.Characteristic time of an oscillatory function.Damping ratio. The ratio of actual damping to the criticaldamping of a damped sinusoidal oscillation.(PF)( )[qinqout](S)(S) ( ) [qinqout]Fourier series coefficient of a real function of time, q(t).Fourier transform as a continuous function of the angularfrequency, w , of a real function of time.[FT(w)][q(t)]Iyy[(KC) XY] Nn(PA)(osc)(PF) [qinqout][(PSD) (w)]q()(t)Re[ ]I[RMS (q)](RT)s[(SKC)x i xi+n(n)]N(S) ()[qinqout]Complex confugate of the Fourier transform of a real func-tion of time.Value of a designated definite integral.Moment of inertia of the airplane about its y axis.Correlation coefficient between two samples of N variates.Real integral number.Phase angle of a damped sinusoidal oscillation.Performance function of a designated system for the designatedinput and output. The function is equal to the Fourier transformof the Unit Impulse Response, [(UIR)(t)] of the system.Power spectral density of a real function of time, q(t) .Most easily obtained as the Fourier transform of the correla-tion function of q(t) .Real function of time which may be designated further byproper choice of subscript in place of the open parentheses.Real part of the complex function of the variable w in thebrackets.Root-mean-square value of a real function of time. It is equalto the square root of the mean power.Response time of a given dynamic system. Defined as the timerequired for the response to decrease to and remain less than5% of its maximum output magnitude.Dummy variable of integration with respect to time.Serial correlation coefficient of a finite time series of totalnumber N lagged by the interval of n variates.lim a (PF) ia twto. 0if t a) [qinqout]Newtonian time variable. In this report the units are in seconds.T(cor)[UIR (t -vVAwWA -IA -Iay6(aovnocoPeriod of the fundamental frequency in a Fourier series expansion of areal function of time, q(t) .Time interval of significant correlation.Unit Impulse Response of a designated dynamic system delayedin time by the interval, -. A unit impulse is defined as adelta function of unit area.Airplane velocity response along Y axis.True velocity of the airplane in feet per second.Airplane velocity response along Z axis.Vertical velocity component of a turbulent air mass with re-spect to inertial space.Rate of change spanwise of the vertical velocity of a turbulentair mass with respect to inertial space.Control angular deflection. Parentheses to be replaced bydesignated control.In Appendix m, only, this symbol is usedto represent a delta function.Airplane rate of pitch response.Dummy variable of integration with respect to time.Dummy variable of integration with respect to time.Newtonian time interval.Airplane rate of roll response.Airplane rate of yaw response.Angular frequency in radians per second.Undamped natural frequency of a damped sinusoidal oscillation.Equal by definition.Symbol for a number which is allowed to increase withoutbound.Appendix XBIOGRAPHICAL SKETCHGerhardt Christopher Clementson was born in Blackearth, Wisconsin,on May 3,1917. Shortly thereafter, his parents moved to Minneapolis, Minnesota, where heobtained his primary schooling. He was graduated from South High School in Januaryof 1937.In May of 1937, he enlisted in the 3rd Infantry, then stationed at Fort Snelling,Minnesota, and won a competitive assignment to the 7th Corps Area West Point Pre-paratory School. In March of 1938, he was appointed a cadet at the United StatesMilitary Academy, West Point, New York, by Congressman Henry G. Tiegen of theMinnesota 5th Congressional District as a result of his standing on a civil servicecompetitive examination. He was graduated from the United States Military Academywith a degree of B.S. in May, 1942. After graduation, he was assigned to pilot fly-ing training in the West Coast Training Command. On receiving his wings, he wasassigned to the 4th Air Force as a trainee and later as an instructor pilot in the P-38type aircraft.In June of 1944, he was assigned to a refresher course at the U.S.A. F. Engi-neering School at Wright Field, and after completion was assigned to the CaliforniaInstitute of Technology to complete a course of study in compressibility effects inaerodynamics. He was elected to Sigma Xi, and awarded the degree of M.S. in June1945. He was then assigned as a flight test pilot and engineer to the Flight ResearchSection of the Flight Test Division at Wright Field, Dayton, Ohio, where he special-ized in stability and control flight testing.In June of 1947, he applied for and was assigned to a course of study in FireControl Instrumentation in the Aeronautical Department of the Massachusetts Insti-tute of Technology where, in September of 1948, he was awarded the degree ofMaster of Science in Aeronautical Engineering. He then was granted a two-year ex-tension of his tour of duty to complete a course of study leading to the degree ofDoctor of Science in Instrumentation.He is co-author of a paper published in The Journal of the Aeronautical SciencesVol. 17, January, 1950, entitled "The Pulse Method for the Determination of Air-craft Dynamic Performance."FLIGHT TEST SUPPLEMENTThe entire set of airplane response to turbulent air oscillograph records arepublished in this supplement in order that this data may be preserved in a formwhich might be useful to future investigators in this field.FLIGHT NO. 85DATE: 15 August 1949 Duration: 1:75 hoursAIRPLANE: B-25J No. 44-30328CREW:Pilot: C. CollinsCo-pilot: G. C. ClementsonInstr. T.O.: F. SmithPURPOSE OF FLIGHT:1. Instrument shakedown2. Rough air dataAIRPLANE CONFIGURATION:Gross Weight - 26,100 lb.C. G. Percent MAC - 26.1INSTRUMENTATION: Instrumentation installed for measuring normalacceleration, lateral acceleration, rate of pitch and rate of roll response toturbulent air. Stops installed for keeping controls (aileron, rudder and eleva-tor) fixed on the trim condition of 175 m. p.h. I.A.S.METEOROLOGICAL CONDITIONS: Unstable air mass, scattered tower-ing cumulus.FLIGHT PROCEDURE:1. Airplane trimmed at 175 m.p.h. at 9,000 ft. P.A.2. Controls stops adjusted to trim control positions.3. Controls held fixed against stops and sensitivities adjustedon oscillograph.4. Static calibration of oscillograph by master pickoff.5. Rough air response measured at trim conditions.6. Re-calibration of oscillograph.RESULTS AND COMMENTS:Noise level on oscillograph records excessive. Appears to be primarilyengine and prop vibrations. Data can be used by smoothing obvious noise roughness.FLIGHT NO. 86DATE: 21 August 1949 DURATION: 1:5 hoursAIRPLANE B-25-J No. 44-30328CREW:Pilot: C. O. BostromCo-pilot: G. C. ClementsonInstr. T.O.: F. SmithPURPOSE OF FLIGHT:1. Test of modified instrumentation vibration mounts.2. Rough air dataAIRPLANE CONFIGURATION:Gross Weight - 26,100 lb.C. G. Percent M.A.C. - 26.1INSTRUMENTATION: Same as No. 85METEOROLOGICAL CONDITIONS: Hot Summer day, towering cululus,thermal heating.FLIGHT PROCEDURE: Same as No. 85RESULTS: Normal accelerometer malfunctioned. Vibration mountsunsatisfactory. Will try complete removal of mounts and rigid tie-downon next flight.FLIGHT NO. 87DATE: 26 August 1949 DURATION: 1:25 hoursAIRPLANE: B-25J No. 44-30328CREW:Pilot: C. CollinsCo-pilot: G. C. ClementsonInstr. T.O.: R. WhistlerPURPOSE OF FLIGHT:1. Test of rigid instrument mounts.2. Rough air dataAIRPLANE CONFIGURATION:Gross Weight - 26,100 lb.C. G. Percent M.A.C. - 26.1METEOROLOGICAL CONDITIONS:Hot summer day, ground thermals obtained by flying over water-land discontinuities from Lowell, Mass., to Newburyport, Mass.FLIGHT PROCEDURE:Same as No. 85RESULTS:Rigid mounts reduce engine and prop. noise pick-up to anacceptable level. Instrumentation is satisfactory.FLIGHT NO. 89DATE: 2 September 1949 DURATION: 1:15 hoursAIRPLANE: B-25J No. 44-30328CREW:Pilot: C. O. BostromCo-pilot: G. C. ClementsonInstr. T.O.: R. WhistlerPURPOSE OF FLIGHT:1. Rough air dataAIRPLANE CONFIGURATION:Gross Weight - 26,100 lb.C. G. Percent M.A.C. - 26.1METEOROLOGICAL CONDITIONS:Same as Flight No. 87FLIGHT PROCEDURE:Same as No. 85RESULTS:Satisfactory records.FLIGHT NO. 90DATE: 9 September 1949 DURATION: 2.0 hoursAIRPLANE: B-25J No. 44-30328CREW:Pilot: C. O. BostromCo-pilot: G. C. ClementsonInstr. T.O.: R. WhistlerPURPOSE OF FLIGHT:1. Rough air dataAIRPLANE CONFIGURATION:Gross Weight - 26,100 lb.C. G. Percent M.A.C. - 26.1METEOROLOGICAL CONDITIONS: Cold front passage, low thunderstorms,high ground winds.FLIGHT PROCEDURE: Same as No. 85.RESULTS: Satisfactory records.FLIGHT NO. 91DATE: 16 September 1949 DURATION: 2:5 hoursAIRPLANE: B-25-J No. 44-30328CREW:Pilot: C. O. BostromCo-pilot: G. C. ClementsonInstr. T.O.: R. WhistlerPURPOSE OF FLIGHT:1. Rough air data at two different airspeeds, 175 and 230 m.p.h.AIRPLANE CONFIGURATION:Gross Weight: 26,100 lb.C. G. Percent M.A.C. - 26.1METEOROLOGICAL CONDITIONS: High ground winds, flown overmountain terrain.FLIGHT PROCEDURE: Same as No. 85.RESULTS: Satisfactory records.Flight No. 85Run No. 1Date 15 August 1949Airplane 3-25J No. 44-3Altitude 8000 feet- 0.1 degree per secondI seon11.0 degree per second. IA -.I , - i ,4 , -, ,1Lateral accelerationmal acceleration. . *4"*4* !;4. 4,'4 UI~ ~'~~** ':I ~ I....4. 4~.~*.,. I12,0I 4..4, 44,' 1~~1 1.Flight No. 85Run No. IDate 15 August 1949Airplane 11-25J No. 44-30328Altitude 8000 feetAirspeed 175 mphAirplane center of gravity 26% MACMeteorological conditions Unstable air mass,scattered towering cumulus.Rate of rollV.~1'<1..11.7VELateral act - t er onC . . , . - •I'I. JII I';I~IL.:i. :'~,I 1 i I iFlight No. 85Run No. 2Date 15 August 1949Airplane B-25J No. 44-3032&Altitude 8000 feetAirspeed 175 mphAirplane center of gravity 26-,NMeteorological conditions Unstascatt(M1ACble air mass,ered towering cumulus.J ...."U:.WI.oil l 4 ... 2 . ... LI! riil:iH i'a* I4I ij r"I V85 tAirspeed 175 mph 72 Airplane center of gravity 26 % MAC15 August 1949 i Meteorological conditions Unstable air mass,B-25J No. 44-30328 1scattered towering cumulus.8000 feet ,,.I. , , ! .~~il , 7 , , . . , Jilt" ' [ :l 'r '' + w ! ,, q : i !' + : !'!V,1l'l'tli : i 'jj;i:i$0.1 degree per second1I.0 degree per secondS0.01 gravity- 0.1 gravity. .. ... }....Rate of roll,t 1 4 I..s 'No r mal acceleration,Y Itime -Flight No. 85Run No. 2t 1949S44-33284, iAirspeed 175 mphAarplane center of gravity 26' , MACMeteo ological conditions Unstable air mass,scattered toweringh j Vol.iIWO85215 August 1949B-25J No. 44-30328Air peed 175 mphAir pane center of gravity 26% MACMet, rological conditions Unstable air mass,scattered towering cumulus., I I ' I ' , 1 : : ' r t15 AugustD-25J No.i i I I 'li..I I I.1IAirspeed 175 mphAirplane center of gravity 26% MACMeteorological conditions Unstable air mass,J scattered towering cumulus.I I l l I l IL .. 'r,:.....I Flight No. 85- RunNo. 3Date 15 August 1949Airplane B-251 No. 44-30328lilAltitude 8000 feetAirspeed 175 mphAirplane center of gravity 26% MACMeteorological conditions Unstable air mass, -II scattered towering cun0.1 degree per second J ]iRate of rollIl i; : :ItimeI1t~'14JJIn'1.i• , l ii'1llFlight No.Run No.'VIFlight No.Run No.DateAirplaneAltitude..85 ""." T """ "''''' "'"'''"''""""Airspeed 175 mph '"3 Airpane center o gravity 26'% MAC15 August 1949 Meteorological conditions Unstable air mass,D-253 No. 44-30321 scattered towering cumulus.8000 feet I" I . r - - , III85415 August 1949B-25J No. 44-303288000 feet4 '1 ~".'"Si.lit.L..ftI) VI *1I I,11; 1:ii,1 ';i111Y l:1, I " i\* '1~i i iw!ir~l"!;0. 1 degree per seRate of pitch1.0 degree per secondSNormal accelerationL- I . 1, I I,Ia.0.1 gravityS'IRate of rollS Lateral accelerationNormal acceleration 'timetime-tij4'I~I . |Flight No.Run No.DateAirplaneAltitude'S T" I85415 August 1949B-25J No. 44-303288030 feet• 1V1 '4"I ~'ti"Flight No. 85Run No. 4Date 15 August 1949Airplane B-25J No. 44-30328Altitude 8000 feetAirspeed 175 mphAirplane center of gravity 26% MACMeteorological conditions Unstable air mass,scattered towering cumulus.1+ t | ~. A. I I I ,I I , I I' I -I IAirspeed 175 mphAirplane center of gravity 26% MACMeteorological conditions Unstable air mass,scattered towering cumulus.$4,oFl'i/'94AI.- I'', ,>. .... ,i. ..... l ..... t !...... .85 Airspeed 175 mph4 Airplane center of gravity15 August 1949 Meteorological conditionsB-25 No. 44-30328I I - I Icumulus.I , ... I . 1 i* I -Airspeed 175 mphAirplane center of gravity 26% MAC49 Meteorological conditions Unstable air mass,4 -30328 scattered toweringtime --I.Rate of pitch4.rI~.' L1K 1D ~'1:11S IiII whllIlI F I--' --';-' '':;' *; '';i--"' -Y~""'**I"~~~ -----I41rt ** * **nke• ilii! I i• i:!I:,_r'Rate of pitch:Rate of.... .iiI' irFlight No. 85Run No. 5Date 15 August 1949Airplane B-25J No. 44-30328Altitude 8000 feetAirspeed 175 mphAirplane center of gravity 26%Meteorological conditions UnstaI ;I. IscatteMACble air mass,ered towering cumulus.'. I I I I4 ,".4- ': i-L -' -;-II ..L. .r ... i ...... .L.-i .-.1. ' .. .__1.; .. I . .I~ .. ' I ~I - I .1.- :~~_~~ 1 1:.I .. ------ 1-1 ...r ..... i.....:...r :..( : I .I _ I.... ...~~i.:;;;,It,i!!!'! ' ' "+"z l+li!l- 0 1 -d r , se on0 1 degree per second1.0 der e per secondRato of pitch " - •• '-i "* .' ' " ' ' " ,%'r :" '5 . .. 3 A Ahw," . ... .4it-* vv~4.N 6'4..'V A4%~I Itime -APate of rol0.61I* A. .......'00":4Lateral acceleration~V __AA~dA,,v v 7v--/ ..'-,,Normal acceleration0. 1 degree per second,i ,, ...- 1.0 dee per second75 0FlIhiNo. 86Run No. 1Date 21 AugustAirplane B-25J No.~Rva iA" .' de 80 0feet - ..... Airspeed 175 mph I1949 AIrpane center of gravity 26% MAC44-30328 Meteorological conditions Hot summer day, scattered-,cumulus, thermal'heating.teof pitch'.time --- *9.5Rateoroll 0.0 gravityLateral accelerationA 4%P4 0 ~'- ,,- . '.,4-IA.A 'A'A-A."..,4-' 4~4.'VV'A'Af'V/I /V'4.-~4.-/ '.4,.0 1 degree per secondRate of pitch'A- sl- I A.. 0 degree per second " 1" . .0.5 . time -Rate of roll.,0.01 gravity0-rLateral acceleration '., 0.1gravity ",'INV V VNormal accelerationVS2.5' -- " ,Flight No.Run No.DateAirpane.86221 August 1949B-25J No. 44-30328Altitude 8000 e.. ..Air"ped175 mphAirplane center of gravity 26% MACMeteorological conditions Hot summer day, scatteredcumulus, thermal heating.S)csLf3.0N4.0r . .. ~ -. . .. AAAt.IA20.1 travityV A': - :.9.00. 1 gmvityoNormal acceleration-Flight No. 86Run No. 1Date 21 August 1949Airplane B-25J No. 44-30328Altitude 8000 feetAirspeed 175 mphAirpne center of gravity 26% MACMeteorological conditions Hot summer day, scatteredcumulus, thermal beating.65 7.0-- ----~---C------------ -? I"f~C----------~U--~c"-----U---; i:-- I"h?.j.: '• t ,rII\CI -O-NJ~LV~;' ' '.. ukor.I " - V V v ,% -11111^ -SoFlight No. 86 Altitude 8000 feetRun No. 2 . Airspeed 175 mphDate 21 August 1949 Airplane center of gravity 26% MACAirplane B-25 No. 44-30328 Meteorological conditions Hot summer day, scattered. .. ...No cumulus, thermal heating.0. degreesi per s cond1.0 degree per secand5.0Rate of pitch5.5~v7.0 9.060 * 6.5o.0/A(~ t V~..%10.5a time .-- ,, -(.." "v I •v-A .... ... .. ... ...01La.Leza acveAaloLateral acceleration0.1 grv/tyNormal accelerationt !V \". . .~IA~ V V~ p~A~ ~A.''* V~d ~'7A %~A~'V* .1.. A Ai2,WAAA* Fliht No 86 ltltue 800 fee --Flight No. 86 Altitude 8000 feetRun No. 2 Airspeed 175 mphDate 21 August 1949 Airplane center of gravity 26% MACAirplane B-251 No. 44-30328 Meteorological conditions Hot summer day, scattered" " cumulus, thermal heating.0. 1.degree.per..ii-0Rate of iftch op"A. ,,, ^ .,~ M -. . ... ,.,,,. / "1.0 degree per second12.5 13.0 15 5 14014.515.0 15.5 16.0 16.5FRaeof roll 7 -0.01 gravity Lateral acceleration ____ ,~0-7-v\Phf~A ~ V V.--4-0.1 gravity-0: NormalacceleratioNormal acceleration- . vyyFV %./*\ ,.1A,~*1A. A'.A~I*17.01.. 18 18. ".. 19--'1 . : : -I - : ;::: -::-:::-- :;-I ::::::-:; i:: -- :- :: : -:i ;rc~7.0 9.0 io.5: .. iirL"A , , I" , , , v~ ~L~Af v-1S517.5 MaO 18.5 19.01time:~ -- :---:- --- *SRat of pitchN:i1.o pee per 2m-pp.1./DY-s.NIAltitude 8000 feetFlight No. 86 Airspeed 175 mphRun No. 3 Airplanecenter of gravity 26% MACDate 21 August 1949 Meteorological conditions Hot summer day, scatteredAirplane B-25J No. 44-30328 cumulus, thermal heating.I-IV A3 . 5A.5 6.50.01 gravity - .0.1P 17vd AA&7 v\I\f ~ 0j~ h. -, . . . ,, : vi^ ,^ . W . ,", . " ",I5 -N V I I I.r*" /\*~/,1%.1...- ----,-. 2--. I I--- . ni-.-i--- ~'A~~~D5OWS f,VAltitude 8000 feetFlight No. 86 Airspeed 175 mpoTRun No. 3 Airplane center of gravity 26% MACDate 21 August 1949 Meteorological conditions Hot summer day, scatteredAirplane B-257 No. 44-30328 cumulus, thermal heating.l~ V5/ -~ ~ ~ .B~ V.'V~~AVPV%V\.~PP~I. . . . .VAA~ -'V/10.0 10.5 11.0 ILS '110 ' I'. rV-, : V N.P3_ v-0. Q V .\.• ' A., 100"-i1T Xvf\/ I14.0,'.IVF\,.Id-I0.1 degree per second0.5uime--2D A~ ~V./ .'N', . IL- ---- -----bc,roIA0. 1 per 3....1.0e~vv tatroll p// -N-* 4 %S15.5 . . . .r . . . , M5095t O7 A rm mai ; :-:-..: ; v:ii :::: : Ii:~,1It, -.. ++ + + ++ + + .... . . . .." La" " rd " tme.-..+a t m+ . _0.01 -o. . "- . .21.5 22.0 22.5 23.0 23.5 24.0 24.5 25.0 2600.1 degree r secmd0- -I RatmeaFlight No.Run No.Airplane86 Alm 8000 feei3 -Irsee '15 mp"h21 August 1949 ?Arpl cer gravity 26% MACB-253 No. 44-30328 Meteoologlcal conditions Hot summer day, acattm edcumulus, thermal bmetia:.h'V'NV v016.5A\Ak~\s~2AP'I:*IflU'- i..I.' I -1i 1 .. 3-I7'~--~;; ~.9--4... 'P " * ,. -At,'fit 4-1tWIi7~71~'.11 JS~,k~1-I0r~ L-L F-C~ll =Ih* *.L04, I Altr : I *- *- ,-i l ... .._. ... .i.* -. -...- ........ ... I..... ... .-..- ,------- -G " llI .•.1-- 4.. • ...:. ' I.- ,... .. I. ,: -CII-j7* I. _____4. ~ 1~ _______--. -I- -~_______* .1 ____T7"* .- .. , .:'i io , .LIi:;'f:. 7- 7k.4iF ', "°. Y7T. TWA I_ _;V W4 _tNoZA (* 1 '- .. ... s -ip44'1'.. r 5 i,.4.I~I.il I u0.4 1L,.7;;PF!TALIIToitTO.L- 1,14 .---.-i C.I 1 ;I --r--rri. _.-ILV-1V-i- ... .. , k-P *,~-I-T-;li-m lv .Tr-I-r--- --. _M , I., v; 1, .; 1 ! A moklip --t m --.I *b.1 ---i " -'.- .-Iftk -IwTI =I"- .. m -,, q ., Ov 1 4 !--:: :i --- --,@ W -mll --- ---4 ~- 4 w 4 -, I A..acI k"Ar-W-,-~--~-..~.-_II -- --1.------• ------ j ! t177I 'U, i -i ..... ii ..iI i-. I11-w: ....... ,4 ' -- -- il'P ' , "-_ ' -I_.. .. .... ._ .P ... i --TLb _-4---B£1r'I% , I .* T\J:A AAi A: __ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _ __ _ _ _ _ _ _ _A~d OkkvVI-8 S,,,.4. I . I " "3K K.j I .: ..T 7.0 7.5 .0 8.5 9.0 9.5 10.0 10.5.44vrr - - h.I .1.-~... ..~ ~''r ~; --~At; AV d AL0" v v vvvyt,.5 12.0 1"..... .... , , , , v K IA, ,,,_Ron " •No.Sr . ' ap d 175DateAirplAuiwwaoos13.5tot1021 August 1949-. 1 No.44-M0U3I . . . .. . .. dim p" s ml ' I% d,LS doree er seid : - -R a' - .. ../'I5o 15Vt.~- ~'/Df t w16.5 17.0V-I..5 Sao0~A.-- ix--- - -. 19.0 . 19.5 2,o 20521AaAA A\ /\~ vv-V I- f U1-wvAI~' ~. I~VFI__ No. 88RunNo. 10DMS 21 Aqupst 14Airplane -251 No. 44-M02.8Alitude s00 feet-. AU "5p 7 1 r5 m tyAr c 2It6 n% MACMeteorologclal cooditins Hot summer day, scatteredcWou Ans, brmar hesti.xA IlIN;4 am !- i i I K1'5/ ~ 4A..-it_11__7W A- j0Am.I I __I--~ Ik5j .iv- x.- t4 ~uJ~IP-- u -H~pmILV .I~1I---- rr- i- f#A=-- - -- ---- -- ---- '' ----- -- _-c~i-----~- ---- -- ,-- -- -;--kb~jltC~-'" '' r r --- ,,,_,,c_ 3 ar:-- ---- ----~------~--- -~L3L~ IiL~~n;;li~J~"' L;~t4' -- -- I *,.: : :-It,.r4krA--- 4 & i - fm+-Ir;: : .:: :: :: :: :; : ; :: .:::. -:rW, , J -II IL--- ~ -- ~-- ----T------ I IF 1 -0 1 me iJ.a~ arnar~r - --KV22--kifigLm-1i• . --- ,. -L-- L .I:Il~he'.:T,V7,W-, is~]~71"::~:~; ,&r~~fV.. .LSf\ t~2.0 2.5, 3.0 3.5 4.0 4.5 .0 5.5 5 7.0 7.5V.V-~I-"..,Normsal acceleratkonData matisfaryd0 9 .5 O O,-10 .0,.Raton roU* Vp~PVJV,Lral acelFlight N"""" Run No.DateAirplaneAltitudeAeMeteoro_ ; --,p,!,,,, .. .-- . -, . - :-- ..-- ..----*I. N crN ele raioDgsata lafactoryDateAirptAltit-I*0. 1 degree per second NRate of pitch01.0 degree per second10.5 .0 RateAAArollo " ".,,~ o .s0. 5 1.0 1.520 2.53.0 3.5 0I 4.5... 0. grlavity __'Lateral acceleratoo A f0 1 A g s 94 - V 7.2. .9 R No. i-II-------+ .--4- ....:B-2U No. 44-30328 Normal acceleration Airplane B800 fed Dta unsatisfactory26% MAClogical conditions Hot summer day scattered L. .... Meteorologccumulus, therma. eating. . --mod.*8.0._..No. 86No. 921 Augt 1949ilane B-2s No. 44-30328ude am00feetqwd175 mphcenter of Vvfty2% MACeorolocdl d Hotu anouer dy scattered.camas, 6m aisti g.,cI s ,c l h5.0 V vW V-1..27 o 444033 " -0( vV -er o(ravity % MAC& Iondition Hot summer day, scaotredcumula, thrml bst g.~tt . .S.lbps.psrminiI~.~ *~~ . . , St10 degreePe nIII- ------ _ _ ___ I ~ I---~ --- ------ I - -- ------ --,-1~.~~~~.1~1~.~..^~.~--11-.~.~-------.1~- -I-.AMotoI: -: :_: ~ ;-:: _:-;l;:-l-:-i:l -: --:_:::i:e~-.~-'::ii:-: :: ::: i i: :. :-:~_~;;-~.-l~,~~ c;; ~: :_:: - :~:1 f 0 deg rev' ptr aetondIIllllhilI[ IRate of roll.Ul gravity aclrto 1~I Lateral acelraio~l II f.IOlfl~IIII ith ~i t'11i lol Ihi I Ili. 0. degree per seco nd Pa of lptclihII rudhaililt, 01 II I Il grvit~, ~, *; f1, aterl a t li~atio I~I ~ I If 1I'~iiI~h II III I I II II I itI~ ~ Nra acceleration II II II1 II l[ IKI ~ ~~~ ~ ~ Drt unstifajf ' (II!H If [I! I liIi1.0 degree per second1.0 degree per second0.01 gravityRate o( pitchlate of rollLateral accelerationtimne -iil?ormal accelerationData unsatisfactoryd ~~Vi[iiiillMIIiiIi'II1.0 degree per second1.0 degree per second0.01 gravityRate of pitchRate of rollLateral accelerationS111III111111111timerw~11(111iititud 000feetFlight No. 87 Airspeed 175 mph MARun No. 1 Airplane center of gravity 26t MACD ane 2A.5, u . 30328 Meteorological conditions Hot summer day,1ilane 11 - o.44-32ground heating![[llllj][llijjllillt~lllijH i j I IitIfIfiIIIllH4fIifHIHHH44IIHfe4III)HH4H+4444+4H444444444L444I44444H4INormal accelerationData unsatisfactory1(ii lll !llllf l[l illlllll1111 11 l1 1 l l1 1 a l !!!l~ llin aI 11 11lllll 1 1 ll 1 1 1111 llll111Run No. 1 Airspeed 175 mphDate 26 August 1949 Airplane center of gravity 26't MACAir lane B-25 No. 44-30328 Meteorological conditions Hot summer day,ground heating.,I [IIfillIlrli iiilssiiiliiniiliililillciiliiiiilIIIIIIIIIIIIIIIIIIIIIiiilllilllllllrlWlrl1111~1/1/11110 degree pe s coI1.0 degree per second.0 degree per second0.01 gravityRate of pitchFlight No. k'7 Altitude I!l0 feet 1itttIttti1 1Run No. 1 Airspeed - 175 mphDate 26 August 1949 Airplane center of gravity 26, MACAir lane 13-25J No. 44-3u32 Meteorological conditions Hot summer day,ground heating.Rate of rollLateral accelerationStimeI 111 1 1111111111111111111Normal accelerationData unsatisfactory1.0 degree prllc1.0 degree per second1.0 degree per second0.01 gravityRate ~l~lli~ IIiRate of pitchRate of rollLateral accelerationNormal accelerationData unsatisfactoryFlight No. 57Run No. 1Date 26 August 1941,Airplane B-25J No. 44-33328iiFAltitude 0 eeit llIIIAirspeed 175 mphAirplane center of gravity 26%, MACMeteorological conditions Hot summer day,oun etinIlu lul1111" ..... . III.M liIIIIIIII'1~Il IIImefRate of pitch1 . degree per se.- cont IIII 11illIl111111f lltl '1 I i IIIii II I I II N1 i i I 1 1i 1ii i IIII1 11114 11 t-fl II I II I II IIIII IHI IIIIN111ii1 1 I1 1 I I11111 11 II I Flight No. 87 titude 800q feetRun No. 2 Airspeed 175 mphDate 26 August 1949 Airplane center of gravity 26% MACAirplane B-25J No. 44-3,328 Meteorological conditions Hot summer day,ground heating.~~~~~I iI I lltll11llllll .Rate of roll.,. dg...r.e per ..cond..f .A. I d gMe I'p IIIsecond110. ul gravit L ateral accelerationWAMUM"40" I I I I i I A~ u tllwn ....I ..uU 1011P....Illllllillli ll HITlllllllllM IINormal accelerationData unsatisfactory[IIIIIlIII1llII. i li1.0 degree per second1.0 degree perll' ffIlMaII mMIIII0.01 gravityRate of pitchl lRaeof rollILmttH$$f ~I~HI HI II4I44I4I4III4li IILateral accelerationNormal accelerationData unsatisfactoryI-II Iftime -aFlight No. 87 Altitude 8000 feetRun No. 2 Airspeed 175 nphDate 26 August 1949 Airplane center of gravity 26% MACAir lane B-25J No. 44-30328 Meteorological conditions Hot summer day,ground heating.IIS !! :!!! !!Z :: :'I11III1111111111111111111111111111111111111111IHIIIIIll m I III IIm I I IIIII i i H4 i i i IIIIIIIIi h IIIk M i I)IHiHtIIIHi iHH it HHt ii ltittIIiil-Aij111111111111111110ll11111IIIII1111 1HillIHillIIIIIIIIIIIIIII IIIIIIII I I I I IIHIIUnt!ttttiHtt1tttfltttt tttt1tftttttittti tttt1 it ttttt 11111f l1 iIII i1HIII II11111911111HI I I II IiIII IIIIi I I IIIIII II IIIIII II Iu II IIIIIW IIIIIIH II II uII u IHIII uI uII I uIII I 11111111111111111111IlIIIIl1IIIIII1IIIWIII-n..... .II II IT111' 'lTil"i TH!T MtttTTI'TI I'u 111111 111l1111111l111111l1111111111111111111111111fllllillii rlIllllifllllililiiiula"illlllllllllllllltl1.0 degree per second{I .0 degree per secondI IIlII ........ HI"f-'-' . l I"ftlllMttt li t im llllll I0.01 gravityRate of pitchRate of rollLateral accelerationNormal accelerationData unsatisfactoryFlight No. t7 Altitude b'u 0 feetRun No. 2 .irspeed 175 mphDate 26 August 1949 Airplane center of gravity 26% MLACAirlane 1-253 No. 44-3. 32~. Meteorological conditions Hot summer day,ground heating.1.0 degree per second[tiiue -~'I'IiII'Rate of pitch1.0 degree per second1 Rate of rolln inamStime ----. grav y IIIIIIIIlIIIII lIILateral accelerationNormal accelera donoData unsatisfactoryFlight No. 87Run No. 3Date 26 August 1949Airplane B-25J No. 44-30328Altitude 8000 feetAirspeed 175 mph11rplane center of gravity 26% MACMeteorological conditions Hot summer day,ground heating .i1i1111111 111 11i l inlliMinu;llllinu tlinit ill1t1t nu nu l smu usiuiun um mIIIIII~~um uu "II liRate of pitch1.0 degree per second1.0 degree per secondRate of rolltime0.01 ravitL a lio'I Lateral acceleration14111111111111111 !!1 111mu11u1IJ41UJ1S1wnfi4III 'I II 1111 II Flight No. 87 Tde 800 feetRun No. 3 Airspeed 175 mphDate 26 August 1949 Airplane center ofgravity 26% MACAir lane B-251 No. 44-30328 Meteorological conditions Hot summer day,ground hetng'I fI~ II ~ijNormal accelerationData unsatisfactoryIII L A1A,1 IIII IIIIIII 111 i 1 i ll II t Ii t II I IIIIII11111 IIII11111 111 111111111;11 1iiliiiH i l ll lliIIii I i U,,I I W i lIu" LLIWWWWWIIIJULI[I lANUMALIIIIIII1111ULIIIIIIIUIIIIIIIIII11111111l111111111111fftmlt:lltlttlltlnllmttntttttttlnltmtlllmmmtlmt n ttmmttmtmmt~mmttrtmmttrnnmmnmnrrrmmrrrmr ~-~:IIIIII1III\:ItlK !I. U degree per second1.0 degree per secondII IlIIIIII l II llJ. 01 gravityItate of pitchlate of rollLateral accelerationNormal accelerationData unsatisfactoryfill1111 II Flight No. 87 titude , I IetRun No. 3 Airhpeed 175mphDate 26 August 1949 Airplane center ogravity 26'" MACAilane 13-251 1 44.30328 Meteorological conditions Hot summer day,ground heating.IIIS S!.1.0 degree per second Rate of pitch1.0 degree per secondRate of roll II III time0. 01 gravityUIlII11I1 , sLateral. acceleration...... . . ........ . .. ......l| III iII ULLLlll fillllL llllll1111 V i I'4 0,aFlight No.Run No.DateSAirplane87326 AiB-25iiIf~Airspeed 175 mphigust 1949 Airplane center of gravity 260 k MNo. 44-30328 Meteorological conditions Hot summer day,ground heating.. . . . . M1Normal accelerationData unsatisfactory11I 1111111111111 111I1.I1 N,' 4f.fY H HH HH F iH ttHHHi)t lt t Hti ittflfttHliltilMMttil fttHt III!11ll IM 1111IM -.-lnllH I I I I ttitti f IUIfI f tf~~ItItttHittW I ittmtiif fItfIIftIff I fmffHttttttfIllittIitttt"I tl: ItmtHttitt ttHH Hli stmu mmuftifti"H tiff tttitltitHII IIII I Iio ni I InI mInII 11ttii 11itif1il Hinitin fiinli i i 1ini 1III1.0 degree per second Mate of pitchiRate of rolli degree per second0. Ol gravityLateral accelerationNormal accelerationData unsatisfactory111111111111111111111I 112 .llllll Ill lllllll I N El l l l l llll ll1 111111111111 1 11 1light No. 87 Altit ,de 8000 feetI in No. 4 Airspeed 175 mph)ate 26 A :gust 1949 Airplane center of gravity 261 MACrlane B-25J No. 44-r2 3.leteorological conditions Hot summer day,ground heating.1 11111. degree per second ate of pitchRate of pitchI. 0 degree per secondRate of rollU.01 gravity,fLateral acceleration~ II IIl~lIINormal accelerationData unsatisfactorygill 11 IIFlight No. 87Run No. 4)ate 2Airplane .; August 1949-253 No. 44-303281UIII lI IIIIIII II lII lII I I I I I I I I I l IIIIIII Il I III II IIf I I I I III I I I IIIIIIIII . .. .. . .. .....t'I I III tilm l. gravityAltitude 8000 feet......Alrspeed 175 mphAirplane center of gravity 21Y;'. , CMeteorological conditions Hot summer day,ground heating.1. ) degree per second1. degree per second1 1 11 lllll~ I llllllllllllLateral accelerationNormal accelerationData unsatisfactory I liU iMMIIIIII IHII IIi iiill lUl lliiiliiiiillllilllllllllii iillllllllIIllsl1l1iilllllllllllllIRate of pitchRate of rollLlIIIIIIII1II11LI111I.0 degree per second~te of pitch1.0 degree per secondFlight No.Run No.DateAirplane87526 August 1949B-25J No. 44-303285 5II I!!111111 1 If I11 lMl Iu lmpl ll g Iu'J ai Ii% AititUat ?uuu 1;ee iAirspeed 175 mphAirplane center of gravity,Meteorolog.cal conditions1h 1 11lllll I M Il l Iili IIIIIII i 11l1267 MAHot sungroundlTllllllIlllllIII'j~ Flght NA ltitud 8000 feetRun No isee 7 pCDate 26 August 1949 Airplane center o gravity 26 MACnmer day, Airt e B-25 No. 44 -30328 Meteorological conditions Hot summer day,heating. I ground heating.1.0 degree per secondI11L.u degree per second,,II0.01 gravityiIIIIIII m 11111111 111I IF'Normal accelerationData unsatisfactoryIII iI'4,o il , I11,1Normal accelerationData unsatisfactoryLI t acceeratI iii11ater .2lii Ii2 . 11..11111 1.....01 gravity. e,Lateral acceeraioninUii 11 MI J1U I..- I., I .i!Nra cclrtotimeII IU 1 J.UliI]L11411144 44444 4441444+i1 : 1f iItTIT1TT 1111fIffIfIfI IftItIt Hillfil.I I I 11111111111111111! 11 1 H40 44MIlllllli 1lllll H I IT tllmlllltI|lUI nUIi| H-- ---------II -IA titra R n)f pllI I f H lI lI I lII II lI lIl-11nI nunnII| IIn H| 1111111 1111111 MIMMHMff"Mi H " H i Mi HHn mLA ¢L mL6a 4a414-If !HHlHHHMM M " Hl miT - lTrIlIll Ill I Ilm IIl IlIl I IIIIIllK II l I Ill I I I" """""ll """"""""""liIIIIl" lIIIIIIII m1II fI IIIIIIIII IIiI I I IIIIIM III I I II I I I I H I I I I I I I t I I I I I Iinen llllnlninn llllllunlllllllllllllnlllllllnu sll ICIIUICIIIUHUIUIIIIII~Ullt~WUIIU1H~LU'~U141 WI.t, | | 1.44 $I t . .i- tItt t t t , ' t t tt440 t tHI1t14 4t tiI "1 t tItfH fttttttttttItttfIIff! t t II tIIII!! f t t t t 1111 tit 11 IIl tttHmnOI I 1111111111[tl l 11111111fffilillZ411111111I1 1 n m III H IIt iI I I H fII tfffI fIf I tfiltfIIIOt fHI fi lII fUUI~UU~ r""7TM I " TT" rMl IIT II rTl I lll I IIf TlI IlITlIIumemlumimmunuulloIuI(uLII\iWUlnalFlight No. 87 Altitude 8000 feetRun No. 5 Airspeed 175 mphDate 126 August 1949 Airplane center ofgravity 26"; MACDlane B-25 No. 44-30328 Meteorological conditions Hot summer day,A1p111V25 . 4-0 ground heating.IIIIIIIIIUlllillllll1IIIIIII1Ullllillllllr 1 11time----+LU''ii'' llII J1. 0 degree per second Rate of pitch,Rate of roll1.0 degree e second.01 gravityj Lateral accelerationme ----OWW11111111IIIIi ' I lfI I IIII III I FlightmN8 liue 80 et-I III II I I I uB I !Flight No. 87 i Attd 00fRun No. 60 Airspeed 175 mphDate 26 August 149 Airplane center of gravity 26, MAClane B-25 No. 44-3328 Meteorological conditions Hot summer day,roud heatUV0 t'...............IIIii n II w HiNormal accelerationData unsatisfactory1.0 degree per second1.0 degree per second0.01 gravity11 i h l 111 11 1111,Rate,......f pitcIIII'11111111 1 1 11111 1111111111111111111111111111111111111111111111111111111111 1 11ate of rol-*1I~ j[ .~iLateral accelerationIIIllltlllllllltllliilllilllllttINormal accelerationData unsatisfactoryV 111111111I]I II 111I IiI.11 Il 1 Altitude E1U11(jtJO feet111111111111 H I lilllN .l8llIIlIIil17mp 11h111111111111111111111111111 14 11 141l A ttud..........Flight No. 87 Airspeed 175 mphfRun No. 61Date 2 August 1949 Airplane center of gravity 26%'MAClAirpame 125. No. 4430328 Meteorological conditions Hot summer dayirpl B-25J No. 44 2ground heatground leatbng,.................................... . ...................... .. .:.:. .i:. ::.. ..........WEIrllfYIAII11111IIIIIIIIIIIII~ftmti; -tmtt tnmTmm i mTmmmn111r1111111111warirI I L I 1111I IIIA"iIII I A I g IIti 11 1 11HIIi 11 14 1 1 I 1 1 1ItI IfII I I ff t tf IIII t"t"II tf TfItI I llI" It I II I "I "ItI" 1I t It I 4 I I I ITIgI ITII I I1 11 III! H4fHittttttm rr 1 T lU MtI 111ttm mn 111111111111 m111111111 HIIliIIIIMII1 11 11 1 1 I IIi II4111 11111111 IIl 111111111111111111 111111l I Ii1 11 1111 1 11i Hi 11 HMm11 14141-1410 111 i i I lN k :Ilr~UIIIII~UIIIlIIII1111l1l111111111111111 1II 11111I1 L 1111111111 1111m111 Ilul~P~armtl~t8~+lyIULllrUr~Ur...TMIi t I l++ 11H44i H W((((44 (Hm4+1444if Ii H i W i i HH"- fIII IrIil-111L111111111111111111111 Illlllllllilllllflrl,,cIIIIlllll lllillllll I1 IIII 1IIIIIIIIIIIII IIIIIIIIIIIII1. U degree per second Nate of pitchl ll i 1111IIt f I i i f 11 I IIIIIIIIU IIIIper secondFlight No.Run No.DateAirplane1'""mI uullnnIIIIIgree626 August 1949B-25 No. 44-303B-2b] N. I'll".Rate of rollllDf l.'. ...me ---0.0 gravity14Lateral accelerationNormal accelerat ,mData unsatisfactorymill1iq!11 1111 ii i iii i 1 IIII II I II II IIIIIIIII i l I H l i lll IIIII l WII iI iii Ill lll lIit u 8 nI00 f elS Altitude 8000 eet.....S Airspeed 175 mphAirplane center of gravity 26% MAC28 Meteorological conditions Hot summer day,ground heating..ll.1.I W.U.1.i. l l l.U.2i1.0 degree per second Rate of pitch1. 0 degree per secondRate of rol0.01 gravityLateral accelerati(Normal accelerationData unsatisfactory1111111l llll l 1 1 111 1111111 111111111111 11 tme,on I1m- iFlight No. 87 Aise 8 5 feetRun No. 6 Airsped 175 mphDate 26 August 1949 Airplane center of gravity 26% MACAirple 25 No. 44-30328 Meteorological conditions Hot summer day,groundb eating.... diiidIII I IIIIII I II IIIIi l I I I I I I* I I II .......... .... ............. ..S~H-H+I'H'H'Mm H'MMtttfft1tttttttttTlitT II nU l LLLU- LLUUUW 1 l lltIII.[ifODl grI av11 ty111111 IIlIIllIllllII IIIIIIIII II I -liiiihilillfiiiiiiillillillilllliiiilf4U411I 111111 11H4II I IIHI I IIIII mllIIfiIIIIIII I i ffio 11111141111111111nI ftIi ll islll nllll I llllll;I'IIIIIIIIIIlIIl ll lRate of pitch10der rsecondRate of roll.1.0 degree per secondtime -grNteralacceleratic rIData unsatislactoryllllllh'llll =eo rmll a: eData unsatisfacor.....................Flight No.Run No.DateAirplane 26 August 1949B25 No. 44-303218Ait ...... 000 feetAirspeed 175 MphAirplane center of gravity 265 MACMcterological conditions Hot summer day,ground heating.IuNI.nnual l111Uminunu1uin4uuul14unu4uul4ul4111umulu 1411:H !Rlu11 4l4o11001$Ll l II4 I+IIII!!!IIIII HII4I4$I4IHIII1i+9+I I II I llllttl'Ii) 111: I De 1 1Iiti IL IIIIRate of pitch.1. 0 degree per second11111 5111 ~Mti tt ui t g + g lytt tttttt iMtllulRunight No. 7 Airspeed 175 mphDa 26 August 1949 Airplane center of gravity 26" MACAirtane B256 No. 44-30328 Meteorological conditions Hot summer day,Airplane B-25JNo. 44-308ground heating.f i IH iilRate of roll1.0 degree per secondIateral accelerationormal accelerationData unsatisfactoryIJJlllJllIllIUfIII U Ifff 1f 111 iiti i Illnm r mllmlllmlmlll4m1 111 HIlllllrHI T1m IlHII llnunllIl[llII"t '" t TT"" IIIfIiiiIIf IIIillII.flLL I ffII' II time-0.01 gravi ty'111111I fI I I I I I I I I I I I IItt l i t I I I I I I I I I I I 1 1 1 1 1 1 1 1 1 1 1 1 1 l l l i I 1 1 1 1 1 1 I I IIiI l l l l l ll l l l l l il l i l l l l l l l l l l llll l l i Ii i I I i I I l i l l l lll l ii i i l l l l l l l .. . . .. . .. . . . ' ;mlnnllrlrmH11FIIII1I1lnllllllllllll1llntttlllt~tlllltfnt~lnnmrm~lnrm~llIlllmllHfftmfttfHmttt(ttfftmtffffftmftlt'ftmtfIII III t" f Hillfill "f If Imit mm nm mm ma n nmI muni nIInI1IICI)~*~U(CC))(UU'~UL"1L" ""'LLL 'TnITTTIIII II TlTllllllTlTllll l rll |M I I IIIIIIIIIIIIM I TTt""M tt111111IllIIII II I II I I I II I III1IIIUUllaIUIIIIIIIIIIIIIUUIIIIUI~UII !ttfll mmttmmtmttmmtmtmtttlMAYASH Nit.ffffffffff ffft f If if !!If !if t f tff fftTItI ifin"" I II] I III I II lllllll "l J[Iilllllll lllll lllll llllll lllllll lllllll llllI llI llllI' I IfI IIIIII?I us JV A ,~......ililllllllillllUII11,:1111111111111l11111 IIIII I1IIII1IWimWI IIIII IIIIIIIIUIII IUlII LIIII llIIIIIIIIII1IIIIItIIIIfvl E Ate of pitch1.0 degree per secondI. degree per secondRate of roll0.31 gravity1t U U UU IUIIIIULIII I III87726 AugustB-25J No.time -II1III lt1 1il l H IM I III II I HII I I I I H ill 1 111111 11 [it III I I HIII t I I 111111111111liAtrlaccelerationNormal accelerationData unsatisfactoryIIJJJ 111ifr f r llllil.................1.0 degree per second1.0 degree per secondaall ! :: lillllIlU. 1 gravityFlight No. 87Run No. 7Date 26 AugustAir lane B-25 No.Rate of pitchRate of rollfl l ltime --Al11 11 11 li I IlIIllI 111\10\\\\ lel i l l I I I I I II11111 -l 11 I lllilpAirsieed 175 mrpAlte 800 ee1949 Airplane center o gravity 26% MAC44-30328 Meteorological conditions Hot summer day,round heatIateral accelerationNormal accelerationData unsatisfactory!! l ll ,A! i I I I|I h h Ili'hstll l IFlight No.Run No.DateAirplaneII.,"U"III HI H 1LhEl IIIIIIIIIIIIIIIII 1II 11Illi lIllll l l l 1111111111111111111WI TITII I If IIIIIII Hl l IfII tl T t ttf ttll t tIf t l lIIIIIIf I f IIII l U Hl l11- - U "4 MI "&"4fjH4" &4&U " J;4L .........LL IJI u~l IIill II iI LWIIII IIiuul l u lA l e ...... 000 feetAirspeed 175 mph1949 Airplane center of gravity 26% MAC44-30328 Meteorological conditions Hot summer day,ground heating.t tI t tttt tt tlff f ffi ittH aii WH H H4 " 1411 mI 111111,1UIIR 1I I III 11 11Ill ll II11MII I IIIIIIIIlIIIIiIIIIIIIIIIIilIIIlflil II III iIl I I2 i m i I H ii 0 ttttm ii MH i i i mi n mi Y Pm H T i t . . iTftfiti m i 2 i i t ! "V t V|if ! " Y tY'rtf~f~t~fti v ttttttttV Y I M MTr I fTT t Yt I i tT tt fit I V IIIIIIUIIIIIUIIIIIIIllllliiiiilIllll11TIII TTIII 111111TI I IIIII III I I I1IlTTTlITIlITTllIfITI:.a o 7 .;|! H ft H1 IMHi i fl ttff"tttfttMIltl IIIIIIkII I L llg&111 ]U" L II111 1111[llIIII.II IU L Ii I II 1 I I I I W I I I I 1 1 IIt i I 1 1111111 111 III 111111 11 1111111111 lllllull llLL L II I m f 11l lllHWANHHH! 'Ifftftff ttmn tt fftrmlrrltrmtttttttttrtm ititfIII: Iff lflff tfluffttll Nll11Titt1t Tt11T i]1 1 M 1 t ttttltnH~ttt~~HILU ILIIIW IIIIIL llllL W IILII Ij [ll ll11111111111111111111111 111111 :IliltI.Al/liIlllllili;,l,', ,I I iiii,ii ill iihI~itlIIII~l~iill Rate of pitch1. 0deg r econdRate of roU0 " degree per s cndme -p0.01 gravityLateral accelerationformal accelerationData unsatisfactorya. !HlllllM1Illl i lIIIItiIIIIIII1t1 tIIIIIIIIIIII1 iuu lii! I IIIIIIIHIIHIIUIIII HUIIIIIIIIIIIII II I1~~l ttfIlf~ ttt 1tt l ttl Flight No. 87 Airs peed 175 myRun No. 8 Airp ne center oDate 26 August 1949 iMeteorological coAirplane B-25 No. 44-30328 e ci tlftttti l1t i iii~ ~iiiiiii i }ii 1111111UIIUtH.IIIIIW 9 , ........ ............. .. ....phgravity 26% MACnditions Hot summer day,ground heating.1111111111111111 lllll ItM llllllllifill Ilim llll I I l.....11I111I Fl ight No. 87 AispRun No. 8AirplDate 26 August 1949 Airpl1.0 degree per second Rate of pitchII1.0 degree per secondRate of roltime -0.01 gravity[tateral accelerationNormal accelerationData unsatisfactoryeed 175 mphane center of gravity 26% MACorological conditions ot summer day,ground heating.Illlrllllllllllllll 1111111111111111111 11111111111111111 11111 1111 11111111111 11111 11111111111 IIIIIIIIIIIIIIIIIIIIH 11 11111111111111111111111I.... ... . . . ..IIIIIIHI IIIIIIHIIIIffIfIfI ItF ll ltfIfI I)t tllllN tl f 1tt ttll I fI I I It f l iftfftillwi) nflll1l1111111111IllllirlllllllHIIIIIIllfllllllifl~tlllllH iW ii i iMiui im ! mifl II 1 ,'H,"fLIIIIIUIIIMIMMI11\+'+ " 1444- M !H444M4+44444W444++i111! ! RIIIUU IP, I, Iflf I , ItR III II ! H t tt tttttf ttfl f tllfltf)tttflflflflttttfl HtAMIIIIIII IIIIII IIII IIII IIII IIIIII IIII IIII1111111111 1111111wli!IIUIIIIIIUUIIIIIIUUIIIIII UUIIIIuUUUUIUUUu llltu IIUUIIIIIHH( IIIIHH(IIII114111 IfR t ntf t ffilltttR l ttitt Ri tt I I liffl Ill 1 11R1111 f it mt mm lttl mmmm tt1tt1m1n. .... ... ..... . ... .....k.Ab . ... . ...... W ... ...... ................................................I .................................lliillillS. t l 4 . .... . ....... ... .I I . . ...... . . .. ...... . . ... .. .. .. .. .. . .. . . .. . . .. . . . - -- - - -- - ... . .. . . .. . . .. . . .. . . .. .. .. . . .. . . .. . . .11!111 nIIIIIIIIIIllIIIllll 1111111 Iil1 ulllllllllllllllllllllllllllllllll i i l illllllll!Flight No. 87Run No. 8Date 26 August 1949Airplane B-25J No. 44-30328Altitude 8000 feetAirspeed 175 mphAirplane center of gravity 26% MACMeteorological conditions Hot summer day,ii. fr nor! JAIIIIUdIi. u degree per seonu IIIII.IIIII ISI Rate of pitch1.0 degree per second Rate of rol0.01 gravityLatormeral accelerationHormal acce aleratoData unsatisfactoryFlight No. 87 AlRun No. 9 ARate of pitch Arplane -25u . 280.1 degree per second0.1 degree per second Rate of roll.... .. .01 gravity Lateral accelerationNormal accelerationData unsatisfactory- ground heating.Itltude 80tirspeed 175 mphIrplane center of gravity 26% MACeteorological conditions Hot summer day,ground heating.... ...... ........S5............Altitude 8000 feet. .....................Flight No. 87Altde tunFlight No. 987 Airspeed 175 mphDate 26 August 1949 Airplane center o gravity 26'. MACAir lane u-251 No. 44-30328 Meteorological conditions Hot summer day,I ll l i......ii.................. ...... ... ground heating.Flight No. 87 Altitude 8000 feetAirspeed 175 mphR No. 26 August 1949 Airplane center of gravity 260 MACAir lane B-25 No. 4430328 Meteorological conditions Hot summer day,g r I rou nd heating.1.0 degree per second Rate of itch0 degree per secondRate of roll..i ..... .....ltthill!t ifittttttttttttttltttIttttttt t!! tfftt ttttiIffftfttttfti l 11 t t t fIII ift i f 11111!,111111111111111N111411119 41111t1 91919 1 t9 1111 9li9 itI tltttt91 t9i9t1t4 9999t 19 99, 911999 tt4 9I9t i911 tt ! II t iUILIIII.L I iIIIU&&1 I .iu 114UU IIUII UlI ll ilUiH 1 1.11 It,Flight NoFlight No.Run No.DateAirplane87 ' Altitude .80u) feet10 -Airspeed 175 mph26 August F)49 Airplane center of gravity 26i MACB-25J No. 44-30328 Meteorological conditions Hot summer day,ground heating.a ilM I IiII IIIIiii It ~.S4IfLateral accelerationNormal accelerationData unsatisfactory... . . . .. ................ .... ii i ~1.0 degree p r second Rate of pitchFlight No. 87 Altitude 8000 feetRun No. 10 Airspeed 175 mphDate 26 August 1949 Airplane center of gravity 26% MACAirplane B-25J No. 44-30328 Meteorological conditions Hot summer day.ground heating........ .. ...II S0 d e g r e e p e r s e c o :Rn d aI e0.01 gravty Lateral accelerationNormal acceleration'Data unsatisfactoryIll Ii iii. 'I1 lI lll'IiI i H II IIIIf I I I vIll IIlI Il IIlIlII" ll llllHlM lll lIIl It l I I I t I I It I1t II I I H ill1till1I1111111111 111 H I Ili lII IlilI I IIIlIlilI I Il11111l1 I l'l--- ----------------1111111l1l1l11111111111I111Il111I1Il1IlI1IIlIlIU n~nllalll~ltlUllII1II~~~Uli 11l111111111111 IIIIHIIILlUIIII~4 Auc "I M I1T I II I ITtillT t lttT1l Yt t ll Ill AtttT ttttm tt t l!I11111ttt I T 111111111 ttfl tlt t i I If I, IT I IT I lllf I In T IttmI I fly II IllI I f "Il I I ITItII ll I I I I MIT Ill Il l I I I I I "l If I [IT i m II I I M I I II 1 I IlIf I* m i n Il I HillI I I IIM ITI I I TI II T FTl IITllI11111111 I Il T IIIfI 1 II I Ill 1111111111IT II II IllIlll19~mB)))))))~fffffff))~~t~H)~~~~~)~tttt(~tf II~ Ittt~Hlf ft~t~llllllf ttttflllll~lllll tttttf in~))~tilt~~tttt~tllIlltHlll~ll~~t~tt~~l II11II~11I1 IfIIIIIUJI14 ii l l U W111N !Wl 1 ||II | || I i IIIIITIT''II1.. .......fffttftffIffi f ttt"f H MI tiI " I II" IIlt"tlfi 111 111I, I "tM II tM "I III 11 TT"tTT........... ............. . .mtI f 11 1 11IIIIIIIIULJ+"Ww" W'fftt mflmttl mttt!tI if I! Offi f ttttttttttftfftttttttttt tttt HtttIttttt ttt Hfftttt ttItItttttltttttttttlittftttttttt ttflt IH IH1/1i,0 il i~ iiii llllr ll,i HiI I111111111111111111111I l1l11ll11lill1lll11i11111111111111111111 lllllllllIrlll1lliilIfllflrlillllrillll III. degree per second FRate of pitchtime1. degree per secondRate of rtollIIIIII li ii iiiii jiiiiiuiiiiiii 111111.14 1111111111111Flight No. 87 Altitude bt teet[un No. 11 Airspeed 175 mphDate 23 August 1949 Airplane center of gravity 26'. MACAlane -25J No. 44-30128 Meteorological conditions Hot summer day,ground heating.Lateral acceleration0. 01 gravityNormal accelerationData unsatisfactory1.0 degree per second1.1) degree per second0.01 gravityRate of pitchIriluliiim m aIuiilt e -------Rate of rollLateral accelerationNormal accelerationData unsatisfactoryII1:1 II1iit1~lI aI I 1111119 1111111111111 11111 111111111111111111111111 4 m Il i ilm lla ill IIIa lFlight No. 87 J Altitude 8.0 eetRun No. 11 Airspeed 175 mphDate 23 August 1949 , Airplane center of gravity 26% MACAirplane B-25J No. 4 4 - 3 03 2 81 leteorological conditions Hot summer day............. ........ -groui za incr ~IIIliljgrounu iheating.II ii lltill ill lII i, l:ill1 1HP hila2 @!!Ulll! M,! t~l i illni ' lM ill t !!!@lI tFlight No. 87 Altitude d.OC, feetiun No. 11 Airspeed 175 mphDate 2 August 1949 Airplane center of gravity 26' MACAirplane 13-25J No. 44-30328 Meteorological conditions Hot summer da%,llill!l! Ilillltl!lrltllllll~llll l ll i ground neating.1111i111111111111t 1 ! 11 1 Sli ht ,N I .I tIll ne . !5- silii ' 2 No. 87,lArplane t1125.1 * ' .,i, 1 !,41) ri u 'ent r ,if lrvily I(;'; MA('lso. 44-.. I;. Metiorologl'mll roindlloN Ilot uumnier dav,iiiii11 ! 11111111111111 .. .. Kr,,und h .1 g.\11 it ude ( !eel\rspeed :17. ,,Iph'19419 1 planve center of gravitv 2-V"N \C44-3032A8 Meteurol hgtcal lodltlions liot suntuiter day.lttfll llliii,, ground hating.Hun Rate of pitch.degree per second1.0 degree rscnRate of roll). 1 gravity Lateral accelerationNormal accelerationData unsatisfactorylillllllllllalls11111/11111111111111. ight No. 87 iAltitude 8000 feetRun No. 12 irspeed 175 mphlate 26 lugust 1949 iAirplane center of gravity 26% MACI 'irplane 11-25J No. 44-3)328 (4,ieteorological conditions Hot summer day,IlIII III lll~llltilllllllllllllllllil1111111111111 [ ground heating.l 11ttllll 11 [l lll lll lll ll ll lll ll I l l!11111111111111111 11 111111111111111111 I ~ l U f ll lFlight No. 87 Altitude 8000 feetHun No. 12 Airspeed 175 mphDate 21 August 1949 Airplane center of gravity 2;' ° MACAirlane B-25J No. 44-30328 Meteorological conditions Hot summer day,ground heating.V f hIlJ ~i~!I1.0 degree per second Rate of pitch----------- ate hiiin1.0 degree per secondiii llIIIIillll ili ii lllRate of roll01 gravityLateral accelerationilIIIIIIlillillulltl.,II llo il.. IIS llllll l l l l i 1 1 lllllIIU U1 ll.1 llltime-II VtIllI IIIIIllIll VNormal accelerationData unsatisfactoryI, tiiiiliii..II I 1 11 i .- 1Flight No. 87 Altitude 8090 feetRun No. 12 Airspeed 175 mphDate 26 August 1949 Airplane center of graviAir lane B-25J No. 44-30328 Meteorological conditio1.0 degree per second ,Rate of pitch iM~l~IA~ill~F!t i II ,'Rate of rollIityateral accelerationNormal accelerationData unsatisfactory,Li•I i iiiii I II i II IIIII. .........lot ~ iii I1.0 degree per second.n..i.......... H71.11.11! IHl l141 144l1 ! 1 7Illllll11111111111111111llllllil llllllll0.01 graviI; i~i i ii ' ;;lli iiiility 2;% MACns Hot summer day,ground heating.F77Flight No. 87 Altitude 0 feetRun No. 12 Airspeed 175 mphDate 263 August 1949 Airplane center of gravity 26% MACAir lane B-25J No. 44-30328 Meteorological conditions Hot summer day,iground heating.[li""li . [i . .. on im[an I " I" i" m n I"men""Hon I1II1LlYUlltllllllluuuI'uu nruulrrnulrrrr IiIll l 11lllllllllll tiIIUIUIIIIIIIIUIIIUIIUUUIUIURIIIUIUUIIIIII&IWIHlttttm(t(HCtttmmmmttt+m(((((tHnt Ht~ I11111; LIIIIII1L~LIIIIIIIII11111111111111111111 IInill|U1 t111111111t111... ... .. ... .. ... .. .1...1.. ... .1111.. ... I...I.. .. II. . .I.II. .111111111.11. .1.11111...H . ..i.l I . .IM .IIIIIIIJIMIIIIIIII 1 1 1 1 1 1 1 1 1 1 [ 1 I l i %lI I II i Il RIT%1ll111ililllillllliiiiriirliii lill411tiiliilillililli illtliiiiiilltiiiiitttllillllillillllll iiiIliiiitlliiIIiilll llri h r l iii--ll ---l ---- lllsalllnalllllsrebiell1 III III ll 1 1111111ll IIIIIIIIIIIIIII 11 Tlii 1111111111111111111111 11111111111111111111111111 ... ...............PIH* II.!1 i~ ~~~0 l tliill 111!; t !, 1111 1 llli ilt.~' 4~iiFlight No. 8qRun No. 1Date 2 September 1949Airplane B-25J No. 44-30328Altitude 8000 feetAirspeed 175 mphAirplane center of gravity 26% MACMeteorological conditions Hot summer day,!~Ilht!I IhNIIIl!tIitll 'Itl U [ ilI[fhI l ground heating.S Norm acceleration'~Normail accelferationff1IiIt1~LII'I,I J'I.2i~tz'0re, 1. J rft r r~f I 4 je '[11I'-.*4 _.I.L + I l~~ 4 ~ l 4 - L L 4*4 4 I iA4 -.4 -4 ,.M4 4 .. ,.4.4 . r* wi4LL -I 1I _~ M.YU~- ,l,* L I'u(JFlight No.Run No.DateAirplane8912 Se tember 1949B-2J No. 44-30328Altitude 8000 feet -Airspeed 175 mphAirplane center of gravity 26% MACMeteorological conditions Hot summer day,ground heating.I,.-i: -[, !i'I; ,i iItt!lltli: : :iiill 1ARate of pitch'tto.. .. ... ... *' i iRate of roll2,0 5 o .5 :sq 0aitotime.111IM M il ' I°Lateral acceleration :~ 1 I~j1I1I111F~1IDkilllStjj Iill ,,1 itt i iqNormal acceleration,.,:!l., I II . ... :I:. . . . : iS _ _ _ 4 _. A i A L41 m -i 1 & , , .Rate of pitchRate of rolli l l l '*1 "lj fli 'i '2.: /..... .. ,S Flight No. 89Run No. 2Date 2 SeptemberAir ane B-25J No. 4111 IMAltitude 8000'feetAirspeed 175 mph\irplane center of gravity 26' MACMeteorological conditions Hot summer day.Altitude 80E0 feet-irspeed 175 mphAirplane center of gravity 26% MACMeteorological conditions Hlot summer da"I ground heating.--ii iiIIiIll ii1:1.1I i i: I'" " . I"'" " t",' .l i Flight No. 89 TFlight No. 8Run No. 2 uNo 3Date 2 September 1949 Date 2 September 1949Airplane 13-25J No. 44-30328 Airplane B-25J No. 44-30328Altitude 8000 feet Altitude 8000 feet7ispe T175 mphAirspeed 175 mph ]'te of pitch Airspeed 175 mphRate of pitch Airplane center of gravity 26, MAC Airplane center of gravity 26(" MACMeteorological conditions Hot summer day nditions Hot summer dayground heating. Iground heating..Meteorologicalscond c" r ditions go umrdh a . I *,4. ° - L,0.1d r pr ... secoi. I degree per second I*- ..14 W* ..1. 0 egree per se Ol 1.0 degree per second . Rate of roll. . . . .Ri ftime... . 1 ime -Sle onLateral accelerat: t "1 . ."0. graviy if aiLateral acceleration VI '' 44ma ra 4a4oaNoramace acceleration e rt4' "' *...4t, Ion,4'' '~~~~~ Normal acceleration *~t."[ II I ~ ~~4~ ~ ::. $~"i~'4,as lp a ma no e *spns sl4um* II lme* "ea am a .. :: '= Flight No. 8' Attud 800 feet. .... ~... . .4.. *... 4.... D t . Setm er1 Airp lanecenter of gravity 26% AC4ne St embe441 0 2 Meteorological conditions Hlotusumner day,Rat of pitch01 degree per second f .,4L, ' . . .144'"' ''" "'.. .. 41.. .... " , .. .. .. ' : ' '4144'" ... •I ' 4444 f .' 3 ,, .. ",- 'r.."•'.'-- ..'. ' '' .."44. ..4. . . 4......to.. ****son****1.0 degree per second Rate of roll .. --*-I-. g Tl--* I**-- . --0.5 o . 051540455 6O5time0.01 gravity J10"0 ... ts Lateral acceleration I.1 !gr ty, 01 ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ... gr.t....'. 4 . .4 ~.. .... ~........ -......j.... .. 4444Normal accelera ion w,"W il ! .t.4 4' 4 4- ---------1gill. 1degree ofijisecond- ---------1. 0 degree per second',, .. . 10.01 gravity"' . r,, t-o0. 01 gravity. . ' ,S. " " HIIIa1H;Rate of pitch'Rate of44/atera.:iirollLl accelerationNormal accelerationjI,~ Ititi1 II ~ 14III* I1~*** i I~, ~'J*4,,~4 r4~F~iii~.44WItime44: L i IO II'I'.......I II. .. L : " . I " . -- -I" . .. .. . 1..... .... ..-4 4iiO4-,Il Y4 i+j +4...I ...~.i.i.11.I.,l .. .. . .+ .. ..I;I IfI~II ft ...........: .."... '" ......... ...... t .... I ... . . .$ 111 Ill i &A. ..li a-; .... .Flitght No. 8 .Hi- -. Run No. 4 Airspeed 175 mphDate . 2 September 1949 Airplane center of gravity 26% MACAirplane 3-25J No. 44-30328 Meteorological conditions Hot summer day,I ground heating.T it ;J ::Ii 2 ,~~ l L* . ..2 " 4 -+,' ',.t...,+,:+I4. *4'*4 t444. 944 *4. 4.1 + w i%+++ ,r L l441-41,-I--~...~;.UY~~.*1 l ..~. i. ;-"Hi~;" "" J '"""-u~ccrutll~~ * ~mrtrrrrr~r175 liiiii jtili19444 4 1 1 T '1 ''UlIii -W I 4* &Iw 9igulii ~ggI ..-. ~ 4fil.. ...... .. ..i-I;I I -II I 111 i ; : . I , I rX k ., I - I , .. , I ! ;IT:11..1____ :.i__ .U_.I .I~_:..l...i- : Ir.: .. J : _._.1 _ -I '':II.., : :_! ' '._...t 1.,1 .._...ll.l!liiilllli.. ;Illlllii..I:!EI-~:I:I:!l~,~c~,~~ --.~..i.,Y~_.I.~-:...--L~ IUU~U ~i 41 !L ,1,1.1t -i .I I . I& &1 1 1 - I1l!ill-i, , - -I I I l-_ -- II . l i ij ! lt A. L L. . ..... .L ICC C IC~CUnaix".-I.' _ ..l....l.-.i-. .---1.. ~i.L-.-- .- 'L L' Y --~~II-_---~~-~ ---I I -- '----- -'---"~-L-'~"'~~'~ -------.UCU L') ~ "~UII?~ UI(~~U ~UHII~CI ~ PIIIIUtllC1 ~1" TI I I I I.-4---4-li: iI;I'.,llt'lfP'•- , l+1UINbIIU . itill1titir~u r+~L4,I+++s,"vl i,++ +:,!',!,:i+ti * *WiI T+ ,. "? , •'Z+-It1:I':INormal acceleration~1. IA__ I,Fkivht No. 8Iur No. 5Date 2 September 191Airp'lAne 3-2ST No. 44-30328A' -de 800& feelA, ,ed 175 mphA ,.Aawe , nter of graity 26' MACN orologizcal (,coltions Hot summner day.ground heating.-~ I I8952 September 1949B-25J No. 44-30328I I IAltitude bo0 feetAirspeed 175 mphAirplane center of a. ,yMeteorologica paditions,* 'I '.9,.,Ht . ,Iite dA),I o,,nd heating.Flight No.Run No.DateAirplaneI t ''i'i! '~i. . . -- - - -: .l.. I -- -- -i . .~ ---C - -~--- ---- -_~X----~ LZW .hL0. i 0 . ;i ai AaI I i:i~II-~L--'H'0.1 degree of second'i . .. t ,0.01 gravity$2I' ~ j ~Rate of pitchRate of roll10 4ft = 1 a -I!11.I .1 ..4---, 1Lateral accelerationS Normal acceleration1 $got *41lt..........." '" " A ltitud e 8000 feetFlight No. 8 Airspeed 175 mphRun No. S Airplane center of gravity 26%, MACAirlane B-25J No 44-303September 1949 Met orological conditions Hot summer day,Air lane 1-25J No. 44-3032 . ground heating.kormal accelerationI *I 1 .1 1SFlight No. 8'Run No. 5Date 2 September 1949Airplane B-25J No. 44-30328Altitude 8000 feetAirspeed 175 mphAirplane center of gravity 26% MACMeteorological conditions Hot summer day,ground heating.'4Itt i, ]I I,.- tI 1tc~wc~...4i A o- A!61- ~-- -==PrrI 1I . .. ~1.. . . .. . .Ili.~CFlight No. 8. Altitude 8000 feetRun No. 5 'Airspeed 175 mphDate , 2 September 1149 Airplane center of gravity 26% MACAirplane B-25J No. 44-30328 Meteorological conditions Hot summer day,"I "I " ' ; p hlll iI:!I ' ground heating.Rate of pitch igravity'0.1 gravity',I- I'Lateral acceleration'Normal acceleration'hh.Flight No. 89Run No. 6Date 2 September 1939Airplane B-25J No. 44-30328Altitude 8000 feetAirspeed 175 mphAirplane center of gravity 26 MACMeteorological conditions Hot summer day,ground heating.T ' " i l o t.rif, [ #'k~ it -,Lateral acceleratione 'I *i*t~p ii,I t1Altitude 8000 feetAirspeed 175 mphAirplane center of gravity 26% MACMeteorological conditions Hot summer day,ground heating.I1' 1*I 1I III I0. 1 gravity......1.;... ' ' ..--r---~11rrrrc~-rmti ne--.I m it,-IiJ1Ifiiii.-. w4..Aa-.1 1...... 4.-- + - - -1 i .4 "... .... 140 4.5.4~tiiil1 1lIFlight No. 89*Run No. 6Date 2 SAirplane B-September 194925J No. 44-30328Altitude 8000 feetAirs eed 175 mphAirplane center of gravity ~6% MACMeteorological conditions Hot summer day,ground heating.1 'i .I v 1 v 3, 1 7 , - ! 1 1 -14 "It"lowo.II4S: I;jkillIJ . ... .- . .... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .i1 m Y -1, l- Ii -0 i-0 0-1 0-1 - 11 1 -p a & . . i - 6 1 1 i-i I a .. 1 T & . 1 . . 1 a i 1 A !1 1 i 1 1 1 1 ,- i - i 1 I i j 0 1 1 1 11 iL - 1 -. . . . . I.. . I. . . . w. . . . . . . ,.. . . .I; 1'I/Iik".4 'V51A -ln.~ ~4 - t' r".1y 1 00,141101 1 r,? ,ii], r (H~i, iii ! ill llihI I " . I I1.0 dgree per IondS1Ogrereoi:-40.. I & .1 i . -! 1"" i 4 --1 -d--ree r---- on-•1.0 degree pr Secondie14I 14RaitRate of pitchC - C IRate of roll10 200.01 gravity,0.1 gravity',mTr~~wvr ,I"AtLateral accelerationL''ilit-. Normal acceleration "'i. . .. .. .*CCC.I ~I .1 ~I .I .~!_.I I2 5 V 0i33540time o1 **........* *....*........Lit... .. ...... ..iljllip1,idlICCs~~ '~*Flight No. 89Run No. 7Date .2Septetnber 1949Airplane B-25 No. 44-30328Altitude 8000 feetAirspeed 175 mphAirplane center of gravity 26% MACMeteorological conditions Hot summer day,, ground heating..1._ ~I ~. ~,50 5.5n * oI CA Cii ttIIIIIiiI*1IAi.,I$Il&IIttA I,,Flight No. 89 Airspeed 175 mh _TRun No. 8 Airplane center gravity 26% MACDate . 2 September 1949 Meteorokit & Iconditions HoN i.rnmer day,IAirplane B-25J No. 44-30328 ground heating.Altitude 8000 feetI...JIiRate of roll... .... .. .. :. ....... ...15 2,0 25 3.0,time,--60Lateral acceleration............... ...... ... ........ .... * . .• ............ .........., . , ....C........ :7.N m acc .l rtoNormal acceleratio:, | : . ...,li ,il . ! . I .W-Ir:I.. ..L u-.06014. 1 i(I1ft'-t r~l?' ..... rt ..... ..... :- -- r ................. , -1TP-0".,- -ILfill'#t4',14""I-;~:-:::~:: !-r--i;FlightNo. 89 .........S ,Run No. 7Date 2 Se tember 1949Airplane B-2 No. 44-30328I ltitude b000 feet.. .. .....Airspeed 175 mph- .......... .. ............. ....... . .. ... ....................ILateral accelerationNormal acceleration 'I I LL *i77,o.. .....,~11itFlight No. byRun No. IDate 2 September 1949Airplane 3-25J No. 44-30328Altitude 8000 feetAirspeed 175 mphAirplane center of gravity 26. MACMeteorological conditions Hot summer day,ground heating..... -- - - ... ..-.-; ......IlI jI I" ".... .......... "....." " " Flight No. 89Run No. 9Date 2 September 1949Airplane B-25J No. 44-30328Altitude 8000 feetAirspeed 175 mph'Airplane center of gravity 26% MACMeteorological conditions Hot summer day,ground heating..II,,1.0 degree per secondI I I I I .Ijiji'~te1IIllli i~,i I,U;'~wiuII t~i~... ... . ......l i ;I- I::: - :?;.i ...... ..tL.IL :Flight No.Run No.DateAirplane,, Altitude89 Airspeed 175 mph9 Airplane center of gravity 26%N MIAC2 September 1949 Meteorological conditions Hot summer day,B-25J No. 44- 0328 ground heating.8000 feet* es - ,o..,,... o . ,45tFlight No. b" Airspeed 175 mphRun No. 9 Airplane center of gravity 26% MACDate 2 September 1949 Meteorological conditions Hot summer day,Airplane B-25J NO. 44-30328 Iground heating.Altitude 8000 feet-i --. I.. .. .. ..: : ~1. 1 degree per second,.0 degree per secondrT~1 - Tr;';~;r-J;IlA0.01 gravi-0.1 gravity_ " I" , EtyiJ,'.Rate of pitch• ,M. 1D"Rate of IALjLateral accelerationNormal accelerationh~illiuilllliuu 1llli 111uh 11ll 1i. . ..---- .-- - -Itime11..II lllt11111111111 lltllll illitll_ ' "lIIji,I,lilJiSI 4'lII,141,,D.IS........-, i..................'I IL HI II ........ III IIit I IIitIII1110. . .. . . ...... ,. ... . i.:. .-. .. , . . .i.lIh o111Flight No. 89Run No. 10Date 2 September 1949Airplane B-25J No. 44-30328Altitude 8000 feetAirspeed 175 mphAirplane center of gravity 26% hMeteorological conditions Hot sgroun01, 1 4. 1I-J, 1. L I I I0..1Pt'degree per secondI -. I I. .I I0.01 gr ty0.1 gravityIDtKI..I. 9'DI.;'''.I..Rate of pitchRate of rollLV7Lateral acceleration7T,, 7'.Normal acceleration"4 .,S10'UIiiI '!Stime - ftime,-)"U~""~t"Wt""r"""r""l"~Y I.t~7~r #*Df~q7 r7-'III'II... 'a. ...4I I. 'I*DO IM{D.1.j 4,,fh 4iFlight No. 89Run No. 10Date 2 September 1949Airplane B-25J No. 44-30328Altitude 8000 feetAirspeed 175 mphAirplane center of gravity 26% MACMeteorological conditions Hot summer day,, * j~. ground heating.it.447....................... .. " .... . . ... 4. *** ** --1 . . . .degree per second.. ...1 ......... ... . *. . ............ ........I I'.... ---,: ,..... , ..... , -:- --, ... ... .. - ' ... . " L----- ' ------ ..-' -~-- --'-':)---'-- ------' ----- L-- " iL L .......... I .. ........ . ........... .. :~ l~-::- . . . . ,.. .-- .- L " ' " -"" t .... . " ... . " 1 -- '.'- : "L-----~--------l- L l 4- -- - vu l .L.~. .... 1 ... I .. + tl ._l . ... .. . .. . .... . 9r .-Am . ... . -'-- - - ".. - v4 -.. 1:-:----if--:1:1 *. l - ,.......1.i , L.* i.iILi *" m,. ,.. .. . I * . L , +t L | , iIA..1 - 1 1 N,,f.-. ~w4 ! 1 1 -- 1 - 1 ;a- - 1 .& - 1 -A! - 4 - &-+ ---- ... L~..--I.--. --- a! ._..-- .= % ---4 - -'i i , i i iw -) -- ) Ut ?t f., 1 - t---- 1 7~ 1 1 1 1 -, . -..i~ l . lL-. 1 & + A-- .1 . -- -1--.... . _,., ; :=I . - i i - I Iif-!:kk A---w -- 1+ t * 1 14 - .. .. .......... , ,,*-, ,.*,.*,.** * -"L** ****** * * ** * ;- - - - I siq-~ps/pnhiai~asest~ti~H,. .- ,-:-...."1: 41- 1 .. . . ........ t .....";- U I . I --l ..????rlr??? -,-L-- 1 (l~)lrkt rrrt)r~ucl~*lrr)i r~,rtrC;tr 1 ~---:~iL.;l..,Il~ii" ;-' : .. il,~C .iii!llllf IIWI)CIYIIIIIII!IIIII:il.~4jii)**W *** I I r~ lL~~ c.J~I ...... 1.....;...1..~.~...~ .~~...~........ -- ------ --------------- --- ~t"- '-- --- L1- "-:')uurkuwCwro---'--------'--- ---- '-w~ue~ rk rurrJur r •. . ,I ,....*I.. .... -- ,-,i, i .,' ' '= , - i i- i;- - : ." ' - --- --- :- - - - . 1-:- -: .- - "";- :':: :: " . . . . .- 7:.;; :.: . : "1 4----- r l.--" - 1 ;'= I +--MACummer day,d heating.. * °t ",q. " !;,.,.,,,1.,1., i.,l.I.~~ ~ 'l' '- I~ 'I'"~ ~ .,'.',"T'"'""t' "I "I j. .. I1#40 **** * , ~I - -- .I o i11"(., 1KAd,I I.!-,,,,,k,,,,.L.:.,.,IS .i......' l'J ' Iffl,' 1-114,11% k "11#1n,, a, I ,,.11111 I1m lili I iltl iii*ii.i0i i (; I: i0. * . 14".14 0+4 %#0%4,11, 440.,,'Villfulil--f7r '4ol,::,.p.:,.i, 1-..-.-.. - "'.'":-1"" t1.... ...111111111)111111111UtilJi@(@10(i;fi tlGl H1.0 de r eee d" 6 8It i tIJIiillim~li If It: ii+Iorml ace1.4;I ItWfff~t-- 9 l 004449. ...q. ,4 l tw41 4.4i~;iI~I I~i~Ii~Ijl~liiiiI ., I ., h1 . . . ..1E.. U . m, uil Iuil h JiHiAL .iI 175 mj1cent ir o gravity 26% MAClogical Coadtious Low thaderstorms,.u n k :; , lllll!tltS I 'il 1SRun No.-I """6% MACiAircrat 9 149 M32 eOrgal Conditons L owzmnerstors,Altitude0000hgroundrwtnd.I. . .. ...... .i i Tl t ;;11if: f! il i fI lOf j4'' f *n1t fj i~~~~it l , '+ I, ,' "i:i... !iN; l:ll Iinit 1 ILItlq!!li:p l i , 4"1,*1 i'iN-0 it' 4444 4":,t !Y-Y.-"'.'.---'-.'-L--_---- .L _YI i ~- lil_-;- --LL I*tr~rri~~rr~~umwkH~HI1*lcmrI///~;!ii; i!(¢Vq,'I,+iiiiiii:ijllil l !iltllllitiilrl.- go -_w-- ~ - - - -a1 .0 d e g r e e p e r s e c o n d _ _ _ _ -- ---- nt N o .<"^**8, Ai~~~~rna No.. 2 2g pud tdRate o pitch " t rS o. ..... .. .040 43 40 SStimRpg erol1.0 d rre sendNormal accelerationl1git......... .. . .. ... .. .. . .. .. e m a ..... .. ...... ... ...... . a m m- ---- -- .... ... ......... se iI. degree per second Dt e14A..R* _f K1.0 ;lie trte per8secon I., t74 p0i c0te of ravty28%ILLata accelrtciotooonclCniiosIc iaesomtime--- . -*** "4,m1/- -- .. I... .- I ..... ate.e t I .... 1 ... - 19 .... 9Aircotr o gavty 6%MARategra ity Normal cMloration... . ....... ... .... . ........ . ... ...... . .: o * *.. . ... ...... ..... ................... 0.. .... ..... ....I Flght No. 90Run No. 2Date 9 Sept. 1949Aircraft B-25J No. 328Altitude 8000 feetAil cent er ofgravityMeteorological Conditions.4AAALFlight No. 90Run No. 3Date 9 Se 1 9Aircraft B-2 JNo. 328Altitude 8000 feetAirspeed 175 mpArpa center of grity 26% MACMeteorological Conditions Low thunderstorms,high gronad winds......... .. ...!ill l, ' !! t ,,t , '!,,F il, i'ill I ' Ijl1ltl...... .. ,'i 71!! ;:lll~ iIJI i ! * ,'I.4j I ,ih. .L. r i 1 1 i i 1ftts ! i 1 1 ! d 1 M r r 11 1 - & 1-m 6 1 r a 1A i1 a a~W.I i .. m ..P 71illii, li!f,!711f771 i;t 1-- - - --- 4 4,1.0 degrtper second , ..... *-1 irep of pitch5 I30 S404Rateatra1-------- - --u ... .. . . .Ifil.II ccle ation a'1 a o o_ Nornal% . .e p1 c o....J...sf.. ..i. '.. ..... ._,.. .. ... """ ..... ---- -l- .- -- - . "*-u"- ...l,.. ....."p7I IIIorl accelertion".4 I . 'I. 'II,,I, . . .... . . .. .. "I.7 e r; "I- A-----:". _fit(v.-.. low"1.0 degee per secondI IAe o pt ,.?~~4 1.30repe o .- o n .1 .0, s, sn,* ..-.. . ------.-------Normal accelerntim 1 1SI"" Nfl * time""4,'-* -. .4 .'.' -., ,e'roity ..4. r *] *r I1""- -* . .4 --, .....44, 4 ,,;:;I• n~'L I i'".4446 ps oe.og"'"6 .. 0 ......' ?; i i , , t i 'I" I . 7 1. 1 0-T 7 0n:.oight No. 90 r 1mhRun No. 4 Air center o gravity6 ACDate 9 Sept. 1949 Meteorological Condition Low tUmderstorms,Aircraft B-25J No. 328 igh paM windsAltitude 8000 feet . ... .__..._• - - . . ,,". ." ,~, 4 , , -0... 7080 ,' . .. "* *,*0 7.... . -4- -- t. - - --.. .6 111 j.. " Ill Ili Im ..4 444f~' 44' 4,in tiht No.90ir 17 5mph-II--- Run No. 4 At cetragratv yI% .MAC...I& , ., i _S I 14 50 S44 444$~.4444 -4 .4~ ~'4994' 4.44'.4 *~4-44.,444~44' 44~4'444'4'449'4'.' .4 ,,* .44,4I44,4 4.' ~ .4'49~t~ 'V~44', *%,* 9~ 4'.$~4,~ 4 , *4%.4~ 4IPAP ~V.44.,I ~ II......4 1 4 4 4MI 0Date 9 Sept. 1949 Meteorological Conditions Low thaderstorm,Aircraft B-25J No. 328 hIktgh groud vwiadsAltitude 8000 fet.,. : .: '.: : ....z : .......I I fi, . - - - - - - ' . -- - -- - ----- :,4444 4 4 '.4 444. 444 4 4 ~ -4 - - . 'I.,4',,.I ~7UL~I :~I.:.:n:TCYn rrr - UY:~- :.I~..tIi4ii4I/- $Ii ipo"I. -i I I I j I AiIn44,DoLateral acceleratiNormal acceleratij *-0.1 gravity4,1, I'. + I V1.0 2 :i2101.0 degree per second-1 t J J I4,,,f1~1.0 degree per secondRate of pitch1w".." 4- 4- -Is.0 IARat of rol1.0 degree per secodI f~~1 ~ I19.54 ft .4 ' 1; 4_I1ilI ..tK,' .ISIi 1': I- - --- - ------ 1'. . .. . . ., Ir ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ 1 r rj-- rrlrl~ rrtr~ )f ~ -II~ ) ~ t1-~~l- "t'I.*1 I+4, -i+ . _---.- -- J.--+ TWa-Rate of pitchI IRate of roILateral acceleration0.01 gravityNoralacceleration0.1 .T .v.ty'.1~"'*'20.0o -It4. "+,,f44 'IiJu1*f 4 '}4'~I5$J1,iIj.%, 4-. t = iLAi4 1I I 1 13St.... . . ..o..'* 1 . ..3.1.~.~. .... . ... I4 4 4 4 449444. .. i ..........*1*I IJl_=Ii rL~ iA -...-- I,0,*4*' 9....... . .... .... . ...... ..- I - - - - t - I-~-1 -i-~-~-I--.~~'4* 1'1141.1... .'-4~I I I I .i I I * I I -it.esi_ --. - .+..--* *w4l4F lh t N o. 9 O A ir sp eed 17 5 .m ph -- A - - . . . . . ..Run DNo. 4 Air center of gravity 26% MACDate 9 BSept. 1949 Meteorological Conditions Low thunderstorms,".~. T I 'I I L.9," "I '"Aircraft B-2 INo. 328 h igh al w indsltitude 8000mt J-- L - *'T4 4 I~t4' 4J1 ~41A- -I--4I-.A---.5 ... '' 24.02 .M.e.#riti, i, 4--4 +.- .II, Flight No. 90 Atirspeed 175mRun No. 4At 26% MACDate 9 Sept. 1949 Meteorological Cotion Low thunderstorms,Aircraft B-25 J No. 328 high ground windsi .,. °r" , +++ i l "+34I,/..'11fit~I,0U, ,~-r~-s-rl~-ng40.01 gravity•I.. .. .....ILj'9~"! o4 4P._;.. . ,.44,L~I .1 I .I .. I ~..1 _r. -T :--1 --,I-I-, T--I----:7i---11 ? ~11 1~7 - TI~__I T- _I -~_~ ~TI-_~T ~~1 ----i - i i .- :; 1 4 4 itime-*11...ASlog; 4 -- 1 - 1~ --i i i H 1 go- 1 f i - i -- i - +r_1... . cl --- .. L--......L ..--- 1...~ II 1- ,,~,~,,~trwrr t rurt uurtrr rI l l ~L L t l Ill-L4...I -1 ---' --1. .- ' ..~..i.-.. ( .. ...i.I 1 T -i - w~1.. ._.I .I -!.~ -I --- :-! -I - .:l..-~NL tA~--~' ~L~ L-+L-kl L M .-- I -I _ I ) 400 , - . - -1- -- --- -- -- -- - - P. NWL-1 _- - --4_-._ . . ~ .LI I 1 I I I , -rI--- I-- - 4 i i mfliw= -i - i i i i- i i i -LI)hYwht-1"I +#+L .. L tX. . .I. I +1--; I-I .L- -1--- -- ---I I I I I ----I - -__ -+ --i _.-_tl:1.: .. I ~~ . II-~ l-JI--L- lrrLrr~. ~CI -- 311~~/ (I- - I -- v - 1 -- k i i I .I i i I w m -.t , : I+ + J 1 +. ++ I L L~ * _ _ ii-~- -i6 -I:..-- 1 1 1 - 1 1 1 7-lmff c --- -- --- ------- ------- -- -- ---- --T"r _. " ~ i . - -1 . I A A 1" . " .-..or r I' i _I I 1. IIC"~~ 1 ' ~P"-A-~I ..r . ..1.. . ....I I , III :~~1)~ ~I .. 1... .I ~L~.. . I. .L. ...L.. ; .L....1.?~~ lm-----49..i i - i i .. i i-L - I I --r-rrrke*P4w. *1*L-. .o - t"-I"I-M-14--,OfS ' lb',, '.k'+,,P, i!1 .I .II 'Li(t~'".....I,...4,IXJ,"o .1'.11 ,. :,~~~,.i..... -l . , I: '":~11 i I -I 1 ~~"I I*~~ I-I,, 1~'s@r"l,,,..W 111 4~3~~1,~ ' Ir ', ,,tc- ~'11'1,1;,.11"" ' 1r of gravity 26% MACQnditons Low thunderhigh groaaccelerationNormal acceleration8000 feet)A.IA175 mphter of gravityil ConditionsF',J4$I,ofRateatpitch I,1. 14 I 4I** ' % *.1.w"ft t .. *OIit finus1.0 degree peroee 1I-'*44 4,.a tcelerato00g ravity ~ .. *.*4 , , * ,r.......... . ._-A '. .~. ~ i ..4~ ,i 4 .j..' 4 4 . 44 4Normal aceleratio0.01gravityRa e.' it h*''4.* t 4.., ..1.0degree per secaviF. .. . ...at.. ..itch.....* . .. -.. .............. ..0.01 ravit lit'tit acleatoi 0 0 rv,,L4*.... ...................i . .. Y S.. f 2 2 .0- 2 0 .-**** *- **5 ""'" " " "1.0 * *g e* per secondRate ofpricli1 001-t 114''446,1-s 004.1-i IALate ral accelerationk till%. - - - - - - - - - -- - - - - #- - - - - --0% ----- -0. 1 gravity ,4.4 ... 1 '. t444..4...9. ....4.........r L..... -4.... ...........i. .. ..... ... ..... I.Run No. 5Date 9SeAo. Arplane center of jgravity 26% MACAircraft B-2 No. 328 Meteorological Conditions Low thunderstorms,Altitude 8000 feet h groundwinds...".... . . . . . ------- -- ---.. . ---.. . . --. -. ----.-, - - --- .,,---- .. ..--- - -- '..4.1..--L- A .-- 44- ---,O. ' .. ..444 ', 4 ,,Fllght No. 90 ,,S * 1RanNo. 5 . . --- - 4e-,.Date 9 S n -. 1949S . Aircraft B-No. 328Altitude 8000 feetAirspe 175 mphAirpan center of Kravty 26% MACMeteorological Condition Low thunderstorms., ''444 '. l.,d , , I4 4,,4 ,,,+ . :: I4 , . I I• - '-,lhig ground"NondV 1.021i-.... o.5 .- - . -Nte ~**9 et. 14. . .... .... ........ ........ .. ....... . . ...... ....... .. ..... s. ... ,..... .. - -.... .... ..... -...... .. .. .. . ... .. .._ _ _ _ _ _ _ _ _ . iI ......I - -I . .I.- - . .. .-S1.0 degree per seconda. c Rith4,* ,1 L O 3 31timeert oRate of roll*11. 0 doese per second 4-4---k 4 k-o.o srantyL.L4-0.1 rityI:.4 .. ),, lolltJ44, :'t.~10degree per secondf., , ***Rte ofpiHchLLJ- r 4...,. , , ! .44I!.4~4 ~ 4 44 44 4W44.:3 3441.0 degree per sec on...f.d Rateof roll0.01 ravity Lateral accelerationeA I.. . , ., . . . ." i, .. ._ ,, " i.. ....-0.1 ravitK .................No acceleration....... KF........ ......... .. . ..... ... ......... ... .. ....time II 1. 'ft.. C ,I "~9~4,P, ' "4 4" "o,!.I --.- - ..... Ii....... -... .. "4.1>0I ~, ,34 'SftIh.l . .. ...4.0 45 4Z0. 4 ... - ..... . . . i i iI 1 ~ , 1 l ! t, 1t I I , .', - : 1t I ,i i I, . . ; i ' / . .. "..'~E---~""z~i~~.u..I.[::;..:.j..::..::.,*- . . . . ---'0II4W...., .,- -. I I -1 , I . .-- -" I.Flight No. 90 Airspeed 175mphRun No. 5 Airplane center of gravity 26% MACI Date 9 Se. 1949 Meteorological Conditions Low thunderstorms,Aircraft B-25J No. 328 ,. hi graa windsAltitude 8000 feet ,. I ,.*.1 "4-,." .I t I-_- - - . . ....LOI I~~ . .. ...... I 15 I ' '.1 1Lateral accelerationNormal colerstiom....... .,Flight No. 90 Airspeed 175 mphRun No. 5 Airplane center of gravity 26% MACDate 9 Sept. 1949 Meteorological Conditions Low thunderstorms,Aircraft B-25 No. 328 . high ground windsAltitude 8000 feetI ***J - * ...- .4 1 1 - -"-4-1 -4- - 1 --:- ' rrJ uu- - -- 1' --- -- 1 i i - -- L-- - '- --- Y ~-L~_ ___li-I--~-~ I ~----~- _ ~---L_-_--_~-.~ --I~ - --I ._Y 1 - 1 lwwIcuqw"....~,..1.,~....~.........l,,,,n..L.r~Hc -'-- ---'-- -----'- -- --' ------ ---' ..n"-"l".'-.......'-....~-1 ...... I. ...Le..l.~T~;i ~Y I 1 4 -"a.-4 .1 -m - 1 m a & i , f -i ,, m I .m i , , m 1 q 6 0 .1 1 1, 1 1 !1 0 - i - I - -"r 111 ! , I I - i 1 1 ! -1 !-! 4_ -----4- -- 1 --- -1 1 - -.11 r ! Ilm nip- 14 0 fl o q t1,-- - 'rrrr ~rrri :~ ~ U ~ LIII ~~~~ t) C ) C C Lj ) L ij _-11-1 +Fab " - : -: ; - :::::::: -" = A::: ::::: 4 -::: .-- ;:::::::: :::::- :;-- 1 .. 1 f j+r q lj I -! i '; I o 1 L Y- mm..--U + #b 'Plo+ i -. 4~-ir'r-' ---L~ ---- I ~ C- IUI~-Cuuru)rrruyrrrtr ~~rr ~rru(rUrrtr)m i im - a 1 4 6tpw66- lft 4- 4 mi.... -I. CL. _I-~l--- - oip f____n I - 11 f---Laft Al~ ;._*I,th*. l" -"i i:ili!,i i~-....C ~ c.J:i:r ,Fill., -Z Ilv ~:1~) :11 wl:i~r' II'""i ;14,,.~"il~.... .t"'~S,.- -~CZCI1# ..1-mos , I eI. 1 .11'iO..... ..... ....- 1.0 degree per secondS .... . Rate of pitchi "'*n4.5- .o aegree per s.0.1 gravity..,...1 4ecoI -IRate of rollin!Lateralacceleration.% %Normal acceleration- 0.1 gravity... . ... ...~i K j ".41I.11. ..........46o 44time ---. 4.4I I~ ~i5.44...1 .i:*..-r-4,-' -- -~ "- ' --' ---' ---' '' -L.: -- _ CII )~ -)- --- ~ll*- { I. .. .4! I1. r" ";!'i ' : i .. . " !.. I ... I... .... .!....... *. . . . . ....., ' .... ....1,----- - -L ii' -~- --' - L-~- -~ ' --r-i--- -~.; -- .~L~,,~- - r -- ~ rr -ru l r~- c*- rrl~ ~-.i.-,r+~~ - -u C ,--C +r J-- --'--- --r~-r ~-r -- Cr ~ - ~ CI rn + ~rr . -~r+ -~ -~ -)---r - r r * ,- 1 _ ~_~. r--4 i -i i i +~'----4., ... ." t. .~1...i i.....ItN...ht No.No.ecrafttude.490 . ......5 Airspeed 175 mph9 Sept. 1949 Airplane center of gravity 26% MACB-29 No. 328 Meteorological Conditions Low thuderstorms,8000 feet bh ground winds*~.*. ..:.FligRunDateAircAlti. ..I 4-i0*'((lii'.1.5i ]4 1Iii Ij))5D as.'..S. . ......--I''5.& fb i i i i i 1 - -,I no 4----- L~ .i i 1 - 4' 1 i . i -04114 ., !- i - 1 -6-i.. U _ ._--- L-11 -"1 .-- 6 - I .I .t.. L ---' ''~-- ;"" ~~--'-'Y~~~"-' ~------ -- IIIIWUUI-' 'i.. i I ; - -- 4' --- 4, -, -, , :4 -v i - i i a, i i --- -- 1 - , , '401,024to I - I !.I[. ~-- - . --. ....I r. -- -- - -I--------- -1.*-rr , ~r ur(-L -.. I.-A.-I -- -1"7 t~,, ~,U. ~JI~4~CI i,~JlrryJ*ukl~. :~ ;l ,: ~d v:.:_ _ _ _T~~:h to.~ Da"64pt 1it ..... Ai,0ra1 t- 5 o. lilt~~~~ "' II lttme ) fe'E " -- ---4 -944~ ------ ------ww . . w. ..--- ------l~iepopeso.,u loII4 ~ ~ ~ ~ ~ ~ ~ .. .44 .... 4 .. , 4. ....0.1t"*a..... . ....... ........... . . . . . ......... . . .. . . ..... ... ....... ....... ... ........... .......1w .7 '.. . I . . I. I4 ";I. I. ..~~ I.4 .. , a .1loll$*~~i~iA A Ipit ,, Aicrt u-j o.iab71ie'* 44 44.Hl I4~ . I Is4~ ~ . ...... 4.. 4 .... "41 0 * o pe eeoI ,, ,* "... 1.',IT - ----- --- -A o -o~ -'~4 --,.. -- . 4. . . - .- .44. 4 . 4 . ...... - 4.'-44. . -II p... ... '4... . 4... .. .. 4.4 440.01 gml0.1 ...... . ..... ....... ..... ... .14444 4. ... . . ... .. . ... . .... ........ . .......... .... ..... .......... .. ... ....... ............... .......... ...... ............... ......... .. .... ........W ill4~4 ~Normalaccolratia'Norml acceleratio.7N]. .,l,,,i..........7 ,(. . 1i 1iIII,* *, H"-~ ~ -. w4.4 ~S Flight No. 90- Run No. 6Date $Sept. 1949Aircraft B-25 No. 38Altitude 8000 fe 2, iMeteorological Co diAtrp of IvIt1,9,1119?Low tUndest=ms,high groed wtains.Flight No. 90ReaNo. SDate 9 p 1949Aircraft B--J No. 325Altitude 000 ft*~Cm ~c.terravty 20% MAC...i' q, Metorooical Comittlres Low timada'soi 'M II IT' ' ",*.,,10 1 ii fI, I IJ .. I *~ .. *Its *J j ...tI .*..11~iIIIILffiL.* 'i imiiVA41;.~U1 rc rH Wl~c~~ ki~rHl~(k~ ( U(~LIIHI9 ~^ . LIIYII- l.llr-~! a 1o.,, ;lil,,[i, :II ;' I" "".. .... .....0 degree per Aecod'ft ijNio. 328Rt of pit 0, t!tfeAi center of gravity 26% MACMeteorological Couditoms Low thnderstorms,it1.0 degree per 1eco1 Oiritiue ooa0.r1 17 pt 1, pitch -ct0.t gravity , .!"fl------- . -- -lo-ft -- -Nom tiaclet toIi I 4l111 t I tI*I I.. ",,0 .lrv t Rate of b' if ll -coyIfIto1J li I Z:;, Yoi I,lip0.1 11it fit, itI f of4,. A- :t, -fW. - -fill- -p 9it10"16.. Otto4 II 44 to 'lPul fill.-Flight No. 90Ulii 7 Aircraft B 1J No. 328 Meteorological Conditions Low thwierstorms,teof pitch .:7 hl- ......It f 1 1* -l .s * .. . .** r - - - - ........... -* ___..0 rvtLtraaceetion y .li K......* ...***.* .0.2.5...0 time I I **.o ..---. .1W *- - -' - 4.,*1:1 nLateNrmal CCelerati a0.1 if lf.ii~~liiii~i. .1:i j... ........ -- i - -1Iii!ii -i -:iii -, -i - - -~s FlgtN . 9 A r1I9ift o 'o fAoC-- 1.0 does per second ;Dt t14 eerlgclCssd a o ladrtr:'iI ii I ; : ii rr ii !Iii'I'ilit I i I*!( Iifl U/4.,:-er 44 -i49 -- A itu 80i <.. *: 1' .: ,; k I .! ,1 1 1!-1 iii l;~ !l ri~li! tm --- Tlij 1'1 ~ l li' UI: 1 4~:Ii ii0.01 .1i, J,- - . i .. ur it ,;i~iiiili i~i :!jjj/ ilt !r ii i lii II) I i !I if! Ir I' * R a t o f p it c ji 5 * *1 *0 ijj "' 0 ** * " " " ******* i 'i*r es **4 ***I i i/I : I :Iovy ,111 Ity ,, I ii I :: il t :~i~ iI i ~l; t ! !: time - - 9,AAA_ ..________... _ I .- --- - ---- -- . . - -Jill, Ilk I J160**Normal accelerNM- 0.1 rv ty A,..on cose*-IOf.9 02."k I t'sol-l -- I1.0 degree per second Rate of r oiT -. ra l c ! i ! i i11 i il % :1 l0 . I VMIF'- . 4 .. .. .... . ...... ..... ....4 . .... ......4 4.4. .4 .4 . .....94 ... ....... ....... 944 . 4 . . . ........ . . ........ ... ... ... . ..... .. 4 .4 .... . * M . 14. 4... 4'r l . I Iiir !ii iiiI i /'jlji llijII I I .ii Iiit III:I, . - I " I I . I I . , 1 1 " I I I . . I I I I , . I . I I I . I I "I 1 . I I I I . 11 I . .. - I . 1, I I I - .1 I I I I . I I I I I I I II . I . I 1 . I I I I . 1, t I I I I I I I . . I I-- -_ . - - - &_ _M! ! v M M v0 o 1 1 i I i - !111 ""!'"I" to-- . .06.6w *--.-"""* -- -- A - --- . 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I I I I if j I i , ( f I :' i , !:; , .. , " i .1 .11 i I ;!i; t I 11 iltj ;j ! , ti : i , I : ; I '! it ' [ 1li0 i: . , : ;I:i 1 i i , i O."It"O, 0 , ij' I , i::i.1 . 11_ ,,,! , ,1 111 t if , I : .: ; ,- ij , C '' , ... , ; .t itI , L I 'I, .. ,i , !;ill; 9 :1 i !, I i ! ; I , I ; :,,- . , "i ,: I .I I I ,, ,, l ; .I I I 1 9 , , , t,I, J i I : , I: i I . L I , I , i I t 9 '' I I I i r I . I , .,! , , I , -t; I I, ,I . I . I I 1 , :! ; 1i I , I I ;, 'I I t I It; I Iit"I.0 degres ; r no I I . j it I .. I I i i 9 I I 1: I i f , I tt, - , I , I I I , 1, L , , i - ; I t i L .1 _ ' 9 1 1 . , 1,, 1, . , I . I , , , , . ' t , i IItate of roll ' ' i I 'i it , , , t '.1, I ; :I;I A ; I , , I I 4 r : . . .: " " 1,i.,NliI I i A ,I, ;i-_2 - . . -. - - -I-,' I . A - i , I . . . - . ... .-- -4.-- -, _1!11__ . - -. ; ,1, , I ; '. , ;i_ iik"I!iil , , F - !!I , I N 11 -- '* I I _ti W , " , L , I . - t . - .-1 I ,: I I , .-- 11- i - , L 1- I . il---- 1w, -9 ----- ;ii . - 91 "I : , I ; 9 - - 1- _- 91 - -- - - I - I . 9 - T- I 1-- - _ --- 11 - _ _ - -- I .IiI 1:ti Ill ,;. . I llf;'' T -- - : T --- 71, t , , I '"T :-#-+4 -. , - -- - , , , . 9" 9 . I; .. , , : 1 . 9 ., I :." 1. . ) " " I!! ; rii !l 0 , - , i ! , " I , , , , , i!; 1 9 ,;; , 1 1 1 . " 'i !d fll, ;iiji i . I I 1 , 1 4 th ii ,I I I , I . , ; I1! I 1 9 t ;il; .i 1 , 1 I II . , , I , t , - I , I 1, I i!iili 91 , ' I " I"Itilwit , , ;) I) I: :,! .i lll , : y j " .1 I " 1 i I I I I . Ill 10 '41i"N' I I , I Iflidl k r I * ;, I , , I -.,;, I , I iijil 1 044 , 11 1 " 1: ' , i t I I j!'! , 1 , I I'll ,-, I~ r , I I , 'l'. ..w I i , , e-o"o 7, i ! I I iI it , t, I j , i , 1, , I , , - ili.7TMot. .908 i__17- mph,FitNo. 09 A s1.0 degree per secondft8 . ...No. -lane center of gravity 26% MAC '.0 degree per snwIC1 e i iidIDtit t 9 Sep. 1 Meteorological Codutions Low thunderstrms,0.01f IgravI Rm N. 199 tceteaofgrvitc2%eMCeAircraft B No.N328 wdI die reeierAltitedeoe a oetit1t 7, ° if .!0dill ~j~1'i~ *I I IRate of z.totoa -pt to TtoooIt$1.0 degree per cond Rist o! rol 1.0 degree per second![~~ it ...01 rat.LaIteeral accele1t cce0. 1 P 111! liit. .. .1 1iN I ; II j I i I IcIIii HPilli 11.01 gravity Normal accelerat.Y' •4 o? ,a I-'°'lk , ,y,, ',. ..!: ' : .' 'iW F ;......... . , ..... . ... .... . ' . iFt:' I Hi! !lLi ,4 11411. ..... . .A tl , ! t i t* " ....... .4f10.1 g aviy' ; ! tIlI..i....... .........I9ITI f I...;4a44.O9.9r .9449l4 4 o ~ 49 1. i . 4. 4 14 ?'4 r ' . :: ;. ::.-. . . . .. . .. 9..6 ,......1 .: . . 4. 9 . . 9.............. . . .. 9 I- -t ; : 9L 99999999999 9.....1 ."." *' *""l , ' f '' i!l!iu ][~ i ll 4- rtil .,' tc * : ,* : ..... Ip; xitRab oS49449 p474 949444444y44 9~9. WI - 4449. J No. - -9~~~gtN . 0!Ti--Rn No. 9IDate sep 1949Aircraft B-5 No .328AIlblde 900,eAirspeed 175 mphAtrplanecenter of gravity 26% MACMeteorological Conditions Low thunderstorms,-riQ#T447-4-9 - --9- -,T w nds11li '1"OlilIflyt,4 y w U s ! I 1: 99 Jtime ----'ration'01 " i I i1 H u . 0 Ac e n a g r i t , O A• INIsipii9! 411I I I*.. .. .. '''1 9l 1..... ...... ... .. f- ,I 1-9-.--99. Flight No. 0 ts~ 7Run O. 9Alph center Of gravity 26% MACDate 95S. 1949 Meteoologica Conditin Low thunderstorms,Aircraft B-251No. 38 ihgowwnIsL. ~ ~ ~ :.Al. am feetf Ii~ 99IseIII7T 1o l f 1 ITT!;L 1W' .9 9 ......... 9..........999.....-.9.9.999......99999999..- = . ..- .- -,,• .. .-. .----1.0 degrepersmda e . ,,,.. ._ . - . , , _ -.-. .. . ..-.-.-.-.-....-. -...or 1''*l. . • , .0 * 1,4~ ., ., .5 ID I, , 1Ume -a1.0 , e p. " u " . .. . . .. .... .... " "... . .. ... .. . .. .. ..... -*.*.... " . ....,t-#0.01 gravity latral acelrai*.j* .g Ag W ,s a 14 J5k pA I ........ '." ... • . . . .. * €'" '. " / _: .. . . :: . : :. . . . . _I __.. . . Z ," , - , :.. , "!_ . ..... :. .,......... .. _..T r .i _ _ r ,. ' ! " - -:.i i / ' - .. . .. .. ... .. . - .." -' - ; -. ... . . : : - " . ... .. . . .f. iI .<1" .i 1S. - , .... ........... - -. ....................." .. .... .. .-... .. . .............. . . .: i: ...... ?-:- 'i..... ... , : ; ': .. : . .... ': ;iI ; 1, : ' - i ; l: ; i . .: i " i.. ;' ' '.Flight No. " Airspeed 175 mphRun No. 9 A. . i center of gravity 26% MACDate. 9 Set. 1949 Meteorological Conditions Low thunderstorms,Aircraft B-2 J No. 3286 high pground windsAltitude 8000feet- !5.0 .#I,..".Ito.... IA C 15 14k....U,... , .., .*1 .. 'I." " ' ... " ... .. , . .i...- --- Jp . * .- 'i .. . I'.. --- ---------.I I I1.0 degree per secondof1 pith....*.f*f1 I 1Ip sRat, 1 i I I I r IIK .*.K..*..-0 -'.. . ...... ....S".-- -1±.01 t ,Normalwm acceleistlo.0.1 gravity~. :... . . .......... 4. . .r .:, -.... 4 . . ..* . .. ~. *.. * -I i,"1 . .. "..: I .:: I; I * I, < i I .. . II,.- ,#,, * .1........,.... . ....=.. .11I iI I. .I I~: ...I,., aMight No. to.. Run No. 9Date 9 8e-1949Aircraft B-{5 No. 328IAltituwe 8000Airsped 175 aphlAt center of gravity 12 %MAC'Meteorological Conditions Low th understorms,-rondl wida. .............. ............... 1.................... . II. II IiI .-- ,-0.1 gravitygJY'UIf ~I~=!I.FI :>>4.i,i-;,-.i.i. .lararllaterl"4 ..1P--- ~, ....:I214L 1 -1--- - -------------.W,, ! ,:. OLrI7 rr1I-Y ~ -~ ~II-1-L--- :Llt . .-." "'II i IILiJ..4 3.44.4- t?3w;?z4 ....... i :f4 4 .-44. 4*63 .......... u .... .......-. ... .- .... .., . ..... ..............-.. -. - - . :.. . --10degree per secondt * 7777777777*1Rate fptpic .3.. ,! i! ~ i~ i* *, P 4- ' 4, ,,.*3.44 i..*.,* i!iiii ! il ii il .. .. I . ,'r. v•y"9 ,I 2 7 . ,.," '" ..time1.0 degree per: seco I . ,...*Il, :,., 2.0 2.5 0 25 ... + ... . +......' ". ... ... .t .. ... ' " . . .? ..II"..01, 034 " ,......I•.Norma acoloration0.1 rv ity 010f.o.3...4 . . ... .4..4 ... ... 4.4. . ...44 . .......4.p34 . .. ..... ............. .. .... .... ........ ..... ..... ....... ....... ..... ..... .4 ~ 3- - -" -> - ---1 0 degree per second3Rat of 0t h.** - ......... . r- " -" i ' Z L ] . . .. .:/ , ,,L,in 63 BI3 LO 034 k 34 L5 0st1 e oo r3i.odegreper secondl Raeof roli443 44, . . . . . .. ;':':'.....4.4.4.4.3.4.4.4...... , ".. .ILateral aweeat"ok0,0137 13(,4434 33 ..... ~...4...4... j 1 3 4~~j3.4toNormal ac~.1i**; 1celeration .r* . . . .:,:*** , * - *3 = 3 4 * * : * * 4P'r*. . 4" .... ... . . .- -- -nilght No. 90--~unNo. 9Date 9 Sept. 1949Aircraft B-25J No. 328Altitude 8000 feetAirspeed 175 mphAirplane center of gravity 26% MAC' .1 .',, ,* ,Meteorological Conditions Low thu Irstorms,highgro undwindsI "It'll ! *,344*3 *3434*44444 444 4. 0D , 3.5 313.04&0.L O-. n -1..-I I I''ij, ..- .. . ..... ..... . --. .... . .. 1(i~ :::::...... t;- .; . ; . ;; .;;;;;; •. .).6....... ... l *, 'Flight Nol 903334R3no3 * u19Nol.S-3 . .A rsee 175 nSi) 1949. ; Aircraft B-2 No. 328Altitude 9000 feetMr" 175 mphAirplane center of gravity 26% MAC.I, Meteordogical ConditloUs Low thuinderstorms,4.high groud winds.. . . .. . .. . ... .... .... ioim+ ,l fill+. .. 0 3 3 4-= nh 44..... . .. .: ... .. + ......4 3 1.- ii-tiih • ~,,,4, . . I ii?34 i 443 ' 1j;4 43' ~ 4 '443 * 4 4 I I I4 I 11 ' 1 33I I.4 14 4 3 4 4 4 4 3 -4 3 I 44 3 4 4 4 ~ :.....444*34*44,44 4 ~ I I''1...~.. .,....44................ 3.... 4.1 1 I3 1 4 4.14V 4 4 1 .1. L.,434-~l vI.......... +(,34 . . ...-0.1 gravity-..-.... ...:. 1.0&-p sec-nd ... -.------------------- ----.---I.,I . Iii!.;'.,i i e !'I20 40,45!10Rat of rollIhI II0 aatervil acc leraton - t,. . .. .9 9 '4 j . 1 1 ,? . j ' ' '.4, '9 . 1 9 9Normal rceleratlai ,,0.1 I vty oV 77..' .....I ' ..-. , , 'age- - -ag-mm- ..- .m-s - =- .-.-.. -- - =- =: =a 5 5 =-1.0 degree per second ,,,rSItitt-1.0 degree per sco. Rate of roflloooo ......... i , , I .I,...I I0.01 gravity Lateral acleratlo-NI-Nor0r rmal accel eration ..0.1 gravity ....- 9~...{.94 ~ -~ ~ ~ T.......... .H K-Flig-t NO.,,, RU-No. 10Date Sept. 1949Aircraft B-25J No. 328Altitde 8000 feetAtir=peed'175 mph;AIr u center of gravty 26% MAC.Meteorologal ConiUona Low thunderstorms,15{l1 0" -65.ft." ,Ii III.jI,,I *l '' ili!# '............ Ilk-y, "I'---- -it No. 90NO. 10 Airpee 17.mpo 1 0 Arpanecenter of gravity 2% MACaft B N o. 328 1 Meteorological Conditions Low thunderstorms,ode 8 00 feet h F W din-" 1 0 5 44,: * . * ... ... . I TI ,1 41,- .-----.--........... R u t n No. 10 Airs 175 mpS.0......s c ",Date 9Sept 1949 2% I ,AC' Ai rcraf t B-25>J No. 328 Meteorological Conditions Low thundetratorms,itl! :[~ l~ lllll 1m;1!~~l ll~ li~ i' ....... P ... 11; ' I: :- I: r, , : "11 :: 11 11: .... [. : : I.:;. ,, i It - I --- --- -- - -- -a srat .. so ea *v '"" " w + " '* 5..... ' . ..** ^ j.. rv s.,..ttItree 800 :eth rotioL l accelht i Io~g tr' II I lit I' i I ...... 0L I.0;I 2 ,, :Tillllltli ............... 515 , 555 isht No. So:lit tIt' i~IIt.1t cce er 1) 1 0l c ler i I... t It t....... 44 -------- 4. .... tU . ... t,,. --- -- ;-- - - -- - - -- --- .: *::.:+;, - --- ...... .... - - "' " "..... -- - -.441 .. . MU ... .. .jj~ 4 0 A ljba 4 I] : ++' +,l+ +;*++ + + , ,; /a lP It I i i; ... iI 4I j"t+ 11 1 4, 1 1Frt it it ft fit 2. .ltt if.ii I I +t ii, ~.. . . 444i+ iii ii i ; i ...... ': 4 4 2 :;; ..... I+lit to v .. .114I1 *l4s, ...... . .I i,~ ;j~ bl~ I liJI 11, urn. 14,,°444" ". I'"'l igrav +ity iIt+tL+ ; 14l I'..... ,.L,......., ;tf 1t.I I iitl lil 1 + It d'*1 'I '4'4 i41]+*4*~ 4~4g4t ,. ,jo 4," '... .. .. .. :::!J .- ~ l tl~tM 'l,+ ;..;] 2 :C ;q..... : +: r'*~~~~~ ~~~i f :; i ++' ,+ li ++ ++++ .. ++ +++itIt,. .. +~ l t . .; , ! {-0++ devm per'sm 0~n:01lT~ ...... "tol.~P~i~ l++++1:?w! ititt~II ~ lII'~ l : ;i+++++ !+ Itiii~c C rati"a+,~~i It'illll--- ... .. ----- .... .... ". .!j 1.0 degree per secondRate of pitchree per secondI 0 l , Itil clrolbi. Iii lilt. 1!24 timetteof rollL lc,Lateral accelergtioa*I I/ I I.4, O 4 l:,44,4 ," 44 44 44 43'O-- -..-..]pt 4 4 '44P.' 41411. 4 4444TjI~......... " . ......... . ... ......... ...• " ' ' " I "L' t... r.. .I.F ........ . - .- 1 11 1- 1 - -!,-! - !4 !-- -i . i I. .. .... .... . ......... ...... 4.. . ........ ...I II.. I.... . . .i IJ~rr~rrmJrr --- -- -- ' ---L-------J----W( w ~) ~ ~ ~~ ~Y---- -- II -.. .. .... .. ...... . . ...... . ....... .. .... ........... . .............. . ......... ... .. .. .........2 ........... .... ..... . .. . .... ......... ... . .. ........ ......... .. . ... .......... ... ... .... I ,:2:. . 4:IIII '::::::[:::::r:::.. ....... .'1'II- *444,4 4144I;- :~~il-~I .. 1 1.... I .____ ____1.. il.l il l 4 ...L44-4444~optchLO :i:,,....1.0 perseco Rateof roll0.01 gravity teral acceleration-** , .Z , ,, ,, .0.1 gravity C!Y: ,Normal acceleration1 -iSI II,:#t300 .4414.... .4---; ........... ...............................3' 0..... ... . .... -............. .. .. ..... ....I '1 '1, I 1 .j44 ..j4.4[44 (~&4V4j.4 .~i 4.4 j4.... 4l '*i1..1, 4L.... ,..,L 111 ii II444''AS...%,.3!'iI, . , 4 444ii '4 -4. j, .4I I'.1 ..; ..I "v..II I, i..flFit& No.,go o e iRun No. 10 Airs 175 mphDate 9 Sept. 149 Airplane centor of gravity 26% MACAircraft B-25J No. 328 Meteorologtcal Conditiona Low thal0entorm,Al tie .8000 feethigh nd wdsT T '' 1 1 T 1 T 1 Y ---- ~ r-----r--.---- ~r- ~ -~~~.----- -- ~--~~~~-------* ----4t944L22KL.L12~iI"'F4 4 4 4 14*.,44 4' :I4 ',.L 4 4 J [ ! L.... -..... *... ,..1...1.L1 .O.1. I-l.0de~F44 K-0.1 gravityVpI

The isallobaric wind

Abstract

Extracted data

The isallobaric wind

Abstract

Extracted data

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