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Multifunction Sensor Technique
Report Number: AFFDL TR 65-4
Author(s): Roland Pittman
Corporate Author: National Water Lift Company
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 6/1/1965
Pages: 70
Contract: AF 33(616)-1200
Project: 8222
Task: 822209
AD Number: AD0469205
Photo Enhancement: Complete
Abstract Text:
The applied research study, as described herein, relates to an investigation into the feasibility of a technique for sensing, simultaneously in two axes, angular velocity and linear acceleration in a transducer with one moving part. Techniques for instrumenting inertial interactions in a rotating frame were employed, utilizing piezoelectric electrostrictive devices for instrumentation, and fluid bodies for the inertial reaction member and proof mass. The technique was reduced to practice, resulting in a subminiature, fully integrated, compact, functional prototype wherein both types of outputs were provided in each of two orthogonal sensing axes. An integrated prototype was evaluated for all major performance parameters and operational characteristics. The results have revealed a transducer technique capable of angular velocity sensing thresholds of 1 degree/hr. and linear acceleration sensing thresholds of .0001, with dynamic ranges in each of the two quantities in excess of one million to one. Also demonstrated, within the study, was the potential for high reliability redundant sensing techniques and further size and power consumption reduction while maintaining the extreme sensing thresholds.
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Human Pilot Dynamics in Compensatory Systems: Theory, Models, and Experiments with Controlled Element and Forcing Function Variations
Report Number: AFFDL TR 65-15
Author(s): Duan McRuer; Dunstan Graham; Ezra Krendel; William Reisener, Jr.
Corporate Author: Systems Technology, Inc.; The Franklin Institute
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 7/1/1965
Pages: 216
Contract: AF 33(616)-7501
Project: 8219
Task: 821905
AD Number: AD0470337
Photo Enhancement: Complete
Abstract Text:
The description of human pilot dynamic characteristics in mathematical terms compatible with flight control engineering practice is an essential prerequisite to the analytical treatment of manual vehicular control systems. The enormously adaptive nature of the human pilot makes such a description exceedingly difficult to obtain, although a quasi-linear model with parameters which vary with the system task variables had been successfully applied to many flight situations. The primary purposes of the experimental series reported are the validation of the existing quasi-linear pilot model, and the extension of this model in accuracy and detail.
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Dynamics of Shell-Like Lifting Bodies: Part I. The Analytical Investigation
Report Number: AFFDL TR 65-17 Part 1
Author(s): F. C. Hung
Corporate Author: North American Aviation, Incorporated
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 6/1/1965
Pages: 236
Contract: AF 33(657)-11115
Project: 1370
Task: 137003
AD Number: AD0621146
Photo Enhancement: Not Needed
Abstract Text:
The vibration characteristics of typical shell-like lifting bodies, consisting of an outer skin covering and stiffened with both longitudinal stringers and transverse parallel flexible frames, were investigated using an approach based upon the matrix force method. Following an extensive literature survey, matrix equations were developed for structural flexibility characteristics of a stiffened shell with free-fixed boundary conditions and the equations of motion for free vibration were solved to determine natural frequencies and mode shapes. Equations of motion of a general stiffened shell configuration with free-free boundary conditions were developed and applied to the special case of a stiffened shell with a rigid root frame. A mode modifying matrix was determined which allows solution of the equations using structural flexibility parameters established for the shell with free-fixed boundary conditions. Analytical results for the case with free-fixed boundary conditions are compared with results obtained from an experimental investigation performed upon nine typical configurations and conclusions and recommendations are presented.
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An Evaluation of Procedures for Calculating Aerodynamic Loads
Report Number: AFFDL TR 65-18
Author(s): Leon H. Schindel
Corporate Author: Massachusetts institute of Technology
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 5/1/1965
Pages: 312
Contract: AF 33(615)-1199
Project: 1367
Task: 136715
AD Number: AD0465433
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Abstract Text:
Existing theories are examined with the object of selecting the best methods for computing aerodynamic lift distributions for use in structural design. Subsonic, transonic and supersonic Mach numbers are included. Configurations consist of wing-body combinations such as might be employed for airplane-type vehicles. The present investigation is limited to the linear range of angle of attack. The simplest theories which give accuracy consistent with structural design practice are reduced to computational procedure; the accuracy of a theory having been established by comparison with existing experimental data. In cases where no adequate theory is available or experimental data is lacking, further research is recommended. Future extensions to nonlinear regimes, more general configurations, and higher Mach numbers are also described.
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A Study of Time-Optimal Rendezvous in Three Dimensions, Volume I
Report Number: AFFDL TR 65-20 Volume 1
Author(s): B. H. Paiewonsky and P. J. Woodrow
Corporate Author: Aeronautical Research Associates of Princeton, Inc.
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 1/1/1965
Pages: 77
Contract: AF 33(657)-11319
Project: 8219
Task: 821904
AD Number: AD0624218
Photo Enhancement: Not Needed
Notes: Original has pages 31-46 missing
Abstract Text:
The results of a study of time optimal rendezvous in three dimensions with bounds on the rocket thrust and the available propellant are described. The equations of motion are linearized and Neustadt's method is used to solve the two-point boundary value problem in the seven-dimensional state space. Three convergence acceleration schemes are studied. Examples of terminal rendezvous paths are presented and discussed in terms of the magnitudes of the bounds on thrust and fuel. The dependence of terminal errors on initial measurement errors in position and velocity is also discussed. The range of initial values include position errors up to 25 miles and relative velocity errors of 200 ft/sec. The thrust accelerations of the rockets are on the order of 1 ft/sec-sq; the propellant bounds (ideal characteristic velocities) range between 600 ft/sec and 250 ft/sec.
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Development of High Temperature Flutter Transducer
Report Number: AFFDL TR 65-21
Author(s): David L. Day
Corporate Author: Allegany Instrument Company
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 3/1/1965
Pages: 99
Features: + Foldout(s)
Contract: AF 33(615-1793
Project: 1469
Task: 146907
AD Number: AD0465262
Photo Enhancement: Complete
Abstract Text:
The design, development, and testing of two hightemperature transducers are described. One measures vibration amplitude and frequency, and the other measures acceleration. Both were designed to detect aerodynamic panel flutter during boost and re-entry of the X-20 Dynasoar, then under development. These transducers are electrical resistance strain gage types. Part details discussed are the pendulum, damper, sealing, and case configuration. Both transducers are also discussed in greater detail with respect to natural frequency, damping, strain gage application, and output.
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Investigation Of Propellant Actuated Devices For Use In Emergency Crew Escape Systems For Advanced Aerospace Vehicles. Phase III. Design Study.
Report Number: AFFDL TR 65-26 Part 2
Author(s): Bleikamp, R. H.; Lake, E. R.; McGovern, D. R.
Corporate Author: McDonnell Aircraft Corp St Louis MO
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 4/1/1965
Pages: 194
Features: + Foldout(s)
Contract: AF 33(615)-1292
Project: 1362
Task: 136205
AD Number: AD0464738
Photo Enhancement: Complete
Abstract Text:
This report describes the results of the third and final phase of a study related to the design of PAD (Propellant Actuated Devices) for use in a separable crew escape module applicable to a life/glide re-entry vehicle. Based on results of Phases I and II, preliminary designs have been established for each PAD as a function of component performance criteria. Prime consideration was given to successful abort at any point during the mission profile. It was found possible throughout the entire Phase III effort to evolve component designs for each PAD function without exceeding to any great extent the present state-of-the-art. As a result, the areas mentioned for future research and development are generally concerned with characterization of the more promising new explosives and propellants, and the presentation of several concepts, which, if developed, would offer secondary improvements in the overall system weight, reliability, or cost.
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Investigation of Hypersonic Inlet Shock-Wave Boundary Layer Interaction: Part II - Continuous Flow Test and Analyses
Report Number: AFFDL TR 65-36
Author(s): Paul H. Kutschenreuter, Jr., David L. Brown and Werner Hoelmer
Corporate Author: General Electric Company
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date:
Pages: 272
Features: + Foldout(s)
Contract: AF 33(657)-11747
Project: 651-E
Task: None Given
AD Number: AD0636981
Photo Enhancement: Complete
Abstract Text:
The computational procedure developed in Phase I for estimating laminar boundary layer properties through impinging shock induced laminar boundary layer interactions was modified to account for entropy change of the inviscid streamlines in that isentropic assumptions were used in the initial formulation. Perturbation studies on the effects of wall shear on interaction length have identified the importance of the profile shape factor in such calculations. A Users' Manual for the laminar computational program is contained. Three incident shock models were designed for use in the experimental program conducted in the Ames 3.5 Foot Hypersonic Tunnel. Aided by analysis of the experimental data, a simplified flow model was formulated for the case of a two-dimensional turbulent boundary layer incident shock interaction.
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Ground Simulator Evaluations of Coupled Roll-Spiral Mode Effects on Aircraft Handling Qualities
Report Number: AFFDL TR 65-39
Author(s): F. D. Newell
Corporate Author: Cornell Aeronautical Laboratory, Inc.
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 3/1/1965
Pages: 56
Contract: AF 33(615)-1253
Project: 8219
Task: 821905
AD Number: AD0468857
Photo Enhancement: Complete
Abstract Text:
A systematic investigation of the lateral handling qualtities of fighter aircraft on an en route IFR mission was made in a fixed-base ground simulator. The suitability of a wide range of roll and spiral mode root locations was examined with particular emphasis placed upon determining the effects of complex rollspiral roots. The complex roll-spiral roots were produced with several feasible combinations of stability derivatives. Interaction effects of the Dutch roll mode roots were examined, including the effects of the proximity of these roots to the complex roll-spiral mode roots. Assessment of the flying qualities is reported in terms of the evaluation comments and ratings given by two pilots. In general the complex roll-spiral configurations that were evaluated were too difficult to control in roll to consider their handling quality characteristics as acceptable for fighter aircraft.
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Computational Methods in Optimal Control Problems
Report Number: AFFDL TR 65-50
Author(s): James A. Payne
Corporate Author: University of California Department of Engineering
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 8/1/1965
Pages: 134
Contract: AF 33(615)-1794
Project: 8225
Task: 822501
AD Number: AD0622081
Photo Enhancement: Not Needed
Abstract Text:
This report considers the application of optimization techniques to the development of methods for the control of engineering systems. The systems considered are those physical processes which are subject to independent control forces and in which the dynamics of the process are of central importance. It is assumed that the process can be described by a system of ordinary nonlinear differential equations. The optimization, with respect to a general criterion function, of such systems is considered. The conditions and equations which specify the optimal system behavior are derived by means of the Maximum Principle. System trajectories which satisfy the optimal conditions, i.e., optimal trajectories, can only be obtained by numerical computation. Various approaches to this computational problem are reviewed and their primary limitations are discussed. In order to provide a realistic evaluation of certain computational methods, the optimization of a particular engineering system is considered in detail. This system is a variable lift aerodynamic vehicle during the atmospheric reentry phase. A mathematical model for this system is developed and the optimization of this model is considered. The criterion function is a linear combination of the heating and acceleration effects which are experienced by the vehicle during the reentry phase.
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Study of Electrostatic Effects on Condensing Heat Transfer
Report Number: AFFDL TR 65-51
Author(s): Harry Y. Choi and John M. Reynolds III
Corporate Author: Tufts University and Massachusetts Institute of Technology
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 5/1/1965
Pages: 138
Contract: AF 33(657)-10908
Project: 6146
Task: 614615
AD Number: AD0467747
Photo Enhancement: Complete
Abstract Text:
A study program is presented on the effects of strong electric fields on condensation heat transfer and two-phase flow. It has been confirmed that significant changes in the flow regimes and heat transfer are possible with negligible electrical power expenditure. Over 100 per cent increase in heat transfer has been attained with pressure drop increases which are of the order of 15 per cent in the annular flow regime. These investigations were performed on two separate apparatus: one at Tufts University in which heat transfer phenomena in condensation were investigated and one at the Massachusetts Institute of Technology in which hydrodynamic phenomena in two-phase flow were studied. Results show that the slug flow regime is substantially suppressed. In essence, slug flow occurs only in the region of very low gas flows in which the system is almost entirely gravity dependent. The increase in heat transfer rates is gradual up to a certain threshold value of the applied voltage; beyond this value, the increase is steep. Some progress has been made in analytical and physical modeling of the phenomenon both from the viewpoint of determining pressure drop and heat transfer and of aiding in the determination of the fluid configuration at the heat transfer surface.
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Measurement of Matrix Frequency Response Functions and Multiple Coherence Functions
Report Number: AFFDL TR 65-56
Author(s): N. R. Goodman
Corporate Author: Measurement Analysis Corporation
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 6/1/1965
Pages: 36
Contract: AF 33(615)-1418
Project: 1370
Task: 137005
AD Number: AD0619993
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Abstract Text:
Fundamental concepts involved in the statistical analysis of multiple-input single-output time-invariant linear systems are described. The definitions of a matrix frequency response function and a multiple coherence function are presented. Formulas for computing simultaneous confidence bands for all elements of the matrix frequency response function are obtained, using the standard 'F' distribution. Expressions for the confidence bands are given both as a function of the various types of coherences and of the elements of the spectral density matrix. The effect of the various quantities on the width of the confidence bands is discussed in detail. Confidence bands for the gains and phases of the frequency response functions are also developed. The interpretation of linear system computational results in terms of a time invariant nonlinear system model is described. It is shown how the linear system results provide what may be thought of as a 'best' linear fit to the nonlinear model. The multiple coherence function then gives a quantitative measure of goodness of this fit. In this sense the coherence function may be used to provide a test for system linearity.
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Gaussian Approximations to the Distribution of Sample Coherence
Report Number: AFFDL TR 65-57
Author(s): L. D. Enochson; N. R. Goodman
Corporate Author: Measurement Analysis Corporation
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 6/1/1965
Pages: 33
Contract: AF 33(615)-1418
Project: 1370
Task: 137005
AD Number: AD0620987
Abstract Text:
This report describes the results of an empirical study to develop a normalizing transformation for sample multiple coherence. The 'Fisher z- transformation' is employed. The expected value (including a bias term) and variance of the transformation have been experimentally determined. Numerical values of the transformation which is developed (including the bias term and variance) may be obtained with a reasonable amount of computation. Tables of the Gaussian distribution can then be used to obtain confidence limits and perform statistical tests. The computational methods and the digital computer program used for the study are described in detail. Flow charts of the program are given. Numerical results from the program results are presented. Examples of the use of the transformation are given for developing confidence limits for multiple coherence. A recommendation for a further theoretical study is presented.
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Aerodynamics of a Rectangular Wing with a Peripheral Jet for Air Cushion Take-Off and Landing
Report Number: AFFDL TR 65-59
Author(s): K. Dau; B. Etkin; D. Surry
Corporate Author: University of Toronto
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 9/1/1965
Pages: 56
Contract: AF 33(657)-8451
Project: 8219
Task: 821907
AD Number: AD0623827
Photo Enhancement: Complete
Abstract Text:
Subsonic wind tunnel experiments on a GETOL wing are reported. The main results relevant to performance, stability and control are presented, and applied to a hypothetical vehicle. Short-field capability is demonstrated to be possible. Stability and control problems are analysed, and shown not to be prohibitive.
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A Closed-Form Solution to Lifting Reentry
Report Number: AFFDL TR 65-65
Author(s): Roland N. Bell
Corporate Author: Air Force Flight Dynamics Laboratory
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 1/1/1966
Pages: 73
Features: + Foldout(s)
Contract: Laboratory Research - No Contract
Project: 1366
Task: 136602
AD Number: AD0631590
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Abstract Text:
This report derives closed-form expressions for predicting the longitudinal and lateral range attainable by lifting reentry vehicles. The resultant equations sensitively and accurately define the influence of L/D ratio, bank angle and entry velocity variations over a spectrum of values. To illustrate the usefulness of the method, the derived expressions were used to conduct a parametric reentry study covering a range of L/D ratios from 0.5 to 4.0, bank angles from 0 to 75 degrees and entry velocities from 0.89V sub c to 0.99V sub c. The results of this study are compared with those obtained from a high speed computer study using the same range of reentry conditions. As an aid to future investigators, a series of curves is presented giving longitudinal and lateral range values for various selected L/D, bank angle and entry velocity values. For those wishing to investigate reentry under conditions not covered by these curves, a detailed 'recipe' for utilizing the method is included in an appendix. A comparison of the results of this method with those of more rigorous methods for the same reentry conditions shows that the closed-form solution has sufficient accuracy and sensitivity to be of considerable value to those persons requiring a rapid, preliminary estimate of vehicle performance.
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Weight Minimization of Honeycomb Heat Shields
Report Number: AFFDL TR 65-66
Author(s): Robert T. Achard
Corporate Author: Air Force Flight Dynamics Laboratory
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 6/1/1965
Pages: 26
Contract: Laboratory Research - No Contract
Project: 1368
Task: 136804
AD Number: AD0620677
Photo Enhancement: Not Needed
Abstract Text:
A procedure for the design of minimum weight honeycomb structures for use as radiative heat shields is presented. Formulations are applicable to panels critical to intracell buckling and face compressive yield. Minimum weight is shown to occur at the condition where design variables produce a critical buckling stress equal to the compressive yield stress.
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An Analytical Study of V/STOL Handling Qualities in Hover and Transition
Report Number: AFFDL TR 65-73
Author(s): R. L. Stapleford; J. Wolkovitch; R. E. Magdaleno; C. P. Shortwell; W. A. Johnson
Corporate Author: Systems Technology, Inc.
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 10/1/1965
Pages: 172
Contract: AF 33(615)-1300
Project: 8219
Task: 821909
AD Number: AD0625599
Photo Enhancement: Not Needed
Abstract Text:
The hover analysis considers pilot attitude and position control tasks in the presence of horizontal gusts. The effects of each of the stability derivatives on the difficulty of the control tasks and on the closed-loop gust responses are determined. It is clearly shown that the handling qualities studies of control sensitivity and angular damping must consider the influences of M sub u (or L sub v) and should include gust inputs. These conclusions are substantiated by previous variable-stability-helicopter experiments. The effects of vehicle size and geometry are investigated by several approaches. The key result of increasing size is found to be a reduction in M sub u and L sub v which can, in turn, lower the requirements for control power and damping. The handling qualities during transition of two vehicles, a tilt duct and a tilt wing, which were previously tested on a simulator are analyzed. It is shown that both trim control and perturbations about the trim conditions must be considered. In fact, part of the increased difficulty in landing transitions, in comparison with takeoff transitions, is due to more difficult trim control; the much more stringent position control requirements in landing are also a contributing factor.
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Tests for Randomness, Stationarity, Normality and Comparison of Spectra
Report Number: AFFDL TR 65-74
Author(s): J. S. Bendat; L. D. Enochson; A. G. Piersol
Corporate Author: Measurement Analysis Corporation
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 8/1/1965
Pages: 54
Contract: AF 33(615)-1314
Project: 4437
Task: 443706
AD Number: AD0621906
Photo Enhancement: Not Needed
Abstract Text:
This report contains material for carrying out certain practical tests for randomness, stationarity, and normality of physical data, as well as details on how to test for equivalence of two power spectral density functions. The tests for randomness are qualitative inspections of measured properties from sample records, such as power spectra, probability density, auto-correlation functions, which may be part of a regular data reduction procedure. The tests for stationarity are nonparametric statistical procedures, based upon Run and Trend Distributions, which require simple quantitative calculations for acceptance or rejection. The test for normality is a statistical hypothesis test based upon sample measurements of the amplitude probability density function at seven equispaced amplitude levels from zero to plus and minus three sigma. To test for equivalence of two spectra, a straight-forward procedure is recommended which requires knowledge only of the number of degrees-of-freedom associated with the spectral estimates, and the full bandwidth occupied by the data. A special case of this procedure is to compare an unknown spectrum to a 'white' spectrum.
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Probability Calculations on a Digital Computer
Report Number: AFFDL TR 65-75
Author(s): Robert K. Otnes
Corporate Author: Measurement Analysis Corporation
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 8/1/1965
Pages: 34
Contract: AF 33(615)-1314
Project: 4437
Task: 443706
AD Number: AD0621907
Photo Enhancement: Not Needed
Abstract Text:
The purpose of this report is to discuss computer implementations of tests for normality. Some of the underlying statistical considerations and random process theory are briefly reviewed to provide a background for subsequent material. Methods for digitally computing basic statistical parameters, such as the mean variance, skewness, kurtosis, etc., are given, along with procedures for computing the sample probability density function. Problems arising from the digital and discrete nature of the data are discussed, as well as sample sizes required for for the tests. The central part of the report consists of a detailed discussion of the computer implementation of the chi-square goodness-of-fit test as applied to testing for normality, followed by computer program flow charts, suitable for use in coding the procedure for a digital computer. Sufficient detail has been provided so that a programmer unfamiliar with the material should be able to write a program which will make maximum use of the time which is frequently lost during periods of input and output of data from the computer. The report concludes with an appendix which lists standard approximations for some of the mathematical functions required in the calculations.
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Turbulent Wall Pressure Fluctuations Under Separated Supersonic and Hypersonic Flows
Report Number: AFFDL TR 65-77
Author(s): J. D. Revell and R. E. Gleason
Corporate Author: Northrop Corporation
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 8/1/1965
Pages: 450
Contract: AF 33(657)-11712
Project: 1471
Task: 147102
AD Number: AD0622395
Photo Enhancement: Complete
Abstract Text:
The objective of the project was to conduct an exploratory theoretical and limited experimental program to obtain the parameters that are important in the occurrence, magnitude, frequency content, and effective areas of forcing functions arising from separated flow, wakes, base pressure fluctuations, and oscillating shock waves. Two models were used to obtain pressure fluctuation data generated by the above mentioned phenomena from wind tunnel tests. These models were purposely constructed to generate separated flows, oscillating shock waves, and base pressure fluctuations. The fluctuating pressure data obtained during the tests were reduced in the form of one-third octave band spectra. These reduced data are compiled. Analyses of these data were made, and are given. Comparisons were made of the effects of Mach number, angle of attack, frequency, and Strouhal number on the sound pressure levels generated.
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Trisafe Single Axis Flight Control System
Report Number: AFFDL TR 65-89
Author(s): H. L. Ehlers, R. D. Blosser and H. O. Williams
Corporate Author: Autonetics Division of North American Aviation
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 9/1/1965
Pages: 132
Features: + Foldout(s)
Contract: AF 33(615)-1479
Project: 8225
Task: 822504
AD Number: AD0474100
Photo Enhancement: Complete
Abstract Text:
The TRISAFE Single Axis Flight Control System developed for the Research and Technology Division of the Air Force consists of a deliverable controller and simulator with associated recorder. This equipment is to be used primarily as a laboratory demonstration model of a triple redundant, self-adaptive flight control system. The controller incorporates the Autonetics developed triple redundant, analog circuit technique called TRISAFE that represents nearly optimum in redundancy, efficiency and reliability. To compensate for the normal increase in size and weight due to the triple redundancy, the use of a square wave 400 cps carrier has been employed to reduce the number of components, and molecular integrated circuits are used to reduce the size of the components. A multi-layer circuit board is used to further reduce the weight and volume of the controller. The controller measures 3 x 9.7 x 12 inches and weighs approximately 6 pounds. Plug-in modular packaging is used for maintainability. The controller is based on the dynamics of a high performance tactical aircraft and provides stability augmentation for the pitch axis. To provide for optimum gain throughout the performance range of the aircraft, a self-adaptive system is used. Known as the dither-adaptive technique, it employs a low level test signal to measure the response of the airframe and adjusts the gain accordingly.
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Self-Adaptive Flight Control by Multivariable Parameter Identification
Report Number: AFFDL TR 65-90
Author(s): P. P. Shipley, A. G. Engel, Jr. and J. W. Hung
Corporate Author: North American Aviation, Inc.
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 8/1/1965
Pages: 152
Contract: AF 33(615)-1882
Project: 8225
Task: 822501
AD Number: AD0474224
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Abstract Text:
An approach to adaptive flight control is described which uses outputs from a relatively simple parameter tracking computer to adjust flight control system parameters. A unique characteristic of the parameter tracking mechanism is the ability to function with almost any type of disturbance as an input, including normal pilot activity, wind turbulence, and oscillations due to control loop instability. This may be accomplished without special test inputs or limit cycles.
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Similitude for Normal Shock Waves in Non-Equilibrium Flows
Report Number: AFFDL TR 65-91
Author(s): R. E. Thomas, D. Brooke, S. L. Petrie
Corporate Author: The Ohio State University Research Foundation
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 10/1/1965
Pages: 50
Contract: AF 33(657)-10416
Project: 1426
Task: 142604
AD Number: AD0627031
Photo Enhancement: Not Needed
Abstract Text:
Similarity parameters are developed which govern the length of nonequilibrium zones behind normal shock waves. Non-equilibrium effects produced by both vibrational relaxation and dissociation are considered. The parameters can also account for arbitrary levels of free-stream vibrational energy or dissociation level. The validity of the parameters is examined using numerical computations of the properties of the non-equilibrium fields. These computations are made with the aid of experimentally based rate expressions. The parameters, when written in a form describing the variation of non-equilibrium zone length with Mach number, are shown to have acceptable accuracy.
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Evaluation Tests for Statistical Analyzers
Report Number: AFFDL TR 65-93
Author(s): R. D. Kelly
Corporate Author: Measurement Analysis Corporation
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 6/1/1965
Pages: 102
Contract: AF 33(615)-1418
Project: 1370
Task: 137005
AD Number: AD0621035
Photo Enhancement: Not Needed
Abstract Text:
This report describes a series of tests designed to evaluate the performance of statistical analyzers. The types of analyses that these analyzers typically perform and that must be evaluated are: (1) Instantaneous amplitude probability density, (2) Instantaneous amplitude probability distribution, (3) Negative instantaneous amplitude probability distribution, (4) Peak value probability density, (5) Expected number of maxima per unit time, (6) Expected number (total, positive, or negative) of threshold crossings per unit time, (7) Joint instantaneous amplitude probability distribution, (8) Joint instantaneous amplitude probability density, (9) Extreme value density, (10) Extreme value distribution. Tests with both periodic (sinusoidal and triangular) and random (broadband Gaussian, narrow band Gaussian, and clipped Gaussian) signal inputs are delineated for each of the above analysis modes. Tolerances on the output wave shapes of the periodic signal generators are described so that generators whose outputs will not contribute significantly to the measurement errors can be selected. It is suggested that the random test signals be recorded on magnetic tape so that the identical signals can be analyzed by the statistical analyzer and a digital computer. The digital computer analysis will accurately define the statistical properties of the actual test signal so that the problems associated with imperfections in the random noise generator and statistical uncertainty fluctuations can be avoided. The analytical derivation of all of the above statistical functions for sinusoidal input signals are included to illustrate the operating principles of this analyzer.
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Systems for the Collection and Analysis of Dynamic Data
Report Number: AFFDL TR 65-94
Author(s): R. D. Kelly
Corporate Author: Measurement Analysis Corporation
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 8/1/1965
Pages: 98
Contract: AF 33(615)-1314
Project: 4437
Task: 443706
AD Number: AD0621909
Photo Enhancement: Not Needed
Abstract Text:
The machine errors are discussed of equipment used for the conditioning, collection, recording, editing, and analysis of data from dynamic processes such as acoustics, strain, or vibration. The specific equipment items studied include special features of signal conditioners (e.g., automatic gain control), signal conditioner to tape recorder transmission line, magnetic tape recorders, gross analyzers (e.g., voltmeters), frequency analyzers, amplitude analyzers, and time domain analyzers. (The machine errors associated with transducers and basic signal conditioners are presented in 'Transducers for Sonic Fatigue Measurements.') Where these errors are controllable, such as the smoothing error associated with the rate of scanning an amplitude window for probability density measurements, pertinent equations are presented for determining the magnitude of these errors as a function of the controllable parameter(s). In addition, the report describes practical usage of the analysis equipment for the detection of non-normality, nonstationarity, and periodicity.
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Random Fatigue Test Sampling Requirements
Report Number: AFFDL TR 65-95
Author(s): S. C. Choi; L. D. Enochson
Corporate Author: Measurement Analysis Corporation
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 8/1/1965
Pages: 76
Contract: AF 33(615)-1314
Project: 4437
Task: 443706
AD Number: AD0622086
Abstract Text:
Basic considerations are discussed for determining sample sizes and record lengths for various statistical tests and estimates which are important to random fatigue testing. Methods for determining minimum sample sizes when comparing means and variances of normally (Gaussian) distributed random variables are described. Procedures for reducing a relatively large sample to a smaller sample are presented. Elimination of outliers and systematic resampling are two methods given. An explanation is presented of the requirements and problems involved in the determination of record lengths necessary for an estimate of a given accuracy for autocorrelation functions, ordinary power spectral density functions, cross-correlation functions, cross-spectral density functions, frequency response functions, and probability density functions. Due to its importance in random fatigue testing applications, the basic properties of the Weibull distribution in terms of its parameters and the failure rate are summarized. A presentation is given of estimation and statistical testing problems related to the Weibull distribution. The best available methods of estimating the parameters are described. Methods of determining sample sizes needed for various analyses are developed. Some problems of reliability analysis applicable in fatigue testing are discussed. New methods of decision techniques for comparing two or more systems are proposed in terms of reliability. The report concludes with an example of the application of the Weibull distribution to actual fatigue test data.
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Development Of Aircraft Shock Absorbers Using Friction As The Energy Dissipator
Report Number: AFFDL TR 65-96
Author(s): Fricker, Walter W.
Corporate Author: Cleveland Pneumatic Co OH
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 10/1/1965
Pages: 86
Features: + Foldout(s)
Contract: AF 33(615)-2033
Project: 1369
Task: 136903
AD Number: AD0476615
Photo Enhancement: Not Needed
Abstract Text:
The purpose of this study is to evolve and evaluate a number of preliminary aircraft landing gear designs or concepts utilizing shock absorbers based on friction energy absorption methods adaptable to high temperature use (1000 F and up). Initial studies developed as many concepts as possible, without attempting to size components, but merely to portray an idea. Four concepts were selected from the initial study and preliminary designs of the selected concepts were prepared based on landing and take-off characteristics of the USAF F-100 aircraft. Scale model drawings were then developed based on the full scale landing gear deisgns to experimentally evaluate the proposed designs. Data indicates that friction methods have extremely high energy absorption capacities, that the coefficient of friction is relatively insensitive to temperature variations and that a centrifugally controlled friction device has sufficient advantages to warrant further research effort.
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Air Pressure Measurement in the Rarefied Gas Transition Region
Report Number: AFFDL TR 65-101
Author(s): Fred S. Brunschwig
Corporate Author: The Boeing Company
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 8/1/1965
Pages: 87
Contract: AF 33(615)-1793
Project: 1469
Task: 146907
AD Number: AD0473766
Photo Enhancement: Complete
Abstract Text:
Presented are parameters and pressure corrections for a low air pressure (1-100 p.s.f.a.) measurement system consisting of a pressure transducer and tubing ported to a hot surface at temperatures to 2800 F. Included are results of laboratory measurements with argon and air under conditions of both thermal creep and slip flow occurring together in a pressure transmission tube under temperature gradients. Both temperature functions, thermal creep and slip flow, were found to affect the system pressure. Dynamically, the temperature dependance of slip flow affects time response for tubes since it has the temperature dependancy of gas viscosity. Integration of the tubular time constant, modified for slip flow along the tube's temperature gradient, is carried out and compared to measurements; fair agreement is shown. Work reported includes calibration of a commerical airborne alpha emission pressure transducer; also data is presented on adsorption/oxidation at temperature for pressure tubing material.
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Calculation of Laminar Separation with Free Interaction by the Method of Integral Relations: Part I - Two-Dimensional Supersonic Adiabatic Flow
Report Number: AFFDL TR 65-107
Author(s): Jack N. Nielsen; Larry L. Lynes; Frederick K. Goodwin
Corporate Author: Itek Corporation
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 10/1/1965
Pages: 120
Contract: AF 33(615)-1591
Project: 8219
Task: 821902
AD Number: AD0626160
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Abstract Text:
Methods are presented for calculating the laminar boundary-layer flow through separation to reattachment under the influence of a prescribed pressure gradient or, in the case of a supersonic main stream, under the influence of 'free interaction' between the boundary layer and the main flow. The present method is based on the Dorodnitsyn method of integral relations and uses a rational velocccity profile which accounts properly for the separation singularity. As a result, the possibility of higher approximations is inherent in the method. The calculated solution for free interaction goes smoothly through the separation point and is in good agreement with certain features of the Navier-Stokes solution in the neighborhood of separation. Good agreement is exhibited betweeen experimental and calculated pressure distributions up to reattachment for the several cases for which the comparisons were made. A computer program based on the work was prepared for two-dimensional flow. It is planned to continue the work to cover nonadiabatic boundary layers and axisymmetric bodies.
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Calculation of Laminar Separation with Free Interaction by the Method of Integral Relations: Part II - Two-Dimensional Supersonic Nonadiabatic Flow and Axisymmetric Supersonic Adiabatic and Nonadiabatic Flows
Report Number: AFFDL TR 65-107 Part 2
Author(s): Jack N. Nielsen; Larry L. Lynes; Frederick K. Goodwin
Corporate Author: Itek Corporation
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 1/1/1966
Pages: 90
Contract: AF 33(615)-1591
Project: 8219
Task: 821902
AD Number: AD0630765
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Abstract Text:
A calculative method is presented for determining separated, laminar, boundary-layer characteristics from in front of the separation point to the reattachment point under the influence of 'free interaction' between the main flow and the boundary layer. The analysis covers supersonic flow over two-dimensional and axisymmetric configurations with adiabatic or nonadiabatic wall conditions. For nonadiabatic wall conditions, theories based on first-order coupling and second-order coupling between velocity and total temperature profiles were presented. The theory based on first-order coupling was included in a machine calculation program with options for two-dimensional or axisymmetric flow and adiabatic or nonadiabatic wall conditions. Extensive systematic calculations were made to determine the range of possible separated flows over a two-dimensional configuration as a function of separation point location and wall temperatures. Comparison between experiment and theory for separation pressure distributions on two -dimensional or axisymmetric adiabatic configurations shows generally good agreement.
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Investigation of the Acquisition Problem in Satellite Attitude Control
Report Number: AFFDL TR 65-115
Author(s): A. Sabroff; R. Farrenhopf; A. Frew; M. Gran
Corporate Author: TRW/Space Technology Laboratories
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 12/1/1965
Pages: 318
Features: + Foldout(s)
Contract: AF 33(615)-1535
Project: 8219
Task: 821904
AD Number: AD0628062
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Abstract Text:
The acquisition function of a spacecraft attitude control system consists of properly orienting the vehicle with respect to specified reference directions starting from large initial attitude and rate errors. The resulting control system design problem was examined by establishing suitable mathematical representations, comparing competing control concepts, developing a practical optimization approach, and evaluating a new technique for applying Lyapunov stability theory to the acquisition problem.
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Compilation and Analysis of Flight Control System Command Inputs
Report Number: AFFDL TR 65-119
Author(s): David H. Weir
Corporate Author: Systems Technology, Inc.
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 1/1/1966
Pages: 73
Contract: AF 33(615)-1818
Project: 8219
Task: 821904
AD Number: AD0483621
Photo Enhancement: Not Needed
Abstract Text:
Flight control command input data are presented for automatic approach and landing, automatic terrain following, and manual control. The data are reduced to analytical forms useful in preliminary design where possible, e.g., servoanalysis methods and approximation techniques appropriate to the use of the data are discussed. Preferred data forms and areas of continuing data need are summarized.
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Flight Control Data and Information Exchange Program: Part I. Investigation of Need and Feasibility
Report Number: AFFDL TR 65-120 Part 1
Author(s):
Corporate Author: Systems Technology, Inc.
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 11/1/1965
Pages: 60
Contract: AF 33(615)-1818
Project: 8219
Task: 821904
AD Number: AD0626923
Photo Enhancement: Not Needed
Abstract Text:
The document reports the results of an investigation of the need for a permanent flight control data and information exchange program. Direct mail questionnaires were used to solicit the opinions of flight control specialists. The results of the opinion survey are summarized. Three major abstracting and announcement media were critically examined from the standpoint of identifying information relevant to flight control systems. A literature survey was also conducted to determine the current status of technical documentation and dissemination. A group of specialized information centers of interest to flight control specialists are described. Based upon the findings, the general structure and guidelines are presented for a specialized information center designed solely to satisfy the information needs of flight control specialists.
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An Experimental and Analytical Investigation of Hypersonic Inlet Boundary Layers
Report Number: AFFDL TR 65-123 Volume 1
Author(s): J. F. Stroud; L. D. Miller
Corporate Author: Lockheed-California Company
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 8/1/1965
Pages: 110
Features: + Foldout(s)
Contract: AF 33(657)-8833
Project: 1366
Task: 136605
AD Number: AD0621343
Photo Enhancement: Complete
Abstract Text:
Detailed boundary layer surveys were made on four axisymmetric compression surface models simulating typical hypersonic inlet compression surfaces at free stream Mach numbers ranging from 4 to 8. The four models were designed to provide isentropic compression at design Mach numbers of 5, 6, 8 and 10. The Mach 8 design model had provisions for wall cooling. Quantitative heat transfer measurements were made on the Mach 8 model at free stream Mach numbers of 5, 6, and 8. Two existing turbulent boundary layer theories were modified to account for the various phenomena found to be of importance in hypersonic boundary layers. Theoretical results from these methods were correlated with the experimental data. A significant observation of the present program is the powerful favorable effect of centrifugal force phenomena on boundary layer development in continuous adverse pressure gradients. It was found that these effects become more pronounced with increasing Mach number and reductions in free stream Reynolds number.
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An Experimental and Analytical Investigation of Hypersonic Inlet Boundary Layers
Report Number: AFFDL TR 65-123 Volume 2
Author(s): J. F. Stroud; L. D. Miller
Corporate Author: Lockheed-California Company
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 8/1/1965
Pages: 407
Contract: AF 33(657)-8833
Project: 1366
Task: 136605
AD Number: AD0621344
Photo Enhancement: Not Needed
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Investigation of the Requirements for Combined Environment Testing of Air Force Material
Report Number: AFFDL TR 65-126 Volume 2
Author(s): E. R. Wilson, W. P. Rader, H. N. McGregor and J. D. Donahue
Corporate Author: Martin-Marietta Corp.
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 12/1/1965
Pages: 156
Contract: AF 33(615)-1313
Project: 1309
Task: None Given
AD Number: AD0478996
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Abstract Text:
A series of experiments was statistically designed and conducted to determine the effect of environments singularly and in combination upon the performance of a specimen representative of typical aircraft or missile equipment. The test specimen consisted of electronic, mechanical, and hydraulic components assembled in a manner which would produce a measurable deviation from a reproducible norm when subjected to combinations of the following eight environments: (1) high temperature, (2) low temperature, (3) thermal shock, (4) altitude, (5) humidity, (6) vibration, (7) mechanical shock, and (8) sustained acceleration. The experiments consisted of 8 single-environment tests, 21 combinations of 2 environments, 25 combinations of 3 environments, and 4 combinations of 4 environments. In general, the results of the experiments indicated that the response or deviation from the norm of the test specimen when subjected to multiple environments was greater than the sum of the environments when taken independently.
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Experimental Verification of the Analyses and Computer Programs Concerning Heat Transfer Through Semitransparent Materials
Report Number: AFFDL TR 65-136
Author(s): H. Finch, M. Noland and C. Moeller
Corporate Author: Midwest Research Institute
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 7/1/1965
Pages: 86
Contract: AF 33(615)-1801
Project: 1368
Task: 136802
AD Number: AD0468746
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Abstract Text:
An experimental and analytical evaluation of the theory and computer programs concerning heat transfer through semitransparent materials which was developed uncer Contract AF 33(657)-9138. Experimental investigations of the heat transfer through 96% silica glass and aluminosilicate glass were conducted for glaze temperatures to 1000 F. Similar data were produced for the same materials with tin oxide or gold films on one or both sides of the specimens. The experimental, empirical, and analytical tests conducted to evaluate the computer program led to the conclusion that the program in its present form does not yield realistic results and thus is not a satisfactory tool for the computation of heat fluxes or temperature distributions in semitransparent materials. Recommendations for future research are based upon a belief that the theory is sound and that, despite the computer program difficulties, the program can be made into an important tool for the design of advanced systems.
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Investigations of Describing Function Technique
Report Number: AFFDL TR 65-137
Author(s): Dunstan Graham and Lee Gregor Hofmann
Corporate Author: Systems Technology, Inc.
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 2/1/1966
Pages: 110
Contract: AF 33(615)-1474
Project: 8219
Task: 821904
AD Number: AD0631314
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Abstract Text:
Three problems were chosen so as to explore some of the apparent limitations of describing function technique for the analysis of nonlinear systems, and to show how the technique might be extended so as to overcome the indicated deficiencies. The problems were (a) the effects of stick and valve friction in fully powered, manual aircraft control systems, (b) limit cycles in satellite attitude control with off-on jets, and (c) the effects of aerodynamic hysteresis in the stability derivatives of tilt-wing VTOL aircraft. The results indicate that new describing functions can be developed as closed-loop functions provided that specific restrictions are met, that non-sinusoidal, Fourier series describing functions or a generalized periodic input describing function can be successful, but that they are extraordinarily difficult to apply, and that the aerodynamic nonlinearities which were considered are of small practical importance.
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A Study of Conventional Airplane Handling Qualities Requirements: Part I. Roll Handling Qualities
Report Number: AFFDL TR 65-138 Part 1
Author(s): I. L. Ashkenas
Corporate Author: Systems Technology, Inc.
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 11/1/1965
Pages: 82
Contract: AF 33(657)-10407
Project: 8219
Task: 821905
AD Number: AD0627659
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Abstract Text:
The report uses as a point of departure the concept that control of bank angle is the primary piloting task in maintaining or changing heading. Regulation of the bank angle to maintain heading is a close-loop tracking task in which the pilot applies aileron control as a function of observed bank angle error. For large heading changes, the steady-state bank angle consistent with available or desired load factor is attained in an open-loop fashion; it is then regulated in a closed-loop fashion throughout the remainder of the turn. For the transient entry and exit from the turn, the pilot is not concerned with bank angle per se, but rather with attaining a mentally commanded bank angle with tolerable accuracy in a reasonable time, and with an easily learned and comfortable program of aileron movements.
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A Study of Conventional Airplane Handling Qualities Requirements: Part II. Lateral-Directional Oscillatory Handling Qualities
Report Number: AFFDL TR 65-138 Part 2
Author(s): I. L. Ashkenas
Corporate Author: Systems Technology, Inc.
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 11/1/1965
Pages: 73
Contract: AF 33(657)-10407
Project: 8219
Task: 821905
AD Number: AD0627989
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Abstract Text:
This report is a codification in two parts of conventional aircraft handling qualities criteria. The results of this effort are to serve as an intermediate design guide in the areas of lateral-directional oscillatory and roll control. The roll handling qualities portion of this report uses as a point of departure the concept that control of bank angle is the primary piloting task in maintaining or changing heading. In the lateral oscillatory portion of this effort, in defining requirements for satisfactory Dutch roll characteristics, a fundamental consideration is the fact that the motions characterizing this mode are ordinarily not the pilot's chief objective. That is, he is not deliberately inducing Dutch roll motions in the sense that he induces rolling and longitudinal short-period motions. A worthwhile approach to establishment of Dutch roll damping requirements is to first establish the basic level, and then to study the varied influences of the disturbance parameters. This approach provides the basis for the material contained in this report.
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Prediction of Space Vehicle Thermal Characteristics
Report Number: AFFDL TR 65-139
Author(s): J. T. Bevans, T. Ishimoto, B. R. Loya and E. E. Luedke
Corporate Author: TRW Systems Group
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 10/1/1965
Pages: 188
Contract: AF 33(615)-1725
Project: 6146
Task: 614617
AD Number: AD0472558
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Abstract Text:
The first phase of a program to improve the prediction of spacecraft thermal performance is reported. The study has consisted of measuring actual joint thermal conductance, correlation of the measured joint conductance, programming an improved method of thermal radiation analysis, and performing an experimental comparison of predicted radiation exchange for a simple geometrical system. Three types of structural and three sizes of component mounting joints were tested and the conductances measured. A successful method of correlation was developed for the unfilled component mounting joints. A method of radiation analysis has been programmed which uses directional thermal radiation properties and accounts for the specularity and/or diffuseness of these properties. The results of this program can be readily incorporated into most existing thermal analysis programs. The user has the choice of the specular, the diffuse, or the specular-diffuse assumption. The prediction of radiation exchange using these assumptions for simple geometrical arrangements has been compared to experiment. Although the results were within the over-all experimental tolerances, further improvement in the predicted values is believed possible.
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Self-Organizing Spacecraft Attitude Control
Report Number: AFFDL TR 65-141
Author(s): Roger L. Barron, Samuel Schalkowsky, John M. Davies and Richard F. Snyder
Corporate Author: Adaptronics, Inc.
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 9/1/1965
Pages: 128
Contract: AF 33(615)-1864
Project: 8225
Task: 822508
AD Number: AD0475167
Photo Enhancement: Complete
Abstract Text:
Results are presented from an investigation of self-organizing attitude control and stabilization for spacecraft. Self-organizing (SOC) control is achieved through high-speed assessments of performance values of successive random experiments with respect to a generalized control criterion, followed by a reward-punishment reinforcement process to obtain on-line synthesis of plant actuation signals. The logic is of the Probability State Variable (PSV) type, i.e., reinforcement signals are used to bias the probabilities associated with the SOC experiments. Convergence of SOC output signals to appropriate, time-varying levels generally occurs within several milliseconds, resulting in rapid, well damped, stable control over a very wide range of controller, plant, and disturbance characteristics (including induced artificial failures). A laboratory experimental self-organizing controller has been fabricated. Evaluations of this SOC have been conducted using single-axis analog computer simulations of a representative orbital vehicle. Compared to a conventional controller for this vehicle, the SOC produced superior transient and comparable steady-state performance. The SOC adapted to a range of plant characteristics over which the conventional controller did not provide uniformly satisfactory performance.
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Hot Structures Thermal Correlation
Report Number: AFFDL TR 65-142
Author(s): James F. Clawson
Corporate Author: The Boeing Company
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 11/1/1965
Pages: 254
Contract: AF 33(657)-7132
Project: 1467
AD Number: AD0477775
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Abstract Text:
Test data generated during the early X-20 (Dyna-Soar) phases are compared with therma2l analysis methods evolved throught the X-20 Program. Data are taken from the Hot Structures concept model test program. This model was similar in shape and concept to the X-20 design. The thermal analysis approach and methods used follow closely those which created the X-20 design temperatures. Generally good correlation is shown for two-dimensional cross-sectional cuts, a simple three-dimensional nose region analysis, simple structural joint analyses, and certain other detail areas. Some additional light is shed on joint interface effects. The only major problem evolved was convection currents in and around the test specimen. This program in combination with an earlier insulated panel correlation program provides general confidence in the X-20 thermal analysis approach and methods.
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Papers on the Control of Distributed Aeroelastic Systems
Report Number: AFFDL TR 65-145
Author(s): M. L. Bandy; W. E. Langlois; P. K. C. Wang
Corporate Author: None Given
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 11/1/1965
Pages: 164
Contract: AF 33(657)-11545
Project: 8225
Task: 822501
AD Number: AD0627048
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Abstract Text:
This work was undertaken in order to gain a more fundamental understanding of the control of distributed parameter systems, with emphasis on the control of flexible aerodynamic vehicles. The main effort was on the development of a control theory for distributed parameter systems rather than the development of techniques for approximating distributed parameter systems by lumped parameter systems for which existing control theory is applicable.
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Table of Contents
Report Number: AFFDL TR 65-145 p. i-iv
Author(s):
Corporate Author: IBM San Jose Research Laboratory
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 11/1/965
Pages: 4
Contract: AF 33(657)-11545
Project: 8225
Task: 822501
AD Number: See AD0627048
Photo Enhancement: Not Needed
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Introduction
Report Number: AFFDL TR 65-145 p. 1-4
Author(s):
Corporate Author: IBM San Jose Research Laboratory
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 11/1/965
Pages: 4
Contract: AF 33(657)-11545
Project: 8225
Task: 822501
AD Number: See AD0627048
Photo Enhancement: Not Needed
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Equations of Motion for Elastic Bodies Entering a Planetary Atmosphere
Report Number: AFFDL TR 65-145 p. 5-28
Author(s): P. K. C. Wang; W. E. Langlois
Corporate Author: IBM San Jose Research Laboratory
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 11/1/965
Pages: 24
Contract: AF 33(657)-11545
Project: 8225
Task: 822501
AD Number: See AD0627048
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Application of Lyapunov's Direct Method to Stability Problems in Elastic and Aeroelastic Systems
Report Number: AFFDL TR 65-145 p. 29-64
Author(s): P. K. C. Wang
Corporate Author: IBM San Jose Research Laboratory
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 11/1/965
Pages: 38
Contract: AF 33(657)-11545
Project: 8225
Task: 822501
AD Number: See AD0627048
Photo Enhancement: Not Needed
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Asymptotic Stability of Equilibrium of a Simplified Aerodynamic Vehicle with Flexible Tail
Report Number: AFFDL TR 65-145 p. 65-71
Author(s): P. K. C. Wang
Corporate Author: IBM San Jose Research Laboratory
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 11/1/965
Pages: 9
Contract: AF 33(657)-11545
Project: 8225
Task: 822501
AD Number: See AD0627048
Photo Enhancement: Not Needed
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Stability Analysis of a Simplified Pitch-Controlled Flexible Aerodynamic Vehicle Via Lyapunov's Direct Method
Report Number: AFFDL TR 65-145 p. 72-83
Author(s): P. K. C. Wang
Corporate Author: IBM San Jose Research Laboratory
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 11/1/965
Pages: 12
Contract: AF 33(657)-11545
Project: 8225
Task: 822501
AD Number: See AD0627048
Photo Enhancement: Not Needed
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Optimum Control of a Class of Mixed Distributed and Lumped Parameter Systems
Report Number: AFFDL TR 65-145 p. 84-106
Author(s): P. K. C. Wang
Corporate Author: IBM San Jose Research Laboratory
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 11/1/965
Pages: 23
Contract: AF 33(657)-11545
Project: 8225
Task: 822501
AD Number: See AD0627048
Photo Enhancement: Not Needed
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Estimates for Truncation Errors of Infinite Dimensional Systems of Linear Ordinary Differential Equations
Report Number: AFFDL TR 65-145 p. 107-126
Author(s): M. L. Brady; P. K. C. Wang
Corporate Author: IBM San Jose Research Laboratory
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 11/1/965
Pages: 20
Contract: AF 33(657)-11545
Project: 8225
Task: 822501
AD Number: See AD0627048
Photo Enhancement: Not Needed
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An Improved Estimate for the Error of Truncation for an Infinite System of Ordinary Differential Equations
Report Number: AFFDL TR 65-145 p. 127-140
Author(s): M. L. Brady
Corporate Author: IBM San Jose Research Laboratory
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 11/1/965
Pages: 14
Contract: AF 33(657)-11545
Project: 8225
Task: 822501
AD Number: See AD0627048
Photo Enhancement: Not Needed
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Theory of Stability and Control for Distributed Parameter Systems. An Annotated Bibliography
Report Number: AFFDL TR 65-145 p. 141-164
Author(s): P. K. C. Wang
Corporate Author: IBM San Jose Research Laboratory
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 11/1/965
Pages: 26
Contract: AF 33(657)-11545
Project: 8225
Task: 822501
AD Number: See AD0627048
Photo Enhancement: Not Needed
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Experimental Program to Determine Effect of Crack Buckling and Specimen Dimensions on Fracture Toughness of Thin Sheet Materials
Report Number: AFFDL TR 65-146
Author(s): R. G. Forman
Corporate Author: Air Force Flight Dynamics Laboratory
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 1/1/1966
Pages: 64
Project: 1467
Task: 146704
AD Number: AD0483308
Photo Enhancement: Complete
Abstract Text:
This report presents test results on dimensional similitude requirements for plane stress fracture toughness testing of centrally notched Griffith panels. In addition to the similitude requirements data, the report also presents test results on crack buckling, slow crack extension, and crack tip yield zone size. This data is particularly useful in substantiating recent theoretical studies in fracture mechanics.
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Nine-Channel Data Acquisition System
Report Number: AFFDL TR 65-151
Author(s): Rod Sackett and Dan Hobel
Corporate Author: Whittaker Corporation
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 9/1/1965
Pages: 93
Features: + Foldout(s)
Contract: AF 33(657)-9574
Project: 1390
Task: 139001
AD Number: AD0626653
Photo Enhancement: Complete
Abstract Text:
This report describes the Nine-Channel Data Acquisition System developed for the U. S. Air Force by the Electronics Division of Whittaker Corporation under Contract Number AF 33(657)-9574. The Nine-Channel Data Acquisition System is designed for airborne recording and ground station reproduction of eight channels of flight information plus elapsed time. The system features a crash-proof magazine assembly to allow recovery of the recorded information in the event of a crash and subsequent fire. The Nine-Channel Data Acquisition System is intended for use in measuring and recording time histories of the principal flight parameters from which structural loads experienced by weapon systems in tactical roles can be detected. These structural loads can then be analyzed when the recorded data is processed and interpreted.
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X-20 High Temperature Side Window Test Evaluation
Report Number: AFFDL TR 65-155
Author(s): John C. McGinnis
Corporate Author: The Boeing Company
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 11/1/1965
Pages: 222
Features: + Foldout(s)
Contract: AF 33(615)-2013
Project: 1368
Task: 136802
AD Number: AD0477758
Photo Enhancement: Complete
Abstract Text:
The purpose of this program was to experimentally verify the X-20A side window assembly and provide experience for improved window design. The objective was to verify the structural integrity of an X-20A high temperature window design in the X-20A flight environment and provide test data to evaluate the design analysis and development procedures utilized. The window was subjected to a low-level boost vibration environment, outward acting (partial vacuum) limit boost pressure of 7.7 psia, and a simulated reentry heating time-temperature history. The window failed during the re-entry temperature cycle. The primary cause of failure was the high temperature gradient through the depth of the window frame of approximately 850 F which exceeded by a factor of 2 the ultimate design value. The extreme thermal gradient caused thermal curvature of the window frame which induced glass curvature in excess of allowable. Measured temperature and deflections are presented and compared with analytical values. A thermal analysis is presented and compared with test values. Deficiencies of the X-20 window design as determined from the test program are pointed out and suggested methods of improvement are given.
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Development of Subsonic Base Pressure Prediction Methods
Report Number: AFFDL TR 65-157 Volume 1
Author(s): J. E. Butsko; W. V. Carter; W. Herman
Corporate Author: GD/Convair, General Dynamics Corporation
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 9/1/1965
Pages: 171
Contract: AF 33(615)-1615
Project: 1366
Task: 136613
AD Number: AD0475670
Photo Enhancement: Not Needed
Abstract Text:
A combined analytic-experimental investigation of the subsonic base pressure phenomenon, especially as applied to blunt bodies typical of hypersonic flight vehicles, results in the development of a generalized method to predict base pressure in three-dimensional flow at subsonic speeds. A mathematical description of the fluid mechanics of steady two-dimensional subsonic base flow is developed. Two and three-dimensional wind tunnel testing of blunt based configurations is used to verify the two-dimensional analytic solution and obtain empirical relations which extend the analysis to three-dimensional base flow.
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Development of Subsonic Base Pressure Prediction Methods
Report Number: AFFDL TR 65-157 Volume 2
Author(s): J. E. Butsko; W. V. Carter; W. Herman
Corporate Author: GD/Convair, General Dynamics Corporation
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 9/1/1965
Pages: 125
Contract: AF 33(615)-1615
Project: 1366
Task: 136613
AD Number: AD0475671
Photo Enhancement: Complete
Abstract Text:
The results are presented of the wind tunnel test. The methods and scope of the experimental investigation are presented, as well as, the tabulated, plotted and photographic data obtained.
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The Light-Line-Tethering Technique for Determining the Aerodynamic Derivatives of an Air Cushion Vehicle
Report Number: AFFDL TR 65-159
Author(s): G. Kurylowich
Corporate Author: University of Toronto
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 6/1/1966
Pages: 136
Contract: AF 33(657)-8451
Project: 8219
Task: 821907
AD Number: AD0640209
Photo Enhancement: Complete
Abstract Text:
A complete feasibility study was performed on a new technique for determining ACV aerodynamic derivatives. A circular track simulated 'ground' while the vehicle, tethered to a centerpost by means of a light cable, flew a circular flight path above the track surface. A step on the 'ground' perturbed the vehicle from equilibrium and the resulting oscillations were recorded by a movie camera. The results obtained indicated that many derivatives were functions of height. Although scatter in the data permitted a qualitative study only, it was concluded that the scatter resulted from random errors in the recorded time histories and the manner in which the cable was attached to the vehicle. By making certain improvements in the experimental design and apparatus (especially using a larger track) it was concluded that all derivatives could be obtained with satisfactory precision with this technique.
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General Instability of Orthotropically Stiffened Cylinders. Part 1. Axial Compression, Torsion and Hdyrostatic Pressure Loadings
Report Number: AFFDL TR 65-161 Part 1
Author(s): Roger Milligan; Gerorge Gerard; C. Lakshmikantham; Herbert Becker
Corporate Author: Air Force Flight Dynamics Laboratory
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 7/1/1965
Pages: 114
Contract: AF 33(615)-1228
Project: 1467
Task: 146703
AD Number: AD0623801
Photo Enhancement: Complete
Abstract Text:
The general applicability of orthotropic stability theory to aerospace shell structures was examined experimentally. For this purpose a series of careful experiments were performed on orthotropically stiffened cylinders designed to fail in the elastic general instability mode under three separate loading conditions: axial compression, torsion and hydrostatic pressure. Experimental results obtained during the program verified that for all loading conditions considered linear orthotropic theory results in accurate predictions of cylinder strength. As a result of observed discrepancies between experiment and previously existing theory for longitudinally stiffened cylinders under axial compression, theoretical studies were initiated which resulted in the discovery of a new asymmetric failure mode for this cylinder configuration. Based on this new failure mode, good correlation between experiment and theory was obtained except when the longitudinal stiffened cylinder configurations approached that corresponding to an isotropic cylinder. Other theoretical investigations performed during the program established that cylinder boundary conditions have a pronounced effect on the buckling strength of orthotropic cylinders under hydrostatic pressure loading.
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General Instability of Orthotropically Stiffened Cylinders. Part 2. Bending and Combined Compression and Bending.
Report Number: AFFDL TR 65-161 Part 2
Author(s): C. Lakshmikantham; Geroge Gerard; Roger Milligan
Corporate Author: Air Force Flight Dynamics Laboratory
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 8/1/1965
Pages: 41
Contract: AF 33(615)-1228
Project: 1467
Task: 146703
AD Number: AD0623810
Photo Enhancement: Complete
Abstract Text:
As part of a general program to determine the applicability of linear orthotropic theory to the design of cylindrical shells under various loading conditions, a theoretical and experimental investigation was performed on the general instability of orthotropic cylinders under bending and combined axial compression and bending loading. Based on a simple approximation for the asymmetric buckling pattern, theoretical results suitable for design use were obtained for the buckling of orthotropic cylinders for both bending and combined loading conditions. It was shown that the buckling stress for orthotropic cylinders under bending or axial compression loading are equal which agrees with previous results for isotropic cylinders. Theoretical results were evaluated by means of a series of careful experiments performed on orthotropically stiffened cylinders designed to fail in the elastic general instability mode. For both bending loading and the combined axial and bending loading condition, experimental results were in good agreement with the theory.
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Modeling Techniques for Sonic Fatigue Prediction
Report Number: AFFDL TR 65-171
Author(s): P. Wang
Corporate Author: North American Aviation, Inc.
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 6/1/1966
Pages: 140
Contract: AF 33(615)-1743
Project: 1471
Task: 147101
AD Number: AD0648078
Photo Enhancement: Complete
Abstract Text:
The principles of static and dynamic similitude were applied to typical complex structural components for the purpose of examining the application of modeling techniques to sonic fatigue predictions. Modeled specimens of curved panels, honeycomb sandwich flat panels, and honeycomb sandwich cantilever beams have been tested. The tests were conducted on full scale 5/8, and 3/8 size models. The tests and analyses demonstrated that scale reductions of linear panel dimensions, and other size factors necessary in the fabrication of models, may be separately considered in maintaining the established similitude relationships. Both random spectra and discrete frequency acoustic excitation are considered. Stress correlation is the critical parameter in modeling for acoustic fatigue. True models with exact geometric scaling in all elements are not necessary. Adequate modeling is obtained by maintaining the same aspect ratio and modes for the specimen and model. The frequency and stress then vary at predetermined magnitudes with a functional relationship to damping, amplitude, and cross-section (thickness) geometric parameters. Non-linear effects are dependent on excitation levels. In general, a prerequisite to sonic fatigue tests is a knowledge of the non-linearity induced by damping and amplitude for each specimen. The experimental data confirms the application of basic procedures formulated by Miles, Palmgren, and Miner which minimize the requirement for random excitation in the use of modeling techniques for sonic fatigue predictions.
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The Effect Of Plastic Deformation On The Strain Energy Release Rate In A Centrally Notched Plate Subjected To Uniaxial Tension
Report Number: AFFDL TR 65-186
Author(s): Forman, Royce G.
Corporate Author: Air Force Flight Dynamics Laboratory
Laboratory: AF Flight Dynamics Laboratory
Publication Date: 1/1/1966
Pages: 36
Contract: Laboratory Research - No Contract
Project: 1467
Task: 146704
AD Number: AD0632454
Photo Enhancement: Not Needed
Abstract Text:
By using the Dugdale model for a crack in a plate, an improved formula was derived for the strain energy release rate, G. The formula has the same form as the solution for a linear elastic plate, except a correction factor is used which corrects for both the effect of yielding and the finite width of the plate. Curves are presented giving the values of the correction factor, and they indicate that the nominal stress to yield stress ratio has a pronounced effect on the strain energy release rate.
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Time Based Analysis of Control Activities and Information Requirements for V/STOL
Report Number: AFFDL TR 65-193
Author(s): Clarence A. Semple; Ronald W. Schwartz
Corporate Author: Bunker-Ramo Corporation
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 6/1/1966
Pages: 74
Features: + Diagram(s) + Table(s)
Contract: AF 33(657)-8600
Project: 6190
Task: 619011
AD Number: AD0480325
Photo Enhancement: Not Needed
Notes: Distribution Conflict
Abstract Text:
An analytic study was conducted to delineate operator control activities and information requirements associated with the operation of a hypothetical two-place V/STOL jet fighter aircraft. A vectored lift plus vectored lift-cruise propulsion configuration was assumed. A total V/STOL tactical mission was divided into nine mission segments. Commonalities among control activities during various mission segments are discussed. Short-field and vertical takeoff and landing segments received primary emphasis. Time histories of anticipated control activities during the takeoff and landing segments were analyzed in detail in order to determine information requirements for flight data displays and operational features of thrust vector and thrust magnitude controls. Based upon operator task loading estimates, a suggested gross division of crew duties is presented. Based upon experience gained in using cockpit mockups throughout the study, suggestions for functional groupings of panel console areas are included for a side-by-side seating arrangement.
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A Fortran IV Program To Derive The Equations Of Motion Of Systems
Report Number: AFFDL TR 65-194
Author(s): Westerwick, Robert A.; Brown, J. B.
Corporate Author: General Dynamics/Convair San Diego Calif
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 9/1/1966
Pages: 136
Contract: AF 33(615)-1836
Project: 8225
Task: 822501
AD Number: AD0648720
Photo Enhancement: Not Needed
Abstract Text:
The state of the art of computer development has reached the point where it is now possible to sacrifice some of the extremely high speed of arithmetic computations in order to relieve man of tedium in another area - that of algebraic computation. The report presents the results of a development which uses an IBM 7090/94 computer to derive in nonnumeric terms the equations of motion of a system. This system can be composed of any number of masses which are acted upon by forces due to springs, dampers, gravity, and external forces.
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The Evolution of USAF Environmental Testing
Report Number: AFFDL TR 65-197
Author(s): V. J. Junker
Corporate Author: Flight Dynamics Laboratory
Laboratory: Flight Dynamics Laboratory
Publication Date: 10/1/1965
Pages: 82
Contract: Laboratory Research - No Contract
Project: 1370
Task: 137010
AD Number: AD0625543
Photo Enhancement: Not Needed
Abstract Text:
This report presents supporting data and background information on the origination and development of natural and induced environmental tests intended for USAF aerospace and ground equipment. The information provided in the discussion portion of the test writeups is intended to give the designer, application engineer, and those individuals responsible for specifying test requirements a clearer understanding of the interpretation, application, and relationship of tests as called out in various environmental test documents. The growth of environmental criteria and test procedures is traced from the first Army Air Force specification No. 41065 dated 7 December 1945 to MIL-STD-810A (USAF) dated 23 Jun 1964. Included also in this report are discussions on environmental test specifications MIL-T-5422, MIL-E5272, and MIL-E-4970.
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Skin Friction, Heat Transfer, and Pressure Measurements on Hypersonic Inlet Compression Surfaces in the Mach Number Range 7.5 to 16
Report Number: AFFDL TR 65-199
Author(s): M. O. Ryder, Jr.
Corporate Author: Cornell Aeronautical Laboratory, Inc.
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 12/1/1965
Pages: 194
Contract: AF 33(615)-1845
Project: 1366
Task: 136605
AD Number: AD0627798
Photo Enhancement: Complete
Abstract Text:
An experimental study of boundary layer flow, under the influence of adverse pressure gradients typical of hypersonic inlets, was conducted on two two-dimensional and three axisymmetric compression surface models instrumented with skin friction, heat transfer and pressure gages. Tests were conducted over a Mach and Reynolds number range of 7.5 to 16 and 32,000 per ft. to 4,700,000 per ft., respectively. The boundary layers on the two-dimensional models were laminar and attached for all conditions tested. Local laminar separation occurred for some conditions of the axisymmetric tests. Boundary layer transition occurred for the high Reynolds number runs at a Mach number of 8 on the axisymmetric models but the adverse pressure gradients were not large enough to cause the turbulent boundary layers to separate. The skin friction gages gave a more accurate indication of localized boundary layer separation than either the heat transfer or static pressure distributions on the models tested.
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Application of Pilot-Controller Integration Techniques to a Representative V/STOL Aircraft
Report Number: AFFDL TR 65-200
Author(s): John W. Gaul
Corporate Author: Bell Aerosystems Company
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 10/1/1965
Pages: 158
Features: + Foldout(s)
Contract: AF 33(615)-1866
Project: None Given
Task: None Given
AD Number: AD0633269
Photo Enhancement: Not Needed
Abstract Text:
The report presents final results of a study of the application of Pilot-Controller Integration (PCI) design techniques to the flight control system of a representative V/STOL aircraft. Under this program the validity of the concept was established in the application to the X-22A V/STOL. In this application the PCI technique indicated the areas of the X-22A flight control system where modifications would result in the greatest improvement to the probability of mission accomplishment. Design modifications were made and an iteration using the technique was accomplished and the payoff was evaluated. The digital program was developed and applied to the X-22A has general applicability to other aircraft. Several improvements to this program as well as to the details of technique application are suggested.
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Simulated Landing Approaches of an Unaugmented C-5A Configuration
Report Number: AFFDL TR 65-210
Author(s): F. D. Newell; M. L. E. Parrag; G. Bull
Corporate Author: Cornell Aeronautical Laboratories
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 3/1/1966
Pages: 82
Features: + Foldout(s)
Contract: AF 33(615)-2411
Project: 8219
Task: 821905
AD Number: AD0482810
Photo Enhancement: Not Needed
Abstract Text:
Expected ranges of unaugmented longitudinal and lateral-directional handling qualities of the C-5A class airplane were simulated and evaluated in a variable-stability B-26 for the instrument-landing.
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Statics and Stability of Thin-Walled Elastic Beams: Part I. Formulation of Fundamental Equations
Report Number: AFFDL TR 65-213 Part 1
Author(s): E. Giangreco; M. Capruso; M. Como
Corporate Author: University of Naples
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 1/1/1966
Pages: 59
Contract: AF 61(052)-813
Project: 1467
Task: 146703
AD Number: AD0480031
Photo Enhancement: Not Needed
Abstract Text:
Fundamental equations were formulated of elastic equilibrium of thin walled beams subject to general loads and dislocations starting only from the hypothesis of non-deformed transverse cross sections. Formulation was made of the fundamental equations of dynamic stability of thin walled beams subject to general conservation loads and dislocations by use of a systematic geometrical approach.
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Estimation of Flying Qualities of Piloted Airplanes
Report Number: AFFDL TR 65-218
Author(s): Robert J. Woodcock; Douglas E. Drake
Corporate Author: Douglas Aircraft Co.
Laboratory: Air Force Flight Dynamics Laboratory
Publication Date: 4/1/1966
Pages: 147
Contract: AF 33(616)-6460
Project: 8219
Task: None Given
AD Number: AD0483622
Photo Enhancement: Not Needed
Abstract Text:
Methods, ranging from rigorous and complicated to simple and approximate, are presented for estimating flying qualities in accordance with such specifications as MIL-F-8785 (ASG). Aerodynamic and inertial data are assumed to be known. Intended mainly for design use, the report gives enough detail to indicate derivations and conditions for validity. Topics include the static and dynamic, controls-fixed and controls-free aspects of aircraft stability, control, and trim. Although emphasis is on linear analysis, methods are given or indicated for such nonlinear problems as drag, pitch-up, inertial coupling, and spinning. Appendixes give an introduction to aeroelastic effects, ways to analyze control tabs, a derivation of the controls-free equations of motion, and an introduction to root locus analysis.
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