APPENDIX D 



Analog Equipment for Processing 

 Randomly Fluctuating Data' 



FRANCIS B. SMITH' 



Experimental studies of buffeting, flutter, and atmospheric 

 turbulence produce data which are not amenable to analysis 

 by the usual process of measuring or calculating discrete 

 values of static force, pressure, or moment. Instead, where 

 randomly fluctuating quantities are involved, it becomes 

 necessary to use statistical methods to analyze and describe 

 the phenomenon being investigated. The types of informa- 

 tion usually required are probability distributions, power 

 spectra, and cross spectra. In order to avoid the time and 

 expense involved in using conventional numerical methods 

 for securing the various statistical analyses, the NACA uses 

 a technique of recording data on magnetic tape and playing 

 it back into electronic analog analyzers which perform the 

 desired analyses and automatically plot the results. The 

 magnetic tape recording system and the analog analyzers 

 are described in this paper and their application to aero- 

 nautical problems is illustrated. A discussion of the com- 

 parative accuracy and reliability of the numerical and 

 analog methods is also included. 



Introduction 



In much of the experimental work undertaken in 

 aeronautical research and development it is possible 

 to set up experiments so that the amplitude of any quan- 

 tity being measured remains \-ery nearly constant dur- 

 ing a given test run. In this case a precise measure of 

 the static level is sought and any fluctuations in the 

 level occurring during the run are considered to be 

 "noise" which must be eliminated by filters or faired 

 through on the time-historjf record. 



However, manj' phenomena being studied produce 

 data in which random amplitude fluctuations are in- 

 herent and measurement of average or faired levels only 

 is of little or no value. Typical examples are gun aim- 

 ing errors encountered in fire control systems, loads im- 

 posed on aii'planes by turbulence of buffeting, stresses 

 produced by engine noise or vibration, and aircraft 

 landing gear loads caused b,v rough runwa\'s. In these 

 cases, the information sought must be secured b}' anal- 



' Presented at the Electronic Aids to the Aircraft Industry 

 Session, Twenty-Third Annual Meeting, IAS, Xew York, X. Y., 

 January 24-27, 1955. Reprinted with the kind permission of the 

 Aeronautical Engineering Review, May 1955 issue. 



^ .Aeronautical Research Scientist, Instrument Research Divi- 

 sion, Langley .Aeronautical Laboratory, XAC.A. 



ysis and study of the random amplitude fluctuations 

 about the mean value. 



The most practical way to describe (luantitatively 

 these amplitude variations is to use the statistical tech- 

 niciues which have been devised for analyzing stationary 

 random time series. The simplest and most familiar 

 of these techniciues is the probability distribution, 

 which, for example, has been used for years to describe 

 atmospheric turbulence. Recently, the generalized 

 liarmonic analysis techniciues have been developed and 

 are being successfully applied to many random-type 

 data anal_ysis problems. 



The theoretical aspects of these techniques have been 

 discussed by Wiener [1],^ Tukey [2], and Rice [-3] and 

 specific applications to aerodynamic problems have been 

 described by Clementson [4], Liepmann [5], Summers 

 [()]. Pre-ss [7], Chilton [8] and others. 



These authors have demonstrated that statistical 

 techniques are extremely useful in aeronautical re- 

 search. However, if conventional time-history records 

 and numerical data work-up procedures are used to 

 secure the various reciuired analyses, the application of 

 these techniques to actual samples of experimental data 

 is a time-consuming and expensive process. This is es- 

 pecially true in the case of power and cross spectra de- 

 terminations. In addition to the digital computer ex- 

 pense invoh-ed in making the thousands of required 

 numerical calculations, several days may be required 

 to read the necessaiy number of data points from the 

 time-historj- record. These factors often seriously re- 

 strict the number of statistical analyses that might be 

 made, or force one to limit severely the length of the 

 data samples and to accept the consequent poor sta- 

 tistical reliability. 



To overcome these limitations the XACA has com- 

 bined commercially available electronic equipment with 

 NACA-developed components to pnn-ide an analog 

 data processing facility which produces the reciuii'ed sta- 

 tistical analj'ses rapidly and inexpensively. This fa- 

 cility consists of four basic elements: (1) magnetic- 

 tape data storage and playback system, (2) a probabil- 

 ity distribution analyzer, (3) a power spectral density 

 analyzer, and (4) a cross spectral densitj- anal.yzer. 

 This paper will describe these pieces of equipment, 



^ Xvuiibers in brackets designate References at the end of the 

 paper. 



346 



