352 



THEORY OF SEAKEEPING 



ilar to a spring-mass sj'stem with low damping. (This 

 simple example does not pro\'ide aerodynamic data of 

 any particular value but was chosen to demonstrate 

 the use of the analyzer and the type of problem to which 

 it is applicable.) 



To set up and run these four spectra on the electronic 

 analyzers required about IV2 hours. To read the time- 

 history records and run the same four analyses digitally 

 would recjuire an estimated 40 to 50 man-hours — which 

 explains why no numerically calculated check points 

 are shown in the figure. 



Accuracy and Reliability Considerations 



Electronrc analog analyzers might introduce errors 

 in the order of plus or minus 10 per cent where a digital 

 computer can process data to almost any degree of pre- 

 cision that might practically be desired. Conseciuentl.y, 

 a given data sample can be statistically analyzed by a 

 digital computer more precisely than by an analog 

 machine. 



However, it must be remembered that we are dealing 

 with statistical quantities. Consequentl.y, if an experi- 

 ment or test is repeated several times, sizeable varia- 

 tions in experimental results occur even if the instru- 

 ments and analyzing processes introduce n(j error at 

 all. For example, consider again the wing loads power 

 spectrum, pre\'iously shown in L'ig. 8, which is fairly 

 typical of the type of problems encountered. The sta- 

 tistical reliability in this case was such that only one 

 out of three tests would be expected to yield power es- 

 timates within plus or minus 10 per cent of the true 

 value. If the length of the data sample could be in- 

 creased by a factor of 20, however, 19 out of 20, instead 

 of 1 out of 3, of the tests would be expected to yield re- 

 sults within plus or miiuis 10 per cent of the true value. 



In analysis of actual data .•samples, then, consider- 

 ation of the statistical aspects of the problem usually 

 shows that improved reliability might be obtained, not 

 by improving computational accuracy, but by analj^z- 

 ing longer data samples. 



Longer samples are not always possible, especially 

 in airplane or missile flights, where steady flight con- 

 ditions often cannot be maintained for longer than a 

 few seconds. Where longer samples can be secured, 

 however, the electronic analyzers can economically 

 handle samples of such length that analysis by any 

 other process would be quite impractical. 



In conclusion, the various statistical analyses re- 

 quired in aeronautical research and development can 

 be secured rapidly and economically by the use of elec- 

 tronic analog analyzers. The accuracy of the analog 



analyzers in processing a specific data sample is some- 

 what inferior to that available form digital computers. 

 This factor is normally outweighted, however, by the 

 analog equipment's capability for economically han- 

 dling longer data samples and providing improved sta- 

 tistical reliability. 



It appears that more extensive use of the analog analy- 

 sis technitiues might facilitate further advancement in 

 the application of statistical methods to aerodynamic 

 problems. 



References 



1 Wiener, Xorbert, "Ivxtrapolation, Interpolation, 

 and Smoothing of Stationary Time Series With Engi- 

 neering Applications," The Technology Press, Mas- 

 sachusetts Institute of Technology, Cambridge, Mass., 

 and John Wiley & Sons, Inc., New York, 1949. 



2 Tukey, John W., "The Sampling Theory of Power 

 Spectrum Estimates," Symposium on Applications of 

 Autocorrelation Analysis to Physical Problems (spon- 

 sored by ONR, Department of the Navy), Woods Hole, 

 Mass., June 13-14, 1949, pp. 4ti-(>7. 



3 Rice, S. O., "Mathematical Analysis of Random 

 Xoise," Parts I and II, Bell System, Technical Journal, 

 Vol. XXIII, No. 3, July, 1944, pp. 282-332; Parts III 

 and IV, Vol. XXIV, No. 1, January, 1945, pp. 46-156. 



4 Clementson, Gerhardt C, "An Investigation of the 

 Power Spectral Density of Atmospheric Turbulence," 

 Rep. No. 6445-T-31 (Sc.D. Thesis), Instrumentation 

 Laboratory, Massachusetts Institute of Technology, 

 Cambridge, Mass., May, 1950. 



5 Liepmann, H. W., "On the Application of Sta- 

 tistical Concepts to the Buffeting Problem," Journal of 

 the Aeronautical Sciences, Vol. 19, No. 12, December, 

 1952, pp. 793-800, 822. 



6 Summers, R. A., "A Statistical Description of 

 Large-Scale Atmosphere Turbulence," Rep. T-55 (Sc.D. 

 Thesis), Instrumentation Laboratory, Massachusetts 

 Institute of Technology, Cambridge, Alass., May, 1954. 



7 Press, Harry, and Houbolt, John C, "Some Ap- 

 plications of Generalized Harmonic Analysis to Gust 

 Loads on Airplanes," Journal of the Aeronautical 

 Sciences, Vol. 22, No. 1, January, 1955, pp. 17-26, 60. 



8 Chilton, Robert G., "Some Measurements of 

 Atmospheric Turbulence Obtained From Flow-Direction 

 Vanes Mounted on an Airplane," NACA TN 3313, 

 1954. 



9 Lee, Y. W., "Application of Statistical Methods to 

 Communication Prol)lems," Tech. Rep. No. 181, Re- 

 search Laboratory of Electronics, Massachusetts In- 

 stitute of Technology, September 1, 1950. 



