DOT/FAA/AR-05/19 

Office of Aviation Research 

Washington, D.C. 20591

A Study of Sampling Rate 

Requirements for Load 

Parameter Statistics 

August 2005 

Final Report 

This document is available to the U.S. public 

through the National Technical Information 

Service (NTIS), Springfield, Virginia 22161. 

U.S. Department of Transportation 

Federal Aviation Administration
NOTICE 

This document is disseminated under the sponsorship of the U.S. 

Department of Transportation in the interest of information exchange. The 

United States Government assumes no liability for the contents or use 

thereof. The United States Government does not endorse products or 

manufacturers. Trade or manufacturer's names appear herein solely 

because they are considered essential to the objective of this report. This 

document does not constitute FAA certification policy. Consult your local 

FAA aircraft certification office as to its use. 

This report is available at the Federal Aviation Administration William J. 

Hughes Technical Center's Full-Text Technical Reports page: 

actlibrary.tc.faa.gov in Adobe Acrobat portable document format (PDF). 
 Technical Report Documentation Page

1. Report No.

DOT/FAA/AR-05/19 

2. Government Accession No. 3. Recipient's Catalog No.

5. Report Date

August 2005 

4. Title and Subtitle

A STUDY OF SAMPLING RATE REQUIREMENTS FOR LOAD PARAMETER 

STATISTICS 6. Performing Organization Code

7. Author(s)

John Rustenburg*, Daniel O. Tipps*, Donald Skinn*, and Thomas DeFiore** 

8. Performing Organization Report No.

UDR-TR-2004-00146 

10. Work Unit No. (TRAIS)

RPD-510 

9. Performing Organization Name and Address

*University of Dayton Research Institute **Federal Aviation Administration 

 Structural Integrity Division William J. Hughes Technical Center 

 300 College Park Airport And Aircraft Safety 

 Dayton, OH 45469-0120 Research and Development Division 

 Airworthiness Assurance 

Atlantic City International Airport, 

New Jersey 08405 

11. Contract or Grant No.

01-G005 

13. Type of Report and Period Covered

Final Report 

12. Sponsoring Agency Name and Address

U.S. Department of Transportation 

Federal Aviation Administration 

Office of Aviation Research 

Washington, DC 20591 

14. Sponsoring Agency Code

ANM-110

15. Supplementary Notes

16. Abstract

The objective of the operational loads monitoring research is to support the Federal Aviation Administration Operational Loads 

program by developing new and improved methods and criteria for processing and presenting large commercial transport 

airplane flight and ground loads usage data. This report presents the result of a study to determine the minimum sampling rates 

required for selected parameters to ensure the detection of peaks and peak amplitudes representative of the basic signal for use in 

deriving operational load statistics. The selected parameters included vertical, lateral, and longitudinal accelerations, and pitch 

and bank angle, as well as elevator, aileron, and rudder deflections recorded at higher than normal sampling rates obtained 

during 108 flights of an Airbus A319 used in normal commercial operations. The study included (1) the use of power spectral 

density analyses of some high-activity flights to evaluate the frequency content of the recorded data, (2) an investigation of 

sampling rates required to identify peaks and peak amplitudes based on the frequency content of the parameters, and (3) an 

evaluation of the impact of varying sampling rates on derived operational load statistics. Resulting sampling rates were 

compared to sampling rate requirements specified in Title 14 Code of Federal Regulations (CFR) Part 121, Appendices B and 

M. Although the data used in the study were recorded at higher than normal sampling rates, it was concluded that the sampling 

rates were not high enough to determine the minimum sampling rates for detection of peaks and associated peak amplitudes with 

any certainty. Although the sampling rates specified in 14 CFR Part 121 appear adequate to identify peaks, they are too low to

identify the associated peak amplitude. 

17. Key Words

Digital flight data recorder, Load parameter recording, 

Parameter sampling rates, Parameter statistics 

18. Distribution Statement

This document is available to the public through the National 

Technical Information Service (NTIS), Springfield, Virginia 

22161. 

19. Security Classif. (of this report)

Unclassified 

20. Security Classif. (of this page)

Unclassified 

21. No. of Pages

150 

22. Price

N/A 

Form DOT F1700.7 (8-72) Reproduction of completed page authorized 
PREFACE 

This report covers the results from a study to evaluate the effect of different sampling rates on 

some operational load parameter statistics. The objective of the study was to determine if 

existing sampling rates could provide reasonable estimates of accelerations, pitch and bank 

angles, and control surface deflection occurrences from measured flight loads data. The Flight 

Systems Integrity Group of the Structural Integrity Division of the University of Dayton 

Research Institute (UDRI) performed this study in support of the Federal Aviation 

Administration (FAA) Airborne Data Monitoring Systems Research Program. Mr. Daniel Tipps 

provided UDRI oversight direction for this study effort. Mr. John Rustenburg directed the data 

processing effort, performed the data analysis, and prepared the report. Mr. Donald Skinn 

established data reduction criteria, developed the data reduction algorithms, and provided the 

data. Mr. Thomas DeFiore of the FAA William J. Hughes Technical Center was the program 

manager for the FAA and also provided valuable insight to the accomplishment of the study 

objective. 

As only 108 flights of A319 data were used in this study, it is recommended that the exceedance 

data contained herein not be used for certification or design studies. The 108 flights were used 

only to determine the effects of a variety of sample rates on the precision of selected parameters 

recorded on the Digital Flight Data Recorder. 

iii/iv
TABLE OF CONTENTS 

Page 

EXECUTIVE SUMMARY xvii 

1. INTRODUCTION 1 

2. GENERAL DATA PROCESSING DISCUSSION 2 

2.1 Data Digitization 2 

2.2 Data Sampling Rate 2 

2.3 Power Spectral Density 3 

2.4 Parameter Peak Amplitude 4 

2.5 Downsampling 4 

2.6 Peak Counting 4 

2.7 Effect of Bin Size on Cumulative Occurrences 5 

2.8 Effect of Sampling Rate on Bin Counts 5 

3. SAMPLING RATE STUDY 6 

3.1 Power Spectral Density Analysis 6 

3.1.1 Vertical Load Factor PSDs 7 

3.1.2 Lateral Load Factor PSDs 7 

3.1.3 Longitudinal Load Factor PSDs 8 

3.1.4 Pitch and Bank Angle PSDs 8 

3.1.5 Control Surface Deflection Angle PSDs 9 

3.2 Cumulative Occurrences Statistics 9 

3.2.1 Incremental Vertical Load Factor Statistics 10 

3.2.2 Lateral Load Factor Statistics 10 

3.2.3 Longitudinal Load Factor Statistics 11 

3.2.4 Pitch and Bank Angle Statistics 11 

3.2.5 Control Surface Deflection Angle Statistics 11 

3.3 Minimum Sampling Rates for Amplitude Detection 12 

3.4 Comparison of Sampling Rate Requirements 12 

3.5 Derivation of Flight Control Deflection Statistics 13 

4. CONCLUDING REMARKS 14 

5. REFERENCES 15 

v 
APPENDICES 

A—Appendix B to 14 CFR Part 121, Airplane Flight Recorder Specification 

B—Appendix M to 14 CFR Part 121, Airplane Flight Recorder Specifications 

C—Derivation of Flight Control Deflection Statistics From Data Obtained at 

Low Sampling Rates 

D—Comments on UDR-TR-2004-00146, R. Howes, Cessna Aircraft Company

vi 
LIST OF FIGURES 

Figure Page 

1 Analog Signal to Digitized Binning 16 

2 Digitized Aileron Signal 16 

3 Peak Cropping due to Digitization 17 

4 Sine Wave Sampled at Twice its Frequency 17 

5 Analog Signal Sampled at Different Sampling Rates 18 

6 Vertical Load Factor Time History Sampled at Different Sampling Rates 18 

7 Vertical Load Factor PSD, Preflight 19 

8 Variation of rms Vertical Load Factor With Frequency, Postflight 19 

9 Calculation of Maximum Peak Amplitude Error 20 

10 Downsampling Technique 20 

11 Peak Between Mean Counting 21 

12 Effect of Using Different Class Intervals on an Incremental Vertical Load Factor 

Distribution 21 

13 Effect of Sampling Rate on Phase of Flight Bin Count 22 

14 Incremental Vertical Load Factor Time History, Flight Sequence 3 22 

15 Normalized PSD of Incremental Vertical Load Factor, Flight Sequence 3, 

Preflight 23 

16 Percent of Total Incremental Vertical Load Factor rms vs Frequency, Flight 

Sequence 3, Preflight 23 

17 Normalized PSD of Incremental Vertical Load Factor, Flight Sequence 3, 

in Flight 24 

18 Percent of Total Incremental Vertical Load Factor rms vs Frequency, Flight 

Sequence 3, in Flight 24 

19 Normalized PSD of Incremental Vertical Load Factor, Flight Sequence 3, 

Postflight 25 

vii 
20 Percent of Total Incremental Vertical Load Factor rms vs Frequency, Flight 

Sequence 3, Postflight 25 

21 Lateral Load Factor Time History, Flight Sequence 3 26 

22 Normalized PSD of Lateral Load Factor, Flight Sequence 3, Preflight 26 

23 Percent of Total Lateral Load Factor rms vs Frequency, Flight Sequence 3, 

Preflight 27 

24 Normalized PSD of Lateral Load Factor, Flight Sequence 3, in Flight 27 

25 Percent of Total Lateral Load Factor rms vs Frequency, Flight Sequence 3, 

in Flight 28 

26 Normalized PSD of Lateral Load Factor, Flight Sequence 3, Postflight 28 

27 Percent of Total Lateral Load Factor rms vs Frequency, Flight Sequence 3, 

Postflight 29 

28 Longitudinal Load Factor Time History, Flight Sequence 3 29 

29 Normalized PSD of Longitudinal Load Factor, Flight Sequence 3, Preflight 30 

30 Percent of Total Longitudinal Load Factor rms vs Frequency, Flight Sequence 3, 

Preflight 30 

31 Normalized PSD of Longitudinal Load Factor, Flight Sequence 3, in Flight 31 

32 Percent of Total Longitudinal Load Factor rms vs Frequency, Flight Sequence 3, 

in Flight 31 

33 Normalized PSD of Longitudinal Load Factor, Flight Sequence 3, Postflight 32 

34 Percent of Total Longitudinal Load Factor rms vs Frequency, Flight Sequence 3, 

Postflight 32 

35 Pitch Angle Time History, Flight Sequence 3 33 

36 Normalized PSD of Pitch Angle, Flight Sequence 3, in Flight 33 

37 Percent of Total Pitch Angle rms vs Frequency, Flight Sequence 3, in Flight 34 

38 Bank Angle Time History, Flight Sequence 3 34 

39 Normalized PSD of Bank Angle, Flight Sequence 3, in Flight 35 

40 Percent of Total Bank Angle rms vs Frequency, Flight Sequence 3, in Flight 35 

viii 
41 Aileron Angle Time History, Flight Sequence 3 36 

42 Normalized PSD of Aileron Angle, Flight Sequence 3, in Flight 36 

43 Percent of Total Aileron Angle rms vs Frequency, Flight Sequence 3, in Flight 37 

44 Elevator Angle Time History, Flight Sequence 3 37 

45 Normalized PSD of Elevator Angle, Flight Sequence 3, in Flight 38 

46 Percent of Total Elevator Angle rms vs Frequency, Flight Sequence 3, in Flight 38 

47 Rudder Angle Time History, Flight Sequence 3 39 

48 Normalized PSD of Rudder Angle, Flight Sequence 3, in Flight 39 

49 Percent of Total Rudder Angle rms vs Frequency, Flight Sequence 3, in Flight 40 

50 Incremental Vertical Load Factor Time History, Flight Sequence 35 40 

51 Normalized PSD of Incremental Vertical Load Factor, Flight Sequence 35, 

Preflight 41 

52 Percent of Total Incremental Vertical Load Factor rms vs Frequency, Flight 

Sequence 35, Preflight 41 

53 Normalized PSD of Incremental Vertical Load Factor, Flight Sequence 35, in 

Flight 42 

54 Percent of Total Incremental Vertical Load Factor rms vs Frequency, Flight 

Sequence 35, in Flight 42 

55 Normalized PSD of Incremental Vertical Load Factor, Flight Sequence 35, 

Postflight 43 

56 Percent of Total Incremental Vertical Load Factor rms vs Frequency, Flight 

Sequence 35, Postflight 43 

57 Lateral Load Factor Time History, Flight Sequence 35 44 

58 Normalized PSD of Lateral Load Factor, Flight Sequence 35, Preflight 44 

59 Percent of Total Lateral Load Factor rms vs Frequency, Flight Sequence 35, 

Preflight 45 

60 Normalized PSD of Lateral Load Factor, Flight Sequence 35, in Flight 45 

61 Percent of Total Lateral Load Factor rms vs Frequency, Flight Sequence 35, in 

Flight 46 

ix 
62 Normalized PSD of Lateral Load Factor, Flight Sequence 35, Postflight 46 

63 Percent of Total Lateral Load Factor rms vs Frequency, Flight Sequence 35, 

Postflight 47 

64 Longitudinal Load Factor Time History, Flight Sequence 35 47 

65 Normalized PSD of Longitudinal Load Factor, Flight Sequence 35, Preflight 48 

66 Percent of Total Longitudinal Load Factor rms vs Frequency, Flight Sequence 35, 

Preflight 48 

67 Normalized PSD of Longitudinal Load Factor, Flight Sequence 53, in Flight 49 

68 Percent of Total Longitudinal Load Factor rms vs Frequency, Flight Sequence 35, 

in Flight 49 

69 Normalized PSD of Longitudinal Load Factor, Flight Sequence 35, Postflight 50 

70 Percent of Total Longitudinal Load Factor rms vs Frequency, Flight Sequence 35, 

Postflight 50 

71 Pitch Angle Time History, Flight Sequence 35 51 

72 Normalized PSD of Pitch Angle, Flight Sequence 35, in Flight 51 

73 Percent of Total Pitch Angle rms vs Frequency, Flight Sequence 35, in Flight 52 

74 Bank Angle Time History, Flight Sequence 35 52 

75 Normalized PSD of Bank Angle, Flight Sequence 35, in Flight 53 

76 Percent of Total Bank Angle rms vs Frequency, Flight Sequence 35, in Flight 53 

77 Aileron Angle Time History, Flight Sequence 35 54 

78 Normalized PSD of Aileron Angle, Flight Sequence 35, in Flight 54 

79 Percent of Total Aileron Angle rms vs Frequency, Flight Sequence 35, in Flight 55 

80 Elevator Angle Time History, Flight Sequence 35 55 

81 Normalized PSD of Elevator Angle, Flight Sequence 35, in Flight 56 

82 Percent of Total Elevator Angle rms vs Frequency, Flight Sequence 35, in Flight 56 

83 Rudder Angle Time History, Flight Sequence 35 57 

84 Normalized PSD of Rudder Angle, Flight Sequence 35, in Flight 57 

x 
85 Percent of Total Rudder Angle rms vs Frequency, Flight Sequence 35, in Flight 58 

86 Incremental Vertical Load Factor Time History, Flight Sequence 62 58 

87 Normalized PSD of Incremental Vertical Load Factor, Flight Sequence 62, 

Preflight 59 

88 Percent of Total Incremental Vertical Load Factor rms vs Frequency, Flight 

Sequence 62, Preflight 59 

89 Normalized PSD of Incremental Vertical Load Factor, Flight Sequence 62, in 

Flight 60 

90 Percent of Total Incremental Vertical Load Factor rms vs Frequency, Flight 

Sequence 62, in Flight 60 

91 Normalized PSD of Incremental Vertical Load Factor, Flight Sequence 62, 

Postflight 61 

92 Percent of Total Incremental Vertical Load Factor rms vs Frequency, Flight 

Sequence 62, Postflight 61 

93 Lateral Load Factor Time History, Flight Sequence 62 62 

94 Normalized PSD of Lateral Load Factor, Flight Sequence 62, Preflight 62 

95 Percent of Total Lateral Load Factor rms vs Frequency, Flight Sequence 62, 

Preflight 63 

96 Normalized PSD of Lateral Load Factor, Flight Sequence 62, in Flight 63 

97 Percent of Total Lateral Load Factor rms vs Frequency, Flight Sequence 62, 

in Flight 64 

98 Normalized PSD of Lateral Load Factor, Flight Sequence 62, Postflight 64 

99 Percent of Total Lateral Load Factor rms vs Frequency, Flight Sequence 62, 

Postflight 65 

100 Longitudinal Load Factor Time History, Flight Sequence 62 65 

101 Normalized PSD of Longitudinal Load Factor, Flight Sequence 62, Preflight 66 

102 Percent of Total Longitudinal Load Factor rms vs Frequency, Flight Sequence 62, 

Preflight 66 

103 Normalized PSD of Longitudinal Load Factor, Flight Sequence 62, in Flight 67 

xi 
104 Percent of Total Longitudinal Load Factor rms vs Frequency, Flight Sequence 62, 

in Flight 67 

105 Normalized PSD of Longitudinal Load Factor, Flight Sequence 62, Postflight 68 

106 Percent of Total Longitudinal Load Factor rms vs Frequency, Flight Sequence 62, 

Postflight 68 

107 Pitch Angle Time History, Flight Sequence 62 69 

108 Normalized PSD of Pitch Angle, Flight Sequence 62, in Flight 69 

109 Percent of Total Pitch Angle rms vs Frequency, Flight Sequence 62, in Flight 70 

110 Bank Angle Time History, Flight Sequence 62 70 

111 Normalized PSD of Bank Angle, Flight Sequence 62, in Flight 71 

112 Percent of Total Bank Angle rms vs Frequency, Flight Sequence 62, in Flight 71 

113 Aileron Angle Time History, Flight Sequence 62 72 

114 Normalized PSD of Aileron Angle, Flight Sequence 62, in Flight 72 

115 Percent of Total Aileron Angle rms vs Frequency, Flight Sequence 62, in Flight 73 

116 Elevator Angle Time History, Flight Sequence 62 73 

117 Normalized PSD of Elevator Angle, Flight Sequence 62, in Flight 74 

118 Percent of Total Elevator Angle rms vs Frequency, Flight Sequence 62, in Flight 74 

119 Rudder Angle Time History, Flight Sequence 62 75 

120 Normalized PSD of Rudder Angle, Flight Sequence 62, in Flight 75 

121 Percent of Total Rudder Angle rms vs Frequency, Flight Sequence 62, in Flight 76 

122 Cumulative Occurrences of Incremental Vertical Load Factor, Preflight 76 

123 Effect of Sampling Rate on Cumulative Occurrences of Incremental Vertical Load 

Factor, Preflight 77 

124 Percent of Incremental Vertical Acceleration Peak Counts as a Function of Sampling 

Rate, Preflight 77 

125 Cumulative Occurrences of Incremental Vertical Load Factor, in Flight 78 

xii 
126 Effect of Sampling Rate on Cumulative Occurrences of Incremental Vertical Load 

Factor, in Flight 78 

127 Percent of Incremental Vertical Acceleration Peak Counts as a Function of 

Sampling Rate, in Flight 79 

128 Cumulative Occurrences of Incremental Vertical Load Factor, Postflight 79 

129 Effect of Sampling Rate on Cumulative Occurrences of Incremental Vertical 

Load Factor, Postflight 80 

130 Percent of Incremental Vertical Acceleration Peak Counts as a Function of 

Sampling Rate, Postflight 80 

131 Cumulative Occurrences of Lateral Load Factor, Preflight 81 

132 Effect of Sampling Rate on Cumulative Occurrences of Lateral Load Factor, 

Preflight 82 

133 Percent of Lateral Load Peak Counts as a Function of Sampling Rate, 

Preflight 83 

134 Cumulative Occurrences of Lateral Load Factor, in Flight 83 

135 Effect of Sampling Rate on Cumulative Occurrences of Lateral Load Factor, 

in Flight 84 

136 Percent of Lateral Load Factor Peak Counts as a Function of Sampling Rate, 

in Flight 85 

137 Cumulative Occurrences of Lateral Load Factor, Postflight 85 

138 Effect of Sampling Rate on Cumulative Occurrences of Lateral Load Factor, 

Postflight 86 

139 Percent of Lateral Load Factor Peak Counts as a Function of Sampling Rate, 

Postflight 87 

140 Cumulative Occurrences of Longitudinal Load Factor, Preflight 87 

141 Effect of Sampling Rate on Cumulative Occurrences of Longitudinal Load Factor, 

Preflight 88 

142 Percent of Longitudinal Load Factor Peak Counts as a Function of Sampling Rate, 

Preflight 89 

143 Cumulative Occurrences of Longitudinal Load Factor, in Flight 89 

xiii 
144 Effect of Sampling Rate on Cumulative Occurrences of Longitudinal Load Factor, 

in Flight 90 

145 Percent of Longitudinal Load Factor Peak Counts as a Function of Sampling Rate, 

in Flight 91 

146 Cumulative Occurrences of Longitudinal Load Factor, Postflight 91 

147 Effect of Sampling Rate on Cumulative Occurrences of Longitudinal Load Factor, 

Postflight 92 

148 Percent of Longitudinal Load Factor Peak Counts as a Function of Sampling Rate, 

Postflight 93 

149 Cumulative Occurrences of Pitch Angle 93 

150 Effect of Sampling Rate on Cumulative Occurrences of Pitch Angle, in Flight 94 

151 Percent of Pitch Angle Peak Counts as a Function of Sampling Rate, in Flight 95 

152 Cumulative Occurrences of Bank Angle 95 

153 Effect of Sampling Rate on Cumulative Occurrences of Bank Angle, in Flight 96 

154 Percent Bank Angle Peak Counts as a Function of Sampling Rate, in Flight 97 

155 Cumulative Occurrences of Aileron Deflection Angle 97 

156 Effect of Sampling Rate on Cumulative Occurrences of Aileron Deflection 

Angle, in Flight 98 

157 Percent Aileron Deflection Angle Peak Counts as a Function of Sampling Rate, 

in Flight 99 

158 Cumulative Occurrences of Elevator Deflection Angle 99 

159 Effect of Sampling Rate on Cumulative Occurrences of Elevator Deflection 

Angle, in Flight 100 

160 Percent Elevator Deflection Angle Peak Counts as a Function of Sampling 

Rate, in Flight 101 

161 Cumulative Occurrences of Rudder Deflection Angle 101 

162 Effect of Sampling Rate on Cumulative Occurrences of Rudder Deflection 

Angle, in Flight 102 

163 Percent Rudder Deflection Angle Peak Counts as a Function of Sampling 

Rate, in Flight 102 

xiv 
LIST OF TABLES 

Table Page 

1 Parameter Sampling Rates 103 

2 Figure Layout for Three Flights 104 

3 Peak Counting Criteria 105 

4 Figure Layout for Cumulative Occurrence Data 105 

5 Sampling Rate Requirements 106 

xv 
LIST OF ACRONYMS 

CFR Code of Federal Regulations 

FAA Federal Aviation Administration 

FFT Fast Fourier transform 

Hz Hertz 

PSD Power spectral density 

rms Root mean square 

sps Samples per second 

xvi
EXECUTIVE SUMMARY

The University of Dayton is supporting Federal Aviation Administration (FAA) research on the 

structural integrity requirements for the U.S. commercial transport airplane fleet. The primary 

objective of this research is to support the FAA Airborne Data Monitoring Systems Program by 

developing new and improved methods and criteria for processing and presenting large 

commercial transport airplane flight and ground loads usage data. This report presents the result 

of a study to determine the minimum sampling rates required for selected parameters to ensure 

the detection of peaks and peak amplitudes representative of the basic signal for use in deriving 

operational load statistics. The selected parameters included vertical, lateral, and longitudinal 

accelerations, and pitch and bank angle, as well as elevator, aileron, and rudder deflections 

recorded at higher than normal sampling rates obtained during 108 flights of an Airbus A319 

used in normal commercial operations. The study included (1) the use of power spectral density 

analyses of some high-activity flights to evaluate the frequency content of the recorded data, 

(2) an investigation of sampling rates required to identify peaks and peak amplitudes based on 

the frequency content of the parameters, and (3) an evaluation of the impact of varying sampling 

rates on derived operational load statistics. Resulting sampling rates were compared to sampling 

rate requirements specified in Title 14 Code of Federal Regulations Part 121, Appendices B and 

M. Although the data used in the study was recorded at higher than normal sampling rates, it 

was concluded that the sampling rates were not high enough to allow the selection of minimum 

sampling rates for detection of peaks and associated peak amplitudes with any certainty. 

Although the sampling rates specified in 14 CFR Part 121 appear adequate to identify peaks, 

they are too low to identify the associated peak amplitude. 

xvii/xviii 
1. INTRODUCTION. 

The Federal Aviation Administration (FAA) Airborne Data Monitoring Systems Research 

Program collects and provides statistical loads data from transport aircraft used in normal 

commercial airline operations. The sampling rates used to record the various selected load 

parameter signals vary from parameter to parameter and are often the subject of questions 

regarding their adequacy in obtaining realistic estimates of the actual signal peaks. For instance, 

the relatively low sampling rates, from one to four samples per second, of flight control surface 

deflections measurements has been a particular concern. As a result, the loads data reduction 

and analysis community has been reluctant to use the flight control surface deflection 

measurements to derive usage spectra for design criteria or the evaluation of existing designs. 

Sampling rates must be sufficiently high to be able to not only detect the existence of a 

parameter peak or valley, but also to describe the maximum amplitude of the peak or valley. 

This requires knowledge of (1) the frequency content of the parameter time history, (2) the 

relationship between parameter frequency content and sampling rate for identifying peaks and 

valleys, and (3) the relationship between the parameter’s frequency bandwidth and the sampling 

rate needed to ensure that the maximum parameter peak and valley amplitudes are obtained with 

an acceptable accuracy when a peak or valley is identified. Thus, in its most basic form, the 

sampling rate requirements are determined by the frequency content of the original analog time 

histories. Unfortunately, the basic analog signals are not available, but their digitized or sampled 

representations are available. A sampled time history may provide a distorted picture of the 

basic analog time history that does not faithfully convey all the frequencies in the original analog 

time history. To get an accurate picture of the waveform, a sampling rate of 10 to 20 times the 

highest frequency in the analog signal is usually suggested. Such high sampling rates were not 

available for this study. For purposes of this study, one must assume that the maximum 

sampling rates available provided a representative description of the original continuous analog 

signal. One can then evaluate if lower sampling rates from those available for this study would 

significantly affect the derived statistical load spectra. Based on the assumption that the 

maximum available sampling rates provide a satisfactory definition of the original parameter 

activity, this study conducted power spectral density (PSD) analyses of each available parameter 

for three maximum activity flights (i.e., flights in moderate turbulence) to obtain a representative 

description of the frequency content of the measured parameter. Based on the frequency content 

of the parameter, the study selected the minimum sampling rates necessary to define the 

existence of peaks and valleys as well as to adequately determine the amplitude of the existing 

peak or valley. The study calculated and compared parameter peak count statistics for different 

sampling rates. The effect of sampling rate on the peak count statistics were analyzed with 

respect to the minimum sampling rates selected from the PSD analyses. The minimum sampling 

rates selected from this study were compared with the sampling rates specified in Title 14 Code 

of Federal Regulations Part 121, Appendices B and M. It is very important for the reader to keep 

in mind that the selected minimum sampling rates are based on an already sampled continuous 

parameter signal that does not reflect the exact or entire frequency content of the original signal. 

1 
2. GENERAL DATA PROCESSING DISCUSSION.

The objective of aircraft and systems loading or usage statistics is to provide usable information 

for the evaluation of durability and damage tolerance of existing operational aircraft as well as 

the establishment of design criteria for new aircraft designs. For this information to be useful, it 

is desirable that it reflects the real world experience as accurately as possible within realistic 

limits. For instance, usage statistics of limited accuracy, but derived from available 

measurements, are better than usage statistics based on guesses or anecdotal information. Also, 

the use of highly accurate and detailed operational statistics in analyses that use gross averages 

of such data as input does not improve the accuracy of the final results and some error in the 

input is acceptable. If the operational statistics for a specific aircraft model are used for 

comparison of the operational statistics on other operational aircraft of the same model, some 

error can be tolerated in the operational statistics. If the operational statistics represent an 

absolute environment to which all aircraft are subject, such as atmospheric turbulence, increased 

accuracy is desirable for use on a variety of different aircraft types. In the derivation of usage 

statistics, it is, therefore, important to keep in mind the ultimate use of the data. 

In this study, a review of the general effects of real-world data digitization, signal frequency, and 

sampling rates will be reviewed first. The purpose of this review is to provide a basic 

understanding of the effect of data digitization of an analog signal and the effect of data binning 

during data processing on the final derived operational statistics. 

2.1 DATA DIGITIZATION.

The time histories obtained from the flight loads data recorder represent binned digital 

measurements of an analog signal sampled at specific time intervals. Therefore, the digitally 

recorded time history provides only a representation of the analog signal. The resolution of this 

representation is dependent on the binning interval used for the digitized data. The digital 

binning interval is actually the digital resolution of the analog signal; it is normally quite small 

and is a function of the number of bits used to represent the digitized data point. Figure 1 shows 

an example of the binning of a simple sine wave. Figures 2 and 3 show the effect of this digital 

binning on two short segments of an aileron deflection time history. Figure 2 shows the steps 

resulting from the digitizing process from what was a smooth analog signal. Figure 3 shows the 

cropping of the true peaks in the time history due to the binning process. The two figures show 

digital binning intervals of 0.065 degrees. These values are quite small and are of no real 

concern. They are shown here to emphasize the point that a digitized time history is not an exact 

duplication of the original analog signal, regardless of the sampling rate used. 

2.2 DATA SAMPLING RATE.

For digitally sampled data to be useful in any analysis, the sampling rate must be high enough to 

provide an accurate approximation of the basic signal. If the sampling rate is high enough, then 

the original signal can be approximated by joining the sampled points by small linear portions. 

If the sampling rate is too low, the digitized time history of the analog signal may not capture

larger analog values if they occur within the sampling time increments. This is more a concern 

with rapidly changing data of a short cyclic nature. For slower changing parameters, a slower 

sampling rate may be quite acceptable. A generally accepted theory advanced by Nyquist is that 

2 
as a minimum, the sampling rate should be twice the maximum frequency exhibited in the 

original signal. Figure 4 presents an example of a simple sine wave of 2 hertz (Hz) sampled at 

four samples per second. As can be seen, the sampled data does not accurately depict the 

original signal but does identify the existence of peaks at the proper amplitude and frequency. 

Figure 5 presents a sine wave of 7 Hz sampled at 16, 8, and 4 samples per second. The 

deterioration in the sampled time history, in its ability to represent the original signal as the 

sampling rate is reduced, is quite obvious. In this case, peaks are identified at the proper 

frequency but do not provide the proper amplitude. It is clear that as the sampling rate deviates 

from an absolute ratio of the signal frequency peak amplitude, values may be missed even at 

high sampling rates. As can be seen, a sampling rate of four samples per second, which equates 

to a Nyquist frequency of 2 Hz, results in a sampled time history with a completely different 

frequency content from the original analog signal. This phenomenon is called aliasing and 

results in contributing parameter cycles to the digitized time history at a frequency that may not 

exist in the original analog signal or add cycles to the digitized time history at the same 

frequency that existed in the original analog signal. In either case, subsequent PSD analysis of 

such a digitized time history will include errors due to aliasing, resulting from an inadequate 

sampling rate. Figure 6 shows digitized time histories of vertical load factor for four different 

sampling rates. Upon close examination, the figure shows changes in peak values as well as in 

the loss of peaks. Thus, the higher the frequency of the components in the signal, the higher the 

sampling rate should be. 

2.3 POWER SPECTRAL DENSITY.

Figures 5 and 6 have shown that knowledge of the frequency content of the original signal is 

important in deciding the sampling rate necessary to capture an acceptable digitized 

representation of the analog signal. A time history displays the magnitude of the data parameter 

as a function of time. A PSD provides an indication of the relative contribution of the data 

parameter frequencies to the total variance of the time history as a function of frequency. It thus 

provides insight into the frequencies that contribute the most to the total variance of the data 

parameter. Figure 7 presents a PSD of a sampled vertical load factor digitized time history for a 

ground operational segment. As can be seen, the low frequencies (below 2 Hz) are the 

predominant frequencies in the PSD. Some additional power is evident at the higher frequencies, 

between 6 and 8 Hz. 

The square root of total area under the PSD curve is equal to the root mean square (rms) of the 

time history. Taking the square root of a continuous integration of the PSD over the entire 

frequency band provides an indication of the change in the standard deviation with increasing 

frequency. Figure 8 shows an example of the variation of the rms as a function of increasing 

frequency. The figure shows how the different frequencies in the power spectrum contribute to 

the overall rms level. Steep slopes indicate a strong contribution within a narrow frequency 

band. Shallow slopes indicate little contribution over a wide frequency bandwidth. The figure 

shows that for the data represented by this figure, the primary contributor to the total rms 

acceleration are the accelerations occurring at frequencies below 2 cycles per second. 

Accelerations occurring at frequencies between 2 and 8 cycles per second contribute 

significantly less to the total rms of the digitized signal. In this case, a sampling rate of four 

samples per second (2 Hz) would include most of the signal’s overall standard deviation. 

3 
It must be kept in mind that the flight load time histories used are not true continuous functions 

but represent digitally sampled data that may include aliasing effects as discussed above. Thus, 

the PSD may show power reflected at frequencies below the Nyquist frequency for power at 

frequencies above the Nyquist frequency. The approach to limiting the aliasing effects is to filter 

the original signal to remove frequencies above the Nyquist frequency. It is not known if this is 

done in the airborne data monitoring system used for data recording. Aliasing effects cannot be 

removed from the PSD obtained from sampled data. If the original signal is competently 

sampled, the PSD will approach zero as the frequency nears the Nyquist frequency. If the PSD 

moves toward a finite value, aliasing effects most likely exist in the sampled time history. 

2.4 PARAMETER PEAK AMPLITUDE.

Figure 5 showed that in accordance with the Nyquist theorem, the 16 samples per second 

sampling rate is able to identify the existence of peaks in the analog signal. However, it also 

shows that while the 16 samples per second sampling rate ensures the identification of important 

peaks over the bandwidth of interest, it is not necessarily high enough to sample the true peak 

magnitude. Reference 1 presents a study of the relationship between sampling rate and 

measurement accuracy and shows that the data accuracy is dependent on the ratio of the signal 

frequency to the sampling frequency. Figure 9 shows the signal frequency of 3.5 Hz shown 

earlier in figure 5, with a sampling rate of 16 samples per second offset to portray the maximum 

possible amplitude error. The equation in the figure, as derived in reference 1, shows how data 

accuracy is dependent on the ratio of the signal frequency to the sampling frequency. The figure 

also shows that the maximum error does not necessarily occur during each cycle, even for a 

signal of constant frequency. For a signal with varying frequencies, the relationship between the 

sample time and the time of the analog signal peak is random and the sample time may occur at 

any time during the signal cycle with equal probability. In other words, it is as likely that the 

sample time coincides with the true peak, i.e., 0% error, as it is that it coincides with a maximum 

error value. 

2.5 DOWNSAMPLING. 

The parameters used in this study were recorded at the fixed sampling rates shown in table 1. To 

obtain representative digitized time histories representative of slower sampling rates, a 

downsampling technique was employed. Downsampling in its basic form is the process of 

reducing the number of samples in a time history without the use of a low-pass filtering 

operation. This is accomplished through the application of a decimation factor M equal to the 

input sampling rate divided by the output sampling rate, thus, M = input rate/output rate. In 

practical terms, this means that for a sample rate reduction of M = 2, every other point in the 

time history would be retained while the intermediate point would be deleted, for a sample rate 

reduction of four, only every fourth point would be retained, etc. In this study, downsampling is 

used to change the primary time history based on a higher sampling rate to one or more based on 

lower sampling rates. Figure 10 illustrates the application of downsampling. 

2.6 PEAK COUNTING.

A counting technique is used to interrogate the digitized time histories and place the selected 

points into fixed class intervals or bins. A variety of counting techniques are available, but 

4 
practically all available statistical data is obtained from peak between mean readings. UDRI has 

used this method of peak counting in deriving operational load statistics. In this method, a peak 

is defined as the maximum excursion of a mean time history trace between successive crossings 

of the mean level. Figure 11 illustrates the peak-between-mean criteria. This method counts 

upward events as positive and downward events as negative. Only one peak or one valley is 

counted between two successive crossings of the mean. A threshold zone or dead band is 

normally used in the data reduction to ignore irrelevant loads variations around the mean. 

Therefore, the peak between the mean counting method requires determination of the mean level 

for the peak-counted parameter time history. Most parameters exhibit a nearly constant mean 

level throughout the time history, and the peak counting technique was used for all parameters in 

this study. 

2.7 EFFECT OF BIN SIZE ON CUMULATIVE OCCURRENCES. 

Operational statistics are generally presented as cumulative probabilities or cumulative 

frequencies of a given parameter. For the purposes of obtaining cumulative occurrences, the 

point in the bins are accumulated from the points in the highest absolute bin size to the lowest. 

When the accumulated occurrences in each of the data bins are plotted to obtain cumulative 

distribution plots, it is common practice to draw straight lines between successive points of 

cumulative occurrences in each bin rather than by steps or in a histogram format. Since 

cumulative occurrences are viewed as exceedances, the cumulative occurrences or bin 

frequencies are plotted at the inner boundaries of the bin increments. As a consequence, 

accumulated points may be plotted at lower or higher bin boundaries, depending on the 

magnitude of the bin increment used. This becomes especially critical at the highest bin values. 

In theory, the greater the number of increments, the more accurately the distribution can be 

presented. Figures 12 shows the cumulative occurrences for an identical time history, but at 

varying bin increments. The most negative count was -0.183 g, while the most positive count 

was +0.134 g. Notice that the most negative load factor count of -0.183 g is plotted at -0.18 g 

when using a bin increment of 0.01 g. As the bin size becomes larger, this occurrence is plotted 

at lower and lower load factor levels so that for a bin size of 0.05 g, the -0.183 g peak is plotted 

at -0.15 g. For positive load factors, a similar situation occurs for the occurrence between 0.13 

and 0.14 g. Thus, the bin size used influences the accuracy of the statistical curve. For a bin size 

of 0.01 g, the error for the -0.183 g reading was -0.003/-0.183 = 1.64%. For a bin size of 0.05 g, 

this error changes to -0.033/-0.183 = 18.03%. A fixed bin size results in a varying error as a 

function of the parameter value with the errors changing from high values at lower parameter 

values progressing to lower errors at the higher parameter values. 

2.8 EFFECT OF SAMPLING RATE ON BIN COUNTS.

Sampling rate effects the magnitude of the counted peak as well as the flight phase into which 

the peak is placed. Figure 13 shows an analog data signal sampled at 16 and 8 samples per 

second divided into preflight, in-flight, and postflight phases. When sampling the analog signal 

at 16 samples per second, the first peak identified would be point A. This peak would be placed 

in a bin of 0.9 to 1.0 g for the preflight phase. When sampling at eight samples per second, the 

first peak identified would be point B. This point would be placed in a bin of 0.3 to 0.4 for the 

in-flight phase. Thus, in this particular case, the same analog peak would be binned in different 

bins as well as flight phases, depending on the sampling rate used. Similarly, for points C and D, 

5 
point C would be binned in -0.8 to -0.9 g and point D would be binned in -0.7 to -0.8 g, but both 

peaks would be counted in the in-flight phase. Points E and F identify the last analog peak based 

on 8 and 16 samples per second respectively. Point E would be binned in 0.3 to 0.4 g in the inflight phase, while point F would be binned in 0.9 to 1.0 g for the postflight phase. The example 

discussed here is designed to provide insight into the peak count differences as a function of 

sampling rate, as presented in the following section. 

3. SAMPLING RATE STUDY. 

The database used for this study consisted of selected parameters that were recorded at higher 

than normal sampling rates on 108 flights of a single Airbus A319 aircraft while conducting 

normal flight operations. Table 1 presents a listing of the parameters and their sampling rates. 

For this effort, the impact of changing sampling rates was studied for the vertical, lateral, and 

longitudinal accelerations, pitch and bank angles, and the elevator, aileron, and rudder deflection 

parameters. Because pressure altitude was not available, the time histories could not be broken 

down in the mission phases used in previous studies. However, since the squat switch parameter 

was available, the missions were broken down in preflight, flight, and postflight segments. 

3.1 POWER SPECTRAL DENSITY ANALYSIS. 

To conduct the PSD analysis, time histories were derived from the database for three flights (3, 

35, and 62) that exhibited maximum load factor activity. For each of the flights, the time 

histories included the vertical, lateral, and longitudinal load factors, pitch and bank angles, and 

aileron, elevator, and rudder deflections. For each parameter, PSDs were calculated using the 

fast Fourier transform (FFT) technique. For the load factor parameter, PSDs were calculated for 

the preflight, in-flight, and postflight segments of the time histories. For the pitch angle, bank 

angle, and control surface deflection parameters, PSDs were calculated for the in-flight segment 

of the time histories only. The square root of total area under the PSD curve is equal to the rms 

of the time history segment on which the PSD is based. All PSDs were normalized to a unit rms 

by dividing the PSD by the square of its rms value. As was shown in figure 8, the square root of 

a continuous integration of the PSD demonstrates how the standard deviation or rms changes 

with increasing frequencies in the measured parameter and, thus, provided insight into the ability 

of increasing sampling rates to capture the higher magnitudes of the parameter. Dividing the 

continuously integrated rms by the total rms, as obtained from the area under the PSD curve, the 

rms can be plotted versus frequency as a percentage of the total rms. Applying the Nyquist 

theorem that a minimum of two samples per cycle is required, the percentage can be evaluated as 

a function of the sampling rate. The results are presented for each of the three flights 

independently. Within each flight, each parameter is presented in the form of the time history, 

the PSD, and the variation of the rms with frequency. Table 2 shows the layout of figures 14 

through 121 for each of the three flights. Review of the PSDs will show that in all cases the 

power does not approach zero, but will maintain an almost constant value as it approaches the 

Nyquist frequency. As mentioned previously, this is an indication that the sampled data contains 

aliasing effects. This in turn suggests that frequencies higher than the Nyquist frequency existed 

in the original signal and the selected sampling rates were too low for the sampled signal to get 

an accurate picture of its power content. On the other hand, the change in the rms values as they 

6 
approach the Nyquist frequency will be seen to be quite small, indicating that the aliasing effects 

are correspondingly small. 

3.1.1 Vertical Load Factor PSDs. 

Figures 15, 51, and 87 present the PSDs for the vertical load factor for the preflight phase of the 

three flights. As can be seen, the normalized PSDs for the three flights are virtually identical. 

This is as would be expected. The PSD of the acceleration is shaped by the frequency response 

characteristics of the airplane to an external input. Because the flight profiles in terms of speed, 

altitude, and airplane weight distribution are expected to be similar from flight to flight, the 

frequency response characteristics of the airplane will also be similar from flight to flight. While 

the overall amplitudes of the inputs may vary, the frequency content of the inputs, such as 

runway roughness and atmospheric turbulence, will also be similar from flight to flight. As a 

consequence, when the calculated PSD of the response is normalized to account for amplitude 

differences of the input, they should be very much alike. 

Figures 16, 52, and 88 show the cumulative changes in the relative rms values for the preflight 

segments of the three flights as a function of increased bandwidth of the 16 samples per second 

digitized time histories. As can be seen, most of the cumulative rms is contained in the spectrum 

between 0 and 3 Hz, after which the gain in the cumulative rms starts to level off. 

Approximately 95% of the total rms in the digitized time history is contained within a bandwidth 

from 0 to 4.0-5.0 Hz. The remaining 5% is accumulated as the sampled bandwidth is increased 

to 8 Hz. This suggests that there is little additional dispersion in the digitized data as a result of 

frequencies above approximately 4.5 cycles per second. Selecting a cutoff frequency of 5 Hz 

would require a minimum sampling rate of 10 samples per second to ensure adequate 

representation of peak counts. 

As would be expected, the normalized PSDs for the in-flight cases, as presented in figures 17, 

53, and 89, and the variation in rms, as presented in figures 19, 55, and 91, are also almost 

identical. However, in the case of in-flight operation, the primary frequency content of the 

digitized time history is found to be below 1 Hz. For peak count purposes, a minimum sampling 

rate of two samples per second would be indicated. 

The postflight load factor PSDs of figures 19, 55, and 91 and the variation in rms, as shown in 

figures 20, 56, and 92, again show them to be virtually identical for the three flights. In addition, 

the PSDs and the associated rms variations with frequency for the postflight phase are very 

similar to those observed for the preflight phase and the same observations apply. 

3.1.2 Lateral Load Factor PSDs. 

Comparisons of the lateral acceleration PSD and rms variation plots in figures 22, 58, and 94 and 

23, 59, and 95, respectively, for the preflight phase of the three flights show the same close 

agreement, as observed for the vertical acceleration. Review of the figures shows that 95% of 

the total lateral load factor rms is contained within a bandwidth of less than 1 Hz. A sampling 

rate of twice this bandwidth or two samples per second would identify practically all peaks. 

7 
Comparisons of the lateral acceleration PSD and rms variation plots in figures 24, 60, and 96 and 

25, 61, and 97, respectively, for the in-flight phase of the three flights also show close 

agreement, as observed for the preflight case. Review of the figures shows that 95% of the total 

lateral load factor rms is contained within a bandwidth from 0 to slightly above 1 Hz. Again, a 

sampling rate of twice this bandwidth or two samples per second would identify practically all 

peaks. 

Comparisons of the lateral acceleration PSD and rms variation plots in figures 26, 62, and 98 and 

27, 63, and 99, respectively, for the postflight phase of the three flights also show close 

agreement, as observed for the preflight case. Review of the figures shows that 95% of the total 

lateral load factor rms is contained within a bandwidth from 0 to 0.5 Hz. In this case, a sampling 

rate of twice this bandwidth or one sample per second would be acceptable for peak counting. 

3.1.3 Longitudinal Load Factor PSDs. 

For the longitudinal acceleration, the PSDs of figures 29, 65, and 101 again show very close 

agreement for the preflight phase of the three flights. The same observation is made for the rms 

variation shown in figures 30, 66, and 102. The rms variation shown in the last three figures 

shows that the primary activity occurs at very low frequencies, less than 0.5 Hz. A sampling rate 

of one sample per second should, therefore, identify the majority of peaks. 

For the in-flight phase of longitudinal acceleration, the PSDs of figures 31, 67, and 103 again 

show very close agreement for the three flights. The same observation is made for the rms 

variation shown in figures 32, 68, and 104. The rms variation shown in the last three figures 

shows that the primary activity occurs at very low frequencies less than 0.5 Hz. A sampling rate 

of one sample per second should, therefore, identify the majority of peaks. 

The longitudinal acceleration PSDs of figures 33, 69, and 105 for the postflight phase of the 

three flights also show very close agreement. The rms variation as shown in figures 34, 70, and 

106 are also in close agreement. The rms variation shown in the last three figures shows that the 

primary activity occurs at very low frequencies less than 0.5 Hz. A sampling rate of one sample 

per second should, therefore, identify the majority of peaks. 

3.1.4 Pitch and Bank Angle PSDs. 

The pitch angle information contained in figures 36, 72, 108, 37, 73, and 109 show the same 

close agreements observed for the accelerations with the major activity occurring below 0.25 Hz. 

Thus, a sampling rate equal to once per 2 seconds should be adequate to identify the important 

peaks. 

Similarly based on the bank angle PSDs of figures 39, 75, and 111 and the rms variation shown 

in figures 40, 76, and 112, a sampling rate of once per 2 seconds should be more than adequate to 

detect the major peaks. 

8 
3.1.5 Control Surface Deflection Angle PSDs. 

The aileron surface deflection PSDs of figures 42, 78, and 114 and the rms variation shown in 

figures 43, 79, and 115 again show close agreement for the three flights and indicate that a 

sampling rate of once per second is adequate. 

The elevator deflection PSDs for the three flights shown in figures 45, 81, and 117 are not in as 

close an agreement as the agreements observed for all previously discussed parameters. As a 

consequence, the rms variation shown in figures 46, 82, and 118 also show less of an agreement. 

Overall, the important activity still is at very low frequencies, and a sampling rate of one sample 

per second would account for 95% of the total activity. 

Finally, for the rudder deflections, the PSDs of figures 48, 84, and 120 and the rms variation 

plots in figures 49, 85, and 121 indicate a sampling rate of one sample per second to be sufficient 

to detect most peaks. 

3.2 CUMULATIVE OCCURRENCES STATISTICS.

The effect of different sampling rates on peak counts was evaluated through comparison of the 

distributions of cumulative occurrence at different sampling rates. Table 3 presents an overview 

of the parameters studied and their respective sampling rates, dead band, and binning increments 

used. 

As discussed previously, digitization of a continuous signal without prefiltering results in 

aliasing information at higher frequencies into lower frequencies. Time histories for the different 

sampling rates were obtained through down sampling of the digitized time histories available for 

the maximum sampling rates, as shown in table 1. Unfortunately without filtering this process, 

results in further aliasing frequency information above half the sampling rate into the lower 

frequencies. Nevertheless, cumulative occurrence statistics were obtained for different sampling 

rates using simple down sampling from a database containing digitized time histories for 108 

flights. 

The accelerations cumulative occurrence was obtained for preflight, in-flight, and postflight 

operations. For the pitch angle, bank angle, and control surface deflections, only in-flight 

cumulative occurrences were derived. Because this part of the study was oriented towards 

evaluating the effect of sampling rates on occurrence statistics, the gravitational effects on the 

transverse sensitivity of the accelerometers was not considered. For the vertical and lateral 

accelerometers, this effect is not great and has always been neglected. However, the errors 

introduced in the longitudinal accelerometer readings can be significant, especially during the 

departure and climb phases of flight. Fortunately, longitudinal acceleration statistics during flight 

have not been of interest and have not generally been published. 

The cumulative occurrence statistics for each parameter is presented in three formats, as shown 

in table 4. For each parameter, the first figure presents a curve of the cumulative occurrences. 

The second figure contains a table containing a tabulation of the numerical occurrences behind 

the curves shown in the first figure. The table also shows the occurrences as a percent of the 

occurrences counted for the maximum sampling rate. The third figure is a graphical presentation 

9 
of the percentages shown in the table. In evaluating the effect of different sampling rates on 

peak counts, it is important to keep in mind that the effects are presented as a percentage of the 

maximum sampling rate used for the parameter. There is no assurance that the maximum 

sampling rate used in this study was adequate to define all the peaks in the original signal. In 

other words, the peak count statistics for the maximum sampling rates used may be in error. 

3.2.1 Incremental Vertical Load Factor Statistics. 

Figures 122, 123, and 124 present the vertical load factor statistics in three different formats for 

the preflight phase of 108 flights. The figures show that reducing the sampling rate from 16 to 8 

samples per second has an unmistakable but not large impact on the overall load factor statistics. 

For the four, two, and one sample per second cases, the peak counts and the magnitudes show 

significant and unacceptable reductions. 

Figures 125, 126, and 127 present the vertical load factor statistics in three different formats for 

the in-flight phase of 108 flights. The figures show that reducing the sampling rate from 16 to 8 

samples per second has very little impact on the overall load factor statistics. For the preflight 

phase statistics, the peak counts and the magnitudes sampled at four, two, and one sample per 

second show significant and unacceptable reductions. 

Figures 128, 129, and 130 present the vertical load factor statistics in three different formats for 

the postflight phase of 108 flights. In contrast to the preflight phase, these figures show that 

reducing the sampling rate from 16 to 8 samples per second has some impact on the overall load 

factor statistics. For the preflight phase statistics, the peak counts and the magnitudes sampled at 

four, two, and one sample per second show significant and unacceptable reductions. 

In summation, for the purpose of peak counting, the minimum sampling rate for ground 

operations, a sampling rate greater than eight samples per second would be desirable, and for the 

flight phase, a sampling rate of eight samples per second is acceptable. 

3.2.2 Lateral Load Factor Statistics. 

Figures 131, 132, and 133 show the lateral load factor statistics for preflight operations. The 

figures show that, as with the vertical accelerations, reducing the sampling rate to eight samples 

per second has no large effect on the overall lateral load factor statistics in the preflight phase. 

Sampling at four samples per second has an unacceptable effect on the measurement of negative 

peaks, but the positive peaks are acceptably identified. Sampling rates lower than four samples 

per second, however, do not provide adequate sampling of peaks and valleys. 

Figures 134, 135, and 136 show the lateral load factor statistics for in-flight operations. The 

figures show that, as with the lateral accelerations recorded during the preflight phase, sampling 

at less than eight samples per second will result in loss of peak counts. 

Figures 137, 138, and 139 show the lateral load factor statistics for postflight operations. The 

figures show that sampling rates as low as four samples per second will provide results in 

generally equal peak counts. 

10 
3.2.3 Longitudinal Load Factor Statistics. 

Figures 140, 141, and 142 present the longitudinal load factor statistics for the preflight 

operational phase. The figures show that the minimum acceptable sampling rate is eight samples 

per second. The higher magnitudes of positive load factor during the preflight phase are likely 

associated with the takeoff portion of the preflight phase. 

Figures 143, 144, and 145 present the longitudinal load factor statistics for the in-flight 

operational phase. The figures show that the minimum acceptable sampling rate is four samples 

per second. Sampling rates at two or one sample per second result in large peak count losses. In 

the case of the in-flight phase, the higher magnitudes of the positive load factors are associated 

with the departure and climb phases. During these phases, the longitudinal accelerometer 

measures the gravitational forces caused by the pitch angle inclination of the accelerometer axis 

from the horizontal. 

Figures 146, 147, and 148 present the longitudinal load factor statistics for the postflight 

operational phase. The figures show that the minimum acceptable sampling rate is four samples 

per second. Sampling rates at two or one sample per second result in large peak count losses. 

The more severe negative accelerations during the postflight phase are the result of braking 

forces during landing. 

3.2.4 Pitch and Bank Angle Statistics. 

Figures 149, 150, and 151 present the pitch angle cumulative peak counts. Sampling rates of 

four, two, and one sample per second have no significant effect on the peak count data. This is 

consistent with the fact that the frequency content of pitch angle changes is very low. 

Figures 152, 153, and 154 present the bank angle cumulative peak counts. Similarly to the pitch 

angle changes, the frequency content of bank angle changes is also very low. 

Therefore, sampling rates of four, two, and one sample per second have no significant effect on 

the peak count data. The large percent difference noted at the most negative bank angles result 

from the fact that very few peaks were counted. For instance, if sampling at two samples per 

second resulted in a single peak count while sampling at four samples per second resulted in a 

two-peak count, the resulting percent difference would be 50 percent. 

3.2.5 Control Surface Deflection Angle Statistics. 

Figures 155, 156, and 157 present the aileron deflection angle cumulative peak counts. 

Sampling rates of 16, 8, and 4 samples per second are seen to provide almost identical peak 

counts. Only at sampling rates of two and one sample per second do significant differences in 

peak counts occur. This is consistent with the fact that the frequency content of aileron 

deflection angle changes is very low. 

Figures 158, 159, and 160 present the elevator deflection angle cumulative peak counts. The 

figures show a significant change in peak counts when the sampling rate is reduced from four 

samples per second. 

11 
Figures 161, 162, and 163 present the rudder deflection angle cumulative peak counts. The 

figures show no significant difference in peak counts between data recorded at 16 and 8 samples 

per second. However, at sampling rates below eight samples per second, significant peak count 

losses occur. 

3.3 MINIMUM SAMPLING RATES FOR AMPLITUDE DETECTION.

In determining the minimum sampling rate requirements, two questions need to be answered 

(1) Does the selected sampling rate provide for identification of peaks occurring at different 

frequencies? (2) If a peak exists does the sampling rate provide an accurate description of the 

peak amplitude? While the selected sampling rates suggested as a result of the PSD analyses and 

the peak count statistics discussed previously assume the identification of important peaks over 

the bandwidth of interest, the same rate is not necessarily high enough to sample the true peak 

magnitude. Reference 1 presents a study of the relationship between sampling rate and 

measurement accuracy. This study showed that for a sinusoidal signal, a relationship between 

measurement accuracy and signal frequency could be established. This relationship takes the 

following form. 

) 2

2 % cos1(*100 fF Error π −=

Where: F = signal bandwidth frequency 

 f = sampling rate 

The equation can be transformed to calculate the minimum sampling rate required for a specific 

error value and frequency bandwidth. 

⎟

⎠

⎞ ⎜

⎝

⎛ −

= −

100

% 1cos 1 error

F f π

For a maximum allowable error of 10 percent in any amplitude measurement, a sampling rate of 

7 times the data signal bandwidth is necessary. The relationship between the sample time and 

the time of the analog signal peak is random, thus, the sample time may occur at any time during 

the signal cycle with equal probability. In other words, it is as likely that the sample time 

coincides with the true peak, i.e., 0% error, as it coincides with a lower value that results in a 

10% error. This means that the average error would be expected to be 5%. Using the sinusoid as 

a simplistic description of a ground or flight loads parameter, average errors in the recorded peak 

amplitudes can be calculated for different parameter frequencies and sampling rates. 

3.4 COMPARISON OF SAMPLING RATE REQUIREMENTS. 

The evaluation of the PSDs of the various parameters discussed in section 2 provided suggested 

minimum sampling rates for each of the studied parameters. Similarly, comparison of the peak 

counting results for different sampling rates suggested minimum sampling rates that would 

provide peak counts comparable to the counts obtained from the maximum sampling rates used. 

Unfortunately, there is no agreement between the minimum sampling rates gleaned from the 

12 
PSD analyses and the parameter peak count statistics. In addition, these suggested sampling 

rates are based on identifying peaks without consideration of the sampling rates needed to ensure 

identification of the peak amplitudes. 

For the PSD analyses, the minimum sampling rates were selected based on the premise that the 

frequency bandwidth that contained 95% of the total time history rms of the parameter 

measurement would ensure the identification of peaks that are the most important contributors to 

the overall peak count statistics. The minimum sampling rates were selected so that they would 

result in a fixed number of even time increments in each second. From the peak count statistics, 

the minimum sampling rates were selected so that they encompassed at least 95% of the peak 

counts obtained from the maximum sampling rate available in this study. The minimum 

sampling rates to ensure acceptable estimates of peak amplitudes were based on not exceeding a 

maximum 10 percent error over the frequency bandwidth that encompassed at least 95% of the 

total rms of the parameter measurement. Airplane flight recorder specifications are contained in 

14 CFR Part 121, Appendices B and M. Appendix A in this report contains Part 121 

Appendix B and Appendix B in this report contains Part 121 Appendix M. Table 5 presents the 

selected sampling rates from this study and compares them to the 14 CFR requirements of 

Part 121 Appendices B and M. 

Comparison of the selected sampling rates from the PSD analyses and the peak count statistics 

show considerable differences. The selected minimum sampling rates based on the PSD results 

are lower than those obtained from the peak count statistics. Agreement of the PSD-selected 

sampling rates with the sampling rates selected from the peak count, the results can be improved 

if instead of a 95% rms level, an rms level approaching 100% of the total rms is used in the 

selection of the PSD-based sampling rates. It is also worth noting that, except for the aileron 

deflections, slower sampling rates below the maximum sampling rates available for the study 

resulted in measurable changes in the peak count statistics. This raises the suspicion that the 

maximum sampling rates used in this study may also be too low to obtain realistic peak statistics. 

It is interesting to note that different sampling rates are indicated for ground and flight 

operations. 

3.5 DERIVATION OF FLIGHT CONTROL DEFLECTION STATISTICS.

Figures 122 through 163 show the changes in parameter peak count statistics as a function of the 

sampling rate. These figures tend to be interpreted as indicating a loss in the number of peaks 

that are counted as the sampling rate is reduced. Column three in table 5 shows the minimum 

samples per second required to capture a peak as based on the rms frequency distribution of the 

PSDs. Column five shows the minimum sampling rate required to ensure that the recorded 

amplitude of the peak is within a maximum error of 10 percent. Since the sampling rate required 

to capture the correct amplitude is higher than needed to capture the existence of a peak, the 

differences seen in the peak count statistics is more likely due to the inability to record the 

correct peak amplitudes than it is to record the existence of a peak. Thus, assuming that the 

number of peaks counted is more likely correct, then cumulative occurrence spectra derived at 

low sampling rates could be corrected to account for the errors in peak amplitude using the 

approach developed in reference 1. Appendix C presents the results of a subsequent study to 

apply such a correction to the flight control surface statistics. 

13 
4. CONCLUDING REMARKS.

This study used digitized time histories based on relatively low sampling rates. Signal 

information at frequencies above half the sampling rates was placed at lower frequencies through 

aliasing, thus distorting the true signal information. It is conceivable that the original signal 

exhibited important activity at higher frequencies that were aliased into the digitized time 

histories used. For instance, the vertical load factor activity seen at the higher frequencies nearer 

to the Nyquist frequency may have been real or an alias. Intuitively, it might be argued that 

these higher frequencies would be expected to consist of lower peak values, however, without 

the analysis of digitized time histories sampled at much higher sampling rates, this must remain 

an open question. The desired sampling rates derived in this study were based on the evaluation 

of gains in parameter signal power with increased bandwidth and empirical comparisons of 

parameter statistics for different sampling rates using digitized time history inputs. Because the 

digitized time histories were based on low sampling rates, serious questions remain about the 

accuracy of the digitized time histories to reflect the true frequency content of the original signal. 

The fact that reduction of the sampling rates below the maximum available for this study had 

measurable effects on the peak count statistics would suggest that the maximum sampling rates 

used in the study may also have been too low to provide true peak count statistics. In that case, 

using the peak count statistics obtained from maximum sampling rates as a benchmark to 

evaluate the effects of lower sampling rates may result in drawing suspect conclusions regarding 

the minimum acceptable sampling rates. 

Acceleration response during ground operations is spread over a much wider frequency range 

than it is during flight operations, where most of the activity occurs at frequencies below 3 Hz. 

As a result, the sampling rate requirements, as derived from peak count statistics, show 

differences for ground and flight operations. To obtain acceleration peak statistics during ground 

operations with accuracy, similar to those obtained for flight operations, a higher sampling rate 

for ground operations is required. These differences in sampling rate requirements based on 

ground or flight operations suggest a need to change the recorded sampling rate as a function of 

main landing gear squat switch position. 

To be completely rigorous, any conclusions to be drawn from this study are applicable to the 

A319 aircraft only. The power spectral densities (PSDs) of the accelerations represent the of the 

aircraft response to an input. The in-flight response to the input is filtered through the dynamic 

response characteristics of the airplane, particularly the natural frequencies, modes, and 

associated damping as defined by the transfer function. By the same token, the PSDs for control 

surface deflections are representative of the A319 control system characteristics. For general 

application, it is reasonable to assume that the airframe system of other airplanes in the same 

category as the A319 will exhibit the same dynamic response characteristic and, thus, will 

respond in the same dynamic manner to a given external in-flight input. In that case, the 

acceleration sampling rate results from this study would be applicable to such other aircraft. 

Also, if the flight control system characteristics of other aircraft are generally identical to those 

of the A319, the control surface sampling rate results from this study can reasonably be applied 

to such other aircraft. The pre- and postflight acceleration responses, especially in the vertical 

direction, result from runway roughness and are affected by the landing gear damping 

characteristics. It seems reasonable to assume that the landing gear damping characteristics of 

the A319 landing gear are similar to those on other airplanes in its weight class that have landing 

14 
gears with nearly alike design configurations. Again, in that case, the acceleration sampling rate 

results from this study would be applicable to such other aircraft. 

The maximum sampling rates used to form the database for this study were still too low to define 

minimum acceptable sampling rates with confidence. In any case, the minimum sampling rates 

derived in this study cannot be considered conservative estimates. Any specific sampling rate 

recommendation requires further study using digitized time histories obtained from much faster 

sampled signals and with proper filtering to prevent the appearance of aliasing in the digitized 

time history. However, while no specific minimum sampling rates can be recommended with 

any degree of confidence, it is clear that the sampling rates specified in Title 14 Code of Federal 

Regulations Part 121, Appendices B and M are low, and there is no doubt that they should be 

raised. 

5. REFERENCES.

1. Anonymous, “Analysis of Relationship Between Sample Rate, Data Bandwidth and 

Accuracy for Flight Data Recorders with A/D Converters,” Technical Note EER-912, 

Esprit Technology Inc., September 1991. 

15 
-1.5

-1

-0.5

0

0.5

1

1.5

0 0.125 0.25 0.375 0.5 0.625 0.75 0.875 1

Original Signal

Binned Signal

Signal Amplitude

Time (seconds)

FIGURE 1. ANALOG SIGNAL TO DIGITIZED BINNING 

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

1218 1219 1220 1221 1222 1223 1224 1225 1226

Airleron Deflection (degrees)

Time

FIGURE 2. DIGITIZED AILERON SIGNAL

16
-0.95

-0.9

-0.85

-0.8

-0.75

550 552 554 556 558 560 562 564

Aileron Deflection (degrees)

Time (seconds)

FIGURE 3. PEAK CROPPING DUE TO DIGITIZATION 

-1.5

-1

-0.5

0

0.5

1

1.5

0

0.0625

0.125

0.1875

0.25

0.3125

0.375

0.4375

0.5

0.5625

0.625

0.6875

0.75

0.8125

0.875

0.9375

1

Original Signal (2 CPS)

2 samples per cycle

Amplitude

Time (seconds)

FIGURE 4. SINE WAVE SAMPLED AT TWICE ITS FREQUENCY 

17
-1.5

-1

-0.5

0

0.5

1

1.5

0

0.0625

0.125

0.1875

0.25

0.3125

0.375

0.4375

0.5

0.5625

0.625

0.6875

0.75

0.8125

0.875

0.9375

1

Original Signal, 3.5 Hz

16 SPS

8 SPS

4 SPS

Amplitude

Time (seconds)

FIGURE 5. ANALOG SIGNAL SAMPLED AT DIFFERENT SAMPLING RATES 

0.8

0.9

1

1.1

1.2

470 472 474 476 478 480

16 sps

 8 sps

 4 sps

 2 sps

Vertical Load Factor, nz (g)

Time (seconds)

FIGURE 6. VERTICAL LOAD FACTOR TIME HISTORY SAMPLED AT 

DIFFERENT SAMPLING RATES 

18
0

0.0002

0.0004

0.0006

0.0008

12345678

Vertical RMS Load Factor Squared (g2

)

Frequency (hertz)

0.001

FIGURE 7. VERTICAL LOAD FACTOR PSD, PREFLIGHT 

0

0.005

0.01

0.015

0.02

0.025

01234567

Vertical Load Factor (rms g)

Frequency (hertz)

8

FIGURE 8. VARIATION OF RMS VERTICAL LOAD FACTOR WITH 

FREQUENCY, POSTFLIGHT 

19
-1.5

-1

-0.5

0

0.5

1

0 0.2 0.4 0.6 0.8 1

1.5

Original Signal, 3.5 Hz

16 Samples per Second

Amplitude

Time (seconds)

Maximum Error

% Error = 100*(1-cosine(π*F/f)) F = Signal Frequency

f = Sampling Rate

FIGURE 9. CALCULATION OF MAXIMUM PEAK AMPLITUDE ERROR 

-1.5

-1

-0.5

0

0.5

1

1.5

0123456 7

16 Samples per Second

8 Samples per Second

4 Samples per Second

Data Value

Time

FIGURE 10. DOWNSAMPLING TECHNIQUE 

20
-1

-0.5

0

0.5

1

0 10 20 30 40 50 60 70

Time History

Peak Counts

Amplitude

Time

Threshold

FIGURE 11. PEAK BETWEEN MEAN COUNTING 

1

10

100

1000

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

0.01

0.02

0.03

0.04

0.05

Occurrences

Incremental Vertical Load Factor (g)

FIGURE 12. EFFECT OF USING DIFFERENT CLASS INTERVALS ON AN 

INCREMENTAL VERTICAL LOAD FACTOR DISTRIBUTION 

21
-1.5

-1

-0.5

0

0.5

1

1.5

0

0.0625

0.125

0.1875

0.25

0.3125

0.375

0.4375

0.5

0.5625

0.625

0.6875

0.75

0.8125

0.875

0.9375

1

Original Signal

16 SPS

8 SPS

Amplitude

Time (seconds)

A

B

C

D

E

F

Pre-flight In-flight Post-flight

FIGURE 13. EFFECT OF SAMPLING RATE ON PHASE OF FLIGHT BIN COUNT 

FIGURE 14. INCREMENTAL VERTICAL LOAD FACTOR TIME HISTORY, 

FLIGHT SEQUENCE 3 

22
10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

01234567

Power Spectral Density (RMS g)2 / Hertz

Frequency (Hertz)

8

FIGURE 15. NORMALIZED PSD OF INCREMENTAL VERTICAL LOAD FACTOR, 

FLIGHT SEQUENCE 3, PREFLIGHT 

0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 16. PERCENT OF TOTAL INCREMENTAL VERTICAL LOAD FACTOR 

RMS VS FREQUENCY, FLIGHT SEQUENCE 3, PREFLIGHT 

23
10-6

10-5

10-4

10-3

10-2

10-1

100

101

10

01234567

Power Spectral Density (RMS g)2 / Hertz

Frequency (Hertz)

2

8

FIGURE 17. NORMALIZED PSD OF INCREMENTAL VERTICAL LOAD FACTOR, 

FLIGHT SEQUENCE 3, IN FLIGHT 

0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 18. PERCENT OF TOTAL INCREMENTAL VERTICAL LOAD FACTOR 

RMS VS FREQUENCY, FLIGHT SEQUENCE 3, IN FLIGHT 

24
10-6

10-5

10-4

10-3

10-2

10-1

100

101

01234567

Power Spectral Density (RMS g)2 / Hertz

Frequency (Hertz)

102

8

FIGURE 19. NORMALIZED PSD OF INCREMENTAL VERTICAL LOAD FACTOR, 

FLIGHT SEQUENCE 3, POSTFLIGHT 

0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 20. PERCENT OF TOTAL INCREMENTAL VERTICAL LOAD FACTOR 

RMS VS FREQUENCY, FLIGHT SEQUENCE 3, POSTFLIGHT 

25
FIGURE 21. LATERAL LOAD FACTOR TIME HISTORY, FLIGHT SEQUENCE 3 

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

01234567

Power Spectral Density (RMS g)2 / Hertz

Frequency (Hertz)

8

FIGURE 22. NORMALIZED PSD OF LATERAL LOAD FACTOR, 

FLIGHT SEQUENCE 3, PREFLIGHT 

26
0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 23. PERCENT OF TOTAL LATERAL LOAD FACTOR RMS VS FREQUENCY, 

FLIGHT SEQUENCE 3, PREFLIGHT 

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

01234567

Power Spectral Density (RMS g)2 / Hertz

Frequency (Hertz)

8

FIGURE 24. NORMALIZED PSD OF LATERAL LOAD FACTOR, 

FLIGHT SEQUENCE 3, IN FLIGHT 

27
0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 25. PERCENT OF TOTAL LATERAL LOAD FACTOR RMS VS 

FREQUENCY, FLIGHT SEQUENCE 3, IN FLIGHT 

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

01234567

Power Spectral Density (RMS g)2 / Hertz

Frequency (Hertz)

8

FIGURE 26. NORMALIZED PSD OF LATERAL LOAD FACTOR, FLIGHT 

SEQUENCE 3, POSTFLIGHT

28
0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 27. PERCENT OF TOTAL LATERAL LOAD FACTOR RMS VS FREQUENCY, 

FLIGHT SEQUENCE 3, POSTFLIGHT 

FIGURE 28. LONGITUDINAL LOAD FACTOR TIME HISTORY, 

FLIGHT SEQUENCE 3 

29
10-6

10-5

10-4

10-3

10-2

10-1

100

101

10

0 0.5 1 1.5 2 2.5 3 3.5

Power Spectral Density (RMS g)2 / Hertz

Frequency (Hertz)

2

4

FIGURE 29. NORMALIZED PSD OF LONGITUDINAL LOAD FACTOR, 

FLIGHT SEQUENCE 3, PREFLIGHT 

0

10

20

30

40

50

60

70

80

90

100

0 0.5 1 1.5 2 2.5 3 3.5 4

Percent of Total RMS (percent)

Frequency (Hz)

FIGURE 30. PERCENT OF TOTAL LONGITUDINAL LOAD FACTOR RMS VS 

FREQUENCY, FLIGHT SEQUENCE 3, PREFLIGHT 

30
10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

0 0.5 1 1.5 2 2.5 3 3.5 4

Power Spectral Density (RMS g)2 / Hertz

Frequency (Hertz)

FIGURE 31. NORMALIZED PSD OF LONGITUDINAL LOAD FACTOR, 

FLIGHT SEQUENCE 3, IN FLIGHT 

0

10

20

30

40

50

60

70

80

90

100

0 0.5 1 1.5 2 2.5 3 3.5 4

Percent of Total RMS (percent)

Frequency (Hz)

FIGURE 32. PERCENT OF TOTAL LONGITUDINAL LOAD FACTOR RMS VS 

FREQUENCY, FLIGHT SEQUENCE 3, IN FLIGHT 

31
10-6

10-5

10-4

10-3

10-2

10-1

100

101

10

0 0.5 1 1.5 2 2.5 3 3.5

Power Spectral Density (RMS g)2 / Hertz

Frequency (Hertz)

2

4

FIGURE 33. NORMALIZED PSD OF LONGITUDINAL LOAD FACTOR, 

FLIGHT SEQUENCE 3, POSTFLIGHT 

0

10

20

30

40

50

60

70

80

90

100

0 0.5 1 1.5 2 2.5 3 3.5 4

Percent of Total RMS (percent)

Frequency (Hz)

FIGURE 34. PERCENT OF TOTAL LONGITUDINAL LOAD FACTOR RMS VS 

FREQUENCY, FLIGHT SEQUENCE 3, POSTFLIGHT 

32
FIGURE 35. PITCH ANGLE TIME HISTORY, FLIGHT SEQUENCE 3 

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

FIGURE 36. NORMALIZED PSD OF PITCH ANGLE, 

FLIGHT SEQUENCE 3, IN FLIGHT 

33
0

10

20

30

40

50

60

70

80

90

100

0 0.511.5

Percent of Total RMS (percent)

Frequency (Hz)

2

FIGURE 37. PERCENT OF TOTAL PITCH ANGLE RMS VS FREQUENCY, 

FLIGHT SEQUENCE 3, IN FLIGHT 

FIGURE 38. BANK ANGLE TIME HISTORY, FLIGHT SEQUENCE 3 

34
10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

0 0.5 1 1.5 2 2.5 3 3.5 4

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

FIGURE 39. NORMALIZED PSD OF BANK ANGLE, 

FLIGHT SEQUENCE 3, IN FLIGHT 

0

10

20

30

40

50

60

70

80

90

100

0 0.5 1 1.5 2 2.5 3 3.5 4

Percent of Total RMS (percent)

Frequency (Hz)

FIGURE 40. PERCENT OF TOTAL BANK ANGLE RMS VS FREQUENCY, 

FLIGHT SEQUENCE 3, IN FLIGHT 

35
FIGURE 41. AILERON ANGLE TIME HISTORY, FLIGHT SEQUENCE 3 

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

01234567

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

8

FIGURE 42. NORMALIZED PSD OF AILERON ANGLE, 

FLIGHT SEQUENCE 3, IN FLIGHT 

36
0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 43. PERCENT OF TOTAL AILERON ANGLE RMS VS FREQUENCY, 

FLIGHT SEQUENCE 3, IN FLIGHT 

FIGURE 44. ELEVATOR ANGLE TIME HISTORY, FLIGHT SEQUENCE 3 

37
10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

FIGURE 45. NORMALIZED PSD OF ELEVATOR ANGLE, 

FLIGHT SEQUENCE 3, IN FLIGHT 

0

10

20

30

40

50

60

70

80

90

100

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

Percent of Total RMS (percent)

Frequency (Hz)

FIGURE 46. PERCENT OF TOTAL ELEVATOR ANGLE RMS VS FREQUENCY, 

FLIGHT SEQUENCE 3, IN FLIGHT 

38
Rudder Angle (degrees) 

FIGURE 47. RUDDER ANGLE TIME HISTORY, FLIGHT SEQUENCE 3 

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

01234567

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

8

FIGURE 48. NORMALIZED PSD OF RUDDER ANGLE, 

FLIGHT SEQUENCE 3, IN FLIGHT 

39
0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 49. PERCENT OF TOTAL RUDDER ANGLE RMS VS FREQUENCY, 

FLIGHT SEQUENCE 3, IN FLIGHT 

FIGURE 50. INCREMENTAL VERICAL LOAD FACTOR TIME 

HISTORY, FLIGHT SEQUENCE 35 

40
10-6

10-5

10-4

10-3

10-2

10-1

100

101

10

01234567

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

2

8

FIGURE 51. NORMALIZED PSD OF INCREMENTAL VERTICAL LOAD FACTOR, 

FLIGHT SEQUENCE 35, PREFLIGHT 

0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 52. PERCENT OF TOTAL INCREMENTAL VERTICAL LOAD FACTOR 

RMS VS FREQUENCY, FLIGHT SEQUENCE 35, PREFLIGHT 

41
10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

01234567

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

8

FIGURE 53. NORMALIZED PSD OF INCREMENTAL VERTICAL LOAD FACTOR, 

FLIGHT SEQUENCE 35, IN FLIGHT 

0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 54. PERCENT OF TOTAL INCREMENTAL VERTICAL LOAD FACTOR 

RMS VS FREQUENCY, FLIGHT SEQUENCE 35, IN FLIGHT 

42
10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

01234567

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

8

FIGURE 55. NORMALIZED PSD OF INCREMENTAL VERTICAL LOAD FACTOR, 

FLIGHT SEQUENCE 35, POSTFLIGHT 

0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 56. PERCENT OF INCREMENTAL VERTICAL LOAD FACTOR RMS VS 

FREQUENCY, FLIGHT SEQUENCE 35, POSTFLIGHT 

43
FIGURE 57. LATERAL LOAD FACTOR TIME HISTORY, FLIGHT SEQUENCE 35 

FIGURE 58. NORMALIZED PSD OF LATERAL LOAD FACTOR, 

FLIGHT SEQUENCE 35, PREFLIGHT 

44
0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 59. PERCENT OF TOTAL LATERAL LOAD FACTOR RMS VS, 

FREQUENCY, FLIGHT SEQUENCE 35, PREFLIGHT 

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

012345678

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

FIGURE 60. NORMALIZED PSD OF LATERAL LOAD FACTOR, 

FLIGHT SEQUENCE 35, IN FLIGHT 

45
46

0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 61. PERCENT OF TOTAL LATERAL LOAD FACTOR RMS VS FREQUENCY, 

FLIGHT SEQUENCE 35, IN FLIGHT 

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

012345678

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

FIGURE 62. NORMALIZED PSD OF LATERAL LOAD FACTOR, 

FLIGHT SEQUENCE 35, POSTFLIGHT 
0

10

20

30

40

50

60

70

80

90

01234567

Percent of Total RMS (percent)

Frequency (Hz)

100

8

FIGURE 63. PERCENT OF TOTAL LATERAL LOAD FACTOR RMS VS 

FREQUENCY, FLIGHT SEQUENCE 35, POSTFLIGHT 

FIGURE 64. LONGITUDINAL LOAD FACTOR TIME HISTORY, 

FLIGHT SEQUENCE 35 

47
10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

0 0.5 1 1.5 2 2.5 3 3.5

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

4

FIGURE 65. NORMALIZED PSD OF LONGITUDINAL LOAD FACTOR, 

FLIGHT SEQUENCE 35, PREFLIGHT 

0

10

20

30

40

50

60

70

80

90

100

0 0.5 1 1.5 2 2.5 3 3.5 4

Percent of Total RMS (percent)

Frequency (Hz)

FIGURE 66. PERCENT OF TOTAL LONGITUDINAL LOAD FACTOR RMS VS 

FREQUENCY, FLIGHT SEQUENCE 35, PREFLIGHT 

48
10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

0 0.5 1 1.5 2 2.5 3 3.5

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

4

FIGURE 67. NORMALIZED PSD OF LONGITUDINAL LOAD FACTOR, 

FLIGHT SEQUENCE 35, IN FLIGHT 

0

10

20

30

40

50

60

70

80

90

100

0 0.5 1 1.5 2 2.5 3 3.5

Percent of Total RMS (percent)

Frequency (Hz)

4

FIGURE 68. PERCENT OF TOTAL LONGITUDINAL LOAD FACTOR RMS VS 

FREQUENCY, FLIGHT SEQUENCE 35, IN FLIGHT 

49
10-6

10-5

10-4

10-3

10-2

10-1

100

101

0 0.5 1 1.5 2 2.5 3 3.5

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

102

4

FIGURE 69. NORMALIZED PSD OF LONGITUDINAL LOAD FACTOR, 

FLIGHT SEQUENCE 35, POSTFLIGHT 

0

10

20

30

40

50

60

70

80

90

100

0 0.5 1 1.5 2 2.5 3 3.5

Percent of Total RMS (percent)

Frequency (Hz)

4

FIGURE 70. PERCENT OF TOTAL LONGITUDINAL LOAD FACTOR RMS VS 

FREQUENCY, FLIGHT SEQUENCE 35, POSTFLIGHT 

50
FIGURE 71. PITCH ANGLE TIME HISTORY, FLIGHT SEQUENCE 35 

FIGURE 72. NORMALIZED PSD OF PITCH ANGLE, 

FLIGHT SEQUENCE 35, IN FLIGHT 

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

51
0

10

20

30

40

50

60

70

80

90

100

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

Percent of Total RMS (percent)

Frequency (Hz)

FIGURE 73. PERCENT OF TOTAL PITCH ANGLE RMS VS FREQUENCY, 

FLIGHT SEQUENCE 35, IN FLIGHT 

FIGURE 74. BANK ANGLE TIME HISTORY, FLIGHT SEQUENCE 35 

52
10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

0 0.5 1 1.5 2 2.5 3 3.5

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

4

FIGURE 75. NORMALIZED PSD OF BANK ANGLE, 

FLIGHT SEQUENCE 35, IN FLIGHT 

0

10

20

30

40

50

60

70

80

90

100

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

Percent of Total RMS (percent)

Frequency (Hz)

FIGURE 76. PERCENT OF TOTAL BANK ANGLE RMS VS FREQUENCY, 

FLIGHT SEQUENCE 35, IN FLIGHT 

53
FIGURE 77. AILERON ANGLE TIME HISTORY, FLIGHT SEQUENCE 35 

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

01234567

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

8

FIGURE 78. NORMALIZED PSD OF AILERON ANGLE, 

FLIGHT SEQUENCE 35, IN FLIGHT 

54
0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 79. PERCENT OF TOTAL AILERON ANGLE RMS VS FREQUENCY, 

FLIGHT SEQUENCE 35, IN FLIGHT 

FIGURE 80. ELEVATOR ANGLE TIME HISTORY, FLIGHT SEQUENCE 35 

55
10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

Power Spectral Density (RMS degrees)2 / Hertz

F equency (Hertz) r

FIGURE 81. NORMALIZED PSD OF ELEVATOR ANGLE, 

FLIGHT SEQUENCE 35, IN FLIGHT

0

10

20

30

40

50

60

70

80

90

100

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

Percent of Total RMS (percent)

Frequency (Hz)

FIGURE 82. PERCENT OF TOTAL ELEVATOR ANGLE RMS VS FREQUENCY, 

FLIGHT SEQUENCE 35, IN FLIGHT 

56
57

FIGURE 83. RUDDER ANGLE TIME HISTORY, FLIGHT SEQUENCE 35 

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

012345678

Frequency (Hertz)

Power Spectral Density (RMS degrees)2 / Hertz

FIGURE 84. NORMALIZED PSD OF RUDDER ANGLE, 

FLIGHT SEQUENCE 35, IN FLIGHT 
FLIGHT SEQUENCE 35, IN FLIGHT 

FIGURE 85. PERCENT OF TOTAL RUDDER ANGLE RMS VS FREQUENCY, 

0

10

20

30

40

50

60

70

80

90

100

012345678

Percent of Total RMS (percent)

Frequency (Hz)

FIGURE 86. INCREMENTAL VERTICAL LOAD FACTOR TIME HISTORY, 

FLIGHT SEQUENCE 62 

58
10-6

10-5

10-4

10-3

10-2

10-1

100

101

01234567

Power Spectral Density (RMS g)2 / Hertz

Frequency (Hertz)

102

8

FIGURE 87. NORMALIZED PSD OF INCREMENTAL VERTICAL LOAD FACTOR, 

FLIGHT SEQUENCE 62, PREFLIGHT 

0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 88. PERCENT OF TOTAL INCREMENTAL VERTICAL LOAD FACTOR 

RMS VS FREQUENCY, FLIGHT SEQUENCE 62, PREFLIGHT 

59
10-6

10-5

10-4

10-3

10-2

10-1

100

101

01234567

Power Spectral Density (RMS g)2 / Hertz

Frequency (Hertz)

102

8

FIGURE 89. NORMALIZED PSD OF INCREMENTAL VERTICAL LOAD FACTOR, 

FLIGHT SEQUENCE 62, IN FLIGHT 

0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 90. PERCENT OF TOTAL INCREMENTAL VERTICAL LOAD FACTOR 

RMS VS FREQUENCY, FLIGHT SEQUENCE 62, IN FLIGHT 

60
10-6

10-5

10-4

10-3

10-2

10-1

100

101

10

01234567

Power Spectral Density (RMS g)2 / Hertz

Frequency (Hertz)

2

8

FIGURE 91. NORMALIZED PSD OF INCREMENTAL VERTICAL LOAD FACTOR, 

FLIGHT SEQUENCE 62, POSTFLIGHT 

0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 92. PERCENT OF TOTAL INCREMENTAL VERTICAL LOAD FACTOR 

RMS VS FREQUENCY, FLIGHT SEQUENCE 62, POSTFLIGHT 

61
FIGURE 93. LATERAL LOAD FACTOR TIME HISTORY, FLIGHT SEQUENCE 62 

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

01234567

Power Spectral Density (RMS g)2 / Hertz

Frequency (Hertz)

8

FIGURE 94. NORMALIZED PSD OF LATERAL LOAD FACTOR, 

FLIGHT SEQUENCE 62, PREFLIGHT 

62
0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 95. PERCENT OF TOTAL LATERAL LOAD FACTOR RMS VS 

FREQUENCY, FLIGHT SEQUENCE 62, PREFLIGHT 

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

01234567

Power Spectral Density (RMS g)2 / Hertz

Frequency (Hertz)

8

FIGURE 96. NORMALIZED PSD OF LATERAL LOAD FACTOR, 

FLIGHT SEQUENCE 62, IN FLIGHT 

63
0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 97. PERCENT OF TOTAL LATERAL LOAD FACTOR RMS VS 

FREQUENCY, FLIGHT SEQUENCE 62, IN FLIGHT 

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

01234567

Power Spectral Density (RMS g)2 / Hertz

Frequency (Hertz)

8

FIGURE 98. NORMALIZED PSD OF LATERAL LOAD FACTOR, 

FLIGHT SEQUENCE 62, POSTFLIGHT 

64
0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 99. PERCENT OF TOTAL LATERAL LOAD FACTOR RMS VS 

FREQUENCY, FLIGHT SEQUENCE 62, POSTFLIGHT 

FIGURE 100. LONGITUDINAL LOAD FACTOR TIME HISTORY, 

FLIGHT SEQUENCE 62 

65
10-6

10-5

10-4

10-3

10-2

10-1

100

101

10

0 0.5 1 1.5 2 2.5 3 3.5

Power Spectral Density (RMS g)2 / Hertz

Frequency (Hertz)

2

4

FIGURE 101. NORMALIZED PSD OF LONGITUDINAL LOAD FACTOR, 

FLIGHT SEQUENCE 62, PREFLIGHT 

0

10

20

30

40

50

60

70

80

90

100

0 0.5 1 1.5 2 2.5 3 3.5

Percent of Total RMS (percent)

Frequency (Hz)

4

FIGURE 102. PERCENT OF TOTAL LONGITUDINAL LOAD FACTOR RMS VS 

FREQUENCY, FLIGHT SEQUENCE 62, PREFLIGHT 

66
10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

0 0.5 1 1.5 2 2.5 3 3.5

Power Spectral Density (RMS g)2 / Hertz

Frequency (Hertz)

4

FIGURE 103. NORMALIZED PSD OF LONGITUDINAL LOAD FACTOR, 

FLIGHT SEQUENCE 62, IN FLIGHT 

0

10

20

30

40

50

60

70

80

90

100

0 0.5 1 1.5 2 2.5 3 3.5

Percent of Total RMS (percent)

Frequency (Hz)

4

FIGURE 104. PERCENT OF TOTAL LONGITUDINAL LOAD FACTOR RMS VS 

FREQUENCY, FLIGHT SEQUENCE 62, IN FLIGHT 

67
10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

0 0.5 1 1.5 2 2.5 3 3.5 4

Power Spectral Density (RMS g)2 / Hertz

Frequency (Hertz)

FIGURE 105. NORMALIZED PSD OF LONGITUDINAL LOAD FACTOR, 

FLIGHT SEQUENCE 62, POSTFLIGHT 

0

10

20

30

40

50

60

70

80

90

100

0 0.5 1 1.5 2 2.5 3 3.5

Percent of Total RMS (percent)

Frequency (Hz)

4

FIGURE 106. PERCENT OF TOTAL LONGITUDINAL LOAD FACTOR RMS VS 

FREQUENCY, FLIGHT SEQUENCE 62, POSTFLIGHT 

68
FIGURE 107. PITCH ANGLE TIME HISTORY, FLIGHT SEQUENCE 62 

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

FIGURE 108. NORMALIZED PSD OF PITCH ANGLE, 

FLIGHT SEQUENCE 62, IN FLIGHT 

69
0

10

20

30

40

50

60

70

80

90

100

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

Percent of Total RMS (percent)

Frequency (Hz)

FIGURE 109. PERCENT OF TOTAL PITCH ANGLE RMS VS FREQUENCY, 

FLIGHT SEQUENCE 62, IN FLIGHT 

FIGURE 110. BANK ANGLE TIME HISTORY, FLIGHT SEQUENCE 62 

70
10-6

10-5

10-4

10-3

10-2

10-1

100

101

10

0 0.5 1 1.5 2 2.5 3 3.5

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

2

4

FIGURE 111. NORMALIZED PSD OF BANK ANGLE, 

FLIGHT SEQUENCE 62, IN FLIGHT 

0

10

20

30

40

50

60

70

80

90

100

0 0.5 1 1.5 2 2.5 3 3.5

Percent of Total RMS (percent)

Frequency (Hz)

4

FIGURE 112. PERCENT OF TOTAL BANK ANGLE RMS VS FREQUENCY, 

FLIGHT SEQUENCE 62, IN FLIGHT 

71
FIGURE 113. AILERON ANGLE TIME HISTORY, FLIGHT SEQUENCE 62 

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

01234567

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

8

FIGURE 114. NORMALIZED PSD OF AILERON ANGLE, FLIGHT 

SEQUENCE 62, IN FLIGHT 

72
0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 115. PERCENT OF AILERON ANGLE RMS VS FREQUENCY, 

FLIGHT SEQUENCE 62, IN FLIGHT 

FIGURE 116. ELEVATOR ANGLE TIME HISTORY, FLIGHT SEQUENCE 62 

73
10-6

10-5

10-4

10-3

10-2

10-1

100

101

10

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

2

FIGURE 117. NORMALIZED PSD OF ELEVATOR ANGLE, 

FLIGHT SEQUENCE 62, IN FLIGHT 

0

10

20

30

40

50

60

70

80

90

100

0 0.25 0.5 0.75 1 1.25 1.5 1.75 2

Percent of Total RMS (percent)

Frequency (Hz)

FIGURE 118. PERCENT OF ELEVATOR ANGLE RMS VS FREQUENCY, 

FLIGHT SEQUENCE 62, IN FLIGHT 

74
FIGURE 119. RUDDER ANGLE TIME HISTORY, FLIGHT SEQUENCE 62 

10-6

10-5

10-4

10-3

10-2

10-1

100

101

102

01234567

Power Spectral Density (RMS degrees)2 / Hertz

Frequency (Hertz)

8

FIGURE 120. NORMALIZED PSD OF RUDDER ANGLE, 

FLIGHT SEQUENCE 62, IN FLIGHT 

75
0

10

20

30

40

50

60

70

80

90

100

01234567

Percent of Total RMS (percent)

Frequency (Hz)

8

FIGURE 121. PERCENT OF RUDDER ANGLE RMS VS FREQUENCY, 

FLIGHT SEQUENCE 62, IN FLIGHT 

100

101

102

103

104

105

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

16 sps

8 sps

4 sps

2 sps

1 sps

Cumulative Occurrences

Incremental Vertical Load Factor, Δnz (g)

FIGURE 122. CUMULATIVE OCCURRENCES OF INCREMENTAL 

VERTICAL LOAD FACTOR, PREFLIGHT 

76
16 Samples per Second 8 Samples per Second 4 Samples per Second 2 Samples per Second 1 Sample per Second 

Vertical 

Load 

Factor 

nz

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

0.2 2 100 2 100 2 100 1 50 1 50 

0.15 37 100 35 94.59 27 72.97 12 32.43 6 16.22 

0.1 110 100 105 95.45 79 71.82 32 29.09 13 11.82 

0.05 639 100 620 97.03 415 64.95 203 31.77 84 13.15 

 

-0.05 9713 100 9334 96.1 5663 58.3 2395 24.66 1218 12.54 

-0.1 767 100 735 95.83 492 64.15 252 32.86 99 12.91 

-0.15 125 100 124 99.2 87 69.6 40 32 15 12 

-0.2 23 100 23 100 11 47.83 4 17.39 2 8.696 

sps = samples per second 

FIGURE 123. EFFECT OF SAMPLING RATE ON CUMULATIVE OCCURRENCES 

OF INCREMENTAL VERTICAL LOAD FACTOR, PREFLIGHT 

FIGURE 124. PERCENT OF INCREMENTAL VERTICAL ACCELERATION PEAK 

COUNTS AS A FUNCTION OF SAMPLING RATE, PREFLIGHT 

77
100

101

102

103

104

105

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

16 sps

8 sps

4 sps

2 sps

1 sps

Cumulative Occurrences

Incremental Vertical Load Factor, Δnz (g)

FIGURE 125. CUMULATIVE OCCURRENCES OF INCREMENTAL VERTICAL LOAD 

FACTOR, IN FLIGHT 

16 Samples per Second 8 Samples per Second 4 Samples per Second 2 Samples per Second 1 Sample per Second 

Vertical 

Load 

Factor 

nz

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

0.55 2 100 2 100 1 50 1 50 

0.5 3 100 3 100 2 66.67 2 66.67 1 33.33 

0.45 5 100 5 100 4 80 3 60 1 20 

0.4 6 100 6 100 6 100 3 50 1 16.67 

0.35 8 100 8 100 8 100 4 50 2 25 

0.3 27 100 27 100 17 62.96 7 25.93 5 18.52 

0.25 82 100 81 98.78 68 82.93 46 56.1 33 40.24 

0.2 269 100 266 98.88 215 79.93 166 61.71 106 39.41 

0.15 702 100 697 99.29 597 85.04 469 66.81 329 46.87 

0.1 2072 100 2054 99.13 1787 86.25 1358 65.54 966 46.62 

0.05 7000 100 6898 98.54 5877 83.96 4468 63.83 3122 44.6 

 

-0.05 19327 100 19058 98.61 16048 83.03 11980 61.99 8345 43.18 

-0.1 5961 100 5878 98.61 4939 82.86 3658 61.37 2517 42.22 

-0.15 1639 100 1617 98.66 1365 83.28 988 60.28 644 39.29 

-0.2 490 100 483 98.57 402 82.04 279 56.94 161 32.86 

-0.25 167 100 165 98.8 136 81.44 85 50.9 40 23.95 

-0.3 56 100 53 94.64 41 73.21 24 42.86 10 17.86 

-0.35 22 100 22 100 14 63.64 9 40.91 4 18 

-0.4 3 100 3 100 1 33.33 1 33.33 

FIGURE 126. EFFECT OF SAMPLING RATE ON CUMULATIVE OCCURRENCES 

OF INCREMENTAL VERTICAL LOAD FACTOR, IN FLIGHT 

78
FIGURE 127. PERCENT OF INCREMENTAL VERTICAL ACCELERATION PEAK 

COUNTS AS A FUNCTION OF SAMPLING RATE, IN FLIGHT 

100

101

102

103

104

105

-0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8

16 sps

8 sps

4 sps

2 sps

1 sps

Cumulative Occurrences

Incremental Vertical Load Factor, Δnz  (g)

FIGURE 128. CUMULATIVE OCCURRENCES OF INCREMENTAL 

VERTICAL LOAD FACTOR, POSTFLIGHT 

79
16 Samples per Second 8 Samples per Second 4 Samples per Second 2 Samples per Second 1 Sample per Second 

Vertical 

Load 

Factor 

nz

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

0.35 2 100 2 100 1 50 1 50 

0.3 8 100 6 75 3 37.5 1 12.5 

0.25 22 100 18 81.82 14 63.64 6 27.27 3 13.64 

0.2 51 100 48 94.12 35 68.63 18 35.29 8 15.69 

0.15 118 100 117 99.15 83 70.34 53 44.92 19 16.1 

0.1 258 100 260 100.8 197 76.36 120 46.51 48 18.6 

0.05 1183 100 118 97.89 809 68.39 440 37.19 199 16.82 

 

-0.05 10717 100 10335 96.44 6494 60.6 2506 23.38 1260 11.76 

-0.1 1054 100 1028 97.53 682 64.71 352 33.4 143 13.57 

-0.15 179 100 175 97.77 133 74.3 73 40.78 23 12.85 

-0.2 41 100 41 100 32 78.05 18 43.9 6 14.63 

-0.25 9 100 9 100 5 55.56 2 22.22 1 11.11 

-0.3 6 100 6 100 4 66.67 2 33.33 1 16.67 

-0.35 5 100 5 100 2 40 1 20 1 20 

-0.4 1 100 1 100 

FIGURE 129. EFFECT OF SAMPLING RATE ON CUMULATIVE OCCURRENCES 

OF INCREMENTAL VERTICAL LOAD FACTOR, POSTFLIGHT 

FIGURE 130. PERCENT OF INCREMENTAL VERTICAL ACCELERATION PEAK 

COUNTS AS A FUNCTION OF SAMPLING RATE, POSTFLIGHT 

80
100

101

102

103

104

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

16 sps

8 sps

4 sps

2 sps

1 sps

Cumulative Occurrences

Lateral Load Factor, n

y

 (g)

FIGURE 131. CUMULATIVE OCCURRENCES OF LATERAL 

LOAD FACTOR, PREFLIGHT 

81
16 Samples per Second 8 Samples per Second 4 Samples per Second 2 Samples per Second 1 Sample per Second 

Lateral 

Load 

Factor 

ny

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

0.17 1 100 1 100 1 100 

0.16 1 100 1 100 1 100 

0.15 1 100 1 100 1 100 

0.14 2 100 2 100 2 100 1 50 

0.13 2 100 2 100 2 100 1 50 

0.12 6 100 6 100 6 100 4 66.67 3 50 

0.11 7 100 7 100 7 100 7 100 6 85.71 

0.1 10 100 10 100 10 100 10 100 8 80 

0.09 21 100 21 100 21 100 16 76.19 13 61.9 

0.08 49 100 49 100 49 100 40 81.63 34 69.39 

0.07 91 100 91 100 91 100 77 84.62 58 63.74 

0.06 123 100 123 100 121 98.37 104 84.55 86 69.92 

0.05 208 100 208 100 205 98.56 180 86.54 142 68.27 

0.04 331 100 331 100 326 98.49 261 78.85 202 61.03 

0.03 667 100 667 100 656 98.35 497 74.51 369 55.32 

0.02 1244 100 1244 100 1210 97.27 889 71.46 595 47.83 

0.01 4577 100 4576 99.98 4436 96.92 2811 61.42 1583 34.59 

 

-0.01 8963 100 8961 99.98 8663 96.65 5497 61.33 2805 31.3 

-0.02 2467 100 2465 99.92 2409 97.65 1694 68.79 1063 43.09 

-0.03 1168 100 1167 99.91 1149 98.37 865 74.06 609 52.14 

-0.04 524 100 523 99.81 514 98.09 412 78.63 314 59.92 

-0.05 342 100 341 99.71 336 98.25 277 80.99 208 60.82 

-0.06 201 100 200 99.5 197 98.01 165 82.09 137 68.16 

-0.07 151 100 150 99.34 147 97.35 122 80.79 107 70.86 

-0.08 110 100 109 99.09 106 96.36 85 77.27 57 51.82 

-0.09 68 100 67 98.53 65 95.59 48 70.59 32 47.06 

-0.1 50 100 49 98 47 94 33 66 25 50 

-0.11 37 100 36 97.3 34 91.89 23 62.16 15 40.54 

-0.12 33 100 32 96.97 30 90.91 21 63.64 12 36.36 

-0.13 29 100 28 96.55 26 89.66 

-0.14 26 100 25 96.15 23 88.46 17 65.38 11 42.31 

-0.15 22 100 21 95.45 19 86.36 15 68.18 10 45.45 

-0.16 21 100 20 95.24 18 85.71 14 66.67 9 42.86 

-0.17 9 100 9 100 8 88.89 5 55.56 3 33.33 

-0.18 5 100 5 100 4 80 3 60 2 40 

-0.19 1 100 1 100 1 100 1 100 1 100 

FIGURE 132. EFFECT OF SAMPLING RATE ON CUMULATIVE OCCURRENCES OF 

LATERAL LOAD FACTOR, PREFLIGHT 

82
FIGURE 133. PERCENT OF LATERAL LOAD FACTOR PEAK COUNTS AS A 

FUNCTION OF SAMPLING RATE, PREFLIGHT 

100

101

102

103

104

105

-0.2 -0.15 -0.1 -0.05 0 0.05 0.1 0.15 0.2

16 sps

8 sps

4 sps

2 sps

1 sps

Cumulative Occurrences

Lateral Load Factor, ny (g)

FIGURE 134. CUMULATIVE OCCURRENCES OF LATERAL 

LOAD FACTOR, IN FLIGHT 

83
16 Samples per Second 8 Samples per Second 4 Samples per Second 2 Samples per Second 1 Sample per Second 

Lateral 

Load 

Factor 

ny

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

0.17 1 100 1 100 1 100 1 100 1 100 

0.16 1 100 1 100 1 100 1 100 1 100 

0.14 1 100 1 100 1 100 1 100 1 100 

0.13 1 100 1 100 1 100 1 100 1 100 

0.12 3 100 3 100 2 66.67 1 33.33 1 33.33 

0.11 9 100 9 100 6 66.67 2 22.22 1 11.11 

0.1 25 100 25 100 22 88 11 44 6 24 

0.09 48 100 48 100 44 91.67 28 58.33 13 27.08 

0.08 94 100 94 100 88 93.62 56 59.57 32 34.04 

0.07 188 100 188 100 181 96.28 121 64.36 67 35.64 

0.06 273 100 273 100 261 95.6 185 67.77 103 37.73 

0.05 649 100 649 100 631 97.23 466 71.8 282 43.45 

0.04 1138 100 1138 100 1113 97.8 823 72.32 478 42 

0.03 3067 100 3066 99.97 3003 97.91 2205 71.89 1382 45.06 

0.02 7211 100 7206 99.93 7046 97.71 5173 71.74 3219 44.64 

0.01 36810 100 36805 99.99 36047 97.93 26718 72.58 16074 43.87 

 

-0.01 23608 100 23607 100 23142 98.03 17742 75.15 11667 49.42 

-0.02 6559 100 6558 99.98 6434 98.09 4997 76.19 3273 49.9 

-0.03 3126 100 3125 99.97 3067 98.11 2318 74.15 1455 46.55 

-0.04 1166 100 1165 99.91 1142 97.94 856 73.41 518 44.43 

-0.05 658 100 657 99.85 639 97.11 459 69.76 294 44.68 

-0.06 285 100 284 99.65 278 97.54 194 68.07 122 42.81 

-0.07 173 100 172 99.42 170 98.27 108 62.43 66 38.15 

-0.08 88 100 87 98.86 85 96.59 48 54.55 30 34.09 

-0.09 43 100 42 97.67 42 97.67 29 67.44 13 30.23 

-0.1 31 100 30 96.77 30 96.77 23 74.19 9 29.03 

-0.11 18 100 17 94.44 17 94.44 12 66.67 4 22.22 

-0.12 9 100 8 88.89 8 88.89 5 55.56 2 22.22 

-0.13 7 100 6 85.71 6 85.71 5 71.43 2 28.57 

-0.14 4 100 4 100 4 100 4 100 2 50 

-0.15 1 100 1 100 1 100 1 100 

-0.16 1 100 1 100 1 100 1 100 

FIGURE 135. EFFECT OF SAMPLING RATE ON CUMULATIVE OCCURRENCES OF 

LATERAL LOAD FACTOR, IN FLIGHT 

84
FIGURE 136. PERCENT OF LATERAL LOAD FACTOR PEAK COUNTS AS A 

FUNCTION OF SAMPLING RATE, IN FLIGHT 

100

101

102

103

104

-0.3 -0.2 -0.1 0 0.1 0.2 0.3

16 sps

8 sps

4 sps

2 sps

1 sps

Cumulative Occurrences

Lateral Load Factor, ny (g)

FIGURE 137. CUMULATIVE OCCURRENCES OF LATERAL 

LOAD FACTOR, POSTFLIGHT 

85
16 Samples per Second 8 Samples per Second 4 Samples per Second 2 Samples per Second 1 Sample per Second 

Lateral 

Load 

Factor 

ny

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

0.17 1 100 1 100 1 100 

0.16 2 100 2 100 2 100 1 50 

0.15 5 100 5 100 5 100 3 60 2 40 

0.14 14 100 14 100 14 100 9 64.29 5 35.71 

0.13 17 100 17 100 17 100 14 82.35 6 35.29 

0.12 30 100 30 100 30 100 25 83.33 18 60 

0.11 45 100 45 100 45 100 36 80 28 62.22 

0.1 66 100 66 100 65 98.48 58 87.88 48 72.73 

0.09 81 100 81 100 81 100 75 92.59 60 74.07 

0.08 120 100 120 100 119 99.17 112 93.33 87 72.5 

0.07 175 100 175 100 173 98.86 151 86.29 127 72.57 

0.06 240 100 240 100 238 99.17 207 86.25 169 70.42 

0.05 355 100 355 100 349 98.31 294 82.82 247 69.58 

0.04 461 100 461 100 450 97. 61 384 83.3 309 67.03 

0.03 768 100 769 100.13 756 98.44 589 76.69 459 59.77 

0.02 1289 100 1292 100.23 1263 97.98 905 70.21 636 49.34 

0.01 3476 100 3480 100.12 3374 97.07 2132 61.33 1261 36.28 

 

-0.01 5988 100 5989 100.02 5807 96.98 3606 60.22 2000 33.4 

-0.02 2305 100 2306 100.04 2256 97.87 1569 68.07 1032 44.77 

-0.03 1395 100 1396 100.07 1370 98.21 1018 72.97 708 50.75 

-0.04 824 100 825 100.12 815 98.91 620 75.24 445 54 

-0.05 601 100 602 100.17 590 98.17 445 74.04 339 56.41 

-0.06 422 100 423 100.24 412 97.63 316 74.88 236 55.92 

-0.07 331 100 332 100.3 325 98.19 253 76.44 191 57.7 

-0.08 235 100 236 100.43 230 97.87 174 74.04 132 56.17 

-0.09 161 100 162 100.62 159 98.76 117 72.67 83 51.55 

-0.1 119 100 120 100.84 117 98.32 83 69.75 57 47.9 

-0.11 84 100 85 101.19 82 97.62 58 69.05 41 48.81 

-0.12 65 100 66 101.54 65 100 42 64.62 31 47.69 

-0.13 40 100 41 102.5 41 102.5 23 57.5 16 40 

-0.14 28 100 28 100 28 100 17 60.71 12 42.86 

-0.15 17 100 17 100 17 100 10 58.82 6 35.29 

-0.16 13 100 13 100 13 100 9 69.23 5 38.46 

-0.17 7 100 7 100 7 100 5 71.43 2 28.57 

-0.18 2 100 2 100 2 100 2 100 2 100 

-0.19 2 100 2 100 2 100 2 100 2 100 

-0.2 2 100 2 100 2 100 2 100 2 100 

-0.21 2 100 2 100 2 100 2 100 2 100 

-0.22 1 100 1 100 1 100 1 100 1 100 

-0.23 1 100 1 100 1 100 1 100 1 100 

-0.24 1 100 1 100 1 100 1 100 1 100 

-0.25 1 100 1 100 1 100 1 100 1 100 

-0.26 1 100 1 100 1 100 1 100 1 100 

FIGURE 138. EFFECT OF SAMPLING RATE ON CUMULATIVE OCCURRENCES 

OF LATERAL LOAD FACTOR, POSTFLIGHT 

86
FIGURE 139. PERCENT OF LATERAL LOAD FACTOR PEAK COUNTS AS A 

FUNCTION OF SAMPLING RATE, POSTFLIGHT 

100

101

102

103

104

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

8 sps

4 sps

2 sps

1 sps

Cumulative Occurrences

Longitudinal Load Factor, nx (g)

FIGURE 140. CUMULATIVE OCCURRENCES OF LONGITUDINAL 

LOAD FACTOR, PREFLIGHT

87
8 Samples per Second 4 Samples per Second 2 Samples per Second 1 Sample per Second 

Longitudinal 

Load Factor 

nx

Cumulative 

Occurrences 

Percent of 

8 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences

Cumulative 

Occurrences

Cumulative 

Occurrences

Percent of 

8 sps 

Cumulative 

Occurrences

Cumulative 

Occurrences 

Percent of 

8 sps 

Cumulative 

Occurrences

Percent of 

8 sps 

0.38 1 

0.36 1 100 1 100 1 100 

0.35 2 100 2 100 1 50 1 50 

0.34 2 100 2 100 1 50 1 50 

0.33 3 100 3 100 2 66.67 3 100 

0.32 10 100 8 80 5 50 3 30 

0.31 17 100 14 82.35 11 64.71 6 35.29 

0.3 24 100 22 91.67 18 75 15 62.5 

0.29 26 100 24 92.31 19 73.08 16 61.54 

0.28 31 100 29 93.55 24 77.42 21 67.74 

0.27 32 100 30 93.75 25 78.12 23 71.87 

0.26 33 100 31 93.94 26 78.79 23 69.7 

0.25 33 100 31 93.94 26 78.79 23 69.7 

0.24 33 100 31 93.94 26 78.79 23 69.7 

0.23 33 100 31 93.94 26 78.79 23 69.7 

0.22 33 100 31 93.94 26 78.79 23 69.7 

0.21 33 100 31 93.94 26 78.79 23 69.7 

0.2 33 100 31 93.94 26 78.79 23 69.7 

0.19 33 100 31 93.94 26 78.79 23 69.7 

0.18 33 100 31 93.94 26 78.79 23 69.7 

0.17 33 100 31 93.94 26 78.79 23 69.7 

0.16 33 100 31 93.94 26 78.79 23 69.7 

0.15 33 100 31 93.94 26 78.79 23 69.7 

0.14 33 100 31 93.94 26 78.79 23 69.7 

0.13 33 100 31 93.94 26 78.79 23 69.7 

0.12 33 100 31 93.94 26 78.79 23 69.7 

0.11 33 100 31 93.94 26 78.79 23 69.7 

0.1 34 100 32 94.12 27 79.41 24 70.59 

0.09 35 100 33 94.29 28 80 25 71.43 

0.08 36 100 34 94.44 29 80.56 26 72.22 

0.07 40 100 38 95 31 77.5 28 70 

0.06 59 100 57 96.61 47 79.66 41 69.49 

0.05 95 100 93 97.89 80 84.21 71 74.74 

0.04 165 100 162 98.18 126 76.36 113 68.48 

0.03 357 100 352 98.6 276 77.31 237 66.39 

0.02 894 100 869 97.2 625 69.91 471 52.68 

0.01 4272 100 4137 96.84 2500 58.52 1740 40.73 

 

-0.01 2629 100 2579 98.1 1928 73.34 1571 59.76 

-0.02 1241 100 1225 98.71 1009 81.31 874 70.43 

-0.03 746 100 740 99.2 624 83.65 534 71.58 

-0.04 330 100 327 99.09 267 80.91 233 70.61 

-0.05 205 100 202 98.54 159 77.56 135 65.85 

-0.06 85 100 83 97.65 62 72.94 49 57.65 

-0.07 46 100 44 95.65 29 63.04 20 43.48 

-0.08 26 100 24 92.31 14 53.85 8 30.77 

-0.09 22 100 20 90.91 11 50 4 18.18 

-0.1 18 100 16 88.89 7 38.89 2 11.11 

-0.11 12 100 10 83.33 5 41.67 1 8.333 

-0.13 9 100 8 88.89 4 44.44 1 11.11 

-0.14 8 100 7 87.5 4 50 1 12.5 

-0.15 6 100 5 83.33 3 50 

-0.16 5 100 4 80 2 40 

-0.17 2 100 1 50 

FIGURE 141. EFFECT OF SAMPLING RATE ON CUMULATIVE OCCURRENCES OF 

LONGITUDINAL LOAD FACTOR, PREFLIGHT 

88
FIGURE 14 PERC OF LO GITU L LO FAC PEAK OUNT S 

A FUNCTION OF SAMPLING RA , PRE HT 

FIGURE 1 UDINAL 

LOAD FACTOR, IN FLIGHT 

2. ENT N DINA AD TOR C S A

TE FLIG

43. CUMULATIVE OCCURRENCES OF LONGIT

100

1

2

3

4

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

10

10

10

10 8 sps

4 sps

2 sps

1 sps

Cumulative Occurrences

Longitudinal Load Factor, nx (g)

89
8 Samples per Second 4 Samples per Second 2 Samples per Second 1 Sample per Second 

Longitudinal 

Load Factor 

nx

Cumulative 

Occurrences

Percent of 

8 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences

Percent of 

8 sps 

Cumulative 

Occurrences

Cumulative 

Occurrences

Percent of 

8 sps 

Cumulative 

Occurrences

Cumulative 

Occurrences 

Percent of 

8 sps 

Cumulative 

Occurrences

0.39 1 100 1 100 1 100 

0.38 1 100 1 100 1 100 

0.37 1 100 1 100 1 100 

0.36 2 100 2 100 3 150 2 100 

0.35 5 100 5 100 6 120 5 100 

0.34 7 100 7 100 7 100 5 71.43 

0.33 19 100 19 100 18 94.74 15 78.95 

0.32 37 100 39 105.4 38 102.7 39 105.4 

0.31 52 100 55 105.8 56 107.7 53 101.9 

0.3 61 100 63 103.3 65 106.6 68 111.5 

0.29 67 100 69 103 73 109 73 109 

0.28 74 100 76 102.7 81 109.5 82 110.8 

0.27 75 100 77 102.7 82 109.3 84 112 

0.26 75 100 77 102.7 82 109.3 85 113.3 

0.25 75 100 77 102.7 82 109.3 85 113.3 

0.24 76 100 78 102.6 83 109.2 86 113.2 

0.23 76 100 78 102.6 83 109.2 86 113.2 

0.22 76 100 78 102.6 83 109.2 86 113.2 

0.21 78 100 80 102.6 85 109 86 110.3 

0.2 79 100 81 102.5 86 108.9 89 112.7 

0.19 84 100 86 102.4 90 107.1 92 109.5 

0.18 87 100 89 102.3 94 108 96 110.3 

0.17 96 100 98 102.1 103 107.3 104 108.3 

0.16 105 100 107 101.9 112 106.7 112 106.7 

0.15 116 100 118 101.7 122 105.2 123 106 

0.14 129 100 131 101.6 134 103.9 135 104.7 

0.13 149 100 150 100.7 152 102 149 100 

0.12 177 100 179 101.1 181 102.3 182 102.8 

0.11 204 100 205 100.5 201 98.53 198 97.06 

0.1 261 100 263 100.8 257 98.47 250 95.79 

0.09 297 100 299 100.7 294 98.99 284 95.62 

0.08 384 100 385 100.3 377 98.18 362 94.27 

0.07 466 100 468 100.4 460 98.71 438 93.99 

0.06 525 100 527 100.4 511 97.33 497 94.67 

0.05 663 100 665 100.3 640 96.53 611 92.16 

0.04 750 100 752 100.3 722 96.27 693 92.4 

0.03 956 100 957 100.1 902 94.35 853 89.23 

0.02 1150 100 1146 99.65 1064 92.52 1001 87.04 

0.01 1707 100 1698 99.47 1487 87.11 1322 77.45 

 

-0.01 1261 100 1246 98.81 1072 85.01 921 73.04 

-0.02 657 100 652 99.24 592 90.11 554 84.32 

-0.03 484 100 482 99.59 453 93.6 435 89.88 

-0.04 303 100 303 100 290 95.71 280 92.41 

-0.05 214 100 211 98.6 201 93.93 194 90.65 

-0.06 130 100 130 100 126 96.92 121 93.08 

-0.07 94 100 94 100 88 93.62 83 88.3 

-0.08 56 100 55 98.21 51 91.07 50 89.29 

-0.09 28 100 27 96.43 25 89.29 24 85.71 

-0.1 19 100 19 100 16 84.21 15 78.95 

-0.11 10 100 10 100 10 100 9 90 

-0.12 7 100 7 100 7 100 5 71.43 

FIGURE 144. EFFECT OF SAMPLING RATE ON CUMULATIVE OCCURRENCES OF 

LONGITUDINAL LOAD FACTOR, IN FLIGHT 

90
F RE 145 RC OF LO ITU AL LO FA R PEA OU AS 

A FUNCTION OF SAMPLING R E, IN

FIGURE 146. CUMULATIVE OCCURRENCES OF LONGITUDINAL 

LOAD FACTOR, POSTFLIGHT 

IGU . PE NT NG DIN AD CTO K C NTS

AT FLIGHT 

E

100

01

02

03

04

-0.4 -0.3 -0.2 -0.1 0 0.1 0.2 0.3 0.4

1

1

1

1 8 sps

4 sps

2 sps

1 sps

Cumulative Occurrence

Longitudinal Load Factor, nx (g)

s

91
8 Samples per Second 4 Sa16les per Second 2 Samples per Second 1 Sample per Second 

Longitudinal 

Load Factor 

nx

Cumulative 

Occurrences 

Percent of 

8 sps 

Cumulative 

Occurrences 

Cumul9tive 

Occurrences

Percent of 

8 sps 

Cumulative 

Occurrences

Cumulative 

Occurrences

Percent of 

8 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

8 sps 

Cumulative 

Occurrences

0.1 1 100 1 100 1 100 1 100 

0.09 4 100 4 100 2 50 1 25 

0.08 9 100 9 100 5 55.56 4 44.44 

0.07 16 100 16 100 12 75 10 62.5 

0.06 30 100 29 96.67 22 73.33 17 56.67 

0.05 67 100 64 95.52 48 71.64 39 58.21 

0.04 101 100 97 96.04 71 70.3 57 56.44 

0.03 268 100 262 97.76 166 61.94 116 43.28 

0.02 773 100 747 96.64 464 60.03 308 39.84 

0.01 3670 100 3545 96.59 2147 58.5 1478 40.27 

 

-0.01 2676 100 2612 97.61 1980 73.99 1572 58.74 

-0.02 1504 100 1479 98.34 1211 80.52 1000 66.49 

-0.03 1077 100 1063 98.7 869 80.69 725 67.32 

-0.04 631 100 617 97.78 505 80.03 427 67.67 

-0.05 447 100 438 97.99 346 77.4 302 67.56 

-0.06 299 100 291 97.32 234 78.26 202 67.56 

-0.07 252 100 245 97.22 202 80.16 182 72.22 

-0.08 203 100 199 98.03 170 83.74 157 77.34 

-0.09 178 100 174 97.75 146 82.02 137 76.97 

-0.1 168 100 164 97.62 142 84.52 133 79.17 

-0.11 157 100 153 97.45 133 84.71 125 79.62 

-0.12 148 100 145 97.97 127 85.81 123 83.11 

-0.13 140 100 137 97.86 123 87.86 121 86.43 

-0.14 136 100 133 97.79 120 88.24 118 86.76 

-0.15 128 100 126 98.44 118 92.19 114 89.06 

-0.16 118 100 117 99.15 111 94.07 108 91.53 

-0.17 108 100 106 98.15 102 94.44 96 88.89 

-0.18 88 100 88 100 85 96.59 79 89.77 

-0.19 78 100 78 100 75 96.15 69 88.46 

-0.2 68 100 68 100 65 95.59 57 83.82 

-0.21 60 100 60 100 56 93.33 51 85 

-0.22 48 100 47 97.92 44 91.67 43 89.58 

-0.23 41 100 41 100 40 97.56 39 95.12 

-0.24 36 100 36 100 33 91.67 30 83.33 

-0.25 31 100 31 100 29 93.55 24 77.42 

-0.26 27 100 27 100 24 88.89 20 74.07 

-0.27 15 100 15 100 13 86.67 12 80 

-0.28 11 100 11 100 9 81.82 7 63.64 

-0.29 8 100 8 100 6 75 6 75 

-0.3 7 100 7 100 6 85.71 4 57.14 

-0.31 4 100 4 100 4 100 3 75 

-0.32 4 100 4 100 4 100 3 75 

-0.33 2 100 2 100 2 100 2 100 

-0.34 2 100 2 100 2 100 2 100 

-0.35 2 100 2 100 2 100 2 100 

-0.36 1 100 1 100 1 100 1 100 

-0.37 1 100 1 100 1 100 1 100 

-0.38 1 100 1 100 1 100 

-0.39 1 100 1 100 

FIGURE 147. EFFECT OF SAMPLING RATE ON CUMULATIVE OCCURRENCES OF 

LONGITUDINAL LOAD FACTOR, POSTFLIGHT

92
FIGURE PERC T OF L GITU L LO FACT EAK NTS

A FUNCTION OF SAMPLING RATE, POST HT 

FIGURE 149. CUMULATIVE OCCURRENCES OF PITCH ANGLE 

148. EN ON DINA AD OR P COU AS 

FLIG

101

102

103

104

4 sps

2 sps

1 sps

Cumulative Occurrences

100

-20 -15 -10 -5 0 5 10 15 20

Pitch Angle (degrees)

93
4 Samples per Second 2 Samples per Second 1 Sample per Second 

Pitch 

Angle 

(degrees) 

Cumulative 

Occurrences 

Percent of 

4 sps 

Cumulative 

Occurrences

Cumulative 

Occurrences

Percent of 

4 sps 

Cumulative 

Occurrences

Cumulative 

Occurrences

Percent of 

4 sps 

Cumulative 

Occurrences 

19 4 100 4 100 4 100 

18 12 100 12 100 12 100 

17 68 100 68 100 65 95.59 

16 128 100 128 100 125 97.66 

15 184 100 184 100 184 100 

14 210 100 210 100 210 100 

13 214 100 214 100 214 100 

12 214 100 214 100 214 100 

11 216 100 216 100 216 100 

10 216 100 216 100 216 100 

9 222 100 222 100 221 99.55 

8 256 100 255 99.61 253 98.83 

7 326 100 325 99.69 325 99.69 

6 408 100 407 99.75 403 98.77 

5 568 100 566 99.65 558 98.24 

4 734 100 731 99.59 724 98.64 

3 902 100 898 99.56 894 99.11 

2 1194 100 1189 99.58 1185 99.25 

1 1766 100 1761 99.72 1750 99.09 

0.5 2048 100 2039 99.56 2022 98.73 

 

-0.5 1456 100 1454 99.86 1435 98.56 

-1 1076 100 1076 100 1065 98.98 

-2 480 100 480 100 479 99.79 

-3 240 100 239 99.58 237 98.75 

-4 82 100 82 100 82 100 

-5 32 100 32 100 32 100 

-6 10 100 10 100 10 100 

FIGURE 150. EFFECT OF SAMPLING RATE ON CUMULATIVE OCCURRENCES 

OF PITCH ANGLE, IN FLIGHT 

94
FIGURE 1 . PER H AN E PE OUNT S A F TION OF 

SAMPLING RATE, IN FLIGHT 

FIGURE 152. CUMULATIVE OCCURRENCES OF BANK ANGLE 

51 CENT OF PITC GL AK C S A UNC

100

101

102

103

104

105

-40 -30 -20 -10 0 10 20 30 40

8 sps

4 sps

2 sps

1 sps

Cumulative Occur

Bank Angle (degrees)

rences

95
8 Samples per Second 4 Samples per Second 2 Samples per Second 1 Sample per Second 

Bank 

Angle 

(degrees) 

Cumulative 

Occurrences 

Percent of 

8 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences

Percent of 

8 sps 

Cumulative 

Occurrences

Cumulative 

Occurrences

Percent of 

8 sps 

Cumulative 

Occurrences

Cumulative 

Occurrences 

Percent of 

8 sps 

Cumulative 

Occurrences

32 2 100 2 100 2 100 2 100 

30 20 100 20 100 20 100 20 100 

28 52 100 52 100 52 100 51 98.08 

26 164 100 163 99.39 163 99.39 161 98.17 

24 372 100 372 100 372 100 372 100 

22 436 100 436 100 436 100 435 99.77 

20 502 100 502 100 502 100 502 100 

18 632 100 632 100 632 100 631 99.84 

16 714 100 713 99.86 712 99.72 712 99.72 

14 832 100 832 100 832 100 832 100 

12 890 100 890 100 890 100 890 100 

10 1000 100 1000 100 1000 100 999 99.9 

8 1088 100 1088 100 1086 99.82 1086 99.82 

6 1224 100 1222 99.84 1221 99.75 1218 99.51 

4 1586 100 1582 99.75 1576 99.37 1565 98.68 

2 3218 100 3212 99.81 3180 98.82 3105 96.49 

0.5 11018 100 10970 99.56 10836 98.35 10461 94.94 

 

-0.5 29972 100 29861 99.63 29523 98.5 28531 95.19 

-2 5780 100 5760 99.65 5695 98.53 5515 95.42 

-4 1904 100 1902 99.89 1894 99.47 1877 98.58 

-6 1478 100 1478 100 1476 99.86 1472 99.59 

-8 1260 100 1260 100 1259 99.92 1258 99.84 

-10 1136 100 1136 100 1135 99.91 1134 99.82 

-12 1024 100 1024 100 1024 100 1023 99.9 

-14 928 100 928 100 928 100 927 99.89 

-16 822 100 822 100 822 100 822 100 

-18 730 100 730 100 730 100 730 100 

-20 596 100 596 100 596 100 593 99.5 

-22 536 100 536 100 536 100 536 100 

-24 446 100 446 100 445 99.78 444 99.55 

-26 290 100 290 100 289 99.66 285 98.28 

-28 100 100 100 100 100 100 99 99 

-30 52 100 52 100 52 100 52 100 

-32 12 100 12 100 12 100 12 100 

-34 4 100 3 75 3 75 2 50 

FIGURE 153. EFFECT OF SAMPLING RATE ON CUMULATIVE OCCURRENCES 

OF BANK ANGLE, IN FLIGHT 

96
FIGURE 154. PERCE UNCTION OF 

SAMPLING RATE, IN FLIGHT 

FIGURE 155. CUMULATIVE OCCURRENCES OF AILERON 

DEFLECTION ANGLE 

NT BANK ANGLE PEAK COUNTS AS A F

100

1

102

103

104

105

-20 -15 -10 -5 0 5 10 15 20

16 sps

8 sps

4 sps

2 sps

1 sp

01

s

Aileron Deflection (degrees)

Cumulative Occurrences

97
16 Samples per Second 8 Samples per Second 4 Samples per Second 2 Samples per Second 1 Sample per Second 

Aileron 

Angle 

(degrees) 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

Cumulative 

Occurrences 

Percent of 

16 sps 

Cumulative 

Occurrences 

17 6 100 6 100 6 100 6 100 4 66.67 

16 32 100 32 100 32 100 30 93.75 24 75 

15 102 100 102 100 99 97.06 90 88.24 79 77.45 

14 140 100 140 100 135 96.43 124 88.57 108 77.14 

13 202 100 202 100 201 99.5 187 92.57 163 80.69 

12 256 100 256 100 251 98.05 237 92.58 210 82.03 

11 346 100 346 100 342 98.84 325 93.93 285 82.37 

10 468 100 468 100 459 98.08 433 92.52 388 82.91 

9 618 100 618 100 608 98.38 574 92.88 511 82.69 

8 798 100 797 99.87 784 98.25 747 93.61 661 82.83 

7 978 100 976 99.8 966 98.77 923 94.38 828 84.66 

6 1156 100 1154 99.83 1141 98.7 1097 94.9 997 86.25 

5 1406 100 1404 99.86 1395 99.22 1333 94.81 1214 86.34 

4 1806 100 1804 99.89 1790 99.11 1717 95.07 1583 87.65 

3 2350 100 2348 99.91 2325 98.94 2233 95.02 2062 87.74 

2 3864 100 3862 99.95 3840 99.38 3695 95.63 3426 88.66 

1 6754 100 6750 99.94 6703 99.24 6444 95.41 5919 87.64 

0.5 10880 100 10875 99.95 10824 99.49 10497 96.48 9608 88.31 

 

-0.5 20208 100 20207 100 20168 99.8 19803 98 18380 90.95 

-1 12154 100 12153 99.99 12128 99.79 11845 97.46 10819 89.02 

-2 4972 100 4971 99.98 4949 99.54 4805 96.64 4429 89.08 

-3 2628 100 2627 99.96 2615 99.51 2544 96.8 2378 90.49 

-4 1280 100 1280 100 1271 99.3 1229 96.02 1149 89.77 

-5 742 100 742 100 734 98.92 716 96.5 657 88.54 

-6 304 100 304 100 299 98.36 284 93.42 261 85.86 

-7 62 100 62 100 61 98.39 60 96.77 53 85.48 

-8 10 100 10 100 10 100 9 90 9 90 

-9 6 100 6 100 6 100 5 83.33 5 83.33 

-10 4 100 4 100 4 100 4 100 4 100 

-11 4 100 4 100 4 100 4 100 4 100 

FIGURE 156. EFFECT OF SAMPLING RATE ON CUMULATIVE OCCURRENCES 

OF AILERON DEFLECTION ANGLE, IN FLIGHT 

98
FIGURE 15 PERC AIL N D ECTION ANGLE PEAK COUN AS A

FUN ION F SAM NG R E, IN FLIGHT

FIGURE 158. CUMULATIVE OCCURRENCES OF ELEVATOR 

DEFLECTION ANGLE

7. ENT ERO EFL TS 

CT O PLI AT

100

101

102

104

-20 -15 -10 -5 0 5 10 15 20

4 sps

2 sps

103

1 sps

Cumulative Occurrences

Elevator Deflection Angle (degrees)

99
4 Samples per Second 2 Samples per Second 1 Sample per Second 

Elevator 

Angle 

(degrees) 

Cumulative 

Occurrences 

Percent of 

4 sps 

Cumulative 

Occurrences

Cumulative 

Occurrences

Percent of 

4 sps 

Cumulative 

Occurrences

Cumulative 

Occurrences

Percent of 

4 sps 

Cumulative 

Occurrences 

7 6 100 4 66.67 3 50 

6 8 100 6 75 4 50 

5 22 100 15 68.18 12 54.55 

4 88 100 72 81.82 61 69.32 

3 250 100 212 84.8 176 70.4 

2 912 100 819 89.8 674 73.9 

1 3250 100 3017 92.83 2578 79.32 

0.5 8570 100 7967 92.96 6931 80.88 

 

-0.5 9466 100 8770 92.65 7619 80.49 

-1 3654 100 3347 91.6 2813 76.98 

-2 1084 100 977 90.13 802 73.99 

-3 462 100 397 85.93 339 73.38 

-4 324 100 291 89.81 251 77.47 

-5 272 100 247 90.81 214 79.78 

-6 230 100 205 89.13 182 79.13 

-7 178 100 156 87.64 141 79.21 

-8 108 100 87 80.56 84 77.78 

-9 78 100 63 80.77 62 79.49 

-10 58 100 45 77.59 44 75.86 

-11 36 100 26 72.22 27 75 

-12 20 100 14 70 14 70 

-13 10 100 6 60 5 50 

-14 4 100 2 50 2 50 

-15 4 100 2 50 2 50 

FIGURE 159. EFFECT OF SAMPLING RATE ON CUMULATIVE OCCURRENCES 

OF ELEVATOR DEFLECTION ANGLE, IN FLIGHT 

100
FIGURE 160. PERCENT ELEVATOR DEFLECTION ANGLE PEAK COUNTS AS A 

FUNCTION OF SAMPLING RATE, IN FLIGHT

FIGURE 161. CUMULATIVE OCCURRENCES OF RUDDER 

DEFLECTION ANGLE

100

101

102

103

104

-10 -5 0 5 10

16 sps

8 sps

4 sps

2 sps

1 sps

Cumulative Occurrences

Rudder Deflection Angle (degrees)

101
102

16 Samples per Second 8 Samples per Second 4 Samples per Second 2 Samples per Second 1 Sample per Second 

Rudder 

Angle 

(degrees) 

Cumula

Occurrenc

Percent of 

 sps 

ulative 

urre

Cumulative 

nc

f 

lative 

s 

Cumulative Cu Cumulative 

c

Perce

16 s

Cumulativ

urr

mulative 

Percent of 

8 sps 

Cumulative 

es Occurrences 

Percent o

16 sps 

Cumu

Occurrence Occurrences 

Percent of 

16 sps 

mulative 

Occurrences O currences Occ

nt of 

ps 

e 

ences 

Cu

Occurrences 

tive 

es 

16

Cum

Occ nces Occurre

6 2 100 2 100 2 100 2 100 2 100 

4 14 100 14 100 12 85.71 11 78.57 10 71.43 

2 98 100 98 100 91 92.86 83 84.69 78 79.59 

0.5 1658 100 1658 9.88 2 3 1567 94.51 1406 84.8 9 163 98.4

 

-0.5 4826 100 4823 9.94 9 4762 98.67 4590 95.11 41.81 86.63 

-2 170 100 170 100 168 98.82 163 95.88 140 82.35 

-4 16 100 16 100 16 100 13 81.25 11 68.75 

-6 4 100 4 0 10 4 100 4 100 3 75 

-8 2 100 2 0 10 2 100 2 100 2 100 

FIGURE 16 ING R ON C NCES OF 

DER LECT ANG IN FL 

FIGURE 163. PERCENT RUDDER DEFLECTION ANGLE PEAK COUNTS AS A 

FUNCTION OF SAMPLING RATE, IN FLIGHT 

2. EFFECT OF SAMPL ATE UMULATIVE OCCURRE

RUD DEF ION LE, IGHT
TABLE 1. PARAMETER SAMPLING RATES 

Parameter Units Sampling Rate 

Vertical Load Factor g 16 

Lateral Load Factor g 16 

Longitudinal Load Factor g 8 

Pitch Angle degrees 4 

Bank Angle degrees 8 

Aileron Position degrees 16 

Elevator Position degrees 4 

Rudder Position degrees 16 

Spoiler Position degrees 2 

Radio Height feet 16 

Gear Compressed discrete 16 

N1 and N2 % rpm 1 

Ground Speed knots 1 

Airspeed knots 1 

103
TABLE 2. FIGURE LAYOUT FOR THREE FLIGHTS 

Figure Number 

Parameter Figure Description 

l

35 Seq ence 

F ight 

Sequence 3 

Flight Sequence Flight 

u 62 

Vertica oad F or l L act Tim Histo e ry 14 50 86

Preflight PSD 15 51 87

Pr ht rm eflig s 16 52 88

In-flight PSD 17 53 89

In-flight rms 18 54 0 9

Postflight PSD 19 55 91 

Postflight rms 20 56 92 

Time History 21 57 93 

Preflight PSD 22 58 94 

Preflight rms 23 59 95 

In-flight PSD 24 60 96 

In-flight rms 25 61 97 

Postflight PSD 26 62 98 

Lateral Load Factor 

Postflight rms 27 63 99 

Time History 28 64 100 

Preflight PSD 30 65 101 

Preflight rms 31 66 102 

In-flight PSD 31 67 103 

In-flight rms 32 68 104 

Postflight PSD 33 70 105 

Longitudinal Load 

Factor 

Postflight rms 34 70 106 

Time History 35 71 107 

In-flight PSD 36 72 108 

Pitch Angle 

In-flight rms 37 73 109 

Time History 38 74 110 

In-flight PSD 39 75 111 

Bank Angle 

In-flight rms 40 76 112 

Time History 41 77 113 

In-flight PSD 42 78 114 

Ai

In-flight rms 43 79 115 

leron Angle 

Time History 44 80 116 

In-flight PSD 45 81 117 

Elevator Angle 

In-flight rms 46 82 118 

Time History 47 83 119 

In-flight PSD 48 84 120 

Rudder Angle 

In-flight rms 49 85 121 

104
TABLE 3. PEAK COUNTING CRITERIA 

Parameter Sampling Rate Stu Thr died eshold Binning Increment 

Vertical Acceleration 16, 8, 4, 2, 1 ±0.05 0.05 

Lateral Acceleration 16, 8, 4, 2, 1 ±0.01 0.01 

Longitudinal Acceleration 8, 4, 2, 1 ±0.01 0.01 

Pitch Angle 4, 2, 1 ±0.5 1.0 

Bank Angle 8, 4, 2, 1 ±0.5 2.0 

Aileron Position 16, 8, 4, 2, 1 ±0.5 1 

Elevator Position 4, 2, 1 ±0.5 1 

Rudder Position 16, 8, 4, 2, 1 ±0.5 2 

TABLE OUT FOR TIVE OCCU ENCE DATA 

Figure Number 

 4. FIGURE LAY CUMULA RR

Parameter 

Figure 

Description 

Cum 

Occurrences in 

Graphical 

Format 

Cumulative 

Occurrences in 

Tabular Format 

Cumulative 

Occurrences in 

Relative Percent

ulative

Preflight 122 123 124 

In flight 125 126 127 

Vertical Load 

Factor 

Postflight 128 129 130 

Preflight 131 132 133 

In flight 134 135 136 

Lateral Load 

Factor 

Postflight 137 138 139 

Preflight 140 141 142 

In flight 143 144 145 

Longitudinal Load 

Factor 

Postflight 146 147 148 

Pitch Angle In flight 149 150 151 

Bank Angle In flight 152 153 154 

Aileron Angle In flight 155 156 157 

Elevator Angle In flight 158 159 160 

Rudder Angle In flight 161 162 163 

105
TABLE 5. SAMPLING RATE REQUIREMENTS 

Parameter 

Frequency 

Bandw

Includ

of To

Minimum 

Sampling 

uired 

 PSD 

lysis 

m 

te 

Required From 

Peak Count 

tistics 

te 

r 

M m 10

Error in 

mplitude 

easurement 

ecified 

mpling 

Rate 

idth Rate 

Required to Req

e 95% From

tal rms Ana

Minimu

Sampling Ra

Sta

Sampling Ra

Required fo

aximu % Part 121-

A

M

Sp

Sa

Vertical Load 

Factor 

Groun

Flight

2 Ground ≥16 

Fli 8 

40 

10 

,3 d < 6 

 < 1.5 

1

3 ght ≥

81,2

Lateral Load 

Factor 

< 1.5 Ground ≥8 

Fli 16 

10 ,3 3 

ght ≥

41,2

L

L

Ground ≥8 

Fli 4 

1 ,3 1 

ght ≥

41,2 ongitudinal 

oad Factor 

< 0.1

Pitch Angle <0.05 1 2 1 2,3 1 , 4 1 

Bank Angle < 0.05 4 1 2 2,3 1 11, 

Aileron 

Deflection 

< 0.3 1 4 2 22, 43 11, 

Elevator 

D

< 1.0 4 7 22, 43 2 11, 

eflection 

R

Deflection 

<0.5 1 8 2 4 11 udder , 2

1

 For aircraft manufactured pri

2

 For aircraft manufactured aft before August 3

 For aircraft manufactured aft

or to July 1996 

er July 1996 and 

er August 2002 

 2002

106
APPENDIX A—APPENDIX B TO 14 CFR PART 121, 

AIRPLANE FLIGHT RECORDER SPECIFICATION

A-1/A-2
APPENDIX B—APPENDIX M TO 14 CFR PART 121, 

AIRPLANE FLIGHT RECORDER SPECIFICATIONS 

B-1
B-2
B-3
 

B-4
B-5
 

B-6
B-7
B-8
APPENDIX C—DERIVATION OF FLIGHT CONTROL 

DEFLECTION STATISTICS FROM DATA OBTAINED AT 

LOW SAMPLING RATES 

C.1 INTRODUCTION. 

The main body of this report provides the results of a study of sampling rate effects on load 

parameter statistics including flight control surface deflections. The results of the study showed 

that lower sampling rates affect the resulting cumulative occurrence spectra of the parameters. 

The extent of the effect is related to the frequency content of the parameter time history. The 

inclination is to interpret this effect as a reduction in the number of peaks counted due to the 

lower sampling rates. Table 5 of the report shows that the minimum sampling rate required to 

identify a peak amplitude within a maximum error of 10 percent is greater than the sampling rate 

required to identify the existence of a peak. Since the sampling rate required to capture the 

correct amplitude is higher than that needed to capture the existence of a peak, the differences 

seen in the peak count statistics are more likely due to the inability to record the correct peak 

amplitudes than it is to record the existence of a peak. If it is assumed that the correct number of 

peaks is counted, then using the approach of reference C-1, the cumulative occurrence spectra 

derived at low sampling rates can be corrected to account for the errors in peak amplitude due to 

low sampling rates. 

C.2 GENERAL POWER SPECTRAL DENSITY DISCUSSION. 

The power spectral density (PSD) of a time history displays the variation in parameter root mean 

square (rms) magnitude (power) as a function of the frequencies inherent in the time history. 

Figure C-1 shows a sinusoidal time history of 0.05 cycles per second. The PSD of the sinusoidal 

signal is presented in figure C-2. As can be seen, the signal’s primary power is centered at the 

signal’s frequency of 0.05 Hertz (Hz). While the total power of the sinusoid is in truth centered 

exactly at 0.05 Hz, the fast Fourier transform (FFT) technique used to calculate the PSD tends to 

average this total power that exists at a distinct frequency over a fixed frequency window, 

dependent on the sampling rate of the signal. Nevertheless, it still shows the important 

frequency peak. Figure C-3 shows the same sinusoidal time history, but with secondary random 

frequencies, such as noise, superimposed on the basic signal. Figure C-4 shows the PSD for this 

noisy sinusoidal time history. Note that the primary sinusoidal frequency is still shown as a 

power peak, but the power associated with the superimposed frequencies in the signal is shown 

at the higher frequencies at considerably lower levels of power. The same PSD presented on a 

linear scale would show the power at these higher frequencies to be insignificant. These higher 

frequencies would not be counted as separate peaks in the derivation of a cumulative occurrence 

curve. The higher frequencies shown in the example are representative of the frequencies seen in 

the control surface deflection time histories. They represent control surface deflections of small 

magnitude and high frequency experienced at fixed control surface positions during level cruise 

or superimposed on large, slower frequency deflections associated with maneuvers. 

As shown in section 3.1, integration of the PSD provides insight into a possible choice for a 

cutoff frequency to be considered for data sampling. 

C-1
Figures C-5 and C-6 show the increase in power as frequency increases for the PSDs of figures 

C-2 and C-4, respectively. In both figures, a frequency cutoff associated with 90% of rms 

accounts for the primary frequency. 

C.3 PEAK AMPLITUDE ERROR DISCUSSION. 

Table C-1 presents the frequencies at which the rms level reaches 90 percent of its total value for 

the aileron, elevator, and rudder from the three flights shown previously. 

According to the Nyquist theorem, a sampling rate of twice the cutoff frequency would detect the 

peaks existing in the signal below the cutoff frequency, if not the correct magnitude. From the 

cutoff frequencies shown in the table, a sampling rate of once per second would appear to be 

adequate to identify the existence of a peak within the frequency range of interest. 

Reference C-1 provides a means to estimate the maximum error in peak magnitude as a function 

of the sampling rate for bandwidths below the cutoff frequency. 

f

F

error

2

2 % cos1(*100 π −= (C-1) 

where: F = bandwidth or cutoff frequency 

 f = sampling rate 

As pointed out in section 3.3 in this report, the actual error may be anywhere from zero percent 

error to maximum error. Assuming an average error equal to one-half the maximum possible 

error, figure C-7 shows the average peak error as a function of signal bandwidth and sampling 

rate. 

Figures C-8 through C-10, reproduced from figures 155, 158, and 161, present the cumulative 

occurrence counts at different sampling rates for aileron, elevator, and rudder respectively. If the 

primary signal frequency is less than or equal to one-half the sampling frequency, then no peaks 

should be lost. The sampling rates presented in the figure are faster than twice the cutoff 

frequency at 95 percent of rms, as shown in table C-1. Thus, the differences shown in the 

cumulative occurrence spectra are likely due to errors in the magnitude of the counted peaks 

rather than the number of peaks counted. 

Figure C-11 shows the percent change in peak count magnitude that can be expected when 

changing the sampling rate to 2 samples per second from 4 and 16 samples per second. These 

curves are based on the information shown in figure C-7. 

From figure C-11, for an aileron frequency cutoff equal to or less than 0.15 Hz, a sampling rate 

of two samples per second would be expected to result in an average error change in peak 

magnitude from 16 samples per second of approximately 1.25 percent. For the elevator cutoff 

frequency of 0.5 Hz, a sampling rate of two samples per second would be expected to result in an 

average change in peak magnitude form of four samples per second of approximately 10.44 

percent. For the rudder cutoff frequency of 0.35 Hz, a sampling rate of two samples per second 

would be expected to result in an average change in peak magnitude form of 16 samples per 

second of approximately 7.4 percent. 

C-2
C.4 APPLICATION OF ERROR CORRECTION. 

In the procedure discussed in section 3.3, the selected cutoff frequency is determined by the 

frequency at which the rms reaches 90 percent of the total rms or 90 percent of the area under the 

PSD curve. At the same time, the overall PSD curve is defined by the sampling rate and the 

frequency content of the time history. Figure C-12 presents the variation of rms as a function of 

sampling rate for an aileron time history. The figure shows that the frequency at which the rms 

reaches 90 percent of the total rms under the PSD curve is little affected by sampling rates of two 

samples per second or faster. Figures C-13 and C-14 show similar results for the elevator and 

rudder. This suggests that the primary frequency of the flight control surface deflections, at least 

for the A-319 on which this study was based, is below one cycle per second, and that the two 

samples per second is adequate to capture the primary peaks. It is a fair assumption that the 

flight control surface deflections rates on other aircraft are similar, and that flight control 

deflection data based on sampling rates of two samples per second can be used to calculate 

necessary PSDs and determine the desired cutoff frequencies for the 90 percent rms level for the 

aileron, elevator, and rudder. Given this cutoff frequency, the average expected error can be 

obtained from figure C-7 and used as a correction to the counted peak magnitudes. The 

procedure would be as follows: 

• Use the time histories for a control surface deflection for a number of random flights to 

calculate the PSDs. 

• For each PSD, determine the increase in rms as a percent of the total rms as a function of 

frequency. 

• Select the cutoff frequencies at the 90 percent rms level. 

• Select the highest cutoff frequency from the randomly selected flights and determine the 

expected maximum error in peak magnitudes from figure C-7. 

• Increase the peak magnitudes in the cumulative occurrence graphs to account for the 

error in magnitude. 

⎟

⎠

⎞ ⎜

⎝

⎛ = +

100

% 1 error

corrected δδ recorded (C-2) 

Because the records sampled at 16 samples per second also contain some error, this correction 

will provide cumulative occurrence spectra slightly more severe than would be obtained from the 

16 samples per second time history. 

Figures C-15 through C-17 show comparison of the spectra adjusted from two samples per 

second to the spectra measured at the maximum sampling rates for the aileron, elevator, and 

rudder respectively. The corrections were based on the 1.25, 10.44, and 7.4 percent errors 

discussed in section C.3. 

C-3
C.5 CONCLUSIONS. 

The study discussed in this report concluded that the sampling rates used for load parameter 

recording, including flight control surface deflections, were too low to ensure that correct peak 

magnitudes were counted. However, it was shown that the approach of reference C-1 might 

provide reasonable estimates of the average expected magnitude errors. Depending on the 

selected cutoff frequency, figure C-7 will provide an estimate of the expected average error for 

the sampling rate of interest. Increasing the peak count magnitudes to account for this error 

should improve the cumulative occurrence spectra to levels more consistent with those expected 

from faster sampling rates. 

C.6 REFERENCES. 

C-1. Anonymous, “Analysis of Relationship Between Sample Rate, Data Bandwidth and 

Accuracy for Flight Data Recorders with A/D Converters,” Technical Note EER-912, 

Esprit Technology Inc., September 1991. 

C-4
-1.5

-1

-0.5

0

0.5

1

1.5

0 20 40 60 80 100 120

Amplitude

Time (seconds)

140

 FIGURE C-1. TIME WAVEFORM OF A PURE SINUSOID 

0.001

0.01

0.1

1

10

102

0 0.1 0.2 0.3 0.4 0.5 0.6

Power Spectral Density (rms deflection)2 / Hz

Frequency (Hz)

FIGURE C-2. POWER SPECTRAL DENSITY OF A PURE SINUSOID 

C-5
-1.5

-1

-0.5

0

0.5

1

1.5

0 20 40 60 80 100 120

Amplitude

Time (seconds)

140

FIGURE C-3. TIME WAVEFORM OF A NOISED SINUSOID 

0.001

0.01

0.1

1

10

102

0 0.1 0.2 0.3 0.4 0.5 0.6

Power Spectral Density (rms deflection)2 / Hz

Frequency (Hz)

FIGURE C-4. POWER SPECTRAL DENSITY OF A NOISED SINUSOID 

C-6
0

20

40

60

80

100

0 0.1 0.2 0.3 0.4 0.5

Percent of Total RMS (percent)

Frequency (Hz)

FIGURE C-5. PERCENT OF PURE SINUSOID RMS VS FREQUENCY 

0

20

40

60

80

100

0 0.1 0.2 0.3 0.4 0.5

Percent of Total RMS (percent)

Frequency (Hz)

FIGURE C-6. PERCENT OF NOISED SINUSOID RMS VS FREQUENCY 

C-7
0

5

10

15

20

25

30

35

40

45

0123456789

50

10

1 sps

2 sps

4 sps

8 sps

10 sps

16sps

20 sps

Average Error (percent)

Signal Bandwidth (Hz)

FIGURE C-7. AVERAGE PEAK ERROR VS BANDWIDTH BY SAMPLING RATE

100

101

102

103

104

105

-15 -10 -5 0 5 10 15 20

16 sps

8 sps

4 sps

2 sps

1 sps

Cumulative Occurrences

Aileron Deflection (degrees)

FIGURE C-8. CUMULATIVE OCCURRENCES OF AILERON DEFLECTION 

C-8
100

101

102

103

104

-20 -15 -10 -5 0 5 10

4 sps

2 sps

1 sps

Cumulative Occurrences

Elevator Deflection Angle (degrees)

 FIGURE C-9. CUMULATIVE OCCURRENCES OF ELEVATOR DEFLECTION 

100

101

102

103

104

-10 -5 0 5 10

16 sps

8 sps

4 sps

2 sps

1 sps

Cumulative Occurrences

Rudder Deflection Angle (degrees)

FIGURE C-10. CUMULATIVE OCCURRENCES OF RUDDER DEFLECTION 

C-9
0

5

10

15

20

25

30

35

40

45

50

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

2 to 4 sps

2 to 16 sps

Average Peak Error Ratio (percent)

Signal Bandwidth (Hz)

FIGURE C-11. AVERAGE DELTA PEAK ERROR VS SIGNAL BANDWIDTH 

80

85

90

95

100

0 0.511.5 2

16 sps

8 sps

4 sps

2 sps

1 sps

Percent of Total RMS (percent)

Frequency (Hz)

FIGURE C-12. PERCENT OF ALERON RMS VS FREQUENCY FOR 

DIFFERENT SAMPLING RATES 

C-10
80

85

90

95

100

0 0.511.5 2

4sps

2 sps

1 sps

Percent of Total RMS (percent)

Frequency (Hz)

FIGURE C-13. PERCENT OF ELEVATOR RMS VS FREQUENCY FOR 

DIFFERENT SAMPLING RATES

80

85

90

95

100

0 0.511.5 2

16 sps

8 sps

4 sps

2 sps

1 sps

Percent of Total RMS (percent)

Frequency (Hz)

FIGURE C-14. PERCENT OF RUDDER RMS VS FREQUENCY FOR 

DIFFERENT SAMPLING RATES

C-11
100

101

102

103

104

105

-20 -15 -10 -5 0 5 10 15 20

2 sps adjusted

16 sps

Cumulative Occurrences

Aileron Deflection (degrees)

FIGURE C-15. COMPARISON OF ADJUSTED AND MEASURED AILERON 

CUMULATIVE OCCURRENCES 

100

101

102

103

104

-20 -15 -10 -5 0 5 10 15 20

2 sps adjusted to 4 sps

4 sps measured

Cumulative Occurrences

Aileron Deflection (degrees)

FIGURE C-16. COMPARISON OF ADJUSTED AND MEASURED ELEVATOR 

CUMULATIVE OCCURRENCES

C-12
100

101

102

103

104

-10 -5 0 5 10

2 sps adjusted to 16 sps

16 sps measured

Cumulative Occurrences

Aileron Deflection (degrees)

FIGURE C-17. COMPARISON OF ADJUSTED AND MEASURED RUDDER 

CUMULATIVE OCCURRENCES

TABLE C-1. CUTOFF FREQUENCY AT 95% RMS 

Control Surface Flight Sequence 3 Flight Sequence 35 Flight Sequence 62 

Aileron 0.02 0.01 0.15 

Elevator 0.5 0.07 0.43 

Rudder 0.25 0.15 0.35 

C-13/C-14
APPENDIX D—COMMENTS ON UDR-TR-2004-00146, R. HOWES, CESSNA 

AIRCRAFT COMPANY

Although this report expresses concern about the aliasing effects in general terms 

the specific effects of aliasing were not explored in this report. Mr. Robert L. Howes, 

Manager of Loads, Acoustics and Structural Dynamics at the Cessna Aircraft Company 

has pointed out that down sampling without proper filtering may result in aliasing and 

will skew the results and underestimate the final peak exceedances. This addendum 

contains his note discussing the results from a small test case. The results in the note 

underscore the conclusions of the report that existing sampling rates are too low and that 

the minimum sampling rates derived in this study cannot be considered conservative 

estimates.

. 

Comments on UDR-TR-2004-00146, “A Study of Sampling Rate Requirements for 

Some Load Parameter Statistics.” 

Introduction 

The study (ref 1) under discussion was conducted in support of an FAA Airborne Data 

Monitoring Systems program. The objective of the work was to determine the impact of 

sampling rates on flight and ground usage data. Flight data was taken from three flights 

on a typical commercial transport aircraft. The data was acquired at 16 samples per 

second. The sampling rate was then successively reduced and the impact on parameter 

exceedance data was examined. Sampling rates of 8,4,2 and 1 s/s were considered. 

The original flight data was processed to reflect the reduced sample rates using a 

downsampling technique. Downsampling refers to the practice of reducing sample rate 

by simply selecting every nth sample. This technique invites frequencies in the original 

data that exceed the new Nyquist frequency to alias into the downsampled data. Any 

aliasing that occurs will skew the exceedance calculations. If the reduced sample rates 

are generated from the original data by filtering and decimating, the bias introduced by 

aliasing is eliminated. An example is offered here to demonstrate the possible effects of 

this bias. 

Discussion 

Consider a second order system with the transfer function shown in figure 1. This is 

intended to represent the CG acceleration response to atmospheric turbulence. In fact, 

the system was chosen to represent a rigid body response around .5 Hz, a structural 

response at 2.5Hz another at 3.0 Hz and one at 6.0 Hz. These values were chosen as 

an approximation to the data shown in the referenced study, taken from the spectral data 

included there. 

D-1
Figure 2: Impulse response, sample system 

The resulting output was downsampled to 8 samples/second and filtered and decimated 

to 8 samples/sec5

. In each case the resulting time histories were processed with a peak 

counting routine and exceedance data were extracted. Figure 3 shows the resulting 

exceedance curves. 

Figure 3: Exceedance calculations 

 4 See [3], stmcb function

5 See [3] downsample and decimate functions

D-3
Figure 1: H( ) f for sample system 

The model in figure 1 was constructed from the following modal parameters1

: 

Table 1: Modal parameters for sample system 

Frequency, 

Hz, i f

Damping, 

%, ζ i

Weighting, 

hi

0.5 2.0 1.0 

2.5 2.0 0.2 

3.0 1.0 0.2 

6.0 5.0 0.8 

Sampled data for this test case was generated using a random number sequence for the 

input2

. The output was generated at 16 samples/second by filtering the random input 

with a FIR filter3

 derived from the impulse response of the system shown in figure 14. 

Figure 2 shows the impulse response used to derive the filter. 

 

1 System was synthesized using 2

2 ( ) , (1 ) 2

i

i i

i i ii i

f Hf h i fβ β β βζ = = − + ∑ 2 See [3], randn function. 

3 See [3], filter function. 

D-2
Figures 4a and 4b show PSD estimates calculated from the output for each case. 

Notice that in the downsampled case there is a significant peak around 2 Hz that is not 

present in the other two cases. This is aliased data generated by the downsampling 

done without filtering. It is the 6 Hz content folded around the new Nyquist frequency of 

4 Hz. It is this extraneous peak that has skewed the results. Notice that PSD for the 

data generated at 8 samples/second by filtering and decimating the original data looks 

like the PSD for the original data minus the 6 Hz peak. 

 Figure 4a: PSD of 16 s/s data Figure 4b: PSDs of 8 s/s data 

0.1 1.0 10.0

10-3

10-2

10-1

100

101

102

Freq, Hz

Mag, g**2/Hz

0.1 1.0 10.0

10-3

10-2

10-1

100

101

102

Freq, Hz

Mag, g**2/Hz

filter and decimate to 8 s/s

downsample to 8 s/s

From reference 2, the exceedance curves of figure 3 are given by 

2 1

2

0

z

z

N Ne σ

⎡ ⎤ ⎛ ⎞ ⎢− ⎥ ⎜ ⎟ ⎢ ⎥ ⎝ ⎠ ⎣ ⎦ = (1) 

or 

2

0 2

1 ln ln

2 z

N N

σ = − z (2)6

where 

 (3) ( ) 2

0

z zz σ S f df

∞

= ∫

and 

( )

1

2 2

0

0

1 zz

z

N fS f d

σ

∞

f ⎡ ⎤ = ⎢ ⎥ ⎣ ⎦ ∫ (4) 

 

6

 (2) has the form, 2 f ( ) x ax b = + where f ( ) ln x N = , 2

1

2 z

a

σ = − and b 0 = ln N . Note that 

2

2 2

() 1

z

dfx

dx σ = − 

D-4
Inspection of (2) and (3) shows that Introducing extraneous peaks in Szz artificially 

increases the integral in (3). This results in an increase in σ z and skews the 

exceedance data at higher values. The effect on N0 is less dramatic. 

Conclusion 

The signal processing procedures used in the referenced study to reduce the sample 

rates of the data under consideration likely skewed the results in some cases. This 

effect would not change the conclusion, e.g. insufficient sample rates introduce 

inaccuracies in the resulting exceedance data. Rather it understated the errors that are 

introduced. A final look at figure 3 shows that when sample rates exclude higher 

frequencies the exceedance data at higher values is significantly underestimated. 

List of References 

1. Rustenburg, J.;Tipps, D.O.; Skinn, D.; UDR-TR-2004-00146; “A Study of Sampling 

Rate Requirements for some Load Parameter Statistics”; Sept 2004. 

2. Jones, J.G.; “A Unified Discrete Gust and Power Spectrum Treatment of 

Atmospheric Turbulence”, Royal Aircraft Establishment; Technical Memorandum 

Aero 1315; April 1971. 

3. Signal Processing Toolbox for use with MATLAB, User’s Guide, Version 5, The 

MathWorks, Sep 2000. 

Robert L. Howes 

Manager, Loads, Acoustics and Structural Dynamics 

Cessna Aircraft Company 

D-5/D-6