NAT'L INST, OF STAND & TECH etereno

NBS

PUBLICATIONS

AlllDb 3M0DfiM

\

* '^^iZ ":

^''^fAU Of " NBS TECHNICAL NOTE 1069

U.S. DEPARTMENT OF COMMERCE / National Bureau of Standards
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards' was established by an act ot Congress on March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and technology

and facilitate their effective application for public benefit. To this end, the Bureau conducts

research and provides: (1) a basis for the Nation's physical measurement system, (2) scientific and technological services for industry and government, (3) a technical basis for equity in trade, and (4) technical services to promote public safety. The Bureau's technical work is per- formed by the National Measurement Laboratory, the National Engineering Laboratory, and

the Institute for Computer Sciences and Technology.

THE NATIONAL MEASUREMENT LABORATORY provides the national system of

physical and chemical and materials measurement; coordinates the system with measurement

systems of other nations and furnishes essentia! services leading to accurate and uniform

physical and chemical measurement throughout the Nation's scientific community, industry,

and commerce; conducts materials research leading to improved methods of measurement,

standards, and data on the properties of materials needed by industry, commerce, educational

institutions, and Government; provides advisory and research services to other Government

agencies; develops, produces, and distributes Standard Reference Materials; and provides

calibration services. The Laboratory consists of the following centers:

Absolute Physical Quantities- — Radiation Research — Chemical Physics —

Analytical Chemistry — Materials Science

THE NATIONAL ENGINEERING LABORATORY provides technology and technical ser- vices to the public and private sectors to address national needs and to solve national problems; conducts research in engineering and applied science in support of these efforts; builds and maintains competence in the necessary disciplines required to carry out this research and technical service; develops engineering data and measurement capabilities;

provides engineering measurement traceability services; develops test methods and proposes

engineering standards and code changes; develops and proposes new engineering practices;

and develops and improves mechanisms to transfer results of its research to the ultimate user. The Laboratory consists of the following centers:

Applied Mathematics — Electronics and Electrical Engineering^ — Manufacturing

Engineering — Building Technology — Fire Research — Chemical EngineeringTHE INSTITUTE FOR COMPUTER SCIENCES AND TECHNOLOGY conducts

research and provides scientific and technical services to aid Federal agencies in the selection, acquisition, application, and use of computer technology to improve effectiveness and

economy in Government operations in accordance with Public Law 89-306 (40 U.S.C. 759), relevant Executive Orders, and other directives; carries out this mission by managing the Federal Information Processing Standards Program, developing Federal ADP standards

guidelines, and managing Federal participation in ADP voluntary standardization activities; provides scientific and technological advisory services and assistance to Federal agencies; and

provides the technical foundation for computer-related policies of the Federal Government.

The Institute consists of the following centers:

Programming Science and Technology — Computer Systems Engineering.

'Headquarters and Laboratories at Gaithersburg, MD, unless otherwise noted; mailing address Washington, DC 20234. 'Some divisions within the center are located at Boulder, CO 80303.
[pATIONAt BUREAU ^ PF STANDARDS

LIBRARY

VOR Calibration Services Q<^

lOO

Neil T. Larsen ^

Electromagnetic Technology Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

Dominic F. Vecchia

Statistical Engineering Division

Center for Applied Mathematics

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

George R. Sugar

Retired (formerly with the Electromagnetic Technology Division, National Bureau of Standards)

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued April 1985
National Bureau of Standards Technical Note 1069

Natl. Bur. Stand. (U.S.), Tech Note 1069, 180 pages (April 1985)

CODEN:NBTNAE

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1985

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402
CONTENTS

Page

SYSTEM OVERVIEW

1. Introduction 1 1.1 Hi story 1 1.2 Organization of Report 1 2. Technical Basics 2 3. Description of the VOR Calibration Services 5 3.1 VOR Phasemeter Calibration Service 5 3.2 VOR Generator Calibration Service 6 4. Design Philosophy 7 4.1 Generator Design 7 4.2 Phasemeter Design 8

VOR GENERATOR

5

.

Generator Detai Is 8

6. Specifications 10

6.1 Audio Signal Outputs 10

6.1.1 Individual and Composite Signal Outputs 10

6.1.2 30 Hz Reference and Variable Phase Outputs at Filter Output 10

6.1.3 FM Output 10

6.2 Other Outputs 11 6.3 Frequency and Phase Stability 11 6.4 Error Detection Circuits 11 6.5 Built-in-Test Circuits 12

6.5.1 Circuit Tl in Figure 6-1 12

6.5.2 Circuit T2 in Figure 6-1 12 6.6 Control s 12

6.7 Indicators 13

6.8 Other Characteristics 13

7. Operating Procedures 13

7.1 Normal Operation 13

7.2 Error Conditions 13

7.3 Testing Bearing Angle Settings 14

8. Generator 14

8.1 General Approach 14

8.2 Generating the 30 Hz Sine Waves 14

8.2.1 Basic Method 14

8.2.2 Use of Differences to Reduce ROM Size 16

8.3 Generation of the Frequency-Modulated 9960 Hz Signal 17 8.3.1 Basic Method 17 8.3.2 Use of Differences to Reduce PROM Size 18

8.4 Accuracy Considerations 19

8.4.1 Frequency Accuracy 20

8.4.2 Phase Setting Accuracy 20

8.4.3 Amplitude Distortion and Noise 21

8.4.3.1 Quantizing Noise 21 8.4.3.2 Converter Nonlinearity 21

8.4.3.3 Converter Switching Spikes 22

8.4.3.4 Amplifier Noise and Nonlinearity 22

8.5 Error-Detection and Built-in-Test Circuits 22 8.5.1 Overview 22

8.5.2 Inherent Error-Detecting Capabilities 23

8.5.3 Error-Detection Circuits 23

8.5.4 Built-in-Test Circuits 23

9. Power Supplies 23

10. Verification of Performance 24

10.1 Memory Pattern Verification 24

10.2 Analog Performance Verification 25

10.3 Digital -to-Analog Circuit Timing Verification 26

10.4 Analog Filter Characteristics 26

11. Maintenance Procedures 27 11.1 Adjustments 27 11.2 Performance Checks 28

11.3 Trouble Shooting 28

m
12,

13.

14. 15.

16

17

18

Suggestions for Future Designs..,

12.1 30 Hz ROM and Accumulators,

12.2 Reduced Sampling Rate ,

VOR PHASEMETER

Phasemeter Detai Is 13.1 Phasemeter Design Principles...,,

Hardware Detai Is , Software Detai Is , 15.1 General

Initialization

Data Acquisition

Data Processing , Utility Subroutines and Programs

Sample Outputs ,

1515

1515.5

15.6

EVALUATION OF TOE STANDARDS

18.2

18.3

Appendix 3. Appendix C. Appendix D. Appendix E.

29

29

29

30

30

31

33

33

33

34

34

35

38

VOR Measurement Principle 38

16.1 Measurement of VOR Waveforms 39

16.2 Verification of Mathematical Model by Simulation 41

System Performance and Provisional Uncertainty 49

17.1 Systematic Errors 49

17.2 Statistical Model for Bearing Measurements 49

17 .3 Observed Data and PI ots 58

17.4 Statistical Analysis 59

17.4.1 Detection of Outliers 59

17.4.2 Parameter Estimates and Tests 60

17.5 Overall System Performance 62

17.6 Provisional Uncertainty 63

Process Control and Updating Parameters 63

13.1 Control Charts and Tests 63

18.1.1 Control Chart for Short-Term Error 64

18.1.2 Control Chart for Individual Measurements 64

18.1.3 Tests for Out-of-Control Conditions 67

Updating Process Parameters 68

Procedures for Correcting Out-of-Control Conditions 69

19. References 69

Appendix A. VOR Phasemeter Program Listing A-1

Test -Data Listings B-1

Graphical Illustrations C-1

BMDP3V Program Listing D-1

Sample Report of Calibration E-1

TV
VOR Calibration Services

Neil T. Larsen, Dominic F. Vecchia, George R. Sugar

National Bureau of Standards

Boulder, Colorado 80303

The National Bureau of Standards has designed, constructed, and evaluated a standard

for the support of very-high-frequency omnidirectional range (VOR) air navigation aids.

The standard consists of two instruments: (1) a digital waveform signal generator for the

composite VOR audio waveform, and (2) a standard phasemeter based on time series analysis

of this waveform. Experimental results, a statistical analysis of them, and the principal

software listings are included.

Key Wordsj_ air; calibration standard; navigation; omnidirectional; range; very-high frequency; VOR

SYSTEM OVERVIEW

1. Introduction

1.1 History

The origins of the air navigation system now known as Very high frequency Omnidirectional Range

(VOR) go back to about 1928, in England, when work was started on a phase-comparison system. About

1940, the Civil Aeronautics Administration examined and developed the technique, and finally presented

it to the Radio Technical Commission for Aeronautics in 1945. In 1946, it was offered by the U.S.

Government to what is now the International Civil Aviation Organization (ICAO). It was accepted as part of ICAO's Standards and Recommended Practices, where it is stated:

"In localities where conditions of traffic density and low visibility necessitate a shortdistance radio aid to navigation for the efficient exercise of air-traffic control, the

standard aid shall be VOR (vhf omni-range) of the CW phase-comparison type conforming to the Standards contained in Paragraph 3.4 of Chapter III of this Annex [1]."

Since that time, more than 1,000 stations have come into use around the world. However, in spite

of its use by commercial, military, and private aircraft, there has until now been no standard or technique by which VOR instruments could be calibrated, either directly or indirectly, at the National

Bureau of Standards. Reference 2 is a very good overview of the VOR system. It describes the origins

and evolution of the system in considerable detail and is recommended to those interested in the

history of VOR.

1.2 Organization of Report

This report comprises four main parts. They are:

I. A general overview of the VOR system and the calibration services designed to support it (sections 1 through 4).

II. A detailed description of the NBS VOR generator, including specifications, operating procedures,

and theory of operation and maintenance (sections 5 through 12).

III. A similar description of the VOR phasemeter (sections 13 through 15).
IV. A statistical evaluation of the VOR generator and VOR phasemeter when they are used together as a system (sections 16 through 18). A large amount of both simulated and measured data is

abstracted and discussed. The statistical theories used in the analysis are given. Finally, a provisional statement of uncertainty is made.

The appendices provide graphical and tabular illustrations of the actual measurement results.

The software listings for the NBS phasemeter and for some of the statistical work are included.

Throughout this report, the terms phasemeter and generator appear many times. In every case, a VOR

phasemeter or a VOR generator is meant, but for brevity, the modifier will often be omitted.

Throughout this report, the terms phasemeter and generator appear many times. In every case, a VOR phasemeter or a VOR generator is meant, but for brevity, the modifier will often be omitted.

Areas where the designs of the generator and phasemeter have influenced each other are noted. Since

there exists no independent means of checking either the phasemeter or the generator, the two must be

regarded as a system, and, of necessity, there is a strong interdependence when it come to the

evaluation of each.

2. Technical Basics

The VOR signal is radiated from a transmitter that produces a spinning pattern. The spin may be produced by a mechanically driven goniometer or other means. The antenna field pattern is not omnidirectional; a contour of constant intensity follows a curve known as a "limacon." The shape is nearly circular, as shown in figure 2-1. As the pattern turns at 1800 rpm, the field intensity at a remote receiver fluctuates sinusoidally at 30 Hz. The 30 Hz signal obtained by demodulating the VHF carrier is called the "variable phase" signal. If a timing reference were available to determine when

the peak of lobe passed magnetic north, then the phase of the 30 Hz signal measured relative to that

reference would vary in space as the bearing angle between magnetic north and the receiver, measured

at the transmitter.

(I) degrees rotation (c) S0 degrees rotation C3) 90 deg'-ees rotation C4) 200 dearees rotation

Figure 2-1. The rotating VOR horizontal field pattern. A dashed circle is shown for comparison,
Reference signal at all points

Variable signal at point Z\l

Variable signal at point [2D

cn

LZl

Variable signal at point C3] 150*

Figure 2-2. Reference and variable phase signals as received at three typical locations.

The required reference is transmitted by means of a 9960 Hz subcarrier that amplitude modulates

the same VHF carrier. The 9960 Hz is frequency modulated at 30 Hz. The subcarrier is obtained by

demodulating the VHF carrier, and the 30 Hz "reference phase" signal is then extracted from the subcarrier. The reference phase signal does not change in phase as the receiver moves in space. It is therefore possible to determine the bearing angle simply by measuring the phase angle between the two

30 Hz signals. The antenna spin is phased such that the field intensity at a receiver due north of

the transmitter peaks at the same time as the 30 Hz reference phase signal. Due north corresponds to

a bearing angle of degrees.

Typical signals received at three different locations are shown in figure 2-2. Note that the

reference signal, derived from the 9960 Hz subcarrier, is the same at all points. At point [1], the

variable phase signal lags the reference by 45 degrees, which is also the bearing angle from magnetic

north. Proportional phase lags are seen at the other two points.

Figure 2-3 is a representation of the audio signals from which the bearing angle information is obtained. The top waveform is one fundamental period of the reference signal. The second waveform

represents the 9960 Hz subcarrier. Note that the peak positive frequency deviation occurs at the
-1 •-

+1 r

30 Hz Reference Phj

-2«- Composite Rudio Signal Cbearing-0 degrees)

Figure 2-3. Simulated 30 Hz and 9960 Hz waveforms. Time is distorted for clarity,

positive peak of the reference signal. The sum of reference and variable phase signals is known as the "composite audio" signal, shown in the bottom curve. This is the signal that is obtained at the

output of the am detector of a remote VHF receiver. It is the signal produced by the NBS standard

generator and measured by the NBS standard phasemeter.

Note that the time dimension in figure 2-3 has been greatly distorted to make the frequency modulation of the subcarrier visible; however, the phase relationships are correct for a bearing angle of zero degrees. The figure is intended only as an aid to visualization.

The composite signal shown above can also be described by a mathematical model. This model is discussed in much more detail beginning in section 16. It consists of two parts: the variable phase

waveform and the frequency modulated 9960 Hz waveform.

The variable phase waveform is

v(t;_e) = a-^ cosC2Trf^t + 0^ + 62].
The FM waveform is

s{t;_e) = a^ cos[2Trf2t + 63 + B sinCZTrf^^t + 92]].

The composite waveform is defined by the sum of these two functions. The variables are as follows:

t = time

_0 = a vector of unknown three unknown phase angles

ai = amplitude of variable phase signal

f]^ = frequency of variable phase signal (30 Hz)

G-j = VOR bearing angle; i.e., the quantity to be measured

82 = an arbitrary phase offset included in the model for generality

02 = amplitude of the FM subcarrier

f2 = frequency of the FM subcarrier (9960 Hz)

Go = an arbitrary phase offset included in the model for generality

B = the modulation index of the FM subcarrier (nominally = 16)

It is the purpose of the VOR generator to generate a signal that conforms to this model, and it

is the purpose of the VOR phasemeter to determine the actual value of Q-^ ^'''^'^ measurements on the signal. The hardware aspects of the generation and measurement are described at length in sections 4 through 15; the statistical aspects of the measurement system are covered in section 16.

3. Description of the VOR Calibration Services

Two services are offered to support the calibration of VOR instruments. NBS has designed and

built a standard VOR audio generator, which is used to calibrate unknown VOR phasemeters, and a standard VOR phasemeter for the calibration of unknown generators. Both of these services are for audio

generators and phasemeters; direct generation or measurement of standard rf signals is not a part of

this service, although some effort is being made in that direction. To avoid confusion, each of these

services is discussed separately.

3.1 VOR Phasemeter Calibration Service

An unknown phasemeter is calibrated by connecting its input to the output of the NBS standard

generator. The generator provides a composite audio signal that is the sum of two signals, each 1 V rms (+1 percent) in amplitude. The first is simply a 30 Hz sinusoid, and represents the variable phase

signal as it would be recovered from the original vhf signal. The second is the frequency-modulated

9960 Hz subcarrier. Most commercial VOR phasemeters cover the entire 0° to 360° range, and so does

the standard. It is possible to set the standard, by means of digital thumbwheel switches, to any

bearing angle from 0° to 399.99° in steps of 0.01°.
Calibrations of VOR phasemeters are documented with a report containing the following statement:

The assigned values o/ VOR phase angles are the nominal bearing from to 360° in inovements of 0.01°. The overall uncertainty of these values has heen estimated from test data

at hearings from 0° to 260° at 20° increments. Thus, each of the nomi'nal hearings has heen

assigned a provisional overall uncertainty of +/- 0.0028°, hased on estimated hounds of +/-

0.0022° on the systematic error and a computed standard error of 0.0002°.

It appears that the NBS generator is more accurate than presently available generators by about a factor of 10, and better by an even larger factor than the needs of operational systems. It is not possible to fly an aircraft, using VOR, to 0.25°, even with an autopilot. Ground effects perturb the

field of the transmitter enough that more typical uncertainties in the air are on the order of 1° or

2°.

At present, the most suitable transfer standard appears to be a commercially made phase meter.

Neither the NBS generator nor phasemeter are portable. Another possibility is a generator that has

recently been developed at the National Physics Laboratory, England, by White, Clark, and Yell [3].

We do not yet know its properties, although one intercomparison with their portable generator has been

made. There appear to be no commercial generators that are suitable for use as a transfer standard in connection vyith the NBS standards. The problem is mainly with short-term jitter and noise. This may

change; however, any commercial phase meter used as a transfer standard must demonstrate shipability.

3.2 VOR Generator Calibration Service

An unknown generator is calibrated by the NBS standard phasemeter. The output of the generator

is connected to the phasemeter. In addition, a digital timing reference signal must be provided by

the generator to the phasemeter. Some commercial instruments provide such a signal internally; others

do not. Of those that do, only two have been found suitable for calibration, so far. This is because

the operating principles of the NBS phase standard require good short-term phase stability in the timing signal. This is discussed further in section 13.1.

Because of the short term (30 ys) phase jitter of most commercial generators, they cannot be calibrated by the NBS standard phasemeter. Instead, a transfer must be made through a commercial

phasemeter that has been calibrated against the NBS standard generator. Commercial phasemeters do not show the sensitivity to short term fluctuations that the NBS phasemeter does. This is usually due to the use of analog phase-locked loops and averaging circuits that reduce sensitivity to this type of

noise. The price paid is that the commercial phasemeter is not reliable as a primary standard and must be calibrated against the NBS generator immediately before use as a transfer standard, to minimize the degradation of the accuracy of the NBS generator. Hopefully, industry will design stable

generators which provide a timing reference for the NBS phasemeter.

Because of the complementary nature of these two services and the limitations of commercial

generators, the best transfer standard for either a generator or a phasemeter calibration is a commercial phasemeter, as discussed in section 3.1, above.

A sample report of calibration appears in appendix E.
4. Design Philosophy

At the beginning of the standards development effort, it was decided that it would be necessary

to design both a standard signal source and a standard phasemeter, since otherwise there would be no independent way of checking either one. Two instruments working on different principles, that agree

closely with each other, give some assurance that they are both performing as desired. This agreement, of course, must not require any adjustments or "twiddling" of either instrument. This condition

has been achieved. In addition, other objective means can be used for evaluating the performance of

each instrument independently of the other, up to a point. For example, a common signal sampled by

the phasemeter through a single-pole double throw switch should result in a zero phase difference,

which it does, to within a standard deviation of less than 0.0005°. For the generator, precise matching of differential time delays between the various signals, extending through the digital-to-analog

converters (DACs) is possible. This is discussed in more detail in section 10.3.

It was also decided at the outset that it would be necessary to minimize the number of linear

circuit elements in the signal paths, such as capacitors, amplifiers, resistors, and filters. In order to attain the desired ±0.01° uncertainty objective, elements with significant time or temperature drifts could not be used. This requirement suggested the heavy use of digital circuits. It resulted in a design in which the remaining essential analog components have very little effect on the

phase integrity of either the generator or the phasemeter (see sections 10.3 and 10.4).

As above, the generator and phasemeter are discussed separately.

4.1 Generator Design

The generator comprises three digital waveform synthesizers, all driven by the same crystal

controlled clock. It produces three digital outputs, 16 bits wide, reset every 0.01° (about 925 ns).

Only 14 bits of data are actually generated, because of present DAC resolution and speed limitations.

Binary numbers from -8188 decimal to +8188 decimal are generated. This comprises 16377 different

codes, or 2^'*-7. These codes are used to drive three 13-bit digital-to-analog converters (DACs). The

lowest bit is not used. The converters are made as nearly identical as possible and are designed in

such a way that differential time delays between them can be made negligible (less than 10 ns). The

analog outputs represent the 30 Hz variable phase signal, the 9960 Hz subcarrier, and the 30 Hz signal

that is, in principle, frequency modulating the subcarrier. Actually, there is no frequency modulator

in the generator, as this would require unstable analog circuitry. Instead, the subcarrier is synthesized directly as the modulated waveform. Note that the subcarrier waveform does not change with

bearing angle settings. The 30 Hz reference phase is not needed in a calibration but is useful for

other purposes; e.g., a 30 Hz phase angle standard.

Normally, the composite audio signal used for calibrating phasemeters is obtained by combining

the variable phase and subcarrier signals in a passive linear resistive adding network, which introduces insignificant phase shifts. This network is followed by a 7-section linear-phase LC filter with

a 100 kHz cutoff frequency, to remove residual digital switching noise and higher harmonics present in the waveform due to the quantization in the DACs. The filter measurement and evaluation techniques

are discussed in more detail in section 10.4.
4.2 Phasemeter Design

As with the generator, analog circuitry is avoided as much as possible. The phasemeter consists

of three main elements, all of which are commercially available: a 16-bit analog-to-digital converter

(ADC), a programmable time delay generator (TDG), and a desktop computer-controller.

The critical consideration in the phasemeter, as in the generator, is to avoid differential time

delays between the variable phase signal and the reference phase signal present as modulation on the

subcarrier. Most methods of analog FM demodulation cause unacceptable instabilities. More importantly, they require at least some adjustments. Adjustability would defeat the objective of a truly

independent phasemeter. A sampling technique provides a solution, since a sampling ADC gives constant

time offsets, to a first order approximation [4]. The phase angle of the variable phase signal relative to the reference phase signal can then be computed via a fast Fourier transform (FFT).

VOR GENERATOR

5. Generator Details

An aircraft determines its magnetic azimuth relative to a ground-based VOR transmitter by measuring the phase difference between the two modulation components of the received signal. The generator

described in this report was developed to serve as the phase angle standard for these modulation com- ponents. It consists of three separate audio generators, arranged to function with controllable phase

relations among them. There are two 30 Hz sine-wave generators and one frequency-modulated-wave

generator. The FM signal is a 9960 Hz carrier, modulated by a 30 Hz sine wave at a modulation index

of 16. The nominal deviation is thus ±480 Hz.

The phase relation between the two 30 Hz signals, which are called the 30 Hz reference phase signal and the 30 Hz variable phase signal, can be set for a lag of 0.00° to 399.99° in steps of 0.01°.

The phase of the FM signal is fixed relative to the 30 Hz reference signal such that maximum frequency

of the 9960 Hz signal occurs at the positive peak (90° point) of the 30 Hz reference signal (see fig.

5-1).

The unique characteristics of the generator are low distortion of the outputs and the highly

accurate control of the phase relations among the three signals. These features were accomplished

through the use of synchronous (clocked) logic as much as possible within the instrument. This design

minimized the number of analog circuits used.

All three generators use similar circuits; they generate digital representations of the desired

waveforms. The output data are then converted from the periodic numerical sequences to varying voltages which are filtered to provide the desired sine and FM waveforms. In each generator, a new digital value is produced each 0.925925... ys for every 0.01° of a 30 Hz waveform. A 13-bit representation is used, giving a numerical resolution of almost 1/4096 of the peak value. An output filter

serves to interpolate between the discrete voltage steps, changing the stairstep output to a smoothly

varying one.
Ph ase Lag

0-399 . 99

Deg r ees

30 Hz

Reference Phase

Gene r at o r

9960 H 2

Subc ar r

1

e r Ge ne r at o r

30 Hz

Var 1 able Ph as e Gene r at o r

Figure 5-1. Simplified block diagram of generator.

The general principle is illustrated in figure 5-2. The output of the counter changes each

0.9259... ys and repeats after 36,000 counts, or 1/30 sec. The output of the Programmable-Read-OnlyMemory (PROM) changes accordingly, and gives a 36,000 point digital approximation to the desired wave- form. The exact form is ideally a staircase with a 1.08 MHz step rate. This signal is smoothed with

a 100 kHz low-pass linear-phase filter to achieve the required accuracy. See section 10.4 for a discussion of the filter.

1 . 08 MHz

Clock

1 Coun t e r |(Di V i de b y

1 36, 000) H

Read

On 1 y

Memo r

y

DigitalIto-fln a 1 og

Con ve r t e r H

100 kHz

Loujp as s Fi Iter

SINENflVE

OUTPUT

Figure 5-2. A waveform synthesis technique.
The actual implementation differs somewhat from the above simplified version, primarily to reduce

the cost of the PROM tables that store the waveforms. When this design was frozen, the cost of the

memory alone for a direct sine lookup table was about $10,000. Since then, there have been large

reductions in the cost of PROMs; this factor should be considered if this type of instrument is built

again. Four techniques were used to reduce the required memory size without loss of accuracy:

1. The symmetry of the desired waveforms has been used to reduce memory size by a factor of 4 for the 30 Hz generators. Only one-fourth of a 30 Hz cycle is stored; i.e., 0° to 90°.

These data are used 4 times, with appropriate address changes, to produce each 30 Hz cycle.

2. In the 9960 Hz generator, one-half cycle of the desired waveform is stored and used twice per

30 Hz output cycle.

3. Both 30 Hz generators share the same PROMs through multiplexing. The 4-phase clock permits

this approach without introducing phase offsets.

4. The PROMs do not store the actual waveform amplitudes; instead, they store the second or third difference between each steps. With this method, only two bits are required for each

30 Hz step, and only 4 bits are needed for each 9960 Hz step. Simple digital accumulators

sum the successive incremental changes to obtain full 14-bit representations for the DACs

(only the top 13 bits are used).

These techniques are, of course, not free of side costs. Their use, particularly the use of

incremental values, has added significant complexity to the remainder of the circuits. However, a substantial net saving in overall size and complexity has resulted. We now see where further simplification is possible and discuss this in section 12.

6. Specifications

6.1 Audio Signal Outputs

6.1.1 Individual and Composite Signal Outputs

Amplitude: 1 V rms at filter output

Output impedance: 600 Q, unbalanced to ground at filter output

Load capacitance: Not more than 100 pF; larger values may cause nonlinear phase shifts.

6.1.2 30 Hz Reference and Variable Phase Outputs at Filter Output

Purity: Total harmonic distortion less than 0.01%

Noise: Less than 0.5 mV rms from to 300 kHz

Phase lag setting: Variable phase output relative to reference phase, adjustable from

0.00 to 399.99° in steps of 0.01°, lagging.

Phase lag uncertainty: ± 0.002°

6.1.3 FM Output

Carrier frequency: 9960 Hz Modulating frequency: 30 Hz Modulation index: 16 Purity: The differences between the measured and computed amplitudes of the various lines

in the spectrum are too small to measure. Harmonic distortion components were below the

spectrum analyzer sensitivity of -75 dB.

10
Noise: Noise, as determined by measuring the amplitude of selected lines, is too small to

to measure accurately.

Spectrum: See figure 10-1.

6.2 Other Outputs

Synchronizing Pulses--0° Reference (Reference Phase [RP] 0°, Variable Phase [VP] 0°, 9960 DET)

Timing: 30 Hz channels —pulse occurs 0.00324° (110 ns) before the positive-going zero crossing

of the output signal. Note that this time offset, which is fixed, does not enter into

the phasemeter uncertainty estimate, because it affects all time samples equally.

FM channel --pulse occurs 0.00324° before the positive-going zero crossing at the maximum

positive frequency excursion.

Duration: 0.9 ms Amplitude: Nominal 3 V Source characteristics: Unloaded TTL output with 100 Q. series resistor added.

Synchronizing Pulse--90° Point of 30 Hz Reference Channel (RP 90°)

Timing: Pulse occurs 0.00324° (110 ns) before the 90.00° point of the 30 Hz sine wave

Other characteristics: As above

Master Clock Pulse {<^i)

Timing: 1.08 MHz repetition rate, 4-phase

Other characteristics: As above

Square-Wave Outputs--RP Cycle, VP Cycle, FM Scan

Timing: 30 Hz square waves with rising edge occurring at the fall of the corresponding 0° reference pulse

Other characteristics: As above

6.3 Frequency and Phase Stability

signals are derived from

Nominal uncertainty: 1 x 10

All signals are derived from a single 4.32 MHz temperature-controlled quartz master oscillator

-7

Short term stability: 5 x lO"-'-^ rms Aging rate: 3.5 x 10"°/week

Output timing jitter: Less than ± 1 ns

6.4 Error Detection Circuits

An audible alarm sounds when any of the three generators loses synchronism with the other two or when an erroneous output value is computed by the digital circuits. Indicator lamps show which error

condition has occurred. These comparison circuits are indicated by the circled letter "C" in figure

6-1. All comparisons are made 30 times per second.

11
30 Hz

Reference Phase

Count e r

Phase L ag

Con t ro

1

30 Hz

Var 1 ab 1 e Ph as^

Coun ten

9960 Hz

FM Subc ar r 1 e Counter.

Ph ase

Compe ns at o r

--____

30 Hz

ROM

^--—

Doub 1 e Re c u mu 1 at o r

Doub 1 e

flc c u mu 1 at o r

Triple

flc c umu 1 at o r

DRC

Tl

1-lon

^

LirHw

'

Res 1 St 1 \/A

fldder/

DRO^

/

1

/

/ '

'

Louip ass

Pi 1 ter

Compos i te

flud 1 o Output

Figure 5-1. Error detection circuits. Digital comparisons are made between the pairs of

digital signal paths as indicated by the heavy arrows. Clock is not shown.

6.5 Built-in-Test Circuits

5.5.1 Circuit Tl in Figure 5-1

This circuit compares the two 30 Hz generators at and 360° phase lags and lights an error lamp

if they disagree. This test is made manually from the front panel.

6.5.2 Circuit T2 in Figure 6-1

This circuit compares the FM generator with the 30 Hz variable phase generator at 90° phase lag

and indicates an error if they disagree. This test is made manually, from the front panel.

5.6 Controls

Power switch.

Connectors (5) to select the components of the composite signal and timing references

Phase lag—5 decade lever switch, to 399.99°

Error indicator reset pushbutton

Built-in-test operate pushbutton

12
6.7 Indicators

Power on: 1 lamp

Error indicators: 5 lamps, 1 audible alarm. Indicator latch ON if tripped

Test indicators: 2 lamps

6.8 Other Characteristics

Power input: 117 VAC ± 10%, 350 W Size: 58 cm high by 50 cm wide by 46 cm deep

Ambient temperature: Normal laboratory environment, 22 ± 5°C

Signal connectors: BNC

7. Operating Procedures

7.1 Normal Operation

Turn on ac power and wait one hour for warmup. Connect short (1 m) shielded cables to the 30 Hz and 9960 Hz outputs. Connect the two cables to the resistive summing network. Connect the output of

the network to the input of the linear-phase low-pass filter. The composite signal is then available

at the filter output (see fig. 7-1). Set the lever switches to the desired bearing angle. Proceed

with measurements. It is normal for the error alarm to sound briefly and for the phase lag error indicator to glow briefly whenever the bearing angle switch setting is changed. There is a problem

only if the alarm continues to sound. See sections 8.5 and 11.3.

RUDIO FM

Std. Generator

HUDIO VflR

Res i st i ve

Rdder

Loup ass

Fi Iter

UNIT

UNDER

TEST

STflNDRRD COMPOSITE AUDIO SOURCE

^

Figure 7-1. Connecting the standard VOR generator, adder, and filter to a unit under test,

7.2 Error Conditions

Continuous sounding of the alarm after a phase lag change, or momentary sounding of the alarm at any other time during operation, indicates that an error has occurred. The indicator lamps show which

circuits are involved. The RESET button turns off all error indications but does not affect any other

circuits. An automatic power-on reset circuit clears all error indicators five seconds after power

turn on. Since the generator circuits are self correcting (as described in section 8.5), an occasional error indication is of no consequence unless it occurs during a measurement. Any error lamp

that is lit during a phasemeter calibration means that the run should be repeated, as the data may be

13
invalid. This is a rare occurrence, and is usually due to a static discharge between the operator and

the system. Frequent errors or a continuous alarm are reasons for concern, and their cause must be

determined and corrected.

7.3 Testing Bearing Angle Settings

Set the bearing angle settings successively to 0.00° and 360.00° and press the TEST button. The

respective indicator labeled 0° or 360° LAG should light. It should not light for other nearby

values. Indications that differ from these result from faulty 30 Hz generator circuits or faulty test

ci rcuits.

Set the bearing angle to 90.00° and press the TEST button. The correspondingly labeled indicator

should light. It should not light for other nearby bearing angle settings. Any other indication

shows a circuit failure. Note that the indicators will also light for a few settings well removed

from the prescribed settings. This condition is normal and is of no concern.

8. Generator

8.1 General Approach

The overall design concept was to reproduce the desired waveforms from internally stored tables

of numbers which are associated with the waveform. The last stage is signal generation by means of a DAC and filter. In the actual implementation, a number of steps were taken to reduce the required

amount of programmable read-only memory, the most expensive part, by a factor of 14.

In this section, the basic scheme is described first. Then, the various techniques used to reduce ROM size are discussed.

It should be noted that this design does not attempt to minimize the number of samples per cycle

required to represent the required signals. The 1.08 MHz sampling rate used is well above the Nyquist

rate of about 22000 samples per second. In fact, the design approach was to use the highest sampling

rate that could be readily implemented, in order to minimize the generation of unwanted signals.

See section 12 for possible future improvements.

8.2 Generating the 30 Hz Sine Waves

8.2.1 Basic Method

The 30 Hz signals were generated from stored numeric representations by fetching each successive

value from a table and sending it through digital-to-analog converters. In order to get a phase resolution of 0.01°, it was convenient to work with 36,000 values, one for each 0.01° of a complete cycle.

Portions of a sine table, based on a full scale amplitude of ±8188, are shown in table 8.1.

It is readily seen that the size of such a table can be reduced by a factor of 4 by using the

symmetry properties of the sine wave, as follows:

14
Table 8.1. Selected values of 8188 sin e and its first and second differences,

degrees

^\

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

89.99

90.00

90.01

179.91

179.92

179.93

179.94

179.95

179.96

179.97

179.98

179.99

180.00

180.01

180.02

180.03

180.04

180.05

180.06

180.07

180.08

180.09

269.99

270.00

270.01

359.91

359.92

359.93

359.94

359.95

359.96

359.97

359.98

359.99

13

4

6

7910

11

13

8188

8188

8188

13

11

10

9

764

3

1

-1-3

-4

-6

-7-9

-10

-11

-13

-8188

-8188

-8188

-13

-11

-10

-9

-7-6

-4

-3

-1

The table is used directly for angles (6) between 0° and 90°. For 9 between 90° and 180°, the

values for (180-9)° are used, scanning the table backward from 90° to 0°. For angles between 180° and

270°, the entry for (9-180)° is used but with the sign of the value changed to minus. For angles

between 270° and 360°, the entry for (360-9)° is used, again with a negative sign for the value. Thus

the size of the table is reduced by 4 with no loss of information.

The scanning of the table is readily controlled with the aid of a digital counter which is

changed by one count each 0.93 ys (1/36000 x 1/30 s). The count is incremented for the first 9000

counts, decremented for the next 9000, then incremented for 9000 counts, then decremented for 9000

15
counts for four scans of the PROM. During the second half of this cycle, the sign of the number is negated, thus producing a normal sine wave output.

8.2.2 Use of Differences to Reduce ROM Size

When the 30 Hz sine wave generators are implemented as just described, the minimum size of the

lookup table is 9001 13-bit words. However, it can be seen from table 8.1 that the changes (the

"a^^") between successive words are small. If the function is generated from its stored differences,

the length of each word in the table is substantially reduced. This reduction is shown in table 8.2

in the column labeled "First difference."

Table 8.2. Sine function and differences,

grees 8188 Sin

0.00

0.01 1 0.02 3 0.03 4 0.04 6 0.05 7 0.06 9 0.07 10

0.08 11 0.09 13

First difference Second difference

Since sin{e) changes most rapidly around 0°, the first differences at other angles will not be any larger than those near 0°. A thorough examination, in fact, shows that the range of first differences

is to 2 for 9 between 0° and 90°. By using a conventional binary number representation, this range

could be covered by using two bits per entry, instead of the 13 bits required to represent 8188

sin(e). In the actual system, we chose to carry this one step further and use second differences^

that is, the differences between first differences. In that case, the number range is -1 to +1. This

approach still requires two bits to represent all required values.

When differences are used instead of the actual function, the circuits must be modified to generate the function from the differences read from the table. This is done by providing two accumulators, as shown in figure 8-1. The first accumulator adds the successive values of A^, the second

differences read from the table, and forms A^, the first difference. The second accumulator adds suc- cessive values of A^ to get the desired function, 8188 sin 0, which supplies the input to the DAC.

Additional circuits are required to insert the appropriate initial values into the accumulators at 0°

and to change from addition to subtraction when the table is scanned in the reverse direction.

^This decision was made early in the design process, before it was recognized that there is no advantage in using second differences in the 30 Hz generators. Indeed, upon examining a complete computer

printout of the occurrences of all first differences, it was discovered that the 30 Hz memory could

have been cut in half again by the addition of a single flip-flop. With such an arrangement, only a single bit is required in the lookup table for each value of the sine function first difference. See

section 12.1.

16
30 Hz

Reference Phase

Cou n t e r

Ph ase Lag

Con t r o

1

30 Hz

Var 1 ab 1 e Ph ase

Coun t e r

9960 Hz

FM Subcarrier

Counter

t Phase

Compens at o r

rl

30 Hz

ROM

Doub 1 e flccumu 1 at o r Ref. Output

Doub 1 e flccumu 1 at o r DflC

1 .08 MHz

System

Clock

- Van . Output

Res 1 s t 1 ve

Rdder

H

9960 Hz

ROM

Triple

flc c umu 1 at o r DflC

H

FM

Subc ar r i e r Output

Loujp ass

F i Iter

Compos i te

flud i o Output

Figure 8-1. Overall generator block diagram.

8.3 Generation of the Frequency-Modulated 9960 Hz Signal

8.3.1 Basic Method

The method used here is similar to that used for 30 Hz generation. The values corresponding to

the third differences of the desired frequency-modulated signal, computed at intervals of 0.93 ys, are stored in a table, integrated appropriately, and reproduced through a DAC. The 9960 Hz generator is driven from the same clock as the 30 Hz generators; this approach maintains synchronism among all signals. The 9960 Hz FM signal has only a two-fold symmetry, in contrast to the four-fold symmetry of a sine wave.

The function represented in the table is

F(<(>) = 8188 sin [332 <}> + |^ sin <}>]

where cj) is the phase of the 30 Hz signal relative to its 90° point. This function, when interpreted

as a sine wave of slowly varying frequency, sweeps ±480 Hz around 9960 Hz. The computed spectrum is a

17
LIMITS OF

UNCERTRINTY

IN PHASE

Figure 8-2. Relationship between amplitude distortion and phase uncertainty.

set of discrete lines spaced every 30 Hz around 9960 (there is further discussion of the spectrum in

sections 10.2 and 16.1). The -80 dB points of the spectrum are at ±810 Hz relative to 9960 Hz. This means that almost all of the information contained in the composite VOR signal appears in the line at

30 Hz and the band between 9150 and 10770 Hz. For purposes of the standard generator and the standard

phasemeter, it can be shown [5] that sufficient information to perform a calibration to an uncertainty

of less than 0.01° can be obtained from the 30 Hz line and those between 9420 Hz and 10,500 Hz.

The PROM table stores half of this FM waveform, using 18000 locations to do so. The other half

is obtained by reading the table backwards.

8.3.2 Use of Differences to Reduce PROM Size

As in the case of 30 Hz signal generation, a table storing the function F(((>) would be quite

large, 18001 13-bit words. Again, because the function changes relatively little between successive

entries in the table, it is feasible to use differences to reduce the required word length. The use

of third differences reduces the word length to 4 bits, as indicated in table 8.3.

18
Table 8.3. 9960 Hz FM signal function and its first three differences.

(j) First diff. Second diff. Third diff.

Degrees F(<|)) (a^ (a^) (a^)

-2 -1 -3 -3

-6 -1

-7 -3

-10

-10 -2

-12

8 -2

6

6 -1

5 -3

2 -1

0.00 497

0.01 497 495

0.02 992 492

0.03 1484 486

0.04 1970 479

0.05 2449 469

0.06 2918 459

0.07 3377 447

179.93 -3083 423

179.91 -2660 431

179.95 -2229 437

179.96 -1792 443

179.98 -1349 448

179.99 -451 451

180.00 —

There is a priori reason to assume that the higher order differences will have numerically

smaller values. The design approach was to select the lowest order differences that had reasonably

small absolute values. Table 8.4 shows that for F((t)), the maximum magnitude of the differences

decreases up to a^ but then increases again. Accordingly, A^ was chosen as the function to be stored

in the table. This optimum approach was ascertained by a computer algorithm that tested the zero through fifth differences.

Table 8.4. Maximum value of the first through fourth differences for the 9960 Hz FM waveform.

First difference: \a^\ < 496

Second difference: JA^j < 31 Third difference: I'^^l ^ ^ Fourth difference: Ia'*! < 7

The circuit arrangement required to implement this approach is also shown in figure 8-1. Three

digital accumulators are required to determine the values of A^ from A^, a^ from A^ and F(<f)) from A^. The accumulators are initialized to correspond to the values given in table 8.3 for (j) = 0.00°, namely

F(O.OO) = 0, aI(O.OO) = 497, and a2(0.00) = -2 since this information is not stored in the PROM. A similar initialization, but with different numeric values, is also used at 180.00°.

8.4 Accuracy Considerations

The general design goal has been to achieve an overall uncertainty of ±0.01° in the various outputs of the signal source. This goal affects the design in three critical areas:

19
a. The short- and long-term accuracy of the output frequencies;

b. the short- and long-term accuracy of the phase differences between the three output signals;

and

c. distortion and noise at the three signal outputs.

8.4.1 Frequency Accuracy

All outputs are derived from a single 4.32 MHz quartz crystal oscillator with an aging rate of

less than 3.5 x 10"°/week. and a short-term stability of 5 x lO"-'-^ rms. After allowing for temperature

and voltage effects, the estimated frequency accuracy is about 1 x 10" . The frequency error required

to produce 0.01° error would be 1/36000 or 2.8 x 10"^. Thus, errors from the crystal oscillator frequency instability should not exceed (0.01) (10"'')/(2.8 x IQ-^) or 0.000035°, a clearly negligible

amount. This oscillator, and that in the phasemeter time-delay generator, are conveniently calibrated

directly against the NBS atomic clock. Routine calibrations have resulted in corrections of less than

5 X 10"^°, which is still negligible.

The second potentially significant source of uncertainty is the short-term variations in timing

of the circuits that use the clock signals. The system design uses synchronous logic so that variations in time delays will accumulate over only a few logic elements. The short-term variations in

delay through the critical path from the clock oscillator to the inputs of the digital-to-analog converter are less than 5 ns (54 microdegrees) . This is well below the 926 ns clock period and therefore

could contribute at most a negligible uncertainty.

8.4.2 Phase Setting Accuracy

The desired phase shifts between the various outputs are produced by delaying the 30 Hz variable

phase generator in increments of the clock period, 926 ns. At any delay setting, the actual delays

have a variation of less than 5 ns, a negligible amount. The clock signals are distributed in a manner which ensures that significant fixed differential delays are not present. Residual delays that

appear at the analog outputs are reduced to less than 5 ns, as noted below.

The composite signal is obtained by adding the 9960 Hz FM and 30 Hz variable phase signals in a passive resistive network. A passive low-pass filter follows the adding network. The filter has a cutoff frequency of 100 kHz, well below the 1.08 MHz clock frequency. It has a Bessel (maximally

linear phase) response and contains seven sections. It is designed to work between 500 n source and

load impedances and is terminated by a 600 9. load. This design provides a fixed output level of 1 V rms for each of the two components of the composite signal. It was found that most commercially

available 600 fi "T-pad" attenuators were not sufficiently phase linear to provide for an adjustable

output. Such an attenuator could be added at the price of a slight increase in the phase uncertainty.

A Bessel filter with seven sections closely approximates the ideal. In such a filter, the time

delay (phase shift divided by frequency) is nearly the same for all frequencies. This is another way

of stating that the filter has low group-delay distortion. Obviously, if all of the significant com- ponents of the spectrum are equally delayed in time, there is no effect on the VOR bearing angle.

Computer simulations of the effects of the actual filter, with its measured imperfections, have shown

that the differential time delays from 30 Hz to 10,770 Hz (a band that includes virtually all of the

composite signal power) are negligible in so far as the bearing angle is affected. See section 10.4

for measurement details.

20
A third potential source of uncertainty in the bearing angle is the instability of the filter

characteristics due to component drift. The filter is passive, with no operational amplifiers.

Bessel filters tend to have a low sensitivity to component drift; inductor "Q"s for a 7-section filter

need not exceed about 1.1. Finally, since the first-order errors have been found negligible, certainly higher-order errors are also.

8.4.3 Amplitude Distortion and Noise

Noise and distortion are introduced into the output signals in a number of ways. These include

quantizing noise, digital-to-analog converter nonlinearity, switching spikes (so-called glitches),

nonlinearity in the amplifiers that follow the converters, and digital signals that find their way

into the analog signal outputs through subtle paths. All of these have an explicit effect on the

design of the system. All are discussed below.

8.4.3.1 Quantizing Noise

The unfiltered output from the digital-to-analog converter is nominally in the form of a staircase with a step size equal to 2"'^ times the peak-to-peak output voltage, where N is the number of

bits used in the converter. This means that the maximum uncertainty in reproducing any waveform will

be 1/2 the step size. In terms of the peak value of a sine wave with unit amplitude, the maximum

uncertainty is l/(2'^-l).

A useful interpretation of the 0.01° uncertainty requirement is that amplitude distortion of a signal must not shift the time position of a zero crossing, with respect to an ideal 30 Hz sinusoid,

by more than 0.01°. The amount of distortion that produces this phase shift is easily deduced from

the phasor diagram of figure 8-2.

The maximum value of Ae is related to aE by the expression aE = A sin(A9). Thus, for AG = 0.01°,

aE/A = sin(O.Ol) = 1.7 x lO"'^. Thus, 0.017 percent is the maximum allowable distortion for a phase

uncertainty of ±0.01°.

Setting 2"'^ = 0.017 percent, we obtain N > 13. If quantizing noise in one channel were the only source of error, a 13-bit converter would be adequate. However, since there are other sources of error, a more conservative design must be used. Converters that will operate at the required speed

are not readily available for N > 13. Accordingly, 13-bit converters are used, followed by a low-pass

filter to further reduce the quantizing noise. Assuming that the principal quantizing noise component

is at 1.08 MHz, a 7-section Bessel low-pass filter with a cutoff frequency at 100 kHz will reduce this

noise component by more than 80 dB. The quantizing noise from a 13-bit converter followed by this

filter should then be 1.2 x 10"° percent. Note that the total harmonic distortion figures given above

Include the effects of quantizing noise, along with other noise sources, hum, and harmonic distortion.

It is apparent that the quantizing noise is very small compared to the maximum allowable value of

0.017 percent, and in fact is too small to be measured.

8.4.3.2 Converter Nonlinearity

The DACs used have a specified maximum nonlinearity of ±1/2 of the least significant bit (LSB)

relative to a straight line connecting the largest and smallest output values. Thus, the amplitude

uncertainty at a nominal zero-crossing point could be as great as 1/2 LSB, or 6.1 x 10"^. The change

21
in the zero-crossing time that this uncertainty v/ould produce can be estimated by assuming that the

slope of the waveform is constant in this region and equal to Z-n-f for a unit amplitude sinusoid.

There, the offset At for an amplitude uncertainty of Av is given by

At .^. 6.1 X 10-5 ^ ^^^^^ ^^^ 2^f 2^ . 30

or

0.324 us

= 0.0035 deg.

0.925 uS per 0.01 deg

This result, taken alone, indicates a marginal design. However, the uncertainties caused by converter

nonlinearity are only significant to the extent that the resulting distortion components appear at the

output of tne filter described above. All three converters are interchangeable. The harmonic distortion for all three v/as measured at 30 Hz, at the filter output, using a twin-T notch filter with a fundamental rejection of more than 100 dB at 30 Hz. This technique allowed direct measurement of the

total noise and distortion products of the DACs. In all cases, the total was less than the fundamental by more than 85 dB.

8.4.3.3 Converter Svn'tching Spikes

Switching spikes (or "glitches") occur in digital-to-analog converters because of small differential delays in the digital input signals for different bits. The glitches are always present to some

degree, because the current switches turn on in less time than they turn off. The converters used in

the VOR generator are "de-gl itched;" that is, they contain circuits that prevent the glitches from

reaching the analog output. Tnis is accomplished by following the digital portion with a track-andhold amplifier and providing appropriate timing signals. The amplifier is in the "hold" mode while

tne digital currents settle, and is tnen switched to "track" until just before the next digital word

arrives. This technique significantly reduces the spike energy.

8.4.3.4 Amplifier '^oise and Nonlinearity

Tne current-to-voltage output amplifiers in the converters were supplied by the manufacturer.

The Characteristics of these amplifiers are included in the total specifications of the converters.

Actual performance was determined oy ine total harmonic distortion measurements.

8.5 Error-Detection and Built-in-Test Circuits

8.5.1 Overview

In order to maintain this system as a national standard, it is essential to provide a means of

routinely checking for slight degradations in its performance. Major failures will be immediately

obvious when attempting to use the system. However, minor malfunctions, such as a single bit changing

in ROM, might never be detected without repeating the full system validation. Therefore, the digital

subsystems were designed to include error-detecting circuits, as described in section 5.4. It was relatively simple to augment this inherent capability and provide the ability to detect a large

variety of permanent or transient malfunctions in the digital circuitry. Two types of checking are

22
provided. The circuits which function without special attention from the user are called error-detection circuits. Those that require operator manipulation are called built-in-test circuits (see

fig. 6-1).

8.5.2 Inherent Error-Detecting Capabilities

Using the method of differences to generate the output functions provides an inherent capability

for error detection. Any single error in the ROM output data or in any accumulator will continue to distort the output signal until the start of a new cycle. When this occurs in other than the final

accumulator (the "f-accumulator"), the distortion increases continually throughout the cycle. The

result is that consistent single errors are likely to produce a severe distortion of the output signal. This distortion results in a major degradation of performance and would probably be noticed

immediately by the user. It is immediately apparent on an oscilloscope. However, errors that occur

close to the end of a cycle may not produce enough distortion to be obvious to the user.

8.5.3 Error-Detection Circuits

Three error-detection circuits, one for each of the three channels, provide a continuous check on the internal functioning of the digital elements of each channel. They operate by verifying that the

outputs of the 30 Hz channels are correct at their 359.99° points and that the 9960 Hz channel output

is correct just preceding its 0° and 180° points. Two additional error-detection circuits check the

9960 Hz counter and the 30 Hz phase-lag counter, at times just prior to their initialization, to ascertain whether a miscount occurred during the current cycle (see fig. 6-1). The five self checks

are denoted by the letter "C" and the two tests by "T". When an error is detected by any of the five

"C" circuits, an indicator lights, and an alarm sounds briefly. The phase-lag-counter error light

automatically resets after 1/10 s, since this error occurs each time the phase-lag setting is changed

by the user. The other four error indicators must be reset manually. This arrangement allows an extended measurement to be made without an operator present; if one or more of these lights is on at the end of the measurement, it must be assumed that bad data may have been taken. Over a period of

several months of use, the only times that these lights have been lit have been when static discharges

have taken place either nearby or into the instrument itself. There have been no "hard" failures. A power-on reset circuit resets all indicators 5 s after power is first applied.

8.5.4 Built-in-Test Circuits

These circuits (described in section 6.5) compare time delays introduced by the phase-lag circuits with fixed delays in the generator control circuits, thus providing a means of cross-checking

the various digital delays. Checks are performed at 0°, 90°, and 360° lags. In operation, the tests

are performed by setting the phase-lag switch to one of these three lags and seeing if the appropriate

indicator lamp lights when the TEST push-button is depressed.

9. Power Supplies

The digital logic that generates the data presented to the digital-to-analog converters is powered by a single 5 V, 16 A supply. The nominal drain is 12.5 A. The logic is protected by a 6.8 V crowbar circuit. Heavy copper distribution buses and remote sensing are used.

23
Each of the three analog channels has its own power supplies, to reduce the possibility of crosstalk that could contaminate the output signal. Each channel uses a plus and minus 15 V, 350 mA supply

for the analog circuits and a 5 V, 500 mA supply for the DAC logic.

10. Verification of Performance

In this section, we discuss the methods that verify that the digital and analog circuits are, in fact, performing as intended.

10.1 Memory Pattern Verification

The VOR "standard," in a certain sense, exists in the bit pattern of the programmable read-only

memory chips. Therefore, considerable attention was given to assuring that the patterns were correct.

This was done as follows:

1. A BASIC program was written for a desktop computer to prepare magnetic tapes containing the

binary values for all of the PROM addresses for both the 30 Hz and 9960 Hz memories.

2. A second program was written to read the binary patterns from the magnetic tapes to a paper tape

punch. The PROM vendor required such tapes to perform the programming operations. The PROMs are

of the fusible-link type, nonerasable. This choice was dictated by the speed requirements.

3. A third program was written to read back the paper tape and compare the punched pattern with the

original magnetic record. Punching errors were found and corrected.

4. A test jig and interface was designed and a program written to read the programmed PROM patterns

and compare them directly with the original magnetic tape. Programming errors were corrected;

defective PROMS were replaced by the vendor.

5. The PROMS were installed in the generator, and a special interface was designed to allow the

computer to drive the system in place of the normal system clock. Programs were written to allow

rapid access to any part of the waveform cycle (36,000 PROM addresses). This allowed examination

of the bit patterns in the three channels at such critical points as sign changes, memory address

turnaround, and so forth. Memory could be stepped one address at a time for debugging.

6. When all appeared normal, a program was written to step the logic through all 36,000 addresses

and read out to the computer all three 16-bit words appearing at the DAC inputs. These were compared with the proper words computed at the same time, rather than comparing with the magnetic

tape, so that the patterns were compared directly with the algorithm that generated them in the

first place. This test, which involved the computation and comparison of 108,000 16-bit words,

required about 10.5 hours to run. This may be compared with the time required for the generator

to produce them normally, that is, about 33 milliseconds. No discrepancies were found, and it was concluded that the digital portion of the generator was indeed performing as required.

7. Two other points were considered in this verification. First, the question of whether the

computer used to generate the PROM patterns had sufficient precision was answered by generating

the same patterns using a large digital computer capable of maintaining 24 decimal digit

precision. The files were identical, which is not surprising, since the small computer was capable of 12 decimal digit precision. Second, the algorithm used to generate the data was derived independently by several persons, to ensure that it accurately represented the VOR

waveform.

24
RANGE: 5 dBV

-9

dBV

10

dB

/DIV

-89

START:

.-^t _^ - -

-^ ;:-:;:

:

; ; ; ; h ;

[ ....... ^

-*

^\^ A '/I \l\'\ I \i\ .11 \ A. iM^ J'. . 9 960 Hz BW: 3.75 Hz STOP: 10 960 Hz

Figure lU-1. Partial 9960 Hz spectrum. Arrows indicate computed amplitude.

10.2 Analog Performance Verification

Some discussion of the methods used to verify the analog performance was given in section 8. For

completeness, this discussion will be expanded here.

Initially, until the completion of the phasemeter, it was not possible to make an overall test of

the generator. However, the individual components of the analog circuits were tested. Each of the

DACs, in turn, was driven by the digital data from the 9960 Hz data lines. The output of each DAC was examined with a spectrum analyzer. Figure 10-1 is a typical result. Plots were made that showed that

the spectra of the output were in close agreement with the theoretical and that harmonic components

were below the minimum detectable level (about -70 dBc for the FM waveform). Errors such as missing

codes in the DACs, or excessive non-monotonicity, show as unwanted sidebands. The outputs were also

examined across an entire cycle, using an oscilloscope with an expanded sweep, to ensure that the DAC

deglitching circuits were performing properly.

A second set of tests was made on each DAC using the digital input from the 30 Hz reference phase

generator. Since the analog output contained only a single frequency, it was possible to measure harmonic distortion directly by suppressing the fundamental. It was at least 85 dB below the fundamental .

25
Finally, the analog filter was tested to the extent possible before the completion of the phasemeter. In the end, the definitive tests on the filter were made with the help of the phasemeter, as described in section 10.4.

10.3 Di gital -to-Analog Circuit Timing Verification

Ideally, there would be zero differential time delay and jitter between the three analog signals

at the outputs of the DACs. The three DACs are nominally identical, and all are clocked by the same

clock phase. They are provided with two timing adjustments each. Data is presented to each DAC on the falling edge of clock phase 1. When the clock falls, the first of two cascaded monostable multivibrators is triggered. The time delay to its falling edge is adjustable over a small range. Its falling edge, in turn, triggers the second monostable, which produces a pulse with a fixed 50 ns width. During the period of the first delay, the digital data settle at the DAC input. The rising

edge of the second delay enables the DAC, and the data are latched into the DAC registers. At the

same time, the DAC deglitching amplifier is placed in the "hold" mode, so that the DAC switching

impulses do not reach the output.

The DAC contains a second adjustable delay internally, that determines when the deglitching

amplifier is returned to the "track" mode. This adjustment allows optimization of the DAC speed while

allowing switching transients to die out. To match the three DAC time delays, each, in turn, was driven by the 9960 Hz data. Since there are only, on the average, about 108 samples per cycle in this

waveform, the transitions may be clearly seen on an oscilloscope. If the oscilloscope is triggered by

the transition of the sign bit of the reference 30 Hz DAC, at a sweep speed of 20 ns/division, all of

the DACs may be adjusted to equality to within 10 ns or less. The delay from the falling edge of

clock phase 1 to the rising edge of the DAC enable pulse was set to 110 ± 2 ns. Then, the delay from

the falling edge of the clock to the beginning of the analog output transition was set to 300 ± 5 ns. A mismatch of 7 ns corresponds to a phase uncertainty of about 76 microdegrees, a negligible amount.

10.4 Analog Filter Characteristics

The actual characteristics of the output filter were measured as follows. A single-pole doublethrow reed relay was placed at the input to the NBS standard phasemeter. The relay, in effect, permitted time-sharing the phasemeter between two inputs, simulating a conventional two-input phasemeter.

A programmable frequency synthesizer was connected to the filter input, with appropriate padding to present a 600 n source resistance. The filter was also terminated in 600 n. The signal at the filter

input was connected to one of the two phasemeter inputs, and the filter output was connected to the

other. Thus, the phaseshift through the filter was simply the phase angle between the two phasemeter

inputs.

The synthesizer was stepped at 30 Hz intervals from 30 Hz to 10,770 Hz. At each frequency, 256

amplitude samples were taken on each channel, covering precisely one cycle at the signal frequency. A discrete Fourier transform then allowed the computation of the filter phase shift at that frequency.

The reduced data (phase versus frequency) were then fitted to a second-degree polynomial. The phase

linearity was very good, but the conclusive determination was made by using the fitted phase function

with simulated data, as described next.

A complete measurement of the composite signal was simulated by computing 1024 amplitude samples

in which the only noise was due to the 14-digit precision of the computer used for this purpose. When

26
these data were reduced, by the same machine, there was a offset of only about 54 microdegrees. Then

the partially reduced simulated data were perturbed, using the filter function discussed above, to simulate very closely the effects that the actual filter would have produced. There was an insignificant change in the 54 microdegrees offset. The conclusion is that the filter does not degrade the

phase integrity of the standard.

11. Maintenance Procedures

Three areas of maintenance are discussed here: adjustments, performance checks, and trouble

shooting. There is no preventive maintenance as such for the system. The section on adjustments

mainly covers the analog elements of the system and describes the procedures originally used to set the circuits to their design values. The trouble shooting section is quite brief, dealing mainly with

getting started toward finding malfunctions in the digital elements of the system.

11.1 Adjustments

Run the system, for at least 30 min to stabilize internal temperatures, then perform the following

adjustments, in order.

5 Volt Power Supply . The main power supply contains an output-voltage adjustment. Connect a suitable dc voltmeter to the +5 V test-output receptacle. Set the adjustment (labelled 5 ± 5 percent

VDC) for 5.0 V ± 0.1 V.

Oscillator . Connect a frequency counter to the ((> test-output receptacle. Use the adjustment on the oscillator (labelled FREQ. ADJ.) to set the frequency to 1,080,000 + 1 Hz. Note that this oscillator is more accurate than the time bases in some frequency counters, and caution should be exercised

in readjusting its frequency. An external standard may be required.

DAC Adjustments . See section 10.3. Adjust the time delays as noted. Final adjustment is best

accomplished by using the following procedure:

Connect the cable carrying the 9960 Hz FM data to a "T" cable that allows driving two DACs simultaneously with that signal. Connect a two-channel oscilloscope to the unfiltered DAC outputs and trigger

the oscilloscope with the sign bit of the 30 Hz reference phase. Set the sweep speed to 10 ns per

division. Superimpose the two traces vertically, using the oscilloscope controls. Superimpose them

in time by adjusting the time delay on either DAC. Only very minor adjustment should be needed.

Reverse the connections to the oscilloscope to ensure that the channels have a negligible differential

delay. If they do not, compensate accordingly. Replace either of the DACs with the third DAC and

adjust the third DAC in the same manner. In this way, all three DACs have been adjusted to have the

same overall time delays, and differential phase errors are made negligible at the output ports of the

generator.

Low-Pass Filter . There are no adjustments available on the low-pass filter.

Phase Compensation . The phase compensation switches provide a means of advancing (or delaying)

the start of the 9960 Hz signal to ensure that its principal zero crossing occurs exactly 90.00° after

the corresponding point of the 30 Hz reference signal. This circuit was included early in the design

under the assumption that it might be necessary to compensate for phase nonlinearity in a low-pass

27
filter. This has since been found to be unnecessary, and, in fact, undesirable. The switches should

all be set to provide zero compensation (all switches closed). If any switch is open, the 90.00° test

will fail. The test will pass if the thumbwheel front panel switches are set to the value programmed

by the phase compensation switches. This feature has been allowed to remain in the instrument for

possible future experiments, but is never used for calibration purposes. The "untweaked" status of

the generator is thus maintained.

11.2 Performance Checks

In addition to the parameters covered in section 11.1, a few other measurements can be made to verify that overall performance has not deteriorated. There are no specific adjustments associated

with these measurements. If performance has deteriorated, the reasons must be determined through

troubleshooting procedures. However, the performance will be affected by the adjustments of section

11.1, and these performance measurements should be made after final adjustments have been made. It is assumed that the error-detection circuits show no errors and that the internal (built-in) tests have

been performed and passed.

Phase-Lag Tests . Certain failures in the phase-lag setting circuits could go unnoticed in normal

operation. In particular, some switch settings could give erroneous values of lag. It is not feasible to check each of the 39,999 settings. However, it is straightforward to check each digit over

its full range. Proceed as follows. Connect a two-channel oscilloscope to the generator, with one 30

Hz signal to each input. Trigger externally, using the sign bit of the reference signal. Set the

sweep speed at 1 or 2 ps per division. Starting with a phase-lag of zero on the thumbwheel switches,

advance slowly to 0.09° while watching the relative phase of the two signals. They should begin perfectly in phase (less than 10 ns offset) and move apart in nine equal steps of 926 ns, one for each

new step on the 0.01° switch. This verifies that the 0.01° delay is functioning properly. Repeat for

all of the higher order switches, decreasing the sweep speed by a factor of 10 for each successively

higher order digit. The 100° switch, of course, can be tested only to 300°.

Spectrum Measurements . The overall performance of all three channels can be observed by measuring the spectra of the three signals. By comparing these spectra with the data obtained in the original tests of the system, any serious departure from the original state can be detected.

There are two approaches that may be used. In the first, a commercial low frequency spectrum

analyzer with a plotter output can provide a comparison spectrum. Figure 10-1 was made in this way.

If the output amplitude is the same as for the original test, the later plot can simply be laid over

the original to detect deviations. Of course, the 30 Hz spectra should show only a single line at

30 Hz.

The second method involves the use of the NBS standard phasemetei". This is the best method for

checking the performance of the 9960 Hz circuits. The relative amplitudes of the lines from 9420

through 10,500 Hz are compared to the fundamental at 9960 Hz. These amplitudes should follow closely

the predicted values [3].

11.3 Trouble Shooting

The main requirements for finding other than obvious troubles are a reasonable understanding of

the system design principles and circuits and a good oscilloscope. The principles and circuits have

28
already been covered. The oscilloscope should have a pass-band of at least 20 MHz, a two- (or four-)

trace input capability, and a dual time-base. A digitally-delayed sweep is useful but is not essential .

A number of points should be kept in mind.

1. The three channels are independent of each other except for their phase relationships. Any one

channel can fail while the other two still function.

2. The only elements that affect all channels are the 5 V power supply and the clock circuits.

3. The error-detection circuits may not indicate a gross failure in a channel.

4. The simplest test of overall operation is to observe the individual channel outputs on the

oscilloscope. Triggering the scope from the variable phase sign bit permits examination of the

individual cycles of the 9960 Hz output by changing the phase-lag setting. The 30 Hz outputs

should be perfectly clean sine waves, and the 9960 Hz output should have uniform amplitude

everywhere. Any small part of it should appear to be a clean sine wave.

5. A ROM or accumulator failure, no matter how minor, usually results in an output signal that bears

no resemblance whatsoever to the desired signal. If the signal appears normal over only part of

the cycle, noting the precise point of failure helps to localize the trouble.

6. The three DAC cards may be interchanged with each other to localize faults.

7. The (j) signal is the main clocking signal for all channels. Nearly all clocked flip-flops are triggered by the trailing edge of (^ . The other three clock signals are used as synchronizing

and strobe signals in the phase-lag control, phase-compensation, ROM-multiplexing, errordetection, and built-in-test circuits.

8. The internal control signals always lead the actual 0° point of the analog output signals. Do

not assume that these signals are at the zero crossing points of the sine or FM signals.

12. Suggestions for Future Designs

During the development of this system a number of design simplifications became apparent. For

the most part, we chose not to incorporate these simplifications into the present system, since doing

so would have delayed its completion. However, it will probably be cost-effective to incorporate

these into a future system if one is to be constructed.

12.1 30 Hz ROM and Accumulators

In the 30 Hz channels a 14-bit value of the sine function is computed, but only the 13 mostsignificant bits are used. The size of the 30 Hz ROM can be cut in half, using only one bit per word.

Examination of a complete printout of all 9001 first differences reveals that the present precision of

8188 can be maintained with half the present memory by supplying a 1 or from a flipflop. It changes

state from 1 to at some point away from the zero crossing. The pattern shows only "l"s and "2"s in

the region of rapid change, and only "0"s and "l"s near the peak of the wave, where the slope is zero. Thus, only one bit per word is sufficient, if the flipflop is added.

12.2 Reduced Sampling Rate

In the present system there are 36000 samples per 30 Hz cycle and about 108.3 samples per 9960 Hz cycle. If these numbers can be reduced without degrading overall performance, then the size of ROM

can be reduced correspondingly. In the limit, the sampling theorem requires just two samples per 30

29
Hz cycle or per nominal 9960 Hz cycle. ^ In principle, the sampling rate could be reduced by a factor

of about 50 and still be fast enough for the 9960 Hz generator. However, if this were done, the lowpass filters at the analog outputs would need to have much sharper cutoff, so much so that conventional analog filters would no longer be practical. The optimum tradeoff between number of samples

per cycle and filter complexity is not apparent, particularly in view of the need for low group-delay

distortion of the 9960 Hz FM signal. However, if adequately stable filters with accurately known

characteristics can be constructed, then the 9960 Hz FM signal can probably be predistorted to compen- sate for amplitude and phase distortion introduced by the filter. Such an approach might permit a major reduction in the sampling rate and a corresponding reduction in ROM size.

VOR PHASEMETER

13. Phasemeter Details

This section describes the hardware and software developed to allow measurements of the composite

audio signal generated by the NBS standard VOR generator discussed above. A general discussion of the

VOR system was given in sections 1 and 2. For a complete analytical description of the mathematical

model used for the VOR waveform, and for an analysis of the phasemeter measurement principle, see Vecchia [5].

13.1 Phasemeter Design Principles

The phasemeter is very simple in comparison to the generator. It was assembled completely from

commercial off-the-shelf modules and instruments. By far the most complexity lies in the software

that runs it.

In the development of both the standard generator and the standard phasemeter, the approach was

to avoid analog circuitry as much as possible. The design objective for the phasemeter was a bearing

angle uncertainty of not more than 0.01°. The design of filters and an FM demodulator capable of this

uncertainty did not appear feasible. Instead, a sampling approach was used. A block diagram of the

phasemeter is shown in figure 13-1.

VOR Generator

( flud i o Sou rce )

(R) —^- Track-and-Ho 1

d

flmp 1 i f i e r

(B)

RDC

(C)

V

CD)

l\ (F)

Prog r ammab 1

e

Delay Generator

(E) ^

Compute rCon t ro 1 1 e r

Figure 13-1. Simplified block diagram of the phasemeter.

2Note that a "band-pass" version of the sampling theorem indicates that the sampling rate need only

provide two samples per cycle for the bandwidth of the 9960 Hz signal. Since the -80 dB bandwidth of

this signal is about 1620 Hz, the sampling limit is about 3240 Hz, as compared with the requirement

for roughly 20,000 samples/s based on the 9960 Hz carrier frequency itself. However, it is not apparent how to construct a highly accurate system based on the band-pass interpretation of sampling

and data reconstruction.

30
The composite analog waveform from the VOR generator under test is applied to the analog-todigital converter (ADC), which contains a track-and-hold amplifier at its input. A timing reference

signal, such as the 30 Hz reference DAC sign bit in the NBS generator, is obtained from the source

under test. It provides an arbitrary point from which all sample delays are measured. Its phase

relative to the fundamental 30 Hz signal is unimportant, but it must be stable over the length of time

required to take the data (about 6.5 min per set). The controller programs the delay generator for an initial delay of and arms it to output one trigger pulse to the ADC upon the arrival of the next timing signal from the source. Upon receipt of the trigger from the delay generator, the track-andhold amplifier switches to the hold mode and the 16 bit analog-to-digital conversion is completed.

The controller reads the digital data from the ADC, causes the programmed delay time to be incremented, and re-arms the delay generator. This cycle is repeated until 1024 samples, equally spaced in

time, have been acquired. The effective spacing is, of course, 1/(30*1024) s, or about 32.55 us. The

delay generator used has a time resolution of 10 ps, a jitter of 200 ps rms maximum, and an absolute

uncertainty of ±1 ns ± (time base uncertainty). These specifications are critical to the application;

a delay generator with ±100 ns uncertainty or jitter is inadequate. Note that the peak jitter of 282

ps corresponds only about 3 microdegrees at 30 Hz.

Following the acquisition of the amplitude samples, the data are processed by the same computer

that controls the system. A fast Fourier transform (FFT) is used to compute the frequency-domain

spectrum of the composite signal. The fundamental is the 30 Hz variable-phase component. The phase

angle of the fundamental and the phases of all of the other harmonics are relative to the arbitrary

timing reference. By appropriate manipulation of this phase information [5], the VOR bearing angle

can be computed. This computation is discussed in more detail in section 15.

14. Hardware Details

The hardware components used to assemble the phasemeter are listed in table 14.1. At the time of

the original design, all items were available commercially. Since then, however, the manufacturer of

the 16-bit ADC used has discontinued it. Therefore, another unit must be selected if one wishes to duplicate the system. Since replacements for the original unit are not available, we plan to replace

the ADC in the NBS system as well. Specifications of the units used are also given in table 14.1 to assist in identifying suitable substitute components.

It is imortant to understand that the commercial equipment listed in table 14.1 is not necessarily the only equipment suitable for this application; indeed, it may not even be the best suited.

Mention of specific items does not constitute an endorsement of the product by the National Bureau of

Standards; NBS has made no attempt to evaluate all of the various possible choices. Such mention is

made here only to facilitate the duplication of the phasemeter by interested parties.

Finally, it should be noted that NBS, after examining VOR audio generators from four different

companies, has found none that are suitable for use as transfer standards, for various reasons. This

situation, unfortunately, reduces the incentive to build in-house standard phasemeters. The problems

seen in commercial VOR audio generators include excessive time jitter (short term) in the timing signal, inaccurate or unstable deviation of the 9960 Hz signal, and noise. Most generators are not crystal controlled, and even those that are appear to provide insurmountable problems to the NBS phasemeter approach. Consequently, the principal value of the NBS phasemeter lies in providing the assurance that the NBS generator is, in fact, an accurate generator of the VOR composite waveform.

31
Table 14.1. Critical component specifications.

Analog-to-digital converter, including track-and-hold amplifier

Resolution

Accuracy

Linearity

Offset

Gain

Noise

Stability

Gain

Nonlinearity

Power supply sensitivity

Conversion time

Input range

Input impedance

Output coding

Time delay generator

Mode

Range

Step size

Absolute uncertainty

Jitter

External trigger input

Output pulse

Time base:

Aging

Short term

Temperature

Line voltage

16 bits (as tested, 14 may be adequate)

1/2 LSB in laboratory environment

Unimportant if stable and less than 10 mV

Unimportant if stable over measurement time

Less than 1 LSB (153 uV for 16 bits)

+7 ppm/°C

±2 ppm/°C

±0.002%/%

Unimportant if less than 10 ms (see note 1)

±5 V 1000 nn (see note 2)

(see note 3)

Externally triggerable, single cycle

to 33.333333... ms

50 ps minimum

±1 ns ± time base uncertainty

200 ps rms maximum between ext. trigger and output

pulse

Positive slope, threshold at about 2 V, TTL compatible

TTL compatible, or as required by ADC

(see note 4) <5 X 10"-^° per day

<1 X lO"''--'- for 1 s average

<7 X 10-9 for 0° to 55°C

<1 X 10"^^, ± 10% of nominal

Note 1. The conversion time interacts with the track-and-hold droop specification to determine

the overall accuracy of the ADC. For this reason, it is desirable to obtain an integrated module that

is specified overall by the manufacturer.

Note 2. The input impedance is not critical unless the converter is to be capacitively coupled

to the VOR generator. The 1000 Mn specification applies to the NBS unit used.

Note 3. The output coding is not important except to the extent that NBS-provided software is used. It is designed to accept complemented 2s complement binary, because this code requires the

least conversion by the computer.

Note 4. These specifications apply to the unit used by NBS and represent what has been tested

and evaluated, not necessarily what is absolutely required.

32
The computer used in the NBS system is the Hewlett-Packard 9845B, with 186 kbytes of user memory.

The software requires ROM extensions for I/O operations, graphics (optional), IEEE-488 bus operations,

and a real-time clock (optional, but recommended for documenting measurement runs). The software uses statements in extended BASIC that are not available on the older 9845A. The software presumably will

run on the 9845C.

15. Software Details

15.1 General

The program listing in appendix A is the complete code for the phasemeter. It contains all of

the instrument drivers for acquiring the data, and the processing routines for computing the VOR bearing angle. If more than one measurement at a given bearing is taken, it will compute statistics on the set of measurements. It also contains some subroutines which are used primarily for diagnostic

purposes, such as evaluating the quality of an unknown generator, or testing the accuracy of the

phasemeter ADC.

All of the variables in this program are global. Subprograms are not used. Since variable names

and labels may have up to 15 characters in this extended BASIC, variable names can be made mnemonic to

a high degree. Therefore, there was no attempt to partition the code into independent subprograms

with local variables.

In several places in the sample printouts to follow, the term "dtg" is used. This refers to a date-time group, coded as a 10-digit number, that identifies when a particular event occurred. It is

a numerical representation of the date and time in the form YYMMDDHHMM; for example, "8210071430"

refers to October 7, 1982, at 2:30 p.m. The year information is input by the operator at the beginning of each session; the remainder of the data come from the computer real-time clock. This results

in a unique number that identifies every measurment, software revision, and flexible disk. It is also

the means of tracing any printout output back to the original raw data, and provides the time dimension on the quality control charts.

The interactive initialization portion of the program will be discussed first, then data acquisition and storage, and finally data processing. All line number references are for code revision date

"8207140822." See line 100, appendix A.

15.2 Initialization

This portion begins at line 2700. All arrays are dimensioned in lines 2720 through 2840. Line

2860 is used only on certain occasions, as discussed in section 15.4.

The printer specifier. Printer, and the mass storage unit specifier, Disk$, are supplied by the user. It is not necessary to store the data on the same disk as the program, but it is often a good

idea. This practice avoids confusion as to which code revision was used to process the data.

The program asks, in line 3120, what the nominal bearing angle is, Nom_bearing. This information

is used only to compute deviations between the measured value and the nominal value; it is not used in any other way.

33
Next, the user tells the program whether old data is to be processed, or new data is to be taken.

This provision allows data to be taken at one time and then processed or reprocessed when convenient.

Unless the program is interrupted, all new data are processed in the run in which taken. Also, all new data are automatically stored on disk for future reference.

If new data are to be taken, subroutine Check_files checks the disk to see if there is enough

space for the number of measurements specified earlier by No_measmnts. If not, it tells the operator

and suggests alternatives.

This routine completes the initialization process.

IB. 3 Data Acquisition

If new data are to be taken, the loop beginning at line 3340 is executed. Three subroutines are nested within it, and they have further routines nested within them.

"Setup_5359" initializes the time delay generator by sending command strings over the IEEE-488

interface to define the operating parameters needed, including the delay step size. This string is

fixed in this program because the fundamental frequency is always 30 Hz and 1024 samples are always

taken.

"Take_data" begins at line 3940. It prints a date-time group from the real-time clock to identify the printout. It initializes the array. Integer data, in which the ADC output will be stored.

Then it begins the loop that arms the generator, reads the ADC, tests for ADC overload, puts the

sample in the array, increments the delay, and re-arms the generator. The WAIT statements in this

loop are required to allow the delay generator to become "unbusy" after being incremented. In the

aggregate, these delays account for almost 2 min of the 6.5 min required to acquire 1024 samples.

"Store_data," starting at line 5020, is used next to put the data array on disk, along with certain pieces of housekeeping information, such as the date-time group. It names the file, after

examining the files already on the disk, and prints the data to the disk. The file name itself also

becomes a part of the file. A list of the housekeeping items that accompany every data file is given

in lines 1020 through 1400.

This portion of code completes the acquisition and storage of one measurement. This data acquisition loop is repeated No_measmnts times. It is then processed by going to subroutine Retrieve_data,

which is discussed under the next section.

15.4 Data Processing

Data processing begins with Retrieve_data, line 5300. If old data is to be processed, the operator enters the number of the first file in the set and the number of measurements in the set. Various

items are checked by the program, and if the file is valid and unprocessed, the actual processing

begins at line 6460, where the routine Fft_driver is called. This routine puts the 1024 data points

into two arrays, R(*) and I(*), 512 points in each, alternating. Subroutine Fft is then called, and

the transform is computed in lines 10320 through 11680. Arrays R(*) and l{*) now contain the real and

imaginary parts of 512 spectral lines.

34
Following the transform, the signs of the elements in R(*) and !(*) are corrected from a table of

Bessel functions, Jn(*). The phases of each line are computed and the proper quadrant assigned.

The phase angles progress uniformly from spectral line to line, the difference between the phases

of adjacent lines depending on the bearing angle. At most settings, the phase difference exceeds

360°, and it is necessary to add or subtract multiples of 360° to order the lines correctly. This

processing is done in the section labelled Order_lines, beginning at program line 8500.

The remainder of the Fft_driver routine, lines 9240 through 10300, does two linear regressions on the ordered phase angles. The first regression covers only the lines -7 through +7, i.e., 9750

through 10170 Hz. Its purpose is to determine the slope of the phase versus line number plot in order

to best determine the value for the -8th and +8th lines. This regression done, a second regression

covers the entire range from the -18th through the +18th lines.

Subroutine Estimation (line 11700) is called next. It is based on the analysis by Vecchia [5].

The subroutine uses the results of the preceding step to compute three phase angles, and from these

the VOR bearing angle is found. The three angles result from the generality of the waveform model and

allow an arbitrary phase relationship between the timing reference signal used in data acquisition and

the fundamental. As part of the Estimation routine, an estimate is made of the standard deviation

that would be expected if the measurement were to be repeated a large number of times. This estimate

is based on the assumption that noise in the data is random in nature. In fact, it is not, and con- sequently the estimate of the standard deviation tends to be too high (conservative) by about a factor

of 3 to 10. This estimate is, nevertheless, a useful measure of the validity of the measurement and

can be used to flag a bad one. This flagging is done by the program automatically if the estimated

standard deviation exceeds a rather arbitrary threshold that was set to 0.005° after making a large

number of measurements on the NBS standard generator.

If there is more than one measurement in the set, routine Statistics (line 4320) is called. This

routine computes the variance, standard deviation, and mean of the set. It prints these results and

the difference between the mean and the nominal value. If there is only one measurement in the set,

only the result and the difference Are printed.

15.5 Utility Subroutines and Programs

Two utility subroutines are contained in the program, but are only used for diagnostic purposes,

by calling from the keyboard. The first routine is "Meas_print" (line 13520). It prints in tabular

form the real and imaginary parts of the fundamental and 37 harmonics. It also prints the line

amplitudes, unordered phase angles in radians, and ordered phase angles in degrees. This routine is

useful for determining whether there was a misordering of the lines, due to noisy data, for example

(see fig. 15-1).

The second routine. Plot, plots the phase angles of the 314th through 350th lines as a function

of harmonic number, both before and after ordering. With experience, it can be used to determine

whether there was excessive time jitter in the unknown signal or in the timing reference (see

fig. 15-2).

35
Code dtg: 8207140822. Diik dtg: 8204231351

D R T 2 7 : F 8 , H o m i n a 1 b e a.r i r-i g afi g 1 € = 3

F i 1 en arri 'ORl

C o r r F e =1 1 C o r r I rn a g Bes -.

z- i g n part, s i g n E.^11— - ^

1.2369 7162

. 0363 -.0879

.1511 .0628

- .097 2 .2331

- .3151 -.1317

. 1500 -. 3576

.3107 . 1307

- 0622 . 1474

- .0894 -. 0381

1149 -. 2701

.2482 . 1058

- . 0038 .0093

- 23S7 -. 1027

.:i940 -.2180

751 . 0326

- 1 148 . 2646

- 0573 -.0250

1063 -.2430

1177 .0517

- 1004 .2277

- 1 177 -.0519

1073 -.2423

0570 .0255

- 1 175 . 2 6 3 4

- 074 7 -.0333

0974 -.2164

2368 . 1067

- 004 3 . 0090

- 2456 -.1116

1216 -. 2671

0884 .0402

- &€€$ . 1453

- 3061 -. 1408

1623 -. 3519

3098 . 1432

-. 1062 .2289

-. 1482 -. 0690

.0403 -.0861

-.0064 -.0000

Li ne

ariip 1 1.4293

. 0951

. 1636

. 2526

4 15

371

1600

0972

dt' ^y 011:i0 2599

i! -• M

08 19

28: 54 06.15 2652

1285

2439

1287

2650

625

2884

0818

237^

2598

0100

2697

2935

0971

1599

3 3 6 9 3875

3413

. 1635

.0950

.

Rad1 ans

.5249

Deq- L 1 t'le R w Roiv r 6 e 1- n o

.

no

.

-20

1 . 98'.9

- 2 , 7 ;•? 6 2 1 . 1539

.s205

1 . 9906

-1. :48.

.4232

2. 0126

2.7151

-1 1437

. 4269

2.0016

2.710-

1. 1387

. 4 331

2.0051

2. 7056

-1 . 1330

0. 0000

i y . M

I

1 i: 332

19

1 . 1788 -1507 4 314 2 -18

3 9 3 9 -1417 4 3 315 c! -17

1 9659 -1327 3 6 3 1 6 4 -16

£L 7457 -1237 3 2 317 5 -15

1 1736 -1 147 24 318 6 -14

3981 -1057 19 319 7 -13

1 9700 -967 13 320 8 -12

2 7389 - 8 7 6 92 321 9 -1 1

1 1687 -786 96 322 10 -10

402 9 -696 91 3 2 3 1 1 -9

1 9605 - 6 7 6 7 324 12 -8

2 7355 -516 -70 325 13 -7

1 1639 -426 68 326 14 -6

4 102 -336 50 327 15 _5

1 9802 -246 54 328 16 -4

2 7310 -156. 4 8 329 17 _3

1 1585 -66. 38 330 18 -2

4137 23. 70 331 19 -1

203 80 333 21 1 293 89 334 22 2 384 09 335 23 3

- 74 05 336 24 4 16* 03 337 25 5

654 22 333 2o 6 744 25 339 27 7 835 32 340 28 8 924 44 341 29 9 1014 47 342 30 10

1 104 4 6 34 3 31 1 1

1 194 6 8 344 32 12 1284 71 345 3 3 13

1374. 76 346 34 14 1464. 82 347 35 15

1554. 88 348 36 16

1644 98 34 9 37 17 1735. 08 350 38 18

0. 00 39 19

Thetal= 300.000079135

Th€ta2= 90.0716559148

Th6ta3= 1 13. 75906075i

Figure 15-1. Sample diagnostic output of routine "Meas_print"

,

36
Rmi n =

Dnii n =

C o d € r e '. . i s i ci n d t g : S £ 7 1 4 S 2 2 -2.745710863 3 R rn -a; -1507. 54 234 143 Druaj

Ordtred ar-Mglei. 2. 012630331':

1^35. 034024;

Figure 15-2. Sample diagnostic output of routine "Plot".

Data taking began at 82:07:13:16:23:15

Code dtg: 8201011453. Disk dtg: 8204231351. Fi Data stored in file DftT027:FS,0, disk 8204231351

Data taking began at 82:07:13:16:29:42

Code dtg: 8201011453. Disk dtg: 8204231351. Fi Data stored in file DFIT028: FS, 0, disk 8204231351

Data taking began at 82:07:13:16:

Code dtg: 8201011453. Disk dtg:

Data stored in file DRT029:F8,0,

Data taking began at 82:07:13:16:

Code dtg: 8201011453. Disk dtg:

Data stored in file DflT030:F8,0,

36:09

8204231351. Fi

disk 8204231351

42:36

8204231351. Fi

disk 8204231351

Data taking began at 82:07:13:16:49:03

Code dtg: 8201011453. Disk dtg: 8204231351. Fi

Data stored in file DflT031 : F8, 0, disk 8204231351

ename: VORl

at 82:07:13:16:29:41

ename: VORl

at 82:07:13:16:36:08.

ename: VORl

at 82:07:13:16:42:35.

ename: VORl

at 82:07:13:16:49:02.

ename: VORl

at 82:07:13:16:55:29.

Dwt a file

DflT027

DflT028

DflT029

DFIT030

Dl=lT031

Bearing angle

300.0001

300.0012

300. 0002

300.0005

300.0014

Si gmasq

1.671E-02

1.679E-02

1.667E-02

1.653E-02

1.647E-02

Est . St d . de'v'. 4.055E-03

4.065E-03

4.051E-03

4.034E-03

4.026E-03

Code dtg: 8201011453. Disk dtg: 8204231351. Filename: VORl

Mean: 360.000 685 degrees

Nominal bearing 300.00

Variance: 3.460E-07

Standard dei.'iation: 5.882E-04 degrees

Mean minus nominal: .800 685 degrees

Figure 15-3. Sample output resulting from five measurements at one phase angle.

37
15.6 Sample Outputs

The printed output produced during a typical measurement run is shov^n in figure 15-3. The beginning and ending times for each of a series of five measurements is printed as the data are taken. The

disk identification, code name and revision date, and data file name are also printed. All of these

items are stored on the disk with the raw data. After the last measurement in a series, each data

file is retrieved and processed, resulting in the lower part of the printout. Finally, if more than

one measurement was made in the set, the mean, standard deviation, etc., are printed. Some of the

processed data results are returned to the disk to allow quick abstracting of large numbers of meas- urements without reprocessing the data. The information in appendix B was obtained in this way.

If, in the initialization, it was specified that old data was to be processed, the program jumps

to Retrieve_data. If new data acquisition has just been completed, the program jumps to the same subrouti ne.

EVALUATION OF THE STANDARDS

16. VOR Measurement Principle

The principal development of digital methods for decoding VOR waveforms derives from the physical

model for VOR beacons. To represent an ideal VOR signal mathematically requires two periodic functions described by

v(t;_e) = a-^ cos[2TTf]_t + 92^ + 62]

and

s(t;_9) = 02 cos[2TTf2t + 93 + g sin[2Tif]_t + 92]],

where _9 is a vector of unknown phase angles.

The waveform generated by the sum of v(t;_e) and s(t;_e), with some parameters specified, may be used to represent the ideal audiofrequency signal for the VOR navigation system. The specification

for the VOR signal generator demands that

ai = a2 = 21/2 (1 V rms)

f^ = 30 Hz f2 = 9960 Hz (so f2/fi = 332)

e = 16

In the VOR context, v(t;_9) is the 30 Hz variable phase signal, and s(t;_e) is the frequency-modulated

9960 Hz subcarrier. The frequency modulating sinusoid in the argument of s(t;_9) is the reference

phase signal .

The design of VOR beacons is such that, in the mathematical model of the signal, Q-^ provides the

necessary bearing information. The description in the following subsection, which outlines the principle for decoding VOR signals, will therefore emphasize the estimation of e-|^ , although the nuisance

phase angles 82 and 83 are estimated simultaneously by the phasemeter.

38
In practice, either transmitted or synthesized waveforms will be accompanied by noise or measurement error. This distortion is modeled by adding random errors or noise to the ideal signal. The

resulting noise corrupted voltages, say Y(t), can be represented by

Y(t) = v(t;_6) + s(t;_e) + e(t).

The random error process is assumed to be white noise when sampled at the rate specified for the digital phasemeter.

16.1 Measurement of VOR Waveforms

The algorithm used to estimate the unknown phase angles Q-^, 62, 63, relies on a Fourier transform

method to process noisy samples from the generated waveform. This technique requires one complete 30

Hz cycle of the VOR waveform, digitized at 1024 evenly spaced points throughout the cycle. The number

of sampled points is determined by the requirement that the upper frequency limit of the discrete

Fourier transform (DFT) exceed the frequency of the significant FM sidebands of the 332nd harmonic of

30 Hz. Because the FFT algorithm is used, it is efficient to require 2'"(m=10) amplitude samples.

The OFT of the noisy time samples was shown in NBS TN1021 [5] to have Fourier sine and cosine

coefficients, B|^ and A|^ (kth harmonic of 30 Hz), characterized by

E[B.]

I

and

E[Ak] =

2^/2 sin(ei + 62) , k=l

2^/2 J|^_232(16)sin[e3 + (k-332)e2], k=332-K, . . . ,332, .. . ,332+K

2^/2 cos(9^ + 62) , k=l

2^/2 j|^_232(16)cos[93 + (k-332)e2], k=332-K 332, . . . ,332+K

Var[B|^] = Var[A|^] = a'^/SlZ,

where E[«] is used to denote the average, or expected, value of repeated measurements of noisecorrupted sets of 1024 time-samples, Var[«] denotes the expected variability of repeated measurements,

J^(16) is a Bessel function of the first kind, and a is the RMS level of the measurement errors, e(t).

The value of K is chosen to assure that only the most powerful sidebands of the 332nd harmonic are

used to estimate Q-^. Figure 16-1 shows an amplitude spectrum obtained from an ideal VOR waveform.

Apart from the 30 Hz component (k=l, outside the range of the graph), only about 36 harmonics centered

on k=332 have sufficiently high si goal /noise ratio to be used in the measurement algorithm.

Inspection of the Fourier coefficients reveals that the essential bearing angle information con- tent of the DFT is likely to be contained in the phase spectrum of amplitude samples, Q|^* = Arctan(B|^/A|^) for admissible k. Having transformed the DFT coefficients to this form, it was shown

in reference 5 that the expected value and variance of Q|^* (for admissible k) are

39
A

312 317 322 327 332 337 342 347 352

K

Figure 16-1. 9960 Hz subcarrier spectrum, showing relative sideband amplitudes,

The abscissa is the harmonic number relative to 30 Hz.

and

where

E[Q,*]

( 9, + e^) modZij , k=l

[02 + {k-332)e2]mod2Tr, k^l

Var[Qu*] = r^-2a2/5i2.

, k=l

2j\_332(16), lk-332| < K.

40
The equations for E[Q|^*] are essentially linear in e^, 62 and 83, except for the restriction to the

range [0, Z-n) . However, in reference 5 a procedure was outlined for adjusting the Q|^* by defining

Qk = Qk* + Yk 2u.

where the Yk's are integers which reorder the Qk* to be consistent with the physical model. The y^'

s

are easily obtained for the signal /noise ratios rendered by the NBS signal synthesizer in its current

design.

When the Qk have been determined, all phase angles are estimated by a standard linear least

squares technique. The algorithm also provides an estimate of the RMS noise level and obtains estimated standard errors of the measured phase angles from a single sample of the 30 Hz cycle.

The complete model and measurement equations are discussed in reference 5. In this discussion of

the measurement technique, only the algebraic expression of the measured VOR bearing angle is reported. The estimator of 61 and its estimated variance are h-^- %l^ ^ Ji^(16)[Q332,i - Q332_.]

and

S^(ej) = [(1 + C^)/1024]a^

where

C^ = [2 1 i^J.2(i6)]-^

'^ i=l ^

Here a denotes an estimate of the RMS noise level, but will not be further specified because the characterization of the VOR measurement process and establishment of statistical stability only relies on statistical models for repeated measurements of 9^. The single sample estimated standard error of e^ is, however, a useful diagnostic tool because it is sensitive to the effects of isolated erroneous time-samples and other transient influences.

16.2 Verification of Mathematical Model by Simulation

Empirical verification of the measurement method was achieved by computer simulation on a CUC170/750. To more closely approximate an actual system, the simulated waveforms were corrupted by

additive Gaussian white noise. Results of the investigation indicated that measurement of VOR bearing

from the phase spectrum was viable for RMS noise levels which are characteristic of the VOR signal

generator.

Sample printouts of simulated VOR measurements are shown in tables 16.1 A-L. The parameters

listed at the top of each table can be selected to generate VOR waveforms for any configuration within

the following specifications:

41
NUMBER OF OBSERVATIONS

STANDARD DEVIATION

NUMBER OF RUNS

NUMBER OF FREQUENCIES

DEGREE MODE

TIME JITTER

Number of time-samples (<1024)

Standard deviation, a, of additive Gaussian white noise (a > 0)

;

Number of simulated waveforms desired (1 < n < 20);

Total number of spectral lines for measurement (= 2 + 2K; K is number of

sidebands of 332nd harmonic to be used);

Degrees or radians;

If ON will randomly perturb ideal voltage V^ to V|.+y, where u is selected

from a uniform distribution between -1 ns and 1 ns; VAR PHASE AMPLIT

or SUBCARRIER AMPLIT

FREQUENCY (VAR PH)

FREQUENCY (SUBCAR)

MODULATION INDEX THETAl, THETA2,

THETA3

For the simulations shown in the tables, these parameters were assigned the values listed. The

quantity of interest, namely THETAl, was chosen in 30° increments from 0° to 330°. In each case a sample of 1024 amplitude points was computed with each point perturbed by a random amount to simulate

measurement noise. These data were then transformed to the frequency domain using a complex fastFourier transform. The transform gives both the amplitude and phase of the spectral lines in the frequency domain. The bearing angle was then estimated from the transformed data by a least-squares fitting technique to give one estimate of THETAl in the output table. This process was repeated 10 times.

Selected value, a^ , can be randomly perturbed

to a,- + u^, where u^ is uniformly distributed from -1 to 1 V; Ideal specification (30 Hz) can be randomly perturbed from 29 to 31 Hz; 332 (perturbed variable phase frequency);

Ideal index (16) can be randomly perturbed from 15 to 17; and

Phase angles of noise-free waveform.

The first column in the table is simply the run number. For each run the sequence of random

amplitude errors is completely independent of errors in the other runs.

The second column in the table gives the resulting estimate of the bearing angle, THETAl. As can

be seen in the tables, the estimated bearing agrees closely with the selected value, even with a realistic level of measurement noise. The third column is the estimated standard deviation of the

bearing angle estimate in column 2, based on the results of the least-squares fitting procedure.

At the bottom of the printout is the sample mean and sample standard deviation of the 10 estimated bearing angles. A measure of the adequacy of the measurement principle is how well the standard

deviation of the 10 estimates agrees with the estimated standard deviations from the individual runs. Again, the agreement is very good.

The FORTRAN computer program which produced the tables in this section is available from the

authors.

42
Table 16.1-A. Simulation estimates at 0"^

WUNBEB OnSE»V«TIONS • 1024 THET41

STANO*PO 0EVI4TI0N «• .00040 TMET42

NUMBER OF RUNS • 10 THET43 NUNFEB FPEOUENCIES «• 36 0E6REE fODE •• DE6REF

T1«E JITTER • OFF

V»R RH»SE •"PLIT «> 1.00

SUBC4PRIFR 4HPLIT • 1.00

FPFOUFNCY CV»R PH) • 30.00

FREOUENCV (SUBCAR) • 9960.00

KOOULATION INDEX • 16.00

0.00000 ( 0.00 DECREES ) 1.57202 < 90. or DE6REFS » 1.90479 (113.72 DEGREES I

RUN BEARINC ANGLE EST ESTINtTEO STO OEV

10PEAN

STO OEV

359.99954938570990

359.99957171381720

.00014775991736

.00103240123701

J59. 99995492313246

8^9.9995^c5^s69^62

359.99866019857836

359.99967152872341

.00240791006466

359,9999f»309537114

.00004894^22534

.00102160353512

.00119405563495

.00108158915795

.00111276992072

.000959B7655964

.00091899987674

.00082092499755

,00085147429091

.00072194591567

.00078422383887

.00114704596514

Table 16.1-B. Simulation estimates at 30"^

NUHREP r«SEPV»TIONS • 1024 THETAl STANOARO DFVIATION • .00040 TMFTA2

NUMBER OF RUNS • 10 THETA3

NUWPER FREOiJENCIES 38 DEGREE NOnE DEGREE

TIME JITTEP OFF

VAP PHASE AMRLTT • 1.00 SUBCARRIER ANPLIT 1.00 FREOUFNCT (VAR PH) 30.00

FPEOUENCY (SUBCAR) <• 9960.00

NPDULATION INDEX • 16.00

.52360 I 3C.00 DEGREES ) 1.57202 « 90.07 DFGPFES ) 1.96479 1113.72 DEGREES I

RUN BEARING ANGLE EST ESTIMATED STD OEV

10

29.99993963623640

30.00126027535339

29.99861027460952

30.00059817592546

29.99990380965323

30.0006015938?178

29.99^83745969794

29.99850603616278

30.00014411366965

29.99922476116856

.00103392079157

.00098759467156

.00086885085629

.00115525779303

.00103392536103

.00081133852902

•00095294092419

•00078911343697

.90111572526560

.00105429131367

NEAN STD DEV 29.99976261563197

•00093653649249

43
Table 16.1-C. Simulation estimates at 60"^

NU»"BE» OBSfBV»TIPNS

ST»NO«PO DEVIATION

HU"HEB OF BUNS NUMBER FREOUEHCIES

CEGBEE "ODE TIME JITTEB

van »HA5E «<1BLIT SUBC4BBIER »HPLIT FBFOUFNCY (V»R PM)

FBEOUENCY (SUBC4B)

HODULATinw INDEX

102* THET*1

»000*0 THFT42

10 THETI3

39 DE6BEE

OFF

1.00

1.00

30.00

99ft0.00 16.00

1.047?0 ( 60.ro 0E6PEES ) 1.57202 ( 9C.07 DFGPEES » l.«e«>7q 1113.72 DECREES )

BUN BEABINC ANGLE EST ESTINATED STO OEV

10

NEAN

STD OEV

60.0007

60.0007

60.0016

60.001*

60.0002

99.9992

99,999*

99.9991

99.9986

99.9990

3015787370

95877900*2

51285*1852

939*312098

7527279781

511857533*

7757181963

809586?313

218*537*10

97775838**

60.000097587*1135

.00108077939295

.0009

.0009

.0011 .0008

.0009

.0010

.0009

.0011

.0009

.0009

379«)9l*9*0

9936623*93

0351002312

9815327859

6892067312

6782992517

8389805568

**6557166*

629097530*

9*857357*2

Table 16.1-D. Simulation estimates at 90'

NUMBER n^SERVATIONS 102* TMETAl STANDARD DEVIATION .000*0 THETA2

NUMBER PF BUNS 10 THETA3

NUMBER FREQUENCIES 38 DEGREE »ODE DEGREE

TIME JITTEB • OFF

VAR PHASF AMPLIT • 1.00 SUBCAPRIEP AMPLIT 1.00

FREQUENCY (VAB PH

)

30.00

FREQUENCY ISUBCAR) 9960.00 MODULATION INDEX 16.00

1.97080 ( 90.00 DEGREES ) 1.57202 ( 90.07 DEGREES ) 1.98*79 (113.72 DEGREES )

I UN

12

S4

96T

•

10

REARING ANGLE EST ESTIMATED STD DEV 89.999*6766523772 .0009099*066 897 69.9987573900 2388 .0012 99235002*0

90.0001*69*665219 .00112885025322

90.00016768258*51 .0008*625622865

90.0000966703 3 873 .00103*26753 230 90.0003 85 2168 7338 .000762 362*6797

90.0002256192 53 3* .00092631936907

99.99932038*7**39 .0009**6*99**00

89,9992777961892 9 .001018*0209397

89.9981998021 ?998 .0010263901231*

89.999602713*0160

.00073673660291

44
Table 16.1-E. Simulation estimates at 120°.

MUHBER ruSFBViTIONS • 10?« THETIl • ?T*NDi«0 DEVI4TI0N .000^0 THET42

NU«t>Ee TF BUNS 10 THETI3 • NU"BF» FBEOUENCIES 39 DECREE "ODE DECREE

TIWE JITTFB OFF

V«« BMtSE mBlIT l.CO

SUBC*RRIfB *HBLIT • 1.00 " FBEOUENCr (V*R FH

)

30.00

fREOUENrr (SUBCAR) • 9960.00

HOOULATION INDEX • 16.00

2.094«0 llZC.rC DECREES ) 1.97?02 t 90.07 DEGREES I 1.96479 11X3.72 DEGREES I

RUN BEARING ANGLE EST ESTINATEO STD DEV

10

120.0009

119.999*

119.99B9

119.9993

120.0003

120.0000

120.000S

120.0018

119,«Q93

120.0007

718526007

5213320871

1*55*«*6*0

7085692000

8*721*783

529592639*

8927*91500

6687731230

1*6*739^20

*91609626*

.00118097086621

.000982605*3182

.000619379128*6

.0010*969952930

.00103307317101

,00099709829517

.00088536718816

.00101293561*95

.00103729955637

.00109519962560

NEAN • STD OEV • 120.0001206121810*

.00088'91016223

Table 16.1-F. Simulation estimates at 150°.

NUMBER PBSERVATinNS 102* THETAl STANOARn nEVIATlON . .000*0 THETA2

NUMBER OF RUNS .m 10 THETA3

NUMBER FREQUENCIES ,m 36 DEGREE HCOE .m DEGREE

TINE JITTER m OFF

VAR PHASE ANRIIT m 1.00 SUBCARRIFR AMPllT m 1.00

EREOUENCY (VAR RH» 30.00

FREOUENCY (SUflCARI .• 9960.00

NOOULATION INDEX • 16.00

2.61799 (190.00 DEGREES ) 1.97202 ( 90.07 DEGREES » 1.98*79 (113.72 DEGREES )

RUN BEARING ANGLE EST ESTIMATED STD DEV 1*9.998«0566*63*69 .00095*28876970

150.0009998885?07l .00097999567933

150.0007611930627* .00115289776610

1*9.9986*6*0391970 .00079*2732*609

150.0002065679591* .00092282309712

1*9.99977508«02931 .00109220807677

150.000060*5*01009 .00082969369678

150.000P78693390*0 .00093362162696

150.00046679985503 .00093216*92993

10 190.COC06981906109 .00087328061614

NEAN • 150.0000566532*261

STD DEV • •0006775130*661

45
Table 16.1-G. Sirnuldtion estimates at li

NU"fiEt n«SE»V»TIONS

STiNO*l»D OEVtiTIOM

NU**XE» F'EOUENCIES

OFG»EE »'00E n"E JITTEt

$U«C4»t!Et »«»LIT FPFOUENCt (V*P f»)

fBEOUEHCV «SUPC»B)

BOOULiTlPM IMOEI

• 102« THET»1

.OOOiO TUFTI2

10 THETA3

39

> OECtEF

• OFF

1.00

1.00

• 30.00

9960.00

16.00

3.14199 «1«0.00 OEStEFS ) 1,57202 ( 00.07 OFG»EES J 1.96479 (113.72 DECVEES )

(UN BEARIN6 ANCLE EST ESTINlTfB ?T0 OEV

12

)

4

96

7

9

10"EtN

STD OEV

180.000

179.999

179,i;99

179.998

180.000

179.998

180. COO 179.999

180.001

180.000

27022980??!

424*8995126

71257f082«6

263e768')083

51959814118

41136136729

87626080131

74042443228

38923771174

4l647540ng3

179.99990245095978

.00100765321683

.0009

.0010

.0009 .0009

.0010

.0011 .0011

.0010

.0012 .0009

8121728795

6176902454

5223325261

5369457388

4133328262

6657977919

6634640279

2227844207

6099003859

3685659427

Table 15.1-H. Simulation estimates at 210'

NU»»»FB OBSFpViTIPNS •I 1024 THETIl

ST*NO*eO DEVI»TrON 1• .OC040 TMET42 • NU»8E» re ?UMS « 10 T"ET*3 • NU'BEB FBEOUEHCIES « 38 DEGREE t^Cni 1• OFGBEE

T!HE JITTER «• OFF

V»R RH*SE iNHIT • 1.00

SUBCiSRIEB i"RLIT i• 1.00 FBEOUENCY (V»R PHJ I• 30.00 FBEOUENCT (^U8C»R) ' 9960.00

NOOUi*TinN INDE» «• 16.00

3.66519 (210.00 DEGREES I 1.57202 t 90.07 DEGREES I 1.98479 (11^.72 DEGREES )

RUN BEtRINC tN«LE EST ESTIN4TE0 STO OEV 209.99968610688484 ,00117232677909

210.00169319902129 ,00103879407391

210.00138509685712 ,00104332572792

210.00075030373227 ,00085433357839

209,99977936434192 ,00105397423276

210.00070856928414 ,00098892448788

210.00153538982704 ,00081662641280

210.00061107483816 ,00107337446024

209.99768198440333 .00102172874822

10 210.C0231368656478 ,00107614584471

MEAN • 210.00061447759981

STO OEV • .00131989054933

46
Table 16.1-1. Simulation estimates at 240'

NU"nE* qnSEtVATIONS

STANDtIO OFVUTION

NU"BE« or tUHS NUHBEt F'FOUENCIES

DECREE MODE TIXE JITTE*

V«t »H«SE ANFlir

SUOCAKtlEt »»«niT

FREOUENCT (VAR FH)

FREOUE><CY (SUBCAR)

nOOULATION INOEV

xoih TMETAl • .ooo«o THETA2 • 10 TMETA3 • %9 DECREE

OFF

1.00

1.00

90.00

9960.00

16.00

«.iaii79 (240.00 DECREES I 1.97?02 < 90.07 DEGREES ) 1.9a«79 (lis. 72 DECREES I

RUN BEARIH6 ANCLE EST

MEAN STD OEV

240.C012903S930949

2S9.99879072B99099

239.99910914601909

240.00119432692746

239.99990C9913M096

240.00046941727934

240.C0070129116737

240.00l63e6S019fl07

240.COC69038221900

240.00067469649772

240.00039719607230

.00099194314991

ESTIMATED STD DEV .00126233319997

.00104321216620

.00103016997900

.00066904299264

.00080969346617

.00101669979694

.00086373470628

.00103492829297

.00091499996220

.00126760767647

Table 16.1-J. Simulation estimates at 270'

NUMBER OBSERVATIONS • 1024 THETAl

STANDARD DEVIATION . .00040 THETA2

NUMeER OF RUNS .• 10 THETA3

NUMBER FBfOMEHCIES . 38 DECREE MODE .a 0E6RFF

TIME JITTER OFF

VAR RMASE AM»IIT • 1.00

SUBCARRIER AMPLIT . 1.00

FRFOUENCV (VAR PH) 30.00

FREQUENCY (SU^CAR) . 9960.00

NODUIATION INDEX 16.00

4.71239 (270.00 DECREES ) 1.97202 ( 90.07 OEGBEES I 1.96479 (113.72 DEGREES )

RUN BEARING ANCLE EST

1 270.00040220420691

2 270.00140060647391

9 270.00021990966096

6 269.99919306230346

9 269.99922214168199

6 269.99942766246721

7 269.99919627938471

% 269.99914036323207

f 270.00091763902997

10 270.C0122291049991

269.99999369913361

•00067966711769

ESTIMATED STD DEV .00069062261064

.00116341132440

.O00P698PO14943

.00093418991992

.00097760020999

.00126991362416

.00110962199669

.00116160434629

.00113022494941

.0010!9337997a4

47
Table 16.1-K. Simulation estimates at 300°

HUW«E» r%$EBW»TTONS «• 102* THETll

ST4M04I0 0EWT4TI0N •• .000*0 THFT*2 • HU"I6» Cf «UHS « 10 THFT43 - NU"BE« F«E0U£NCIE8 «> 38 OFC«Ee "POE «• 0E6IEE TI"E JITTE* «1 Off

V»« »M»SB fHIT 1• 1.00

SUBC*»tIEI »«^11T .•• 1.00

FtEOUENCT (V»» PH) .•• 30.00

FtfOUENCY ($UIC*») i• 9960.00

MODULATION INOEI •• .16.00

9.23999 (300.00 OEC'EES ) 1.57202 ( 90.07 OECtEES ) 1.98*79 C113.72 OEetEES >

tUN lEARINfi ANCLE EST 300.00016773029711

299.999670609«6*5S

300.C003*1973*366(>

300.000960*87*3399

300.0015910*910039

299.999S68!e5193*9

299.';999519«512907

299.9999775l(t*7699

299.99SC589*2*fe56

300.0009130ft*»M099

ESTIN4TED STO OEV

NE4N STO DEV 300.00007019430632

..00093735*37691

.00088

.00103

.00109

.00092

.00108

.00111

.00087

.00079

.00106

.00079

997971036

3**1*9901

895229361

9*138**90

870233986

7515619*1

1*3692331

582161163

626070899

^23132050

Table 16.1-L. Simulation estimates at 330°.

NU"8E» Q8^EBV«TtOHS "• 102* THETAl

STiNOABO OEVIATIOH • .000*0 TMETA2

NU"8E» Pe BUNS <• 10 THETA3

NUP-BEB FBFOUENCIES ' 3<l 0E6BEE "ODE • 0E6BEE TIKE JITTEB • OFF

VAt BM4$E AKPLIT < 1.00

SU8CABBIEB APiPLIT • 1.00 FBEOUENCY «VAt PH) • 30.00 FBEOUENCY (SUBCAB) i 9960. CO •ODULATIPN IHOEI ' 16.00

9.75999 (330.00 DEGBEES I 1.97702 ( 90.07 OEGBEES > 1.98*79 (113.72 OEC-BEES I

BUN BEABIN6 AN6LE EST ESTIWATEO STO OEV

MEAN

STO DEV

330.000

330.000

329.998

33C.C0C

330.001

329.999

329.999

329.999

330.001

329. Q99

330.00027329607696

.00077989232886

.00100*

.0009P9

.00111*

.001055

.001127

.00122*

.001101

.001070

.0010*1

.001003

12*7692*

83797783

897018*9

32956*92

91309992

78989201

727962*2

9919*876

880276*8

39566269

48
17. System Performance and Provisional Uncertainty

The general design goal of the VOR measurement system was to achieve an overall uncertainty of

±0.01°. The objective of tests described in this section is to establish a statistical model which

can be used to estimate the measurement process parameters and to demonstrate provisionally that the

uncertainty of the measurements is suitably small relative to the allowable error limit. Process

parameters are quantities which characterize the behavior with regard to both the long-term average of

the process and the inherent variability or imprecision of the process.

The complete system consists of:

(a) a standard VOR audio generator, which is used to calibrate unknown phasemeters;

(b) a standard VOR phasemeter for the calibration of unknown generators;

(c) a desktop computer which controls the system.

At the beginning of the standards development effort, it was decided that it would be necessary

to design both the standard generator and standard phasemeter, since otherwise there would be no independent way of checking either one. Thus the two instruments, which work on different principles, are used as independent checks of each other. Because of the complementary nature of the two services,

the procedure to assure that both instruments are performing as desired is to demonstrate that they

agree without adjustment to either one. Other objective means for evaluating the performance of each

instrument independently were described in section 4.

17.1 Systematic Errors

To determine the uncertainty of a measurement process one must quantify both systematic and ran- dom errors. Possible systematic errors related to both of the standard instruments were considered in

section 8.4. For each potential source of offset, either an experiment or analytic derivation was described to show that the upper limit of systematic error was negligible relative to the overall

uncertainty goal. Therefore, in the following sections we focus on techniques that are helpful to establish and monitor random errors, which are the dominant components of the total error budget.

17.2 Statistical Model for Bearing Measurements

The essential characteristic needed to establish control of the VOR measurement process is predictability, i.e., the variability remains at the same level and the process average is not drifting

or shifting abruptly from its established values. The evidence of predictability must come from

redundant measurement of process parameters over a full range of operating conditions. Requirements

for obtaining realistic error bounds and establishing statistical control will be satisfied if the

collection of measurements is from a sufficiently broad set of environmental and operating conditions

to allow all potential sources of random error to influence the measurement process.

In this section we focus on a statistical model which facilitates estimation of components of the

total process variability and allows the implementation of statistical control procedures for the process parameters. The model is sufficiently general to distinguish among three kinds of random variability that may contribute to the total process variability:

49
(a) short-term variability of sequential measurements on a single day;

(b) long-term variability (days, months, years);

(c) differential levels of long-term variability depending on nominal bearing (switch) settings.

In addition to these components of total process variability, potential offsets between the signal generator and phasemeter, which may depend on bearing angle, can be estimated. These offsets

between the two instruments will be used to obtain a heuristic limit on possible systematic errors for

the VOR system. In the section 17.3 we describe data which were collected to shed light on the individual contributions to the total uncertainty of the process.

The statistical analysis for quantifying short-term and long-term variability in VOR bearing

measurements is based on the assumption that H repeat measurements at the I nominal bearings on each

of J occasions can be described by the model:

y^j^, = u + o^ "^ "^j "^ '^ij

"^ ^ijk' i=l....,I; j=l,...,J; k=l,...,M

where

y^^l^ is the observed deviation, or offset, of a single measurement from the i^^ switch setting,

i.e., y = ( 6]_ - nominal bearing);

u+QUj is an unknown, but stable, average offset of measurements at the i^ switch setting, i.e.,

u+oj is a parameter to be estimated and is ideally zero for any i; T^ is a (possible) random shift in all measurements taken on the j occasion; the T^'s are assumed to follow a Gaussian probability distribution with mean zero and variance aj , D^^ is a (possible) random shift on the j^ occasion which is unique at the i^^ switch setting;

the D^-.-'s are assumed to have a Gaussian distribution with mean zero and variance oq ;

e. -L. is the short-term random error of measurement in the k repeat measurement at switch setting

'i jk

i on occasion j; the e^nu's are assumed to have a Gaussian distribution with mean zero and variance cr

,

The statistical analysis of bearing angle measurements quantifies the individual contributions to

the VOR process variability by estimating the various unknown parameters in the model. To be specific, measurements which satisfy the model have the following properties:

ECy^jk] = y + o^-

VarCy^j^] ^ oj^ + oq^ + c^

M E[(l/M) I y ] = y + a. k=l

^^'^ ^

M Var[(l/M) I y .^] = 0^2 + ^^2 + ^2/h

k=l 'J

J M

E[l 1/JM) I I y...J = u + a. j=l k=l

^^^ ^

J M Var[(l/JM) I I

Y. .,] = [a^^ + a 2)/J + a^/JM,

j=l k=l ^J^ ' ^

50
where E[«] denotes the average value and Var[«] denotes variability. Statistical analysis of the VOR

bearing angle measurements provides estimates of the process parameters as follows:

J M Limiting Offset at Bearing i: p + a- = (1/JM) I ) y. ., ^ i=l k=l ^^^

Standard Error of (u + a.): [(a-j-^ + o^^)/J + o^/M] 1/2

Short-Term Standard Deviation (Single Measurement): 3

Short-Term Standard Deviation (Mean of M Measurements at Bearing i

Total Standard Deviation (Single Measurement): [a-.^ + o^.^ + o^

Total Standard Deviation (Mean of M Measurements at Bearing i):

1/2

a2/M]

+ a„2 + o2/M) 1/2

For each measurement y^ii^, a residual 6^-j|^ is computed from 6- .^ = y. .^ - ( u + a- ) • These

residuals are standardized by computing t--. = <5- ./S( 6- •. )

, where S(5i^i,) is an estimate of the

IJK IJ IJK ' J'^ Standard deviation of the residual. The residuals from the VOR measurement data are routinely checked

to assure the validity of estimated parameters and to assess whether the process is in control. In particular, the residuals are used to identify and, if appropriate, to reject individual outliers in the data set. The outlier rejection criterion could conceivably flag an entire day's measurements

that are out-of-control . See reference 5 for a discussion of outlier detection techniques.

1 8 15 22 29 5 MAR APR

1982

12 19 26 3 10 17 24 31 7 14 21 28 5 MAY JUN JUL

12 19 26 2 9 AUG

Figure 17-lA. Bearing angle offsets at degrees.

51
0)

T3

O

CO

•3^.

. -

6

- -

4

- - -

2

_

$ + $

t

+

-2 - -

-4 - -

-6

1 ±. 1 \ i__ 1 1 1 I 1 1

1 1 1 1 1 1111 1

I—1

1 a IS 22 29 5 12 19 26 3 10 17 24 31 7 14 21 26 5 12 19 26 2 9 MAR APR MAY JUN JUL AUG

1982

Figure 17-lB. Bearing angle offsets at 30 degrees.

O

CD

.'3:>.

. .

6

- -

4

- -

2 +

-

-

''K

—

-2 ~

-4 - -

-6 - -

1 1 1 1 1 1 1 1 1 1 1 1 L. t 1 1 1 I 1 1 t 1 1

15 22 29 12 19 26 10 17 24 31 14 21 26 12 19 26 MAR

1982

APR MAY JUN JUL AUG

Figure 17-lC. Bearing angle offsets at 60 degrees.

52
^.

6 -

73

- <D

d) 4

—

i^

Q/) (V

-1— 13 p

H

^ M^ ^^

•i-H S ± +

+

-

"O^

- 05

1 -2 -

1 *-> -4 -

-6

X _L

1 8 15 22 29 5 MAR APR

1982

12 19 26 3 10 17 24 31 7 14 21 28 5 MAY JUN JUL

12 19 26 2 9 AUG

Figure 17-lD. Bearing angle offsets at 90 degrees.

1 8 15 22 29 5 MAR APR

1982

12 19 26 3 10 17 24 31 7 14 21 26 5 MAY JUN JUL

12 19 26 2 9 AUG

Figure 17-lE. Bearing angle offsets at 120 degrees,

53
CO

cu T3

O

. +

-

6

- -

4

- -

2

_ - 1*i

+

-2 - -

-4 - -

-6

1 1 1 1 1 \ 1 1 1 1 1 1 \ 1 1 1 1 \ 1 1—_J

1 8 15 22 29 S MAR APR

1982

12 19 28 3 10 17 24 31 7 14 21 28 5 MAY JUN JUL

12 19 26 2 9 AUG

Figure 17-lF. Bearing angle offsets at 150 degrees.

CO

(U£

(U T3

O

CO

4 -

y 2 -

-

-2 -

5a.

OT _4.

-6 -

1 6 15 22 29 6 MAR APR

1982

12 19 26 3 10 17 24 31 7 14 21 28 5 MAY JUN JUL

12 19 26 2 9 AUG

Figure 17-lG. Bearing angle offsets at 180 degrees.

54
1 8 15 22 89 5 12 19 26 3 10 17 24 31 7 14 21 2B 5 12 19 28 2 9 MAR APR MAY JUN JUL AUG

1982

Figure 17-lH. Bearing angle offsets at 210 degrees.

Vi

(D

o

I

<u

-«li.

. .

6

- -

4

_ +

_

2

-2

+

- + +

+ +

+ t

\\

++

+

++

+

+

+

-4 - -

-6

\ L. ..1.1 1 1 I 1 11111 1 1 1 . 1 __J 1 1

1 8 15 22 29 5 MAR APR

1982

12 19 26 3 10 17 24 31 7 14 21 26 5 MAY JUN JUL

12 19 26 2 9 AUG

Figure 17-11. Bearing angle offsets at 240 degrees.

55
1 B 16 22 29 5 12 19 26 3 10 17 24 31 7 U 21 28 5 MAR APR MAY JUN JUL

1982

12 19 26 2 9 AUG

Figure 17-10. Bearing angle offsets at 270 degrees.

. . 6

- -

1 2

. iH 1 +%

t

+

+

+

+ 8 -2

1

- +

1

- -

-6

1 1 i J ' L. i 1 i i _ L —J 1 1

1 B 15 22 29 S MAR APR

1982

12 19 26 3 10 17 24 31 7 14 21 2B 5 MAY JUN JUL

12 19 26 2 9 AUG

Figure 17-lK. Bearing angle offsets at 300 degrees.

56
DO

T3

O

CO

CO

1 a IS 22 29 5 MAR APR

1982

12 19 26 3 10 17 24 31 7 MAY JUN

14 21 28 5 JUL

19 26 2 9 AUG

Figure 17-lL. Bearing angle offsets at 330 degrees.

6 - w

0)

Si 4

-

0/) Q) Ti• 1—

t

2

— »—

4

• i—t S

. "* o' . + CD

CO

1

-<l

1

CQ -4 —

a> .^,

-6 -

1 8 15 22 29 5 MAR APR

1982

12 19 26 3 10 17 24 31 7 14 21 28 5 MAY JUN JUL12 19 26 2 9 AUG

Figure 17-lM. Bearing angle offsets at 360 degrees.

57
Table 17.1. Measurement occasions,

Date (1982;

Measured bearing

angles (degrees)

Total

No. of measurements

March 4^5

March 9 March 12 March 22 April 29 June 8 July 6 July 7 July 13 July 30

30, 60, ..., 360

30, 60, ..., 360

30, 60, ..., 360

30, 60, ..., 360

30, 120, 180, 240, 300

30, 120, 180, 240, 300

30, 120, 180, 240, 300

30, 120, 180, 240, 300

30, 120, 180, 240, 300

30, 120, 180, 240, 300

70

65

75

65

30

30

30

30

30

30

17.3 Observed Data and Plots

An ac power line conditioner was added to the VOR system in February 1982. It handles the entire

system: generator, phasemeter, and computer. During the subsequent period of operation, data were collected on 10 separate measurement occasions to assess the stability of the system, to estimate possible offsets, and to validate the statistical model for the process. Table 17.1 lists the dates of

these measurement occasions and notes the bearing angles which were measured in each case. At each

bearing at least M=5 measurements were taken in succession, with each measurement requiring about 5.5

minutes to obtain.

To illustrate both the offsets of the process from the nominal bearings and the short- or longterm variability of the measurements, plots of the data are shown in figures 17-1 A through 17-1 M. The value plotted on the vertical axis is an observed measurement minus the nominal bearing angle in

degrees. Offsets of each bearing are plotted on a scale from -0.01° to 0.01°.

In figures 17-1 E (120°), 17-1 I (240°), and 17-1 K (300°), repeat measurements on July 13 and/or

July 31 exhibited a higher short-term variability than the previous history of the process would suggest. However, these unexpected cases are believed to have been caused by intermittent thunderstorm

activity on these days. For this reason, some of the measurements were discarded in the statistical

analysis by the outlier detection procedure discussed below. A complete listing of the 455 measurements, and other quantities which are computed by the VOR system, is given in appendix B.

58
17.4 Statistical Analysis

Because of the complexity of the analysis, the data were transmitted to a CDC 170/750 computer

where parameter estimates were computed using the BMDP statistical software package [7]. In this section we discuss a method for detecting isolated outliers, or uncharacteristic measurements, and obtain

estimates of the parameters in the statistical model for the VOR system. The statistical model has

been found to describe the VOR measurement process adequately during its limited time of operation.

17.4.1 Detection of Outliers

Two types of individual outliers were identified in the set of 455 measurements. The first type

is flagged by excessively large values (greater than 0.005) of the single time-sample standard error

of a bearing measurement. See section 16.1 for a discussion of this quantity. At present, the com- puted standard error is not a reliable measure of the actual short-term random error in bearing measurements, but this is thought to be a consequence of deficiencies in the phasemeter ADC, which fails

to meet the manufacturer's specifications for linearity by about a factor of 30. Nevertheless, the

bearing standard error is a useful indicator of isolated line effects during individual measurement

periods.

Outliers of the second type were identified by excessively large values of the standardized

residuals when the statistical model was fitted to the data. Standardized residuals were denoted in

section 17.3 by

t. ., = 6. .^/S(6. ., ).

The statistical software which was used automatically computes and prints the t^ j^'s for the model

described in section 17.2.

A measurement y^j|^ is rejected if t^j|^ > 3.0 or if t^ [^ < -3.0. This rejection criterion is

motivated by the observation that t^^|^, though its exact distribution is not known, is similar to a Students-t statistic. The critical value 3.0 corresponds to the 0.995 probability level for the Students-t distribution with 35 degrees of freedom. This test is recommended in reference 4 as a good

general approach even though probability levels cannot be computed exactly.

The second rejection criterion was applied to the data set three times iteratively to assure that

extreme outliers could not mask the effects of less obvious outliers. Together, the two outlier

rejection criteria work well for the VOR data in that they reject those measurements which appear to

be unrepresentative of the process either because of isolated errors in the amplitude time-samples or because of transient effects during short measurement periods (for example, thunderstorm effects).

In the future, NBS does not plan to conduct calibrations on occasions when the frequent occurrence of uncharacteristic measurements could perturb the results. Aside from such identifiable transient effects, it is also reasonable to reject isolated wild measurements before estimating uncertainties because these effects do not substantially influence the measurement of analog phasemeters which,

by design, report average phase over many cycles of the generator.

59
17.4.2 Parameter Estimates and Tests

Estimates of the unknown parameters were obtained by a statistical maximum likelihood algorithm

described in documentation of the analysis of variance program BMDP3V [7]. An example listing of the

computer output corresponding to the statistical analysis and parameter estimates discussed below is

given in appendix D.

Table 17.2. Sample offsets and standard deviations.

After Pass 1 After Pass 3 (final)

Nominal Average Average

bearing Count offset St. dev. Count offset St. dev.

49 -0.00125 0.00059 49 0.00125 0.00059

30 48 0.00049 0.00071 47 0.00053 0.00067

60 18 -0.00074 0.00042 18 -0.00074 0.00042

90 20 -0.00032 0.00027 20 0.00032 0.00027

120 48 -0.00227 0.00108 44 -0.00215 0.00086

150 23 0.00074 0.00045 23 0.00074 0.00045

180 56 -0.00195 0.00042 56 -0.00195 0.00042

210 20 -0.0G162 0.00041 20 -0.00162 0.00041

240 48 0.00008 0.00106 44 -0.00012 0.00065

270 18 -0.00092 0.00049 18 -0.00092 0.00049

300 50 0.00041 0.00089 46 0.00029 0.00053

330 20 -0.00077 0.00032 20 -0.00077 0.00032

360 20 -0.00061 0.00027 20 -0.00061 0.00027

Total 438 425

Of the total set of 455 measurements taken at 13 distinct bearing angles, 30 measurements (6.5

percent) were rejected as outliers by the two rejection criteria. Table 17.2 lists the observed average offset at each bearing angle and the corresponding sample standard deviation after first and third

(final) iterative application of the second rejection criterion. Recall that a total of three passes were made in the analysis to flag outliers.

The standard deviations listed in table 17.2 were computed using only the data for a particular

bearing and, therefore, neither partition the variability into short-term and long-term contributions,

nor do they reflect the fact that all bearings are incorporated simultaneously in the statistical

model. Table 17.2 has been included to illustrate in a simple fashion the magnitudes of the offsets,

their overall variability, and the effects of the outlier detection procedure on descriptive statistics.

The statistical analysis for the model described in section 17.2 was used to estimate the offsets

at each bearing, and to partition the total variability into components for both short- and long-term

variations (see section 17.2). Because the data are not evenly distributed among bearings or days,

the maximum likelihood estimates of offset could differ slightly from the observed (simple) average

offsets. Table 17.3 lists the final estimated offsets (through July 30, 1982) of the VOR process and

the estimated random uncertainty in these estimates. We have included the corresponding estimates

from the analysis after the first pass to reject outliers. Sample counts are given in the previous

table.

60
Table 17.3. Estimated offsets and standard errors,

After Pass 1 Nominal

Bearing

Estimated

offset

St. Dev.

of estimate

Final Values (7-30-82)

Estimated St. Dev. offset of estimate

30

60

90

120

150

180

210

240

270

300

330

360

-0.0013

0.0005

-0.0009

0.0002

0.0023

0.0005

-0.0020

0.0018

0.0001

0.0010

0.0004

0.0009

0.0008

0.0002

0.0002

0.0002

0.0002

0.0002

0.0002

0.0002

0.0002

0.0002

0.0002

0.0002

0.0002

0.0002

-0.0013

0.0005

-0.0009

0.0001

-0.0022

0.0005

-0.0020

-0.0018

-0.0001

-0.0011

0.0003

-0.0010

-0.0008

0.0001

0.0001

0.0002

0.0002

0.0001

0.0002

0.0001

0.0002

0.0001

0.0002

0.0001

0.0002

0.0002

We remark that slight differences in the standard errors of the final estimated offsets reflect

the fact that some bearings were measured more often and therefore have a lower uncertainty. That

this difference is not apparent after the first pass for outlier rejection is an indication of the

influence of outliers on the estimated components of total variability.

In the analysis which gave rise to the parameter estimates given in table 17.3, we simultaneously

1/2 obtained estimates of the short-term (a) and long-term (oj^ + 0,2) standard deviations. Table 17.4

gives estimates of a few functions of these components which are used to establish limits to random

errors. The effects of outliers on estimation of variability are more clearly evident in the

tabulated comparison between the first and final passes through the data.

The maximum likelihood technique also provides a statistical test based on the Chi-square distribution to determine if the two long-term components of variability (and, so, the corresponding terms

in the statistical model) are necessary to characterize the VOR process. Non-negligible contributions

to variability are indicated by a small value (< 0.05) of the significance level for the Chi-square

test statistic computed by the software. Table 17.5 gives the results of these tests for the final

data set, and indicates that both long-term components are non-zero. We also list the estimated standard deviations of the estimated variance; however, the Chi-square test statistic is not computed

simply from the quantities listed.

Table 17.4. Components of random error.

Description of

random error Quantity

estimated

After Pass 1 estimateFinal (7/30/82)

estimate

Short-term st. dev.

Total St. dev.

Short-term st. dev. (mean

of 5 readings at 1 bearing)

Total St. dev. (mean of 5 readings at 1 bearing)

(a2+aj2+0u2)i/2

(a2/5)i/2

(a2/5+aj2+oj^2)l/2

0.0006

0.0007

0.0003

0.0005

0.0004

0.0006

0.0002

0.0004

61
Table 17.5. Chi-square tests for contributions to random error (7-30-82).

Standard Chi -square Degrees SigniParameter Estimate deviation test statistic of freedom ficance

o2 1.775x10"^ 0.137x10-7

"T^ 0.518x10-7 0.306x10-7 7.942 1 0.005

°d' 0.916x10-7 0.209x10-7 54.030 1 0.000

17.5 Overall System Performance

In the previous section we obtained estimates of individual offsets between NBS standard generator and standard phasemeter at 13 nominal bearings which are thought to be representative of the system behavior over the full range of 0° to 360°. We also computed reasonable estimates of various com- ponents of random variability about these offsets. In this section we characterize the overall system

performance by computing the limits to random error in the reported values of the individual offsets.

This information about the system performance at 13 distinct bearings has been combined into a single

provisional uncertainty statement, which is reported in the following section.

The limit to random error associated with the i-th bearing offset is 3s^, where s^ denotes the

estimated standard deviation of the reported offset (see table 17.3). Recalling that the estimated

offset at bearing i was denoted by p + a^ , then statistical bounds on the offsets are given by

y + ouj ± 3s^ .

All of the required quantities are documented in table 17.3. The estimated bounds on offsets at the

13 measured bearings are reported below in table 17.6. Note that in each case the maximum limit in

magnitude of the offset is less than the allowable uncertainty of ±0.01°.

Table 17.6 Overall system performance.

Nominal bearing Lower limit Estimated offset Upper limit

-0.0016 -0.0013 -0.0010

30 0.0002 0.0005 0.0008

60 -0.0015 -0.0009 -0.0003

90 -0.0005 0.0001 0.0007

120 -0.0025 -0.0022 -0.0019

150 -0.0001 0.0005 0.0011

180 -0.0023 -0.0020 -0.0017

210 -0.0024 -0.0018 -0.0012

240 -0.0004 -0.0001 0.0002

270 -0.0017 -0.0011 -0.0005

300 0.0000 0.0003 0.0006

330 -0.0016 -0.0010 -0.0004

360 -0.0012 -0.0006 -0.0000

62
17.6 Provisional Uncertainty

At the outset of this report it was noted that the primary criterion for judging the performance

of the two VOR instruments was to achieve a high degree of confidence that they agree with each other.

That is, since they are independent and work on different principles, it is probable that their separate indications are accurate if the nominal setting on the generator agrees with a measurement by the

phasemeter.

Because the reported offsets between the generator and phasemeter cannot be attributed wholly or

in part to either instrument at this time, it was decided to combine the information in table 17.5

into a single provisional uncertainty statement for either instrument alone. Therefore, until individual error analyses are devised, or until international comparisons are conducted, NBS will use the

estimated maximum absolute offset in the group of 13 bearings as the systematic error for either VOR

instrument, and will report the nominal bearings as accepted values for the process. The limit to random error is three times the maximum standard deviation of the estimated offsets in table 17.3.

The uncertainty of VOR bearing calibrations is given by:

The assigned values of VOR phase angles are the nominal hearings from to 360° in increments of 0.01° . The overall uncertainty of these values has heen estimated from test data

at hearings from (f to 360° at 30° increments. Thus, each of the nominal hearings has heen

assigned a provisional overall uncertainty of ±0.0028° , hased on estimated hounds of

±0.002^ on the systematic error and a computed standard error of 0.0002°

.

18. Process Control and Updating Parameters

In sections 17.4 and 17.5, initial accepted values of VOR process parameters were obtained. Once

these parameters have been established, overall process control is maintained by checking the observed

short-term standard deviation and estimated offsets on each subsequent measurements occasion against

their accepted values. As long as the process produces values which are consistent with the accepted

parameter values, the system is considered to be performing within the established control pattern.

Procedures for detecting out-of -control conditions are discussed briefly below, but procedures for

identifying and correcting specific malfunctions from the various statistical tests are evolving as more experience is gained with the VOR system and will not be discussed here.

18.1 Control Charts and Tests

Control charts are used on a continuing basis to monitor the output of the composite VOR measurement system. Given established values for process parameters, the estimated offsets and short-term

standard deviations on subsequent calibration dates are plotted against a time scale. The charts for

offsets includes control limits so that an out-of-control value is immediately noticable. The chart

of the short-term standard deviations provides visual evidence to determine if there has been a change

in the within-day process variation.

The short-term variation on a given measurement occasion can be estimated by describing the data

using a special case of the statistical model given in section 17.2. If M repeat measurements are made at I nominal bearings the model for the measurements is:

63
y^j = y + a. + e.j, i = 1, • • •, I;

J = 1, • • •, M;

where

y^- ^ is an observed offset [Q-^ - nominal bearing];

y + Oj is the unknown average offset at bearing i for the current day;

e^^ is the short-term error of measurement in the j-th repeat measurement at bearing i.

The errors, e^ ^

, are assumed to have a Gaussian distribution with mean zero and variance cr. If the

process is in statistical control, the current estimated short-term standard deviation and the estimated offsets should be consistent with the accepted values of these parameters.

The statistical analysis obtains the parameter estimates after outliers have been rejected by the

methods discussed in section 17. These estimates are then plotted on the control charts and are also

used in statistical tests to determine whether or not the process is in control.

18.1.1 Control Chart for Short-Term Error

Figure 18-1 illustrates the within-day process variation for 17 measurement occasions from

March 1, 1982 through May 6, 1983. The first 10 estimated values of a were obtained from the data

used to establish the current accepted values of the process parameters. For reference, the accepted

value of a is also noted in the figure. The inclusion of estimates from data obtained on July 30,

1983 serves to illustrate that the unusually high short-term variation on July 30 was apparently

caused by thunderstorm activity on that day. In the next four figures, open circles are used to indicate data used in arriving at the estimate and control limits (if present). Plus signs (+) are used to indicate data taken after the estimates were made.

18.1.2 Control Chart for Individual Measurements

Sufficiently accurate control limits cannot be established during the current stage of initiating

the VOR measurement process. However, to illustrate the type of control charts which will be used to monitor the process after a large number of calibration occasions have been inspected, some of the

data used to compute process parameters are plotted in figures 18-2 A-F.

During start-up the process is assumed to be in statistical control. The control limits in figures 18-2 A-F will be used until evidence is obtained which is not consistent with the accepted

values or until enough data accumulates to effectively revise or update the process parameters.

Although charts on the average offsets are more sensitive than those on individual measurements,

the latter was chosen because outlier rejection may result in unequal numbers of repeat measurements

from occasion to occasion. Thus, fluctuating control limits would be required for charts on the average offset.

Limits specified in figures 18-2 A-F were set at

G +

ii ± 3(a2 + ;y2 + ;q2)i/2,

where the estimates of the offset at the ith bearing and the components of error are the initial

accepted values. The numeric values were given in tables 17.3 and 17.4.

64
t3

>

a

-t-> s

a>

I J-o

0.9

0.8 -

773 0.7

0.6

0.5

0.4

0.3

02

0.1

o

o

Estimate thru 7-30-82

o

, o

J I L J I I L MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY

1982 1983

Figure 18-1. Control chart for short-term standard deviation.

T3

o"

I n

«> 0:3

a -

2

1

-1

O

^

o

+ +

-

2

1

_o 8

o

8

+*

++

+

+

+

+

+ 1 *

;

MAR APR MAY

1982

JUN JUL AUG SEP OCT NOV DEC JAN

1983

FEB MAR APR MAY

Figure 18-2A. Control chart of offsets at degrees.

65
? 3

a

Control limits

O

-1

-2

-3 h

MAR APR MAY

19B2

JUN JUL AUG SEP OCT NOV DEC JAN

1983

FEB MAR APR MAY

Figure 13-2B. Control cnart of offsets at 30 degrees.

MAR APR MAY JUN JUL AUG SEP OCT NOV DEC JAN FEB MAR APR MAY

1982 1983

Figure 18-2C. Control chart of offsets at 120 degrees.

so

<D

L,

o

CO

ds

MAR

1982

APR MAY JUN JUL AUG SEP OCT NOV DEC JAN

1983

FEB MAR APR MAY

Figure 18-20. Control chart of offsets at 180 degrees,

66
7iu

0) n

o

as

Control limits

&J

-1 <^

o

-Of t

-2 -

-3

MAR

1982

APR MAY JUN JUL AUG SEP OCT NOV DEC JAN

1983

FEB MAR APR MAY

Figure 18-2E. Control chart of offsets at 240 degrees,

VI

(U

XI

2 -

1 -

Control limits

o° -1 ^ -2 -

v>

a> 3- -3

MAR

1982

APR MAY JUN JUL AUG SEP OCT NOV DEC JAN

1983

FEB MAR APR MAY

Figure 18-2F. Control chart of offsets at 300 degrees.

18.1.3 Tests for Out-of -Control Conditions

Two types of statistical comparisons are used to determine if process parameters may have changed

since previous calibration sessions. These tests monitor, respectively, the process short-term variation and the mutual offsets between generator and phasemeter. Table 18.1 illustrates the procedure

and shows the appropriate statistical tests for comparing current offsets to accepted values. Table

18.2 describes the test for an increase in short-term variation.

Tables 18.1 and 18.2 are presented primarily to illustrate the procedures which are used to

determine if the process parameters may have changed from the accepted values. However, it is clear

from the results, which are based on actual measurements, that values of the components of random

error should be recomputed when more process output is available. This is also suggested by visual

evidence in the control chart in figure 18-1, which seems to indicate that an abrupt shift in shortterm variation may have occurred between June 8 and July 6. If the larger error persists and the process remains within the assigned goal, new values of the parameters will be determined from measurements obtained after June 8, 1982.

67
Table 18.1. Comparison of new offsets to accepted values,

Nominal

bearing

Accepted

offset

Estimated

offset on 9/28/82

Number

observed

Estimated

Std. Dev.

of offset

t-Test

SU) y)/s(y)

30 120

180

240

300

0.0013 -0.0018

0.0005 0.0001

0.0022 -0.0033

0.0020 -0.0022

0.0001 -0.0006

0.0003 0.0008

2.7342 X lO"'* -2.19

3.0569 X 10-'+ -1.31

2.7342 X lO""* -4.39- 2.7342 X 10-^ -0.73

2.7342 X

10"'^ -1.83

2.7342 X lO""* 1.83

*If t > 3, the new value is not consistent with the accepted offset. In this case a malfunction which

affects 120° (or possibly a range of bearings) may be indicated.

Accepted

short-term

variance

Table 18.2. Comparison of new short-term variability with accepted value.

Estimated

variance on 9/28/82

Total

number of

measurements

Number of

bearings

Chi -square (x^)

test

a2 S2 N k (N - k)s2

a2

1.775 X 10-7 3.738 X 10-7 29 6 48.44*

*If x^ ^ X^ fof" i^ (2 - k) degrees of freedom, the current short-term variability is not consistent

O'Ol

with the accepted value. For 23 degrees of freedom, y^ "^ 9.26.

0' 01

Finally, we remark that the t-test and chi-square test were applied assuming that the accepted

values of the process parameters were "known," or at least very precisely determined relative to the

estimates obtained on the subsequent occasion. These tests will be appropriate when the process has

been shown to be in continous statistical control for several measurement occasions, so that highly

accurate values of the process parameters can be established from the combined data. During the present stage of initiating the process, or during the start-up of the process after a substantial system

modification or other out-of-control process correction, it will be necessary to use tests which

incorporate and adjust for uncertainty in the initial accepted values. The appropriate initial com- parisons are an F-test for short-term error, and the two-sample t-test for offsets.

18.2 Updating Process Parameters

Initial accepted values for the VOR system were established after 10 calibration runs from

March 3, 1982 through July 30, 1982. On subsequent occasions, the process is monitored using the control procedures described above to determine if measurements are adequate relative to the assigned

uncertainty goal. Generally, this procedure may be followed as long as the process is confirmed to be

performing within the established control pattern.

Periodically, as data accumulate at the control bearings, new accepted values for offsets and

components of error will be computed by combining current data with previous measurements and applying

the methods described in section 17.4. Initially, the accepted values will be updated after five or six calibration runs and then as convenience dictates (every six months or yearly).

68
18.3 Procedures for Correcting Out-of-Control Conditions

Actions which can be taken when a statistical test indicates an out-of-control condition are currently being investigated. In the absence of specific assignable causes for out-of-control conditions, the following general questions will be considered.

If the process is found to be out of control by a chi-square or F-test, indicating excessive

short-term nonrepeatabi 1 i ty:

1. Was there extreme weather activity during the calibration run (thunderstorms, wind, etc.)?

2. Is the accepted value of short-term error realistic?

3. Has the process variation changed? Is the current variation still adequate for the assigned goal?

4. Is there unusual activity in the laboratory or building affecting power supplies?

5. Equipment deterioration or minor malfunction?

If the process is found to be out of control by a t-test, indicating an abrupt shift in bearing:

1. Only at a single bearing? This may indicate an intermittent or transient external disruption.

2. At several control bearings? Look at bearing histories for a steady drift toward out-of-control

condition. This could indicate a need for system adjustment. If an abrupt change has occurred,

this could indicate a component malfunction in either the generator or in the phasemeter ADC.

The work reported here is the result of vital contributions by several persons over a period of

about five years. M. G. Arthur provided the initial project management. He and C. H. Manney, Jr.,

determined that the use of primarily digital techniques in both the phasemeter and generator was the

only approach that could achieve the desired accuracy. G. R. Sugar and C. J. Roubique did most of the

detailed logic design in the generator, and E. Niesen constructed and assisted in debugging it. The

phasemeter was designed and constructed by N. T. Larsen, and the software was written by Larsen and

0. F. Vecchia.

The task of completing the development, verifying the performance, and writing this report fell to the present authors. The credit for the design belongs mainly to those named above; the authors

however, take full responsibility for preparing this report.

19. References

[1] Sandretto, Peter C. Electronic avigation engineering. New York: International Telephone and

Telegraph Corp.; 1958. 373.

[2] Hurley, H. C; Anderson, S. R.; Keary, H. F. The Civil Aeronautics Administration VHF ominrange. Proc. IRE 39(12) :1506-1520; 1951.

[3] Ijnite, R. A.; Clarke, R. N.; Yell, R. W. VOR waveform synthesis and calibration. lEE Proc.

128, Pt. F(7):443-450; 1981 December.

[4] Note: This design decision was made after a demonstration to us of an possibly similar approach

by R. H. Huenemann, then with United Air Lines. We used the NBS generator to test his method

with good results, but he did not allow us to examine his software. The details of his method

are not known. However, the decision was not made until extensive computer simulations had been

made and the errors analyzed.

[5] Vecchia, Dominic. Fourier transformation of the nonlinear VOR model to approximate linear form.

Nat. Bur. Stand. (U.S.); Tech. Note 1021; 1980.

[6] Barnett, V.; Lewis, T. Outliers in statistical data. New York: John Wiley and Sons, Inc.; 1978.

[7] Dixon, W. J.; Brown, M. B., eds . BMDP-79: Biomedical computer programs P-series. Berkeley:

Univ. of California Press; 1979.

69

Appendix A. VOR Phasemeter Prografn Listing

Rev$="8207140822"

Di sk$=" " Filenanie$="VORl"

8201011453: Adde

This program tak

form and stores

venter and the t this program can the processing a results and stat

! This must be a 10-digit number.

! A 10-digit no. picked up from the disk,

! Filenames is this program's name,

d year to Time$. Added MATPRINT Theta to Meas_print.

es 1024 time samples of the VOR composite audio wavethe data on disk. It drives the analog-to-digital con- ime delay generator. After the data have been stored,

retrieve and process the file. The final results of

re then stored in the original file. (Intermediate

i sties on sets of measurements are not stored.)

A single measurement results in one file, 17 records of 256 bytes each.

The first 16 records are completely filled by the 1024 integer precision data points. The last record is completely filled by a 32-

element array used for housekeeping purposes.

This program has been tested using simulated, noisy data. To process

simulated data, 3 changes should be made:

1. Check that the sine transforms are not negated in Fft_driver,

line Changel.

2. Do not MAT READ Housekeepi ng(*) in Retrieve_data, line Change2,

3. Delete the PAUSE in Retrieve data, line Change3.

Rev$ and Disk$ are stored in Housekeeping(6) & (7), respectively.

They are the code revision date and the disk identification, and are

used in documenting printed output.

Sine transforms negated, 8005280905.

Routine Fft uses code adapted from the Hewlett-Packard 9835 Numerical

Analysis software package.

Arrays used in the Estimation subroutine: Qd( Xt( Theta(*)

Arrays used in the Xt subroutine are dimensioned by label Xt_dim:.

This line is disabled to conserve 25 kbytes of memory.

Integer_data(*)=integer precision time series data, the raw output

of the A/D converter. This is the data stored on disk; integer

precision data takes less disk space.

Real_data(*)=the full precision array into which the data is loaded

from disk for FFT processing. As stored, it is integer data, but

before it is processed, it is converted to volts by multiplying

by 5/32768.

To convert to volts, multiply by 5/32768.

Housekeeping(*) holds the following elements:

1: Ending date-time group (dtg) of a data run: Time_no.

2: Nominal bearing angle, degrees: Nom_bearing.

3: Number of measurements in the set: No_measmnts.

4: Number of this measurement: Measmnt.

5: Number of data points in the set taken in overload (bad).

6: Revision dtg of the code: VAL(Rev$).

7: Disk dtg: VAL(Disk$).

8: File_no of the measurement, DATnnn.

9: Thetal, the VOR bearing angle (=0 if data not processed).

10: Theta2

11: Theta3

12: Sigmasq, a measure of the precision.

13: Est_std_dev, the estimate of the standard deviation.

14: Processed, a flag that identifies processed data.

15

32: Unassigned (=0) for future use. May be used for customer ID, instrument ID, last recalibration dtg, etc. See label Housekeepi ng.

A-1
1420

1440

1460

1480

1500

1520

1540

1560

1580

1600

1620

1640

1660

1580

1700

1720

1740

1760

1780

1800

1820

1840

1860

1880

1900

1920

1940

1960

1980

2000

2020

2040

2060

2080

2100

2120

2140

2160

2180

2200

2220

2240

2260

2280

2300

2320

2340

2360

2380

2400

2420

2440

2460

2480

2500

2520

2540

2560

2580

2600

2620

2640

2660

2680

2700

2720

2740

2760

2780

DelayS=5359A command string.

!(*) See R(*) , below.

Jn(*) Holds tne values of Bessel functions of the first

kind, orders -18 througn 18 (37 numbers). Loaded with file "Xt",

Meas(*)

abou

cont

(i. rows

1.

2.

3.4.

is organized as follows: Tne first row contains information

t the 30 Hz fundamental frequency, and rows 2 through 38

ain the same information for spectral lines 314 through 350

e., lower sideband -18 through upper sideoand no. 18). All of Meas(*) conform the these column assignments:

Real part from R(*)--note that the rows do not correspond.

The first row of Meas(*) results from tne second row of R(*]

I(*); etc. Imaginary part from I(*)--same rows as aoove. Magnitude or amplitude of the lines.

Phase, in radians, after selection of quadrant

placed in Qr(*), for use in the estimation of

Phase, in degrees, derived from col. 4. This

in Qd(*), which is used in the bearing angle e SGN of Jn(Row-20), the sign of Bessel function

Pointer("*') value for that row. The value is o tne harmonic number.

. This col . is the std. dev.

col . is placed

stimation.

s -18 to 18.

ne greater than

Pointer(*) is set up in the FFT driver to indicate tne desired lines in

R(*) and I(*); only lines 1 and 314-350 are used.

Qd(*) is a vector = to col. 5 of Heas(*). Angles have been ordered.

It is used in the estimation of the bearing angle, Theta(l,l).

Qr(*) is a vector = to col. 4 of Meas(*). Angles are never ordered.

It is used in the estimation of the standard deviation of the bearing angle, Est_std_dev. This estimation helps identify bad data.

R(*) holds the odd-numbered rows of Data(*); I(*) holds the even-numbered rows. R(*) and I(*) are used in the FFT routine. Conversion

from Data(*) to R(*) and I{*) only requires 4 seconds; but if memory is severely limited, the code can oe changed to store tne

data directly in R(*) and I(*). Otherwise, storing the data in a single array simplifies possiole future processing.

In tne FFT, the elements in botn R(*) and !{*) are replaced by the

real and imaginary parts of tne lines. The first row in R(*) con- tains the DC term and the first row in I(*) contains the maximum

frequency.

Meas(38,7) [q . v.] selects the needed lines from R(*) & I(*) by means of Pointer(*).

Results!*) nolds the bearing angles for all measurements, up to 50 in one set. This may be reduced to conserve memory, since an estimate

of the standard deviation of the bearing angle can be obtained from

only one measurement. (It tends to be overly conservative.)

Stats(*) replicates Results(*) and is then used to compute mean, s.d.,

etc, to preserve Results (*), if needed. Memory may be saved by

allowing Results(*) to be altered in the processing, otherwise.

Tneta(*) contains the estimates of the three (tneta) angles in the

model of the VOR signal. Theta(l,l) is the estimated bearing

angle.

Mai n_program: ! OPTION BASE 1 COM REAL Xt(3, 38), Jn(37),Pointer(38),Ck, Years

DIM Real_data ( 1024, 1 ), Del ay S[80], Housekeeping (32), I

( 512), Meas( 39, 7) DIM R( 512), Results (50,1), Stats (50,1)

A-2
2800 DIM Qd(38,l),Qr(38,l),Theta(3,l)

2820 DIM X(37),Y(37),Xsq(15),Ysq(15),Xy(15)

2840 INTEGER Integer data{1024,l)

2860 Xt_dim:! DIM X{38,T) ,V(38,38) ,Vi (38,38) ,A(38,3) ,B(3,3) ,C(3,3)

2920 Wait=100 ! 5359A settling delay

2940 Printer=16

2960 LINPUT "Printer select code? (Default is 16.)",Resp$

2980 IF Resp$="" THEN 3020

3000 Printer=VAL(TRIM$(Resp$))

3020 PRINTER IS Printer

3040 LINPUT "What is the msus where the data and program are stored?", Msus_data$

3060 Msus_data$=TRIM$(UPC$(Msus_data$))

3080 IF Msus data$[l,l]<>":" THEN Msus_data$=" : "&Msus_data$

3081 IF DiskTo"" THEN 3100

3082 LINK "DTG"&Msus_data$, 32000

3083 GOSUB Disk_dtg

3100 No_samples=1024 ! This is fixed, in this program.

3120 INPUT "Nominal bearing angle (degrees)?" ,Nom_bearing

3140 Housekeeping(2)=Nom_bearing

3160 INPUT "Process old data (1), or take new data (2)?" ,01d_data

3180 IF (Old dataol) AND (01d_data<>2) AND (01d_data<>0) THEN 3160

3200 IF 01d_Jata=0 THEN End

3220 IF 01d_data=l THEN GOSUB Retrieve_data

3240 IF 01d_data=l THEN End

3241 IF LEN(Year$)=2 THEN 3260

3242 INPUT "Last two digits of the present year?",Year$

3243 IF LEN(Year$)<>2 THEN 3242

3260 INPUT "Number of measurements?" ,No_measmnts ! Loop for statistics.

3280 IF (No_measmnts<l) OR (No_measmnts>100) THEN 3260

3300 Storing=0 ! A flag for Check_files

3320 GOSUB Check_files

3340 FOR Measmnt=l TO Nojneasmnts

3360 Measurement=Measmnt

3380 No_overloads=0 ! No_overloads counts bad data points.

3400 GOSUB Setup_5359 ! Resset 5359A for every Measmnt.

3420 GOSUB Take_data

3440 GOSUB Store_data

3460 NEXT Measmnt

3480 PRINTER IS 16 3500 PRINT PAGE

3520 PRINT "Data acquisition is complete. All data in this set of measurements have been"

3540 PRINT "stored. Processing is in progress."

3560 File_no=VAL(File$[4,6])-No_measmnts+l ! If data has just been taken,

3580 ! this resets the File_no to the

3600 ! first file in the set, for

3620 ! processing.

3640 PRINTER IS Printer

3660 GOSUB Retrieve_data ! Retrieves and processes the data;

3680 ! prints out results and stats.

3700 End:!

3720 PRINT LIN(2)

3740 PRINTER IS 16 3750 STOP!

3780 Setup_5359:!

3800 REMOTE 716

3820 Delay$="W200E-9,OA5,000,DSS"

3840 FLOAT 11 3860 Del ay$=Del ay$&VAL$( 1/ ( 30*No_sampl es ) )&" ,TPONSP ,D0 ,

3880 STANDARD

3900 OUTPUT 716;Delay$

3920 RETURN !

3940 Take_data:!

3960 GOSUB Time

3980 PRINT "Data taking began at ";Time$

4000 PRINT "Code dtg: ";Rev$;". Disk dtg: ";Disk$;". Filename: ";Filename$

4020 MAT Integer_data=ZER

4040 OUTPUT 716;Delay$ ! Reset 5359A for each measurement.

A3
4060 FOR Counter=l TO No_samples

4080 OUTPUT 716;"SCRA," ! Single-Cycle, Re-Arm

4100 WAIT Wait ! Wait=settl i ng delay for 5359A.

4120 Sample=READBIN(2)

4140 IF ABS(Sample)<32767 THEN 4240 ! Test for overload.

4160 BEEP 4180 DISP "" 4200 DISP " OVERLOAD! " 4220 No_overloads=No_overloads+l

4240 Integer_data{Counter,l)=Sainple

4260 OUTPUT 716;"DSU," ! Delay Step Up

4280 NEXT Counter

4300 RETURN !

4320 Statistics: ! 4340 PRINT "Code dtg: ";Rev$;". Disk dtg: ";Disk$;". Filename: ";Filename$

4360 REDIM Stats(No_measmnts ,1)

4380 IF No_measmnts=l THEN 4860 ! If there has been only one meas4400 ! urement, statistics are skipped.

4420 MAT Stats=Results

4440 IF Nom_bearing<>0 THEN 4520

4460 FOR Counter=l TO No_measmnts ! Allows stats near 0.00 degrees.

4480 IF Stats(Counter,l)>350 THEN Stats (Counter, l) = -(360-Stats (Counter, 1)

)

4500 NEXT Counter

4520 Mean=SUM(Stats )/No_measmnts ! Stats(*) now contains all the

4540 ! measurement results.

4560 MAT Stats=Stats-(Mean)

4580 MAT Stats=Stats. Stats ! Square each element in Stats(*).

4600 Variance=SUM( Stats )/(No_measmnts-l)

4620 Std_dev=SQR( Variance)

4640 PRINT

4560 IMAGE "Mean : " ,21( " ."

) ,M3D.3DX3D, " degrees"

4680 PRINT USING 4660;Mean

4700 IMAGE "Nominal beari ng" ,11( "

. " ) ,4D.2D

4720 PRINT USING 4700;Nom bearing

4740 IMAGE "Vari ance: " ,17T"

. ") ,2X,M1D.3DE

4760 PRINT USING 4740;Vari ance 4730 IMAGE "Standard devi ati on

: " ,7( "

. " ) ,2X,M1D.3DE, " degrees"

4800 PRINT USING 4780;Std_dev

4820 IMAGE "Mean minus nomi nal : " ,7( "

. " ) ,M3D.3DX3D," degrees",/

4840 PRINT USING 4820;Mean-Nom_bearing

4860 RETURN !

4880 Time: ! 4900 OUTPUT 9;"R"

4920 ENTER 9;Time$

4940 Time$=Year$&":"&Time$

4960 Time_noS=Time$[l,2]^Time$[4,5]&Time$[7,8]&Time$[10,ll]&TimeS[13,14]&Time$[16,17]

4980 Time_no=VAL(Time_noS) ! Used for Housekeepi ng(*) info., and

5000 RETURN ! 1 elsewhere.

5020 Store_data: ! 5040 Storing=l

5060 GOSUB Check_files

5080 GOSUB Housekeeping!

5100 IF File_no<10 THEN Fi le$="DAT00"&VAL$(Fi le_no)&Msus_data$

5120 IF File_no>=10 THEN Fi le$="DATO"&VAL$(Fi le_no)&Msus_data$

5140 IF File_no=100 THEN Fi leS="DAT"&VAL$(Fil e_no)&Msus_data$

5160 CREATE File$,17,256 ! For Integer_data(*) S Housekeepi ng(*)

.

5180 ASSIGN #1 TO File$

5200 MAT PRINT #1 ; Integer_data, Housekeepi ng 5220 ASSIGN * TO #1

5240 GOSUB Time

5260 PRINT "Data stored in file ";File$;", disk ";Disk$;", at " ;Time$;" ." ,LIN( 1) 5280 RETURN !

5300 Petri eve_data:

5320

5340

Gets data files, processes them,

and prints results.

A-4
5360 IF 01d_data<>l THEN 5420 ! Jumps if processing data just taken.

5380 INPUT "Data files are 'DAT' followed by a number. What's the no. of the first file?" ,File_no

5400 INPUT "How many measurements were in the set?" ,No_measmnts

5420 REDIM Results (No_iTieasmnts,l)

5440 Result_no=0

5460 IF Xt(l,l)=l THEN 5540 ! IF. ..THEN Xt{*) is in COMmon memory.

5480 ASSIGN #1 TO "Xt " &Msus data$

5500 READ #1 ;Xt(*) ,JnT*77Pointer(*) ,Ck

5520 ASSIGN * TO #1

5540 FOR File=File_no TO Fi le_no+No_measmnts-l

5560 Processed=0 ! (Set to 1 when the file is processed.)

5580 Result_no=Result_no+l

5600 IF File<10 THEN Fi le$="DATOO"

5620 IF File>=10 THEN File$="DATO"

5640 IF File=100 THEN File$="DAT"

5660 File$=File$&VAL$(File)AMsus_data$

5680 PRINTER IS 16 5700 PRINT File$ ! Shows the progress in the processing.

5720 ASSIGN #1 TO File$

5740 ChangeZ: ! To process simulated data, READ only

5760 ! Real_data.

5780 MAT READ #1 ;Real_data,Housekeepi ng 5800 ASSIGN * TO #1

5820 Processed=Housekeeping(14)

5840 IF NOT Processed THEN 6180 ! Data has not been processed before.

5860 BEEP 5880 PRINT "File "&File$&" has already been processed.";

5900 IF Housekeeping(15) THEN PRINT " It is a bad file.";

5901 INPUT "Do you wish to reprocess it? (1 or 0)", Reprocess

5920 PRINT

5940 PRINTER IS Printer

5960 Results (Result_no,l)=Housekeeping(9)

5980 Sigmasq=Housekeeping(12)

6000 Est_std_dev=Housekeeping{13)

6020 IF File<>File_no THEN 6100

6040 IMAGE "Data fi le" ,5X,"Beari ng angle" ,5X,"Sigmasq" ,5X, "Est. std. dev."

6060 PRINT USING 6040

6080 IMAGE #,2X,6A,8X,4D.4D,6X,D.3DE,6X,D.3DE

6100 IF Est_std_dev>=lE-2 THEN PRINT CHR$(132);

6120 PRINT USING 6080;Fi le$,Housekeepi ng(9) ,Sigmasq,Est std_dev

6140 IF Est_std_dev>=lE-2 THEN PRINT CHR$(248) ;"P0SSIBLr BAD DATA" 6160 PRINT CHR$(128)

6180 IF Housekeeping(3)=No_measmnts THEN 6260 ! Test No_measmnts.

6200 BEEP 6220 IMAGE "The data file just loaded shows that there were ",K," measurements in the

set,",/, "not ",K,".",/

6240 PRINT USING 6220;Housekeepi ng(3) ,No_measmnts

6260 IF Housekeeping(8)=File THEN 6400 ! Test file identification for con6280 BEEP ! sistency, to avoid false results.

6300 IMAGE "Data in the last file loaded show that the file number is ",K," rather than ",K,".",/

6320 PRINT USING 6300;Housekeeping(8) ,Fi le 6340 Change3: ! To process simulated data, delete the

6360 ! following line:

6380 PAUSE ! There is a file error. 6400 PRINTER IS Printer

6420 IF Processed AND NOT Reprocess THEN GOTO Next_file

6440 MAT Real_data=(5/32768)*Real_data ! Convert to volts.

6460 GOSUB Fft_driver

6480 GOSUB Estimation

6500 Processed=l ! Data now processed.

6520 GOSUB Housekeepi ng2 ! Update the array.

6540 ASSIGN #1 TO File$

5560 MAT PRINT #1,17 ;Housekeeping ! Update the Housekeepi ng(*) file.

6580 ASSIGN * TO #1

6600 Results(Result_no,l)=Theta(l,l)

6620 Signflag=0 ! Used for diagnostics.

6640 Next_file: ! 6660 NEXT File

6680 IF No_measmnts=l THEN 6720 ! Don't do stats if only 1 measmnt.

A-5
6700 GOSUB Statistics

6720

6740 Che

6760

6780

6800

6820

6840

6860

6880

6900

6920

6940

6960

6980

7000

7020

7040

7060

7080

7100

7120

7140

7160

7180

be writt

7200

7220

7240

7260

7280

7300

RETURN ! ck fi les : ! ^Data acquisition' ! Are there enough files left, and

! when Storing, what's the next no? DIM CatS(100)[41]

Skip=Return=0

CAT TO Cat$(*),Skip,Return;"DAT"iMsus_data$,l

IF Cat$(l)<>"" THEN 6900

Fi le_no=l

GOTO 7300

FOR File no=l TO 100

IF POSTCat$(File_no),"DAT")=0 THEN 6980

IF VAL(Cat$(File_no)[4,6])=100 THEN 7140 NEXT File_no

IF Storing THEN 7300 ! File adequacy has been checked, by now.

IF File_no-1+No_measmnts<=100 THEN 7300

BEEP

IF 100-File_no+l=0 THEN 7140 PRINT "There are " ;100-Fi le_no+l; "files remaining on this disk. Either re-RUN and reduce" PRINT "the number of measurements, or use a new disk and CONTinue. All of the" PRINT "measurements in a set should be on the same disk, however."

GOTO 7280 PRINT "The highest-numbered data file on this disk is DAT_100. To store any new data,"

PRINT "some of these data files must be purged, using the program PURDAT. It will"

PRINT "purge all data files at and beyond a specified file number." ,LIN(2) , "New files cannot

en with numbers lower than files already on the" PRINT "disk. Attempting to do so will result in a STOP." ,LIN(1) PRINT "If files are deleted, they should be deleted in complete sets, if possible, to " PRINT "avoid the chance of processing only part of a set at a later date."

STOP

PAUSE

RETURN !

7320

7340

7360

7380

7400

7420

7440

7460

7480

7500

7520

7540

7560

7580

7600

7620

7640

7660

7680

7700

7720

7740

7760

7780

7800

7820

7840

7860

7880

7900

7920

7940

7960

7980

8000

Fft driver: ! (Data processing;

MAT Meas=ZER

Counter=0

FOR 1=1 TO No samples/2

Counter=Counter+l

R(I)=Real_data(Counter,l)

Counter=Counter+l

I( I )=Real_data( Counter, 1) NEXT I GOSUB Fft

Markerl: ! FOR Counter=l TO 38

Meas{Counter,l)=R(Pointer(C

Changel

Meas(Counter,2)=-I(Pointer(

Meas( Counter,

7

)=Pointer(Cou

NEXT Counter

Meas(39,l)=R(l)

Meas(39,2)=I(l)

REDIM Jn(-18:18)

FOR Row=2 TO 38

Prepare R(*) & I(*) for Fft:.

(Fft: is from the hp 9835A Numerical

Analysis package. This driver creates

Meas(*) & Q(*) for use by Estimation

and Diagnostic.)

! This loop needs only 4 sec. and retains

! the original data in one array. It's

! worth the memory.

! Odd rows of Data(*) go in R(*).

! Even rows of Data(*) go in I(*).

! Do the transform.

ounter)

)

! To process simulated data, remove the

! minus sign (if any) in the next line.

Counter)

)

nter)-l

! DC term

! Max. frequency term

Correct the signs of real & imag.

components of the spectral lines.

Pointer(Row)-l=harmonic #.

Jn(Row-20)=Bessel function for

the kth sideband away from 9960

Hz (k runs from -18 to 18). Meas ( Row , 6

) =SGN ( Jn ( Row-20 )

)

Meas(Row,l)=Meas(Row,l)*Meas(Row,6;

A-6
8020

8040

8060

8080

8100

8120

8140

8160

8180

8200

8220

8240

8260

8280

8300

8320

8340

8360

8380

8400

8420

8440

8460

8480

8500

8520

8540

8560

8580

8600

8620

8640

8660

8680

8700

872U

8740

8760

8780

8800

8820

8840

8860

8880

8900

8920

8940

8960

8980

9000

9020

9040

9060

9080

9100

9120

9140

9160

9180

9200

9220

9240

9260

9280

9300

9320

9340

9360

9380

Meas(Row,2)=Meas{Row,2)*Meas(Row,6)

NEXT Row DEFAULT ON FOR Row=l TO 38

! Magnitude

Meas(Row,3)=SQR(Meas(Row,l)'^2+Meas(Row,2)^2)

! Phase

A=Meas(Row,l)

B=Meas(Row,2)

IF A>0 THEN Phase=ATN(B/A)

IF (A<0) AND (B<0) THEN Phase=ATN(B/A)-PI

IF (A<0) AND (B>=0) THEN Phase=ATN(B/A)+PI

IF (A=0) AND (B<0) THEN Phase=-PI/2

IF (A=0) AND (B>0) THEN Phase=PI/2

Meas(Row,4)=Qr(Row,l)=Phase ! This is in radians, unordered.

Meas(Row,5)=Meas(Row,4)*180/PI ! This is in degrees, unordered here.

IF Meas(Row,5)<0 THEN Meas{Row,5)=Meas(Row,5)+360 Place phase

angles in to

360 degrees.

NEXT Row

0rdered=0

Check=(ABS(Meas(21,5)-Meas(20,5))+ABS(Meas(20,5)-Meas(19,5)))*.5

! Don't order the phase angles of the lines if not necessary:

IF (Meas(20,5)+18*Checl«180) AND (Meas(20,5)-18*Check>-180) THEN 10180

Order_lines: ! Put phase angles for sidebands -7 Ordered=l ! through 7 in sequence:

Sidebands -7 through 7 have a large signal-to-noise ratio.

This routine fits a straight line to the ordered phase angles for sidebands -7 through 7. It extrapolates phase angles to sidebands -18

through 18, to be used for ordering lines outside the original interval. Then, if an angle must be changed, it is incremented (up, if

the sideband no. is +, down if -) by 360 degrees. This continues

until the phase angle and its last value have bracketed the value

extrapolated. A comparison is then made of between (the original and

extrapolated values), and (the incremented and the extrapolated

values). The closer is the correct phase angle.

Note that only the measured data is used in the estimation of the

bearing angle. The fitting and extrapolation process is used only

to determine the correct number of multiples of 360 degrees to be

added to or subtracted from the phase angles of the sidebands. The

fitted values are not used in any other way; they help prevent ordering errors when a line's signal-to-noise ratio is low, as for lines

+8 and -8. FOR Row=21 TO 27 ! Order lines 1 through 7.

IF Meas(Row,5)>Meas(Row-l,5) THEN 8980

Meas ( Row , 5

) =Meas ( Row , 5

) +360

GOTO 8920

NEXT Row

FOR Row=19 TO 13 STEP -1

IF Meas(Row,5)<Meas(Row+l,5]

Meas(Row,5)=Meas(Row,5)-360

GOTO 9020

NEXT Row REDIM X(-7:7),Y(-7:7)

PLOTTER IS 13, "GRAPHICS"

FOR Row=-7 TO 7 X(Row)=Row

Y(Row)=Meas(Row+20,5)

NEXT Row GOSUB Plot_data

MAT Xsq=X.X

MAT Ysq=Y.Y

MAT Xy=X.Y

Mean_y=SUM(Y)/15

Slope=SUM(Xy)/280

! Order lines THEN 9080

-1 through -7.

! Set up X and Y arrays to do a linear

! regression on the 15 lines.

For diagnostic use. Squares of the sideband numbers

Squares of the phase angles

Products of (sideband times phase)

Mean phase

Slope of best-fit straight line

Totalss=SUM(Ysq)-SUM(Y)*SUM(Y)/15 ! Total sum of squares

Regss=SUM(Xy)*SUM(Xy)/280

Resss=Regms=Totalss-Regss

! Regression sum of squares

! Residual sum of squares

A-7
9400

9420

9440

9460

9480

9500 ! 9520

9540

9560

9580

9600

9620

9640

9660

9680

9700

9720

9740

9760

9780

9800

9820

9840

9860

9880

9900

9920

9940

9950

9980

10000

10020

10040

10060

10080

10100

10120

10140

10160

10180

10200

10220

10240

10260

10280

10300

Resms=Resss/13

REDIM Y(-18:18)

FOR Row=-18 TO 18 Y(Row)=Mean_y+Slope*Row

NEXT Row GOSUB Plot_curve

FOR Row=28 TO 38

IF Meas(Row,5)>=Y(Row-20

Value=Meas(Row,5)

Meas(Row,5)=Meas(Row,5)+360

IF Meas(Row,5)>Y(Row-20

\/alue=Meas(Row,5)

Meas(Row,5)=Meas(Row,5)+360

GOTO 9620

Residual mean square

Expand Y(*) to accept extrapolation.

Compute Y(*) using fitted line. None

of these values are substituted into

Meas(*); they are used for ordering.

For diagnostic use. Order lines 8 through 18; Row=row in Meas(*).

THEN 9840 ! Row-20=sideband number.

! Save Meas(Row,5) for comparison.

Add the first 360 degrees and test. THEN 9740 ! Y(sideband) has been bracketed,

! Reset Value,

Add another 360 degrees until Y(side-

! band) has been bracketed. Then pick

! the closer value.

Distancel=A6S(Value-Y(Row-20)) ! Test the previous value.

Distance2=ABS(Meas(Row,5)-Y(Row-20)) ! Test the current value.

Test=MIN(Di stancel ,Distance2) ! Select the closer of the two.

IF Test=Distancel THEN Meas(Row,5)=Value

IF Test=Distance2 THEN Meas (Row,5)=Meas(Row,5)

NEXT Row

FOR Row=12 TO 2 STEP -1 ! Order lines -8 through -18:

IF Meas(Row,5)<=Y(Row-20) THEN 10160

Value=Meas(Row,5)

Meas(Row,5)=Meas(Row,5)-360 ! Subtract the first 360 degrees.

IF Meas(Row,5)<Y(Row-20) THEN 10060

Value=Meas(Row,5;

Meas (Row, 5; GOTO 9940=Meas(Row,5)-360

Repeat subtracting 360 degrees until

Y(Row-20) has been bracketed, then pick

the closer value.

Distancel=ABS(Value-Y(Row-20))

Distance2=ABS(Meas(Row,5)-Y(Row-20))

Test=MIN(Di stancel, Distance2)

IF Test=Distancel THEN Meas (Row, 5)=Val ue

IF Test=Distance2 THEN Meas(Row,5)=Meas(Row,5

NEXT Row DEFAULT OFF

FOR Row=l TO 38 Qd(Row,l)=Meas(Row,5)

NEXT Row

RETURN !

Q(*) in degrees (since ordered'

Eventually, order Meas(*,4),

and convert Theta(*) to deg.

10320

10340

10360

10380

10400

10420

10440

10460

10480

10500

10520

10540

10560

10580

10600

10620

10640

10660

10680

10700

10720

10740

Fft:

K=0 FOR J=l

1=2

IF K<

TO No samples/2-1

o_samples/(2*r

K=K-No_samples/(2*I)

1=1+1

GOTO 10400

K=K+No_samples/(2*I)

IF K<=J THEN 10640

A=R(J+1)

R(J+1)=R(K+1)

R(K+1)=A

A=I(J+1)

I(J+1)=I(K+1)

I(K+1)=A

NEXT J G=.5

P=l

FOR 1=1 TO 10-1

G=G+G

THEN 10480

The "10" is the power of 2 equal to

No samples. See hp original.

A-8
10760 C=l

10780 E=0

10800 Q=SQR((l-P)/2)

10820 P=(l-2*(I=l))*SQR((l+P)/2)

10840 FOR R=l TO G 10860 FOR J=R TO No samples/2 STEP G+G

10880 K=J+G

10900 A=C*R(K)+E*I(K)

10920 B=E*R{K)-C*I(K)

10940 R(K)=R(J)-A

10960 I(K)=I(J)+B

10980 R(J)=R(J)+A

11000 I(J)=I(J)-B

11020 NEXT J 11040 A=E*P+C*Q

11060 C=C*P-E*Q

11080 E=A

11100 NEXT R 11120 NEXT I 11140 A=2*PI/No samples

11160 P=COS(A)

11180 Q=SIN(A)

11200 A=R(1)

11220 R(1)=A+I(1)

11240 I(1)=A-I(1)

11260 R(l)=R(l)/2

11280 I(l)=I(l)/2

11300 C=l

11320 E=0

11340 FOR J=2 TO No samples/4

11360 A=E*P+C*Q

11380 C=C*P-E*Q

11400 E=A 11420 K=No samples/2-J+2

11440 A=R(J)+R{K)

11460 B=(I(J)+I{K))*C-(R(J)-R{K))*E

11480 U=I(J)-I(K)

11500 V={I(J)+I(K))*E+(R(J)-R(K))*C

11520 R(J)=(A+B)/2

11540 I(J)=(U-V)/2

11560 R(K)=(A-B)/2

11580 I(K)=-(U+V)/2

11600 NEXT J 11620 I(No samples/4+l)=-I(No samples/4+1)

11640 MAT R=R/(No samples/2)

11660 MAT I=I/(No samples/2)

11680 RETURN !

11700 Estimation:

!

11720 Bad_file=0

11740 MAT Theta=Xt*Qd

11760 MAT Qr=(180/PI)*Qr ! Convert to degrees,

11780 IF Theta(l,l)<0 THEN Theta(l ,l)=Theta(l ,l)+360

11800 Thetal_2=Theta(l,l)+Theta(2,l)

11820 IF Thetal_2>180 THEN Thetal_2=Thetal_2-360

11840 IF Thetal_2>180 THEN 11820 ! Iterate if needed.

11860 IF Thetal_2<=-180 THEN Thetal_2=Thetal_2+360

11880 IF Thetal_2<=-180 THEN 11860 ! Iterate if needed.

11900 REDIM Jn(-18:18)

11920 Sum=(Qr(l,l)-Thetal_2)^2

11940 FOR 1=314 TO 350

11960 J=I-332 ! J=sideband number.

11980 K=I-312 ! K=harmonic number.

12000 Theta2_3=Theta(3,l)+J*Theta(2,l)

12020 IF Theta2_3>180 THEN Theta2_3=Theta2_3-360

12040 IF Theta2_3>180 THEN 12020

12060 IF Theta2_3<=-180 THEN Theta2_3=Theta2_3+360

12080 IF Theta2_3<=-180 THEN 12060

12100 Sum=Sum+Jn(ABS(J))^2*(Qr{K,l)-Theta2 3) 2

A-9
12120 NEXT I 12140 Sigmasq=No_samples*Suni/35 ! No_samples is fixed at 1024, in this

12160 ! program. The 35 results from using

12180 ! 38 lines in this estimate and 3 degrees

12200 ! of freedom when estimating Theta(*).

12220 Var=(l+Ck)*Sigmasq/No_samples ! Ck came from file "Xt ". 12240 Est_std_dev=SQR(Var)

12260 IF File<>File_no THEN 12320

12280 IMAGE "Data file" ,5X, "Beari ng angle" ,5X, "Si gmasq" ,5X, "Est. std. dev."

12300 PRINT USING 12280

12320 imGE #,2X,6A,8X,4D.4D,6X,D.3DE,6X,D.3DE

12340 IF Est_std_dev>=lE-2 THEN PRINT CHR$(132);

12360 PRINT USING 12320;Fi leS,Theta(l,l) ,Sigmasq,Est_std_dev

12380 IF Est_std_dev>=lE-2 THEN PRINT CHRS(248) ;"P0SSIBLE BAD DATA"

12400 PRINT CHR$(128)

12420 IF Est_std_dev>=lE-2 THEN Bad_file=l

12440 RETURN !

The routine belov^ is used to compute

and store Xt(*) in file "Xt ". To use this code, lable Xt_dim: must be enabled. In most cases, it is simpler

to COPY file "Xt " from an existing

copy.

Set up Pointer(*).

12460 Xt: 12480

12500

12520

12540

12560

12580 Pointer(l)=2

12600 FOR Counter=2 TO 38

12620 Pointer(Counter)=313+Counter

12640 NEXT Counter

12560 REDIH Jn(-18:18)

12680 Jn(0)=-. 174899073984 ! Jn(0) S Jn(l) are used in the following

12700 Jn(l)=. 0903971756613 ! recursion to generate Jn(-18) through

12720 FOR Counter=l TO 18 ! Jn{18), where n=15.

12740 IF Counter=18 THEN 12780

12760 Jn(Counter+l)=Counter/8*Jn( Counter )-Jn(Counter-l)

12780 Jn( -Counter) =(-l)"Counter*Jn( Counter)

12800 NEXT Counter

12820 Ck=0 ! Compute the constant Ck.

12840 FOR J=l TO 18

12860 Ck=Ck+J^2*Jn(J)-2

12880 NEXT J 12900 Ck=l/(2*Ck)

12920 REDIM Jn(l:37)

12940 MAT X=ZER ! Compute Xt(*).

12960 MAT V=ZER

12980 X(1,1)=X(1,2)=1

13000 V(l,l)=l

13020 FOR Row=2 TO 38 13040 X(Row,2)=Row-20

13060 X(Row,3)=l

13080 V(Row,Row)=l/(Jn(Row-l)*Jn(Row-l))

13100 NEXT Row 13120 MAT V=V*(2/No_samples)

13140 MAT Xt=TRN(X)

13160 MAT Vi=INV(V)

13180 MAT A=Vi*X

13200 MAT B=Xt*A

13220 MAT C=INV(B)

13240 REDIM A(3,38) ! Re-use MAT A. 13260 MAT A=Xt*Vi

13280 MAT Xt=C*A ! Re-use f-IAT Xt. 13300 ON ERROR GOSUB 13440

13320 CREATE "Xt ^^',1,3*38*8+37*8+38*8+8

13340 ASSIGN #1 TIT^Xt " 13360 PRINT #l,l;Xt(*),Jn(*), Pointer!*), Ck

13380 ASSIGN * TO #1

13400 OFF ERROR

13420 END 13440 IF ERRN=54 THEN RETURN

13460 BEEP

A-10
13480 PRINT ERRM$

1350U STOP!

13b20 Meds_print: ! Prints Meas(*) for diagnostics.

13640 PRINT CHR$(27)&"8ilOT"; ! Supress margins on perf. paper.

13560 PRINT "Code dtg: ";Rev$;". Disk dtg: ";Disk$;". Filename: ";Filename$

13580 PRINT File$J4" Nominal bearing angle-" ;Housekeepi ng(2) ,LIN( 1) 13600 IMAGE "Corn" ,2X, "Real ", IX, "Corr" ,3X,"Imag" ,X, "Bess" ,3X," Line" ,6X,"Rad-" ,7X, "Deg-

",3X,"Line",X,"Row",2X,"Row"

13620 PRINT USING 13600

13640 IMAGE "si gn" ,2X,"part" , lX,"si gn" ,3X,"part" ,X ,"si gn" ,3X, "ampl " ,6X, "i ans" ,7X, "rees" ,3X,"

no.",X," no.",X,"-20"

13660 PRINT USING 13640

13680 PRINT

13700 IMAGE 3D, 2D. 4D, IX, 30, X,20.4D,X,30,X2D.4D,X5D,4D,X7D.2D,2X,4D,X,3D,2X,3D

13720 FOR Row=l TO 39 13740 IF (Row<>39) AND (Rowol) THEN 13800

13760 S1=S2=J3=0

13780 GOTO 13880

13800 Sl=SGN(Jn(Row-20))*SGN(Meas(Row,l))

13820 S2=SGN(Jn(Row-20))*SGN(Meas(Row,2))

13840 J3-SGN(Jn(Row-20))

13860 IF Signflag THEN S1=S2=0

13880 PRINT USING

13700;Sl,Meas(Row,l),S2,Meas(Row,2),J3,Meas(Row,3),Meas(Row,4),Meas(Row,5),Meas(Row,7),Row,Row-20

13900 IF (Row=l) OR (Row=4) OR (Row=9) OR (Row=14) OR {Row=19) OR (Row=20) OR (Row=25) OR (Row=30)

OR (Row=35) THEN PRINT

13920 NEXT Row

13940 Signflag=l ! Prints CSGN's only first pass.

13960 ! They are meaningless after that.

13961 PRINT "Theta(*):"

13962 MAT PRINT Theta

13980 PRINT "&136T"; ! Restore margins.

14000 RETURN !

14020 Plot: ! Used for diagnostics.

14040 PRINT "(410T"; ! Supress auto feed at perforations.

14060 INPUT "Do you want a GRAPHICS dump? (Y or N)",Dump$

14080 Dump$=UPC$(Dump$)

14100 GCLEAR ! Kill this line for overlaid plots.

14120 LINE TYPE 1 14140 FRAME

14160 GRAPHICS

14180 Rmax=Dmax=-lE99

14200 Rmin=Dmin=lE99

14220 FOR Row=2 TO 38 14240 Rmax=MAX(Rmax,Meas(Row,4))

14260 Rmin=MIN{Rmin,Meas(Row,4))

14280 Dmax=MAX(Dmax,Meas(Row,5)

)

14300 Dmin=MIN(Dmin,Meas(Row,5))

14320 NEXT Row

14340 SCALE 2,38,Rmin,Rmax

14360 FOR Row=2 TO 38

14380 PLOT Row,Meas(Row,4)

14400 NEXT Row 14420 SCALE 2,38,Dmin,Dmax

14440 MOVE 2,Meas(2,5)

14460 LINE TYPE 6 14480 FOR Row=2 TO 38

14500 PLOT Row,Meas(Row,5)

14520 NEXT Row

14540 LINE TYPE 3 14560 MOVE 12,Dmin

14580 DRAW 12,Dmax

14600 MOVE 20,Dmax

14620 DRAW 20,Dmin

14640 MOVE 28,Dinin

14660 DRAW 28,Dmax

14680 IF POS(Dump$,"Y") THEN Graph_pri nter=0

A-11
14700 IF NOT POS(Dump$,"Y") THEN Graph printer=15

14720 PRINTER IS Graph_pri nter 14740 PRINT File$,"Code revision dtg:";Rev$,

14760 IF Ordered THEN PRINT "Ordered angles."

14780 IF NOT Ordered THEN PRINT "Angles not ordered."

14800 PRINT "Rniin=",Rmin,"Rmax=",Rmax,LIN(l);"Dmin = ",Dmin,"Dinax=",Dmax

14820 IF Sigmasq THEN 14880 ! False values for the variance and

14840 GOSUB Estimation ! est. s. d. will result if Estimation

14860 ! has already be done once. 14880 IF P0S(Dump$,"Y") THEN DUMP GRAPHICS

14900 PRINTER IS Printer ! Restore printer designation.

14920 PRINT "&136T"; ! Restore margins at perforations.

14921 EXIT GRAPHICS

14940 STOPlLpLp

14960 Plot_curve:

!

14980 GRAPHICS

15000 FRAME 15020 SCALE -20,20,Meas(2,5) ,Meas(38,5)

15040 AXES 1,10,0,0

15060 MOVE -18,Y(-18)

15080 FOR X=-18 TO 18 15100 DRAW X,Y(X)

15120 NEXT X 15140 PENUP

15160 LORG 1 15180 CSIZE 3.3

15200 MOVE .5,-15

15220 IMAGE 22A,D.DDE

15240 LABEL USING 15220

15260 LABEL USING "5A,14X,4D.4D" ;"Mean=" ,Mean_y

15280 LABEL USING "6A,13X,4D.4D" ;"Slope=" , Slope

15300 LABEL USING 15220;"Total sum of sq.=" , Total ss 15320 LABEL USING 15220; "Regression sum of sq.=",Regss

15340 LABEL USING 15220; "Residual sum of sq.=",Resss

15360 LABEL USING 15220;"Residual mean sq.=",Resms

15380 RETURN !

15400 Plot_data:!

15420 GRAPHICS

15440 LORG 5 15460 CSIZE 1.7

15480 FOR Row=-7 TO 7 15500 MOVE Row,Y(Row)

15520 LABEL USING "2D";Row

15540 NEXT Row 15560 PENUP

15580 RETURN ! 15600 File_list: ! Checks DAT files for bearing angle.

15620 PRINT "Code dtg: ";Rev$;". Disk dtg: ";Disk$;". Filename: ";Filename$

15640 ON ERROR GOTO 15860

15660 FOR N=l TO 100

15680 IF N<10 THEN Fi 1 e$-"DATOO"^VAL${N)

15700 IF N>=10 THEN Fi le$="DATO"&VAL$(N)

15720 IF N=100 THEN Fi le$="DAT"&VAL$(N)

15740 ASSIGN #1 TO FileS

15760 MAT READ #1 ; Integer_data,Housekeepi ng 15780 PRINT FileS;": Nominal bearing angle=" ;Housekeepi ng(2)

15800 ASSIGN * TO #1

15820 NEXT N 15840 END 15860 IF ERRN=56 THEN 15940

15880 PRINT ERRM$

15900 OFF ERROR

15920 END 15940 PRINT FileS;" not yet assigned."

15960 OFF ERROR

15980 STOPlLpLp

16000 Re_store: ! Called by key 20. Assures that program

A-12
15020 RE-STORE "VORl"

16040 STOPlLpLp

16240 Housekeepingl:

16260 MAT Housekeeping=ZER

Housekeepi ng( l)=Time_no

Housekeeping(2)=Nom_bearing

Housekeepi ng( 3)=No_measmnts

Housekeepi ng(4)=MedSurement

Housekeepi ng( 5 )=No_overloads

Housekeepi ng( 6 )=VAL(Rev$)

16280

16300

16320

16340

16360

16380

16400

16420

16440

Housekeeping! 7 )=VAL(Disk$)

Housekeepi ng(8)=Fi 1e_no

RETURN !

! is RE_ST0RE'd in the file identified by

! Re_store:.

! Used when data is first stored.

Date-time-group data were stored.

Nominal bearing angle, deg.

Number of measurements in the set. Number of this measurement in the set. Number of ADC overloads.

Program revision date-time-group.

Disk serial number.

Data file number (1-100).

16460 Housekeepi ng2:

16480 Housekeeping(9)=Theta(l,l)

16500 Housekeepi ng{ 10 )=Theta( 2,1)

16520 Housekeepi ng( 11 )=Theta( 3,1)

16540 Housekeeping(12)=Sigmasq

16560 Housekeepi ng(13)=Est_std_dev

16580 Housekeeping(14)=Processed

16600 Housekeeping(15)=Bad_file

16620 RETURN !

Used after data is processed.

Computed bearing angle.

See analysis.

See analysis.

See analysis.

Estimated s. d. for a large set,

If =1, data has been processed.

Flags files with excessive est.

32000 Disk dtg:!

32010 DiskT="8204231411'

32020 RETURN

A-13

Appendix B. Test-Data Listings

These data lists are abstracted from the "housekeeping" files of the permanent magnetic records

maintained on every measurement. The result from the processing of the raw data taken by the phasemeter ADC. Each row represents a single measurement of 1024 time samples at a given bearing angle.

Each block of five rows represents (usually) a set of five measurements at a given angle, taken over a period of about 32.5 min.

The columns present the following information for each measurement;

1. RUN DTG:

2. BEARING:

3. SET:

4. NO.:

5. DISK DTG:

6. FILE;

7. THETAl;

8. THETA2:

9. THETA3:

10. SIGMA SQUARED:

11. ST.DEV. THETAl

This is a 10-digit numerical representation of the date and time in the form

YYMMDOHHMM, where the first pair of digits is the the last two digits of the

calendar year, the next two give the month, then the day, hour, and minute.

This results in a unique number that identifies every measurement. It comes from a real-time clock in the measurement computer.

The nominal bearing angle set on the front panel switches of the standard

generator. The number is not used in the estimation of the bearing angle,

only in the calculation of the deviation between the setting and Thetal , the

measured angle.

The number of measurements in the set. The number of the measurement in the set. This is another date-time group having the same interpretation as the RUN

DTG. Is is recorded on the disk when it is first initialized, and becomes a unique serial number identification for that disk. It is recorded in every

data file on that disk and allows tracing processed results back to the

original raw data, for further study.

The file number of a measurement. It ranges from 001 to 100, and the cor- responding data file names are DATOOl to DATIOO. The file names (and numbers) are computed automatically by the software and allow tracing processed

data back to the original file.

The estimated VOR bearing angle. It is stored as a full-precision result,

without rounding.

The second angle measured by the phasemeter. See the equation for the model

for interpretation. It is a result that is not directly involved in the

final answer, but is useful for detecting certain system instabilities.

Note that it does not change appreciably from measurement to measurement or from month to month.

Similar to THETA2; see above.

An estimate of the mean square error in the voltage measurements in a single

bearing angle measurement.

An estimate of the standard deviation of THETAl, again based on a single

measurement. It is not the standard deviation for the set of measurements.

Usually, the standard deviation for the set is one-third to one-tenth this

estimate, which is therefore conservative.

J-1
o o o o o

I I I I I wlj u^ OJ Oj uu

Jl "-i P~ -O D

J- (Vl ^ J. (NJ XI p*- -n -T- -O B ^ J^ iTi o

f^ 23 —

O O

fsj O -^ J^ ^*

r- --\ r~- J- -^ ^ >r o -r !M

•f .n ,» 23 CD

•r -H >»• .o 13 .r i~> -o m -o

ro n^ f^ (^ fl o o o o o

I I I I I nun !? r^ -r

<^j o -r o o r~ O J^ tM r- J' »n ^^ m ^

x\ iri m

(NJ f^ OD O 23 S3

X^ ^ ^

a 13

13 O

J- >» J- >r ^

o o o o o

I I I I I _Lf ^ij UJ UJ OJ

r-l » >r -O -O

C^ (^ ^ rt rn O O —I o o

o o r- M ,»• J^ LTi m 00 o

>r -^ i-i o (M O fsj ^ .fj lf\ O r~ » -H CD

33 ^ ~»- -r N. ^ 1^ -o a -i ^ f^ IM O -H

o

1 I UJ LU

CM .O

r^ -a

r\ o

O ri

P- J- o -o

o o o

I I I LLl aj LU

3! ^ iTi -r -r -o in u^ ^.

J^ i-i O

» 30 o

in .n

•O T\ O"

-< Z> >H O I*! >r

•o m in T x> n

m mO

1 I UJ OJ

(O m O O

—

r» o o

m o

M O & m

o ^

in r-

'*> c^ m o o

1 I I LU UJ UJ

r- ^ ly

f<i JO ~r -^ -I o

^J OJ (M

-r ou oD a3 o OJ

•H o .o D ~0 f^ m O 13 P- (^ CD

o o o

I I I UJ UJ UJ

«r f^ »H O 23 CO ^ » ro

-H ^ OJ

in m rn

r» 33 p^

in r- m

o -^ >r

f^ ffi ® ^ (Ti .n

-r <r -*•

f<1 roo

1 I m <o D in s O

OJ O ^ IQ OJ O

P«- o

i> o

o o

I I UJ UJ

<3 in o O

0» m

-*• o

1-1 m

OJ .H

-o -r o rin •»•

f*^ ffl po o o

1 I I UJ UJ UJ r~ c> -r

fn -o O

•r o- o

fO -H O

D .r -n > o «

r^ OJ p~

ao f^ in ^ —< O

-H o P- m * ,»

O O

I I UJ UJ D in m OJ

-» .n

t> OJ

-H Pvn o

OJ .o m —4 m rn m o

o o o

I I I UJ UJ UJ m •-( p». m -r y-

~j- ^ o o o o

as n >r OJ ^ p- o -O -r

t-l -o P~ ^ 1-1 m

<0 -O «

O O

I I UJ UJ o o

OJ .n M !>

J- P*

J- OJ O rj O «o m o * en

M ro m

O O

I I I UJ UJ UJ

OJ CD O mom 01 f>- ^

OJ a- ^- ^ m in r- m -^

.-I ^- o

J3 -o -« O Oj 9

-O •H O

p- -r tn s ^ iS s s

o o

I I

J- ^ -r o o

1 I I

01 O

OJ a- M m

(sj m

O OJ n r~

OJ o^

i-n o P- m

33 -r in o

-o J^ -O ^ rO rH

r^ (s. <3

33 J- 33

-O O -4

r~ in ;^ -r —

I

-o O -^ O

O « o i> o

pn m m

o O

I I I OJ UJ UJ

r^ O 00

33 lO OJ

01 P~ J1

>r -r ^

o ^ D

X O •* T -<J 1-1 o o «

.-n r»l o

o m XN OJ OJ rj

m pn O O

I I

OJ o

-O P«-

<0 03

r>- m

s <o o w

« .n ^ pOJ OJ

-r *

o o

I ( UJ UJ

•O POJ in in y n o

CD *

03 O

O OJ O m

r\i p»

OJ i-< in IS

o o o

I I I UJ UJ UJ moo OJ 33 OJ O -< f\j m CT- .>

<3 P- O

OJ o -O

in o OJ o -< >r O P» >o OJ m >r P- OJ *

m m o o

I I UJ UJ

J^ OJ

O- --

x\ m

i-i ji -4 m

<? Pp«- ^

o o

p~ m

O 33 m *

o o o

I I I 'jj UJ UJ

33 O i>

-^ OO Pin -H o

J- m OJ O (? iH

r*- OJ o

o -H ^ O m -<

•* o .f B ^ in -^ m >»

m m

o o

I I UJ UJ ^ P^

in o

X o

in o

OJ o

CO o

o- ,*• .r 33 OJ 03

f-i «

o o o

I I I UJ UJ 'JJ y O -4

OD O -^ O m <y OJ o ^ m r« o

OJ <?• .* m OJ OJ

P~ c »

-O P» O

^ in in

f-t OJ M

m m

o o

I I UJ UJ

.n o

O O

(y -^

P- 13 CO tn

p- -o 33 m

^» ffl P» o

•r to ^ o

m m m

o o o

( I I UJ UJ UJ m ^ p» -o <o o

in j^ o

33 CO P- O P>- -H OJ (?. o

o m pI-* so o

i-< P-- -O

-o ^ m

-H o -H

m m

o o

I I

33 O

m 9- o CO m OJ O m

in 9-

•O CO O O

m rj

O o O

I I I UJ UJ 'JJ -O o m

ID OJ r-t OJ o m

-r m -^ m OJ ^

OJ rH p^ M O -O m in .-4 OJ o P". OJ in ^ m OJ ,H

m m

O O

I I UJ JU O r^

O- O -» O

33 O

OJ -O

(T- -^ O rH m OJ o -^

1-1 -^

m m m

O O O

I I I UJ UJ UJ m m OJ m OJ •»• m OJ m

o r- •» « p- -f rH P- -r

in OJ ^

(y m .H

.O in ^

m m OJ « « r.

m m o

o o o

I I UJ UJ UJ

33 P^ P- ^ * OJ

•r te\ tr\ 03 OJ m

>»• « p«- •r O' <-t m D OJ ^- OJ -^ P- CO * O o .»

m m

O O

I I UJ Ui

O' OJ

>»• r- m o m n

in in m ^

m ^

P~ 13 oj m o o

r-. r» p~ r^ r>- OJ <M OJ OJ OJ 33 P- C » CO OJ OJ OJ OJ OJ ^ <^ en en m OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ PJ OJ OJ OJ •^ ^ OJ .H

OJ OJ o o

OJ OJ P\J O O SJ

UJ JJ UJ iJJ UJ

p^ —4 fh m ^

vl- OJ O O O

1-4 m m

J1 OJ -O fH O 1-4 •o ~r <D (?(? o

OJ OJ OJ

m -4 o -o

J' >

OJ OJ r- N- ^• r~ ^• m rn m m m

PJ OJ OJ OJ OJ O O O O O

* +

UJ UJ UJ UJ UJ ^ 33 o o m

^ in 'O m ^

1-1 ^ 33 ^ O

in rH i> m CO

J> OJ O 33 -^

>r CP o -^ OJ

^. P» ^. 03 CO

P\J OJ OJ OJ OJ

p~ p~ p~ p~ p» m m m m m

OJ Oj O o

OJ 33 O m

O -o m m

03 1-4 ~i Pvj

OJ OJ OJ O O O

+

1X1 JJ UJ > m -^ O ^ P^

.-4 m o

P~ >»• O

in p~ m

•r ^ O

OJ OJ m

m m m m

OJ (\J o o

OJ (M OJ o o o

UJ UJ UJ m M m

O m F^

-4 p» 'ri P- -»• O

ly m m

CD O CO

-»• -r <r

1-4 m

«» -»• m -a o -o

-H r-

-»• -r m m

r- p«. r»- P- P» m m m m m

OJ OJ OJ OJ OJ O O O O O

* * + *

x\ p- ^ in .O p~ O -^ * m

OJ ,r » P" m

CO CO in <n o

O -^ ^- CO OJ m •* OJ m <3 OJ M OJ OJ OJ m m m m m

^. p. p- p» p- m m m m m

OJ OJ o o

UJ UJ p- r-- in lO p~ o

in m

•O CO

rj m

m m

m m

OJ OJ OJ O O O

UJ UJ UJ

OJ rH OJ

CD O •»• f <B 9- O 1-1 —4 o •r -f p~ m *

m m m

h- h- p- m m m

OJ OJ PJ o o o

-f LU UJ UJ o m o

m o ,H

p- in in

1-4 CO -o p» 33 o O ^- rH m tn >r m m m

O (T- m -H

-r m

J- -o -H m

.o ^- * -r m m

m m m m m

OJ OJ O O

+

UJ UJ

•o a> * ^- -H p» •H m

9 m o <M m ji m m

r» p- m m

OJ (SJ OJ o o o

* * *

UJ UJ iJJ o p^ m

-* CD o

» m ^

-» -r OJ p» w j> moo in in in p" p- p- m m m

OJ OJ OJ o o o

m » m

p- SP O

o m OJ

r-t X\ \C\ O CO m

o O m O r- «* m m ^-^ t^ r- ^

OJ PJ O O

UJ UJ o m

•o o

r^ m

33 m

•o -r m CO

o o o o o

+ +

UJ UJ UJ UJ UJ

J1 OJ --I o O

-J J3 1-4 OJ OJ

-^ m "H -o -H

vO -o -o in 33 O m -O P>- -^ -^ O fh o fh

j> ji j-i -»• n

ooooo ooooo +

UJ UJ UJ UJ UJ O CD -^ OJ O

a -c 9 9- x> O OJ o o iC o P» P- -H o

1-4 f~ o -H >» o s ^ o Pji ^ J^ <3 in

+

UJ 'UJ JJ UJ UJ

1-1 OJ nO CO o

h- rH CO m ^

-H ji c <o o

OJ ?• O m in

OJ j> o 33 in n in o 'n r*

p~ r«- P- P- P~

OOOOO + +

LXJ UJ JJ UJ LU m o ® in CO

33 oj h- p» o

33 o r>- o J^ m o P>- >0 •* O >^ -H 33 »

CO O -H .» rH

J- m XI n in

OOOOO •* +

UJ UJ 'UJ UJ UJ o o O CO

P~ .O O- JS o

o -r f- 9 X) ^. OJ o -o o

rH OJ PVJ o o

!D o o "^ f>

>r * .n r> «^

ooooo

UJ**UJ UJ UJ UJ

OJ m p" f\j m

P^ CO 'D O OJ

OJ PJ rH o m

m o -n in ®

m 03 OJ OJ m

m o ;> rH o

•O O in o O

UJooooo •'• UJ UJ UJ UJ O -r * P>- OJ

-M » p- ^. p»

<r OJ IS m rH » OJ 15 m m

m o » p^ in

>»• m rH m '^

•O -o -o -o -O

ooooo*

111 111 111 111 1 IJ o N- » o m

O P>- -^ -r -H

fvi OJ (M o m

* O (VJ ^ P"

-H »• p~ in o

o r- o <o o

-» >r in -r >^

ooooo *•**

lU UJ UJ UJ UJ ® m in p* O

O in m o *

lO m o in >o O rH rH * -H © CO in —* m

^- -H m 03 -^ o P- PSI >o p^ ooooo

p«. p. pw r^ ^. ooooo ooooo

p- f» p~ p~ p» ooooo p~ p- p~ f^ p« ooooo p^ fw p» f» f^ ooooo ^. ^. f- N. p^ ooooo ^. p>. p» r- p- ooooo ooooo ooooo ooooo ooooo

^ cp :> o ;> o ^ c^ ^ o 9 9 9 9 o- 9 o 9 v o 9 9 9 a- 9 O O i> » * J> o o * o o » » o * <f 9 <J- 9- f'

OJ OJ PJ J^ OJ rH -4 -J •-I 1-1 OJ Pvj OJ OJ OJ og OJ OJ OJ OJ rH rH rH rH rH OJ OJ OJ OJ Psl OJ OJ Pvj OJ OJ OJ OJ OJ rvj OJ pH •H rH r^ -< o o o O o o o o o o o o o o o O o o o O O o o o o o o o o o o O o O O O o o O o o o o O O

+ * + t * + * l * •* * + ^ * ^ + * * + * '*' +• > * + « * * « ¥ ¥ • + * *• *

UJ UJ LU UJ LU UJ UJ UJ LU LU UJ LU 'JJ UJ LU LU UJ LU LU LU LU u UJ UJ UJ LU LU LU LU UJ UJ LU LU LU LU LU LU LU UJ LU LU LU UJ LU LU

CO <o >r o ^ o OJ «r ^ -0 in OJ -0 J^ OJ m P~ r>- o m CO ^- f^ O m P- <# •o r«r in M m rH m OJ -o m <o m •o >r 33 •o O -O

OJ ^^ lA O J1 33 J3 O LO 03 <-» o 33 -H xO in -» o m m o p» m P" OJ o •o m o p» •O O -» o O o- in CO o p«- rH O o 33 *

o- ^ 3^ O ^ ^ n -f r>- P^ OJ 33 —4 >y o •*• 33 OJ D •O p>- OJ m o o p^ r- OJ rH 33 m •H CO rH f^ o- rH p- o- ~r >^ o p- o o

OJ 33 -r O PJ OJ o s 33 o •» m .n :> in •-H O CO CO m OJ m m o o o o p~ •o -r rH m o ^. m <o 0 O J-1 fH f-4 m OJ r-4 rH

33 PJ in o rH rH in r« rH o p~ rH o m m -o m •o m OJ » m *• CO -f •f m m •r * O fVI OJ m o m CO OJ m m O -r -»• m lO rH f»- •o PJ OJ CO p- a O OJ -H m o OJ o CT' rH o CO « r^ in m m -0 p- in <0 rH OJ PJ o p«. m o o OJ m 33 •»• *H •r -4 ,r m

O O ^ o 9- B -o •r m OJ CD p» 33 33 33 CO o o 33 (y rH OJ i> OJ CO 03 o CO O O 03 93 r>- CO p^ o o o o o (S m p- J^ OJ

Ji o- ^ p~ o >J o o o o o- J- a- <y O o » «> J' O 1^ 1^ o rH o a- o <r- sr- C^ O o o o ST- o o o o o a- o- p~ 3' <T- a- J> a- o J> o O o o o o- o 9- o t> 0» ij- o ^ ffi o o o O o ^ » .> o o a- o IT- o C o o o o o o- o r^ O- O

o ;? a- o 0- O O o o o o- ? 9- 0- O o o CP o- ly o o o o o IJ- o a- o o o- o J> o o o o o o o o- 9- a- !> O

^ in ji f- 0-1 o o o o o p- r^ r- p- P» -o 0 o •o <o o o o o o rH pH 1-4 ^ rH o o O o o o o o o- o 9- V? o- O O

m m m V m a- o- o v o rH —4 rH -4 rH PJ PJ OJ OJ PJ m m m m m rH -H —» rH rH OJ OJ OJ OJ OJ m m m OJ m in in m in in

-4 ^ m <r in -o p- 33 o m rJ OJ m •»• in •0 p^ 33 c^ o ^^ OJ m ^ in •o Po 33 o o rH OJ m •r m •O ^- CD o o rH OJ m V J> o o o o O o o O o o rH ^ r^ rH rH rH r-4 rH rH PsI OJ OJ OJ OJ OJ OJ OJ OJ OJ m m m m m m m m rP> m •r >r •r ^ -r «r o o o o O o o O o o o a o o O o O o o o O O o o o o O o o o O o O o o o O O o o o o o o o

in J1 s\ .n J1 in m in J^ in in X\ J> m m Ln J1 in J^ in J> in in •r\ T\ m in J> x\ in in J1 in s\ J> m in in J^ in ji m in in in o

1^ o o orH o

rH o o

rH o1^ OrH O

rH O O

-H O o O

rH o

-H o o

—4 o

-H OrH o

rH o

-H o

rH o•H orH o

-H O

rH o

rH orH o

rH o

1-^ o

rH O

rH o

-H orH o o

-4 o

rH o

rrH o

rH o o

rH rH o

•H o orH

•r

-H H rH

-r rH rH rH rH rH

•r rH rH rH rH rHJ- rH -H rH rH rH rH rH

•J- —1 rH rH

J- rH r-l rH rH <H •-* rH .H rH rH rH

rH

-H HrH

OJ

-H

—4

OJ-^

rH

OJ

rH

OJ OJ-J

—1

PJ

-H OJ

.H

OJ OJ-H

'H

OJ

rH

-H

OJ PJ-HH

OJ^^

rH

OJ-H

rH

OJrH-H

OJ OJrH

rH

rJ

rH

OJ

rH

OJ

rH

f\J OJ

rH

rH

OJrH

—4

OJ

rH

OJrH

rH

PJrH-H

OJ-H

rH

OJrHOJrH

•H

OJ OJrH

rH

OJ-H

rH

OJrH

OJ

rH-H

OJrH rH

-H

OJ

rH

rH

OJ OJ

rH r-< H rH

OJrH

-H

OJ

r-H -H

OJ

»^

-4

33 X D -D X S> S S S X CO X X X CO X X X X X 00 (X 'T^ fy? OO X X X X ^3 ^D ^D CO CD CO CO CO ^0 ^^ ^S CO ^0 CD QD iX

-H OJ m -r Xi f^ OJ m -J- J-1 r^ OJ m >r m ^ OJ m >»• J^ ^^ OJ m -* XI -H OJ m .*• XI ^H OJ m -r Xl f-M OJ m J- XI rH OJ m •f XI o O a O O o O o o o o O o o o O o o o O o o o o o o O o O o o O O o o o o o O o o o o o o

o o o o o o o o o o o O o o o O o o O o o o o o o o o o o o o o o o o o o o o o o o s o O

in m ji in J> m Xi n in J-1 n in in in XI in x> in XI in Xl J^ Xl x\ Xl Xl Xl in XI Xl Xl Xl Xl in XI ji XI in XI Xl in Xl Xl Xl Xl o o o o o O o O o o o O o o o o o o o o o 3 o o o o o o o o o o o o o o o o o o o o o o o

o o o o o o o o o o o o o o o O o o o o o o o o o o o o o o J o o o o CJ CJ o o o o u o o o

o o o O o o o o Q o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o

o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o

o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o

o o o o o o 1^ o- a- 'T 33 CO 33 33 33 Pw p^ p~ Prr p- m m m m m OJ OJ OJ >N( %l -H •H rH —4 -H o o o o o -o o o ~o o o o o o o o o o o o rH >~t '-' <-i -« OJ r\J OJ iNJ OJ o o o o o rH rH i~i -H -H OJ OJ ^J OJ OJ m m m m m o o o o o

u^ o XI u x\ o „, p- m J- m 33 -r f* r- m 3- iil ^ p- Xl f^ p~ m o OJ 33 •f rH p- Jl OJ 33 XI f\J 0- m O o» -» Xl -> 33 Xl OJ

,-i -»• o m A-1 -H -r o f^ LTl OJ J- -H J- o OJ -r rH •f o •H •r o m in m x^ OJ n r-* Xl OJ ~r —4 >r -H >» f^ n o Xl 'M -r .H -r o o -n o n ^^ r^ ~r o -a -n :> o ^ -f •r ~> P~ m o w4 p* >r O ,o j> -H 33 -J- —t p~ •*• o N- m 'y n OJ 33 Xl > >0 OJ o n m m •T J- ji rH rH r\J m i-n xi in o —4 -H m ~r >r Xi o OJ OJ m J- .» o -4 1^ OJ m o *-* OJ OJ m -r j"i O o rH -»• XI o a rH

33 33 33 CD 33 c^ T a- ^ o- CT- o- o o o O o o O -H rH .H -4 -H rH OJ Oj OJ OJ OJ m m m m m m m .* J- -f >r J- a*^ XI Xl O -3 O o o o o o o O O -> rH -4 ^4 -H rH -H <H -H rH -H -^ —4 -H w~i ^M -H -H —4 —4 -H —4 -4 ^^ -H —4 rH -4 -H —

H

-H —4 rH —4

~r J- J- -»• -r J- -i- >r J- •r -r •T J- ^ J- J- .r ~J- ~r >r nT -J- nT sT -r T r -r J- •r nT ^ <r J- -r •>» -T T J- r >» J- -r J- >» J o o C3 o o o o CJ o o o o CJ o o -3 u o o o o o O o O o o o o o J o O o o o O o o o o o o o

m -n .-o m -o m m rt -n -^ m -n rr m m ^ ^ i-n rn m m m rri -n .-01 m m m pn m -ri m m m m m m m m m m m m m m o o o o o o o O o o o o O O O o O -3 o o o o o o o o o o O o o O O o o o O o o o o o o o O

OJ r\J OJ Oj -SI OJ .\J ->J .-\J OJ OJ fNj Om ^ OJ OJ ^J OJ vj !>J OJ OJ OJ OJ <% OJ %1 OJ i\j OJ OJ OJ OJ •Nl OJ ^ ^ rM OJ OJ -M OJ OJ OJ OJ

33 3) 33 33 33 33 CD 33 CO CD 33 33 33 33 33 33 33 CO 33 33 CD 33 s 33 33 33 33 33 33 CO 33 33 33 CO 33 33 33 S3 33 CD 33 33 33 33 IZ>

B-2
fn fT*) ro fO

m o o o o o I I I I I -H t— O O rH -< o o r>- -O lA -H o ao c^

<T) 33 0>

U-> ^ O

PJ ^ ^• O ry. fH) (VI <M

ro «f JD CM O -O

-*• >»• fO >» r~ CD fM -o ^ m

oo o

<*> fo <^ o o o I I I VXI LU LU

r^ CM -o o -r ^

r- o ^

C\J if! fO O iTl o

-< o m

>0 tM ^

,r -I sT

«r -o >r m u nj

in -» •* o o I I LU UJ ^ iTl o in

in ppo o D •»• O ro —

x>

ro in

inm

<^ Cf^ Cfl O O O I I I UJ UJ UJ

CD *o in in vO ro •n r- ,D m -( o O in .> -^ O CD O (M O O f> -J- t\j in o

-r .J- r-

-* nT ^ m i-o o o I I UJ LU m CO r- o O CO oj J- m ^

3J <M

r- -o

'^ -r

•O ru

ro rno 1 I UJ UJ

a> as ^ <M

ro

O

ro o o r~

>-) £> CO 4- in m

(T- ^

.-1 rg

fO ro (n o o o I I I UJ UJ UJ

,o -o in

(\l -o ^ O ro ^ O O OO

-r -o in

>o «r .o

rvi r- ro ^ ^^ ^-

ro fo nO

rvi r>-

W

-J- -J- -r J- * o o o I t I UJ UJ OJ

r- J- o O -^ -r CO -^ .»• (C * ro

in o >»

fVJ r-« CD

<D (> (M

OOI I UJ UJ m ro

-H P«

in in

in rvj CO O ^ PCO p" ro rM r>- ro r~ pj

•o ro p~

-O ro ^

r- ID

oo >»•

a

UJ

ro • • -^ •

<-< • •—4 • • • •H •

i-H •

1-H • rH ••H •CM •PJ •IM 9 •PO • CD •OO •00

m

m CO CO

ro ro ro ro ro CM ro (*> ro ro ro ro ro ro CI ron ro ro ro -r •r -»• J- •*• o o O o o O O O O O O o o o O O o O O O o O o O O

UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ uu Ol UJ

(O OJ r- CO CM f>- cs o> -H

O >*• CD o o- >«• P- o o ro o -* •£> -o

OO

CM -r o 1-1

O CO o o PO o o O- -o •o <y ^ •o o oo o P- x> PJ oo o O P- CD >r CM f-H iX> -o in o -r p- o ^0 in •T o m -O CO <o ro p- rvi r*

43 £7- -r o tT- ro .-» ro o o -o

O in in o .n p- roO p- .» •4- o o ro

r\j oo CD

n O) •-H .*

O r«. •r pj o- >o PJ

r

m in * PO o -o ro 3J in PJ

Tjm

—(

ro 00 -r rH ro PO CM in 3> o- •O o fO PJ <o I^ r- in PO

O o >o

in r-t * rsi ro o -o oo ro

O r~ o ro f~ o <o ro ^n CO o CO v-^ CD f-t —1 o r* ty r-l O o 3> •r •O r^ S5 ^H -O o o -o p- o rH p- PJ O r~ (M PJ

CO >o o <D rM o ro iH

O ro PO •r ro o PO 3> PJ PJ a> PO <o ro (M o *

in r» r~ .»

O CD -r o J5

O

H (M PO r^ 'O c> PO PJ 0> o PO •o o -H rH

0>

O o o o O <M o O

O rH iH PO -H o <o r-tO p~ a- 03 o PO

O PO

-• rvj •M r-t rvj CM CM rM PJ (M PO PO PJ PO PO -»•

n in J- •r p- p- p* 00 t*.

•M CM rM CM <VJ (M <\J IM PO (M PJ PJ PO PJ PJ PJ PJ PO PJ PO (V) PO PO PO PJ o o O O O O O O O O o O o o o o o o o o o o o o o * + • > * + +• »• • •• * ¥ ^ • *

lU UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ O rM f-t -o o N»- •o <J- -»• ~»- -H o lO •r ^ p- a- o (O ,-> o> >r * o> po« ^. O .o p- CO ^ O •O >* PO PJ ^ ro ro r~ ro o PO m PJ PJ p- -» o o -o CO *• in m ro ro 9- (H o CO o ro •O •o in -H (O CO o ro ro ^ CO m <\i —1 o- r- r>- -»• oo <D in fH o PO in O o -r CD o O PJ O in o o O ro o in oo CM ro -^ •r ^ in o -H p- -» in <o rH fH O- o O PJ (o >r O ^ •o >o CM O -O O ro •H in p- —t o OO fO •r ro PO rO ro * -r <D (O •r * -r -» <»• ro in in -r >r in in in -r *• PO ro ro ro ro ro (O fO ro ro

ro CO en ro ro

O CM (VI (M pij pj rvj PO PJ PJ PJ PJ PJ (M PJ (M PO PJ (M PJ

P- f>- p«. r>- P- «» r>- r- h- p- r>- r» p- r- r» r>- P- p~ f^ P". P- p- r>- P» Pro ro • • ^ -4

CO

r*4•

f-l

ro

r-l

ro

rH•

-<

ro•

ro••H

ro

-H•H—1

ro-<•

-H

(O

rH•rH

ro•H•

i-t

-H

ro•rH

ro

r-t•rH

rH

ro

<-*•

-H

ro-H•rH

ro

r-l•rH

-4

(OrH•

-H

rorH•rH

rorH•

-4

ro

rH•rH

r-t

rorH•rH

rH

rorH• rH

-H

rorH•

r-\

•-<

PO ro

rH ,-4 • •

r-t r-t rH rH o o o o o + ••

UJ UJ UJ UJ UJ

,r p- ro -O o

PJ ro ,o in PO p» « O m ro O (O m in ^

p* in ^ in rH

in »r •» * pin in in u'^ in o o o o o o o o o o o o*•o o o

UJ UJ UJ UJ UJ

in ^ p- o P-

-H rH 23 03 oo 'O oo O PO <o

00 -O p- P-

(?> rH ^ PJ

W

O CP -H rHO

in in >o o o O rH -H rH rH

,o P^ P~ P~ P- o o o o o o o o o o o o o o o

•• + +

UJ UJ UJ UJ UJ O rH -« * >»• in p~ PO -O CO o oo in o PO o in m o PO

rH ,^ o o p~ o p~ >o O P- O -O O P- o

rH -< -H rH rH

P» p. p. P- p» o o o o o o o o o o O•+•• D O O O

UJ >JJ IXI UJ UJ p" * O in -H

in ^ m >o ^ O CO O- oo -H

PO in t^ >»• p-

<j- 9- •*

m f^

.H rH ro

O PJ

in

m in -^ in

p- p~ p» r^ r^ o o o o o o o o o o o o o o o + •• UJ UJ UJ UJ UJ

•* o <\i o <y- ~0 rH ^ 33 P~

rH ^ PO

O ro o .o o o <o (O PJ ^ m rH

ro ro PJ PO in in in in in in rH rH -H -( rH

P«. p. p. p. ^. o o o o o o o o o o • •

a- (J- • • • • m • • • o (y o • • • o • •a- • • • •o • •

<y • • • •

PJ PO PJ PJ PJ PJ PJ PO CM PO PJ PO PO PJ PJ PO PJ PO PO PO PJ PO PO PJ PO o o o o o o o O O O o o o o o o o o o o o o o o o * • + + >• * * * * • ¥ -^ * * + V ^ + * 4' UJ UJ UJ UJ UJ UJ OJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ O ro -O PJ o o o O rH O nT PO PO O -O PO in 00 ro <o -o oo PO ro PO

-O in o -*• o o o CO

O 00 •r o o ro o ro o rH P- PJ o o m -A rH

-» o P- o ts in o ro

m PO o p» oo -» -o

m -n o- rO o r4 o m o o

•r o Jm >»• -o

m o -*• o >*• (7- ao ID r^ oo o P« rH <o 00 ^ ro J- pPJ PJ O- PO ro p» in O 00 o PO PO ^H PO p- p- ro 00 CD p- en ID m r~ o

rH ro rH P- PJ o ro rH

O (7- •H <oO -O o o CO rH ro oo >o rH -o p~ prH -H -H O —1

pO rH

OO o o o o o (J- CO <f i> CO o <yO o o o o o o O o o o o o o o <? o o o> a- <y O- o O" o o o- o o o o o o o o o o o o CP o o o o r> o- o <y o t> a- o o o o o o o o o o o o o <? o- o o <7> (y o CP J- o 0» o 1> o m in m m in m in in in in * ro ro PO •r PO PJ PJ PO PO m m in in m

rH rH rH -« -H rH rH rH rH rH (M PO PJ PO PJ ro ro ro PO ro ro ro CO ro ro ^ p- T) O o cy PO ro ^ in o p- oo o o -H PO ro ~»- in •O r^ CO O O

3- •*• J- -» in o- XN in in in

m j> in in o -o

O o o •o yO o •oO f^

O

O o o o aO o o o o o O o o O

O o o o o o o o o o

in in in in in r< in

m in in in in in in in in in in

n in in in

m in in 3

rH o

T~4 o o

—4 o

^H o OrH

O

rH

O

rH o

rH o*-*

O

rH o OrH

O

rH

O

O

rH -H o

•H

O

O

rH ^ o

r-4 orH o

rH o

rH orH

rH rH rH

JrH -t•r rH rH rH rH rH rH

•r rH -4J- rH rH

-*• rH rH

•3- rH rH rH rH rH rH

J- rH

PO

rH

•H

PO

rH CM

—4

PJ—4

-H

PJ

-H

•H

PJrH

rH

PJ

-H

-H

PJ

-4

—4

POrH

rH

rH

PJrH

rH

PJ

rH

PJrH

PO

rH

rH

PJrH

PJ CM

rH rH

•H rH

M

rHrH

PJ PJ

rH rH

'-t rH

PJ—1

rH

PJ

-H PO

r<4 PJ

rH

—4

PO

rH

rH

OO OO CO CD 00 CO CO 00 CO CO ^ ^3 ^D CO GO OO OO

® CD 00 GO CO ^3 CO 00

rH ^ ro J- in rH PJ CO .»

n rH ro ro ~J- in -H PJ rt3 .*• ^ —4 PJ ro -»• J> o O o O o o o O o o o O O o o O O O O o o o O O O o o o O o o o O o O o O O o o o o O o o o o o o o

in in J^ in

m in in inm in J->

m in

m in in in in

m

m x>mm in in o o o n o o o o o o o O o O O o O o o o o O o o o o o o o o o o o o o o o o O o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o 3 o o C3 o o o o o o o o o o o o o o o o o o CJ o o O o o O o o o o o o o o o o o o o o o o

in in inn in in x> -n in ^ ^r >* J- * J- ro ro ro ro ro J3 -o o o -o

'-< -H -H •H rH rH rH rH rH rH PJ NJ PJ PO PJ ro CO ro ro ro ro rO ro en PO o P- m ro o o in rH -o rH o -o ro o p- p- in PO o oo ro o to m PO

in —4 -r —4 >r —4 ro o PJ jr, o PJ -n PJ .r in CM •n PJ •r PJ

m rH >r -H o p- ro o t> o O ro (T n -H p- ro o -o —4 ro J- —4 p* n rH :t3 >r rH

ro ro -1- in

n o O

H -4 PO -J- >»• in o o PJ PJ rO -J- -J- ^4 PO PO ro ^

ir.n •n

n j^ p- P- r^ P- P- r^ p» p- CD

a CO x> X) CD CD o o aO rf

H rH rH rH rH o o o o o o o o O

O

O o o o o o o o o o

>r -r

T >r J- in Xln in

n in inn in j~\ ^ n ^ n in in in ^ n in o o O o o o o o c-3 o o o J o 3 o O o o o o o o o o

CO ro ro ro ro ro ro ro PO

n ro ro ro ro rOm ro rO rO ro ro ro ro ro ro o O CJ O O O O O o o O O O O O o O O O O O o O O O

PO PJ PJ INI PJ PJ PO PO AJ PJ PJ PJ PJ PJ CM PJ OJ PJ ^ PO PJ PJ fVJ PO PO D CO ID ro OO 00 CO CO CO oo CO CO OO oo ID CD D CD -o CD <o 00 D oo CO

B-3
3 * J- >r * * ro CO fO CO CO ro en ro ro ro ro <n o^ en en ro ro

m ro ro ro ro

m ro ro ro ro en

m

m ro ro ro ro en ro

m ro CO ro o o o OO O o o o o O O O O O o o o o o o o O o O o O o O O O o o o O O O O O O o O O O O

LU UJ UJ UJ Ol UJ UJ UJ UJ Ul UJ UJ UJ UJ UJ Ui UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ LU UJ UJ UJ UJ UI UJ UJ UJ UI UJ 'U UJ 1 1 UJ UJ O m -^ >-) r- >r o (SI m o> O * O- p- <o CO r- f>- (^ r- •o >»• CO r~ m o rH -H o o CM o o CO CO ro 00 ro ro ^ f^ rH f^ O O

o> o l*>

m o * o O ^ r«- ^ m •-I •r •r ro •r F-« o 00 CO o o lO ro o -o -H

m ^r <o >r rH -1- CP ro P- OO iM ^ CM -H P- o -t

ir> in o J" o in o O OO

m fM r«- ro CM •o r-* P- -»•

O CO r- —^ p- in

O

m o -»

O rH OO -H * <o -4O ro

D (NJ JO *• •» CM ^

GO fO <jm o cy o m -o in cn in » <D o ^- .* CM ^ o rH rm rH p» in 1} -H (M •»• CT- r^ P- <M rH >r

O in (M in f-t <NJO en OD ^ j^ m f-« <o r-^ r» f- -r -r r4 ro -r r^ -r oo * CM o ^ m in >-i •o CO r*" o m in -o O fj- >r r>- o o> >r p- O OO O ro in O ^

rom r» .D <D -< rm CM c^ •r o •r <D 9 •* * ro rH ro CO o CM OO o ro CM o r^ in o •o 03 CM p> rH o fO -r !> -o X> -D

m in rH O o r^ r4 o rO t- >»• ro CO •o m o in <o rH o en in ^^ in ro CM -o o (M nO r- >o * o ^ (M ro CO in in CM •r ^ o O ro ,o

<SJ

O « -r r- -»• (SJ N. CVJ i-t (*» in

m CM OO * <x> o o o (NJ ro

O o •r in o o pw ID f^ CM f»- (MO P- •O -H PD 00 03 ro rH in

<\J o m

m fO OO <\J a- o ID en o CM ro >r <r ro en rH -r

w CO -r ro o •o (M o o ro CM P- 3> rH P» in o CM CO CD r* .»• OD CM in

in OD rH CVJ

V .H ^- CM fO in in in •oO CO <j> rvi <s r~ <0 r- CM rH -*• »H CO •o o aa o> 00 -o CM o OO rH rH P- * ro en est

O CD o (\j <-> in in r- ro ro ro ro ro <o in in in m >r m ^ ^ -r in in «n in in r«- f^ OO r>- p» in in 0 -o in O o •O •o O o O o o o

O". o i> o oo evj <M CM CM CM fH i-» -H i4 pH ^ rH iH rH rH rH rH rH -H rH rH rH t-» -H rH ft •-I -4 -H -H f-4 ^ ft •H rH rH CM (M -H rj

.* •*• >r J- -r <o fO PO ro ro ro ro ro ro ro ro en ro ^y

m ro ro en en ro ro en ro ro (n ro ro ro ro ro ro ro rO ro ro

m ro ro ro ro o o1 1 oI o1 o o o o o 1 t o o o o o 1 I o o o o o o O o O O o o O o o O O O O O O O O O O o O O O O

IXI Ui tu UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ 1X1 JJ UJ UJ UJ UJ UJ UJ UI UJ UJ UJ Ol UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ ^ -o -o o o r- »H ^c*» <o en r-C r- p- CM m O -O -O f» ^^ in CO in (NJ ro rH -* ,^ en CO * •H O P- P- f^ (y O in -» en o o o

-H

O o <\J <N» '^ e- -4 (O •o •o

O IS ro CM (O P- ^-

O CM •o in •o o (M

OO rH <> ^ CM -* P-.O f^ o •o CM « p- a- <o ^ 33 CD

O rt o o CO f- ro ro ^ •o »H in -o CO ro o rH ^ CO ro o <o o -r r- (M * o CM OO o O- t^ 'H ro ro •* r-^ in OD •fO in en ro o m M <o <M CM P- CO <\) in •r •4- 'H ro r» r- « o » .-• en ro o >r o <M t^ »H P- -O <?• rH CM CM *• o o rH O ro •T wM <NI p- ro

-O r- h- o f* •-•

m •Om o !-• OO CT P- CM o in o P- -H ^ en

M CM (M (M P- o> •3- eor 03 p- ro in o o rH !> o O ^H .»•

O ^ m f^ -I « •H * -o r«- * o pH CM ro •O «r o f>- CM CT- <J o -o o O -H OO oo (O -H P~ CM (M rH CM r-t -r O CO (7- in ^ -H x> O in

(y o.

mm r» C^ r» CM fO fH o r- r- o ro CM en * rH O- o rH ro

O i> rH in roO CP * O ro

O in (M •oO >r <o i-t C> o •O i^ -H o ^ o m >-l * « in f* ro -O o •o o •^ rH •« r\j m OO (M O O O o ro O -» ro ^ >»• rH rp o ro •o r~ p- p- en m -H •o in r- o o * •o •-I ^- •r o <y r- CM (J> (M •-) O (> f- rH O ro ro 00 w P- (M * <M * O in in in -» <D fvj in o rH (D in .n .s -H o

o- ^ (T- fH

m o r-l rHm

r ^ •r r*. OO in •o in <n o <I3 ro r~ CM -H ^ 4-

m

O in « * o o o m in en

r o (M

—1 o 1^ 3> -o • • • • CO• • • in in • • • • • • • • CM• en CM CM rH • • • • in• ro• ro• •

ro• CM• rH• CM• CM CM • • in• • •o• • • o• • 33•

p-• • OO• rH• o• o^ o• •

00 00 ^ ^ r^m in in

mm CM CM CM CM CM CMCMCMCMCM (NJ(MCM(NJfM en (n en en en (M (NJ CM (M CM CM CM CM CM rM en -r * ro J- CMeMCMCMCM CMCMeMCMCM CMfMCMCMCNJ eMCM(M(M(NI rMCVJCMeNjeM rM(M(MCMCM CMrMCMCMeM CMCNICMCMCM (NjevjCMCMCM OOOOO • OOOOO OOOOO OOOOO OOOOO OOOOO OOOOO OOOOO OOOOO +4'^«^ > > «>4''»> >>>^^ ^^H-i^^

UIUJUJUIUJ UJUJUJUJUJ UIUIUJUI'U UJUJUIUJUJ UJUJUIUJUJ UJUJUJUJUJ LU'XJLUUJUI UJUJUJUIUJ UJUJUJUJUJ cM«rP»rHO rocO'OrH'O mo**^ O o- o -o ^^ «^min,op«- -ooeMrHro mo-omcM om^i^in p-o^rrocM o •*' -^ -o •* c^^mroin <oin<rino rHro-^-TrH •hocmp--*' ro.r^'-oro oomp-cM roro>r(Min p-in<naOrH ao>r<oo>n ^rcMOino enino*(» cn-oocMCM >rM(Mp-cM op-oroen j-ct-ooo oo(Njroen rHomrH^ ©rHf^Bin mrHincMin co<rcMCMtn om-j-CM-r cmp-woo rHin»o-r >»-ro.rcno p-OrHp»o «ina--o«

>l-0'OCMO roo>®«»-0 rH^CMP-en cMropjaj« CMl>0^•-^• r^rOrHcoro ooOO<»-P~ cneMroorO cMP-roeMCM ©•^fo^ro p>cO'«<oco r»OP»om ocMinoo rHro<yin>r ^mrHCMr^ -^inrnmo -oo>rp-ro p»cMP-cncn *encMrH.^ ooo^o »0000 o^ooof*- oop-o-oo mmmmin p-r^p~<o-o >oo-o-OP» minmin-o

CMCMCMCMeNl CMCMCM-H-H ^(MrHCMrH CMrHrHrHrH rHrHrHrHrH fl ,-4 f4 r-t r-i rH-irHrHrH ft ^ ^ ^ ~4 ^ ^ r^ —t -t enencnencn encnenenen enencnenen enenrocnen roroenenro rorocoenen enromenen enenromm eo(n(nro(n

OOOOO OOOOO OOOOO OOOOO OOOOO OOOOO OOOOO OOOOO OOOOO ^ ^ .^ ^ * 1^^^^^ ^4i««^ >>4i^^ ^^^.^^ 4.^^>4. ^>^^^ >^>^> ^H-'^'^'^

UJ UI UJ UJ ui UJ UJ UJ i^ UJ UI UJ UI UJ UJ UI UI UJ UJ UJ UJ UI UJ tJJ UJ UJ UJ UI UI UI UJ UI UJ UI UJ UJ UJ UJ UJ UI Ul UJ UI UJ UI ^•^-^enrH OrnoO® P-CMro^-O »CM-OCM^ (MOO-^* c\l ft if\ O -r ^inomo P~.0*OrH c>^-!X>inro CMrHroo-*' cMOOooO coom-*-* oinoomro rorMO-Hoo .y^oo-OO ro(NjP-** p-«inino roroocMO

•TrHO^P" wOCMinO <x30P"in-0 oo»oo^ coaorH<M-H p-ininmin oop-<^ro-H ooP-mcvi* -^^-ro^-0

inoocorHin P-Oro^•9 rHOmmm p»oooroen rnooo^cNi p~oom.ocn o- ft c\l •* ^ cMOm^oo P-.OJNP-P- -H*IDrO« OinOOCMCM OrH-O-OP- CO <\t <D O -T 0*.OCM^ OO'OOOrHP- rOP-.TrHrH rH-o-Oinco (MtnOinio

rHenNTCMrH in^p»co>0 •*

a

O <y •*• h»N-Oinoo O' O- ir\ -o -r O0ln^0ln oomom (NjrM-nOrH m^oo* o<o<o>o<o inmminin om^om-o <#«r>*--''-«' <o<o>0'0<o >r<r<*-<*--*- minminm mininmm ^-r>r<r<r ooaz

Of

rH -H

f^ P» O O

rH rH rH

P«. P« P" O o o

rH -H

P» P» O O

rH rH rH

P« P- ^ o o o

p« p. p> p.. p. OOOOO

rHO

ft ft ^ ft

p. pw f^ p- o o o o

ft

P~o ^ rH p- r^ o o

rH fH

P- p. o o

rH ^ o orH rH o o

p»o

rH

P-o

P"O

rH

P»o

rH .H

p- r^ o o

rHO

rH f*

P» P- o o

ft rH

P- P- o o

p-o

ft ft

P- P- O oP- P» O o O O o O O o o OO o O O O O O O O (3 o o OOOOO o o o O o o o o o o O o O o o o o o o o

<y <f o o o o o o o » o » O

O o o- <y <?• <y cy <y <y <y o o <y cy o ty ty ty ty ty ty ty ty cy <y o o> cy ly

O ty CP

CM CM CM CM CM CM CM (M pg CM (M CM CM CM CM (M (M CM PJ CM ft rH rH rH rH PJ CM (M CM CM PJ PJ PJ PJ PJ PJ CJ PJ PJ CM ft rH rH rH rH OO o o o O O o o o o o o o o O O o O O o o o o o OOOOO o o o o o o o O o O o o o O O * ^ * * * •• > f * * A- > * • • 4' '^ '^ UJ Ul UJ Ul Ol Ul UJ UJ UJ Ui Ul Ul Ul Ul UJ Ul UJ Ul UJ UJ UJ Ul Ul Ul Ul Ul Ul Ul UJ Ul Ul Ul Ul Ul UJ Ul Ul Ul Ul Ul UJ UJ UJ Ul UJ o -o o O in ^. * * P- en CM -O en O » <o -r PO * O f^ O O m rH rH fO r- rH ro a- * (D ty OO -» O p- OD ro .0 •»• ft 00 <o P" -H in ^. OO OO ro O O O -H O •O rH P- •^ o •o r>- o 00 <r CM •O ro O PO o o « p- ft rH p- •f P- PJ m OO P- en o- PJ o in

P- * p- ro en «lO P. o -» PO 00 CM

O rH ro ro o en ^ CO in cy en rH in 9- .fi <o P- .r rH OO cy 00 t> * O CP oo in >> .r PJ (M

CO P- in

O en

m o- ro <o ft rH in

O P- » * "»O r^ -o in rH > O rH ro ty in rHO o CO <o -o 0- PO -t OO

O en >r cy

O CO cn CM rH CM o p- o- CM in (M •O -H CM ro O <M OO •o ro O <o O rH OO in t^ O o in o iH m ft ty r* p- P» CO OO <y OO o cy <» O

en P» rHO rH •»• •* in ro •» o en PO rH Pil OD PO ty pj tn in

O f- ty o o> o in in P>- rH o o <y PJ P- o ID •r 00 PJ o in •r CO

<y oO

w o <y OO a- O"O o o <y <y CM a- o (y -•O in o p.

O <M

O r-l o o o CO ty 00 r* 00 (y ty OO OO OO -»• rH ro rH lO

<fw o o a- o c^ o- o O o o g. (y. o <y o (y OO o> <y J) o o o o o o o <y ty o- cy ty cy <y ty ty CP ft rH rH rH rH o (y CP O- o o » o o o O (?• <y cp o <y o cy o o ty ty ly O CP o o o O o <y ty ty cy ty ty ty ty ty CP o o o o o

(J. o o O- o> a- ty (f o- o o o cp a- o o- o (y o o cy ty o- cy ty o o o o o ty ty cy cy o cy ty <y cy <y o o o o o

in in

m in

m CM CM CM CM <M * ro fo cn * * in •rmm <y CP o> a- ty o o o o o o o o o o ft ft ft ft ft o o o o o • • en en ro ro ro en en • • "

po cn CO CM CM CM CM CM rH rH ft -W rH

m

mm inm PO en PO cn en PJ CM (M PJ PJ rH rH rH rH -H cn ro cn ro ro

rH CM ro -rm •o f- OO o o O CM fO •*• o <o p- OO <y o rH (M ro ^ in •O P- OO o o rH CM ro -rm -O P~ =0 -H PJ ro .»• in

O o O o o o o o o rH O- rH rH t-H <y ft ^^ ft rH PJ CM (M CM oj ro CM PJ CM PJ ro ro ro ro ro ro ro ro ro <n •f -* -> •*• J- » OOOOO o o o o o (J. O O O <y o o o OO OOOOO o o o o O O o o O O O o o o o O o o o o

(J- o- o o O o> o- o o o OO CP o o <y <y cy cy o O ty ty o o (?- o l> <J> tyO ty CP o ty

O cy CP ty o ty CP o ty ty (M (M (M CM fM fM CM CM CM CM (M CM CM CM pj CM CM (M CM CM PJ nj rM PJ CM PO PJ Pd rvJ CO PJ OJ (Nl PJ PJ PJ PJ PJ CM PJ PJ PJ PJ PJ CM

CO (O CO <o OD CO CD OO a> <B 00 OO CO GO OO CO OJ CO lO CO OO CO CO OO CO OO OO OO 00 00 00 CO to CD CO CO CD <D 00 (D

D 00 OO CO OO o o O O O o o o o o o o o o o o o o o o O O o o o o o o O o O O O O o O O o o o o o o o o

CO CO OO CO OD 00 OO OO (O CO OO OO iXj OO OO <B CO ID OO CO (O CO CD (X3 IX> CO (S CO a> OO 00 33

D OO 03 OD CO (D OO OO OO 03 CO 00 <o o o o o O o O o o o o o o o o o o O O O o o o o o o o o CJ o O O o o O ^ o O o o o o o o o

en

m ro CO ro ro

mm ro ro en ro en ro PO ro ro PO en en ro ro ro ro PO

m ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro o o O O o O o o o o o o o o o o o O o o o o o o o o o o o o O o O O O O O O O o o o o o o

CM CM rj CM (M CM CM IM CM CM PJ CM CM (M CM pj CM (M CM CM (M CM Pd <M CM CO (M PJ (M (M tM (M PJ PJ PJ (\l 'M PJ PJ PJ (NJ PJ PJ PJ PJ

OD <0 CO OO <o CO OD OO <o to 03 ID OO <o (O CO 00 OO <D <X> 03 CO CO 03 CD CO 03 CO CO a> OO 00 CO «> 03 s iS CD OO OO OO OO OO 00 (D

r^ CM ro -r in -c PJ ro .* in rH

M

m >* in fi CM PO >r

m »H CM ro J- in rH PJ ro * in ft (M ro >fm rH PJ en •r JN rH PJ ro J- in o O O O o O o o o o o o o O o o OO o o o o o o o O O O o o o o o o O o O O o O O o o O o O o O o o o O o o o O O O O o o o o o o o o o o o o O o O O o O o o O o o o o o o o O o o

in inm

m a> in ON in in in UN in in in rfNm in in in J%m <n in inm in in in in

m

m

m in in in

m in in in in in .n in inm o o o O O o o o o o o o O o o o o o o o o O O OO o o O O O O o o o o O o O o O o o o O o o o o o O o o o o o o o o o o o o o o o o o o O O o o o o o O o o <^ o o o o o o o o O J o o o o o o o o o o o o o o o o o o o o o o o o O o o o O o o o o o o o O O o o o o o O o o o o O o o o o o o o o o 3 O o o o O o o o o o o o o o o o o o o o O o O O o o o o o O o o o o o o •o •o •o • • o o •o • • o o • • o o •o • • o o o o o • • • o o o • • o o • • o o o • • o o o o o •O o •o o o o o •o o O • • o o o -o -o o -0 ro ro ro ro cn •J- -T sT ^ •f in m m in in o vO o •o -o o o o o o ft rH -H »H >H PJ (NJ (M CM PJ ro ro ro PO en m fO ro ro en .-o ro ro ro ro CM (NJ CM (M CM ft -H r^ ft -t o o o o o ro ro cn PO ro rvl PJ PJ PJ CM rH rH ft ft rH O O O O O o n O «r CO (M CO •» O in rH P- ro O- -O ro ty in ft p» p» PO ty -O PsI 03 m CM ty •O -o OJ cy 4J (O ro ty !>• r -^ o- 43 ro ft cy

en

m rH * o ft ro o <n in in ft sr o rO en in CM in rH ft •r o en

O -t -f ft ro o -H -» o ro o o CJ in CMn -1- ft f ^ PO > in rvj D in o O ro > n O P- ro o -O ft p- J- O P» (M OO in -t o ro ry O (M o J- o p« ro o in rH r*- >» o in PJ 33 in ^

•n o rH rH <NI * >!

n in o <NJ CM ro ,*• -t- o o rH (NJ (M ^ .r in o o PJ (M ro -f -* o ft rH (M rn -» in in o -c CNP ro ro * in

O r~ P- r^ P- p- P- p«- r>- 03 OO OO CO CO CO o o o ty cy o ty ty o o O

O

O o o ft -H ft f^ ft ft fi ft PJ PJ (M PJ PJ PJ PJ

O o o o o o O o o o O

O

OO o o o o o o o o o .-1 -t i-t rH ft ^ -H -t -1 .^ ^ ft rH rH ft -1 -H ft ft -H -4 -* o o o o O o > O o i> <y a- <y cy <y <y <y CP ty ty o ty ty ry ry a o <y o O cy ty CP cy cy ty CP ty cy cy cy o cy o ty o o o o o o o O O o o o O O o o o o o o o o o o o o o o o o o o o o o o o o o o o o o O O

ro ro fn ro ro en -n ro ro ro

m cn ro rO ro POm ro

n ro ro ro ro ro in rO ro ro PO en ro ro ro ro -n ro fO

m ro ro

m ro ro PO cn

O o o o O o o O

O

O o o O o o o o O

O

D o OO o o o o O o OO o o OOO o o OO

OOO

O

O

(M CM CM (M <M (M CM CM INJ CM (M <M (M (M (M (M eM (M tM <NJ (M CM PU <NJ CM CM (M (Nl CM (M <M INJ (NJ (M CM (M PJ INJ PJ PJ PJ PJ PJ PJ PJ

OO 'O <s CO <Z> 00 'O CO OO OO TO OO OO OO CO 00 00 no CO OO CO OO CO <D OO OO a> CO OO OD OO •a CD a) <D CO 03 OO (D 00 to OD 03 CD <S

B-4
m

n

m .n <n >» * -r * ,r ro ro ro ro ro >*• -r * * * o o O O o o o o o o o o o o o o o o o o 1 1 t LU LU LU

•^ 1 4 1 1 LU 1 1 UJ 1 LU 1 LU t *

LU UJ 1LU LU 1 LU 1

LU LU UJ LU LU 1 1 LU LU

»— 1 r- ro o f\l fO r- ro •o o M r>- CD .-1 OO in o in oj rm

LU 1 x> ro rvj o CO

M CO o ro OO 00 t> •* o i-i

m o ro -O

O

X 1 m -r o O 00 •O o .* (M .o rsj fO CO o ro

O

O o> * o

f- ( O o CO in r- <y o o <o ro

O * .H OO >»•

O

m PJ OO P»J o l-O ^• J- IM •r in .-• r~ >»• m o O r- o pj -* * ro o • 1 -o o in -»• O o OO ro <r ^» 03 o r<- ro !«• pj <y PJ 1-t in » 1 -^ r- -vj fi —

r<-m >« o> <M

O •o o rO i-^rm

O PM

UJ 1 r>- in ^H » o- o r- 33 OO r\j r~ in 00 pjO CO ro >r in in

C3 1 o r^ cy f>. o « t-* «M ro r- ID o pj •o PJ o -r 9 in in • 1 s i^ o 33 m r- o ly r»- o ro o * m 3> r^ O ro »H o

t- 1 >o X) in

n in -H <y CO o- o m •o o o in OOO •o r- o

l/l 1 1-1 -^ ^ ^ >H o- as OO OO <x> i-i •-I -H -4 f-t 00 o s OO OO

i-n

mm rO fO •r ^ * •» -r Cl ro ro (O ro -*• *• *•<»• <r

O 1 LU 1 o 1 1 oI o o o o o III o o o o o 1 OO1 I O

OOO o 1 a 1 i 1 iu 1 LU LU LU 1 LU LU LU LU LU 1 LU LU LU 1 LU LU 1 1 UJ LU UJ LU LU

Of 1 «r 'H 00 rr, <o •o H< o o i-« <Si o O in r^ <»

O o "^ ^• < 1 in in in •O CO OO m <*• <M lf» <y o <0 h~ in o o -o r>. ro 3 1 oo o '* <M « o o- ^ m <M o (M o- O in f-4 in -o o * 9 1 <M o> >^ O <o h- ro <-t ro •r ro o o CO i-t fH xt ro t* CO v» 1 O o o- o >r in J> r- m r-« rj m m (» -» in ro in .« o

-o o m r-t o O

r r^O in «r tj- «NJ p~ o <} I-I r- ty -r < 1 CO J- iU aj <M O o O -^ o r«- * •O O m •C o ro CO o S 1 t>» o o f«- ^. f^ r^ o CO r~ •r h- o O f~ Pd m ro in in

v9 t o iH 00 f^ ?\j in a- •r ^ o in CVI r-< f^ Pvi PO h- ro l>- o

i-t 1 o s o <o o m r\ cr> OO o o o * CD -IO ro <S -4 «

(/) 1 <y in in in >»

m rH

O rH

O f •o r«- rm o pj in r- r-« • n <M • • • ~ ~

OO 00 00 <X> <NJ <\j esj po pj r- CO r- r» a)

«M CJM fSJ <M <M tvj pj PJ r\l rsj pj PJ pj pj CM PJ PJ PJ PJ

O o o o o O o o o O

O o O o o o o o o o

4' * ••

¥ •f * >

LU LU OJ UJ UJ LU LU LU LU UJ LU LU UJ LU LU LU LU UJ LU LU

o- o « -o r-> -H o m X>

m o t* o m «>4 >r o) PJ <o <o <D •o r- o (SJ t» o> r- ro fVJ ro •o <-4 O O rvi in in * PJ

po 1 O r>- !D -o <VJ -r ^H •o in rO •o CO r- in PJ OO OO -< <*» < 1 <\l «-i OO ^3 .-ri o <\J <n <D o -^ t-t r-t o •r OO O PJ ro « M 1 •J> ^H OD <M ^ r- o ro OO O in o -o m o ro * o o ^>

UJ 1 m * m <n >r 'O rom <M a> r-t ro «VJ

O PJ <o o o rm I 1 .o >»• n n fO r-4 ro r-» •4 •H <y <?• O a> 00 O f4 o o o

>- 1 -t •—1

i-t ^ -4

M i\j

MM <SJ i-t ^ rH -* •H PJ (\i PJ PJ PJ

e>- r^ r- N. f«- r« r- t>- r~ f- h- ^«. r>- ^- r- r- f^ t". f^ r«- m m ro m fl ro ro ro ro ro ro ro ro ro ro ro ro <*i ni (^ o o•o o o o o o o o o o o o o + •• + * * -^ * *

LU UJ LU LU LU LU LU LU UJ LU 1 II 1^ UJ LU LU o in o in (*> aj PJ O O •© ro •» PJ PJ O

(D o m -r .»• (Z> o <o Fxm (?

O PJ 00

O o PJ .r m -4 <y .» PJ in o ro in o » in r4 J- J- o <o 1-1 h- CO O O in ro f>- ro O O <0 r-< <D PJ CO o m CO PJ PJ ro ^ CO PJ

r^ ^ 00 CO PJ

m roO rO

—1(^ o in in <*i in in -^ nT in ^ o -o -o -o in in in in in o o o o o *¥*¥*

LU UJ LU <JJ LU

PJ

O * ®

O

J- iM o o ro

00 o O

O i-t fo o 1-1 ,r o

>o >o ^ o o

.H ^ 1-1 PJ r>

>o >o <o ^ m

-4 -4

P-

-4 -4 1-1 -4 1-4 i-« 1-4 1-1 —1 .-4 o o o o o o oo o o o o o o o o o o o o • o• o• o• o• o• o o o • • • o• o• o• o• o o• • o• o• o* o• o• (> ^ ^ <^ o O' O^ ^ o^ <y^ O O ^ O' ^ (^ o c^ ^ O"

PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ r-l I-I <-t r-l •-I PJ PJ PJ PJ PJ o o o o o o o o o o o o o OO o o O o o + •« •t- ^ * + * * +

LU LU LU LU LU IXI LU LU LU LU LU LU LU LU LU LU LU LU LU LU

r>- r~ OO •-t o o m r~ o CD PJ -o r»- en ro o OO CO •* (y

•o -o o in ro •-t -o o ro o •O OO o PJ o r~ <» r~ o •o

-4 in o o ^ PJ o ro o in •o ro o -o *• o P» o o rr«- PJ o r- in o o O PJ I-I OO ro o r* r» m ^ -r o m

p- 00 r- in PJ r^ J- CD * O- J3

m PJ -f PJ CO CO «NJ r^ ro

PJ -0 (j> j^ •I- ^- o t> ro r«- PJ in o o o PJ -4 CM CM

m

-4 o o o- o r- a) r- CO r«. h- ro ro o 1-1 o Ch

O 03 o O -H CJ- o o O o o- «»• o- o o o o o a- <y a- o> <y o o o o o (J' o o> o o o o o o- o o- CJ> o <y o o o o :> o o o- o a- o o o o » o o- <y o- o <y r- r- o <o -o t^ h- r- r>- f>. o o o <f o m in m m in

pj PJ PJ PJ PJ rH 1-4 i-t 1-1 r4 o <y o OO o ro ro ro ro ro o o as l> o »H PJ ro * m o I*- a> i> o r^ PJ ro -»• m o <y ^ -T in in in in in in in m j> in -o -o o «o o -o

l> o o O o O o O o o o O o o o o o O o o o o o o o o o o > i> » O <y o o o- o> o » <?> Pd PJ OJ iM PJ PJ PJ PJ PJ PJ PO CM PJ PJ r\i PJ ivj PJ PJ PJ

CO a> OO

D z> OO CD CO iS CDD CO

D <D <D CD

D ID CO CO o o o O o o o o o O o o o o o o o o o o

CD 00DaD CD CD CO CO CO s to <o o D ID OO OO ro CD o o o o o o o o o o o o o o o o O o o o

ro rom ro ro PO ro ro CO ro ro CO CO ro po ro ro ro ro ro o o O O O o O O o o o o o o o o o o o o

pg 'M IM PJ r<J PJ PJ PJ PJ PJ PJ PJ PJ PJ CM CM PJ PJ PJ PJ

CD OO (D -D <r> CD CD <D OS ro CD 00 00 CO <o -O CO 00 CO 00 —1 rg ro -r in r-4 PJ ro -» in f-4 PJ ro •f in r^ PJ ro -»• m O O o o o O O O o O o o O o o o O o o o O O o o o O o O o O o o o o o o o o o o

1.%

m .n >f\ J^

m

m J> in in in

m in

n in

m

m in in

m o o o o o -> o O o o o o o o o O O O o o o o o o CJ o o o o o o o o o o o o o o o o o o 3 o o o o o o o o o o o o o o o o • • • • o• o• o• o o• o• o o• o• o• o• o• o o• • o rj o o o

r- r- p. r- r>- CM PJ CM "M CM

(J- -O J- PJ £7- ro o m o CM

«0 '^

O -C ^M

O .-I ^ PJ ro

CO CO ro CO ro

C3- 0- C7-

T J' o o o o o

CO 'O CO CVI ro O O O O O

'Nj PJ CM rsj CM

CO OO CO OO CD

O

O

OO

O

CO '^ CD ID 00

CM o^ r*-m ro

»»•

O ro o ro

h* ^ O ^*- CO

-r in o o -^

ro rn •*•» >*

o- <y -> '3- O' o o o o o m ro ro ro ro O O O O O

PJ rM Od PJ rM

OO CD ID CO 00 o o o o o O v> o o o O O O O o f>- in ro PJ CM -»• -4 -r -4 O O (O o -o ro ro ^ •«» in

~»- J- J- -r J-

(y :7- o- a- Cf o o o o o

ro (^ ro t^ ro o o o o o

PJ .\J PJ CM PJ ^ CO 'O S ID o o o o o o o o o o O o o o o O CD (^ O -« CM »• -4 -r -^

-4 f>- -r o rrH —4 CM CO ro

in

mm in in

3' cy o o c^ o o o o o

ro CO

m ro CO

O

OOO

O

CM (VJ PJ (M CM

CD CD CD GO ^3

J-5
o oI I LU UJ

CO (\J o >>• <\1 o o o

(VJ

O

i-< o

•»• o

•*• ^ J- o o 1 I • Oi UJ UJ

-H CD t\) <M in OS

lA ^ <D

•O rn ^ o o o O fSi ^

rO P- ,»• * sO «M

CD ^- -^

•o i-t fo ^- r»- pCO fO f*l o o o I I I UJ UJ uu m -o ®

Cyl ro rH O O -* O fO

en iCt •*

(\l

m fO

ir» o M N IS r-l O <M OO ro ^ -r

«f <»• -» o oI I uu UJ

>o

m

r~ OO

P- J- <0 (M o o O rH O OO r- >»

r-t -r

ro «*> o oI I Hi UJ o m

<\l rn

if> in

in r-t m <s O fH

in ro

~r f>

«r »• •o -o

c*l (*1 ro o o o I I I UJ UJ UJ

-r <vj r- O OO o

in » >» -H -»• o

-^ rsj in

r~

O rH

in * ro

in r- o> <o o o o o r«-

iT) o o O

O

OO

O I I I I I

r«- r- o *

>» i-t <o »

OO r~

in r4 O OS o -r

CO « (M

>o -O i7> in <»> oj ^ ^ o m «*• o

CO fM fvj <M fH •« « o m O >H -i^ ro OO -O •o f' <a

ro ro o oI I UJ UJ

CO .O

<o c\j —I fO O .H O -4 O ro

f<- P>- -O -f * CO

r«. «

ro to fO o o o I I I UJ UJ UJ O O in r- o in

•^ O^ tr\ ro o TV

t>- in -y O «• Ti

r~ <N4 <r * ro r-

-» r- r- m <? oj O -O 43

ro ro O OI I UJ ui

r- ,0 ro O

r\ rvj in ~o

eo 00

00 o

rvi t-i ro r-4

fvj

m

**1 ro ro 000 I I I UJ UJ UJ

f»- ro 1-4 ro (Sj m

rsj ^ -f to r^ « O -4 O

i-< o «*>

»\J o- o

t-t 00

M

o- c -o ro (Nj r- 000

ro roo1 I UJ UJ

OO f^

-»

O o r^

,» 00 ro -o <M m m in

00 o

r-t t-t in V

r- 4)

ro (ti f*> 000 I I t OJ UJ UJ

r-t Pg

O 4 00 ro

>0 (M

O

ro J- r~. in r-< o

00 ro ro

<0 33 -« * ro M

in c> 30 o r« m

ro ro o oI I UJ UJ O r-i •o r\j V in

in OO r- rM o in

<-« 00 CO (M o in

a- o

r» 00

f^ ro o 000 I I I UJ UJ UJ

r- ^ ro O ro r- O m o

-o

m r^

rvj ro o

-^

O (NJ o -o o

ro ro ^

r- po ^

u^ in 00 p^ f»- ^-

fo ro <*) 000 I I I UJ UJ UJ

fO 03

O

OO i-t

r\j

O c

13 ^ ro

CD 45

m

OD o >^ o J- in <M O OJ

r-t

O

M

r-t (?• hrH O O

ro -<OI I 01 UJ

o- -o

•O OO

43 r\j <S -O

•r o O r-t m .c o r- • • 00 00 CO •

CD •CO •PJ PJ • •

PJ PiJ PJ • •

r-t rH •<-t •rH •r-t • • rH rH •rH • •

r-t ro •

rH •

r-t •r-t •rH •rH •r-t •rH •

r-t •t-l rH • •

rH rH 9rH 9 9 ft r-t •rH •ft •

r-l • •

ft ft •PJ •PJ PJ 9 9 PJ rH

•» -r -r -» -»• ro ro trt ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro ro tn ro ro ro ro ro ro ro ro to -H 1 1 1 1 1 1 0000 III 00000 1 1 I • 00000 a 1 i I J. I 1 I 000 1 * 1 i 1 1 1 001 1 1 I 1 g I 1 1 *

Ui IXI 1 1 UJ UJ 1 UJ 1 UJ 1 UJ 1 UJ 1 UJ UJ lU UJ 1 1 UJ UJ UJ UJ UJ 1 1 UJ UJ UJ UJ UJ Ui UJ i Ul 1 Hi i UJ 1 UJ LU UJ 1 Ui UJ 1 1 Ui UJ 1 UJ 1 1 UJ Ui 1 Ui i Ui UJ 1 IXI Ui 1x1 1 Ul 1 1x1 43 43 43 r^ •*• 43 ro ^. ro f«- rO (D in •H ro ro PJ ro 43 * 43 * r^ p- r-t -»• -»• r>- 43 O- «» p- p» p- ~o •r r-t P- O- 43 -H

OO CJ

m in rH 43 rH PJ CJ- >-t rH PJ rH 43 rH P» PJ P- PJ r*m rH ro rH CO g. to ft rH ro *• rm to O-

<»• >*• r- PO CO ro

m 00 4) rH OO r-t PJ CO PJ

m in 00 inm rH <y f*. o- OO P- r» ro p- ^. •* sy o- t^l 43 PJ rH 00 PJ ty «

cu CO ro OJ -^ .» ^. f^ r- rH •r CO <D O" #• p" ro P» PJ r~- ro 43 CO ^ r-t r-t ro PJ -r in ro ro ro 43 PJ 43 0> PJ

43 -r 43 f»- •*

mm ro P- -r rH PJ p» ao ro ro CO 00 -r 33 in ro PJ f>.

m r-t in p- ro PJ ty PJ P<- rH ft >» OO PJ in ro fvi 0> ^ CO 00 if> 43 PJ 43 .r PJ 43 »H ro 43 -r r^ PJ to PJ 43 in «»• in PJ r- PJ (J- in r-t in * in r* p- in 00 r^ 00 pro CO •»• r». ro r-t o- PJ 00 <y ro 43 »• trt CD PJ m rH <»• <o <7> ro 43 PJ O- rH rH .» 03 PJ rH ro m a- in ro in PJ CO <o -r ro rM ~»- «\i ro PJ >o ft «M -0 43 4) ^ ro PJ •r r«- CO p- •0 fH -r ro ro 00 ro r-t -r <o ft rH p~ CD r^ .»• 43 CO a PJ

o- a- r-t ft in •r om PJ r- to (J> ro p- rH r-t PJ * ro rHO nT -r ro >r P>- CO in inm to ft rH ^• o> P- 00 ro PJ PJ

00 -»• r-t (M •r ro r-l CD ro p~ »• * CO 43 PJ

m PJ rH o- a> CD PJ

m PJ PJ CO 43 -H

m 43 » ty ftm fl to PJ 43 43

m 4> r^ 43 CO r~ r^ »• r*- p- m CD 00 r- p- PJ in <o P^ OO p- o- 00 p- rH O- o- 00 P- PJ tn rH rH PJ m «f ro r

f~- 4J r^ • p" 43m 43 in 43 pj PJ PJ •PJ PJ • • PJ PJ •PJ en rH • —

ro PJ •PJ PJ •

PJ ro ro •ro fO ro • • ro PJ •PJ • • rj PJ • •ro •

1*1 • • tn ro • • • • •

-» to

PJ tM (M pj pj PJ PJ <<j PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ 000 000 000 00000 00000 > • + •• •¥ ¥ • + • * > 4- + + f H- f H- • * f

UJ 1X1 UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ Ui Ui UJ UJ UJ UJ UJ UJ UJ UJ 1x1 UJ Ui Ui 1x1 IXI UJ iXI UJ Ui Ui UJ Ul 1X1 UJ Ui

in in >» rO

m

m -r f* t> PJ ro r^ o- 00 <D ro rH CO 43 P» r- 4) PJ rH 00 43 r- r^ <y fO tM <0 03 ft <y r- ft r^ * 43 r-t .» ro PJ 43 p» ro •r PJ PJ in in ro p» r» <o in in OD •»• a- » * 00 p" m p~ ro r-t .* ty <y ft PJ rCD CD ~^ * PJ <x> -^ p- 43 43 in r-t f-H ro in 03 ro 43 r^ m -»• -* h- 33 CD p» 43 c^ PJ CO p~ 03 r-t •0 r-t to in P~ ro

rH -r •0 cn PJ f»- r>- PJ OO PJ t^ PJ ro p- rH PJ -»• PJ 43 PJ f- PJ rHm p- PJ p- * m 43 ro PO

m PJ -O ft r-t

O PJ

•r in •r PsI CO p^ CO rH <» <o <o r^ rH PJ ro r-t -0 in PJ 43 43 PJ 43 * >»• PJ •»• 43 in rH ^r tM p- rH tn PJ ro P- m <M 43 r^ PJ O' PJ 43 1> •0 ro PJ S) to V as •r >n •r PJ W ro P- P- to r-t p^ m o CO #• 00 m (y tn m 00 03 in ft

r-t rvi r\J ro ro PJ PJ PJ PJ PJ >»• inm ^ in PJ PJ PJ rH ro ro PJ ro PJ ro ro <*> ro ro PJ ro ro ro ro ro PJ PJ ro ro -r in in

mm 9

ro ro rom ro ro ro ro ro ro ro fO ro ro ro ro to <*l ro in ro en ro ro ro ro ro ro ro to ro ro ro ro ro ro ro ro ro tn ro ^ ro tn »

r^ r>- f^ r~ P- P- p~ P- P~ P- P~ P- p- P- P- p- r~ h- P- P^ p~ r- r>- p- r^ t^ P^ p- l^ P- p- p- P- P- P- t^ P- P~ p- r^ P- p- P» r>- •* ro ro

rH t-t • •

ro

r-t ro ro

r-l•

ro

r-t•

ror^•ro ro rH •-* • •ro

r-t•

ro ro rH r^ • •

rH•

ro

r-t•

«o

r-^•

ro to

•-t "H • •

ro

»H•

ro ro rH r-t • •

ro

r-t•

ro

r-t•

co

I-t•

to

r-t•

ro

r-t•

ro

r^9

rorH•ror^•rO

rH•

ro

r-t•

ro ro

r-t r-l • •

en

rH•

ro tn

ft ft • •

rorH•

ro

rH•

ro

r-t9

in tn

ft r^ 9 9

tnft•

ro

r^9

ro

ft•

ro in

r-t fl • •

r-t rH

r-l

—t

r-t r-i

r-t r-l

r^

r^ r-t r-t .^ r^ <H 0000

rH ^H -^ rH rH -4 000

rH

rH

^H

-H

^A rH

rH rH rH

^t rH

-H rH r-t

r—t

rH r-t r-t ^ 000

^H

rH r-t r-t -t r-t 0000

r-t »H

r-l rH r-l

r-t r^

r-t r-t rH ft rH ft rH 00000

r^

rH

r-t

r-l ft

f4 ^

fl r-t * * * * * * •• ¥ > ^ •• * •f * * * *• * 4' * •^ •

UJ UJ UJ UJ UJ UJ UJ UJ Ui UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ Ui UJ UJ Ui UJ UJ UJ 1X1 UJ Ui UJ UJ IJJ UJ 1X1 Ui 1X1 Ui Ui 1X1 Ui UJ IXI UJ UJ ro ro in r- PJ ^- f-t pw •0 in ro ^. PJ in PJ in 43 43 in 00 m PJ 03 p- r-4 in OD ro rH 43 P- 43 P- >*• to PJ PJ ft 00

r«. in r- rn r-t f^ 43 43 ro ^ rom •« -f f* P- 43 CO ro p>. ro <J- ro 43 PJ >r PJ CD 43 in PO rH 00 rH

m 43 ro OO- (M 43 4) r-l r-t m PJ CO rH r~ >r * •* P- * ro •H m r«- rH PJ rH >r •# p- m CO CD p- p- 1^ 4^ ro f«. >r f- r43 sT ^• r» CD r-l ro PJ ro m ro 00 r- ro p- rH 00 43 -r PJ 00 r- 43 rH ro PJ O- ro f^ 00 -* * ro ty 03 PJ in tM

r~ in ro (D r^ * rH in * *• in -t t> rH * CO f«- PJ ro •0 43 PJ f^ r-t OD 43 * a> .o ro ty ft ro ro ,* to in >r ro in f>- m CO m m ro ro ro 1^ r^ o> p- 43 •*• ro ro rH * -r m PJ in m ro m •0 -* 43 43 in m y 43 P- 43 in P- 43 in ty r43 43 43 43 43 43 43 43 43 •0 43 43 43 43 43 in m in in 43 P- P^ p~ P- p- m m m in in m in in m m in 4> in m m m 4> 43 in PJ

fl

r>- ^-

•rt P"-

fr4 PrH

Pr-4 ^

p- p- rH

p. 1^ i^ r^ |Z t^

rH r-^ rH -H w4

p- ^-

r-t

—

f<- r^

P>- pr-t

P«. r^

P~ rj

p- ^ r^

r- p1-^ pr-t r-4 p- rft

p«. r—t rH

Pr-t .-H r^ p- pr-t 000 000 00 000 rH 000 000 000

ty <y <^ a- <y 9' o> a- » <y- <f o> o- Q. (J. O" ty ty ty ty O- <y ey ty

r\j rvi <M PJ PJ ru PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ rH r-t t-t r-t rH PJ PJ PJ PJ PJ tM PJ PJ PJ PJ PJ PJ PJ PJ PJ r-t r-l rH r-l rH 000 000 000 000 • * * • + * * * > * * • * ¥ •f * > H- •• * • * 4- ^ * •

UJ UJ UJ Ul UJ UJ UJ UJ LU UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ Ui Ui Ui UJ UJ UJ UJ UJ Ui IXI IXI IXI UJ UJ UJ 1x1 Ui Ui Ui Ui Ui IJJ UJ Ui Ul Ui ro p- <\j r»- -r ro P~ * P- * >*• •* 43 rH PJ * r>. <3 p~ P- 00 43 ro •r 9 43 r-t P- in ro ty CO ty -r PJ 00 1^ p- -0 4) PJ PJ *• PJ ro -» ro p- in P- p~ PJ r^ PJ 43 ro 0 43 r-t in ro ro in * ey f~ -»• in ty •r ro CD

fVi (NJ >»• r- -0 rH ^ P- 43 r-l 43 r^ t> PJ p- PJ r-t CO -» r- in PJ * P~ to ro •0 00 PJ PJ f^ 00 to PJ PJ rH <?• in 00 43 .»• rH l> 43 P- •» m m >r (S PJ o- 43 r-t 43 (y m r^ ro in f^ m 43 r^ <> 43 ro p~ ty tn in OD in m to

0> ro 00 r- P~ PJ O- PJ CD PJ PJ PJ PJ r- o- <o r- * •r PJ »r ro r-t p- CO ro PJ PJ r^ t^ ro 43 f«- ro PJ PJ

m ro ft to

ro ^- ro ro » ro ^^ 00 PJ '^ PJ >r ID rH PJ -r ^. r^ o- 43 •r 00 00

m PJ o> r^ PJ PJ 43

m 00 t^ CD 43 CO r-t in -r PJ <y <o ty ro •0 in 43 •r 43 CO 03 00 CO CD OO CD OD CO in .*• CO en >r

g. (J. t> i> o> o> 000

m rH <y to a> 00 o- <y CP ty ty ty ty ty ty <y r-t CD

tf <y a- O- CP <y <y a- ty ty ty ty (y <y <y 43

O- O- O- a- CT- 000 CP o> CP a- ty ty ty ty a- ty .y m in m m m PJ PJ PJ PJ PJ r «• •r -r -r m in m in •$ o- o> <?• 000 •H ft ft r-t ft 00000

ro ro ro ro ro ro ro ro rom PJ PJ PJ PJ PJ rH rH -H rH rH 4)

m

m in in ro ro ro PJ ro PJ PJ PJ PJ PJ r-t fi

—1ft r-^ ro ro ro ro ro

rH tVJ ro -r in 43 P- OO ^ PJ ro -*• in 43 p. OO PJ rO ^ m 43 r^ OD 3- r-t OJ ro ^ m 43 p- OO <y ft PJ ro •f in rH rH rH .H rH rH rH rH —1

r-t PJ PJ PJ PJ PJ PJ PJ PJ PJ ro ro ro ro ro to ro pi ro ro •*• -» >! »• -1- -r

t> 000

in in in in in in

mmm in in in inm

m inm in in in in in

m in

m in vn

m in

m in in in in in in inm in

m in in in 4> in ^ * -J- * -»• «r •* J- -r * J- >»• •r -»• >r •» >» -» >r •»• .»• * .»• J- <»• * -» •r * >f >r ^ >» •J- -r ~r ~»- * >i- .» J- * -*• .< •»• r- f^ f>- h- p- r^ p» f>. p- p- P~ r~ p- r^ r- p- f- p- f^ r^ p~ f~ r-- p- P- p- p- p- p- p- r- p- P- p- P- p- p- r^ p- p- (^ r^ p- (^ r~ o c^ ro oj rH r-t (M

r^ r-l PJr-l PJrH

PJ

r-» PJ PJ rH rH

PJ

rH

PJ PJ

<-t i-H PJ PJ PJ

r-t PJ PJ rH rH PJ

rH

PJ PJ

rH r-t PJ

r^ rH

PJ PJrH

PJ

rH PJ PJ

r-t r-t PJrH

PJ PJ PJ

r-t r-t PJrt

PJ PJ ft fiPJ

ft

PJ

ft

PJft

PJ PJ

-t ft

PJ

rH

CM

r^

PJ

r-l PJ PJ ft r-l

V cn tn en en ro en ro tn ro to

</3 00000 00000 *-H PJ PJ PJ PJ PJ PJ PJ PJ rM PJ

CO 00 QD 00 00 QO ^Xf 00 ^0 QO • -H PJ ro .*• in r-l (\j CO ^ in 00000 00000 ^ 00000 00000

in in inm in 00000

00000 00000

in in tn in

n 00000 00000

00000 00000

en ro en tn en 00000 rj tM t\J tM CM

^3 00 00 00 ^3 rH PJ ro -f m 00000 00000 m in in in in 00000

00000 00000

en ro en en en 00000 tM PJ tM CM PJ

CO CO CO CO CO -H PJ ro ^r m 00000 00000

inm in in in 00000

00000

tn ro eo en ro 00000 PJ PJ PJ PJ ^i S 00 00 00 CO fl PJ PO sT in 00000

in

m in

m in 00000 00000

00000 00000

ro ro eO en ro 00000 PJ PJ PJ PJ PJ

00 CD ^3 CO CO

r-l PJ ro -r in 00000 00000

in in in in in 00000

00000

ro rO ro en en 00000 PJ CM PJ PJ CM ^ CO S OD 00

ft PJ ro ^ in 00000

in

n

m in in 00000 o <j o o <:> 00000

ro en ro ro ro 00000 PJ CM PJ PJ PJ

ry) CO CO CO GO rH tM ro •»• m 00000 00000

in in in

m in 00000 00000

00000 00000

rO ro ro CO en 00000 CM PJ CM CM PJ A "O ^3 ^3 ^3 rH PJ ro -» m 00000 00000 n in in in in 00000

00000

00000 •o >o 43 ^ >o en ro eo ro en O 43 rH ^- ro O CM li^ rH >» ft p- m o 43 O O 'H fM PJ

00 CO CD CO CO 00000 PJ CM PJ CM PJ

00000 en ro ro en <n en en ro en ro

CO * o 43 rvi >r ft ^ O to fl -o -J- ft p^ -»•» in o O

(O CO CO ^ ^ 00000 CM CM PO CM CM

00000 >f *-»•* .J- PJ PJ PJ PJ tM

CM 33 in rH r^

PJ s^ ft •*

O

PJ lO in -H CO PJ CM ro -» ^»• cy <y ty 9 cy 00000 CM tM CM CM esi

00000 in in in in in

>r o 43 iM 33 —I v^ o ro in o o ro o in ft ft PJ PJ ro 00000

00000 O 43 43 O 43 00000

PJ 00 -r ft r^

>r

O ro o PJ PJ o in CM lO

in in

O rH rH

O

O -I fl ft

00000 00000 tn m ro ro ro

p- ro o l»- »r -* r-« * O ro ro O 43 ro (> ro »*** in in

00000 ft ^ r-t rH —t

PJ PJ PJ PJ 'M

in CM COm oj

O en j^ CM

n

f^ enO sO PJ

ro ^ Nfm o

PJ CM ro PJ tn

00000 PJ CM CM PJ PJ

~i- o r^ >> .^

-r ftm o ro

00 in

—t 3) ^

fl PJ ro ro ,r en ro en en en

00000 ro en rO en rn 00000

in -H CD 43 ro O ro n CM m O 43 iM CT* in O O rH rH PJ

PJPJPJPJPJ PJPJPJPJPJ PjeMPJPJPJ PJCMCMPJPJ CMPJPJiMiNJ rocMPJCMPJ

m en en eo

m 00000 PJ CM CM fM CM

00 "O "O

© CO

en en en en en 00000 CM PJ CM CM PJ

CO ^O ^3 ^3 CO

ro tn en en en 00000 PJ PJ tM PJ PJ

CO to CO CD OD

ro en en en en 00000 pg CM PJ PJ PJ

00 CO CO CO CO

en

m en in en 00000 CM CM tM CM CM

CO CO CO CD CO

ro ro ro rn en o o o o o

ro CM CM PJ PJ

00 CD CO CO CD

en en rO en

m 00000 PJ PJ ro PJ CM

CD CO 1> CD CO

en eo en ro en 00000 rj PO rj PJ I'M O ^ CD 00 CO

'n en en en ro 00000 PJ PJ CM PJ PJ tO CO s 10 CO

B-6
<*> f*> c*^ o o o I I I UJ UJ UJ

o- r~ -r

rH -o o

tNJ CD ^

^H CM IT* ^- 1-1 O O f^ i> m o 1) 00 (SJ O

(o <n r^

(\J ^ fO

r«- ^ r- o1 I UJ UJ

CO r>- O CD O <\J

co ^ o1 I UJ UJ

-O (M

•r o

r~ -I o ^o rH O

.o in

(vj

m

O f)

rm ^ >»• -< o o o I I I UJ UJ UJ

•T C3 >-> (> ir> ^

-H if< r«-

<sj r» o- .H ro Pd O fO o * lr^ o

oj o r^

in

O

O o irt r>> * <VJ -H

-r -I >»• o o o I I I UJ UJ UJ

•O f\l <x>

i\) o» -r G m r-t O o r-

<! X) >0 r- -*• o ^ m rH

in <\i <*> 00 CO OO

fO CT' <D "t r-t m o o I I UJ UJ O O

u-\ >»• tn »-H CO .o o r-- o roo o

-*

m J- o o o ( I I UJ UJ UJ -HMO

u^ ro >»- ro iTi ir\ m -O O O O" M

(Nj CO r^

-O in rH ^ CO >o

iri i-H OO

r>- o r~ O O rH o o I I UJ UJ

l»- ro

00

O

OO r>- O <\J T3 J- o o- o o

rO rr( oi O O O I I I UJ UJ UJ rH -r ro

fO

m

O

^- iTi CO

r>- in >» m CM -H o r>- -J- Pd -O OO c> in -o o r- >»• 03 in (^ o oI I UJ UJ O -H

>o -o m o

f-. in

<M o O r«.

en fo

00 r-i r^ 00

-o -o

•* -r -t -t * o o o o o I I I I I fo in •»

in J- CM

in CM rH

ic\ o- w-1 r~ O r^

csj o m

•* r- <» »^ •»• <VJ rH ® -» rO CO P- O PO o O rHp~

m

O

O

f>- OO o

1/5 O

HH

01 • • rH rH •rH •

<-> •rH • •rH 0> • • •

o> O- PO • • •a- • •

00 • •rH • •CD •OO • • • -H <-t •

rH • rH • • CO CD • • •

00 CD

m C<1 rri fn CO rH ^ •r •* <-t * r-i >»• -r N^ >»• CO •r

r «f rO -O CO CO CO •r -r •r J- -r o o o o O O O o o o o o o o o o o o o o O O O O o o o o o o 1 1 1 1 1 * 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ m OJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ

cy

m rH •-* JO cr>O

O ro rH f-* •O

O o o PJ -» CO J- ro O- CO r^ rO -O p» »>- -o o o o PO O o O * « -O O r- CD -r •o «r W-* ^ •o i-H PJ PJ OO fO CO •r -o in o- o

•o o r\ rH CO r- «rt (S

m <o >0 r»- f*. o a- <o Pd CI o r- -»• >» -O -o CO PJ o r- PJ r^

rH (^ OO rH o CD in

OO rf^ »r CD ro o m

a -H in CO cor r>- r» -o o OO 00 >»• >o -O in o rH -H 0> m CO m ^ r-l -o in >o m o -o <r -H CO o CM •o <r J> »^ o in o o- -o rH CM •» in rH P- »H CO (7> -O en o CO o o- ^ r~ CO -H PJ CO PJ -o in o r»- -r <c ^ a- en CO CO rH PJ m r- O in PJ rH r- •*• rH rH (J- •o CO CM -»• <y in <u PJ CM CO en PJ m o"

•o r- <D o OO fsj o OO o « <D in om -o o r- PO f- o w* ^ 00 o> rH rH rH 00

V OO

•r pj f>- >om in >^

O o rr -o ^r •* •o (O o- o O in rH <-i (^ rH PJ in

Cm PJ r^

m rH •o (O o -r ro >» rH a> CD •* in rH * <o •-I in rH -»

O O- rH JD r»

O -I- -o CO CO o o• • o• • • W PJ • • rH (>. r«- • • « • •*• • • •

CO

O• • m • • 03* • • OO•

CO I-H rH • • CO• o o• CO cvj en <n (M PJ O o- OO J- CO rH CD CD r~ 00 rH OO r^ f* CM <NI PJ CM CM CD f^ OO ^- r>«

PJ PJ o o

(M PJ PJ o O o + + *• + 1 1 1

UJ UJ UJ UJ

-H PJ

PJ

O

CO .»• PJ ^ o ra- in rH CO

>r •»

CO CO

rH CO »• 1^ m PJ

r- -* (o

CD

m -o

O CO o O >» PJ * in o

-»•>»•-»

r»i r- r»

en CO CO

CM PJ PJ o o o

UJ UJ UJ

in PJ -r O >» in

PJ OO in

-»• -o r«- in rH o

r- «r PJ rH O O

r^ in in * r» ren en en

PJ CM o o

UJ UJ o -r o o

CO in o »•

in ^

CO rH

o> CO

*• rr- >»• CO en

PJ PJ PJ CM <M o o o o o m CO

•* -r J- PJ r- o

•O CO PJ *

OO ^4 r f-t CO CO o o -o ^ rH CO

o- r- o

<o in .f

CO rH PJ O CO 'O

OO h- l»- .»•-**

p» r^ r>- en en en

CM PJ o o

UJ UJ

rH <\| o oen en

PJ PJ PJ o o o + +

UJ UJ UJ r^ m en

£1 rH >» in PJ Jj> •*• CO o -»• o

OS (D in

•o o -o

•T -r -* p- r«- r>- CO CO CO

PJ CM PJ CM <M o o o o o*

£> 3) r-t in ® CO en o r- o o r-

-o f~ r^

PJ -O CO

CO CO .*• -f ^ .» r~ r^ r.

CO CO CO

,0 en en -O CO f- O OO

in CO O 1^ ^ CO

-r <r CO CO

PJ PJ o o

>• UJ UJ

PJ o

£) rH PJ o o o

CO rH o in

-o in

>»• >t- CO en

PJ PJ CM O o o

UJ UJ UJ

«»•

O CO

O CM CO

in fH CO

•r in OO

<y. CO

m

rH CO r^ m •*• >r

-»• ^ ^

r>- r- hen en en

OO+

UJ UJ

-O OO PJ J5

in -o f~ o

CO rH

rH

m

in in o o o ***

UJ UJ UJ

CM •«• eo O O rH

r~m *

CO o rco CO f~ m m en

in in

m

p- ^- r«- f-- r«- o o o o o o o o o o o o + •

UJ UJ

in ft O in

OO (j> CO CO o -o O rH

cy. r- O rH O f^

-H

O o o o•o o

UJ UJ UJ

in * CO

OO PJ 't' >r PJ o * rH m

in PJ <3 o cy CO

h- ^ CM

r> r^ CO o o o o o o o o

UJ UJ

h» -H

O- CM

in CO

>-> PJ

PJ 05 CM en

r>.

O

rH

O o o o o o o o •»• +

UJ UJ UJ

ro r^ in O ej- 00

CO ro

•O >0

m

PJ r>- o 00 o o

<£> J3 <£) rH -H rH

p- r- r«- o o o o o o o o o o o + + +

UJ UJ UJ UJ UJ

in r- PJ PJ rH

PJ en <D ^ f^ o m in o o

PJ -*• rH

O PCO in O^ rH CM

PJ ^- rH in PJ

r~ r- p- r^ r-

-t r-t ^ r-» r-4 p» r« p- r>- f~ o o o o o o o o o o o o o o o o o o o o + •• + + 4. •• + •• tU UJ '^ UJ UJ UJ UJ UJ UJ UJ

PJ vO CO in PJ ^ OO CD (D

O

CD CO >0 >0 rH in CM <5 in rO

PJ in P- CO rH a>

m rH PJ PJ

P- OO <?• -O in pm * p. f>- m CO CO o OO OO O * 00 in

in •* CO ^ PJ PJ rH rH rH o O JS .O 'O o r. r>- p> r^ P". p- p~ p- r«- f>- o o o o o o o o o o

r* N- p- r>- p- o o o o o o o o o o o^-o

9^a • • • • • O (J. • • •<y •cy • • cy • • • •<y • m

o- cy •cy • • •

cy • cy • • cy •cy •cy • cy • • <y o

PJ PJ CM CM PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ f^ rH rH rH t-i OJ PJ CM PJ PJ o o o o o o o o o o o o o o o o o o o o o o o O o o o o o o + •• ¥ * f + + •• + • + > + * ^ + +• UJ UJ UJ UJ UJ ai UJ UJ UJ UJ UJ UJ UJ UJ iXI UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ m UJ

OO o rH in CD <0 -»• OO

O cy ro rH o PJ >*• o -r o cy CO OO P- ~r

O PJ CO <-i IM •*• r- o o PJ PJ cy f>- cy r~ >-i PJ m >» <o ro en -o CD in cy «* •O •H cy rj r-i o CO J3 CM in

in PJ <-i OO rH 03 -<•

m rH PJ «o CM o in rom r- * -< in •o

m o PJ <y f- -f •O p- in

-o in o OO CO CO OO -*• * rH r>- OO cy p.

O in pj en PJ rH 00 r- r-i -» CM

O inO CO PJ

O J3 o- rH •-i CO o o PO J- <o -o x> CO rH >r in CO f«- PJ r-* o m P- cy •o -O CM -r m o- in 00 in PJ rH -o o in in D CO o PJ O -r rH p- PJ J3 ro •* ro «*• O CM *• CO CO

CX) f^ CO OO cy r-i OO P~ OO ft pO CO OO CO CO OO CO r*. <o

O rH o rH r-i <y cy cy cy cy

i> o o o- o CO <y cy cy PJ cy o cy CJ- o cy <y cy cy cy o o o o O cy cy cy cy cy

a- o o o- cy CD cy o o rH cy CO cy cy <y o cy cy cy o- o o O

O o cy cy o <y cy

<y cy o o> o cy cy cy (y o cy ey cy cy cy o- cy (y cy <y o o o o o i> cy cy cy cy o o •o o -o f»- r- 1^ p- ro p- p- p- p- p- r^ p- p- r~ p- o o o o o in m m .*•% m

PJ PJ CM CM PJ •H •H t-i rH rH rH rH i-i rH rH rH rH rH <-i rH cy ly <y cy cy ro CO CO CO CO o r- OO cy o rH PJ en * in O P- •o cy o r-i <M ro •* in J3 p~ CO cy o rH PJ CO * m

>r <i- >r >* in

m inm in in in ,n

n in •o £> o >o •o o -o -o •o -o f^ r^ r^ p- p- P- o o o o o O o o o o o o O o o O o o o o o o o o o o o o o o

in in

m in

m in in in

m in in in in in

m in in in in

mmm in

m in in in inm

m

-* ^ >»• 4- -r * # ^ .*• -»• -r •* «r -*• «»• -*• •r <» -»• -* >*• ^r * -r * * -» -> -r .»• r~ p~ p- r- p- r- p- p- f~ p- p' r~ p. r^ p~ f^ p- f^ p- r- r> p- p- p- r>- p~ P- P- p- p- o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o

PJ PJ

rH r-i PJ PJrH pj

rH PJ CM PJ PJ^i PJ CJ CM PJ

r-i PJrH PJ

,-4 PJr^

PJ OJ

r-i OJ CMrH PJ CM OJ PJrH

CM OJ PJ OJ PJ OJ

rH r^

CO CO CO PO en CO en ro CO CO ro CO CO ro en CO CO ro eo ro ro en ro CO CO CO ro CO CO ro o o o o O O O O o o O o o o O o o o o O o o O o o o O o o o

PJ PJ PJ e\J rg CM PJ PJ PJ PJ PJ PJ OJ PJ PJ PJ PJ PJ OJ PJ PJ CM CNJ OJ PJ PJ PJ OJ CM OJ

CO CD 00 CO CO 00 CD eo CO CO CO OO CO CD 00 CO CO CO OO OO OO TO CO CO CO CO CO CO CD CO

rH PJ CO >»• in r-i PJ ro <» in rH CJ CO -J- in l-i PJ ro ^^

m r-i PJ ro >»• in rH rj ro * J> o o o O o o o o o o O o o o o o o O o o o O o o o o O o O O o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o

inm in in s^ in in inn in in in

m J-\ in in •n in in in in in in in in in in J^ J-> u-\ o o O o o o O O o o o o O O O o o o o o o O o O o o o o o o o o o o o o o o o o o o o O O o CJ o o o o o o O 3 o o o o o o o o o o o o o o o o o o O O o o o o o o o o o O o o o o o o o o o o o o o o o o o o O O o o o o o o o o o o o o o o o o o o • •o •o o •o o o • o o o o •o o •o o o o o o o o o o o o o p- p- p» r^ r^ (D OO ao OO CO CD <D CD 00 CO CD -o X) to CO cy o- cy ly cy o o o o o

cj rj PJ PJ PJ rH rH r-i r-^ r^ rH -H -i •H rH r-i r-i rH -i r-* o o o o o J) o o o o

CO »r o •o CM P- -r PJ cr r>- •n CO •-i cy >o CD in -J- OJ o in CO OJ >-i o cy p- J> J- CO

CO o en in rj o ro o PJ in CO o ro in PJ

O CO o s"0 CJ

O ro o ro o o ro o CO o O CO o n cNI -r O p- CO cy p- r o o CO o o ro o o in r-i D -J- rH -o OJ o ^ 'M CM CO ro •r in -» in in o o cn •r m j~i o PJ CM CO ro >» o rH rH CM ro J- in in O rH m m m in in J3 o o r~ (^ cc XI CO CO o- ey o cy ty cy o O o O O o o o rH r-i r^ r-i -H ,-i —4 rH -H -H r^ r-i rH r-i •-4 rH rH -H 'H rH rH -H "M OJ OJ OJ OJ CJ OJ OJ OJ PJ PJ CM

r-i rH PJ

-H

PJ

•-i PJ

-i CM

-H fM

-i

evj rH

PJ

—i PJ

rH

Pj

r-i rM

CM

-H

CNI CM

rH

OJ

r~i rj

rH

OJ

—i

OJ

rH

OJ

rH

OJ

•H OJrH

CM

-H

OJ-H OJ

rH

OJ OJ

—i

CNJH

-M "J

-1 -H

rn

m <n -^ ro o o o o o

(Ni fNJ CSj

V rvi

'3> CO 00 00 <Z>

''^

mm <^ f*) o o o o o

fN4 CM 'Ni CNi (\J OO OD CO 33 <^

fO rO ro fO rO o o o o o

OU f\I (\J (\J (\J GO 00 CO "^ 00

ro ro (^ rn 1^ o o o o o

c\j og ^ OJ 04 ^ 13 <3> 00 "13

fo ro ro ro v-n o o o o o

nJ *\J f\j -M c»J CD D OO CO OO

fOO rO fO fO

O

O

O

O

O

f\| CM "NJ t\J PJ

1) CD OO <D <D
m ro —< o o o I I I LU UJ UJ

J3C -C

r~ o .-I j^ in x> (M ir\ rH

CO eg c O -c m

CM vn f-< J- -*• o

<M iTl 1-H O <M CT- -r >j- r^

ro

m o oI I LU UJ

-»• —4 m m

IM

O c * m eo

<\j o O

OI I

o> o o -o O 03 o o o I I I UJ OJ LU

r~m i«- o r~ ro O if> o O 03 03

(33 -O -D in # ro n f>- o

ao -o (M

Jm 03

r-i (y ^^ O !I3 o o oI I LU LU X <\] >r 33 m in

•O rvJ (M o

as -o -O o

-r -t) o o o I I I

r-) O" nn

(^ CO ro rn fO O O O o O I I I I I

fVJ CM

GO rn ^H

OD r- o m in ^

rw CT- f^ o m o

in -rm

r^ ro rri m < i-t CM r~ ^

03 .n r- m

r-l

O

r>- i> ^ cc

r>- o

rH (E in o

r^ o

00 1^

kH in o M (M rg COO o 03 fn C O 03

4- -O -O O O rr> O- CVJ m

1-1 in .»• 03,^

O- CD

O

m

m o oI I LU UJ

-H ^

(NJ CD m in o o O CD

£> CD O O -H m CM

CNJ (M

OD 33

cT) fn c*i O O O I I I UJ UJ LU C m "-I o in CM

•-I in o m <M O m o -<

J- r>- r- » -O CM

r- 33 >»• p» m m

o- o <D

f»- 33 r»

fOd <T1 o o o I I I LU LU LU m CD r33 CM .-< -H 33 O

-»•

O CT) -H O i-l O rr, cj- fM ,» 33 f X> ^ o r- •-» rn ^ m

OD ^ CO o1 I UJ LU

CO 33

<3 S3 m cTi in O

eo r~ m o O iH O -^

.-4 -f o m

O- CD

-»• -r J- >»• nJ- o o o o o I I I I I r <3 -o

^^ -r in m i-i CM -HMO

CM o ri-i r- -o

33 ^- r-l <r (y -r <? r- r>- 03 —< m

CD CM o ^ 33

33

O

>n

m

f>-

O

r^ o

CM en O f^

-»• <r -T -r -»• o o o o o I I I I I UJ UJ LU UJ ' ' 

o o CM r- ^n CD * c\j CD rvj t> •» xT CM r- m r^ o -o -n

cy o r^ CMD

tD r* -T CO ^

r- ^- rm .^ m -H CM in h»

en 1-1 CM o cy o o> p~ P~ •* —< >#• r^ n ^»

c*i en <n

m ffi o o o o o I I I I I LU LU UJ UJ LU

-»• pn .r

—t o ^ -r CM rn iH

—1 (D

O ro fO o in o ^ rvi 03 <3 CM rn ^

r^ -T tn -r -r

J- -o

m io

m o •-< o o m

CM 03 in ^^ (*) r- Psi o o o O <-! -H O "H • CM •CM • CM • CM •CM - •-4 • • —

m • 3) • 33 •03 33 •

S3 • ••-H • r^ ••H •rH • rH • rH • • rH • • rH • •rH •rH • rH •(J- • •S3 • a- o 33 • • •33 • 33 • CM • CM •CM « • CM CM

c*lm i-l en en

m cn cn cn cn -> >r -r » >»

m cn cn in cnm cn

m cnm cnm cn cn cn •r ^ >r •f •*• •r •r •r -r •r cn cn en en fn o o o

LU o o o o O o O o o o o o o o o o o O

O o o o o O

OOO o o o o o o O o O o O o O

O

O

LU LU LU LU LU >V UJ UJ LU LU LU LU LU LU LU LU LU UJ Ol LU LU LU LU LU LU UJ LU LU LU UJ LU UJ LU LU LU LU LU LU LU LU LU IXI LU LU

rH -H r- -»• -O o- i-H f-4 <o o J- cn ~r o O r~ nT f>-

m rH •O

O -*• cn

—tr-- rH rH •O o cn •o r- cn r-t rO en h- rH r~ rH en >»• hf^ m r- o> o * in ^ -r •1- f-t O i-H CO CD rH rH cn O f- O CM x^ >» m m cn rH -»• CM •* -r o 33 cn h- 33 <o O N- p- m •»• r~ ^- m J- (j >» 33 m CM •o >o o in O m o >o in O CO m •r cn •r .o r- CM XI O 1^ CD rH .o CM CM 33 o co CM o m r- o o rH p- e'- ^3 m r- J- m in -» f»- 33 <-l >!• o o CM m rH o r^ CD cn o- r- •o O •-I cn r*. o O o r- cn rH m 03 a- ^H CM ^-t o m CD * en cn

i> IM in

m o a- o -r in f~ CM CO CM

m

O o cn •o •n rH a- -o f^ »»•

m

O r- ^ CD >r •o en 33

O o rH -r

O cn CM CM rH cn -»• <e\

m -rmm

v -u *• o t-H 33 in -r CM CM

O CM

n r-t •-I

O 33 o 33 j-i o> >»• en ^ C? -*• cn

O r- f^O o en OD cn en cn oO

O r4

o- CO 03O a- rm o- cn CM o o cn CM o 33 cn o CM .r o -r

O r\

m e'- 33 9 r^ <-i cn s rH •e\ •om r~

m h»

V S) a> p- 33O

T CD CM rr,

m o D CM in cn o o CM o in J- CO cn 33 o m -H •a o •f en cn -O CD •X) cn r-^ o rr- o <*• CM in -» <^ r* •r

m ff

O o o r~ rH O r- m in cn 33 cn <x> ^ r* r^ CM o in O •r r- cn cn in rH o p- rH rH cn O rH ID CM <D rH in r» <r <o K^ rH * m in

<o r~ r»O 33 CM

m CM •r cn r>- 33 o <o cn r- r- r^ T-t CM co f- 03 o cn CM in 03 rO 03 <o CM cn <3- f«. CM -* o- f- •O o o rH

O • cy• 33• O• CD• CO• • • C • • CM• 33• • m• J^• •om • • • cn• cn• CM• cn• fM• • • r• -0• • (M• 33• o• • CM• • cn• • • • cn • • cn .r • •

*0 in ^ j^ lA cn cn cn <n cn ^ r^ o ^ p- cn en en cn en cn cn cn cn cn cn cn cn cn cn (S S 133 S 00 o r» CO ^- r- <•<•*-**

CM CM O O + +

ijj LU O —I

IM CT- r-{ m

cn cn O cn in CM o r~

CM (M

r»- r>- m en

CM CM ^J o o o

•f + +

UJ LU LU O P~ rH

<M ODm

!> o r» m 03 o

CM >0

O

cn rH >H

cn p- f*

P^ (M CM o r^ p^

cn cn en

CM CM O O O CM

OO

cn o> m in m o

cn o

33 CO

PU CM P- P~

cn cn

CM CM CM O O O + +

LU LU LU

•o in p» O >»• -H

cn 'O

m

in 33 in

CM

O CM r^ -r cn

p" p- pfM CM CM

p- p~ r^

cn en cn

CM PO O O

03

O

CM CM CM O O O + •• UJ LU UJ

en o (M ID O >0 o CO -r o p~ m moo •O rH rM

f^ CD CD

<J> pr^ o

CM -O 33 CP o -o CM CM CM CM CM

p- p- p. p- pcn en cn ^ cn

CM CM CM P4 CM o o o o o + 1 1 I 1 1 1

UJ UJ LU

P~ •»•

O 03 *• o o -o "> p~ o 'tf' o en in m O P" en to rH O O O >» O P- P- m

(?

OOO rH

CM cn cn cn en

p>- F^ p- r^ P»

cn cn in cn cn

CM CM CMM CM

O

OOO

O *

i-t

O

CO

O

CTO

•r cn

p- o

rH

O

OD 03 CM CM P- Pen cn

inm rH

m CM rH

CM 03 CM rH cn 33 O cn o

en cn CM

33 OO CO

CM CM (M

p- p- r^

cn cn cn

fM CM O O

LU LU

O- P- rH rH m *

CM cn

~o o

<n ^-

<y o

CM CM

P- Pcn cn

CM CM (M O O O

LU LU UJ

P- >>• CM O rH 00

-o o o

CM >»• >»• rH CM CM O rH O

CP

O

CM en cn

p- p. p~

cn en cn

CM CM O O

LU LU O in

0> o O r-l

S3 cn o o

CM cn cn en

(M CM CM O O O

UJ LU LU

CM -r o

r~ -r ft o ^ p~

rH rH CM rH ,#• en O P- o cn CM cn

cn cn cn

cn cn cn cn cn

CM CM CM CM fM O O O O O * ^ m rH CM rH f^ cn ® ^ cn * CM O a CM CM P~ ^- O m

P- •»• r»- {> rH

in 00 o rH cn

fM CM cn cnm

cn cn ^ rt cn p» p- p. p- r^

cn cn cn cn cn

M CM O O

LU LU

>r o O rH

33 -O

<o -r f^ o o m

<n cn en cn

fM fM fM o o o

UJ LU LU

CM * rCD fn rH

P*

O h- f* O O

in rH fO fM oo ^r

cn ^ fn

en cn cn cn o o o o o + + + +

LU LU LU LU LU O CM cn cn in

,0 o O CM c

tn >»•

O P» P~

CJ. J- o 33 -o CM C O -< Pp- cn J- o o

•O -O P~ ^ O o o o o o * + +

III 111 III 1 1 I 111 O m .H (D f*

«»• .0 -o <» o

in >» CM o P~

CO CM CM >r pCM M ^- O O

p" vO P» in in

in

m .n x^ ^ O

OOO

O

¥ * ^ * * 1 1 1 1 1 1 1 1 1 . 1 1 1 1 i O CM vn o in * in o »» O

cn •» 33 CM en

-O in

m 33 OJ

O -»• rH cn ^

fn fM CM fsj cn p» p. p. p. p- o o o o o *

ill 111 III III 111 o p- in n cn -H CM CM cn o

p» * fM o m ^ CP <NJ p> o O en in in ^ m -^ cn o cn

p- p- p- p» pO*••* O O O O

UJ lU UJ LU lU o o >o in ^

rH CM o in CM m -O O CM fM o in o in t-H O cn ^ in 00 O O 03 o o

in <o in in in o o o o o

•*O rH ^ O CO O P- r^ -O rH

03 *• -r f\j

m

P- P~ CT- in rH o !> o oo en

-O -O

O rH rH ^ '^ j> in in

OO

O

O

O +

i±J 111 III 111 111 m en o rH in fM p- rH o en o m o en m

fM o <)

OO

O fM » m rH O O CD P>- ^

-OO 'O -o

O

OO

O

O ^ * * * *, LU UJ UJ UJ LU cn o -r .O -O rH O O P4 en O P* O O -o O m O rH rH p- <0 O i> cn CM -f rH CM ^- o o o o o + *

UJ III III LU III » cn oo * o

p. rH p. CM .O <M CM cn in «M O 33 00 rH O

en 00 fM fvi CO

oo r^ 33 o r^

in in

m inm

r~ p- o P- p- o o o o o o o o o o

fw p- p. p^ p» o o o o o o o o o op- p~ p. p~ N. o o o o o o o o o o o o o o o o o o o op. p- p. p. p. o o o o o o o o o op. p^ p~ p~ p. o o o o o o o o o op> p> p. p- p- o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o <? o o <? O O O O CP <y o cp o o O" 9- O- O- O- CP O » l> » O O O 0> ffi o^o»^ o^^^^ O O 9. 9 9>

Q

z.

1~i •-I T-t r-* -H <M CM fM CM CM CM CM CM CM CM r^ rM r-t rH rH rM ft -H rH ft CM fM CM OJ fM CM (M CM fM fM fM OJ pj OJ PJ fM PJ OJ CM OJ 000 ^ + 4- * + ^ * • + + + * * * * * ^ • * '^ * * * * * * * ^ * *

LU LU LU Uj LU LU LU LU LU LU LU LU LU LU LU LU LU LU UJ UJ LU UJ LU LU UJ LU LU UJ LU LU lU LU UJ LU LU LU LU LU LU LU LU LU LU LU UJ

>r CP O" cn 33 r~ -0 cnmm p- CM fM cn fMX -r fM 0 J- ^ 0 *•m 0 •0 <o OJ fn

X in

X OJ P- .0 ft 33 en CD r^ en >» ^ P- in (M rH r^ P* cn >r P~ cn r~ rH CM CM fM en OJ in b- in OJ OJ X rr. .^ p- m in <o

33 33 in .»• cn om aa fM 33

m cn rM en •0 .0 P- P- •* OJ •-H <o -O c CM OJ r~ f* •0 -* (f » *

CO <n -»• -r rH p^ •0 <3 p» fM 0 n CM rH S3 <y ft -0 <o -»• P- P- »• in J>n OJ

mX P- fn cn .» •r rH >H p» CM 0 cn CM -r CM •r >»• cy (7- p- fM cn en rH en ft X X ft 0 -»• P«. CM m cn X p- p- m X X c^ m en P- p- rH •0 en

-0 P- <?> in 03 CM CM p- » 33 CM r^ CM cn >»• j> •o p- rH •r •H I>

m CM

m

X •0X vn p- rH in OJ OJ

X t-H <3 f*.m cn

33 P~ -0 -0

m CO 33 CO CD OD o- oa

m 0 r~

r -r in en

m ft pX r^X <DXX <D CP P»

X r*

X

(J- o- <y a- o> CP o- o- O- t> CP CT- CT- o- O- o> aCM C o- o> o- CP 0- o a- o- <J- CP o- CP »

P» o- <y Cf o> c J" (y <? o- CP CP O- o> (7-

O (y

0- vS

m in in in

m CP o> o- o- 0-1m in tn ^ r~ f- f* P~ rm

m

m inn i-t iHH rH rH

mm fM cn cn CM CM CM fM CM cn cn cn en cn in

m

mm

m o- CP rH rH rH ft ft ft r^ ft ^M rH en fn fn fO cn .-H rH •H rM rM

-H CM a- -»• in •0 P~ 03 rH IM cn -* in •0 P- S3 a- rH CM cn * in •0 P»

X ft Pvlm f in -0 p^X rH fM fn ,r

m

a- -H >-l ^^ -t ^^ -t '^ rM ft -H fM IM CM pj CM CM CM fM OJ CM cn cn cn cn cn

m cn cn pfim ^ >» •r <»• •»• -r

C CT- 1^ p- p- p. p- (^ r^ P- p- p. P» P- p- p- p- p» P~ P-. r^ P- P^ P- f~ p- P- P- P- p~ P- p» r«- p- p- P^ p- r^ p- p- p- p- P~ p. ^ p- pCM CM fM fM CM CM (M CM fM CM CM rvj CM CM fM CM IM fvj CM CM fM CM CM IM fM CM CM OJ OJ IM 00 OJ OJ OJ OJ OJ oj fM pj OJ OJ OJ OJ pj PJ

CD 33 0 00 CO CO CD 33 <x> UD 33 33 33 33 33 OD 33

X

X

X

X

X

X

X

X

XX

X

XX

X

X

X

XX

X

XX

X

XXX

X

X

7- <? rH

CP o- a- <y (7" a- CP O- CP

,_4

•J- CP

rH

a- I> CP c- t> o- PH

i> ^H ^H ^H

CP

rH

,-n cn cn rr, cn

m cn en en cn cn <n cn rr,

m cn cn cn en

m cn er^

m

m cn rr. cn cnm cnm cn cn rr, cn en cn cn

m fn fn cn en rnm

CM CM (M CM CM (M CM CM CM CM CM CM CM IM CM CM IM CM CM IM CM IM CM CM CM OJ CM OJ (M OJ OJ OJ OJ OJ OJ CM OJ OJ OJ PJ OJ OJ rj OJ PJ

33 33 CD CO CO 33 00 33 CO 33 33 OD 33 33 33 CD 33 3)

XXX

XX

XX

XX

X

X

XX

XXXXXX

XX

XXXX

X

X

r-< rvj cn -r in rH CM

m J- in ft ^ cn J- in ^ fM cn ^ m ^M CM en >» in rH CM cn •r in rH fM

m -r in ft OJ cn -r in rH OJ cn ^ Ift

C

"^

in in

m iT.

m in in

mmm in J^ inm inm in

m J^ in in

m

m in in in iTim in in in

m in

m in in

m •n

m \e\ inmm in

m

<i3 (J <^ • • • o m m m cn cn .—1

-( .-H -H T^ ^0 0 -0 -0 0 ^ o- o> cy CT- in S\ in

m inXX

X

X

X OJ IM PJ OJ PJ

CM fM IM CM <M .n cn in en en 3 ft ft rH -M -H ft ft rH rH mM ft ft ^M ft rM

p- rH P- CM r»- r~ cn cr »1 —i CM CD ~r J- 0- in 0 X *r -0 CM cn -0

m o- p- -r ^M P» •r >r rH

X -r rH p- •r rM

-r rH

m fM CM in rH J- rH en

n CM in CM

n CM ~J- cn

m in CM —1 <n rri in pH -r f-Hm in OJ ^ -H «r >»• cn PJ

-D

n ^H 33 Jm CM 33 in r> -0 CM -> in <M CD J- -H p- IM J- J^ ^H

X cn •0 •MX «r 3 p. <n J- rH p- >r r> OJ

X

n rH

in rH rH CM cn •r ri in CM CM cn en J- -H CM CM J- •f in ou IM cn ^ ^ rH rH OJ ro ^ inm ft OJ

m rr, ^ in

43 t^ r^ P- r^ N- r^ p- p- XI OD 33 33 CD 33 oC CP o- a- ft -H rH -H rM rH ft ft OJ OJ OJ rj PJ CM PJ O —1

rH t^ rH -H rH—1rH -H f4 •H ^M rH rH -H rH ft ^M -H frj -M -H

CM <M (M IM CM CM CM <M CM CM CM IM CM CM IM CM CM rM CJ IM CM OJ CM IM IM r\l •M 00 IM OU CM OJ OJ OJ OJ CM OJ OJ OJ Oj IM OJ OJ OJ PJ

CM CM CM CM <M CM CM CM fM (M OJ CM CM CM iM CM IM IM ;M CM IM IM CM IM CM OJ OJ OJ OiJ OJ OJ

M CM OJ OJ OJ OJ OJ Oj OJ Oj IM OJ OJ PJ

-n cn cn cn

m -n tn

m cn rr. cn cn cnn -n rr.

m cnmm enm .n cn cnm cn

m cn cn cn ,n cn cnm in cn cn in cn

mm

m rr, rr, o

CM CM <M CM CM CM CM CM CM CM CM CM CM CM

M CM CM CM CM CM CM -^ CM IM CM OJ 00 OJ OJ OJ OJ OJ IM OJ OJ OJ OJ OJ OJ OJ OJ OJ PJ PJ OJ

CD OD 33 CO 33 CD X) CO CD CO CO CD 33 33 CO 3: 33

X

XXX

X

XX

X

X

XXXX

X

X

X

XXX

X

X

XX

XXXX

X

B-8
cT)

m fO

m

mn CO ro ro ro CO ro ro ro en ro ro ro rri ro o o o o o o o o O o o O O O o O o o o OI 1 1 1 UJ lU 1 UJ 1 UJ 1 UJ 1 UJ UJ 1UJ 1 UJ UJ 1 UJ 1 ' Ui UJ UJ 1 UJ 1 UJ 1 UJ 1 UJ 1 4 UJ UJ o m o CM r- »H ^ 00 ro CM r-4 in 1-4 CM c>- CM ro m -» -O rH INJ o- r-> n o O in O ro CT- oo CD o- CS I^ ro o p- 00 O -H CVJ m * -o .-1 «-i O —4 O CM -^ u- o -o O Cf o ^

>r oo •-I CM

O in fO ro ro -»• in rH ro CM CM ro o rM rH

O o c oo O rn »H o (M O ro ro ^ ro O rH CT- o in in OD

<D ir\ •o •o

m r- .-4 O"

O o>

a "M

O CM CT- ^^ •o o JO

rH (\JM CM in •o •* r-4 <o

O CM ro in 03 O- <D ro r-4

O rH

O in C\J fO CM •o N. -*• ^ (D CM -H 00 ~r r» o -H o >* r~

(vjm >o ^4 <M o (M CM 00 CO

O iM

O -o o •o

O r- rH OO

-»

n <r) o CM

m -^m o- ro -o

O o .-4 f •o o p- (y o O C3> o> o o- CM CM CM t-l CM <y- O" w O o- •o r- •o p- pi-H —)

t-« f-« -H CM CM CM CM CM -H -H rH r-^ r-t CM CM CM CM <M

fO

O

n rOm trn PO CO CO CO ro ro ro CO ro ro ro ro ro o oI 1 o1 O1 oI et O1 1 O O O 1 oI OI O1 O1 o1 o1 o1 o O O1 1 1 1 UJ LU 1 UJ 1 UJ 1 UJ 1 UJ UJ 1 UJ UJ UJ 4 UJ 1 UJ 4 UJ • UJ 1 UJ 1 UJ 1 UJ UJ 1 4 UJ UJ o o- '-t o CO •O -0 c*> r- o CO -»• >» O o fO o ro o >r o -o r- CVJ oo (M CM » m •f * ro in CM CO -* CD OO J- PP" o *• m m O «» Cl ro <o CM P- h« rH ro o m r>- O rH

r^

m r- •o •r CO

mm

V * o P- o o CM u-\ rH o >r 33 -H r- m r- p" -r in CO o o •r .n O r- f- in ro rH CM r^

<\J oo r«- <o -u CM

O CO f«- <o ro 1-4 in CM r- rH l>-

m in CO

to CO o o ro <D o o> (j. (J. CM t-4 CM CM rH o » rH

OO

fVJ OJ o M -4 -*•m -» -r ro

O in * -O o- in •-I CM in CO

in a> a> UJ -r o >r * o CM CO *-^

O rHO •o o < o <o

m o O o m * f>-m f^ o>

O rHO ro CM CM *• (O rH oo OD r- 00 o r>- »H O rH o O o- <J- O- f^ CO CM r- CM (y P- • • <n • ro •in w in • m CO ro 9ro ro • CO • • • P» P-

<\j f\j <VJM CM (M CM CM CM <M CM CM CM CM CM CM CM CM CM CM o o o o o O O O OO o O O O O o O O O O

•• * ^ ¥ •• + *

LU UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ O <\J ^H •» in CM w CM O CM o O ro •O rvj r4 <o o ro o

<x> oo •f f-t CO

O en f-t in

O ro ro h- •O •o ro ro >r CMO

r«. CO

O •r

mm CM O- CD CO t- CM >* ro rH o ro in o o o r^ •o CO o r- o a- •O CO * p- O in ro CD f4 O m o

f-t o- oo in <y o O CM CM fO •* rH CO t»-

O P- CO «*• p- o

w* OD fOm fM r~ —4 o CM CM >r CD CM ro <o •*• o o CT- CM

r- .o f- ^• a> oo » O" o o> o O rH ^ t-t

O rH t-tO rH

ro ro cn (*i cri ro ro ro rrt ro -r * -»• •r •» * •f •r •f -f r« r- ^- r- h- r- f^ f>- r~ h- r- r- ^• f>- f»- r>. r- h- P- P-

«»1 tr> t-« 1-1 • • •

1-4•

C*l• •

fO

1-4•

fO

-4•

ro

•-4•

COrH•rofH•

ro

1-4•

rorH•

co

rH•

ro

rH•

roft•rorH•ro•

po ro

•-> -t • • ^ iH -4 iH ^ o o o o o

-^ 1-4 o orHo orHo

•H

-HO-H -H O O

O

rHo

f-t o

f^ r—

rH rH o o

rH rH

-H rH o o '^ * > ¥ > > * • *

UJ UJ UJ UJ UJ UJ UJ UJ Ol UJ UJ IXI UJ UJ UJ UJ UJ UJ UJ UJ o o- o ,o o CO o -4 o <D CO CM r\j O >^ CM o CO •f m o ^ in (T) O •O CM CO CM CM CM P- CM CM in CM o r» o o

oo CM f>- r^ * -»• r-t

O CM in <x> rH r^ h»

m ro CO p- CM -r »• -O >r fO (?• <^ iH •^ CM M ^- ^. rH O in r~ ro o- ro CO

.o -rM

m

O >4 o O •-4 CO <y o -c

O in rH r~ •e ro ro

i-t o 1-4 csj o o in CM CM o o ro •r ro CM >»• -^

m in J-

<0 iTl £> <o -o

m •o •O •O o o r>- f- r~ r- r- !>«• r>- P- P- ^.

»-4 ^4 rH —4

H

Pr-i rH

P-- r». o o o o o o o o o o o o o O o o o o o o o o o o o o o o o o o o o o o o o o o o

CTO (J. {^ » o- Cf o o> (7> • o- o o>

O <y o> CT- o o M (Si <NJ fM CM CM CM (M CM CM CM CM CM CM CM CM CM CM CM CM o o o o o o o O o o o O O o o o o o o o « * * <» * H. 4' + •f • •

UJ 'JJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ O f>- oo iTt « 1-4 r- <r ro »• ^. CD CT- CM >r -o oo OO O -H O rH r- r- oo r-4 fO m f~ m -H o •H O CM •-t rH * ~r o

-O -H >*• in in CD in

m J- CM in oo P- CO CO OD OO r*- .\J CM

(M <0 •r >» r~ <o o -r o f>- J- CM

m .»• -O

r in

m ro ro

CO ^ •r CM <r >»• inm

O

m * O rH c> o m -» 00 in

O

O <VJ <NJ r-4 •o •o t-^ o in •r ro r^ OO 00 ro

O CM r- rvj oo Cf O O O <o o o o o o O O <> o o O- t7> o <y oo

O- <J> oO o o- o o o> o o o o o o o O o O CT- o o (y O o o o o (y o O o O" o o V O o- o <y- o> o> o- O o o- o o o o o o o o o o o o ry CP o -o • •

•om • •

(7-• o• o CT-• o• • ro CO• • • CM• CM CM• CM CM • • CMCMCMCMCM cjrorocMro cmcmcmcmcm

>o p-© ^ o

J- -r * -*

m o o o o o

1-4 CM ro * m

in in

m in in o o o o o o p- oo o o

in

m in in >o o o o o o

CI ro CO ro ro

rH CM ro .»•

m o >o >o -o o o o o o o

CM CM CM CM CM

oo ^ 00 CD CD o o o o o

ly If ly- o- <yrvi CM rvj CM CM

OO QO ^3 CD ^D o o o o o o ^ o o o

CM CM CM CM CM

00 OO OO ^ s O O O O O O CT" CP ^ ^

CM CM CM CM CM

<o ^ ©

® OO

OOOOO o o <J> cy o

5£ ro ro ro ro ro V> O O O O O •-• CM CM CM CM CM o OO OO CO oo CD • -4 INJ ro .»• in

<3

OO o o o Z r> o O O o

in in in in in O O o O o o o o o o o o o o o o o o o o

CO CO ro ro cO o o o o o

CM CM CM CM CM

^3 CO CD ^D ^3

.H CM ro *•m

O

OO

O

O

O

OO

O

O

in *n

m in

m o o o o o o <^ o o o o o o o o o o o o o

CO ro CO c** CO o o O o o

CM CM CM CM CM A <0 OD OD CO

rH CM ro >»

m o o o o o O O O O O m in in in in o o o o o o o o o o o o o o o o o o o o

CO CO CO C^ CO o o o o o

CM CM CM CM CM

CD CO CD CO CO

•H CM CO -»m o o o o o o o o o o

in in in

m in o o o o o o o o o o o o o o o o o o o o o o o o o

c>~ p» p. r>- p.

CM CM CM CM CO

rH

O -O -» rH

CO in (\j in CM o rvj "> in CM O rH r4 CM ro

c*) ro CT> cr> CO -H -H -4 ,H -H CM M CM CM CM

CM -M CM CM CM

CO CI CO ro c*> o o o o o

CM CM CM CM CM

OO

A ^ ^ 00 o o o o o o o o o o

ro CO c*l CO CO rH CD -O -r rH

CM >r rH ^t- rH

p" cn

O -O C4> -r in O O rH

CO ro -^ * J- -H -H -4 rH rH CM CM CM CM CM

CM CM CM CM CM

en CO CO ro CO o o o o o

CM CM CM CM CM C OO ^3 OD CO o o o o o

J- >r .» -J- sj- CM CM CM CM CM

(O

m ro rH CT* CM J^ CM in rH

CD J- —4 p. -r rM <n -»-» in

>» -r J- .» •»• rH -4 rH rH rH

CM CM CM CM PO CM CM (Nl CM (M ro ro ro ro en O O O O O

CM CM CM CM CM A OO 00 OO 00 o o o o o

ro ro CO ro cti CO ro ro CO CO

rm ro rH o o ro o en o o o en o o

rH -4 -M CM ro

in 'n

n in .n rH rH -H rH rH

>\J CM CM CM IM

rsj fM CM CNJ CM

en en en in en o o o o o

CM CM CM "M CM

00 CO

D CO

O

B-9
m pn rn

m CI J- * * ^ >r tn pn on pn

m pn pn

m pn

m

m pn pnm rn •r * >r * •* o o O o o o o1 o o o1 o o o O o O O o1 O o O1 o o o o O o o o o

1—4 < 1 LU t OJ 1 LU 1 UJ 1 LU 1 UJ 1 LU LU 1 LU i LU 1 *

LU LU t LU i LU 1 LU 1 LU LU 4 LU LU UJ 1 LU 1 LU 1 ' '

LU 1 1 LU LU 1 LU 1 i i LU LU 1 1 UJ LU

t- r~ r^

m f- •r pn o 1-4

O 1-4 o pn -4O -O o m <£} 33 r^m <y o S3 •* >-< -* f»- •r -o UJ o- o CO ^ 05 ^ » o -» m o o m (SI pn GO r^ OO r- CO OJ -0 OJ r- (SI •o o P«i •O (O X LC -J- lO D CO J- r^ f^ o m <r ~r f-i •* in OJ c O •o OJ p^ OJ in OJ OJ p~ in P- m o

t- (\J -c o CO in PSI CO <y o 33 h- OJ F^ 33 OJ OJ o- OJ o r^ pn r- -r pn o CO o P- 00 in

J- ^J -r ^. in pn 03 o pn ^ in

m o r^ r^ o- p~ f>. OJ ^ p- o OJ r- o 33 o ^ o -e

m ^ o o -r r~ in f^ •r ly OJ o 33 r<. 1-4m o o in 00 OJ fm * OJ

O •f

m <y # p~ » O in r- m CO (SI ID pn •o pn o in O ^^ o r-- r- r» CO f^ m m O m OJ m CI (y 1-1 *•

UJ o r» o « o (O tn ^- in o f>- o •o 0^ o J3 >»•

m CO CO OJ » m (B OJ h- pn CI o -r

a (? r- r«- .0 •o o -4 o CD o OJ OJ r~ ^H o m •• •-4 * <y •r o •r pm

r o ^ OJ •* • 1-1 a; cc o o f •a pn m m r>- r- co o ^- m in m m m •o * 1-4 •r m #• pn CT- O Pr-^ o o ^H '^ m 35 in m OJ m m in J3 tf^ OJ fSI OJ pj OJ •f ^ •* * * OO 1-4 P~ o o

<M (SI (SI PVJ (SI 05 GO OJ (D CO OJ OJ (SJ OJ OJ OJ OJ OJ OJ rj OJ OJ PJ OJ fSJ OO <y o 9- (O n n m pn (n •»• >»• -» ^ •»• m on pn pn pn pn pn m pn m pn pn m pn (T) -r •r -»• * ^ a

UJ o1 o1 o O1 o1 o1 o1 o1 O1 o o1 o o1 I o O o o o1 o o o o1 oIIIo o o1 o1 o1 o o1 1 1 UJ 1 1 LU f LU 1 LU 1 LU 1 LU 1 LU i LU LU 1 LU I LU LU LU LU 1 'UJ LU 1 LU 1 LU LU 1 LU iXI i LU LU LU 1 UJ 1 LU 1 LU 1 1 LU LU

OL -o ^H <? o pn o fH r» o- o on -r >0 o o f*

m o o r«-

O -O 1-4 -H -O (n o •O

O P«. < M o * 05 o •o m 1-4 (SI PVJ OJ f^ o o OJ pn •r CO 00 h- O •O O h- O •* OS •4- e m 3 03 ^H o m in o O in c^ o pn r» «»• PI PNJ r>- o o en r«- o p- OJ <y r- 33 OJ o OJ V

ri <o J- o <o (VJ o o •O -r OJ o •o <Jr OJ o 03 * 1-4 OJ CO o o pn « m CI <y o m

1/1 o r-4 •r o- CO 00 •r -r fSI o 83 (SI J- OJ OJ 33m -»• t> OJ « in r-4 o -r

O o p~ o m

m r* OD o (SI 4- <SI pn o- 1-4

O 33 <r 33 o OJ

m cs on OJmm 1-4 <j- in i-> « ^ <SJ -O < m o o« r- (Q r- m to m (SJ -*• -r OJ m pH pn Cl pn r~ en r pn r~ ^ m ert r>- OJ OJ <y

s: irv ~i- ~»' o o o a> -o (SJ vO >o t> OJ o m >r (? •c .n OJ ^ (SI -* P- -4

O OJ «» CO OO o ^ o in o o in ^- pn o •o •* m pn o O o m o -r p- o- OO pn r- in CO -o OJ •* <•

t—1

-0 (SI (SI o o (SJ r- o o 1-4 OJ OJ o r~ pH .o •o in r* o <! <y OJ CO osi «» 03 in CI ^

1/1 ;n J- * m in -^ o <n o o- r- ^>. a> CO r~ 1^ -H 1-4 o o 1-4 o 0>

OO O' •*• CO OJ o •

-I- •4- • ^ • • ^- p- • • lO •a >0 • •o • m in • •in • • •

•o • ~ ~ m .o o • •

CO ^• • •

pj (SI (SI (SI PVJ (SJ (SI PM fSI OJ (SI OJ OJ OJ OJ OJ <SI OJ OJ OJ OJ OJ OJ PJ OJ OJ PSI PJ OJ OJ o o o o O O o o o o o o o O o O o O O O o O O O O O o o o o * • + •• ^ * + * + * ^ * * + * • >

LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU UJ

(M <C in (^ -0 pn r- -a CD 3) OJ

V 1-4 OJ * 35 iH <C o m h- •O OJ PJO PM p>- 1-4 P- o-

>C r»- r~ -o •r r-( -» 1-^ o !?• CO o in 33 o r- 0> ^< f-4 r- pn OJ 35 .r

m (D «»• ^ m o

fO -r .o vA r- ^ r- 33 (SI -H P- o in •r ^4 CO r^ CD OJ >»• m4

m * PJ 33 ^ P~ OJ IS P- o < r» a- (SI -H •o pn O- M pn r^ m o- 05 O r- N- OJ F^ m r- OJ •r •O r- m (y -o m fpi 9

V- o ITi -^ fH f~ o (<1 pn >» <n 1-4 pn o •t rO iH

O o « wM r^

m r- -Hm •r <*• o rUJ 1—t m o O 05 «^ O >0 ty -r OJ >»• r- o CI rt r- o 1-4 m •H •o ^ <o <B «T) m t> OJ r4 X 1-4 o o —4 O w o- o- o- o o o o o 1-^ cn pn -J- >r •r >o in -o £> -O •o •o JD p* rt— -r -J- -» >* >» pn m pn pn >r ^ •J- >» >r ~»- •r -*• «r -f •r ^ -»• ^ f » * * r -r -f

r«. r~ r- r~ r^ r«- h- r- r- p- ^• ^. r- r- r~ p- r- h- r- r- f^ p~ p» P~ f«- r- ^- p- f>- f^ •

pn•pn•

ppi•

pn

--(•

pn

1-4•

Cl

1-4•

(Tl•

pn•pn•

pniH•

(n

1-4 pn1-4•

pn•

pnpH

pn• •

pn9pn• m

iH•

on

<-4•

pn

iH• •

pn CI

i-< i-i • •

C1iH•pn• • • o o o o O o

1^o o

1-4 o

1^

1-4 o o o o o o o

iH

1-4 o O o

l-H O oi-H rH O O o O o o o + •*• + * * + +• + * * *• * ^ •^ + * •¥ ^ LU LU UJ LU LU LU UJ LU LU UJ LU LU LU LU LU LU LiJ LU LU LU LU LU LU UJ LU UJ LU LU LU

r^ ^ y- (SI >» o (SI ^- -r CO o o PSI o ^»

O in •or * in ^H -^ o * •* -0 o in ^.

m >Jm o in in o H pn CO o f* o f- o 33 .»• o o (D s^ s>

rO CI •*

m OJ OJ ^•

rH 03 -O •r pn r~ o -^ 1-1 .o pn

m r>- •0m 33 (n -r o O r4 <y * in 9 CI p" CI -r o

<M (SI rO (SIm -o -r o o o OJ OJ PSI •r o >o

O pg o m .0 r- pH in -o p- •o

O CO o < ^^ o (SJ PO in »H o <» -a in o ~»- pn 33 r- r- a o OJ * o IX> -r ^ .H o tf> CI — »• - o r«- CD r^ -0 * « ^ ^ OvI 1-4 OJ OJ OJ o m OJ 1-4 PJ <»• <y CO o CD 1-) OJ <-t pn PSI OJ X

r~ ^ O -o >0 h- r» r» r- r»

m in in in ^ inm

m in in

m in -o in -c o o <c •o -o

r^ r>- r^ r» ^4

P«. ^

r- p- P- f. p» •^ iH

P«- P- o o o o o o o o o o o o o o o o o o o o O O o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o

(y o a- o (y » g. o- O' o » o- o o o o o 9 <y o (y ^ w ty <> <^ » (T- <y o M (SJ (SJ (SI (SI fSI M (S) (SI OJ ^ —( 1-4 1-4 1-4 OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ Pvl OJ PJ PJ CM o o o o o o O o o o o o o o o o o o o o o O o o o O o o O O * * * * •• * * * + * •¥ * + * ^ + * • +

UJ LU LU UJ UJ LU LU LU LU LU LU UJ LU LU LU LU LU LU LU LU LU LU UJ LU LU LU LU LU LU LU

(M o r- r- -O pn r-« (> (SI (D f^ ^ CT- o 1-4 (S 35

O <y o CO o OO o tn

O OJ i-l

m o O m -0 >r pn (D tn -f r- r~ rw in OJ ^4 pn 35 S3 vf PJ -c m m pn •o o 33 CD •o 9- OO

—1 o ^H —1 o o PSI o h- in co r~ OJ OJ ^ •o OJ •O •*• pn

m -0

O OO o o •O OJ ^- OJ OO < •-I o m m *• O fvi pn ^^ -»• CO OJ OJ CD o O OJ P- m o CO » OJ ^- -< o (S> -o O O

H- o (T1 (SI ^ r». 03

m

r -r r- o ^ o ^^ r~ >a pn

m fSI OJ PJ

O ly p» ^ p- r»- 1-4 S3 rt

UJ in CO

r

a o OM ^H as p- •o •r 00 r^- •r (? Cf

OV o OJ r- <o o <o PJ o CO OJ 9 X O- !> o o o o o t> 03 33 o r~ f- o OJ N. r~ P- t- p- O <y o o o 33 s p«. S> P«. - O >^ c> o- ^ o o 17' O !? ^H o O o O o ^ (J- o (y o o- o o o- CT- <y o O {> o o o o- a- o Cf o- o (J- o o O o o t> o <y (y <y o <y o o o <y CT- o CT- O

a- (?> a- o CT- o if

O o <?• o o o o o t> o> o- (y <y o <y

OO ff- CT- (y (T- CT>O

m

m

dm pn

m

m in inm o o o o o 1-4 -^ 1-4 1-4 1-4 o <?

OO 9- p*- ^" P- r>- h-

(SI

M (SI (SI (SI pn pn pn

mm pnm

m

m pn r-4 .M i-H 1—4 1-4

m OJ

m pn OJ 1-4 1-4 1-4 1-1 »H

LU •—4 (SI fn •rnO r^ (C o o fH OJ pn •r

m lO p«- 33 (y

O 1-4 OJ (n .»

m •o p~ 35 o o

—J o O 3 o o O o o o ^^ ^J i-H rH 1—4 i-4 1-4 ^^ 1-4 1-^ PJ OJ OJ PJ OJ OJ OJ OJ OJ OJ PO

U. o O

O o o o o o o o o o o o O

O o o o o O o o OO o OO

O

O o O O o o o o o o o o o o o o O o o o o o o o O O o O o o o

-»• -»• ~r J- J- •f »r ^ >» •# •» J- -r >» -i- -*• J- •r •r .r ^ >^ ^ >»• >r

r «• * -r * O

^-

m

m

m PPI (nm pn pn

m (n pn pnm pn rr,

m pn pn pn

m (n

m <n pn CI pn

m CI pn pn

m fnm pn pn

m pn pn pn pnm

1"^ pn

m (n pn pn pn pn rri pn pn pn pn pn pn pn pn pn ^4 ^pn en

(SI (SI (SI (SI C<J (SI tsi PU OJ OJ OJ OJ Oj OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ (SI OJ PJ PJ PSI OJ PJ

s; -r ^ -*• >f •*• -*• •J- >»• ^» .f -r »• •r •*• * •» -* -» J- ^ •* » ^ * * -r •r * •r -r

1/1 o o o o o o o O o O o o o o O

O o o O

O

O o o o o o o O o o *TM* ^ (SI (SJ OJ (Si rj (SJ PU fSI OJ OJ OJ OJ OJ OJ OJ OJ OJ PSI PJ OJ OJ PJ (SI tsj OJ PJ PJ PJ PJ Q X) z> 03 X) 35 CO 05 35 33 CO 03 33 03 03 33 33 o 35 OO 3> CO CO 33 33 CO CO CD S3 03 00 • ^ (SI PO •r m ^ PU pn -» in 1-^ OJ m >* m 1-4 OJ en <r m 1-4 OJ pn >^ in -4 PJ pn -» J^ a o o O o O o o o O o o o o O O o o O o O o o o o o o O o o o

•r o o o n o o o o o o o o o o o o o O o o o o o o o o o o o o

>- ^ ^ J^ in in in in

n in in in inm r\m in inm inm in

m in

mm

m rf^

m in rf^ UJ o o O o o o o o o o o o O o o O o O o o o o O o o O o o o o

;/1 o o o o C3 o o o o o o o o o o o o o o o o o o o o O o o o o O o o O o o o o o o o o o o o o o o o o o o o o o o o o o o o ^ o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o

(Z o o o •o o o o o o o o o o o o o o o o o o o o o o o o o o o < •r »• T -r -I- o o o o o pn pn pn pn pn OJ OJ OJ PJ OJ o o o o o CO CD CD 33 <0

jj (SI (SI -SI IM (SI o o o o o o O o o o 1-J ^H '-' p-4 1-4 pn pn pn pn CI pH f* ^ r* ^ ^

o- (n o o pn -o ^ <o

_ •o o * o J- o p^ OJ P~ PJ r- P- OJ P^ PJ go in -< •o OJ P«

—I J- o pn in ~r <-4 pn o OJ •r 1-4 pn o m pn o OJ in .H -J- -< pn

O PJ in OJ •r r-( pn o m ^.t (C «* o r- *• o r*. m o •D OJ o in •*• >H 0- m o 03 m p^ 33 .r 35 m ^ 35 ^

1— <SI

m pn -r in o ^H OJ (SJ pn J- in

O o •^

m o o -^ PJ

m ^ inm o PJ rr, •f J- in o -o o <o •o C 35 05 X 33 33 33 33 o o o o o o o o o o O o -^ p^ 1-1 <-t i-t ^ o o o o o o o o o O o o o o o o —i

1-4 ^^ —4 -H 1-4 —4 -^ i~t ^ -^ r-t ^ z o- o- o o o o- o- 0- o- o- o- a- o (3- o o- >> CT- 3- o (y (y <y <y cy (y o o 9 9 3 IS) (SI (SI rsl PVJ (SI (SI (SI OJ p^ PVJ OJ rsi OJ (SI OJ ISI OJ PJ PJ OJ OJ PJ OJ OJ OJ OJ OJ PJ <SJ nc -r .»• >r -f J- ~r -r -r >r -r -r >f >r J- ^ J- >r •r -» -* -* -»• -r ^ -»• «J- 'T -»• >> •* 1 o o o O o o o o o o o O o o o o o O O o o O o O O o o O O O 1 <SI <SJ fV (NJ (SI PSI PVJ PSI OJ (SI OJ OJ OJ OJ OJ OJ OJ OJ OJ PJ OJ OJ PJ OJ OJ PJ OJ OJ PJ PJ 1 <X) (S an CO 35 CO a> 35 O) 03 CO CO 35 CD 33 33 CD 03 3> 03 03 CD 33 CO CD 35 00 33 <X} <D

B-10
1 «*) fO rr> fO fO >«• * <n * «»

m <n <n <n <*> ro ro PJ ro en en en en en en ff^ ^ en ^^ ^^ 1 o o O o o o o O1 o o1 1 o o o o o 1 1 1 1 O O O III OO1 1 O o o O o III! o o o O O 1 i 1 1 1 1 1 UJ UJ 1 UJ 1 UJ 1 UJ 1 UJ 1 UJ 1 UJ UJ UJ 1 1 < 1 1 UJ ^i ^1 iXt iXt 1 1 i UJ UJ UJ UJ UJ 1 1 1 1 1

11 1 ^ ^ 1^ ^^ 1 1 1 1 UJ UJ UJ UJ UJ ^ u> <o CO m <x> >o o O •r m o o o -o r» •*• PJ m ro ft »r CT' xT o <o >o (^ PJ r- o

UJ 1 •-' o o CO o <*l * in r^ CO •H 9 m .o PJ fH o m S> CO ID •M ^ ro PJ in tf> CD in p- X ^ <D in o CD r. PI m in r4 W O CO » «»> -- in PJ O ro in m OO CD o >f in PJ o OO H" ft o r- o> o O -^ o CO m .r i-i m PJ <o PJ in 4- •r ro 9 OO en 00 O in CO •« o o

r- -1 ft •o <M rm o ro r^

O »•O PJO » ^ r- o -o 9 PJ PJ ^ OO o p4 « m o • in r- CO o r- •o •O o (T) o o ro m o •* ro *• m ft o en *• o P" f«- CM m f4 p- o » r~ m (M O •r •o o ^• h- O * o ^ -o r- CT) * •*• en CO pj m « <o r^ PJ <0 CO « -^

Ul in in ^ in o in •o <y o m PJ xT

m

O ^ PJO -O ^ m PJ

O PJ PJ PJ •-t ••^ CO OO CM o a m f>4 o- o pj PJ PJ S> 9- «> OO rn ^ # 1-1 ^ m PJ O' <»• <> ro ^ * en PJ PJ PJ PJ • «\j .» m f- >-t ^ F^ .-• r- -« » p» PJ p- m PJ o> o PJ m m « « o o r~ p- in OO o

t/1 PJ fSJ OJ *H (NJ »• CO o o o t» f- OO f>. P» in in 9 in tf^ •o -o -o -o f^ o o o o o • • rn CO »n o o- -• 9 r^ fO ^ ^^ ^ ^^ en CO * en ro ro ^t ^^ ^ ^^ M (M M (M pj •»• *• m cn <*> PJ PJ PJ PJ PJ CM PJ o PJ PJ PJ PJ PJ PJ PJ en ^1 ^i fo fo o

Ui o o o o 1 1 o1 oI o o o o I A • o o o o o 1 1 1 1 1 o o 1 1 41 UJ UJ Ul o1 1 OO

O OO 1 1 1 1 1 O

O OO o 1 1 1 1 1 UJ ^J UJ UJ ^J 1 1 UJ UJ UJ UJ 1 UJ 1 UJ 1 UJ UJ UJ UJ 1 1 1 1 1 111 111 UJ UJ 11 1 1 • UJ Ul 1 1 1 1 111 111 m 111 111 ac m t- O <o O •r -e >ct 9 m 00 in t-4 >4 ^4 en ^i ro PJ m PJ en •© m en PJ ^ ^ ro p» < 00 « tH PO >4 r- P IB O O ^ (T) f»- PJ in .^ ro ro en h- O O m p~ o in PJ « m ^ 3 r- p>j CM o m pj PJ f-i «r in fn * r- w O f. .»- * pj r- <*• o r- en 00 tH <o aH m ro

C7 fvj CO r- ^ <o -»• o # P- o i-l PJ ^ PJ <V1 t^

O 00 ^ f* 00 en « o O 9' rH 00 -0 in K1 CO o- —t •o f-l o r- -I * ic o in o m (M O rsj r4 o m ^ PJ O OO -o CO m ^. CO PJ

CM <H <f <n (M in «n PJ CO P- CO •« fo ««> *• o r» CO CO OO PJ f-t

O OO en

O tf^ tH ^ m « cvi r- o « ^ en (n r^ i-l o ^ in o PJ (M en in o 00 » OO OO o ^ O O r4 OO >r o K ^. <o r~ o f. » OO in h- ^ <o ^ PJ f-i m ^- in o m e e •» -f \e\ ft O 9 PJ en 4- o f^ <D o ^. <NJ •r PJ PJ i-« m PJ o m r~ PJ ^ >» m O PJ <o m ro .O ^ O r> « ,4 «

»H

n <o •o <NJm

m CO •r

M in « m CO .^^ ro in .H -r •O f in « .© <© ^ p- <o PJ » >r

1/1 o o• • o• o o• • •o

PJ

hOO

O • • • • >r >»••••* >r PJ ro * • • •

PJ PJ • • en enm en en • « • • • r^ ft ft ft f*

CM (M ^ —

«VI fVI PJ PJ PJ PJ PJ PJ PJ PJ PJ

p^ fH CM

PJ PJ PJ

^4 ^H

PJ PJ PJ PJ PJ PJ PJ PJ «M PJ PJ PJ o o o o o o o o o o o o o o o o o o OO O O o o o o o o o o + * •

Ul UJ UJ UJ UJ UJ UJ UJ UJ UJ 111 1 1 1 1^ Ul UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ r * •* in •o OO l-l « ft PJ OO CO <NJ CO (*) PJ m i-t in PJ o (T- in ^- c p- o p» « in

»vi o -I r- •r CO

m

O CO 00 o r~ * t-t ro rvj o O- o ro in 9 9 m in <0 o in 'O 9 m o tn •O i>- in o •-I <? o o <0 OO o ro o P- O PJ •f •* PJ in PJ f»- PJ ro <o en OO -O < o in f- 1-4 00 cr> f»i OO •r o 1-1 « CO ^ PJ OO r^ ro fH <o ro * en r- -o OO 9 m .« iH t- 1 o- ^ 00 'O f«- iH •* * » m CO p- « « en r«- o« m PJ en OO r« r^ o 00 •^ >r ro PJ e

LU o> «^ * o <o ^• PJ fOm « rom ^ r^ pa in PJ 9 OO « 9 « o en a> 9 PJ PJ

O f-l I o OO CO o h- •O ^ r^ p- r~ •*•>»•* m m m in o m m OO CD ^ ^ (D ^ S ® CO OO - fO M «VJ <M INJ e\l PJ PJ PJ PJ CM PJ PJ PJ PJ IM PJ ^ rvj PJ PJ PJ PJ PJ PJ PJ PJ <M PJ PJ

r- r- r«- r» r^ r» r- r^ r^ f". f^ p. h. h- r* ^>. r~ « p- l>- p. p. p. r» ^ p. ^ h. p. r- m tr\ ro en o m <n PO m <*> CO ^ ^ ^ ^ en ro en cn ro m ^) m ro ^^ en en <n en en o o o o o o o o o o O O O o o o o o o o o o o o o o o o o o

UJ*111 ^ill *IIJ *111 ^

UJ UJ UJ•

UJ UJ LU*

UJ*LU^UJ*

LP^

Ill II».1 111 111 ^ 11 1 ^ ^ 1^ 1 1 1

LU LU LU LIJ LU

PJ p4 & O P- f4 en CD « PJ

O PJ OO PJ PJ PJ in CO >r in •O ^ •» » OO 00 -r -r o » O PJ ro PJ * •H <^ CD o m PJ 9 p. CO in « ,H en PJ PJ <# O « CO O O « P>- OO f4

r-t in o <-< ^ >r i> rj

O CO <0 PJ » PJ rj in .r

m pi. ro 00 e ^- F^ CO iM f4 e in # ^ CM ro PJ ro <o m o <o CM <y- r^ •«•» (J- O •« in PJ ro PJ CO t-« m p~ o CO in sT ^ » en » P- o -» ro -O P- m o ^ ro ^* ^ •* ^ in o » PJ <0 ^4 in o •*• PJ in p- p~ « 00 m in ^ O O <0 ID CO » O ro en en PJ lO (H en r-i in '4* >o 9 *> h. CD OO 9' o o in in in in CD p. p- P- p- •r in m m in ro PJ >0 en ro in in m in m en en en en <n o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o

O- O- O' 9- O- (^ 9- O' 9 O' 9 O- 9 9 9 9^99 9 9 9 9 9 ^ o* ^ ^ ^

PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ •-• 1-1 I-l p4 r^ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o • * • ^ ^ * ¥ * * ^ *¥* *

LU UJ LU

m UJ 111 LU LU LU LU UJ UJ LU UJ LU 11 1 11 1 11 1 ^J 11 1

LU

U UJ UJ LU LU UJ tU UJ UJ

m o m ^• pH ro in

O ^ « ^ in •o p. 9 ^ en o en OO p4 ro p> .^ en in 9 O in ^

en 9 •-I PJ CD 9 OO r* ^ ,o 9 -O ro

O PJ <s o 'O

m o m * o ® PJ OO o O <> iH

f4 00 9 en o PJ en s> •O 9 -o p. 9 p- PJ r«. ^ O ^^ ft ft •H PJ

O PJ p> ,#• o- o •*• t> < 1 m r « •* r4 * o •TOO in f4 ^ CM en ^ P- * PJ o p- ^ •• PJ ® PJ PJ •# PJ o

•- 1 m o 9 CO

m OO OO

r CO in •O PJ PJ PJ 9 P- fH ro *\ o o <o rj r>- P- PJ 0> ro o »

UJ PJ * CO in 9 * ro xT •<> r^ in f^ <o ro r^ ^ « PJ -O en <r iH * m » in ^ ^ PJ ^ X o 9 9 9 9 o CO OO CD CD ,»• en o f4 PJ P- P- »4 p» p- o o o o o (O OO CO CD OO 1- o 9 9 9 9 9 9 a- (> * o o o o o o O Pj ^ 0> o o o o o- o ». » O 9 o 9 9 9 9 9 9 O O (J. o o o o o o O O o » o o o o o- o- o t> o o> o 9 9 9 9 9 9 O- ^ CT' o o o o o o ^ o o o o o o o ^ (J. O- > O (J. * ro ro CO en m in m m in o o o o o iH ^ PJ f-l 1-1 o o o o 9 p> p. ^ p- p.

PJ PJ PJ PJ PJ ro CO ro en ro en ro ro en en ro ro en en PJ

UI -• PJ ro •* in J3 p- CD o o f4 PJ ro •r

m

O P" CD ^ O

M PJ en .^m <o P- «> 9 o

-1 1 en ro ro rom ro <n ro en .* >« * ,»• •r ^ -r -r # * m

m in

m in in

m in in in <o >4

u. o o O o o O

O

O o O o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o * -^ -» * r •r * <»• -r * * * •r •» •r •r ^- -r 'T 'T >r <r •* *• -r •*• >r * .*• •• o en ro ro en en m en en en en en en m fO ro en en ro en en ro ^ en ^ ^^ m en ^ ^ m ^- f4 ft -4 1-4 i-t ^ iH r4 iH »-• »• f4 1-4 "4 iH rH ft i^ ft ft iH iH 1-4 >-t ^4 ^ 1-4 r4 r4 f4 o ro ro m m CO ro ro en CO en en ro ro en ro en en en en en ro rt ^^ en ro en ro ^ en en

PJ rj PJ PJ PJ PJ PJ PJ PJ PJ CM CM PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ CM PJ (Ni rsj PJ e\j PJ PJ

a£ >»• f * * •r ^ * •»• ^ * * •* ,»• ,*• * ,»• xf ,»•>* * <r ,* >^ >r * -r -*•*>*• -r

'/»

O

O o o o o o o o o o o o o o OO o O

O o o o o o o O o o o 1-4 PJ PJ PJ CM <M PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ CM CM PJ PJ PJ PJ CM rvj PJ o CO OO 03 <D <o OO CO O CO S9 CO » <D <o » 00 <s a> OO OO A OO OO A ® S) CO QO OO ^0 • -4 PJ ro •r m p4 PJ ro .^ in -4 PJ ro * in 1-4 PJ ro >* m »H PJ en ,*• m ^ PJ en >r in o o O O O O o O O o O o o o o o O O O O O o o o o o o o o o o z o o o o o O O O O o o o O o o O O o o o o o o o o o o o o o

tm

m J^ in Ml in in

m

m in

m in in in in

m in

m in in

m

mm inmmm in in

m

UJ

O o o O

O

O o o o o o o o o o o o o O o o o o o o o o o o o m o o o O o o o o o o o o o o o O O O O O o o o o o o o o o o O o o o o o o O O O O o o o o o O O O o o o o o o o o o o o o z o o o o o o O o o o o o o o o o o o o o o o o o o o o o o o

oc o •O o • o •o • o •O • • • o o o • • • ~ " o o o OO • • • • • o o o o o o o o o o • • • • • o o o o o < •*• «r *• >» * o O o o o ro ro ro en ro PJ PJ PJ PJ PJ o o o o o OO IS o CD CO LU rj PJ PJ PJ PJ o o o o o o o o o o iH .-4 r4 -4 .H en en ^\ en en ft ft ft ft m^

05 en r^ PJ p. in f-4 p» rn o * OO en CD ro o> -o PJ OO

mO -O roO P» 00 in PJ (7- o

.n CM >f •-I en

m rj -» -4 * <n in PJ >r ^ ^ ^ xTO ro -r o en o PJ

m PJm -4 -r o o J5 PJ o in rH <x> -»• -4 p- >r o f~ ro O <i> in -4 OO ,*• ^ -O PJ o in o p- <n o -o H- o «4 PJ PJ m in m O -4 ,H ro J- * m O 1-4 PJ ro en ,r in o 1-4 ^ PJ m in o 1-4 -4 Q p- P- p. p. ^- p- p- CO CQ OO CO CO CO o 9 o o o o e> o o o o o O O r4 iH ^ oo o o o o o o o o o o o O O o o o o o O 1-4 1-4 •H >4 M 1-4 iH r4 1-4 Z 1 ro 00 CD <D <o (D (O CO CO GO OO CO CO CO 00 (X> CO 00 CD CO QO op 00 ^D QO 00 O (S GO CO O 1 O o o o o o o o o o o o o o o o o o o o o o o o o O O O O o Of 1 O o <o -o •o •o o -0,0 o -o •o -o « -o -o -o « -o o >o .o -o -o o « o o o 1 O O o o o o o o o o o o o o o o o o o o o o o o o o o o o o 1 PJ rj PJ PJ PJ PJ (M PJ rj PJ PJ PJ PJ (SI PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ CM PJ PJ CM PJ 1 <s CO (S <o <o CO OO A CD O CO CO CO CO ID CD CO OO OO o OO flO OO QO 00 CO CO OO OO OO

B-11
Q

UJ

ro enm (<1 PO PO PO PO

m CO PO CO (« PO

m CO PO PO PO PO rr\

m PO CO PO PO rr> co CO * O O o o o O o O O o o o o O O O O O O o o o o O o O O O O O

UJ UJ UJ UJ LU UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ —< m m in PO CD <0 p\j O » >»• r- o .H U- PO r«. r- >r m r- o r « o O O IS o m f CM <M M M CO 00 00 o x> CO o o fO » <D o 1-4 m CM CM -o m m a- <^ CO o CO o 00 «1 iTi ^ pH ^^ m in <o (O o m m -^ m •r f~ CO CO o * f~ IS •r o- o o PVJ -r CO

f«- ^ <M OO <-• PVl CM •* PO -r rm PO ^ ^ in <M o o o ^ o ^ i-H om •O o m ph o -- r~ m J- O •O o CD CM m * -H CI f". f* m CM PO 1-4 fVI CM CO -H 4- PO •O OO O OO

l\J * ^ o f-l wM 9-i u^ r^ CMm <-4 CM PO iH •H *H

n

m o o >r * <o PO CM

O p^ o r-

<t> oo if>

O 1-4 <o * r- PVJ PO 9 O^

O f- • CO CM CO •O <M ^ 1-4 <o

m CD CM

m r- .»•m ^ -o fn M r- -*• -H * f^ <o (M 1-4 cri (T) PO •» * o m ^ O f~ PO PO PVJ r o CVJ O PO

r- (M -o <M r>- (M CM ir» r^ •r

OO tf^ ^ m

m o f* » ^ CM CM « r PO o o O 9- rCO 03 OD CT- r1 O 33 PVJ PSI >H r* m CO 33 CO ^ "T m •r PO rt -O o 93 •O 1-4 CO CM p» ain J^ in m « CM -H <M PO CM 1-^ 1-4 --4 f-H ^ o O o o o -^ O o o o o o o o <> m m m m PO r^ 1-4 -H w* -I •* >r • •r -r PO PO c*> »n PO «» -f r -r •r f-4 rH t-4 ^ o-

(SI (M r\jM <M cn POm (TJ PO CM fVJ CM CM CM CM CM CM fvl CM CM CM tM CM CM PO cn PO PO c*»

O o o o o o o o o o O

O o o o o O o o o o o o o o o o o o o

UJ UJ UJ UJ UJ LU liJ UJ UJ Ul UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ Ul UJ m (M m m >r O PO o -o >r r- •o o PO r- <? CO CO r^ r» r- f* h- m m CO o r- O 9 « m O ^ -r O M o CM fO C*1 in o o o CO m O m (S tr> -4 » •r fO m CO » pj en

-0 o- a^ in <o o O o o •r

O CO PO

m r» r- r- CM -» •r

m ^ r^ -o PO o •T CM vn o

f>» £>

O >r o- o •f fO

m CM rm 1-4 >r 1-4 o r a- CO

M in CO t> •a CZ> in >r O- <n fh

<M (M CD o- •r

m PO r- o » (M CM -o

O CO o fO 'T f-4 o en ^ o p4 ^ o w4 O- -H rv

m (Mmm •o o W o ^« o O CM O} 00 CM <D »•

m •r (*t f-4 1-4 PO in f-4

r o in •* o

(M OO ^ (M o rw

w CM f*4 ITI •r r- CO t-l « ^ (M -* ^- o m (S

O CM r- o a- in <

rO r- o p- o r- ^. o » O

m •o PO r»m

m * CO >r » i> o CO «»• CM o m o -r r^ •* <o t-t o o- i> m ^H e •o h» o- o o f~ p» •o * CM r- o (T- * ^. r- r» r- CM m o o o —1 CM o ^ CM o- o « in f- r* ^» m t<- o o r- f-4 r- »«• O r* co r- in 00 ^ m m• • rt r-l •

1-4 •1-4 •

»-4 •

1-4 • m• -4 • • •

(-4 •f4 • • • ft >-4 •1-4 •

1-4 •

1-4

m•

>-4

m•

1-4

r- -o • • o• •

f-4 •-4 o o o • • • ^ ^ ,-t

-4 o• • fH i-t CMPvlCMCMCM CMCMCMCMCM PMPvICMPvlCM PvlMCMCMCM PVICMCMCMCM CMfMCMCMCM ooooo *

ooooo ** ooooo ooooo ooooo ooooo «^^^^ ^^^^> ^^^^^ ^^.^««

UJUJUJUJUJ UJUJUJUJUJ UJUJUJUJUJ UJUJUJUJUJ UJUJUJUJUJ in 1 1 1 hi hi ii f ^•|-4ooo•* •oomo.*' « ^ o- r^ 9 i-4p-off'po ^i-4^ino poibojo^

•^•'OPsioin 9 o c o \r\ CMPvJOfH^ ^4ioos(Min i-4POinr"f>- ©inOfM-^

r\i -a tyj -O ^H 9 -Om t\i >0 ^ihcmcmo r^pom^o inaooo»i-4 -rooos^co

h-KsipocM inr~port,r «i-4*^in po^^-oo o o 9 m ^ f\t <-> o 9 t^ ^pof^-OPvj fOCMcoh-* f-4«0'*ph mcoh-mo c*iCMCMeo-o ®mOi-4i-4

CM^rf"-©* >Oini^»CO rHCI^COCM CMi^r^^CI »fO^CMiH ff'CO^OO-*

i-4r-40—40 & o- 9 a to •r-rcnpo.*- m^pocvid .MfMfMcnPO cmcmcmpmpo

CMCMPvJCMPvJ fH>4i-4i-4o4 .^^p4fH.H i-4f-4^i-4iH i-4pHi-4i-4-4 i-4<Hi-4i-4i-4 r«-h-^.r*h- ^.^-^»^-^. r>.h.p»^-r^ r~r>.r>-r»r« ^.^.^~^-^. ^r>^.^.^.

c^foc^if**^ cocoococt^ PO <n CO CO PO

m PO CI PO rt en ci co c*i co en c*> CO en

w

OOOOO •* ooooo ooooo ooooo ooooo ooooo ^^«^« ^ ^ ^ ^ 4, ^ ^ .^ ^ ^ >^««^ UJ \U UJ UJ U ^ UJ l^ UJ U ^ ^ 1^ ^ l^ LU LU UJ W LU U U U U UJ lU U UJ LU UJ in^rmo-i.^ or-*®in PvJ^J^.ow• ^00'0>* ocM'O^m cmo^ooo »^OSPOin com^h-* f~rvj«M-0» po«—4Ln^ cM'^OcO'* iH^oom*

poa>cMin^» -o-0f-4opo pvjr-opvj^ rm-ov-m en'#'0«<H '^m'«-i-40

CT'OCMPvJfM COr^m-OO -O-^PvJPOff- CMr>-<00-'0 h-000'-4<r Pv4-0>r»PvJ ^poi-4.0^ Off'PMPOCM co^cnoOfH coi-4m<oo f^J^-•«nen^- lHlno^o^-

^poPvjfoo poi-4CM>*-PO pvj^-4m^ i-4POfMO^ -o-riorv-po in-^-rm*

in £) o •o -O -O

C <o

OC popvjpopvjesj popopopopm "r-r**-^ *•*«*** z3

fH -4 o o O o o-4o O

f-4 O ^ f-4 o of-4 o

1-4 o

-4 -4 f4

^- h- r>. o o o

-4 -4 o o-4^-o

iH -4 o o O

p4oiH^-or4oiHO

iHo-4 fH -4 iH

fw h. p. fw o o o o o o O o O o O o o o o o o o O o o o OO O O o o O ooooo

c^ o- a- 17- 9 ow o- o o o- o- o- o o o o o o O 9 9 o 9- 9 9 9 ff.

O ff.

CM CM p\i Pv] (VJ PVJ CM CM CM CM m* 1-4 -4 -4 ^ CM CM CM fvi CM CM CM CM CM CM (NJ CM CM PM PM o o O o O o o o O o o o o o o o o o o O O O o o O ooooo * * ¥ * ¥ * * * * * * * * *

LU LU UJ LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU LU UJ LU LU LU

-H Pvl O) PO o PVJ CO -r

O in o 1-4 CO 00 in r^

m -r in

O •o •H

O

O -4

m en CM in «n

-H -» o O <X>

m CO as -4 PO PVJ

r PM CO •r -r o 1-4 o r^ en >r CM o (M •o en .«• CM CM

PO AJ ^- o #• en fH

m

m CM •fl o -O CO r~ * pg OO

O

O

m PM r- CM

O 9 f"

m ,^ f»i -r r-l CO n r- CO r- h- CM •o PVJ en -*• CO m •o b- o fH in (f o oo O O •r en >r ^. *

pH i-I PO 1-4 r- •O CM •o * CO CM h- o m •* ft P" -o r* en « r o in PM •*

m o m -r

in

V o m in CM •r <o -r 00 -4 <o in o f» f o O CM en -r fvl <c iH o o PO 9' CO <a

(Z>m o o o CO 00 IS r- r~ in o PO en CO o -o ^-

m •o o O o o O r~ CO o r- p-

<y o o o- o 0- 0- o O o o o o o CO o>

O o- <y o oO o o O 9 9 <y o o O C3- o o- o o o- ly a- o o 9 o o o- (? o- (y o- o (y (> o o O 9 9 (J. o o

CT- O- o o- o O o 9 a- o- o <?• o o o o o <?> o- o <y c? C7> o o 9 9 o ^ ^

PO PO •r PO * in

m

m in

m o 9- o o o fH 1-4 fH iH p4 <y » o- o o

CM PM CM (M CM CO PO PO CI en PO CM PO PO CM -H 1-4 iH fl r4 PM PM CM PO PO fl w4 fH r4 rH

-^ CM en •r

m •0 r»

® 9 o -H CM PO -*•m o ^- a> o O iH CM en •f in •o h- OO

OO

OO

O o o o o o o .-4 iH -4 1-4 p4 ^ ^ fHH ^ CM CM CM CM CM CM PM PM CM PM PO

O

O

O o o o o o o o o O o o o o o O

O

O o o O o O o o O o o o o O o o o o o o o o o o o o o o o o o o o O O o o o o o o

sT •* •r J- •* -»• -r -*• <r •r ^ -r -» •r •* ^ >r •* ^ * ^ •*• -r a- *• •r

r -^ <^ -»

fO PO PO PO PO CO PO PO PO PO PO en en PO en PO PO PO PO en PO en en PO PO PO PO en PO c^

PO PO en PO PO CO PO PO en PO PO PO PO en PO PO PO PO PO PO PO PO en PO CO PO PO en en ^

PVl PVJ CM CM CM <M CM CM CM PM f\J PVl CM PVJ CM CM PVl CM PVl Pvl PM PM CM CM CM CM PM PM PM CM

.*• nT -r J- >f -r >^ * * * -r -»• -r -# >r

r •r -r -» •f •r •r •* ># •r * «»• ^ >»• * o o O o o o O o o o o o o o o o o o o o o o O O o o O o o o

(VJ PO (\j CM CM CM CM CM PVJ CM PM fM (M CM CM PVJ PM Pvl CM PVl PVJ (M CM CM CM PM CM CM CM <M

00 s CO s (B -o CD CO OO CO 30 <D 00 CO 00 00 OO CD CD <D !X> CO 33 CO 00 CO <X> S CS CD

»H P4 PO ^r

m -4 CM PO -^

m rH CM PO -r in -4 CM PO vT

m -4 PM en •r

m •H CM PO •*• in o o O o o o O o o O o O o O O o o o o o O O O O o O o o o o o o o o o o O o O o o O o O o o O O o o o o O o o o o o o o m in in in m m iTt li-1 in in m m m m in in m m m in m in m m in m in m in m o o O o o o n o O O o o O O o o o o o O o o O o o o o o o o o a o o o o O o o o o o o O o o o o o O o >-> O o o O u o o o o o o o o o O o o o o o o O o o o o o O o o o o o O O o o o o o O o o o O o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o O o o o o o o o o o o o o o o o o

-I- -r ~r -r -«• o o o o o PO PO PO PO PO PVJ PVJ PVJ CM PM o o o o o CO CO 03 OO o

PM PM CM CM CM o o o o o o o o o o 1-4 —t 1-4 •H -H PO PO fO PO PO -4H -4 iH iH o >r V CO CO PO ID -r cy •r -4 -o CM r» CM o in 1-4 <3 CM o Pvl r~ PO CO o •o CM CO -r

>^ -4 PO o CM PO in CM >r -t >» o PO j\ PVJ in -4 -»•

O PO r-4 >f o PO in •r o PO in CM

PO o •O PO t> =0 -»• -^ r- •r o r«- PO o- o PO o o PO o ly

m CM CD -»•

O r>. PO o ^

ro >r

r in in -4 PVJ PO PO •r o o -4 -4 CM -r

m in

O o •r in o o -4 PO en >»-*•

m o o o o o o O o o o -4 1-4 •-4 1-4 -4 fH -4 fH CM CM PO PO >*• r •r -» ^ >» -f •* o o o o o fH -H <-4 -H r^ r-» f4 -4 1-4 -4 -4 -4 f4 iH fl ^4 —4 p4 •H -4 fH iH ^ iH r4

-O <3 -0 o o o o o <3 •o o -o

O o -o 0 o •o •O -O -o o •o -a o o •O

O -OO o o o o o o o o O O o o o o o o o o O o o o o o o O o o o o

h- r~ h- f>- r- ^- f^ h» h- f>- r- f«- f^ r>. r^ r« p» p» r- h- r- p- r^ r~ r>- r^ r^ r>. r~ r- o o o o o o O o o o o o o O o o o o O O o o o o o o o o o o

CM PM CM CM CM CM CM PVJ CM CM CM PvJ CM CM PvJ CM PVl CM PM (M CM CM CM CM PM CM PM PM CM CM

CO a> cs CO CO as CO s to OO OO CD S CO CO OO 05 OO CO CO CO IS CD CD CO OD IS CO 00

O

B-12
3OOoo

-z

<*i ro fo ro fO ro

m fO |Ti ro (O ro ro ro fO ro ro ro ro (Ti ro (O ro (O ro ro CO ro (O PO o o o o o O O o o o o o o o o III O o o O O III o o o o O o o o o 1 1 1 1 1 1 1 1 UJ UJ Ui 1 1 UJ Ui UJ 1 UJ UI 1 1 UJ UJ 1 1 LU LU 1 UJ 1 1 LU LU u^ 1 Ui 1 1 1 LU LU UJ 1 1 1 LU Ui Ui LU LU 1 1 1 1 1 1 11 LXi UJ ^ UI

J- to (y J. (J. o- (D o- r- r- <vi in C7> r^ OO in rvl <o rH in

O <0 ro

m

O

m rH (VI rH

m

<-•

O <s J- o >o O- rsi CO CO -r (VJ ro in 1*. o O ro rvl ^ (VJ o m t-> t^ o -»• o >o oo

m » o o o ^ ty in -4 CO ^ oo oo IM f^ o -*• -H o o O f~ o <z> ^^ •a- -r iTi •o cy- r4 (\i (M o o I-I a- ro <o «r >o .«• o o o r^ OO p~ ro ro nO o ro o ro « ro o m N- M O -^ ^ o in ^ ao •O OvI in oo ro ro (VI -r (X> o CO -r rH ,*• O •r ro (VI m .«• rH o

c^ >-4 •*• r- <D

m >o N- o <o o •»• CO o> o CO o ro

O ro o r> a> *• (O p.O o (VI

m

1-t fO

O r-l •*

m o (M

m -»• •fO <y <3 r-! in rH rH P- rH ro (VI oo <t)

O .*• ro iH (VJ rITN <M >0 ^ «o O o O o f- 00 o o O (VI -H m moo o rH <y 00 rH rH o m « f- m pg « m o >o o <o (VI o •£> m <y in o- •* o o rH m rH O ro o o « P- O m rH

33 <o r- in o a> r- r- •o o « <VI CVI iH

O (O (VI ro ro r- -O rH (VI o r- (VI rH

m ro <r

<o <) « <o -o -4 ^ F^ .H "4 <Vi (VJ rg (Vi (VI o O OO

O •H r4

O

O o rH rH

O rH

O • • •

(t> rt (^ • • •

•-< •r-l a-l • • * ^ •* •ro •# (O (*> ro • • • *

>r * -r >r •

(*i

CJ fM CM (M <\J f)

m PO ro tn (VJ rvi (VI (VI (VI ro (VJ (VI (VI (VI rvl (VI (VI (VJ (VJ (o (O fO (O (o o o o III o o1 1 O O O 1 o o1 1 o o o 111 o1 1 O O1 I o o o III O O O O III' o1 O O O O o

III i 8 1 i 1 UJ LU UJ 1 1 LU UJ 1 UJ UJ UJ 1 1 Ui UJ Ui UJ UJ 1 1 LU UJ 1 UJ UJ III Ui UJ UJ III LU LU LU UJ 1 UJ 1 1 1 1 1 II 1 II 1 II 1 II 1 1 1 1

r» tf% * r- CO O- lA rH (D 9 CO oo oo >-* (VI

O o oo

m

m •r o m

mm o OD o m oo 9 O OD f^ o O O m (M rsi -r •»• ey O -r •O •r rvi O ro >r r>. r~ oo (VI r» ro h- O rH

or r- iH (V) fO •»• « o CO * •o -o (VI ro -o -o (VI o m «> .* CD J- o pO ro ro (O r~ o -^ in ^ in o o o ro rH o -o in (VI o r^ M (D oo o r«. * rvi p- r- r» O m rH (VI 4- m .f r^ -o r« f>- m o ^ 00 r* <0 CO ^ O rvj 1^ (VI o o r> <o ro o m m o m *

(SI ir> ^ oo in o co r-l

O <M r» » O (>• o> ro (VI o <o o (VI

m -r r- t- (VI « p" <•

m

«vi

d in •o o o am (D

m

O iH fH

a -*> o o (7- ro -O 'O -r rr> <y i-t <o <£ rm <r in O fo in .o (Tt r- •H ro O o ^ r-i in o m CM moo oo « rH (VI f O P- O <VJ o

<» f\jm f^ fH

m o m ro ro o- >r r~ «n o rvj rvl o o « o ro

m o r-t ro <y >r o (VI ^. o r>- in o in o o r- oo >»• I-I rH o o r~ •«• o r- o m (VI -» (VI o O O ro rH O

Cl f*1 fO • • • • • • • • (O CO • •

oo o• •OO• CD OO • • m• •o• m

m -o • 4 •r>- r^ <o • • • ^4 ^H iH •

•O•fH(VI (VI rH (O rH

fVI <SJ (\J (VJ (M (SJ (M

9^

«NJ (VI (VI (VJ (VI (VJ (VI (VI (VJ rvi (VJ (VJ (VJ (VI (VI fvl fVJ <VI (VI (VI (VI (VI rvi

O

OOO

O

O

O o o o oo o oo

O

O

O

OO

OOO o o OO

O

OO

••*• • > <» '^ + • * ^ « > ^ ^

UJ UJ UI UJ Ui UJ UJ UJ LU LU LU LU UJ Ui Ui Ui UJ UJ LU UJ LU UJ UJ UJ Ui 1 1 1 i II 11 1 ^ II 1 o oo in •o o •o a> in (VJ CO cy. oo CD O (O <y (VI iH O ro rH ^. o o m « m m m o O * 0> in m o O (\j f- ro o> o PsJ (VJ O £> O CO rH .« o <r o <s rH -r m r- in rH * ^ OD m m (M m ro * -O in o r^ ro (VI ro ro rvl m (VI (VI oo o (VJ o m o o -o o O fl ~o ^- (M m •r m (VI m <M O fVI m (VI r~ rH >0 (O >r o rvl m m ro O (VI (VJ <#• fvj i-t r- <o m -o o r- oo -r ^ r- ix> <o iH CM m >o o <o m .# m o m O >o m r- o m m o >» oo a- ^ «M ff CO o m r- o- o o <« o m r> 9 m h- -r (VI N ^ ^ O 00 -o

•*• ^ o o o CO o> s> a> ^ m

m

m in o •o in r- « (VI rH

OO o #•

m (VI rvi <r o

<^ i-< .-1 rH ^ O

O

O

O

O OO

O o o o o o o o rH (VI (O (O * m ^ (O (VI rvl

r>. t«- h- f~ f^ r- r*. f>- h- 1*- r«- r- f>- f>- r» r- r- h- h- ^. ^- ^- r- r- P- f- r- p- p- ^-

t*% (*i (f\ <H ^ r^ • • • _j ^j ^ • • m• •

rn

f-i•

(O ro ro ro IH l-< • • rH ^ro ro ro

iH w4 • •

(O

rH•

ro•(O (O (O rH rH rH • • •

(O (O (O

rH rH rH • • •

ro•

rorH•(O PO (O (O (O >4 rH rH rH rH ^^ ^^ ^ r^ r^

rH .-« 1^ r-t rH O O O O or-l O ^ ^ ,H p4 O O o o

1-4 -^ OO -1 rl fH o o o

•Ho

rH

fHo

fH r^ ^H

fH rH -4 o o o

^H fH ^H f-^ i—i

rH rH rH rH rH o o o o o

w^ ,-1 w-l '^ t-i o o o o o

UJ

'^ UJ Ui^

Ui Ui UJ*

UJ UJ*

LU UJ LU¥

LU*Ui lU UJ UJ

<» UI*

LU 'XI LU LU UJ UJ LU*

UJ UJ ULi •»UJ UJ UJ 0(0 « (\J •H •o r4 ro in ^. (O •H in fh ro « m (VI rH * rH m r- (VI (VJ (VI ro o O

(*( eo

O ^ r^ (\J CD o •O <VI in ro ro (O -o (Vi ^• OO rH r- ^- r- o (VJ

m p* oo PO PO (^

c^ * « O (VJ <NJ e> >H .*• in rvl ^• moo (O (O <o o -o (O (VJ (OO rvl p.

O

O o rvJ

(VJd

m

m -»• >4 in fH •O ro ro in (VJ in o O o m >r -H sOO" -o >r <o * O (VI CO o

>0 <VJ * f^ o <\J •o o o ,» <a oo •H (O o r~ •H (O

m r^

m

m o oo (VI •*m rH ro

O * f- ^ f-i m <«1 <\J m »• I-I N- 00 O r>- o in O o o -o m * O rnm (VJ O O rH rH

ro .o <o •* I-* r^

•o

I-I •O <3 iH r4

(VI (VI

I-I I-I

(VJ r^

(VI (O

fH fH

(VI fH

ro•Hro (O •# .4 fH rH<o (VI -r iH rH rH rH rH

<o 00 >o <o

m

rH rH rH rH rH ^ ^« r- o o o o o O

r-o

h» r- r- o o o^. h- h- o o o o o o o^- r- r» o o o

h. h- f^ fw r. o o o o o

p. ^. r> p- ^> O O O O O o o o o o O O O O o o o o o o o o o o o o o o o o o o o o o o o> o> <> o» o o 0> O o> o <y v o- » o o> o o> o O O O O" o o o o o o

(M (\J (\i (M (M (VJ (M (M tvj (Vi rH I-I I-t -* rH

M rvi rvl rvi (VJ (VI (Vi (VI (VI «VJ (VI (VJ (Vi (Vi (VI o o o o o o o o o o o o o o O o o o o o o o o o o o o o o o

•». * * > • •• ^ •».

¥ H- Ui UJ UJ Ui Ui UJ UJ UJ Ui UJ UJ Ol Ui LU LU Ui UJ LU Ui Ui LU LU UJ UJ Ui 1 1 1 11 1 111 1 1 1 11 1

i-i o •»• f>- J- in o PO •r iH J- f^ o o o ^ r» rH

O •»• CO OD ro

m o rm ro OD

O *• (*l <M in N- in d I-I ^- rvi -O -I o <o tf> (VJ a> r OO O o o ^ CO o o -o o «^ m

oo o m CO CO o oo <\J * m oo (VJ 00 (O •O * oo o r>- r~ ro

O 00

m o ro o o o <n

•O c^ iCi (VJ '^ in ro <o ro fO in (VI ao r~ (o •O ro >^ •* <VI -O ro >» (VJ r~

m (VI (VI * ro ^ «M l^- -O f>- in (O rH (VI * oo o- * <y «VI •r r^ O ro o <0 iH * •f o O rH ro ^ <0 ^ (\j -r (M <0 tH (O >-» O O o f- fH ^. eg r oo moo o 00 <r <D m •e •O -O m •*

•H

O

O

O

OO <x> <D o r» .*m -4 in 9- ^- <o <o r» -o (O o o o o O p> CO o eo o o o O o o c> o> o <y o o O o o> o o o o o o o o o <y o- o- (y o o> o o o O o o o <y V t> o o o O O o o- o o o o o o o o o o o u- o o o o o o> o !> <?• o 0> o o o o cy o- o- o o o o o o o o o o o o o * * •• ^ ro m in m in m t* o o V 0» r-l rH rH rH rH o o o o 0- !>. r- r>- r> r~

(\J fVJ (M (M <\J (n (O (> (On <0 (O (VI (Vi (VI rH rH iH rH fH ro (VI ro (O <VJ

1-t rvi «n ^ in « r^ OD o o ^ (VI ro >»- in •o r- OD

OO -H (VI ro » m « ^. <o o o

CI (*> c^ iT> ro rri ro ro ro -r -» * •*• J- >r * * ^ -Jm

m

mmmmm

mmm lO o o o O O o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o * ^ .y ^ -*• * *• >»• J- -» •r .r -^ -r «»• >» sf J- -»• -r -*•»•-» -» # -f * * J- <r

(*1

O (*1 ^ f-l r4 ^ i-t en

•-1 fO

I-I fO"4

ro ro

I-I 1^

ro ro

I-I I-I roiH

ro ro iH fH

rorHm

rH

ro (O CO

rH rH rH

(O ro (O rH iH fH

ro

rH

rorH

{^ ro

d (^ (O

rH rH rH rH rH

(O ro (O ro (O

(VI (Vi (M <VJ (VJ •r ^ -r >r >*• o o o o o

(Vi (VJ (VI (VI (VJ oo o oo oo oo rH (VI ro .» m O O O O O O O o o o m m in m m o o o o o o o o o o o o o o o o o o o o

ro (O (O ro ro

(VI (VI (VJ (VI (VJ •»•>»••**-»• o o o o o

(M (Vi (VJ <VI

M

COno qo OD ^0 rH (VJ (T( ^ in o o o o o o o o o o m m m m m o o o o o o o o o o o o o o o o o o o o

(O (O ro (O (o

(VI Pvl (VJ (Vi (VJ >r ^ ~r >» <f o o o o O

(VJ rvl (VI (VJ rvl CO CD ^^ ^D QO rH (VJ ro » m O O O O O O m m in m m o o o o o o o o o o o o o o o o o o o o

(0(0(0(0(0

(VI (VJ (VJ (VJ Pvl o o o o o

PVJ (VJ (Vi (Vi (VI 'O oo V © ®

rH (VI (O ^ m o o o o o o o o o o m m m m m o o o o o o o o o o o o o o o o o o o o

(O (*> (O (O ro

rvl (VJ (VI (VI (VJ «r >#•.»••*• <» o o o o o

rvi (VJ (VI (VI (VJ CO OD o 00 oo

rH (VI ro .r

m o o o o o o o o o o m m m m m o o o o o o o o o o o o o o o o o o o o

(T) ro (O (O ro

(Vi (VI (VJ (VI (VI * * >r «»• >r o o o o o

(Vi (VI (VI (VI (VI OD oo OO oo oo

rH (VI ro * m o o o o o o o o o o m m m m m o o o o o o o o o o o o o o o o o o o o o o o o o o O o O O

J- -»• * J- .* o O

O o o

rj (VJ <M rvl rvl o O o o o O m o m tr •r 1-i as •r rH

ro

m <VJ -r

O >»• r^ (O o <o

O

m rvl oo JV

M rfm (VJ CD

m o rH rH (VJ •r •r

m o o

oo o o o o o o o o o O O o o o o O O ~1 .H

r- i>- r- r- t^ p- r~ f^ r- r» o O o o o o o o o o p- r^ r«. i>- f»- f^ r- r- f- p- O O O o o o o o o o

(VJ IM (VJ

M (VI

M (VI (VI (VJ (VJ oo oo oo OO (O OO oo ID 00 CO o o o o o

ro (O ro ro (O o o o o o m rH oo m (VI -r rH ro O !^

J- -H («. JO

(VJ ro rO >r in o o o o o o o o o o

(VJ (VJ (VJ (VJ (VJ

rH CDm (Vi

O

ro If, rj in rH

J3 rvi o m pg O rH fH Pvl ro o o o o o o o o o o

c*> (O (O (O (O m rvj O *» (O

.r -H CO o (o

(VJ o m Pvl oo m m O rH rH rH rH (VJ (VI rvl

OOOOO

Q OO OO OO CO

•om o r^ •«

m (VIm rH ^ o r- ro o -o * -»• m o O

ro (*>(*> -.^ ^

r>- (^ h- r~ i»- cj O o o o

r- r^ r- N. (»- o o o o o

(VI ro (VJ PVJ (VJ (D cO OO cT? GO

h» f- h- r^ r- O o o o o

r>» r» (^ («» r>- O O O O o

00 (VI (VI (VI Pvl ^ 00 00 oo oo o o o o o

r- p- r~ r^ r~ o o o o o

PO (VJ tVI PVj Pvl oo 00 oo oo oo

p~ f". f- p~ p- o o o o o

p. r- p~ r- r- o o o o o

PO rvl (Vi CO rvj 00 00 ® 00 oo

B-13
a

m ro m «*1 CI (*i ^ f*i CI m PO en CI pn pn pn CI pn CO PO CO pn fo m PO pn PO m rt rt O o 000 000 00000

UJ UJ LU LU Ul LU LU UJ LU LU LU LU LU UJ UJ LU LU LU LU LU LU LU LU LU LU LU LU LU UJ LU ^ m 1^ o- M r~ f-i oo a 0 ^ !0 ^ OO r-4 in r- a> 9 -^ f~. m r» in » »

•O O <y r- S) OS M m ^ pn P- .*• pn -r m P- m «» ^ pj o- p- PO PJ m ph

r-- m •0 fi in h- >r CM m in -0 (O P- m -0 CO CO •0 prf S) CD •0 -< <? p- ^

in o m •* m OD m pn * m CO pn o> l-i P^ pn r-l p- CO m in 9 oo ^ pn is *•

(J. ^ M .» .0 35 r* -^ m -0 00 >r '-< -0 <M m <r\ fH PJ p4 .o fO -o .0 PJ P^ 05 IS O f* (S m f- IS IM >H I-t <o * -^ m r- p\j p4 cn PJ <0 IB m * -< *

(J. as r- m m •o •r O' PM CM * pn P" pH i-« pj CO p4 p» 0 -r PJ U- P- P- P»

if> ro ^- .»• rw Pg o- ^. CI <-i p" i-i 0 < (O p^ IS •0 cn 00 00

>n CD r- CD in ^ m <y PO m 00 <r ^ r^ * p» -0 ^0 (O in -r * m •0 PJ pH in

en « cy •^ <? M o- m IS l-t o- e 1^ fVI 9- •r pH 9- m ^ m pn pg m S CD 9'

<B CO eo cy M m PVJ ^ ^ «4 -^ N. 0 r- r» •0 *-4 -« m fo m PO n i-H i-« I-t ^ f-4 •r * •» *• •* pn pn co PO cn •*• •r * *• -r p4 ^^ ^4 M r4

<\J (SJ IM M M en 1-1 (*1 m m IM CM fVJ CM CM CM CM fSI M pj CM PVJ Pyl PJ PJ pn d f^ ff> f*> o o 1 1 *

LU 000 00000 000 0000

LU LU UJ LU LU UJ LU LU LU LU UJ LU LU LU UJ LU LU LU LU LU LU LU LU LU LU LU LU LU LU o o- pj -0 (»1 in I-* CM m m CM m pn 9- CO •o ^. * •* CM P- IM IS 0 P^ O h- 9- Ifl I^ m CM -0 •0 -I ^ r«. 00 p»- p^ eo f«- pn Pyl 00 -r P- CO m cn ^ OO o r- PO r~ <>a -» CM r- IS F^ CM p~ pn IS * 9- •0 •*• f-l CO iH p- CO pH in eo p- o * m >» oo •U IM m w IS » pn pn •*• <o p- pn ^ pH m 9' *• m CO CO

00 r- m (*• ro M « CM M o- ^- IS CO PJ co i-< •0 PJ m p^ p^ ^ -r * -O CD H iH ID m » fH CM p» -« CM PO IS rt CO ^ CO 00 p4 pH 9- P- P~ pH J3 ^ fVI m r- 33 pn Cl CM in 00 pn F^ (M CM iH m PO •r ^ pH ^ pH PJ <o PO PO o -* <0 •* ^ « -^ <*• in f^ ^ -< PVJ P- pj eo 9- eo -» ^f ^ •-I pn in PJ ^ ,0 m o- -H <o P- .o P- CM m PO CM in «M 9- IS •0 en 9^ p» pn o 9' « <> ^ f»i * m •4- 1-1 10 S) •» O CM * PSJ eo pj IS P» t»- .0 m * in O- CO »

•r in

• • • in• in

• in

• in• • • CI•

t>- • • • -0 P»

• • • en

• • •

cn

•

<0

• « >0 • • •0• • cn

• p4 PJ ^ PJ• • • • M IM (VJ M PO M M <M CM M CM CM CM CM CM CM CM pj pj Pa PJ PJ pg PJ PJ CM PJ PJ PJ PJ 000 000 0000 * •• * * * * * ¥ * * * * *

LU UJ LU LU UJ LU UJ UJ LU LU LU LU LU LU LU UJ UJ LU LU UJ LU UJ LU LU LU LU LU LU LU UJ * rrt r- t^ F^ pn OO fTI -r pn ph CO P- CO OO P^ CD 00 -• p-4 pH P- PH >»• •-t >r f\j ^ in r- r- 0 CI CO -# CM fO CM •f •* o r> PJ p^ pn m eo >0 CM r*

r^ v •r M *• (M •* m CI m o- fSJ * m PO CO PJ p- PO p- .0 PJ 00 »

o- iH (y # <M 0 00 •0 * o <-^ CM fH •# CO -^ p- m p4 i> P- >*• P- * ^ •*• m f~ r>- <M <o m <# « i-> CO 00 p- 00 m p- fO I-) f-l -0 m PJ -0 e> PJ M

M (M co f^ a PJ i-t •r (M r » * P» * m w^ PO fH * p» ^ in m CI -4

p^ eo h- r* (3- ^ CD •H .# *• «n P- eo o- CI CO •I- * tn 9- 9 9 ^ PJ PJ PJ PO

(M 0 m •» * .^ * -r •* * m m m m m m in in m ,0 <0 'O -o -o

f>. r- h- p- p» P- r- p- r- P- p~ p- p- r^ r- P~ p- P~ p» ^• p. p- p. p- P- p- ^. p- p- p-

(n m ro pr> m m pn pn eri PO pn pn m PO CI eo cn PO pn cn CO pn fo pn cn cn cn cn CO cn

00000 00000 ^ * ^ * *

1 1 1 1 1 1 ^ QJ 1 1 1 ^U ^U ' 1|* ^u ^u

00 PJ >r ph PJ m » <o <o

PJ p- >» >^ fh « « # ^

£> CM iri CI PJ P- PJ ^ pH

p>i <c m GO e r^ CO PJ *

^- PJ p. in p4 PJ ph

o) p- c> p- m .» pn PJ CO in

in -o ^ •£ in r^ P- p00000

UJ 1^ 1^ UJ UJ CM O P- pH ^

PJ O * pn -r o m p- o o

•» m PJ fo •* p» irt ph p^ pn

PJ m (M in o

cn cn pn cn cn

00000

1 1

1

UJ LU UJ LU m p< pn 00 m O PJ o o -o ^ P- IS O i-C P- pH O PJ »

PO ^ pn * pn m 'O '^ in in

•r 'T -f •* -r

00000

II

1

1 1

1

^ ^ 1 1

1

o p-i m m ^

•* m -< >o pn pH tf% 00 P«. P- » ^ PJ p- OO

tf^ O m m CD m cn PO pn PJ

*C -o 'O -o o

00000

UJ UJ UJ UJ ' '

pH pn P- pn P* O -O •*• 9^ o

-O m cn p4 CO pH O CM i'^ Pp-t o p- -r PJ

PM PJ PJ O PJ

<o <o -o « -o p4

p- p«

p-« p- p- p4ppH

P- pH

p- p4 prf p. P- P- -H pH p. PP-l p4

p- pp-l p- P- >4

Pp4 p4 p4 p- p. p- p4Pp4P- p4

P» p4 p4 p- f>- pH r-4 P- PpH

P^

p4 p-I P- P*- 000 00000

• • • • • • • • • • • • • • • • • 000 • • • • • • • • • • • ^ 9 ^ 9 ^ o » » ^ ^ o ^ ^ » » »»»»» »^^^o> ^ ^ c » w

PJ PJ PJ PJ PJ PJ PJ CM PJ PJ p4 pH P-I p4 p4 PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ 000 o 000 • * + • * ¥ * + * * * * 4' * *

LU LU LU LU LU UJ UJ LU LU LU LU LU LU LU LU LU LU LU LU LU UJ LU UJ LU LU UJ LU LU LU LU

<o 9 cn m P- CO m 00 P- pH P» * l> l> CO cn cn in pH P- •0 PJ m pn

r^ p- pH 00 P- P- PJ PJ CO PJ P- l> » .0 pn m pH 00 P" <^ p- ph m

S) pn •0 PJ ^ CD C 9 tn PJ m 9 m -#• P- -- -O 0 P- •! « pn •r- cn p.

•0 pH •0 m pH PJ m 00 -0 p4 is PJ * 9 •O CI m pH 9 P- •r p- pn pn in m

PJ s IS p- PJ CI CO >0 m <o pw a> pn <D ^ PJ PJ p- f^ pn p^ PJ cn oo •0 ^. cn

in in PJ p- PJ * PO •r PJ t^ 9' PO m •r ph -H PJ m ^ •0 •0 1-1 pH * pH » pj IS •0 CO IS CO PJ ~0 eo 9' 1^ -0 p. P- p. -< ^ p- p. p«. CD 9 i-< pH 000 00 9- 9

9- 9 CO i> W 9 O- 9- 9- i> 9- l>

9- o> o- 1> 9- <?• 9- 9- 9- 9- CP * -r cn * •r in in in m m C> (^ pH pH 1-4 r-l pH p- P- P- P» P»

PJ PJ PJ PJ PJ cn PO cn pn PO PO pn PJ CM pn pH •-4 PH pH pH cn cn pn PO PO pH pH p4 pH ^

p- n 9 -* PJ pn •*• m p» a> O- P-* PJ CO -r m 0 p- « 9- ^ PJ PO •*• in <o

>H pH >H p-i pH p-i '^ pH pH pH PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ CO CO PO PO pn CI PO 00000 000

o

a

az

pH M

in in in pH

in pHm

^4

in pHm m

pH

in -Hm in pHm

pHm

pH

in pH pH

in pH pHin pHin

.-1 in pH

in

p4m in pHm

P-I in pHm

pH

in

P-I in pH pH

in m

pn PO m m pn CI CI PO CO pn pn m CO cn PO pn cn PO pn pn m pn m pn pn pn pn cn m cn

fo m CI m Cl CI d cr> pn pn cn pn pn CO m pn pn PO CI pn pn Cl m pn pn PO pn pn m cn

PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ CM PJ PJ PJ PJ PJ PJ PJ rj PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ

-»• -f -»• -r ^ -r •* *• •r * * •r -r •» J- ^ * >»• •f « -f >r >r * •r ••• .» ^ •r *

PJ rj PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ CM PJ PJ PJ PJ PJ PJ PJ CM

IS CD CD 03 s 35 00 00 00 03 s CD eo 35 IS ID s IS CD a> CD 00 03 IS oo CO CO

pH PJ pn -r in pH PJ m .»• m iH PJ CO >» in P-I PJ pn <r m pH PJ pn - in pH PJ pn •#• m

m in m m m m ^ m m m m m m in m m m m in m m in m m m m m m m m 00 ej u 000

-r •»• «r .» «r pn pn pn PO pn PJ PJ PJ PJ PJ 03 00 ts CO

PJ IM PJ PJ PJ I-I pH r-l pH —1 pn pn pn pn PO pH pH pH —1 P-I m PJ 03 m cn CO -r 9- m r>- PJ P- PJ p- PJ <y in pH CD in PJ CP a PO p-i m PJ ain PJ m p^ * m pH •r pn pH -» pn in .» pn PJ pj •r cn in pH <»• P-I CO

p- s^ P- pn i-i IB -* -* p- pn f> •0 PJ CD -*• -H p- •r PO -0 PJ 9 p- pn <o pH PJ cn pn >» p4 PJ pj r s»- in PJ pn m -*• in PJ CM pn * * pH r-t PJ ci pn m m m rri cn >»• >r >r T * » -r -»• in in m in in m m .0 -0 -0 •0 a P- P" p>- p^ p- m rn m pn pn m m pn m pn m pn m pn pn fO PO m m rn ro PO pn PO fO PO pn PO pn pn

p^ p- p. P^ p- P- p- p- p- p- p- r- p- r- p- p«- P- p- p- p~ p- p- p- P- p- r^ p» P- p. PPvl PJ PJ PJ PJ PJ PJ PJ pg PJ PJ PJ CM IM PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ

eo 00 oo IB 05 CO eo <o IS 00 03 03 CO CO eo CD CO 00 s m 03 CO CO (D 33 CD eo 05 CO CO

B-14
m CO ro ro CO ro

m <*> o ro ro ro ro

m fO CM ro cn ro ro en c*> ro ro c*> en en en en ^ o o O O O o o o o o O O o o o O O O O O O O O O O o o o o o

lU LU UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ t^ LU LU ILI II 1 ^ LLJ UJ UJ 1 11 ^ ^ yj 1 1 1

(O ^r r-) C7> "T * m ro •O f-t o- -o o * ro p^ (> r»i c r- CO i-t o o » •o (r in .o >o m i-i (M O CO CD CM r-« ^ m P- * a- -• m m CM m ro o O .-< O CM O •o r- * c o

ro

O <o -O <*•

O •*• f o c> «o J- r-4

m * O CD <*) ^ CM (?© CO PJ ro PlJ CO

O r-l (M

O ^ >c oD

m inm <r> <-i ro

m * ro o p. c>m

m

m CM

O o O ^ m

m pj o p. pO O- f»1 t\j ^ r-- <M O ro ^ ^ ro CO P- p- cp p. o -r en o a- O pj O *• in * m (o m J- so <M O o r^ !0 <> CM r^ o O OO CM m <o o O' so fh CO o m <o p. ^ o o o

OJ <SJ o N- in •o •o -»• r- P- oo CM •o o »• in r« f-i t-i o ro <o CO

O ro en o CM "»• -O (M O o o ^- •-I m o * eg o m CM P- •O p- « PJ o o <0 <»• * O i-i Pki o o f4 in O O * o> (VJ in p- o <0 OD f^ r- <J r~ m in .« so pj « O « ro « CD en .# ,H .H ^

irt ID <X> in p- * a <o CD ^ * m

m CO >o 0> iH -O rt -o

O « fO o»

O <-l ^ »H * « o <o •O o o (VJ -4 H -^ -^ CM CM rvj CM CM « r> o> o o in r-« .-1 iH iH r^ O O O CO m CO tri ro fO f^ ^ pH -^ iH r •*• •r <* •r CM ro ro * -r O i-l p4 l-l ^ M M (\J M (SI m fO ro ro rO CM CM CM «M CM H CM CM (M CM PJ PJ PJ PJ Psl pj m en ro ^ O O O o o O O O O O o o o o o o o o o o 1 1 1 1 1

ill 111 til III HI o o o o o o o o o o

UJ LU UJ UJ UJ UJ UJ UJ UJ UJ UJ UJ Ol UJ Ol III lit III ill tu UJ UJ lU LU LiJ •r ^ O O fO i-t h- o O c»» fO 9- o m >»• pH P- PJ » F^ » f4 ^ O -O r4 O I-I IS I-I

<*> ^rm ro

OO r^ CO f*

O

m 9' p. o- CM in -r -o p» in

m <o o ^ p> o> p» -^

m » m -< O o o> t\i CO •o CO O O '* r-> CO SO in p. ro CO ro nO P- o <o » •-4 P» P~ CM m

in * in r-4 P- o •o fSJ

r o >r o r f\j

m

O P» o fm ro in in .^ ^ so

O <0 ^ P- ro o in ^ ro «^ •*• in m <y h- o -o ^ o r rH so O <* m F^ »H p. <-t pg en >0 CM o w

CVi « (y sT ro •o r» CO r- rt r-t

m -o ir\ 9 >0 ^ CM CM 0> 9 (D 9- 9 (O c m fO pj p- ^ o M m r- CSJ «»• >r ro ^ fH CO ro m in p- -r ^ o « p- o p" » in Cvl O O O O

CM

m <o

O -»• CM <s en PvJ OO -o « in CO -O Pj o 00 ro o o -o CO

m o m pj

m rom

oom (J- o o m CM » O <D <M pH o f^ 00

m r4 o m CO iH en in r^ * in ^ CO iH o m in N> -o r- r- ro <o fo m ro * * « * « o »• ro p» •f « ro CD i-i CO o en o CD • • •

ro «»> • • in•ft • ro•

r-l • • O CD • • CO CO • • <s•r-C

ro < tf\ -o * • • • • •

,-1 p. Pw p. p.

r>i r^ ^ ^ fl

in F^ o F-i CO • • • • • 9 r^ ^ wi O- (MPJPJPJPJ PjrgeMrMCM PJPJCMeMPJ PjrsiCMCMPJ eMCMPJCMCM CMPJCMPsIPJ OOOOO •• OOOOO OOOOO OOOOO OOOOO OOOOO ¥ * ^ ¥ -^ «>>^^ ^>^^^ ^^^4.^ >>^>^ UJ UJ UJ LU UJ LU LU LU UJ LU UJ LU UJ LU Ui LU LU LU LU UJ UJ LU LU LU UJ LU UJ UJ UJ UJ O-OOOO mrH-^com oroi-iiOcn .j-meMi-ir- woso-a-f* poorviroi-t »p--Or-iO f^rMinoo ^cM-O-^m P-o^-OP- cM-OmPJCM 0<MOO"0 sororoopj P-rsim-f^ S-oop-iHO r\i 9 -o o- t-i inro-rro^ 'O •O 9 f^ -O roo-Oco-o P-aoroP--r CMP-r-coo rocn^en* Wt-tcnoo «OincDO

roo»p-a> o«>ocoo o<oincoa) •#-pjeM<-4<-i popj^^om -op-^^p- cMpjop-so oomoj-r pj9soin>-i rop-»p-in Oi-i^cpo ••••••roPOr^PJf-li-l 9'—CpHf^O SOP-P-CDOO 0»»0^ CJPJPJPJrvj OOOf-lO

pjcMrvjpjcM i-tPjeMCMeM •Hi-tp-tfHi^ ,-i w^ r^ r^ r^ pjcMevjPJPJ rvjpiiP<jPJ(M p.p.p.h.p<. p.r.p.p.p. ^.p.^.r>>p. p.^r^^p« p.p.r>p.p. p«p.p.p.p. encnencnm coroenenen cncncnencn encnenrocn cnrocnencn enenrncnm

OOOOO •+ OOOOO OOOOO + OOOOO OOOOO OOOOO ^^^^^ 4,^^^^ ^^«>« LU LU LU UJ LU UJ UJ UJ LU UJ UJ UJ UJ LU UJ LU Ui UJ LU UJ UJ UJ UJ UJ UJ LU UJ UJ UJ LU »r»pu>r>o oao<o>r^ socO'«'SP> p-<ocoropj i-ienin'OP> OPomin.r

•f -O

O

O -o pjOP-m'* OinOP>0 mcMCMi-^o i-»P->rOro ocMmcneM

-r ir\ ^ (^

V inen^^N'CO tnenoP-m inrvimmin <o<^'400<-4 o>i-«inpj.o ^rvio-f* inoo^cM-* mioo<0(vj .iHcmd^'O ^nroi-cenp. inin^cspj CM^^OO P~h-ro«f'# pj^-eroo <.4>-t(ncom min.*f-<.^ coO^rcO'^

•OPjpj^ren roenco-O'O P"CO-*-ooff' PJO^t'eO'*- iHiHpjpapj cMSOro-OO

<O<0<a<OiO <0«'0<00 foromroen pjrororoen mmminin •*-*-*'-rm I 1 F^ I-I I-I p. fW p. 000

<-4 r-l p- r».

1-4 mt

M fH ^

P- P- P» 000

iH >-4 p- p- fH •H p4

r«- p- r* 000

p4 fH fH

P- P- P- 000

H iH p- r- r^ p. f^ fw r^ OOOOO

.H fH

p- p- ^ ^ >4

P~ P- P- 000 000 OOOOO OOOOO 000 OOOOO 9 c^ V o> 9- c 9 9 9 9 9 9 9 9 0^ (> CP 9 9 9

PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ fH fH fH rH iH PJ PJ PJ PJ PJ tM PJ CM PJ PJ PJ PJ PJ PJ PJ 000 000 000 0000 * * * * ^ * * * > * * •• LU LU LU UJ LU LU LU UJ LU LU LU LU LU LU LU LU UJ LU lU LU LU lU LU Ol LU LU UJ LU LU LU

en PJ <D en -^ en PJ

m r~ * •O PJ P- PJ -*• ro SO ro p- -«• <•

mmn ro CM ro

<o fH (3- p. PJ t-l ro PJ •0 iH •r P- .r CO •0 •0 ^ CO en p- fH 0 PJ 00 ro fH en en 0 •*• >* in <r> •0 ro .H ro PJ en p- * in p- 9 9 9 fH P- •e in < in en PJ PJ en ro 35 o- fH ro m .» PJ ro IS <o 9 pH PJ PJ p- en so * ^ 1 a- in ro o- f^ <-! CO o- PJ 9 •f PJ F^ P- 9 p- 9 ro <r •* '^ •0 9 PJ o> »

LU #• CO * r^ ro •r PJ >»• CM -r (O ro ro <D .0 PJ >* pj so 9 en (S fH fH <« rj X CO PJ 00 o> so (O a> f* CO 00 PJ r -o PJ in in CD fH PJ CM 9 p- CO <o

t- CP 9 (O fH

H 9 a> 9 9 9 9 OOOOO 9 9 9 9

(> <y o- 000 9 9 9 9 9 9 9 9 9 9 9 000 c^ CP c> 9 9 9 9 9 o> 9 9 9 9 9 9 9

ro * «r ro ro

m in inm in 9 9 9 PJ fH r^ fH i-> 9 1^ P- p- P- p.

ro PJ PJ PJ PJ ro CO en ro ro •PJ ro ro 9 • PJ PJ »H iH •fH fH r-t • *en PJ PO • •

CO en fH fH fH • •

UJ P- CO •-« PJ ro •»• in •0 P- 00 -* PJ ro .»

m p. CD 9 iH PJ en •r

m «

-1 ro ro ro » >» «r ^ >»• •»• •* •r «» 4-m

m

mmm

mm

m inm <o -0 •0 •0 •0 0 -e

Lt. 000 000 000 m

f4

in

-4

in -4

in in

i-i in

—cm

fHm

fHm

iHm

•H

in

-4

in

-4m

fH ^

inm

fHm

fH

in fHm

fH

in fHm

fH

in fH

in in iH ^ m in fH

in •H

in fHm in

m

ro ro ro ro ro ro ro en ro

^4

PO

m en ro ro ro ro ro ro ro ro en ro fO ro ro

m en en ro ro

ro ro ro ro en ro ro ro ro en en ro ro en ro ro ro

m ro en en rom ro ro ro en ro ro ro

PJ <M PJ r\j rj PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ CM PJ PJ PJ PJ PJ PJ PJ PJ PJ CM PJ PJ

3^ * -*• >»• .r * •r ^ «r -r •» •r «» >»• J- >»• •f J' >» * * r «r •r >!• .r <* •f -r •* •*

l/l 000 *-t Pvl PJ IM PJ PJ PJ PJ pj PJ PJ PJ PJ PJ CM CM PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ CM PJ CM CM PJ

<D s 03 oo CO 00 OS to so CO oo CO <s 00 CO 00 CO 00 (S CO 00 CO CO 00 CC oo CO <S 00 • ft tM m J- in fH PJ ro -»• in -4 PJ ro * m fH PJ ro .* m fH PJ ro ^ m f4 PJ ro -r in 000 Z 000 ^ in in in m m in m m in in m in m m m m m m in m m in in m m m m m in m

LU 00 1/1 000 000 000 z

1-4 oc

-J • • • • • • • C3 < -» J- -» >» -» ro ro ro ro ro PJ PJ PJ CM PJ CD 00 CO 00 ID

LU

CQ PJ <M

M PJ PJ fH »H •H iH iH ro ro ro

m ro -H

H fH fH fH

r^ P- •r p- 0 rj (y •0

m CO in rg 9 -0 fH CO in PJ 33 in PJ p- in PJ <7> P^ in ro

>n -H -t -^ en ro in CMm in r\j in fH ~r PJ •r •H -»• -r

H -r ro ro in PJ

m PJ

•0 PJ in -H p. ro -0 >» -H p- •f 0 PJ in PJ to

m r-i 00 .*• ro 9 •O PJ 9

H- r-l PJ ro en >f ro ro ^ in

mH PJ pj ro -r -4 fH CM en >»• in fH ro

m -r in

m

PJ PJ fM PJ PJ ro

m ro ro ro >r >r * ~r -*

m in in

m in inm 0 .0 >o >0 •0 .0 -o Z

»H fH rH ^4 f^ fH r4 iH

H 3 1 ro m ro ro ro ro ro tn ro ro ro ro ro ro ro ro ro ro ro ro ro ro en ro ro ro ro ro ro ro

Of 1 P- p- p. P- P- P- P- p- P» P- P- P- p- P- P- P- P~ P- P- P- P- P^ P- p- f-. P- P- P- P- P- 11 rsi PJ (M PJ PJ ru PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ PJ CM PJ fSI PJ PJ CJ PJ PJ PJ PJ PJ PJ PJ 1 <o <D (S CO (X> <9 00 00 00 CO CO s> OD CD 10 <r> <o OD 00 CO 00 a> 00 a> CO CO 00 OD CO

B-15
ro fo f*> en en

m enm en cn CM cn cn cn cn cn cn cn cn cn

w cn enm ^^ •r en cn cn en o o o O O o o o o o • III! o oall o o o O O•IB O O O o o o o o 00000 1 1 1 LU LU LU 1 1 UJ LU t 1 1 1 1 III 1 1 1 UJ LU LU 1 • LU LU T t 1 LU UJ LU 1 1 1 1 1 1 1 1 11 1 11 « \^ 111 11till) 1 1 1 1 1 1 1 1 1 1 11 1 1 •

LU 1 UJ LU 1 • LU LU ^ aj f»- .-( en o in OO -o ^- o r^ -r « 00 (X> o <o in in o cn O * rH rH 00 CM orUJ »^ ir> m ^ o r- (? •* o m r r- cn m * 00 CM » «4 « in -o in <s o en rH *• CM.H X e f- w* ^ m o OO CM ,H r- cn -4 O <M en •o <o m » o OJ O rH OO r- rH .0 cn <0 m

h- p» 00 fO -H -r r-l •-< i-t fH -o cn o CM en -r ^ tn 00 r> o r>- in H3 in <r -r

m CM rH

CSJ sO '^ o oo en

mm in OO o- o F-t in cn .o o o r- c c cn ^ CO ^ rH >r 00

m • m » .-4 c^ CM f^ OO « o o * cn -4 o as in m rH CO rH OO m » CM en CM m 4- rH

m > flO O CT) CM <M •H in in .o -r OO O CM O 00 cn « h- rH » O o m C CO CM m ^ CO 9-

lU <D <\J flO -O -4

O •f CM ^ « in fHm cn o 9 09

m rH cn CM o •#• in cn CM CM f~ o <vj ^- -o <« <o <y 'f r^ ^ (f o o> rH r- r- o cn r>- 'O rH •H <y o in iH in in t- • (NJ (D rH m r^ ^> O iH CM O' o r«- m •• m •' cn OO « 4) ^ m CM ># c •r rH CM m ^ OO O CO CO r^ r-l CM CM iH <o -* -r -r * ,H <H ^ rH rH ^ cn cn cn cn QO

t*l **> <*> en en •o -r * * * ***• ^ * rH rH I-t rH

PJ <M C\J CM CM en ^ fo (^ cn

O IM CM CM CM eg CM CM CM CM CM CM CM <M CM * cn en en cn oo o O O o o o o o O O O O O o o o o o o o o o o 00000

a 1 1 1 1 1 1 1 1 1 1 • 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 t 1 LU LU UJ UJ LU LU III Ihl III 111 III LU LU UJ LU LU 111 111 li^ If 1 1^1 1 1 1 yj yj yj ii i UJ LU LU LU UU

oe -4 r- * o 9 .-1 * r~ rt cn O"

m ~r CM cnm o • O K- <o CO in 0 r^ r- rHCM

'< l>~ -4 f^ a> o 00

m in ^ >r tn sT r> 00

m fH in <0m cn -4 .r r- -H o <e in

m 9 CM 3 ^• « r- <o en fo CM ^ CO (M •*• in >* CM »»• «' (s r> OO r« <o c <o cn CM 00 r^ m O r^ O ITl en CM <M o m o * fH cn o h- in <y r4 en « <M O >0 CM OO OO m ^ * rH CM

lO o <M <r

m in CM rH OO tH o CD fH rH CM cn <r o cn « ^ O CD CM (> » o- cn CO rvj « m >o «\j O T^ CM o « •*• m ^r w CM m in r~ cn o rH CM O C CD lO <0 <r CM CM < O <y CO •O in * r* a- • * CM o o ^- <o * O en o o cn ^ r» o o <y CD 00 PO ^ irt r4 .o in .#• h- m in m -4 O en fH <»• CO rH CM .«• * >r O o •«• O <VJ in rH iH ^. o fo m oo o o cn m o « CM rw 00 m 9 OO CM <o iH en 9 r> rH « CD » CO r- * CM rt^ o c\ \C\ O CM f) CM (7' r4 -o O cn rt O r4 ^ cn 00 « m ^. m » rH m >r -r ^• 9 rH

l/> in in ir>

m in * * •• in ^ r» o o o o r- ^ r. ^. p. ^ 9 CO 9' » 00

•-« f-i ^ -) 1-4 * CM CM CM CM rH rH rH -4

CVJ PJ (\J CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM CM IM CM CM CM CM CM CM CM CM o o o o o o o o o o O O O O O O O O O O o o o o o 00000 * * 4- <• 4- * »• 4^ •* 4> •

LU UJ LU LU UJ UJ LU UJ UJ UJ LU LU LU UJ LU UJ UJ LU UJ LU III 111 111 111 111 LU LU LU UJ LU

CM -r f»- o a- f» cn cn CM f^ ft 0> •f o o- rH CM cn CM in rH • CM r4 » •*• cn cn 00 in » CI a- en » ^ CM en c^ CM CM >« -4 OO CM rH in rH 0> C ^- O f^ CO m m CM -O <n rvj o -o o •-• r cn ^. o «) in a- CM cn rH ^ h- in ^ » O CO rH CM ir> >-»>o -r •0 •» < .r <NJ »H so CO cn o OO o O f. « » -r » r4 r- ^ OO m ® <o <r> o » <o <o •0 ^ (\j m «M -4 CM cn 00 CM fH ^ o fH o- '«' in >r o CD in cn cn OO <o '«' <C « ^• 00 UJ r-l 00 *• r- r- o o CM ^- « fH .H cn r- OO cn r- ^ in cn in CO o CM -^ in <o cn CD X <M <vi <» ^ -r •o r~ o o o CM f^ r- f' f* h- « O <0 >o O O rH .H rH r^ ^ fH CM CM - r» r. p. r- r* r> p. r>. 3) CD m r>. ^- h- h- ^. r. r> r. r>- CD QD OD ^0 ^0 00 CD 9 CO OS r- r- r- P". r*. r. h- ^ r> r. r- r> ^• r> r> h- r» ^- r- h- r» t^ ^> r>. »>-

(ti o d

•4 .^ •-« • • »

cn en ^ 1-4 • •

cn cn cn cn cn

iH <-4 f-4 -4 ^

cn en • •en en cn fH iH -4 • • •cn cn ^^ cnm ^ rH rH >4 rH • • • • •cn en cn cn en

r^ ,^ f-t ^m r^

enrH•

cn cn •i rH • •en cn

rH fH • • ^4 ^4 —4

iH t-l t-4 o o o

^4 ^4

<H I-4 o O

•-4 i-l »4 -H fH o o o o o H -4 fH fH ^4 o o o o o ^ ^ r^ ^ ,^ o o o O o ^ rH rH -4 rH O O O O o

rH fH rH rH aH 00000 +• >•• ¥ •¥ * * 4^ 4. LU UJ LU LU LU LU UJ LU UJ ^J lU LU LU UJ UJ LU LU LU UJ LU Ul 1^ ^ LU u UJ LU UJ LU LU m c^ t- •o -o O O O fH 4> r^ -4 00 rH O CO CM OO in m cn o O CM O in l> 4- rH

fO oo in » CM ,-4 in p- vo »> t^ OO "O f^ CD CO OO ^ -O 9 9 CM CM <0

O •* o- r^ CO 9

fh inm h-<0 ^ fM rH * O 00 .H cn * CM

O fiO in o- in 00 CD ^-

O •0

m in *

<VJ o o o <o

M « K

m r-

© iH in

r -O in <0 CM fH CM r» ^- in o » OO CM

W rH CO 4D < * o ^- CM f» CM ^ #• «o ^ O o -r «) m C en cn OO CM .o ^• fH ^ in m fH * CO >• »- o> o> m -4 O- m m ^> in ct o p- r- f- CO m t». o r- m in « 'O « in CO •0 -O LUI

00 00

O CO CO OO 00 OO 00 rA in cn f4

in inm inmm in in r- ^- h- r- ^- o r- f- ^•0

—4 eH F^ <—» f^

h. ro ^. f. ^. o o o o o

^. r- ^• r- h- O o O O O

^. ^. h- f. r. o o O o O

r. f. r- ^ ^. o o o o o ^ ^. r- ^. p. o o o o o

N- ff ^- 000 00 o o o o o o o o o o O O O O O o o o o o o oo o o 000 00

<y <y o o> <^ o- a- o- 9- fr- o o» «^ <> ^ o o » o o> 9 9. 9 9 9 w 9 9

<\J CM

M CM <M CM (M (M IM IM

H ^ rH iH rH CM CM CM CM CM CM CM IM CM CM CM IM CM CM CM o o o o o o o o o o O O O O o o o o o o 00000 00000 4' « + * f 1^ 4. « * 4- 4. * ^ * ^ * 4. 4- 4. ¥ 4- 4- UJ LU LU UJ UJ LU UJ LU UJ UJ lU LU LU tU LU II 1 111 II 1 II 1 11 1

HI 111 111 111 111 LU LU lU LU LU

•*• i^

O

m f«.

O r-l

m CM >0 « ^ r- « cn •o » r- ^" r»

m en in

m cn <0 cn CO eo

O

O OO CM * cn >o in o cn CM iH f" ^ ^- •r ^ CM CM o m cn in t- r* 9 .e •• cn rH

<-l O- -^ en CM (M

O cn rn cn

O IS

O cn >o CM cn o OO cn

m « m .o ^- CO CM in >* CM < CO •* » CT' CO o r~ ^ o » cn OO CD tn in en o> 00 « cn in rH CO CM m ^. CM ^ sO <* p. o in <r o >o CM o- »• rH fH f«. 0> cn ^ CM cn O" rH rH CO in 9 C rH ^ rH CM

UJ r» ^ (vj

O f-4 CM -r CO <o >o r^ as cn ^ « m CM CO en o h- (j> <o •0 en in CM -4 I t> » o o «> o 00 r- r»- r» OO o o m o « ,o ^ ,o f«. rH ^- h- r^ 00 h- w o o o o Cf- O' (f- o- o- a> ^ o> o o <y (J. (y. o o c <y o- v 9 9

«> o o o o o o- o- o- o- o o- o- o o o (j>

a <y o » 9 9 o » o o o o a- o o o- <y o (J. o o <f o- (y o- a- o> (J. 9 9

en o d 'T enmmm in in c^ cy coo .H rH rH r4 rH c> r~- r» r- h- r»

PJ CVJ <\J CM CM cn cn en cn cn CM CM CM en en cn <n en CM en f* -4 rH rH rH

LU r^ CM CO .»•m

O r- CO » o fH CM

m .» in -o ^- 00 » o rH CM en ^ m •0 r» 00 9

-i o o o o o OOOO f-4 rH fH rH rH rH rH rH fH rH CM CM CM CM CM CM CM CM fsj CM en

u. o o o o o O

OO o o o o O

OO o o o o o 00000 o

i-l 1-4 ,H -»-*<*

f>4 >H f-4—< 1-4 •# ^ J- * * ^ —4iH fH fH rH rH

>^ -* *

rH rH iH rH rH

-*• <r •* * *

t-t rH fl

•r >r

r-t rH - rH 1-4 rH —t iH •^ f-4 f-4 fH f-) -^ »H rH rH rH r^ i-l fl w-l r-t iH rH rH rH rH rH rH rH rH r^ a rn on en m en en en cn cn cn cn cn en en en cn en cn cn en cn cn cn en cn en en m m cn CM CM CM CM CM (M CM CM CM CM CM CM CM CM CM CM CM (V) CM CM CM CM CM CM CM CM CM CM IM IM

5i .»•»* -» * «»•*•»*<* * * >» -r -r * * .r >» * * * * ^ >» * -» * J- -»• </> o o o o o o o o o o o o o o o O O o o o 00000 1-^ CM CM (M CM <M CM CM CM CM <M CM CM (M <M CM CM CM (M CM CM IM <M CM IM CM CM IM IM IM CM o 00 ® oo OO OO CO CD OO 00 00 00 CO CO 00 OO CO CO <0 a> OO CD CD CO CO 00 CO 00 CO CO • ^ CM en * in 1-t CM m ^ in ^ CM en * n iH CM cn ^ in rH IM en ^ in r4 CM en >f in a o o o o o O o O O o O O o o o O o O o o 00000 X o o o o o O O O O O O O o o o o o o o o 00000 00

>- in inmmm in in in in in in in inm in

m

m in in in in in

mm inm inm

m

m

LU o o o o o O

O o o o o o o o o o o o o o 00000 I/) o o o o o o o o o o o o o o o o o o o o 00000 0000 O o o o oo o O O O O o o o o o o o o o o 00000 0000 z o o o o o O O O O O o o o o o o o o o o 00000

QC o o o o o O

OOO o o o o o o o o o o o 00000 < r J- -» •T -r o o o o o m en en en cn CM CM CM (M CM 00000 CO CD CO CO LU CM CM CM CM CM o o o o o o o o o o <H -H rH -H rH cn en en en en rH r4 I-t rH .H

fO

r- (M r- <M (O c^ in ,-1 rn in .H r- cn t> en o* -O CM (O in rH r- (O OD •t ^- J-

~»- i-H en

O CM

O en o CM in fH ^ O en in fH en o en

m

m CM in CM T^ sT rH

m o en o o m o in -^ CO >»• o 00 ^ rH f- en <M 00 m rH r- cn -0 CM in r-t 00 * -t V- O -^ 'H CM CM ^ in in o i-< CM m •r -r ir\ rH r4 CM en cn m rH rH cn * >»• in o (D CD 00 (D to CD OO 03 ^ ^ o o o o o- o o o o o rH rH rH rH t-t -H rH iH CM O o o O O o o o o o o o O O O rH rH -H rH rH r^ ^ ,-i ^^ r-i "4 rH rH rH rH z A ^ CO CO CO CO ^D CD CO OO OS OO CO CD O CD CD ® OO OO CD CO QO S> QO CD CD 00 CD CO o CM CM <M (M CM CM CM (M tM <\1 CM CM CM <M CM CM (M IM <\l IM IM (M <M CM CM IM IM CM CM CM

QC O- O- O- o (y O- OO

O O- <y o o o o Cy.O

O C>O (f (y <y 9 1 O O O o o o o o o o o o O O O o o o o o 00000 CM <M CM (M <M CM <M <M <M CM CM CM CM CM CM CM CM <M CM CM IM CM CM IM IM IM (M IM CM CM

OO 30 90 CO OO QO 00 CD ^y ^T^ 00 CO CD

® OO CO CO CD QO® <0 CD 00 OD 00 IS OO 00 00

B-16
Appendix C. Graphical Illustrations*

The purpose of this attachment is to illustrate graphically some of the characteristics of the

VOR measurement process which have been explored. The data were collected to help answer some questions which are often at the core of an examination of a new measurement process, for example,

1. Are there warm-up effects which affect the process?

2. What is the systematic error in an estimated value?

3. Are there within-day or day-to-day differences which will affect the results?

4. Is the bearing measurement system linear?

5. What is the best procedure for monitor the process?

The answers to these (and other) questions are the components of the final documentation of the statistical properties of the VOR measurement process. Quality control, or measurement assurance, procedures follow naturally from the analysis.

Data which are shown in the exhibits were collected by sound statistical practices to answer one

or more of the questions listed above. Whenever data were collected at several bearing angles, switch

settings on the signal generator were selected at random. Various quantities which are plotted are identified by:

1. "Bias": Nominal bearing minus estimated bearing;

2. Theta{l): Estimated bearing;

3. Bear Std: Estimated standard deviation of Theta(l); used to flag individual outliers (see

ref. 3);

4. Theta(2): Auxiliary phase angle (see ref. 3); used to monitor the system;

5. Theta(3): Auxiliary phase angle; also used to monitor the system.

There are four sets of graphs:

Exhibit C.l

Exhibit C.2

Exhibit C.3

Exhibit C.4

Start-up effects

Within-day effects

Systematic offset from nominal bearing

Systematic offset, 5° interval

*The NBS statistical software package STATLIB was used to obtain plots in this

appendix.

C-1
Exhibit C.l

Start-up effects : 20 successive measurements at a fixed nominal bearing were collected on both March

8 and March 10 (1982). Each run began from a cold-start of all system components and continued for

approximately two hours.

Remarks : Approximately 45 to 60 mi n should be allowed for warm-up of the system before performing

calibrations. Theta(3), and its associated DAC, requires the most time to stabilize.

C-2
1 »>^«>-ll-<l-l<-l>-ll-l I M»»«»»M»|-. I U|_>,|-||-.M»M» I «„««««.-.-.-. I MMMM^Hh

® l-l

C71 w

»-| I t~*t~lt-it^t~tt~lt-tt~t>M I ^(^l-IMI-l«-l*-ll-N>-l 1 l-l »-l M 1^ l-l l-l »-« 1-4 *M I »-< l-l »-l l-l l-H 1^ l-l l-l (-4 I l-l l-l »-l Kl l-l l-l l-l IC-3
-i I 11 _ >-< M M l-l ll >-l l-H I » >^ _ 1-1 _! I-I M >- t-l I |_»„M>-I -•-• >-<l-C I — DO

I O) + M •

Vn !^

S ::

« I >

I1

I 9

C-4
3*^O

>

I •1 I t

Vn 1^

C-5
H I >-l l-l I-l •-I >-> l-H >- >-t •-• I t~l<~l >-!>-•>

7n i^

n

n u.

at o

• h- 00 o

J

0.

>

I 1 Kl ^ « - M 1-. « 1-1 I K-l

C-6
n I >-< 00 I 01

ni

ooI CO

.. ni

-<

® 1 UJ *n 9 ^H ni

U) t u> c 1 0) I U) I 00 I in I nI oo I 00 I nI <9 I 9

1-4 • Ui I n c I >I ^I 01 I o> I rt I mI O) I 9I in I o> I in

!-• • I ID I nII r- I (S I oi I m1 r) I CO I O)

C-7
II fli

I ni

1 •<

I «

I 00

I (0

I (0

I U)

I n

I 00

I ni

C-8
I t-it-it-iK-o-il-ii-D-il-l I >-l>-4l-<l-l(-l>->i-i>-ir-< ( t-ii-i »--••->- linn n

I 9

t D

P)>-* nO

T X O

(D a

z

Ul «

« ni

f- 1 «

1 bJ «>

! S

I III-ll-O-ll-ll-O-ll-ll-l I l-ll-ll-lt-ll-ll-II-d-K.

C-9
• I -' 00

I «

inCO ?

E

<B r

>9

in ^^

ni u

n c

t^

>

l-l I I- n

C-10
I %

In 1 « 00 1 «

(U

ni

•-* «1 in 1 p- 1 00 1 0) 1 &111 p- 1 (0 1 <0 1 (fl

t~* * 1 r- 1 Ol 111 m1 00 *^ 1 ift VI 1 <r UiH 1 in 13 1 00 r 11 f: 1 9 z 11 U) v^ 1 ni

t~t • UI 1 n E 1 r- 1 1- 1 m 1 t^ 3

CO 11 fu 1 n) +

ru 1 CO 1 »^ I nI mI 00 I »I u> I ni I (0 1 D1 00 1 g»-« • 1 ni 1 ^1 91 «1 A1 9 + 1 ® 1 l-t

00lA

C-11
1 X 00 1 •IH • 1 ni 1 ni 1 *« 1 91 K^ 1 00 M « 019«4^

tt

U) 1 ^^ • 1 p- 1 01 11r r) 1 00 r^ 1 Ln in 1 Ul

1- IS £ 1 M 1 e 1 s r 1 s1 1/) 1 nj 1 n g 1 [^ 1 1-«n 1 r- D 1 «4 1 r1 9 n 1 ~> « 1 (0 H 11 ¥ I 1- 1 n1 m li.

8ir I «I u> I 01 II p- I (0 I ••

C-12
Exhibit C.2

Mi thin-day effects : 45 successive measurements at nominal bearing 120° were collected on March 2,

March 26, and March 31 (1982). Each run began from a warm-up start and lasted approximately 4 h, 40

min.

Remarks : 1. Theta(l) has no apparent trend.

2. Theta(2) exhibited a trend on 3-26 and 3-31, but not on 3-2.

3. Theta(3) plots depict a thermal drift in the associated DAC on all three days. Note,

however, that the range of Theta{3) is only 0.0074 on 3-2, 0.0128 on 3-25, and 0.0115 on 3-31. The

effect on the drift will be negligible if Theta(3) remains relatively stable during a single determination of Theta(l), i.e., for approximately 6 min.

C-13
s

C-14
I (U I 00 I ni I in I ni II «I «I u>

1^ • I u> I (\l I ni I 9I (71 I <£ I «I IS I «

,^ !^ I «» I sI 00 I »I «I «I (Xl I

C-15
1 M 911 nj 1 00 1 ru 11 ®11 AI 00 1 m1 m1 01 111 «1 «1 91 U3 1 in 1 ni 1 nj 111 «1 s ^^ 1 9 1/) 1 UJ 1 t^ 1 Ol ^ 1 -^ »-< 1 c 1 9 r 1 S11 nj 7» ^ 1 <£ •-t 1 rt 1- 1 iSi ( « 3 1 91 9 a 1 s 1- -4 • VI 1 -^ 11 ^ % 1 Ui 1 m 1 «1 9 u. 1 o 1 00

1- 1 ru o 1 rH ^

a. 11 «1 IS 1 91 U) 3a> I

C-16
I- I (U I M1 nI u> I ni II ni I cu I »1 ru I (n c I (A I «I 9I 9I SI 9I (U

C-17
I < 1-1 _ M « M 1-11-1 1-1 I i-i 11 11 i-i 11 i-i _! 1-1 rH

®

^

9

00n

utnis

9

S

U)

It) (U

nis

« r^ 9 v>UJ

C7) ^

e

S z ®

9 v^ ru

Ol i^

U)

r Is

X

<0

•• ^ a ^ ni 1 n

Ol

1 ?

1 b>

u» I U)

1 P)

I- .

< I n

C-18
*4t-l + >

(flu rt

ni I ni I 9II 00 I U> I nj I ru I U> LlJ 1 Ol I uo I —I 9I 9I «I 9I »I 9I »I nI 01 I 9I sI »I 9

C-19
I Mil MMMM-•-•< I MMMMMMMMM | >-• M ^ I M •

I n

» £

u

lin s :> «Bin '^

rH «(-UlI

:;l i

I/IM M M I MMMMMMMMM | MMMMMMMMM | MMMMMMMMM I MMMMMMMMM | MMMMMMMMM I

M

C-20
1 t-inm-mi-ii-ii-ii-i 1 m

m

-i-m MM•-• - I t^ii nil -•- Mm11 1 -i-m nn- 11 M- I miMli

lAni

nis ^

<n

(0

ti

r* -3 01 Z

£ e

V s o

•4 a.

_ I MMI-IMMI-O-II-II-I I l-mi-aMm-ll-ll-IM I MMMMMMMI-KI 1 «l-l MMn11 -•> M | mMM» 11 IX -IH M | l-l

i i

C-21
I-I I »-• l-t »-l »-l l-l l-l ^ »-< l-t I >-4 »-l (-1 M k-* t-. t-4 l-( »-l I •» l-t l-l M l-l *-I *-4 (-• M^ I M •- M *-l l-l *-l *-i t-t M | |^ M Nri Nl l-l M M l-l M 1 11 O

— nj — a

f- s u.

ru o

(71 - • h- ru o

•1 I Nl (-1 (-1 l-i (- Nl *-l i-l H I MMMMMIMMMM | H *1 W (11- H 1-. >-l l-l H ^ 1-1 I >-l >-. n M >-l >-< t-H >-l >- I

C-22
I ni

I 00

I ni

I »

I «

I (U

I ni

I <s

I 00

I n

I oi

I U)

I «I <»

I .-1

I 9

I «

I nj

I (7>

1 nj

I -I

I s

I 9

I n

C-23
<Xt- I (U I 01 1 P) 1 n1 9 ^* 1 [^ Vl H • u 1 r^ 1 o> 1 -< 2 1 r 1 91 9 z 1 U) 1 ^ IS It! 1 1- 1 r- > 1 U) ea 1 rvi v> 1 ^ « 1 T1 m 1 nt n1 l^ "t 1 0) I ^I cs I CO Il»

C-24
M I |-|»-|(-(MMMMI-((-l t M»-4»-l*^>-ll-IM«MI-4 | »-| t-t *H Ml-l t-l •-• MIM |

n I I c mt->

at UJ

VI 1.

»-« tr- >

w tt

ni "

^ <r T K

" ¥•- n

n u

t- o

fj> K

n> o

^ >J

«-• a. s

P)

c^*«

^

jg^

(0

U)n

n

ni

1 • 00ni

•H I lll-ll-ll-IMMMI-ll-l I -•- >-fl-l>-ll-ll-<>-l>-l I l-ll-ll-OHhll-O-ll-O-l I >-l>-<>-<l-)>-ll-ll-<>H>-l I -• t-l !-• I-I )-• l-l >-l >-• t-< I -•

C-25
C-26
W t *-4MMMMMM|i4l^ I M|^Mt^|-||-|»-«l-*l-l I h-* 1-^ •-* t-t t-* *-) l-« *-t »-l | t~t *~t ^-^ *-t t~t ¥~t t-t t^ *-* I »-« |>« (-( »-t l-l »-«•-* f-t »

i . Ul

Si ^

c

S 1^

i

X

^

Ul o

r- . $

in>

c»

i ?

Ill «>

K4 p)

01

>iJ 1 Ol

3a

>

1 IM 1 l-<Wl-.«Hl-<l-ll-ll-H-l 1 I-H-IMHH1-.I-IMMM | >-| - l-l ll ll ll >-| tl l-l | M M Ml-l 11 H IH » ll | l-l

C-27
C-28
Exhibit C.3

Systematic offset from nominal bearing : The 275 measurements from the first 4 occasions used to

obtain the provisional uncertainty statement for the VOR calibration service are useful to illustrate

the slight offset of the standard phasemeter measurements from the nominal bearing of the standard

signal generator. The various quantities obtained from the set of measurements, excluding outliers,

is plotted versus nominal bearing. There are five groups of plots, each with four separate graphs.

The first group shows the combined data from the four measurement occasions. The other four sets of

plots show each occasion separately, as labeled.

C-29
+ + toinrj^

+ mnunj)* tu

ru m^(u* m

mnjriv + t\j + +

+ + fufururun^ +

ftinu)OJD + nj +

ri-rt-<jin

+ runn^fuinni

9 ft » Ui 9

1 ni o

in Zt3

nj "Z

a-'

«o: 9 uja 9 nuoo

<9 -1<r-j

(D Z<I «z ru E>-" ZO 9 uz

9 u^ -^u> 9 ZO

n 30: S^

9

u.

+ PJ*t^

+ njLncnnjnj Xo

+ fu + r)ru + ;otu

njWT + i/in +

+ + t^nnj + nj

1 1-< t-» »-i »-t i-i »-i »-i »-t I i-i

C-30
I |-IM|^M»^K4l-4fr-i*-i t »-t¥~*>-*t~4t-t^^~**-tt-»

rtr\T +

+ + in »• +

>m ^

Ui + vnjmiD

nj ,4 m

a

H

® bi s f

• u.

nn o

00

n> z

oh-* <e K

A «

(BfO D

UJ

ni a

i/i «

IM • z

Ol-i

i-o:

t» lXl<L <s UJ

<B aea

<s UJ(-->

<il <L^ cz ru »-<•-* l-E

<«o A ujz

<Bs '^ » in ^<n 9 zo 00

D(u +ni iniom

•» + mm *t ii)

o) mruajLT)

nni T ajmojcu

+ r)+ «r +

I M M »^ IH »-l •-< tl Wl-l I l-l t-l 1-4 >-< t-l ^

+ M •

I <9

C-31
rxjoj-t- runj-*- aj +

+ + ru in nj

n + tu njru +ruru ++t/i+ + + + + nj

<» o

r

ni

Ul q:

ni «

Ul

ea 9

^

« « « r-<

U) ro

ni z

«> ^ 3

^

o ni

<s <r 00 1-

UlX

+ + T ¥ + + + + + ++fU-<

+ + tu ru vfu ru -

+ ru + + nnn + n ru

+ fumm + + + + + + + + + +

+ + + + + oj + nj + +01

^ l-l t-l t-H l-» I (-1

C-32
T + + n + ftiw

+ + + + + n

•-• nj+ (u^n

1 •- ®

1 9

1 »

1 U

1 P)

1

1

1 O

1 S i-« «

1

1 nj

1 n

I

1

1 «

1 o

1 9

1 9¥-t •

1 00

1 00

1 ru

1 r> 1

1 s

1 9

1

1 s O

z

1 nj

1 U) £

1 ni a

1 UJ

1 a>

1 s

1 <9 _j

1 9 «

1 9 r

1 (i c

1 ^ o

1 nj r

( Ul

1 9 p

1

1 -^ JL® n

1 9 «

1 00 H

1 — Ul

rnoj n +njD + + nj + + + + +

I 9

I 9

I »-l •

I OS

I 9

I 9

I 9

C-33
I t~* t~* t-t t-t h-t t~t t~t t-t t~, I »-(^

+ nj + +

+ OJ

+ + fU V •

nj •«•

11 I 1-. H -• M 1-1 1-1 >-l M l-< I 1-1 1-1 1-1 >-| 1.

C-34
( MMM*-«*-4»M|«-lMM I MI-tt-ll-tM*-*!-*!-!!^ | MM 1^ M1^ MtM MM I M M 1-4 M M (-1 Ml-l M ) M M M 1-4 M M l-H »i n +

+ + + + +

(U(\J

s

(S<9 o

r

nj

ifl ry

IVJ ^n

9

« ^

« « s r

(0 r

o

ni z

(fl s z> 9

<«

(S> nj « <I n i-LUI

(U+ + + m

o «• -J

-• a

+ +ni

nj ru -f

- - >

I >-i»M>ai^i_«4n» I |_MI-||-||-||-||-|>-<|-I I i-i >- M »>-•>-< d i-i >- I »>-ii->i-ii-ii->>->>->>-i I 11 M i-i i-i >-i >-i >-i h

9

I s

C-35
4 1.^ I-) l_ ,^ M 1.^ M l-l I M l-l ^-1 l-l M l-i i-l i-i f-l I ^H i-l »-< l-H l-l >-*•-• »-l •-• I »-• »-4 »-•»-• »-l M -»•-» »-• 1 »-«l-*l-<l-H»-»>-l*-»»-l»-l 1 »-l

009

nj

0)

cu

o

nj «

ss s

S r

00 IT O

-" I • n

C-36
oiru *

nj*

*ni *

- - >

Oil M

- i

: fe

C-37
— o

cvj r

^ o

" a.

+ ni* *

-t-ni ni

m

9

1 + +

1 M M (-1 l-l l-l l-l l-l M l-l

C-38
ni + + +

+ + + + +

I PI

I

!»

I M

I ni

I 9

I «

I nj

I <s

I «

I 9 »-* •

I vo

I --•

I ru

I «»

» ••

I 9

I 9

I 9

I n

I s

I ni

I

1 Ul

1 n

1 9

1

1

1

1 9

I •-• n

n«4

t^

C-39
(\) + + «I «I 9I (O I cn + (\) + I 00 I 00 I ru I 9II 9I nj I i/> I ru

(M <\j + I «» I sI «I U) I .-1

nj*<^*nj I 9I sI «I 00 I <9 I 9I 9II SI s> I (9 I 00 I 9I '^ + (U +

2i - 1 s1 91 la 1 n1 91 9)1 9 1 1- ®

u>99

C-40
1 I M l-H -. « 1-1 + ru +

+ + + tu

+ •• + +

ru !-• ru «

+ + + + +

s; 2

(J—

+ m + + + fu +

+ ni +

M I 1- 00

4 I »-(

C-41
1 nj +

w 9

9

+ + (\J *

2i -

r-f [ 1^ l-i ^ *-| l-l t-< NH l-l Nl 1 l-l »-, ^ t-H •-« b-l »-t S (O

1/1 «

C-42
+ + nj +

ru +

+ + + + + 9 tUJ ® I1-

<a 1 00 o

r; s

UJ

ea

• u

«• ii •^ o

9

C-43
I I-, l-i 1-1 .1 « « |_ -. „ I ,-,M»^^^rH>->>-< I l-lM^-4K>-l^<Ml-ll-l I l-l •_ >-l _• >- M >-l » >-l 1 ^lil-mHO-ll-IMI-l I

+ + +

nj •-•

(u a

^ ^

1-4 I M l-l i-l t-l 1^ ^ »-| *.4 1^ t M M t-l M l-l t^ l-l ^- ^ I l-t ^-t ^^ >-«•-« ^ r-i »-t •-, I |-< 1-1 l-l k-t »-l l-l » a r- i£ ;c p- t^ r- rC-44
9

I «

* m * *

C-45
Exhibit C.4

Systematic offset, 5° Interval : 73 measurements were obtained at 5° bearing intervals on March 15, 1982. Data collection began at 8:15 a.m. and ended at 2:30 p.m. Measurements at the 73 bearings were obtained in random order. Following are plots of the "Bias," Theta(2) and Theta(3) versus the nominal bearing.

C-46
9

I »

in

:> u) n

01 rl

oo z

11 ®

(A 3 fe « O

<-l I »-H-l < M !- 1-1 « M W I i-i l-l _> >M >-< >-| ^>_| >-| I . 9

lA n9®•' « « s

C-47
-, I «««„„„„«„ I „^^K^^J „-.-.«« I »^»»n»>^.>» , „„„__„„„_ I „„,-,_«««« 1 -, ®

" ^

I-a -

>-> f i-i i-i M li >-l u M M >-i I » M M M ii ii ii i-in I » n » M -. i-i >-i i-i 1-1 | >^ i-i >_ 11 » u i_ i-i i-i | >_ i-i m i-i i-i >-i i-i ii i-i | i-<

ro 9 OQ <£ (U CU •^ 'TH ^

r- r- i^ r- c^

9

C-48
I I »|-||-|MMMI-mM I |-|W|-|MI-I>-II-II-II-I I ^^^^^t-,,-,^^ I „„^-,nn„n„„ I MI-.«l-lH«Ml-l>-« 1 1-1

T O

J ^4 a.

51a I 111 I I- I

2^

M P I-IMMI-O-IM •_>->- I -»»-_»-Ml-, I M »»»,_» l-O-IM I »»»r-<»l-ll-ll-.l-, I M|-|M>-||_»M >-«- | >-t

C-49

Appendix D. BMDP3V Program Listing

D-1
a

lAJ «/) UJ

(9 V> Z UJ W

< -I o

U. CD oooooooooo

ooooooooo • •••••••••o

ooooooooooooo

oooo ••*•••**•

o • • •ooooooooo • ooo(\j(nflOfH-^r-orn<o

0<*^*^^^fHf-*<NJfSi<\jCnm<«

oooooooooo

oooooooooo

ooooooooooooo

•oooooooooooo o************ oooooooooooo **>^^(\iir«^^r^O(<io

t/1 ui

4/1 Q

2 -• O

O X. o

(y^ ^« »-« Z >« I

or z: -i a "I

> UJ <_>

ro C I < u. 3 o »- Lu l; 1-

Oj >- u_ co -. w

Ln «a I z z.

::^ c »— !-• »—

-1 X. -n

CC O O

•I z

c UI tft < LA z

UJ =3

at Ud Z

«/» =D O

Ui z

t/^ I HH

-« »- z o •-• l-t 3 4

u. r o U" UJ

Ui QC

QC (/>

D-2
o o

•o « O « o f»» o o

• o

o -r •

' o •->

I o o

o o

> • o

tn o

r1 m. O

O O O

tl •

• o

o •

UJ >- O z u. 1-t o

o t~ a t/1 »- z i-t Ui QC. 1^ —I on ^ (/I CD LLi O •-. •—

CL <•) Z X

QL UJ - o H^ 1-

<i :> »/ UJ > i-t z> Z ^-. • z

z z =) o UJ Nt

u. Z) t/^ o _) O UJ (/^ O CD t/> UJ o <I X « UJ

oo oo X < I-t _( 1*0 t—

I

U- t— 3 t- —J I-. UJ

t/^ _j e o UJ «r X

> >- u. u> z z at > -

-J »- o c •4 »-• 4 O

« •-• ^ -t UJ ^ o. 2 -J <1 w-i a. *- >

« *— t— 1 QC <4 z C X O V- z UJ D z

—J < c UJ > - (/> Z *—

LL. U. _, o m Uj UJ !-• i/» on c UJ a Z 3 X i-t Ui O O » QL <z < —

i

4 h- I z < £ QC < z z

HI t^ UJ CD < > O D

c >- 2 X a c

LL» 3 Qc t— U_ UJ »-

X. a. C< O u. • • »- a. c •— I" u. •t c: Z. Z »-> C" UJ r c •— r- z UJ UJ oc u _j r^ o >- _i —i QC 0^. •—

_j <i a 1—

U- £D (T 1— »- =>

•a (/I tj «-H (•1 (•1 c: O «/> on o ^ Uj oe a. ft. u. U> UJ

UJ t_) u. <-k LL^ UJ Q. o. QL X c^ 2 ^ C <-) > t— 1-

UJ U- •V U.' X ty C UJ

t; •— > en _) o Z> _j a QC tJ - t- 1—

1

a « c Z >- 4

1 V 1—

1

X X z u. X

i*n o ^- c > Oc on > I Ck. •— o QC UJ u; z f^ h- Ui OL Z o a. u. X =:

a. w > >- Hm < u. CL H- Oc C *a ^•4 o.

i: It. Z c « 1 1 (C X =5 o * 1

X. _l -

^ I ^, «^ te> 1 o o- O o o on <c on

u. *- o o o Z on ut « z z o ^ o o a O >- X « • Uj UJ o «n o o QC

tf> UJ o I X • «^ o o ^ Ui

^-( ^ on H- ^ 1 O o o < f*J « H4 QC o o iH z o u. 4 *«i «ih ^ • • oc

• UJ O o r* 1 • o • ^ k CQ o o o « u. u- - fn *n o A m • on • « UJ « • o a- o tn on 2

(M on O o f- >- • • *-* o HI Z 4 «

• on U 1^ • 1 o o on o oc 4

r- «^ < • w • >- o • >- l-> h- tu. o z o ^ I-t >- 4 «t • 1 —1 »- 4

ik z o UJ 4 4 4 O en < 4 uj O

X (--» H-t on »- - O o «t •k z Z QC o DC on =3 UI UJ • QC o o CD < QC C • ^^ •< UJ X X o •i 4 o ^4 o O U. * UJ ^ • *.o Z ¥~ »- z • • • U U. o o o 4 U. Uj •

• o en m o 3 Ui 1—

I

^4 <J o z t£ o o o •- to CC o

a • -4 ^-1 X O e QC 4 Z z t-4 > o • • 4 z z

fV. * h- Z ^ z z 4 • - 1—

1

•-• • QC • 1 O 4 o HI

U! U. V Ut u. u. 4 4 U. CO U. QC oc >- 4 « QC u. o

or —

<x X —

>

X «ik ec ,•4 X 4 4 4 UJ >- • • QC z - X 4

< - o - H- ir. o o »— UJ UJ Q CC < • t-t IVJ o o Ui

• > c o -o 1 cc (D O on r-t > >- UJ a

on o-t CO UJ « ^t o o m on m on QC ^ on o CC X

U. 1-^ oc o <y • ^^ <-> i-i on on ^- i-i t/n UJ on i-i »-• 4 z o o

—on -«1 o o o < «VJ HN HH »-t 1— HN u. c to ^—

CO - 1—

1

N o h- u.- UJ t— •w O z z UI z z Of UJ UJ UJ < < on O UJ .^ Z o UJ o C Ui Z o c o o ^ o on 3 QC H- i: »- UJ Uj o o d X U» u< UJ Z o o z 4 Ut o a c o cc 4 UJ —

t

C

QC QC H^ z «/ Uj o z z H- > o. K 4 z z 4 oc X z z »— 4 4 UI ^ 4 HI

•c c: 2. < z> on I-t HN u< Uw t—

z 4 4 Z 4 1—

< 4 1—

)

Ck. CC > a > u. 3 z

on

UJ

-J

CD

z

occ

uUJ

u.

QC4

UJ

CD

QC4

U.

CD 4

UJ

d) 4

z

U. U. QC OC o. a.

T

QC

X

OC

X

on

UJ

cc4

on

u*

OJ4

QC4>

U.c

a

UI

4

or4>

z

o^

on

a.

CCz

Q.

Z

>~ < O-i u U. U. U. I Q. o l- - t- UJ a. QC on iS 1— 3

Z) 1—

z l-l 1—

H» 1—

1

h- 3 I-t C c o ^ 4 4 QC 4 Z Z 2 t- -

o. a •4 C on a. CL a o - > > Ui <_) i-« 3 4 z < a. or UJ >- V V z H« CC _j c- U' h- a I

H^ > h- O Q X T X UJ >- u. U T U. UJ z QC 1—

z Ql ^ >*. z

UJ

CCo

QC

c

OlUJ

cczz

a

UJz

z

=3Z4

»-O

e

QCUJ

CCz3

z

CC4

UJ4

<->

4

on

»-Z

onZ

4

CC

Z3

a.z

z

oc

c

u.

CLZ

D-3
tl > ^ ex

1—

a

m UJ

•< X

cc H- o

Q£ <J

o. NM^

^

ft H- < o.

»- z

t >- n </> 2 <

OOOf^OOOOOO^OfsJ OOCmoOOOOOir\oco OOOfVJOOOOOOOO^

z^ ooooooocooooo

^QL ooooooooooooo

Z)uj O • • "CCOOOOOOO

Qt or^-c^i-ti—(^Nf\j(\j(Sjpnr-!m

ooooooooooooo ooooooooooooo ooooooooooooo ooooooooooooo

mpH,-.r-^0fv^00^^^000

CO c^e^(Om^-«-'f^l-Hr^^(7'-r^-oo

ai— or^kTi-^f^or-o^or-rn^cjoo ^^ oaj^t»-"r-r*-(-t^r-tr*-t-ir-f-ir«-co C< OO^"-'—'^.-«'-«i-lr-'^.-"^^CO

z. ^ ooocooooocoooooo -a^- ocooccoccoooocco k-LLj oooooooocoooocoo

I — I I 0^ r-" 1 i

ccooooocoocco oocoooocooocc ocooooccoocoo

i--OOC(VC'-"^CCCOO ococccocoooco cccocccccccoc

r*--0'j'inr-O(^(Nj^^'-t-£(Njir^t-«f-i r-n^^iNjfvj^dJia^-CO'^COJ^CT'

i-.ur>0'cofv,cn->Xi-<r-a:;00000

C'j-c^rf^ir^O'-cO'.-icccT'.^cc.co o^ ,-^r^o£:'-«^-o^-f^.mlr f\-oo

cr-LT'P^rNjcCsrfs.rv-C ^f*"-C(s.OO COO^OOw^i-^^CO^OOO OCOOCOCOOCCCCCCO OOOCCOOCOCOCCCOC

I I I I I I I

I I I I I I

O <— fM (*^

a.zc;c;c;c;c;cot^oooc; ^ t •«-«lZZZZZZZZZZZ2 o —

a-Z<*s-<-<^*s«a-<*i<<i<>-^ _j CXCU,LL.U_a-U^UJU.U-u-U-U-LJ_-flU- *

I

D-4
OOOOOOOOO ooooooooo OOOOOOOOO ooooooooo

I I I I • o o

oooooooooo

oooooooooo

o o o o

o o

o o

ooooooooooo ooooooooooo o o o

o o o o o o

o o o

oooooooooooo oooooooooooo

oooooooooooo

o o o o

o o o o

o o o o

o o o o

I I I I I I I I o o

ooooooooocooo ooooooooooooo ooooocooooooo ooooooooooooo

oooocooooooooo oooooooooooooo oooooooooooooo

I I I I I o o

ooooooooooooooo ooooccocoooooco ooooooooooooooo

ooooooooooocoooo oooooccoooooc-ooo ooccooooooocoooo ooocooooocoooooo

ooooocooooooo I I

o o o o o

o o o o o

o o o o o

o o o o o

o o o o o o

O o o o o o

o o o o o o

o o o o c o

o o o o o o o

o c o o o o o

o o o o o o o

o o o o o o o

I I I I o c

ocoooooo ooooooco oocooooo cooooooo

o o o o o o u o o c o '^ 7

o o o o o O O O O O .-1 o •-•

o o o o o o o o o ^ o o 7

o o o o o O O O rH O O o •-«

o o o o o o o t-i o o o o

J* o o o o o O rl O O O O o l-t

o o o o o •H o o o o o o r-<

!>-) O O O O rH o o c o o o o iH

•a O O o - o o o o o o o o 7

O O .1 o c c o o o c o o 7

=)o

O -J c o o o o o o o c o f-l

rt o o o o o o o o o o o 7

z Ot-tOOCOOCOCOOOOC- ZCtCOOOOCOCOOCOO •-<<30000» • • • •• • • • Q.Li_0 • • •occoocooo Z)cD •ooctvli'0Cl-»-r^-O^^^

Oco »•«

0LOU.UJLiJUjU^UjUJLUUjUJLL:Uj<UJ

QL OL Q:. a. QL Qt QC LULUli-LL^LULiJ^UJ

D-5
o o o o o o

o o o o o o

o o o o o o

o o o o o o

O O O O o o o

o o o o o o o o o o o o o o

o o o o o o o

oooooooo oooooooo oooouooo oooooooo

ooooooooo ooooooooo

ooooooooo

oooooooooo ooocoooooo cooooocooo ooooooooooo o

c o o o

o o

ooooooooooo

ooooooooooo ooooooooooo

o o o o o o

o o o

o o o

• <-i«-(C\jc\ji-ff\j^-f\j*-ic\jf^fvjru J 'OOCOOOOOOOOOO U-COCOOOOOOOOOOO Cii-OOOOOOOOCOOOO

ooco: ooooooo cooccoooooco OOOOOCOOOC.OO OOOOOOOOOOOO

O O O c

O o o o

o o o o

o o o o

u^ mtf^C^|-lrvJ^f^oc^-»-<(^Oco — .-»C-COfVOCV.i-*C^O»-tO OZOOCCOOCOCOOOO f^-CCOCOOOOOOOOOO C^u_. •••••••••••• u- IT I I I I I I I II

Uj ^C00f\.0(\j^0C0C0 ^zccooococcocoo Ol <ooooooocooooo

OOOOCOOCOOCCO OCOOOCOCOOOCO OCOOCOOCOOOCO OOOOCOOOCOOOCC O O O O

C C O O O

C O O O O

C O o o o

Q ^^ e^ m

^-«^^J<*l'*lf^^^0CO^-I^^I-^.-^ o •-< f\. m

O- r- r-l •-! i-i

D-6
o m o f>j 03 fo o t^ ^ >D o m

o o r*- r- «r o

O CO OD P«- *Tt ^ o ^- (M CT' f*i «*>

o I-* o f-< r* m .-I o f*- in CT' m o ir» o m o r^ CD >r o

o -o -^ o o iTi m

«-t m -J- sT IT*

ooajc-si-o-o*-*

-*ujOootr(»r*iriifN,-iooDOiriirvfntf\m^iri^Otf^r^^co.^

I ••••• O^ »-(*-ifvj f-«i-i •-• f-« f-if-H »-t»-»«-*rsj

oooooooooooooooooooooooo oooooooooooooooooooooooo oooooooooooooooooooooooo

Otrvcrm*»-tr«'^*r'0.-* OOsTi—taoasroinmo) 0'4'-J->0'Cor-aDm^ oorHcrr^^j- ^rm

o tr\ o -o o ^ o ^

ocE>i-*-OCT'*»-fni-**c-oirt ocraom.-tco Or-ioo*-* OOrHirOOCC(\J<\|COin o ^ r^ o o o o C7- m

O ac ^

I O'J"O^'*ir»^r^>rf**mDDm(r»rijCD'.0fn<sj»-4C7»r^cDfn'j' OUJO«-'0i-i00O00O00O00000000C,-(0 liJt-OOOOOOoOOOOOOOOOOOOOOOOO >ooooooooooooooooooooooooo

LLi O

«-^r^rH«—•rH*-*»-t^^^Hf-NfMf\:C\JfMrsj<\|r\|f>JCu«—•fH^^i—(rH

• OC/OOOOOOOOOOOOCOOOOOOOOC :> •OOOOOOOOOOOOOOOOOOOOOOOO UjQOOOOOOOOOOOOOOOOOC oooooo

.J CVi

OfvjCT-'T^mccrvfNjt-iac.c

OsJ-f^.—t.-«r-*-4-0' ^'il'lfNs*- omcT'«-*m.otMcC'rLrr^(t) or-cD^ooif>aDOf^. r-CT'i-H O-TIi-HnO I l^lO^^l^-.-^0^C 11^ ^ .-, I I I I I

I I I

o O" o cr o ^ sO ir> o »-< m r^ O n^ sT O

O O r-« c <nmrnfnmiriirvtrtunirCT'000't-<»-<t-4t-tt—(f\jf>dCNjrjcu iij^^^W^^OCOCOOOOOOOCOCC\jf\j(M(MP0 »-'«JCOOOC OOOOOOOOOOOOOOC oooc (_*I-OCOOOOOCOOOCOOOOOCOCOOOO -•^•••••••••••••••••••••••«

O X I I I t I I I I I I I I I I

ooc^^r*--a CiTi^HOfTir-r^o

Ofnc7'irt-Ha.ccO'-4-iJ-tcO'C C^-mr", ^OfTiriCh- ^mo

o*-«,-t^iocE>rror- c^.— oo

o CD r*- -o fi O m r- m tr\ O 11 *- rn CD c ro ir u- •-» O ''" f*»J f*^ (*^ U_'«IOO000»-tr-<t-li-<OO00O000O0<-li-Hi-'0r-t >KOCOOOOOOOOOCOOOOOCOOOOOO aiiJOOOOOOOOOOCOOOOOOOOOOOOO

!(\ipu(si<\jfnfnfnri>j->r*r«*'-4'tr^*r>>r*i'^»r>

D-7
p^J^f^f<<•.*•-*r^J^^C>^PJr^0^noOf^aD^JO.*^lns^mo^0^^-^rO**^*or^JO^^^n^^JCCOcD-^

I _ ^ ^1

occoocccoococcoooocooccoooooccocoooocooooccoooococooooo OOOCOCOCOCOOOOOCOOCOOOOOOOOOOOOOOOGOOOOCOOCOOCOOOOOOOOO cooocooooooooooocoooooccoooooooooocooooocoooocoocooocoo

^a;^-^ncDrH^>-lf^^f^^-^^-0(^JCO<^Jl^^<^J^^^Jr^a''*^<^JO*^J^-'l-HC>^^'OOJl/^l--^^-HC^Jf^J^r^J^O ocoococccccoccoccooocoooooocccooooooocooooooccooooooooo ocococcooooooccococoooccoooooooooooococoocococooococooo oococooocoooooooooococccocooooooooooocooococoooooooocoo

ooooccoococooooocaoocjcjcooooocoooooooooocoooooooooocoooo OOCOCOCOOCCOOCOCOCOOOCCCOOOOOOOCCOOOC-OCOOOOOOOOOOOOCCOO COOOCOCOOCCOCOOOOOOC.OOCOOCOOOCOOCOOCOOCOCCOCOOOOOCCOCOO

irtriT^iru^^r. iri^if>OCOCCxa:a:ccii.^i--t.-ii--»--ii--(,-Hi--f^f-Hr<-rr'rf>f*-. rncoooc-x xc&trcctEccccaca- occcOi-«

coccccoooocooccccocccoccooocococccoccoocccceccccocococc OOCCCOCOOOOOOCCCOOOOOCOCCCOCCLOOCOCCCOCOCOCOCOOCCCCCCCOC

I I I I I I I t I I I I I I I I I I I I t I i I ( t I I I I I f I I I I

ooccococooooccccccoccooocccoocoooocccocccccoococoocccco cccccoccoocccoccoccoooccococ-ocoooccocoocccooccccoocococ

1 I I I I I I I [ ) I I I I 1 I I I I I I I I I I I I

^-co-c^o^^j^r^r^r^-r^f^occcccoccDOO'O'CT'O'

COOOCf--<-'»-'<-'»—•^Jt^j<Nj^-'<MI mn<*ifnnr^{T;fr m(\jCgPsjrsj<\.

D-8
'0f*-^lnf**l-*tf^0^^^l^»<^.'f^J<*>^(^J^f^»-^<Dsr<^J<-H^-HO^^^''^'*'^J^*OfSJf^Jl^^U^0'^^rnft^f^ 0«*^'NJ«H<>'«r^j^O»rtOfsjf>dca<*iN*-cii^HOrnmf-<CNj»«-H^^Oir»«^00'fNJO''*"0»--«tn^.--(-*'fncDO<>®

•-*.H)-l|l*-( II ^fH li-tll *M,Hi-lf-lc-(,-|^^^(\J.-t^ I I It-* II |f-t —t I

ooocoooooooooooooooooooooooooooooooooooooooooooooooocoo ooocooooooooooooooooooooooooooooooooooooooooooooooooooo ooooooooocoocoooooooooooooooooooooooooooooooooooooooooo

^f^^»-ll^^c,-ltf^^^(r>0(^i^^^-(^J(^J^f^•-^^ruC^J^-^f^JOr^r-^^<)a)^l-^.-*<)l^»fno»-*<^^nof^J^,>r0^r^-*^^^ COOCOOCOOOOCCOOOOOOOOO^.-tO.-iOOOO^i-tOOOOOOOCOCOOOOOOOC:oCOOO cccocooooooooocoooooooooooocooooooooocooooooooooocoooco coooooooooocoooooooooooooooocoooooooooooooooooooooooooo

I I I I I I I I I I I I I I I

l-Hf-t^^.t^Jr^J^gr^Jf^Jt^Jf^JCJ^J<-^l-^l-^r-^^--lr^JCM^^J<^J04^-»,-^^-t.-^.-•.-l^-^^-•*-^^^Je^J^^J^ C.tJ^OOOOOOOOOOOOCOOOOOOOC'OO'-JCJQJOOOOOOOOOOOOOOOOOOOOOOOOC^'OO coooooooooooocoooooooooooocc-ooooooooooooooooooooooooooo ccocoooooooooooooooooooooooooocooooooocoooooooooooooooo

»— <--ltf^u^^^ll^*u^^^^^^<^f^^c^^^<*^cr)a:,xaD(I>r^Jf^JfvJf^Jl^^^^tf^^^^lrl--r-*r^ocoOOr-l^-^ COCOCOOOCOOOOOCCOr-t.-i^.-H,-Hr^(\.;rNjf\,OoOOC^^«-Hrvjtv.c^fVvraOOCOCi--'<--'"--'">-tOCC;CC<-H cocoocoococccccocococooccocoococooococooooocooooooccoco ooccocoooooooooococcccoococcooooccocccocooooooooooocooo

I I I I I I I 1 t t I 1 I I I I I I ) I I I I I I I I t I I I I

^^c>cM-rco^^o>roc^.c^(ECOlf>i:ccc^C7'Cc^-0'^\Ju^^-^*r.-H^»'»-^^*-oJ•<'f^JOO^-r^J^^4^-^T-,--^^^ac^ C;OOC.O<-tC>Oi— •-"•OCf-tt-tCCC .-iO(Nj(M.-iO»-««—.-'»-'^r-i»-'f-<CCOfs.'(\jf\-.-'r«jOOOOC OCJOr-tCtJCOO r-tC" coccoccoccoocccoooccooococoooooccooooooooooccooocooocco oocoocoooocoocccooccoooooocooooooocoooooocooccoccoccooo

I t I I I I I I I I 1 I I I I I I t I I I I I I I I I

O^ O' <. ^.OO^mfTimi rn m m m rri fvj (nf-tf-Hi-»t-i»-.ccixiccccccirir^a^ir><Si<\j*vj<\je\ii

D-9
^coro^^^^J^-l^lCCo^f^oCT'•-^^*-•--'0^oJa'CDl--^^o^-(^JOO^'O^Hr--l^^^(D•^^-^^-^^^^fna'OoOlf\'*•fio^f^o^^^

III ^ 1^1^ I I ^ I I ^

ococoocoooooooooooococoocooooooooooooooocoooooooooooooo cooooocoooocoooooooooooocooocooooooocoooooooooooooooooo ocoooooocoooocoooooooooooooooooooooooooooocoooooooooooo

0^oQCfn•-^(^J>3•lf^CTJ^^Of*lln^•0-*^<^iC(*^^vJO(I^OlO«*'OCT0®OOC>cn(^i»rO*'^^^0•-H^Ou^^no*^JO"«^^ OCOCOCOOCCCCOCOOOCCCCoOOOOOr-iO.-lO«-«OOOOCi-iOCOOOCOOOOOCOOOOO ococcoccccccoooocooocoooooooooooooooooooooooooooooooooo ooocooooooooooooocooooooooooooooooooooooooooooooooooooo

I I I 1 I

tj<:jootJc;joot-)o<::'CCOCc:;oooooocoooooc)00«_;cj(_;G>cjooooooooooc>ooot'OCJCO ococooocooococcococcooooococoocooccoooooocoooocoooooooo cccooooooocoooocooooooocoooooooooocoooooooooooooooooooo

oc- oooccccooccocccroccooccccccoooococoooococococooocococo OOOC-OCOCCOCCCOCOCOCCOOCOCOCOCOOOCCOCOOCCCOOCCOOCOOOCOCO

I t 1 I I I I I I I 1 I I t I 1 I I I I I I t I

t—OCJCCOOCOOOCCJC .-».—if-<CC_ C OCt-'i-'«-'.-«»-'—<'-'i-<>-«<-'C.-tOO.-if\.f-"r-iOi-^f^-'-'r\j>—.— ^fV4»-<r-»fs.r-<oO CGCJCCOOCOOOCCCCCCCCOCCCOCOCCOOOCOOOOOOCOOOCOCCCCCCOOOCO coocoocccoooooccoococccccccooooocooococooocoocococoocco

I I 1 I I I I I I I I f I I 1 I I I i I I I I I I

D-10
'J-C^J^f^*^rO^n®.-^^n(^g^*O0D^<>^tf^-Of^d^-r^.--•^U^^*OOO^•*C>(OO0Pu^a0^Of^«*>'»'*'*•-*•#-*O<*^--•^^

oooooooocoooococoooooooooooooooooooooooooooooocoooooooo ooooooooooooooooooooooooooooooooooooooooooooooooooooooo ooooooooooooooooooc^oooooooooooooooooooooooooooooooooooo

oooooooooooo<-«ooooooooocooooooooooooooooooooocoooooooooo ooooooooooooooooooooooooooooooooooooooooooooooooooooooo oooooooooocoooooooooooooooooooooooooooooooooooooooooooo

(>o(\jcv^*-*(-4r->«M«-Hf-tr-tr-t«--«rvjf\jfursjcursjfvjCNjruC\jrgru<ViC\jt\jc\jc\jf\jr\^ COOOOOOOOOOOOOOOOOC-'OOOOOOOC^OOOOOOOOOOOOOOOOOCJC^OOOUOOC^OO oooococooooooccooooooooooooooooooooooooooooooooooocoooo ooooooooooooocoooooooooooooooocoooooooooooooooooooooooo

CoCr--.-'^-i-i,-iCOOC.-H»-'»-"i-'.-tC CC COCOOCOOOOCOOOCOOPOfvjOj<\.(\j*-«»-'i-'f-<»-»f\J<V(>uOJf\j^i-<<-» coocooocooccoocoooococoocooocooccooooocoocoocooocococoo occoocococcocococooooooocoooooocoooocooooooocooooooocco

I I I I I I I I I I I I I I I I I I I I I I I I I I

o^-r-lC^^-lr^^r«-c^cD^**f(^a:^^X"'r^^-^^^crocr^^^fn<^JONr*rc«r^^^^cT•c^^ogC'.J^^^*-*-^ OOtiOOOCC^OOCOO«-»»-ii-..-it-«COC OOOOO«--tOOOOOi-«OOOO<Si»-«C0i-t<-«i-«O^-«-^»-'»-'C\j.-Hr\..-iC; oo CCOOCOOCCOOCOCCOOCOOCOOOOOOOOCOOOOOCOOOCOOCC-COOOCOOOCOO cooooooccooooocoooooooocooooooocooocoooccooooooooooooco

I I t I I I I I I I I I I I I I I t I I I I I I I I I I I I I I I

fp ni m m r~. irsj(Njr\jr\jcDacaDS:a^< mn^cnfn<4'^-^^>r<c^^^^l

D-11
<ooc^r*cDrg^^*^lf^aoCTl^J*-•o^f^Otf^a^l^»oroo<r1f^•Otr\^lf^r*»co^-'0^^a>•-^^f^J^-^c®^w«^0'0<M<^J^rt^^Jml-l^f^ ^OCT'.Olf^o^-r^o«sJ(^J^lr^f-((^J(^JOOl?'f*l^»•o^^*^J<M^*lr^o®*^^^<•l^-^jm^J*rCT•o^^oo^f^^^<^Jmp-f*f^J^^J^•^^

COOOOOOOOOOOOOOOOOOOOCJOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO oooooooooooooooouoooouoooooooooooooooooooooooocoooooooo ooooooooooooooooooooooooooooooooooooooooooooooooooooooo

C0C*•^^^^f^^^^^^r^*-^^rf>*rO^^l'^C^^J^J«rI-^li^o<--t<^|f^^•-^Otf^^JC*l^f^•-^•-l^-l^HO•--^'£)-*•t^Jl^>(^JOc^JC^i^H^lf^Or^l-Hm^f*l oooocoooooooooooooooooocooooooooooooooooooooooocooooooo OOCOOOOOOOOOOOOOCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOCOOOOOOO OOOOCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO

I I I I I f I I I I I I I I I I I I I I I I I I I

O0CC0(->CJ0CJO000000t-<JO0000OCJU000O0C)«JC0OOOC0O000C000CJ000<^00 ocoooooooooooooococcooooooooocoooooooooocoooooooooooooo ooccooooooooooooooooooocoooooooooooooocoooooooooooooooo

,— rHOC:cOOCCOOO.-.rH»-l^^OOOCO^.-|•-t^»-'C:CCOCf^-<^-f^-<^l'^JCCOOO(^Jf^Jf^.t^(^JOOOOC^^•-^ coccooc-oc-ooooocoooccooooocococooocooococccooooococooooo ooooooocoooooococoooococooocooooooooccooooooooooooocooc

I I I I I I I 1111(111111 I I I I I r 1(11111111

0'r^fvj»--'^tnf^(vjf\j-rf^a'act\ir^i-imf\j-c(vjoc^r~C7'*Mrj»-t^^ac:0(\jO»-'C«-''vjMpn^p-<(\jr^C7'p^r'f-(<*^^rH^otf^^^ Ct-HCJO0C;t'COCCO0C,OC>-tOOOOOC0C»-''->»-«OO»-'C(M<MC\jr\,(\iOOO0C^<-''-»(\it-«f\jOCOO0»-t»-'»-» cc-ooocc;occococc:occocooooocccooccooocooocooooooooccoocoo cccoooccococoocoocoooooooooocoocoocooooooooooooooooocco

( I ( I ( t ( I I I I

' O- O' o- o- o- .

CVJ *\J f^ fVj ^jiC>o-crO'Or^»-t^^»-'#-tfv^fNj(sj(\i<\jmiftntr. if\r-tf-irtf-t'-'r-r^r^r*pw(7-^CT'^^^^i-ii-»

D-12
^^^0Dl-*.*•^-o•oa^l^«l^^<*»m«r*'^'O^r^fiCT'(*lf^(^JOf-*<^J»-^tf^^^o-oO''OOO-^m'0(^J«»00^Jf^J^^^a>^-tCT•cD^»(^a<^JOm<y^

(\jOi-<c>ja)r^*r'\Jrrifn<i>^^rjc>j^ir»a)rji-*m(\i»*-f^(\j-acja>irsr-«mtfNOCT'<^'*'OOir«rnr^ir»<7'i--'(\ju>cDirto'^r^<M'00^<r«

I I I I I <\1 -« I r-l I I I (\J .-I I II III rnf\iiMi-*rjf-ti-(^H I | t-^

I I I I I I I I I

OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOl^U(-}(^(L)t-)«^<»>OOC^t-'i^ OCOOOOOOOOOOOOOOOOCOOaOOC3C30C3000(300000000000000000000000

ooooooooocooooooooooooooooooooooooooo~~^ ~" ____ 'OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOO ooooooooooooooooooooooooooooooo oooooooooooocoooooooooooooooooooooooooooooooooooo """""OOOOOOOOOOOOO

f-lO^4<^J|^'«r^nf-4c^Jr^J^^tM•-^tH(^<«^u^^Ht--tf^Jf-l«fOf^J^^^lr^rnr^ma'Ol^«0J<^J^^^HC>aDI/^a)p^<Cr-lrnornr--(rvJ^r^J^n^^r^J OCOOOOOOOOOCOOOOOOOOO'Jr-'OOOOCO—•OOOOO.-lrfOOr-iOrtOOOi-'OrfOOi-iOCOO OCOOOOOOOOOOOOOOOOOOOOOOCOOOOOCOOOOOOOOOOOOOOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOGOOOOOOOOOOOCOOOOOOOOOOOOOOOOOOOOOOO

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

CJOCJCJOOOO c; o o o o o o o o o o o o o o o o o o o o «J c

f-l ft o o CJ o o o o o u o o o o o u of-t 1-t o o o o o o o o cocooooo o o o coo o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o ocoooooo o o o o o c

• • • o o o o

• • • • o o

• • o o o o o o

• • o o o • • • o o o o• • o c o o o o o o • • • o o o

• • • o• o o• • o o

• • c o o o o o• •

•-t,-iC C OOOrv.<\j(\;fVjOOCCCfsj<\Jf\jf\,f\jOOOOOf-«^^.-H^-f--tOOOOO<\i(\J*NJ<\JOOOOO(Vfv.<\jr^'\jOOOOO OOOCOf'OOOCOOCCCCOOOOOOCCoOOOOCOOOOOOOOOOCOOOOOOCOCOOOOO ooocoooooooooooocoocoooooooocoooooocooooooooooooooooooo

I I I I I I I t I I I I I I I I I I

"^fvju^**'!—l^-H^nO'4f^•C4f^*'^Ou^cDC7'^-a:^f^l-HOu^^r^^>fn:Or-•u^O>^f^f-H^^OCT'r^^^l(Df^

.— i-fCOC OOfsjrjr\.(\jOOC.OC;i-Hi--.--t»--«»-->»-i»MOOO"--t»-**--'^urvjOOOO.-^f<>rnc\jrrooOOOfni-Hrnrvjrof^ OO ooococooocoooooocococcocooooocooooooocooooooocooococcoo cocoooocooooocooooooooocoooooooooooooocoocoooococoooooo

II *

I I I* I * I I r I I I I I I I I I I I I I I I I I I I I I I I t I I

f-if-Hfvjojcurjrgifvir. IT m<-ti-Hf-»f-ir-ir-r-f*-r^r«.^CT-c-<7'cr icjc\jf\iru<\j(r\irtmif\r^fHrHt-^f-Hr-r»-r^r-r-^tr^^<^

D-13
I I I -< fvj I rt

oooooooooooooooooooooooooooooooocoooooooooooooooooooooo ooooooooooooooooooooooooooooooooooooooooooooooooooooooo ooooooooooooooooooooooooooooooooooooooooooooooooooooooo

OOOC'000"-'i-lOO'^i-iOt-iOOOO--OCOOi-iOOCOOOOOOOOi-lOOCOOOO-<00000-J^r-iOO OOOOOOOOOOOOOOoOOOOOOOOOOOOOOOOOOOOOOOOOOOOCOOOOOOOOOOO OOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOCOOOOOOOOOOOOOOOOO

I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I I

u

r-i f-l o o o o o o o o o O O O CJ u CJ o CJ O O CP u o o o o u u O <J o o t) o o o u tj o o o o o o o o o o «^ o o o

o O O o o o o o o o c o o c o o o o o o o o o o c o o o o o o o o o o c o o o o o o o o o o o o o o c o o o o

o o o

• • o o o o

• • • o o o o o• o o o o o• • o o o o o

• • • • o o o o o o o o o o o o o o o o o o o o o o o o c o o• o o

• • o o o

r-i.— i"-^^!— OCOOO(\jfVi<\j*N-fvjOOCC<\jr^CNjr\j(>jOO'--»»-^'-'^^OCOCO'V(ve^*fsjfv.OCOCOtV(vrvj(\i<NJCOOO»^ coococcccoocccoooocococcooococccoooccccooc-ooocococccooo ooocooooooocooocoococcoccoooocooococooooccocooooocooooo

1 I I I I I I I I I I I I I I I I I

(C^^^Ol-H^^CT*•-^.o^--'•*•o<>c^J«ra>'*^<^"*^^-^r'OOtI}(>f»-u^o*Vf'^^^JO^*«*^co^H^if^J^r«**^^^f^«(>^f^CT^f^

cocooooococooooooocooooccccccoooocooooccooocoooooooocco ccooooooooooooocoooooooooooccooooooooccoooooooooooooooo

I I I I I I I I I I I I I I I I I I I I

r-it-«rH^^r-t(V(Mrsjc\i<vjirNif\tf\tnkr> l-t^-^l-»r-1^-^*^*^*^"C^^ ,^f-l(-*,-^(^J(^Jl^Jfv*e^il^»^^v^^^^^^(r-<-t•-^^-••-••-*r*^-^-^-^*^c^^O'^H

D-14
I I CM I <M i-t

I I

oooooooooooooooo

tr\(*>ir\(\i^f^ir\t-i(r»#-*^f^f-t-OOevj OCt-IO-<OC.-i.-irt-JOi->000 oooooooooooooooo oooooooooooooooo

I I I I I I I I I

oooooooooooooooo oooooooooooooooo

c^mr". **itr<ir'U^tne\jf\j(^rooocO ^-r-it-t.-.ocoO(\jroOO<\ifvf^co COCOCCOOOOOOOCCO OOOCCOOOOOOOOOOO

ocir\ccir\.-tf\jO>or*«-tc^ccy>C(7'r^

t-i^HIV-r-l.-H,-Ht-tCm^Ht-lCO<NJ»-'»— OO OOCOOOOOOOCOOO OOOOOOOOOOOOOOOO

I I I I I

f-l f-*

D-15
OOOOOOOOO ooooooooo OOOOOOOOO ooooooooo

ooooooooo

oooooooooo oooooooooo oooooooooo oooooooooo

oooooooooo

o o

o o

o o

o o

f-iO ooooooooooo ocooooooooo o ooooooooooo z ooooooooooo i-i ooooooooooo «

o o o

o o o

o o o o o o

• >- oooooooooooo OOOOOOOOOOOO o oooooooooooo z OOOOOOOOOOOO <-• • •«•••••••• QC OOOOOOOOOOOO <

O O O o o o o o

o o o o

o o o o

ooooooooooooo oooooocoooooo ooooooooooooo

ooooooooooooo

o o o o o

o o o o o

o o o o o

o o o o o

• • • • • o o o o o

^CDOCOOOCOCOOoOOPn (ri^CCOOCCCOOOCOOf-»

z i-ii-icooccooooocccr- CC O'COCOOCOOOOCOOC-H a, >-^ Of^ooooooooocjoooo «a^ o»-toooo(»uoooooooo C«I O'-'CCOCOCOCOCOOOC Z>-c OOCOCOCOOCCOOOOO «> OOCOOOCCCCCCOCCO -L1. COCCOCOOOCCCOOOO t/^Q •••••••••••••••• OOOOOOOOOOOOO

oooooooooooooo oocooooooooooo oooooooooooooo

oooooooooooooo

occcoooocooocoo cccoccoococccco o ocooccocoocooco z OOOOOOOCOOOOOOC I—

• •••••••••••• Qt COOCOOOCOCCOOO «

o o o o o o

o o o o o o

c o o o o o

o o o o o o

o c o o o o

o o o c o c o

o c c o o o c

o c o o o o o

o o o o c o o

o c c o c o o

Q> 1—1

,„, >r o c o o c o o o c o o c O -D

-c ^- o c o o o o o o c o o o rf^ r' c c c o c o o o o o o a o ot-H ^ o o c o o o o c o c o o o c

c o <z c o c o c c o c o o o C -H c o- c. o o o o o o o c c o o c c

c ^ o c o c o o c c. c o o o c c

c c o o o c c c c c c o o c c o

o c c o o o o o o o o o c c c o

c c c o o o c o o c o c o o c o

ocoooooccocooc oo OOOOCOCOOOOGOOOO o ccccccccoocooooo z ooooocoocooooooo — ••••••••••••••a Ql OCCOOOCOOOOOOO I <

oooooooo ooocoooo cooccooo oooccooc

oooooooo

1 oocooooooocco

• l^aQCQLOi.a.CroCQCQc:QLQLQL QC <I<3ZZ2ZZZZZ2ZZ2 c:

a.CU.U-u-U-LLU-^U.UJLi.U_-LU<IU- mfficcecssoffi

D-16
C Uj u. ,_

D-17
ooooooooo ooooooooo ooooooooo ooooooooo • ••••••••

I I I t I I o o

oooooooooo o o

o o

o o

o o

I I I I I I o o

1- >- —I ot

>-t

"J I oooa>oooooO'OOr-i OOOir\OOOOOOr-lo<S oooinoooooofMO*

OOOOOOOOOOO o

z11

• •••••••••• QC

I I I ) I I I I o o <

o o o

o o o

o o o o o o

oooooooooooo oooooooooooo o

z oooooooooooo •-" • ••••••••••• QC IIIIIIIIIOO «

o o o o

o O O o

o o o o

o o o o

^co^^'0-or*«roO'<*>«H^h»

CT'r-o^rc-roo.oor-ifi.o-r ^OU%iiOaD^f-ioo^aOQDir\

a'CDir»o»nr^fnir»#-<-OfM<*-f*' »>-'COoaDfsjrH(7'f>ji-i^^^^ <I>^O^<Tl(ntftrH<*l*-t^0tft crOi-tco^-)^Oi^^cof*»00

OODOlTtCT' -OGDfsJOOCVJCorI

OOOOOOOOOOOOO u>z OOOOOOOOOOOOO l-> IIIIIIIIIIOO t

o o o o o o o o o o

o o o o o

o o o o o

-crooDh-fvjrnomOf«^oD^Of>o«o

<r>m^^»*^<^ilf^oc^Jlf^lrl^^f-^r-l^^o^^>

.-*f<if-(r-«i-.-t.o,-i^,-«cro-r-.-tO(\i omCT-'j-otmccrnrimof'^fNjmoo ooDa)cr*o-ro(*iajNror^O'roo

0'4-fvjc\jtrcymcr*sj<yt'^U'fncoo 00>-«^«-*rHr-i^.-t^.-t.-t^f-iOO OOOOCOOOOOOOOOOO COOCOOOOOOOCOOCO OOOOOCOOOOOOOOOO

OOOOOOOOOOOOOO

OOOOOOOOOOOOOO

I I I I I

I I I I I I O O

OOOOOOCOOOOOOOO OOOOOOOOCOOOOOO OOOOOOOOOOOOOOO OOOOOOOOOOOOOOO

o o o o o o

o o o o o o

o o o o o o

o o o o o o

• •••••

I I I o o

c o o o o o o

o o o o o o o

o o o o o o o

o o o o o o o

I I I I o o

I/* r^r^O'TOfn>rao^^fnO(\j<jo^

u- u- 4.crsj-rjoo'^ir<r~f\j'£jr-intf~>o*M

cj n oif>o^iriir>>rLr<rro*-<>J'or^oo

CI t-i Odc\i^t-4ir\p\j»-ii-taof^,'*ir(moo

>- *— o-ii-Of-tf-HO'mmrriO'u^cwO-^-co

I o^ OOO.-'OOf-'r-<»-<0OOOCOO

u- OOOOOOCCOOOOOOOO 1 OOOOOOOCOCCOOOOO

OOOOOOOOCOOOOOOO OCOCOCOOOOOOOOOO OOOCOOOOOOOOOOOO OOOOCOOOOOOOOOOO

OOOOOOOOOOOOOO I

OOOOOOOO COOOOCOO OOOOOOOO OOOOOOOO

I

I I I I O o

I I t I I o

»- t-t

• una^a:Q^Q^QfQcac:aLCi.Qcc^Q:; oc

OL C.U-LUU'lUUjUrfLULLJUjLl;UjLLJ<UJ Ck:OUJUJUjU.UjUJUJU.LL<UjUjUJ<UJ LUC_J^CCCOAaiCD^SlS)^Al<X)Offi

OL d; Ol OL a Ol GL LUU- UJU-U^LU<LU

(CCCCCCDtXiaiOflD

D-18
C^ Uj u. I—

tr tt c- ^

(y% 1-4

D-19
ooooooooo ooooooooo

• ••••••••

I I I I I I o o

oooooooooo

oooooooooo oooooooooo

o o

o o oo

o o

I I I I o o

ooo<->ooooooooo ooomooooooooN ooooooooooooo

o o ooooo o

ooooooooooo ooooooooooo o

z ooooooooooo •-

• •••••••••• ot

I I I I I I I I o o <

o o o

o o o

o o o

o o o

©ooooooooooo oooooooooooo oooooooooooo oooooooooooo

I I I I I I I I I o o

o o o o o o o o

o o o o

o o o o

^uo^-l^>a'cD'^^•0(E)'C<:^•-•

iTiCT-iTi-^'^^-ocviO^rmojCT' c^£tf^oo^r^o>o<«'F^aoo

r^*\jfMeTif-t.-io<yo«*im'0O

**^r*ll*l(*^o^-•-^^-|-^^»Htf^eD ^mooJ'^Ofvtirtrt^-T^i-i o«DO«rr^o^CT'^r*^n(M

*Ofn^O-f*-Oca<sj*-t^>»-CT'm

ooooooooooooo OOOOOOOOOOOOO ooooooooooooo OOOOOOOOOOOOO

ooooo OOOOO ooooo OOOOO

r^-rir»^ir*o^i-^a>o<^^*^o^^o

t^r^ifvc^r-r^O'<\;mr^oir>>rf^'ro z i-iif*CD.c^'C(\j<\j^'^o>roD^rno OC3 0(f^<yJ^r-f^J00>^(^J>r^^l^^(^JOO

tt.^- o(ym(n<^a)r-fvjc?ccr-<*^ir*a;oo <!- oajr-r-»-ttjr-c-)^or-f-<r*-ooo 0<I OOCO«-'»-tO'-iOi^O<-tO*-tOO Zi— OOOOOOOOOOOOCOOO <> OOCOOCOOOOOOCOOO *-uj OCOOOOOOOOOOOOOC

OOCOCOOOOOOOOO OOOOOOOOOOOOOO OOOOOOOOOOOOO© OOOOOOOOOOOOOO

OOOOOOOOOCOOCOO OCOOOOOCOOOOOOO OOOOOOOOOOOOOOO OOOOOOOOOOOOOOO

o o o o o o

o o o o o o

o o o o o o

o o o o o o

o o o o o o o

o o o c o o o

o o o o o o o

o o o o o o o

IT. (NjiE^r^-CcH^flcmooomf^o

^.ijf-tO'Effr^if^a-CdOcvjajirNC^O

ou.c-rcc^>ccO''0»-<f-t^^moo

or-r-»-t(\j>ra3^o^tr>Oir<ir OO

OOO^'OO^^^^t-ti-IOOr-IOOO OOCOOOOOOOOOOOOO OOCOOOOOOCOOCOCO

©OOOOOOOOOOOOOOO OOOOOOOCCOOOOCOO OCOCOCOOCOOOOOOO OCOOCOOOOOOOOOOO

©ooooc©oooooo I

o

©ooooooo oooccooc oocooooo coooooo©

I I I o ©

I I I I I I

• iy^OL.OCC1.0cQLQtOCOLDCa.OLOt QC acOUJUjUJU:UjUJlXJLLIUJU.'U<UJ<LLJ uj0^ffi(Dffiff^CCflC(SCDa.cCffiO^ mcc ffiiscceco^

D-20
O u. UD-21

Appendix E. Sample Report of Calibration

The results of a calibration are reported to the customer using a form letter similar to that in this appendix. There are a number of different phasemeter designs on the market, so there is some variation in the way the test is conducted and the results reported. If the phasemeter is designed to permit the forcing of a self-calibration or autozero, this is done before every observation. Some

instruments have provision for internal digital adjustment by means of switches. Since these switches

affect the calibration, their settings are recorded on the data sheet. If settings have been changed

since the last calibration, results cannot be compared.

The data sheet carries information to identify the customer, the instrument (by make, model, and

serial number), and other useful information. It shows a tabulation of the raw data, the standard

deviation for each bearing angle, and difference between the mean and nominal for each angle. The

customer can then correct the instrument readings using the table.

The data are taken using a computer program named "CALDAT". This program allows the operator to

specify the number of bearing angles, the number of readings at each, and all of the housekeeping

information needed to document the measurement. It then prompts the operator as to the setting to be

made on the NBS generator. When the phasemeier under test achieves a stable reading, the operator

enters it into the computer. In order to minimize drift effects, the generator settings are randomized, both by bearing angle and by the reading number for each angle. The observed readings and

the housekeeping data are stored on disc, along with data that allows unscrambling the order of

reading in a case a future time-trend analysis is desired. The program then prints out the data sheet

for the Report of Calibration.

E-1
.-*"': °''% UNITED STATES DEPARTMENT OF COMMERCE

National Bureau of Standards

325 Broadway

Boulder. Colorado 80303

Reply to the attention of: March 29, 1985

Airframe Manufacturing Inc. 1234 S. Broadway

Needles, CA 99999

ATTN: Standards Laboratory Manager

Dear Si r:

Enclosed is a copy of the data from an informal calibration of your VOR Radial

Standard, (manufacturer and model), Serial No. , NBS Test No. .

The instrument was warmed for a minimum of 24 hours before calibration. If an autozero function was provided by the instrument, it was forced before every

observation. If present, the hexadecimal number displayed during the autozero

period was recorded on the data sheet.

Four observations were made at each of 12 bearing angles. The raw data and

the standard deviations for each bearing angle are tabulated on the attached

data sheet. The bearing angles for the set of 48 observations were randomized

to reduce the effects of any time trends and interactions.

Measurements made on several instruments of this type suggest that repeatability at any bearing angle is about ±0.01 degrees immediately after

autozero.

The NBS standard VOR generator and phasemeter are believed to have a combined

systematic and random uncertainty of less than ±0.0023 degrees (95 percent

confidence level )

.

Sincerely,

Neil T. Larsen

Microwave Metrology Group

Electromagnetic Technology Division

E-2
Test. No. 123456

C L4 s % o rn e r : R i r f r a m e M f g

.

Test date: S4 11281433

Data f i 1 e: riEMDRT

I n s t . ni f r : X fl '..> i o n i c s Zero set: -FFF3-

Disk N.:

Ser. N.:

3 2 1005 3 3

123

NOMINRL RUG NO. RDG NO. RDG HO. RDG NO. STflNDFiRD

BEAR [NG

00

I 2 3 4 DEV.

078 - 057 - 089 - 088 T 95E-02

30 00 30 071 29 910 30 073 29 943 3 55E-02

60 00 59 944 60 024 60 073 60 065 5 92E-02

90 00 89 906 89 993 89 916 90 027 5 88E-02

120 00 119 933 119 955 120 099 119 917 8 33E-02

150 00 150 005 149 913 149 972 150. 095 7 59E-02

130 00 179 977 179 951 179 946 130 077 6 09E-02

210 00 210 031 209 902 209 916 209. 9 3 6 26E-02

240 00 239 992 239 927 240 007 239. 959 3 59E-02

270 00 269 931 270 096 270 055 270. 086 5 22E-02

300. 00 299. 990 300 016 299 982 299. 934 3 42E-02

330. 00 329. 989 330 045 330 075 330. 019 3 65E-02

NOMINAL MSMNT MEANBEARING MEAN NOMINAL

0. 00 -.039 -.039

30.00 29.999 -.001

60. 00 60.026 .026

90.00 89.961 -.039

120. 00 119.976 -.024

150.00 149.996 -.004

180.00 179.988 -.012

210.00 209.938 -.062

240.00 239.971 -.029

270.00 270.055 .055

300.00 299.980 -.020

330. 00 330.032 .032

E-3
NBS-n4A iREv. 2-8C) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET 'See instructions)

1. PUBLICATION OR

REPORT NO. NBS TN-1059

2. Performing Organ. Report No. 3. Publication Dace

April 1985

4. TITLE AND SUBTITLE

VOR Calibration Services

5. AUTHOR(S)

Neil T. Larsen, Dominic F. Vecchia, George R. Sugar

6. PERFORMING ORGANIZATION ilf joint or other than NBS. see instructions)

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS [Street. City, State. ZIP)

U.S. Department of Defense

10. SUPPLEMENTARY NOTES

Document is intended to support the new VOR calibrations service with ex- planatory material, software, and statistical control charts. It is not

intended to supply information required to duplicate the service. ^~ Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11. ABSTRACT lA 200-word or less factual summary of most si gnificant information. If document includes a significant

bi bliography or literature survey, mention it here)

The National Bureau of Standards has designed, constructed, and evaluated a standard for the support of very-high-frequency omnidirectional range (VOR)

air navigation aids. The standard consists of two instruments: (1) a digital waveform signal generator for the composite VOR audio waveform, and

(2) a standard phasemeter based on time series analysis of this waveform.

Experimental results, a statistical analysis of them, and the principal

software listings are included.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

air; calibration standard; navigation; omnidirectional; range; very-high

frequency; VOR

13. AVAILABILITY

[ X I Unlimited

i

; For Official Distribution. Do Not Release to NTIS

[Xj Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

Order From National Technical Information Service (NTIS), Springfield, VA. 22161

14. NO. OF

PRINTED PAGES

180

15. Price

U.S. GOVERNMENT PRINTING OFFICE:1985— 578-960 / 25206 USCOMM-DC 6043-P80
NBS TECHNICAL PUBLICATIONS

PERIODICALS

JOURNAL OF RESEARCH—The Journal of Research of the National Bureau of Standards reports NBS research and develop- ment in those disciplines of the physical and engineering sciences in which the Bureau is active. These include physics, chemistry,

engineering, mathematics, and computer sciences. Papers cover a broad range of subjects, with major emphasis on measurement

methodology and the basic technology underlying standardization. Also included from time to lime are survey articles on topics

closely related to the Bureau's technical and scientific programs. As a special service to subscribers each issue contains complete

citations to all recent Bureau publications in both NBS and non- NBS media, issued six times a year. Annual subscription: domestic

$18; foreign $22.50. Single copy, $5.50 domestic; $6.90 foreign.

NONPERIODICALS

Monographs—Major contributions to the technical literature on

various subjects related to the Bureau's scientific and technical activities. Handbooks—Recommended codes of engineering and industrial practice (including safely codes) developed in cooperation with in- terested industries, professional organizations, and regulatory

bodies. Special Publications—Include proceedings of conferences sponsored by NBS, NBS annual reports, and other special publications

appropriate to this grouping such as wall charts, pocket cards, and

bibliographies

Applied Mathematics Series—Mathematical tables, manuals, and

studies of special interest to physicists, engineers, chemists,

biologists, mathematicians, computer programmers, and others engaged in scientific and technical work.

National Standard Reference Data Series—Provides quantitative data on the physical and chemical properties of materials, compiled from the world's literature and critically evaluated. Developed under a worldwide program coordinated by NBS under

the authority of the National Standard Daia Act (Public Law

90-396).

NOTE: The principal publication outlei for the foregoing data is the Journal of Physical and Chemical Reference Data (JPCRD)

published quarterly for NBS by the American Chemical Society

(ACS) and the American Institute of Physics (AiP). Subscriptions,

reprints, and supplements available from ACS, 1 155 Sixteenth St., NW, Washington, DC 20056.

Building Science Series—Disseminates technical irformation developed at the Bureau on building materials, components,

systems, and whole structures. The series presents research results,

test methods, and performance criteria related to the structural and

environmental functions and the durability and safety characteristics of building elements and systems.

Technical Notes—Studies or reports which are complete in themselves but restrictive in their treatment of a subject. Analogous to monographs but not so comprehensive in scope or definitive in treatment of the subject area. Often serve as a vehicle for final reports of work performed at NBS under the sponsorship of other government agencies.

Voluntary Product Standards—Developed under procedures

published by the Department of Commerce in Part 10, Title 15, of

the Code of Federal Regulations. The standards establish nationally recognized requirements for products, and provide all concerned interests with a basis for common understanding of the

characteristics of the products. NBS administers this program as a supplement to the activities of the private sector standardizing

organizations Consumer information Series— Practical information, based on N BS research and experience, covering areas of interest to the con- sumer. Easily understandable language and illustrations provide

useful background knowledge for shopping in today's tech- nological marketplace. Order the above NBS publications from: Supermiendent of Documents, Government Priming Office. Washington. DC 20402. Order the following SBS publications—FIPS and NBSIR's—from

the National Technical Information Service . Springfield, VA 22161

.

Federal Information Processing Standards Publications (FIPS

PUB)—Publications in this series collectively constitute the Federal Information Processing Standards Register. The Register

serves as the official source of information in the Federal Government regarding standards issued by NBS pursuant to the Federal Property and Administrative Services Act of 1949 as amended.

Public Law 89-306 (79 Stat. 1127), and as implemented by Executive Order 11717(38 FR 12315, dated May 11, 1973) and Part 6

of Title 15 CFR (Code of Federal Regulations).

NBS Interagency Reports (NBSIR)—A special series of interim or

final reports on work performed by NBS for outside sponsors

(both government and non-government), in general, initial dis- tribution is handled by the sponsor; public distribution is by the National Technical information Service , Springfield, VA 22161,

in paper copy or microfiche form.
U.S. Department of Commerce

National Bureau of Standards

Washington, D.C. 20234

Official Business

Penalty for Private Use S300

POSTAGE AND FEES PAID US DEPARTMENT OF COMMERCE

COM-215

SPECIAL FOURTH-CLASS RATE BOOK