PB 151381

*^o.22

PRECISE TIME SYNCHRONIZATION

OF WIDELY SEPARATED CLOCKS

BY ALVIN H. MORGAN

U. S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

NATIONAL BUREAU OF STANDARDS

technical nflote

22

July 1959

PRECISE TIME SYNCHRONIZATION

OF WIDELY SEPARATED CLOCKS

by

I

Alvin H. Morgan

NBS Technical Notes are designed to supplement the Bureau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be

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-1-

TABLE OF CONTENTS

PRECISE TIME SYNCHRONIZATION

OF WIDELY SEPARATED CLOCKS

by

Alvin H. Morgan

Page

I. INTRODUCTION 1

II. METHODS OF SYNCHRONIZING WIDELY SEPARATED 2

CLOCKS

III. TRANSPORTING A MASTER TO EACH SLAVE CLOCK 3

a. General 3

b. Clock Errors 3

c. Time Kept by a Clock 4

IV. TWO-WAY TRANSMISSION OF TIME SIGNALS 5

a. HF Timing Signals 5

V. ONE-WAY TRANSMISSION OF TIME SIGNALS 7

a. Ground Wave Timing Signals 7

b. Ground Wave Propagation Delay 7

c. HF Propagation 7

VI. ACCURACY OF METHODS GIVEN 9

a. Transporting a Master Clock 9

b. Transmission of Time Signals (one- and two-way) 10

(1) General 10

(2) HF Timing Signals 10

(a) One- Way Transmissions 10

(b) Two -Way Transmissions 12

(3) Ground Wave Timing Signals 12

(a) One-way 12

(b) Two-way 13

VII. MODES OF PROPAGATION OF HF SIGNALS 13

a. Introduction 13

b. Maximum Usable Frequencies (MUF) 14
-11-

Table of Contents (Con't)

Page

c. One-Hop Modes 14

d. Multi-Hop Modes 15

e. Control Points 15

VIII. VARIATIONS IN PROPAGATION DELAY OF HF SIGNALS 16

a. Introduction 16

b. Factors Affecting the Propagation Delay 16

c. Estimation of Effect of Normal Variations of Virtual l6

Height

IX. CHART FOR DETERMINING TOTAL HF PROPAGATION 18

DELAY

a. Introduction 18

b. Use of Chart 18

X. ASTRONOMICAL AND "ATOMIC" TIME 18

a. Introduction 18

b. Mean Solar Time 19

(1) Mean Solar Second 19

(2) Mean Solar Day 19

(3) Uniform Time (UT) 19

(a) UT-0 19

(b) UT-1 19

(c) UT-2 19

c. Ephemeris Time 19

d. Atomic Time 20

e. Standard HF Time Signals 20

XL USE OF TIME SIGNALS FROM MORE THAN ONE STATION 20

XII. ACKNOWLEDGMENTS 20

XIII. REFERENCES AND BIBLIOGRAPHY 21

XIV. APPENDICES 22

Appendix A

Great Circle Distance Calculations 23

Appendix B

HF Propagation Delay Times 26

Appendix C

Two- Way Transmission of Time Signals 31

Appendix D

Measurements of HF Timing Signals 33

Appendix E

Standard Frequency and Time Stations 43
IllTable of Contents (Con't)

Fig.

XV, ILLUSTRATIONS AND FIGURES

Great Circle Distance vs Propagation Time 1

Plot of Table I in Appendix B 2

Plot of Table III in Appendix B 3

Illustration of Delay Times; WWV and WWVH 4

Plot of h' vs At/n for Five Distances 5

Sky Wave Propagation Time 6

Great Circle Distance Calculations 7

Geometry of Three-Hop Mode 8

Geometry of n-Hop Mode 9

At vs d for h« = 150 km 10

g

At vs d for h» = 200 km 11

g

At vs d for h' = 250 km 12

g

At vs d for h' = 300 km 13

g

At vs d for h' = 350 km 14

g

At vs d for h' = 400 km 15

g

Calculated Propagation Delay Time, WWV to WWVH l6

Calculated Propagation Delay Time, WWV to Bo\ilder 17

Calculated Propagation Delay Time, WWVH to Boulder 18

Second-to-Second Measurement of Delay Time, WWV 19

to WWVH

Second-to-Second Measurement of Delay Time, WWV 20

to WWVH

Measured Delayed Time on the Path WWV to WWVH 21

-IVPRECISE TIME SYNCHRONIZATION

OF WIDELY SEPARATED CLOCKS

SUMMARY

In many fields of science, such as in astronautics, missiles,

astronomy, etc. , which are being intensely investigated, the needs for

new orders of magnitude of tinning precisions have grown. For instances

the need has been greatly increased for nnore precise determination of

the time of initiation and termination of certain events, which may

occur several hundred miles apart. Or, in the location of bodies in

space flight, the precise determiination of their transit time at known

sites is of major importance.

This paper describes known precise methods of setting a group of widely separated clocks to precisely the same time and keeping

them in close agreennent indefinitely; most of the proposed methods

are now available. An estimate of the accuracies of each method are

given. Also, there is some discussion of high frequency radio propagation theory pertinent to two of the methods and a few sets of measurements of the propagation delay tinne of high frequency signals from

WWV to WWVH are given. Several graphs and tables are included to

simplify some of the calculations.

-1~

Precise Time Synchronization

Of Widely Separated Clocks

Alvin H. Morgan

L INTRODUCTION

The need for higher precision of synchronization of highly accurate clocks, which are widely spaced from each other, has increased

in many fields of science such as physics, astronomy, astronautics,

etc. Only a few years ago the highest precision required was of the

order of 10 milliseconds for most physical experiments. Today, the

need for a precision of better than 100 microseconds is fairly common,

and in a few instances a precision of 1 to 10 microseconds has been

required.

At the present time quartz crystal clocks are the best working

time standards for purposes such as those mentioned above. Atomic

and molecular resonances are useful as frequency standards but not

directly as time standards because instruments utilizing them are not

able to run reliably for long periods of time. However, they are invaluable in maintaining the crystal clocks at a highly uniform rate and

thus in effect making "atomic-time" available.

The problem we are concerned with here is not how to obtain

uniform astronomical or atomic time, but how to precisely set widely

spaced clocks to the same time and keep them in very close agreement,

indefinitely. Of course, this requires very accurate and reliable clocks

and a method of setting and continuously checking them relative to each

other.
-2-

IL METHODS OF SYNCHRONIZING

WIDELY SEPARATED CLOCKS

There are several known methods whereby it is possible to adjust the time of several clocks to a certain degree of agreement even

when they are widely separated. However, most of these methods are

not able to render the required accuracy when it is necessary to set

the clocks to agree to better than one or two hundred microseconds.

One precise method is to transport a very accurate master

clock around to each of the slave clocks, and set each one to it, in

turn. The master clock would, of necessity, have to be controlled

during the experiment by some very stable oscillations in order to

achieve the required accuracy. A second method, which requires considerable apparatus, would be to transmit by radio a high resolution

timing signal from the master clock to each slave clock and they in

turn would immediately retransmit the timing signal back to the master

clock. This would enable one to determine very accurately the signal

propagation time and the great circle distance to each clock, without

prior knowledge of the path lengths. A third method, which is less

precise but which involves considerably less apparatus than either of

the first two methods, is to transmit high resolution. timing signals

from the master to each slave clock. It requires knowledge of their

exact longitude and latitude and that of the master clock, and the calculation of the great circle distance to each from the master clock. Using

this information calculations are made of the delay time of the signal

from the master to each slave clock, which is used to determine their

corrections. This system may employ either gro\ind wave or sky wave

signals. Each is considered separately.
-3-

IIL TRANSPORTING A MASTER

TO EACH SLAVE CLOCK

a. General

This method of synchronizing widely separated clocks is limited

now to clocks at rest on or near the surface of the earth. However,

when space travel becomes a reality it may be possible to adapt it to

use in outer space. The method at present requires considerable apparatus and is cumbersome, time consuming, and expensive. However,

it appears to be the most accurate method of setting clocks, especially

when really portable long running atomic clocks become available.

An appreciable period of time generally will elapse between the

time the master clock is initially calibrated and the time it is used to

correct the time of each of the slave clocks. Unless the master clock

keeps time over long intervals to a precision better than that desired

in the synchronization of the slave clocks, some corrections must be

applied to it at the time of the setting of each clock. In order to do

this, the initial rate of the master clock must be known to a high precision and it must be constant or predictable during the whole measuring

interval, i. e. , from the setting of the first to the last slave clock.

b. Clock Errors

The error observed in the master clock in |jisec, at the end of a time interval P, in days, in terms of quantities observed at a previous

time T , is approximated by: o E=(e+Ae]+P(r+oc— '^ + AP (1)

where: e = error in clock at t = T , fJLSec, fast or slow

r = rate of clock at t = T , u-sec/day. o o '
-4-

oc = accel. of clock, |i.sec/day/day.

Ae = error made by observer in reading clock, jxsec.

AP = error made in determining P, fxsec.

Unless P is a very long interval of time, oc may be considered to be

zero in really high precision clocks, such as present-day quartz crystal

clocks. In case an atomically controlled clock were used as the master

clock, both the r and oc terms would (so far as is known now) be equal

o

to zero, regardless of the length of the time interval.

For quartz clocks, in present day high precision units, the r o

- 10 term is of the order of 10 per day (or less) which, in time increments, is around ± 10 jisec/day. Some special crystal units have been

developed which have a relative rate, r , of 1 usee /day, or less. When

o a high quality master clock is used, in many timing applications a

period of from 10 to 30 hours may elapse between the setting of the

first and the last slave clocks without the necessity of making any time

corrections to the master clock.

c. Time Kept by a Clock

The time shown by a clock, at a time (T), may be expressed in

terms of its rate r at T , acceleration oc, change in acceleration p, o o elapsed time P, and the clock reading A at a time T , as: o o

2 3

T = A + P + r P + -^^^-f -^^ (2) o o 2 6

In high precision quartz crystal clocks, r is generally positive

o because of the aging characteristics of quartz crystals, although it may

sometimes be negative; a: may be either positive or negative; and, p, which is usually negative, may be neglected in all but very, very long

time intervals, such as years.
-5-

IV. TWO-WAY TRANSMISSION OF TIME SIGNALS

a. HF Timing Signals

This method of synchronization has two attractive features inherent in it that may, in some instances, outweigh its disadvantages.

First, because time signals are transmitted both ways over the given

path, the one-way propagation time may be quite accurately determined

without prior knowledge of the precise length of the path. Second, from

this measured propagation time, it is then possible to calculate the

great circle distance with quite high accuracy.

In Appendix C, it is shown that the propagation time, t , from

P

the master clock to a given slave clock, is given, in terms of two

measurements At and 6t, thus:

At - 5t

(3)

where: 5t is the delay time a time pulse undergoes from its reception at

the slave clock until its retransmission, and At is the delay time,

measured at the master clock, between a transmitted pulse and its

return to the master clock. From this, the path length is, obviously:

d = t c P P

(4)

where: d is the apparent path length, at the time of the measurement,

P

from the master to the slave clock, and c is the velocity of light. Also,

it may be easily shown, Equation (13), Appendix B, that the great circle

distance, d , for an n-hop mode, is given in terms of d , as:

g P

d

sin (9/2)

e/2 V(l + T)(^

T

2 sin 0/2

(5)
-6-

where: the s-^nnbols are as defined in Appendix B. Obviously, it is not

precisely known a priori what the mode of propagation will be at the

time of a given measurement. For a given great circle distance and a given ionospheric layer height there is, in general, a definite minimum

number of hops possible and a practical maximum number that would

furnish a usable signal. In practice, the most consistently received

pulse with the least delay time, as observed on an oscilloscope or similar timing device, would be the mode to use in the measurements

indicated above. A brief discussion of ionospheric propagation is given

below.
-7"

V. ONE-WAY TRANSMISSION OF TIME SIGNALS

a. Groxmd V/ave Timing Signals

There are at present some LF radio navigation systems which

use sharp pulses and, therefore, have very good time resolution. These

systems transmit ground wave as well as sky wave propagated signals,

but they can be used to obtain very stable timing signals. By gating to

accept the ground wave part of the signal at the receiving end, it is

possible to synchronize clocks to a high precision, even when they are

separated by distances of several hundred miles.

Figure 1, Section XV, may be used to determine the ground

wave propagation delay time. Of course, it is necessary to know, quite

precisely, the distances from the master to each slave clock. This

may be obtained as shown in Appendix A.

Usually, only one-way propagation of the ground wave signals

would be necessary because their path length is very nearly constant.

However, if higher accuracies are desired, two-way propagation of the

signals woixld be necessary.

b. Ground Wave Propagation Delay

Although it is relatively easy to calculate the ground wave propagation delay time for a given great circle distance, a chart is included

(Fig. 1) to simplify this work.

The distance is given, for convenience, in paralleled scales in

miles and kilometers versus propagation delay tiine.

c. HF Propagation

This method of synchronizing widely separated clocks requires

a precise knowledge of the signal path lengths between the master and

each slave clock, which may be calculated from other known data. The

longitude and latitude at the master and each slave clock must be accurately known along with the average ionospheric layer height at the
-8-

time of day at which the calculation is to be made. In addition, the

mode of the signal being propagated between the master and each slave

clock is required.

This method first requires a calculation of the great circle

distance between the two points on the earth for which the signal propagation time is desired. Although the calculations are, in principle,

rather simple they are quite lengthy, and are best explained by means

of an example. This is done in Appendix A. After the great circle

distance, d , between the master and each slave clock is calculated,

g

the propagation time for a ground wave signal may then be easily

determined from Figure 1 or by the well-known relationship:

t = d / c g g/

(6)

where: d is the great circle distance and c is the velocity of the

g

ground wave and may be taken equal to that of light. The next step is

to calculate the difference in propagation times between a given mode

sky wave signal and a ground wave signal over the path in question. In

Appendix B, this is shown to be given by the expression:

At = t - t P g

^ , sin e/2 \ / (1-1-7) +

2 sin e/2 (7)

where: 9 = ~ and 7 = h'/r. This may be further simplified (e. g. , Appendix B) to:

At = t ( y

g

N/h + P
-9-

^here:

y =

(^ fin_|^

^,

h = ( 1 + T) and

p =

(J

^TlJlTTz )'

Either equation (7) or (8) would normally be evaluated for the given path

in terms of various ionospheric layer heights, h*, and angles (0/Z), and

the mode of the signal, n. This involves considerable calculations for

even one path.

To reduce this labor, a set of curves, Figures 10 through 15,

are included in Section XV, from which values of At may be taken

directly. Each chart has a given fixed layer height, h*, and the curves

are in terms of the great circle distances, d , the modes of propagation,

from n= 1 to n = 4, and the differential propagation time, At.

After the differential time, At, is determined from the charts

in Figs. 10-15, for a given path and mode, it is added to the ground

wave propagation time, t , to obtain the total propagation time, t , for

the path.

VI. ACCURACY OF METHODS GIVEN

a. Transporting a Master Clock

The limits of the accuracy of this method lie in two factors:

(a) long term stability or constancy of the master clock, and (b) reso1 2

lution of the system ' used to compare the master and slave clocks.

If the master clock is controlled by atomic or molecular resonances,

the error due to the long term clock stability is negligible. In case the

master clock is controlled by a quartz oscillator of high quality, the

error would be quite small: from 10 to 100 |jLsec/day is easily attainable.

The resolution of the time comparison system can be made very

good: from 0. 001 |j.sec to 0. 01 jxsec is not too difficult to achieve with

good signal-to-noise ratio.

Thus, the overall accuracy of this method would be from 0. 001

[jLsec to 0. 1 |JLsec, depending on the clocks and the time comparison
-10^

system used. With care and very high quality apparatus and rapid

transportation of the master or reference clock, it is conceivable that

the accuracy could be extended one to two orders better.

b. Transrr\ission of Time Signals (one- and two-way)

(1) General

The systems of synchronizing clocks by either one- or two-way

transmission of timing signals is not as accurate as the one described

above, but they are obviously more convenient, especially when the

clocks are many thousands of miles apart. Because of the different

nature of the problems, the hf and the ground wave timing signals will

be considered separately.

(2) HF Timing Signals

(a) One Way Transmissions

Results of measurements, described in Appendix D, indicate that the stability of the HF delay time is dependent on several

factors. Among these the following are susceptible to control by the

observer: (a) time of day that the measurements are made, (b) method

of observing the received timing signals, i. e. , whether a zero crossing

or a peak of the signal is used, (c) the extent to which the antenna

pattern favors the optimum mode of propagation, (d) whether or not

the propagation mode with the least delay time is used, (e) whether or

not the measurements are related to a precise slave clock at the receiving site so that advantage may be taken of the average (over several

days), (f) the actual frequency used, i. e. , in general, the higher the

frequency (but still below the MUF) the more stable the delay time, and

(g) accuracy of knowledge of path lengths involved.

Other factors which may affect the stability of the relative delay

times of the signals are: (h) epoch of the sunspot cycle; (i) whether or not the radio path passes near or through one of the auroral zones,

(j) whether or not the path is all in darkness or all in daylight at the
11-

tirne of the measurement, (k) signal-to-noise ratio at the receiving

pile, and (I) mirnbcr of hops involved in the propagation of the signal.

Ideally, th.e following should prevail:

F.vctor Ideal Condition

(a) time of da.y for observation

(b) part of signal to nneasure

(c) directivity of antenna

(d) propagation mode to use

(e) measurements

(f) choice of frequency

near noon or midnight at the center

of the path..

zero crossing time of the least delayed pulses.

favorable to mode with the least

delay time.

the one with least, consistent delay

time.

be relative to a very precise slave

clock at the receiving site.

highest available at which a consistent signal can be obtained at the

time of the measurements (see item

(a) above).

as accurate as possible.

near minimum.

well away from both auroral zones.

short enough to be at least 2 hours

all in daylight or all in darkness.

as high as possible.

equal to next integer greater than

the quotient of the length of the

great circle path expressed in km.

divided by 4000,

The accuracy of the synchronization of the slave clock using

this method obviously then depends on how near to ideal conditions the

actual conditions are. Under conditions approaching the ideal, the

accuracy may be better than ±0.1 millisecond, even for very long paths;

however, it will usually be less than this by a factor of from 2 to 5, or

more.

(g) accuracy of knowledge of

path lengths

(h) epoch of sunspot cycle

(i) location of radio path

(j) length of longest ideal path

(k) signal-to-noise

(1) number of hops of path
-12-

At the other extreme, for example if the path passed near or

through an auroral zone, or was so long that it was never in all darkness or all daylight, etc, , the accuracy might be only about ± 10 milliseconds, or worse.

More definite statements of accuracy are not possible at this

time, but it is hoped that further measurements in the future will make

this possible.

Further data on this may be obtained by reference to Appendix D.

(b) Two-Way Transmissions

If a transponder, or similar device, is used at the slave

clock, it is possible to:

1) determine the apparent length of the path, the

long term average of which may be quite precise.

2) increase the knowledge of the accuracy of each

measurement over that obtained with one-way transmissions.

The method of calculating the path delay time from the measurement data is given in Fig. 4. From this, and other considerations, it is

quite apparent that the actual conditions of the measurements will not

need to be as near the ideal, as in one-way transmissions, to produce

quite good results. This is also apparent from the data given in Appendix D.

Using this method, and under quite favorable conditions, as defined in paragraph (a) above, an accuracy of time synchronization of

slave clocks, at distances approaching half-way around the world, might

be about 10 microseconds; how^ever, a more conservative estimate

would be from 0, i to 1 millisecond,

(3) Ground- Wave Timing Signals

(a) One- Way

Because the delay times of ground wave signals are relatively constant, it is possible to achieve, with them, a high accuracy in
-13-

synchronization of widely separated clocks. Within the distance range

wherein the signal-to-noise ratio is sufficiently good, an accuracy of

from 0,01 to 0. I fjtsec is possible. This requires a narrow-band receiver, gating circuits to accept the ground wave component of the

timing pulses, and associated circuitry to permit pulse-locking of a highly precise local oscillator, which drives the clock to be synchronized. It is assumed, of course, that the tiraing pulses are siifficiently

sharp to meet the accuracy quoted.

(b) Two- Way

One distinct advantage of using a transponder, or similar

device, with ground wave timing signals is that it is possible to determine the great circle path length between the master and slave clock to

better than 10 feet up to distances of several thousand miles by using

the results of the raeasurements. This fact may be of considerable

importance in geodetic or similar work and in missile tracking systems.

Of course the above implies: (1) a method of signal gating so as

to receive only the ground-wave component of the timing pulses; (2) precise measurements of the signal delay in the transponder; and (3) use of

timing signals with very fast rise-time to permit (1) above.

The accuracy of this method of time synchronization of the slave

clocks using the latest techniques, appears to be limited only by the

signal-to-noise ratio in the receiving systems.

VII, MODES OF PROPAGATION OF HF SIGNALS

a. Introduction

High frequency signals are propagated between two points on

the earth's surface by means of one or more reflections from one of

the ionospheric layers and the surface of the earth. One reflection

from the ionosphere is called a one-hop mode, two reflections, with a

single reflection from the earth's surface, is called a two-hop modCj

and so forth.
-14-

Only two of the reflecting layers will be considered here, the

F-2 and E-layers, because other layers (F- 1 and Es) may usually be

neglected in considering the propagation of hf timing signals over long

periods of time. Signals reflected by the F~2 or E-layer are called F-2

and E-layer modes, respectively,

b. Maxinaum Usable Frequencies (MUF)

In the hf range, where signals are propagated by ionospheric

reflection, there is an upper limit of frequency which may be transmitted over a path of a given length. At frequencies above this limit,

which is called the "maximum usable frequency" (MUF), the wave is

said to "skip," or pass over the receiving end of the path.

c. One-Hop Modes

Over relatively short distances, sky wave signals are propagated

by means of a single reflection fronn an ionosphere layer; either F-2

or E-layer. Remembering that both the earth's surface and the ionosphere are curved, it is quite clear that there will be a limiting distance for a one-hop mode. For frequencies equal to, or lower than,

the MUF (explained above) for the path, the limiting distance may range

from 3500 to 5000 km (2200 to 3000 mi. ) for the F-2 layer mode, depending on the reflecting layer height, and is an approximately constant

distance of about 2400 km (1500 rai. ) for the E-layer mode. However,

it has been found in practice that the average liraiting distance for the

F-2 layer mode is about 4000 km (2500 mi. ), which will be the value

used here.

Thus, for distances less than 4000 km (2500 mi. ) but greater

than 2400 km (1500 mi. ), the F-2 layer single-hop mode would be predominant. For shorter distances, either the E- or F-2 layer mode

could exist, if the frequency used were equal to, or below, the MUF

for that layer.
-15-

d, Multihop Modes

For great circle paths longer than about 4000 km, it is obvious

that more than one reflection from the ionospheric layer usually must

occur. The minimum number of hops is approximately the next integer

greater than the quotient of the total great circle distance expressed in

kilometers divided by 4000. This mode will be observed during the

time the signal frequency is below the MUF for the path.

As an example, assume the path length is 9, 000 km (6800 mi. ),

It is quite obvious that two hops of maximum limit (4000 km each), laid

end-to-end, would not cover this distance. Therefore, the simple geometric picture of the minimum mode of propagation would be threehops, each of 3000 km length, laid end-to- end.

e. Control Points (see Fig. 9)

Over very long paths, the MUF for the signal may be estimated

by considering the condition of the reflecting layer at only two reflecting

or control points, i. e. , one a distance "d" from the transmitter, call

it point "a", and the other a distance "d" from the receiver, which will

be called point "k". The distance "d" is one-half the limiting distance

for a one-hop mode (i. e. , one-half of 4000 km), or 2000 km (1250 mi. ) for F-2 propagation. The MUF for the path is taken to be the lower of

the 4000-km MUF's for the points "a" and "k".

Unfortunately, the MUF for a given path of any length, varies

from hour-to-hour, day-to-day and year-to-year. Diurnal variations

in the reflecting layers ar e a consequence of the rotation of the earth,

and seasonal variations are associated with the movement of the earth

in its orbit around the sun. In addition, there are longer period variations that have been correlated quite well with the sunspot cycle.

Further information on the above may be found in standard

treatises in the subject, such as Reference 5, Section XIII.
-16-

VIII, VARIATIONS IN PROPAGATION DELAY OF HF SIGNALS

a. Introduction

The propagation delay time of hf timing signals over a given

path are not constant from hour-to-hour or day-to-day, but undergo

soiTie variations « In many tuning problems, such as the ones under

discussion, it is necessary either to measure the variations or determine the maximum variations that are likely to occur at the given time

over the given path,

b. Factors Affecting the Propagation Delay

This subject can only be very sketchily treated here becaxise of

its relatively complex nature. Among the many factors affecting the

velocity of propagation of an hf signal, only one will be discussed here.

This is the variation in the virtvial height of the F-2 ionospheric layer.

Besides its quite regular diurnal and seasonal variations, the F-Z layer

also undergoes severe changes during magnetic or ionospheric disturbances. The ion density of the F~2 layer usually decreases and then

slowly returns to normal over a period of 1 to 3 days. The virtual

height (h'F ) suffers rapid changes during such periods, sometimes by

a factor of nearly two.

This, of course, will introduce unknown but relatively large

variations in the propagation time of the signals and thus seriously

affect high precision work. Data taken during such periods are, obviously, useless in the precision timing problems under consideration

here, and should be discarded; only data taken during normal conditions

should be used.

c. Estimation of Effect of Normal Variations of Virtual Height

The effect of diurnal changes in the virtual height of the F-2

layer may be minimized by: (a) measuring the timing signals at the

same time every day, and (b) selecting this time of day so that the

whole path, from the master clock to the slave clock, is all in daylight
-17-

or all in darkness. In other words, neither the sunrise nor sunset

period should occur anywhere over the path during the time the rneasurements are being made. On fairly short paths, for instance, the measuring period should be selected when it is approximately noon at the

center of the path.

There remains, however, some small and irregular changes in

the F-2 layer height which are unpredictable. To obtain an accurate

value for these changes would require some detailed measurements of

the ionospheric height versus time at the reflecting points of the given

path. This is obviously not a practical undertaking for those engaged

in timing problems.

Alternatively, a knowledge of the effect of changes of the F-2

virtual height on the propagation delay time, for a given path, might be

useful. To make this information available in an easily usable form,

Fig. 5 was devised. This is a plot of virtxial height, h', (in km) versus

(At/n) ([xsec), (where n is the number of hops in the path in question),

along with a third parameter which is the great circle path length, d

g

divided by n. To simplify its use, only five discrete path lengths are

plotted; 500, 1000, 1500, 2000 and 3000 km; the latter curve being

suitable also for the 4000 km path.

To use the chart, determine the desired stability, 6t, in propagation delay time (At) and the nominal virtual height (h* ) for the path.

For example, say h' is 300 km, the desired propagation delay time

stability (At/n) is 10 [isec. , the great circle path length (d /n) is 3000

km and n = 1 (one-hop mode) (see Fig. 5). Then from the curve, the

variations in virtual height, 6h', must be less than 5 km.
-18-

IX. CHART FOR DETERMINING TOTAL

KF PROPAGATION DELAY

a. Introduction

In many timing problems, the use of the detailed curves given

in Fig, 10 through Fig„ 15 along with the chart in Fig. 1 is not necessary,

if a lower precision than given in these charts is acceptable. In this

case, the chart given in Fig. 6 may be used.

b. Use of Chart

This chart gives the total propagation delay time, per hop, for a given path. That is, the delay time in Fig. 6 includes the ground wave

delay time in Fig, 1 plus the additional delay time in Figs. 10-15 caused

by one reflection of the signal from the ionospheric layer.

It is assuined, in preparing the chart, that the total propagation

time was that of one hop mtaltiplied by the number of hops. Thus, the

distance is given as (d^/n), where n is the number of hops, and the

path delay time as (t /n).

For example, if the great circle distance, d , is 9, 900 km,

then assuming a three-hop path, (d /n) would be 3300 km, and the path

delay timie, as read on the chart, assuming a layer height of 350 km,

would be (t /n) = 1 1. 5 ms, which when multiplied by n = 3, is 34. 5 ms.

X. ASTRONOMICAL AND "ATOMIC" TIME

a. Introduction

Until very recently the only unit of time available was that derived from the movements of the earth and it was called solar time.

This is the time obtained by an observer on a given meridian marking

the passages of the sun. Because of variations in the length of a "solar

day" throughout the year, the mean solar day was used as the time

standard; it is the mean of all the solar days throughout a given solar

year.
-19-

In 1955 a inore uniform astronomical time was adopted as the

international time standard and is called Ephemeris Time. It is defined

by the orbital motion of the earth about the sun but in practice it is

determined from the orbital motion of the moon about the earth.

The latest Tiniform time, as yet officially undefined, is based on

the motions of the atoms or molecules subject to electrical and nuclear

forces. Several standards are now in use employing either the cesium

atom or the ammonia molecule.

Definitions of a few quantities of interest to those using time

signals or engaged in timing problems are given below.

8

b. Mean Solar Time

(1) Mean Solar Second

The unit of mean solar time is the mean solar second and it is

defined as the (1/86, 400) part of a mean solar day.

(2) Mean Solar Day

A mean solar day is defined as the mean of all the solar days in a solar year; there are 365 solar days in one solar year.

(3) Uniform Solar Time UT

(a) UT-0

This was the same as mean solar time; it was uncorrected

for perturbations that are known to occur from year to year.

(b) UT-1

Is mean solar time corrected for polar variations.

(c) UT-2

Is mean solar time corrected for polar variations and

estimated annual fluctuations.

Q c. Ephemeris Time

The Ephemeris Second is defined as the fraction 1/31, 556, 925. 9747

of the tropical year for I9OO January at 1200 hours Ephemeris Time.
-20-

o d. Atomic Time

The atomic second is at present not defined. However, if one

maintains a frequency standard whose frequency is derived from the

atom, then a properly geared clock driven by some submultiple of this

frequency would keep "atomic time", its main merit being its uniformity,

e. Standard HF Time Signals

There are at present many nations broadcasting hf standard time

signals, including the two USA stations (WWV, Washington, D. C. , and

WWVH, Maui, Hawaii), JJY (Tokyo, Japan), and MSF (Rugby, England).

All known stations, as listed by the CCIR are given in Appendix E.

XI. USE OF TIME SIGNALS FROM

MORE THAN ONE STATION

If all the world's hf standard timie signals, as broadcast, were

precisely synchronized, it would be possible to use any one of them in

any timing problems and then when necessary switch to another one

without loss of timing accuracy. Unfortunately, this is not the case at

6

present. Except for WWV and WWVH, none of the transmitted standard

hf time signals are synchronized.

This should be taken into account, for instance, when a missile

tracking and timing problem arises wherein, say, the tiine signals from

WWVH are used initially and then later a switch is made to the JJY

standard time signals. Errors up to several milliseconds may occur,

in this case, if suitable corrections are not made.

XII. ACKNOWLEDGMENTS

The data used in plotting the curves in Fig. 10 to Fig, 15, inclusive, was obtained from Mr, A. G. Jean, v/ho kindly consented to their

use in this paper. Also, many helpful discussions were held with

Mr. T.N. Gautier.
-21-

XIII. REFERENCES AND BIBLIOGRAPHY

1. "Comparing outputs from precision time standards," J. M. Shaull

and C- M. Kortman, Electronics, p. 102 (April 1951).

2. "Measurement of tinne interval," chap, "VI, Handbook of Electronic

Measurements Vol. II, Polytechnical Inst, of Brooklyn, edited by

Moe Wind (40 references given at end of chapter).

3. Measurements were made by Mr, H. F. Hastings, of the U. S.

Naval Research Laboratory.

4. "Reference data for radio engineers," International Telephone and

Telegraph Corp. , pp. 732-735.

5. "Ionospheric radio propagation," Circular 462, NBS.

6. "Standard frequencies and time signals WWV and WWVH, " Letter

Circular LC 1023, June 1956.

7. "Ionospheric data, part A," CRPL F-Series, CRPL, National

Bureau of Standards, Boulder Laboratories.

8. "Astronomical and atomic times, " Wm. Markowitz, U. S. Naval

Observatory, Washington 25, D. C. (March 1959).

-22-

XIV. APPENDICES

APPENDIX A

GREAT CIRCLE DISTANCE CALCULATIONS
-23-

XIV. APPENDICES

APPENDIX A

GREAT CIRCLE DISTANCE CALCULATIONS

1, Data Given (see Fig. 7)

Site

B

A

Latitude

,o 38 59' 33. 16" N.

34"" 56' 43. 19" N,

4

2. Great Circle Distance (Z) Calculations

Longitude

76" 50' 52. 35" W.

117° 55» 01. 57" W.

a. Equations Used

tan f ^ " ^

] = cot (c/2)

• / L„ - L,

sin B A

cos f B A

(1)

tan y + X

= cot (c/2)

cos ( ^B

- "^)

2 y

sin ( ^B + "0 7 y

(2)

tan = tan

L„ - L, B A

sin y + X

2

sin X

- X

(3)

Angle C - longitude A - longitude B (4)
I

-24^

b. Calculation of V :=i / ^"d

Si1;e.-s (-B-0 (':^) (s^-a) r^:^^)

B,A 4^ 02' 49, 97" 2° 01' 24, 98" 73° 56" 16. 35" 36° 58' 08. 17"

2° 01.416' 36° 58. 14'

c. Determining Angle (c) and (c/2) and cot (c/2)

Sites c c/2 cot c/2

B, A 41° 04' 09.22" 20° 32' 04, 61" 2.6698'

20° 32,077'

d„ Tabulation of Trigonometric Functions Needed

Angles cos sin tan

L - L

= 2° 01.416' 0.99931 0,03531 0.03531

L + L

36° 58. 14' 0.79896 0.60138

2

e. Calculation of (Z) in degrees

y' ' ^^ = tan" ^ (0. 11799) = 6° 43. 76' (6)

sin ( ^ " ^

) = sin 6° 43. 76' = 0. 1 17 18 (7)

-(H^)----(SII)— <B)
-25-

f l±Ji \ ^ tan" ^ (4. 4369) = 77° 17. 93« (9)

sin f ^-^ ^ = sin 7.7° 17. 93« = 0.9755 (10)

tan ff^ = 0. 03533 (2^9|55|Nj^„_2,4^ (II)

y j = tan'^ (0.29429) = 16° 23.6' (12)

Z° = 32° 47. 2» = 32.79° (13)

f. Converting (Z) to (Z) kilometers (or miles)

Z, = Z° X 111. 195 km/deg = 32. 79 X 111. 195 3 3642 km (14) km ________

Z . = 0. 6214 mi/km X km ^ 0. 6214 X 3642 = 2262 mi. (15) mi ==

g. Determining the Mode of Propagation

For a great circle distance of 3650 miles, the minimum mode

of propagation would be one -hop, i. e. , the distance is less than the maximan\ of 4000 kms for the one-hop mode.
"26-

APPENDIX B

HIGH FREQUENCY PROPAGATION DELAY TIMES
-27-

APPENDIX B

HIGH FREQUENCY PROPAGATION DELAY TIMES

1. Definitions (Figure 8)

(a) d* = ac = ce, great circle distance of one-hop path.

8

(b) d - nd' - aceg , . . , great circle distance of n-hop path.

(c) d* = abc = cde, sky wave distance of one-hop path,

P

(d) d = nd' = abcde, . . . , sky wave distance of n-hop path.

P P

2. Sky Wave Propagation Time (Based on Geometric Paths)

From Figure 8, it is easily shown that, for path abc,

d' = 2 J2r (r + h») (1 - cos 0) + (h')^ ( 1)

P

For simplification, let:

h'/r = 7, and 2 (1 - cos 0) = (2 sin 0/2)^ (2)

Then, using (2) in (1), and factoring:

% - 4>- "" («/2) -^'i + ^'+rmreTz

^

<^>

Then, the propagation delay time, for the path d' , is:

d

p c c V 2 sm 0/2 (4)

Now, the ground wave propagation delay time for the great circle

distance, d' = ac, is:

g

d'

g c
28-

Now, from trigonometry, we know that:

d' = 2re

g

(6)

so,

t' = 2re

g c

(7)

Then, using (7) in (4), we get:

t' = t' P g

sm 0/2

e/2 J (l(1 + T) +

2 sin 0/2 J] (8)

This is the sky wave propagation delay time in terms of the

great circle distance delay time. For more than one hop, say n-hops

both sides of equation (8) are multiplied by n.

3. Difference in Sky Wave and Ground Wave Propagation Times

From (8) and (2):

At = ( t - t P

= t g y g

sm 0/2

0/2 / <'"^'M zsiIe/2

^'

-1 (9)

If we let:

(1 + 7) = h,

2 sin 0/2

- , sin 0/2

= P. and f Q^^ ) = Y, (10)

we may write (9) as:

At=t (yN/h+p^ -1 (11)
-29-

4. Great Circle Distance Determined from Path Distance

Multiply equation (8) by n, and solve for tg:

t = g [

t (0/2)

P

'"' ^'^ ^<' + ^' + (^hre75y

from, which it is obvious that:

(12)

d = t c = g g (^^-^^J^^T^2 sin e/2

(13)

5. Tables for Use with Equations (9) and (11)

TABLE I (See Fig. 2)

—^ versus 9/2

n

n

km

444. 4

888. 9

1333. 3

1777. 8

2222. 2

2666. 7

3111. 5

3555. 5

4000.

(6/2) deg.

1

2

3

4

5

6

7

8

9

(6/2) rad.

0.01745

0.03491

0.05236

0.06981

0.08727

0. 10472

0. 12217

0. 13963

0, 15708
-30-

TABLE II

(y versus e/2)

(e/z)" (9/2) rad. sin e/2 X where:

1

3

0,01745

0.05236

0.01745

0.05234

1.0000

0.99962

sin e/2

y= e/2

6

9

0. 10472

0. 15708

0. 10453

0. 15643

0.99818

0.99586

^/^ = ^

TABLE III (See Fig. 3)

(h versus h')

where:

100 0.0157 1.0157 h = (1 + r)

150 0.0236 1.0236

200 0.0314 1.0314

250 0.0392 1.0392

h'

300 0.0471 1.0471

350 0.0550 1.0550

400 0.0628 1.0628 r :-- 6368 km

-31-

APPENDIX C

TWO-WAY TRANSMISSION OF TIME SIGNALS
-32-

APPENDIX C

TWO-WAY TRANSMISSION OF TIME SIGNALS

L Definition of Symbols Used (Fig. 9)

(a) d = great circle path, A bd . . . B.

g

(b) d = n-hop path, Aabcd . , . kB.

P

(c) 5t = delay time signal suffers, at clock B, from its

reception to its retransmission.

(d) At = time difference between a transmitted and received

pulse at A,

(e) t = timie first pulse leaves A,

o

(f) t = time first pulse arrives at B.

(g) t = time retransmitted pulse leaves B.

(h) t = time retransmitted pulse reaches A.

(i) t = apparent path length.

Now:

and:

so:

t, = t+f—ti] = t+t (1)

1 o y c y o p

t^ = t, + 6t = t + 2t -f 6t (2) 2 1 op

At = t, - t = t + 2t + 5t - t = 2t + 6t (3) 3 o o p op

Therefore:

At - 6t

and:

p y 2

i = ct

P P

(4)
-33-

APPENDIX D

MEASUREMENT OF HF TIMING SIGNALS
.34-

APPENDIX D

MEASUREMENT OF HF TIMING SIGNALS

1. A Note on the Measurements

(a) Acknowledgnnents

The measurements of the propagation delay time of the hf signals

from WWV to WWVH and return, and at Boulder, Colorado, were made

by personnel of the National Bureau of Standards Boulder Laboratories

at Maui, Hawaii, and Boulder, Colorado, of the Naval Research Labora3

tory, and of the U.S. Naval Observatory. In all cases, the measurement precision was at least 0. 1 millisecond for each individual observation.

(b) Definitions of Symbols Used in Appendix D

d = great circle path length,

t = propagation delay time of a signal over a given d . 6 6

r = mean radius of earth; taken as 6368 km,

c = velocity of light in free space; taken as 300, 000

km/sec.

d = length of path of sky wave (ionospherically reflected)

signal.

t = propagation delay time of a signal over a given d . p p

JT = standard deviation of a single observation,

h' = virtual height of the reflecting ionospheric layer,

n - number of hops (mode) of the signal propagated over

a given d . P

2» Measurement of Propagation Delay Times

(a) Data on Following Paths

d

g

(1) WWV to WW\''H 7687 km

(2) WWV to Boulder 2430 km

(3) WWVH to 5270 km

Boulder

tg

mine

n

d /r

g

25, 62 ms 2 1.205

8. 10 ms 1 0,382

17, 56 ms 2 0,825
-35-

(b) Calculated Propagation Delay Times (on above paths)

versus Number of Hops (n)

(1) Figure 16 - WWV to WWVH

(2) Figure 17 - WWV to Boulder

(3) Figure 18 - WWVH to Boulder

(c) Measurements Made on Above Paths (September 1955)

Signals

(1) WWV vs. WWVH

(2) WWVH vs. WWV

(3) WWV vs. WWVH

Meas. Freq. t,P

s

(T Made at Mc J m ms

Maui 5 27. 77 0. 26

10 27. 32 0. 24

15 27. 13 0.22

ave. 27. 40 0, 22

Wash. D. C. 5

10 27. 16 0. 19

15 ave. 27. 16 0. 19

Boulder 5 10. 95 0. 27

10 11. 31 0. 28

15 11. 67 0.37

ave. 11. 31 0.31

(4) Actual Propagation Delay Time, Based

on a and b, above (round trip)

Path

WWV to WWVH

(or vice versa)

(at 10 Mc)

10 27. 24 0. 20

15

27. 24 0. 20
-36-

(5) Calculations of Actual Propagation Delay TimeSj

Based on Above Measureme nts, at 10 Mc

Path Freq. , Mc

10

10

10

t , ms

P

WWV to Boulder

WWVH to Boulder

WWV to WWVH

8. 14

19. 10

27. 24

(6) Use of Charts in Figure 16, 17 and 18 (with h« = 350 km)

to De;te rmine Pr.opagation Delay of S:Lgnals on

Path

r

d

g

km

7687

2430

5270

tg

25. 62

8. 10

17.57

tP

ms n

WWV to WWVH

WWV to Boulder

WWVH to Boulde

27. 19

8.63

19.00

3

13

Meas.

t , ms

P

Calc.

t , ms

P

Difference

ms n

27.24

8. 14

19. 10

27. 19

8.63

19.00

0. 05

0.49

0. 10

3

13

(7) Summary of Above Data at 10 Mc

Path

WWV to WWVH

WWV to Boulder

WWVH to Boulder

Second-to-Second Measurements, at 10 Mc, of Actual Delay

Times of Path, WWV to WWVH (Based on Round Trip)

(1) Figure 20- WWV to WWVH, December 19, 1956

(2) Figure 19- WWV to WWVH, December 21, 1956

(3) Summary of Above
-37-

Max. dev.

Fig. Date

12-19

UT

Time

0200

No.

Observ.

6

Ave.

tp, ms

27. 50

from ave. , ms

Min.

t , ms

P

27. 10

(T

20 0. 1 0. 10

0500 30 27.70 0.3 27.45 0. 15

1100 92 27.40 0.5 27.00 0. 15

21 12-20 0200 26 27.50 0.4 27.20 0. 17

0500 18 27.30 0. 2 27. 10 0. 11

0800 33 27.25 0. 3 27.05 0. 10

Significant Values 27.41 0.5 27.00 0.17

(4) Conclusions Based on Above and Figure 16

Ave. of ., Min. ^ , ,, Ave. t-> i. i-t Max. , Probable , , Probable

ave. t , ms t , ms d , km , , , p

cr, ms p n p

n', km

27.41 0.17 27.00 3 8223 350

(e) Hourly Measurements, at 10 Mc, on Path WWY to

WWVH, June 1956

(1) Measurements, June 20

Meas. UT No. Ave. (T Signals made at Time Observ. Diff. , ms ms

r vs. WWVH Wash. 0600 16 29.01 0.43

D. C. 0900 9 28. 72 0. 24

1200 8 29. 15 0. 21

ru vs. wwv Maui 0600 8 26.43 0. 13

0900 10 27.08 0. 15

1200 _ — - -
-38-

(2) Average, Actual Propagation Delay Times {June 20)

Path

WWV to WWVH

Average Values

UT

Time

0600

0900

1200

Ave.

t , p

ms

27.

27.

,72

90

27.81

Ave.

(T, ms

0. 28

0. 22

0. 25

(3) Measurements, June 22

Signals

WWV vs. WWVH

WWVH vs. WWV

Meas. UT No. Ave. 0- made at Time Observ. Diff. , ms ms

Wash. 0600 11 27. 83 0. 25

D. C. 0900 20 28.09 0.32

1200 4 28. 68 0. 53

Maui 0600 10 26.94 0.21

0900 10 27. 12 0. 10

1200 9 27. 22 0. 10

Average Actual Propagation Delay Times (June 22)

Path

WWV to WWVH

Average Values

UT

Time

0600

0900

1200

Ave.

t , pms

27.,38

27.,60

27,,95

Ave.

0", ms

0. 23

0. 21

0. 31

27. 64 0. 25

(5) Summary of Above (Based on Round Trip Measurements)

Day

June 20

June 22

Path

WWV to WWVH

WWV to WWVH

(3 hour)

Ave. t , ms

P

27.81

27. 64

(3 hour)

(3 hour) ave. path

Ave. <r, ms length, km

0. 25

0. 25

8343

8292
-39-

(6) Conclusions from Above and Figure 16

Ave.

t , ms

P

27.75

Ave.

tr, ms

0. 25

Probable

n

Ave.

d , km

_P

8317

Approx.

h', km

350

(b) Daily Measured Values of Actual Delay Times on Path WWV

to WWVH, 1958

(1) Figure 21 - January 1958 to September 1958 (Based on

Round Trip)

(2) Summary of Figure 21 (WWV to WWVH)

^s

Month V.

Min.

t , ms

P

Ave.

t , ms

P

Max.

t , ms

P

No. da^

Obser

Ave.

d , km

P

Jan. 27. 20 27. 52 27.90 17 8256

Feb. 26.85 27.24 27.80 11 8172

Mar. 27. 10 27.46 27.85 18 8238

Apr. 27. 35 27.63 27.90 9 8289

May 27. 25 28. 12 28.85 12 8436

Jun. 27.45 27.85 28.75 9 8355

Jul. 27. 20 27.65 28. 10 14 8295

Aug. 27. 20 27.59 27.85 16 8277

Sep. 27. 30 27. 67 28. 10 11 8291

(3) Considerations from Above and Figure l£)

a) Estimated Values of n and h'

Month

Min.

t , ms

P

27. 20

Prob.

n

Approx

h', km

350

Ave.

t , ms

P

27.52

Prob.

n

Approx.

h', km

Jan. 3 4 325

Feb. 26.85 2 400 27. 24 3 355

Mar. 27. 10 3 335 27. 46 3 380

Apr. 27.35 3 365 27. 63 4 330

May 27. 25 3 355 28. 12 4 375

Jun. 27.45 3 380 27. 85 4 350

Jul. 27.20 3 350 27. 65 4 330

Aug. 27. 20 3 350 27. 59 4 330

Sep. 27. 30 3 360 27. 67 4 330
-40-

b) Summary of Data (Over a 9- Month Period)

Ave. Max, Min. », ^ ^ , » Ave. Max. Dev. Prob. Ave.

t , nis t , ms t , ms ^ « ^ . n ^ , km

p p p from Ave, , ms n n , km p

27.63 28.85 26.85 1.22 4 345 8289

c) Conclusions (10 Mc)

1) The actual delay time variations from dayto-day (data taken same time every day) were taken about the average,

about 1 millisecond or less.

2) In general, the mode of propagation was

4 hops.

3) Average virtual height of the layer was

near 350 km.

(g) Summary of Above (Items c through f)

Ave, Min. _ , Ave. . ^ , >, Prob. , - Ave. or Prob. Ave.

d , km , Item n p n', km o" t , ms

P

(c) 27.24

(d) 27.41

(e) 27.75

(f) 27.63

t , Pms

27. 00

26. 85

3 8172 350

3 8223 350 0. 17

4 8317 350 0.25

4 8289 345

Average 27.50 26.92 8250 350 0.21
-41-

APPENDIX E

STANDARD FREQUENCY AND TIME STATIONS
42

Xt-H PH

Ph< UWaw

PiP

Pi<P<mhO

COU(—

COn

PiHU<

<!Xu

CO 1 -D 4- = ^ Cl C3 U-> tr) 3 cn o c o ^ CD ir> f— CVI -r JC o 1 1- o

J3 CO **j- o =3 CD

O

O 0>-^ o CO c .— .^ CU CISC. -3 Li-» g I 9 CO CO r— -^ vr> C3 «h 03 X e w a**-- i -^i

CNJ CVI 'Z:: <=

O -l-J CD ^ CO o ^- £- to cr3 c=r- c <0 E

CO CO Ol UD CD ir> t- OO to o

CO r* o • U-) •*—

in 4i| o 1*1 4*1 >nC3 i_=. ~ CVI ,— ^ CO 1 i CO (VI

zz. UJ £ ^t *. -«• 3 CO «~— CNJ CO a> a> UJ -v— ,«t- Csi c=> ir> C3 c: c d^ 1 -f-* t- CSI • CS o o o o o* L. CO CVI e M— z: zz. ss O <D o -f <D o «>| 1 =D OD LO 3- 2; O UJ <o C3 1 -o

CNJ -•• x: jc: CJ> o «: zs ^^ .. », u. CO • rmtm CO •« o o 1 «- o «

CO o 03 • Cl. CJ en CO c=>u o 13. QCO

tU o •^ CD

m lO • ••C3 a>-»

O CD a> »--.•— CU cu

•4-' -D .-^

O -* CM esj

X

B CO -+-' o e « O

CO ,—

CO

a

—

~-CD 1 S- CO>> =c ~ ir> in *l ! CQ

«i> t^ C»>

,<—

CVJ Cs) sc UJ '^ ir> CVI ie> lo C3

tr> CO 1 -° -% CO

». «• >- CVJ oo CM CD -c: 3 at o c e

Csi

—

1 -• -«• o O 1 <- C3 CO ^ C ^T- CO —

CV) f CVJ •'"^ •»• CO CD 3 CD o O Ci. C3

>- nj r^ TO 1 <C3 ..«. o CSJ

C »»..- <uO r—

O

_ -*-< r- CM OO ^^-^

O

K

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DAILY SCHEDULES

1. Weekdays.

2. From 1 1. 00 to 12.00, from 14. 00 to 15.00, from 17. 00 to 18.00,

from 20. 00 to 21. 00, and from 23. 00 to 24. 00 U. T.

3. Pulses of 5 cycles of 1000 c/s tone; no 59th pulse of each minute.

4. Alternately 440 or 1000 c/s.

5. Interruptions from minute to rainute 4, and from minute 30 to

minute 34 of each hour, as well as from 19. 00 to 19. 34 U. T.

6. Pulses of 6 cycles of 1200 c/s tone; no 59th pulse of each minute.

7. Alternately 440 and 600 c/s.

8. Adjustments are made on Wednesdays at 19. 00 U. T. when necessary.

9. Maximum radiation N - S.

10. Interruption from 06. 30 to 07. 00 U. T.

11. Pulses of 10 cycles of 1000 c/s tone; the first pulse of each minute is prolonged (500 ms).

12. If required, the first Monday of each month.

13. Tuesdays,

14. From 01.00 to 04. 00 U. T.

15. From 07. 15 to 07.45 U. T.

16. Even days.

17. Odd days.

18. Signals Al keyed. Duration of each signal 100 ms; the first signal

of each minute is prolonged.

19. From 07. 15 to 07. 18, and from 07. 43 to 07. 45 U. T.

20. Interruption from minute 15 to minute 20 of each hour,

21. Pulses of 5 cycles of 1000 c/s tone; the first pulse of each minute

is prolonged (100 ms).

22. Relative to an atomic standard.

23. Adjustments are made the first day of the month, when necessary.
-44-

24. Two half -wave dipoles on 15 Mc/s; one half-dipole on 2. 5 and

5 Mr/s.

Z5. See (26) to (29).

26. From 07. 00 to 23. 00 U, T. ; interruption from minute 29 to minute

39 of each hour.

27. Mondays. Interruption from minute 9 to minute 19, from minute

29 to minute 39, and from minute 49 to minute 59 of each hour.

28. Wednesdays. Interruptions as for (27).

29. From 21. 00 to 11. 00 U. T. Interruptions as for (26).

30. Transmission suspended for 20 ms; the suppression before

second lasts 200 ms.

31. Maximum radiation NW-SE,

32. From 07, 00 to 07. 30 and from 11. 00 to 11. 30 U. T.

33. Pulses of 5 cycles of 1000 c/s tone; the first pulse of each minute

is repeated 7 times at intervals of 10 ms.

34. Interruptions from 11. 30 to 12- 30, and from 20. 30 to 21. 30 U. T.

35. Interruption from minute 45 to minute 49 of each hour.

36. Pulses of 5 cycles of 1000 c/s tone; no 59th pulse of each minute.

The first pulse of each minute is repeated 100 ms later.
XV. ILLUSTRATIONS AND FIGURES

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1.01 1.02 1.03 PLOT OF TABLE M

FIG. 3

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FIG. 4 ILLUSTRATION OF DELAY TIMES,

WWV AND WWVH

T = delay time of signal from WWV to WWVH

T = delay time of signal from WWVH to WWV

T = delay time introduced into pulses transmitted from WWVH H

T = delay time measured at WWV of received WWVH time

V

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FIG. 7 GREAT CIRCLE DISTANCE CALCULATIONS

FI6.8 GEOMETRY OF THREE -HOP MODE

k

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FIG. 9 GEOMETRY OF n-HOP MODE

APPENDIX IV CURVES OF FIXED h': WITH At (/iSEC) VERSUS DISTANCE d. (KM)

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2400

400

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9 10 tp , MILLISECONDS

FIG. 17 CALCULATED PROPAGATION DELAY TIME WWV TO BOULDER

5100 5400

dp , KILOMETERS 5700 6000

17 18 19 20

fp, MILLISECONDS

FIG. 18 CALCULATED PROPAGATION DELAY TIME WWVH TO BOULDER

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