the design of a celestial navigation microcomputer with

L POSTGRADUATE SOU

Monterey, California

TH oeoTHE DESIGN' OF A CELESTIAL NAVIGATION

MICROCOMPUTER WITH THOUGHTS ON AN INTEGRATED

INFORMATION DISTRIBUTION SYSTEM

Jon Prichet Moore

David Br andt Rainsberger

June 1975

Thesis Advisor: V. M. Powers

Approved for public release; distribution unlimited.

*nxssvf,

CALIFORNIA

NAVAL POSTGRADUATE SCHOOL

onterey, California

THESISTHE DESIGN OF A CELESTIAL NAVIGATION

MICROCOMPUTER WITH THOUGHTS ON AN INTEGRATED

INFORMATION DISTRIBUTION SYSTEM

Jon Prichet Moore

David Brandt Rainsberger

June 19 7 5

Thesis Advisor: V. M. Powers

Approved for public release; distribution unlimited.

UNCLASSIFIED

Jl-.CUHlTY CLASSIFICATION OF THIS P«&Ef»'»i.r f>>(. Ertfr* }

of this nature brings to light the need for an informationdistribution system. Thoughts on a system of this

purpose are presented.

DD Form 14 73, 1 Jan 7;^

S/N 0102-014-6601UNCLASS IFIED

SECURITY CLASSIFICATION OF THIS PACtC*^*" £>•'• Enffd)

The Design of a Celestial Navigation

Microcomputer with Thoughts on an Integrated

Information Distribution System

Jon Prichet MooreLieutenant, United States Navy

B.S., Oklahoma State University, 1968

David Brandt RainsbergerLieutenant, United States NavyB.S., Miami University, 1968

Submitted in partial fulfillment of therequirements for the degree of

MASTER OF SCIENCE IN COMPUTER SCIENCE

DUDLEY KNOX LIBRARYNAVAL POSTGRADUATE SCHOOL.MO^gEY^CAJJEORNIA 9394Q

ABSTRACT

This report lays the groundwork for further development

of a microcomputer that provides full celestial navigation

capability. The physical design specifications and design

philosophy are investigated. The fix algorithm which

allows determination of position without the use of H.O.

Publications is implemented in the BASIC language.

The application of microcomputer technology to devices

of this nature brings to light the need for an information

distribution system. Thoughts on a system of this purpose

are presented.

TABLE OF CONTENTS

I. INTRODUCTION - - - - 6

II. NEED FOR A CELESTIAL MICROCOMPUTER PERIPHERAL- - - 8

III. DESIGN PHILOSOPHY- - - - 11

A. OBJECTIVES ------ 11

B. PHYSICAL DESIGN SPECIFICS - 12

IV. THE CELESTIAL FIX ALGORITHM- 14

V. PROGRAM THEORY AND IMPLEMENTATION- -------- 22

A. THEORY -------- - 22

B. IMPLEMENTATION - - - - - - 31

VI. THE INFORMATION DISTRIBUTION SYSTEM- ------- 36

A. INFORMATION DISTRIBUTION ----------- 36

B. DESIGN PHILOSOPHY- ----- 38

VII. LANGUAGE SELECTION ---------------- 43

VIII. CONCLUSIONS ----- 48

APPENDIX A: CELESTIAL FIX PROGRAM LISTING- ------- 51

APPENDIX B: SAMPLE PROGRAM RUN - 70

BIBLIOGRAPHY- ---------------------- 72

INITIAL DISTRIBUTION LIST ---------------- 74

FORM DD 1473- ----------------------

LIST OF FIGURES

Figure Title Page

1 Celestial Navigation Microcomputer ------ 13

2 Geographic Position (GP) of a Star 15

3 Navigational Fix from Altitudes ofTwo Celestial Bodies ---- ___18

4 Triangles Used for Navigational Fix- ----- 19

5 Overall Celestial Situation with SixIntersection Points Depicted - ---21

6 Information Distribution System- -------41

I. INTRODUCTION

This paper deals with two interleaved subjects. The

two subjects will be discussed with varying levels of

detail and scope. The more specific subject of the two is

the conceptual design of a celestial navigation computer.

A general approach toward a digital information distribu-

tion system is the second subject. The celestial navigation

computer is discussed first, as it is an element of the

entire system, and the design specifics of this device

relate better to the entire system than vice versa.

The celestial navigation computer provides for manual

input of information as well as documentation of the out-

put for legal records. The main reason why a computer is

beneficial for celestial positioning is that it eliminates

errors made in recording, computing and plotting of celes-

tial information. The design efforts attempt to eliminate

manual recording of substantive information and manual

plotting of lines of position (LOP's) for use in determining

position. Automatic information recording is provided.

This paper provides an analysis of the programming

language, program I/O requirements and physiological require

ments of the device. The initial purpose of this paper was

to design the device, then to see how this philosophy and

design process could be applied to other building block

devices applicable to the information distribution system.

Comments to this point will be made in Section VI.

II. NEED FOR A CELESTIAL MICROCOMPUTER PERIPHERAL

It would seem that with all of the fancy new gadgetry

on the market today, the age-old method of navigating by

the stars might just start to fade away. It is conceivable

that this could happen in the civilian world; however, the

military is often more demanding in the constraints placed

upon its ships. The electronic devices which use electro-

magnetic radiation in the position determination loop are

subject to deception, jamming and detection (as in the

case of radar), and support failure, e.g., destruction of

navigational satellites or LORAN stations, etc. The only

other navigation device not subject to standoff disabling

is the ship's inertial navigation system. It must be

pointed out that an inertial navigation system is only as

good as its platform's stability and the stability only

as good as its positional estimates. Thus the longer the

platform goes without being updated, the worse the platform

stability becomes - -truly a spiraling decline in accuracy.

With all of the electronic fixing devices out of the

picture, visual sighting or sonar positioning is all that

is left. Visual sighting is passive and includes celestial

position determination, and this is the reason for main-

taining excellence in position determination by the stars.

The microcomputer is a newcomer to this field. This

technology properly applied allows for increased speed and

accuracy and the reduction of human errors. A need to

determine position faster simply goes along with the increase

in ship speed, e.g., new hydrofoil ships can conceivably

reach speeds in excess of 60 knots. The need for increased

accuracy is an economic as well as operational benefit.

Accurate positioning is needed for proper and efficient

deployment of weapons, efficient navigation and maneuvering.

The submarine force has implemented a celestial naviga-

tion system in the most complete terms. Completely computer

controlled, several "spot shots" are obtained in a moment

and the submarine's navigation systems can then be updated.

The Air Force has used the ASTRO-TRACKER to aid in celestial

navigation.

In January, 1975, Carl Nuese and Dr. Alan Schneider

provided the algorithms necessary to create a celestial

navigation calculator using the Hewlett Packard Model 65

programmable microcomputer [Ref . 8] . The peripheral device

under design in this paper was intended to hit the mark

somewhere between the HP-65 calculator and the submarine

celestial navigation computer- -much closer to the HP-65

side of the spectrum.

The HP-65 calculator solution to navigation problem

lacks the same sort of smoothness that placing a square

block into a round hole does; with a lot of effort it works

but it leaves a lot to be desired. The HP-65 general purpose

calculator uses programmable magnetic cards to hold prestored

programs that are executable on the machine. Though the

device is relatively inexpensive the following drawbacks

are noted:

1. Storage and maintenance of the program cards are

cumbersome

2. I/O is nonexistent.

3. Data format is not "conventional."

4. Record keeping must still be done manually.

5. The device is subject to pilferage.

6. Expansion of programs is difficult in its 100-

instruction memory.

The advantages are the following:

1. Self contained (excluding the magnetic cards).

2. Easier to operate than most terminals.

3. Inexpensive.

4. Good supporting vendor.

5. Applicable to many other mathematical problems.

III. DESIGN PHILOSOPHY

A. OBJECTIVES

The objectives of the design of the device are simple:

1. Implement Nuese and Schneider's algorithms in a

device that does not have the disadvantages of the HP-65.

2. Maintain the advantages of the HP-65 without appre-

ciably increasing the cost/performance factor.

3. Provide for integration into the overall information

distribution system.

4. Provide the fail safe/soft features and hardcopy

printout capabilities.

Two definitions will be stated at this time.

Microcomputer: A small general purpose computer. Itcontains a microprocessor and a small number of (sup-port) LSI circuits. Usually mounted on one or twoprinted circuit boards. May or may not be programmable.

Minicomputer: A computer with larger word sizes andfaster execution times than a microcomputer.

The proposal to specify a microcomputer for the celestial

computer was based on the further observations that the micro

computer can be exactly specified as to the I/O structure,

memory structure and contents, power supply designs, etc.,

whereas the minicomputer requires adjusting of all of the

above mentioned properties to "fit" the minicomputer. The

cost for a microcomputer is also much less than that of the

minicomputer

An eight-bit-wide microcomputer consisting of a micro-

processor, a 128 x 8 bit RAM, a 1024 x 8 ROM and peripheral

adapter cost around $473 in 1974, and by 1976 is estimated

to cost under $100 [Ref . 6] . Though larger than the HP-65

it is still less than ten times as large. An examination

of data equipment suppliers will show that a small mini-

computer will cost around $5,000 and higher.

The device must be self-contained (except for power)

easy to operate and relatively inexpensive. The I/O struc-

ture must allow for keyboard entry, and the formats for data

must be naturalized (36° 15' 33" vice 36.1533°) to the prob-

lem. Note that the algorithm expressed in Appendix A uses

the latter form due to limitations of the BASIC language

I/O structure. As the device would be a small production

lot, vendor support would be minimal or nonexistent; yet

the simplicity of the device should allow for easy onboard

maintenance

B. PHYSICAL DESIGN SPECIFICS

The device must be housed in one unit. The unit must

allow for connection to power and to the data distribution

system. The unit will have a simple ten-digit keyboard with

a N/E (north or east) and S/W (south or west) key. A 16

element five-by-seven dot LED must be placed above the key-

board for verification of entries as the line printer prints

a completed entry.

A 30 character wide line printer (for printing instruc-

tion, entries and calculation results) must be placed in

the unit. The unit is illustrated in Figure 1, and a

sample output strip is displayed in Appendix B.

Data Verification Readout (LED)

Program Selectors

Data Entry Keyboard

Figure 1-Celestial Navigation Microcomputer

IV. THE CELESTIAL FIX ALGORITHM

The purpose of the proposed navigational computer is

to enhance the speed, accuracy and ease with which calcula-

tions such as those used in celestial navigation can be made.

The program presented in Appendix A removes the need for the

user to depend on the Nautical Almanac [Ref. 13] and other

required H.O. publications by computing the values supplied

by these tables.

When taking a fix several phases of sight reduction are

considered: insertion of user values, correction of the

sextant altitude, establishment of the position of the

observed celestial body, solution of the navigational

triangle and displaying the results.

User values include Greenwich date, day, month and year,

the observer's assumed position, the name of the body ob-

served, the time (Greenwich Mean Time), the sextant altitude,

the observer's height of eye or dip and the sextant's index

of correction.

Correction of the sextant's altitude includes changes

in altitude due to refraction, semi-diameter of the sun and

moon and parallax for the moon.

Establishment of the position of the observed celestial

body on the earth (GP) involves the calculation of the

Greenwich Hour Angle (GHA) and declination (Dec) of the body

(see Figure 2) . Associated \\rith each star are eight

5" Star

Greenwich "'eridan

Etouator

Figure 2-Geographic Position (GP) ox* a Star

intermediate constants which are calculated and combined

with universal constants (rate of precession of the equinox,

rotation of the earth on its axis and aberration) to produce

the GHA and declination.

Constants which apply to all stars are the following:

1. Rate of rotation of the earth with respect to the

vernal equinox [Ref . 11]

2. The longitude rate of the sun based on the time

between successive crossings by the sun of the vernal

equinox [Ref. 10]

3. The obliquity for epoch 1975 [Ref. 10].

4. The annual precession rates for epoch 1975 in right

ascension and declination [Ref. 10]

With these common constants, particular intermediate

constants associated with each star are developed. Utiliz-

ing the apparent right ascension and declination as found

in Apparent P l aces of the Fundamental Stars [Ref. 14]

right ascension and declination can be computed to a

reference time through the effects of precession and

aberration. Other constants include the rate of increase

of the mean sun longitude in degrees per day, precession

in right ascension and declination in degrees per day, true

right ascension and declination in degrees, and the time

behavior of the corrections for aberration [Ref. 8]

When the intermediate constants are developed and

applied to the algorithms, the computed GHA and declination

of a star will result. Discussion of the computation of

the constants, GHA and declination is presented in the

next section. With the algorithm for computing GHA and

declination of a star implemented it now becomes a matter

of selecting those stars necessary to perform a sight

reduction yielding a navigational fix.

Considering a three-star fix, the GHA and declination

for each star is obtained as discussed above. Working with

pairs of stars the solution of the associated navigational

triangles will produce intersection points on the circles

of equal altitudes (see Figure 3)

Three triangles are used to calculate a possible position

as shown in Figure 4. The first triangle has vertices N

(north pole), A and B. The angle A is either G1-G2 or

360°- (G1-G2) . This angle represents the difference in the

GHA's. Given the angle A and cosides dl and d2 (the

declinations) , the law of cosines is applied to solve the

third side t. Given the three cosides the angle B opposite

coside dl is calculated. Given three cosides in the second

triangle, HI, H2 and t, the angle B3 opposite HI is found.

Letting m be the sign of the sin(Gl-G2) , the angles

B(l)=mB-B3 and B(2)=mB+B3 are found. Given angle B(l) and

cosides d2 and H2, the third coside L(l) is found. Given

the three cosides d2, H2 and L(l) the angle A(l) opposite

H2 is found. In the same manner L(2) and A(2) are found.

L(i) is equivalent to the latitude and A(i) is equivalent

to the longitude of an intersection of the circles of equal

altitude

Circles ofEqualAltitude

Figure 3-Navigational Fix from Altitudesof Two Celestial Bodies

N (north)

Star A ^~»(GP)

Figure 4-Triangles used for Navigational Fix

Repeating the algorithm considering the third celestial

body and one of the previously used bodies, a second pair

of positions will be found. A third repetition yields two

more positions totaling six (the maximum) possible positions,

as shown in Figure 5.

These six positions are then investigated to determine

the closest three by determining the shortest distance

connecting these three points. With this resulting triangle

the location of the two endpoints of a line which is one-

third away from any side of the triangle is computed. The

center of this line containing the two endpoints is the

center of mass of the triangle and therefore is considered

the celestial fix.

The program will provide for accuracy in mathematical

manipulation of numbers to one part in four billion using

the BASIC interpreter at the Naval Postgraduate School and

implementing the program on the INTEL 8080. This will pro-

vide for the accuracies of .1 or .2 miles as presented in

Ref. 8.

Star A o Star B

Figure ^-Overall Celestial Situationwith six intersection points depicted

V . PROGRAM THEORY AND IMPLEMENTATION

A. THEORY

When computing the constants needed for the program

a common reference time is necessary to provide for the

accuracy of results. If the data is referenced to the mean

equinox and equator of date, or to a fixed epoch then

no error is introduced. The reference time employed in

the algorithms is 0000 29 Nov 1971 as suggested by Ref. 8.

Any data known at some other time is retarded to this

reference time.

Note that the GHA of the star is related to the

Greenwich Hour Angle of Aries (GHA ) and the sidereal hour

angle of the star (SHA) , the latter being 360° minus the

right ascension a. Thus for any time t,

GHA = GHA + SHA (1)Y

GHA = GHA + (360 - a) (2)

GHA = GHA - a (3)Y

The GHA increases at a constant rate, namely, the rate

of rotation, a, of the earth with respect to the vernal

equinox. Knowing GHA at some time t, , then

GHA = a(t - t1

) + GHA±

- a(t) (4)

where t is the present time measured in days and decimal

parts of a day from the time t, , a time in the recent past.

Because it will later prove efficient to refer all events

to an earlier time (t = 0000 29 Nov 1971) this leads to

GHA = a(t - t ) - a(t - t^) + GHA - cx(t) (5)

= a(t - t ) + GHA - a(t) (6)s o yo

where GHA = GHA , - a(t, - t ) (7)yo yl 1 o J K J

The apparent right ascension a at time t is related to

its known true value a ! at some previous time t, through

the effect of precession and aberration.

Therefore (see "Supplement," [Ref. 11, pp. 39-49])

a(t) = a'ftj) + a(t - t^) + Aa(t) (8)

a'(t-,) = the true right ascension at time t,

a = precession in right ascension (degrees

per day)

Aa = correction in right ascension at time t

for aberration (as defined on p. 47,

"Supplement")

In order to refer all data to the common reference time

t , it is convenient to rewrite (8) as follows:

a(t) = a'(t1

) + a(t - tQ

) - a(t1

) + Aa(t) (9)

= ct'(to

) + a(t - tQ

) + Aa(t) (10)

cx'(t ) = a'(t1

) - a(tx

- tQ ) (11)

Inserting (10) into (6)

GHA = GHAyo

+ a(t - tQ

) - ct'(tQ

) - a(t - tQ

) - Aa(t) (12)

= [GHAyo

- a'(to)] + (a - a) (t - t

Q) - Aa(t) (13)

GHA = alg

(t - tQ

) - Aa(t) (14)

a nQ = GHA - a' (t ) (15)18 yo v o J v J

GHA ,- a(t, - t )yl 1 o

a'Ctj) + a(tx

- tQ ) (16)

= a - a (17)

Now Aa must be developed into a usable form. The equation

on pages 47 and 48 in "Supplement" [Ref. 8] shows that aber-

ration at time t is given by

= -k sec 6 ' [cos a' cos X cos e + sin a' sin A] (18)

where X is the longitude of the mean sun measured along the

ecliptic from y , e is the obliquity (angle between the mean

planes of the ecliptic and equator) , k is the constant of

aberration defined on page 48 in "Supplement," having a

value of 20.47", and a' and 6' are the true right ascension

and declination, all values being at time t. Selecting t-,

as a convenient time for determining the mean place of the

star and the obliquity, and regarding a', 6' and e as

constants over the interval from t, to t, equation (18)

becomes

Aa = - ( ?fiA n se c "5-J cos a

]cos e -i) cos X

- (-r^kn— se c <${ sin aj) sin X (19)

= a incos X + a,., sin X (20

"^fioo

cos a\

cos cl

an =" loW1 sec 6

isin a

The factor 3600 enters because Aa will be computed as

fractions of a degree whereas k was given in arc seconds.

Equation (20) can be rewritten as

Aa = a1 7

sin (A + a, .,) (23)

12 \l 10 "11

a i9= J am 2

+ a ni2

-1 ama13

= tan C^ ^ 25 )

The longitude of the mean sun increases linearly with

time according to the equation

X(t) = X(t - t1

) + X (26)

where X- is the known longitude at some convenient reference

time t-. . As has previously been done, it is best to refer

to a common reference time t by rewriting (26) as follows:

X(t) = X(t - tQ

) - X(t1

) + X1

= X(t - tQ

) + XQ

where X is defined as follows:o

X = X. - X(t, - t ) (29)o 1 v 1 J

Substituting (28) into (23) , the results are

Aa = a, sin [X(t - t ) + X + a n ,] (30)12 L v o o 13 J

sin [X(t - tQ

) + a14 ] (31)

where a, . is defined as follows :

a13 (32)

Using (31) in (14) the substitution yields

GHA = alg

(t - tQ ) - a

±2sin [X(-t

Q ) + a14 ] (33)

Because a, q includes earth rate, roughly 360° per day, and

that t - t may be on the order of 30,000 days, to preserve

accuracy in the computation it is worthwhile to separate

a-, q into two parts, one of which, a?

, , is 360° and the

other a ?7 , is the remainder. Let

+ a22 C34)

= 360 (35)

= a19 " 360, ^ 36 ^

In similar fashion, denote the number of days from the

reference t to the time t to be D.d where D is a wholeo

number of days since 0000 Nov 29, 1971, and d a fractional

part. That is

t - tQ

= D.d (37)

Then it is obvious that the product of the angular rate times

the time yields an angle modulo 360° which can be expressed

as follows

(t - tQ

) = (360 + a22

)(D + d) (38)

= 360D + a22

(D + d) + 360d (39)

(D + d) + 360d (40)

(D.d) + 360d (41)

Substituting this result and (37) into (33) yields

GHA = alg

(D.d) + 360d - a12

[X(D.d) + a14 ] (42)

The constants a and 6, precession in right ascension and

declination, for a particular star are obtained using the

formulas on page 39 in "Supplement," except that the values

of the constants have been taken for epoch 1975 from the

American Ephemeris and Nautical Almanac [Ref. 10]. Conver-

sion to degrees per day is

" =3600 x 36S. 24219418 [ 4 6.1060 20.0404 sin a' tan «•] (43)

3600 x 36 5.24219 418 [20.0404 cos «] (44)

This now completes the derivation for the Greenwich

Hour Angle of a star at time t.

Turning attention to the derivation of declination, it

is noted that the derivation is similar to those just

carried out. Declination of a star changes because of

precession and parallax. Letting <5 be the apparent

declination at time t, 6' be the true declination at some

specified time, 6 be the rate of precession of this star

in declination, A6 be the correction to declination for

aberration, the result is

6(t) 6'(t1

) + 5(t - tx

) + A6(t) (45)

where t-. is the reference time of which the true right

ascension and declination are known. The numerical value

of 6 is given in (44) . This form is converted to the

standard reference time t by the same method which haso

been used above. The result is

«(t) = <5'(t ) + <5(t - tQ

) * A6(t) (46)

<5'(t) = 6'(tx

) - 6(t1

- tQ ) (47)

From pages 47 and 48 in "Supplement" the time behavior of

the correction for aberration is

A6 = -k(sin e. cos 6' - cos e, sin a' sin <5,') cos A

-k cos a,' sin 6,' sin A (48)

= a n c cos A + a, , sin A (49)lb lo

a, j-=

vft'nQ (sin £,' cos 61 - cos a' sin al sin 61) (50)

20.47i ' • * i /r-na

3TDT"C0S a

l31n 6

The constants a..5

and a _, are in degrees. Simplifying further

A6 = a, 7 sin (A + tan"1 -^) (52)

17 al6

= yla16

Substituting (52) and (28) into (46),

6(t) - 6'(t ) + 6(D.d) + a1?

sin[X(t - tQ

) + a2Q ] (54)

a20 = X

o+ tan_1

^ft55 ^

t - t = D.d (56)o

The final equations of importance which lead to GHA and

declination are (42) and (54) . Note that eight star-

particular constants are involved in these two equations,

plus A, a constant which appears in all calculations of

GHA and declination of the stars.

The equations involving reference times have been set

up in such a way as to maximize freedom in their selection.

Reference time t was selected to be 0000 Nov 29, 1971, too

facilitate the calculation of time in days with a minimum

number of entries as suggested by Ref. 8.

The reference time t, is any convenient time, presumably

in the recent past, at which the GHA of Aries is precisely

given in some reference tabulation. The time t-. is referenced

to true right ascension and declination as listed in some

reference almanac. The true right ascension and declination

at cx'(t,) and 6 ' (t, ) can be obtained from the apparent

values a(t,) and 6(t,) by setting t = t.. in equations (8)

and (45) and solving for a' and 6'.

The reference time t, is also the time, again in the

recent past, at which obliquity e, , a' 6' and A, are

accurately known. The reference time for A, is such that

the accuracy of the sun's mean longitude is known from some

almanac data. It will minimize the errors due to (a) eccen-

tricity of the earth's orbit, and (b) the leap year cycle,

if t-, is chosen at or near the time of earth perihelion,

in the midpoint of a leap year cycle.

It should be noted that t.. for the known value of GHA

of Aries may be different from the t-. for the known values

of true right ascension and declination. Likewise t-, may

be yet another time for the known sun's mean longitude.

Since all the values (constants) associated with t-, are

retarded to t no difference in t, is objectionable,o 1 J

B. IMPLEMENTATION

The program presented in Appendix A is the result of

several conversions. The first conversion consisted of

taking algorithms expressed in Ref. 8 with the HP-65

programs to produce a debugged FORTRAN IV program. The

HP-65 programs deal with degrees as a unit of angular measure

vice radians. A conversion of all data from degrees to

radians was made for use in the FORTRAN IV and BASIC pro-

grams. General routines 0010 and 0020 provide for I/O

conversion of radians to degrees, and hours, minutes, and

seconds to hours (and vice versa) . These conversions were

needed for ease of data entry and data output.

The HP-65 programs are compact due to the limited

number of registers used for intermediate storage. This

efficiency of memory was carried through to the FORTRAN IV

programs and then to the BASIC programs for the routines

that determine the GHA and declination of the star and the

subroutine that determines the azimuth (Zn) and distance

(subroutine 0300 and 0400, respectively). It was felt that

this level of efficiency need not be continued in the

remainder of the program due to the need for self-documentation

FORTRAN IV was selected as the intermediate step in the

conversion due to the amount of core memory allocated to

the FORTRAN compiler. The BASIC interpreter is limited in

memory on the IBM 360 installation and would not hold the

completed BASIC program.

The reduced precision of the FORTRAN IV version of the

program (as it was not programmed in double precision) was

attributable to the internal formatting of the variables.

High precision was not of great concern at this stage of

development.

As the goal of this process was to provide a program

that would implement the algorithms necessary to complete

a celestial fix on a microprocessor, the FORTRAN IV version

was converted to BASIC. The BASIC program allows for much

greater precision in computation as the values are expressed

in 32 bit floating point, when interpreted by the available

BASIC interpreter in the Microcomputer Laboratory at the

Naval Postgraduate School. The BASIC interpreter at the

W. C. Church Center was not of sufficient size to run the

entire program. Therefore, the main subroutines and all

required support routines were run and debugged separately,

and required information was transferred manually from rou-

tine to routine. Because the BASIC language does not pro-

vide for scopal variables and due to the limited types of

identifiers available much of the self-documentation of the

FORTRAN IV program was lost. Table I correlates variables

in subroutine 0100 in the program listing (Appendix A) to

those variables previously discussed during the theory

presentation.

Subroutine 0100 computes the eight constants associated

with a star and places them in array C (elements C(2)-C(9)).

Element C(l) is the rate of increase of the mean sun longi-

tude (common to all stars)

In order to organize the variables as much as possible

a scheme was invoked as explained below. Since there were

a number of subroutines in the program, a method of passing

variables was constructed. The variables R1-R9 and P1-P9

TABLE I

Identifier Correlation of Variables in Subroutine

0100 and Equation Variables

Subroutine Variable

Equation Variable

<5'(t )^ o y

are passing variables. Variables used in three or more

non-general routines were considered as global and were

selected to be as self-documenting as possible. For example,

the two constants for each star are placed in the array

S(X,X) . The constants used by routine 0300 to determine

GHA and declination which are created from the S array are

placed in the C vector. All other constants were repre-

sented by the format C1-C9.

Several routines use intermediate variables while calcu-

lating the object variables. These variables are repre-

sented by 11-19, J1-J9 and M1-M9. All logical values are

represented by L1-L9. Note that this scheme was invoked

to eliminate problems created by not having scopal varia-

bles. This must be considered in the selection of a

language for other peripherals used in the system. Points

to be considered in selecting a final programming language

for such a system and the peripherals attached to it are

discussed in Section VII.

VI. THE INFORMATION DISTRIBUTION SYSTEM

A. OBJECTIVES

This subject will primarily be concerned with the

integration of a general purpose computer into the existing

shipboard information flow. The "system" in the spotlight

is the navigation suite aboard U.S. Navy ships. The phil-

osophy for this approach is simple and is best stated by

Joseph Weir [Ref . 1]

"Good systems can be designed only in the presence ofpotential users and applications. By using the systemin numerous applications and assiduously watching itsperformance, it gradually can be adopted to the (actual)needs of the application and the user. Ingenious ivorytower solutions frequently do not work or they solveproblems that don't exist."

A close examination of this statement while relating

it to the navigation suites will show that in fact the

"system" has been designed both as far as it need and can

be with the existing equipment. Note that the "system"

comprises geographically dispersed equipment and telephones

for communication links.

The application and needs of the navigation system have

been defined as will be discussed later in this section. If

all this is true then why rock the boat by imposing a

system, apparently complex, on an existing "system"?

Discussion with crewmen aboard the USS Hancock indi-

cated that tiie existing system is cumbersome, subject to

human frailties and is not timely enough for the devices

on board. OMEGA radio navigation sets are capable of

providing information for navigational fixes every few

seconds, yet this information is only used hourly. In

this case the communication link is the "weak" link, and

to eliminate this weak link an information distribution

system must be imposed. The distribution system must

appear translucent and straightforward to the user, for as

Weir mentions

"The more complex the system, the more likely it isthat it won't get used or will be misunderstood ormisused." [Ref. 1]

All systems have sensors and effectors, and some

communication constraints placed on them. Although most

of these sensors for the navigation system in fact exist,

there are always new devices being created.

For example, ten years ago operational OMEGA navigation

sets did not exist. If a system had been created and imple-

mented on the ships at that time without forethought with

regard to new devices, then the information system would

not have been able to integrate the new device into the

network.

In order to fully utilize an information distribution

system there must be "terminals" with which to input informa-

tion and query the system. For example, suppose the bridge

wants to know the average RPM of the four propulsion shafts.

Engineering would have a terminal (either automated or manual)

that would accept certain required data, e.g., tachometer

inputs, transform it into its varied forms and relay the

data to the central processor. The processor would then

transfer the required information to the terminal at the

bridge

B. DESIGN PHILOSOPHY

The question might be asked, "Why try to integrate an

information distribution system with the existing periph-

erals?" The answer should be obvious- -cost of implementa-

tion. Existing equipment must be fully exploited until

it is not wise to continue using it.

By integrating existing equipment into a network instead

of creating all of the component parts of the system anew,

the cost of research and development of all the new sensors

and effectors in the system can be elided [Ref. 2]. Of

course, the use of current equipment will demand the design

of interfacing equipment such as analog to digital converters,

digital to analog converters, fault sensing networks, etc.

However, the cost of these units should be relatively inex-

pensive when compared to the redesign of any one sensor or

effector in the system. The application of the same item

(A/D or D/A, etc.) to many peripherals is a cost savings

when design efforts are considered.

As distribution of existing data is the concern of the

central system and since there is a multiplicity of like

data, the question of which source's information should be

distributed must be handled. A rather trite answer is

"the best." Again a question, "Which sensor is providing

'the best' information?"

A definition of the term "best" is recursive and must

include words like timeliness, accuracy and statistical

validity. As each sensor in the system is operating at

pre-system design rates, some periodic (auto track LORAN C)

and others at non-periodic rates (celestial sightings)

timeliness takes on a meaning associated with the quality

of the source. For example, if the only peripheral capable

of input to the system is the celestial navigation unit,

an output of ship's position would only be considered timely

if the last celestial position had been updated with inputs

from the "best" heading and speed information to provide an

estimate of the current position.

The word "accuracy" when associated with "best" means

most accurate on a timely basis. A position based on a

ten-hour old OMEGA position is usually not as accurate as

a five-minute old celestial position.

This is all well and good, yet how are these descriptors

compiled? A central machine is obviously the device that

will have to provide the software to meet problems based

on statistical properties.

Statistical properties of each measuring device must

be taken into account. The proper error probabilities must

be applied to each input; then based on the result of the

combined statistics, the "best" source is selected to repre-

sent that class of input. It is this source's information

(corrected for time) that must be distributed.

Along with statistical constraints imposed on the data,

a status check must also be imposed on the device. If

the data is apparently correct yet the device has failed,

then the data is obviously of no use. The status determina-

tion system must be as nearly fail-safe as possible. Since

this paper is proposing a centralized star network vice a

fully connected or ring network [Ref . 2] , all the status

checks must be initiated at the central computer (see

Figure 6). In order to design a fail _ safe status monitor,

the following considerations must be employed:

1. Notice of failure of the central computer must be

distributed to all peripheral stations.

2. Failure of each peripheral must affect only that

peripheral and, at worst, place the system in a degraded

3. Status of selected peripherals might have to be

recorded for legal records.

4. Failure of the peripheral must not cause failure

of the status check mechanism.

There are several reasons for designing an information

distribution system. Many operations aboard a ship are

dependent on the same source of information. For example,

the Combat Information Center and radar stations need true

course and speed information. These are parallel operations

and their information must be based on the same source. A

distribution system would be the answer to this problem.

CENTRALCOMPUTER FORINFORMATION

DISTRIBUTIONSYSTEM

Figure 6«-Information Distribution System

All of the discussion thus far has been about distribution

of information gathered from sensors, so where is all this

fine information used? An example may best describe the

answer. Suppose the navigator updates the current ship's

position with the celestial navigation computer. If the

Captain desires to proceed to a desired point, the point

could be placed into the system and the system would pro-

vide proper steering information (great circle steering)

to the Helmsman, or this data could be transmitted to an

auto-pilot upon request.

VII. LANGUAGE SELECTION

The subject of language selection is placed at this

point in the paper due to its applicability to both the

celestial navigation microcomputer and an information

distribution system as described within. The considerations

in selecting a programming language for these two devices

have much in common, the most important of which is the

microprocessor

There are two main considerations in selecting a pro-

gramming language for a microcomputer. The first and most

important consideration is that of efficiency; efficiency of

both memory utilization and program execution speed. The

second point concerns the cosmetics of the language (i.e.,

is the language easy to read and is it self -documenting?)

In consideration of the first property, that of

efficiency, the language must be chosen in the light of

cost/availability of volatile memory. Even though the

addressing schemes of some microprocessors provide for

large memories there may be physical and/or cost limita-

tions placed on the microcomputer design that make very

efficient use of the available memory imperative. For

peripherals operating with unmodifiable code the number of

memory locations can be optimized and placed with a high

degree of efficiency. For processors using programs which

have subroutines with arrays of data created during the

execution of the program, the placing of these arrays

on a metal mask chip or fixing and reserving the addresses

of these arrays is an inefficient use of memory.

The best way to program in an efficient manner is to

use block structured programming techniques utilizing

"scopal" variables. Block structured languages like Algol

60 and PLM [Ref. 12] allow for scopal variables to include

arrays which provide for efficient use of random access

memory and reduce the amount of programmable/read only

memory. By creating arrays as needed, common random

access memory may be used very efficiently allowing for

lower investment in space and cost.

The second area of concern, that of cosmetics, is a

growing concern with all languages. It may be a seemingly

unimportant aspect until the prospects of non-volatile

runtime modifiable LSI memories (e.g., ferroelectric

memories [Ref. 15]), multiplicity of similarly constructed

peripherals and common maintenance support are considered.

The celestial navigation microcomputer program bases

all of the calculations for geographical positioning

of the body constants which vary from year to year.

In order for the device to enjoy extended longevity,

the constants must be alterable. The language must

allow for the documentation to help provide this support.

An assembler program is not a self-documenting

program no matter how efficient it is. Its logic and

meaning are often forgotten with the loss of the programmer.

Indeed, the programmer may lose the logic to his own program

if he has been away from it for a length of time. For

example, the statement below is obvious in its intent:

NO$YEARS = NO$DAYS / 365.

Yet even though the next statement provides for the same

efficiency of calculation it does not connote as clear a

meaning

LIT DAYS; LIT 365; DIV; LIT YRS ; STO; .....

The assembler language form of this statement loses the

easily conceived meaning of the first statement.

Though the celestial fix program in Appendix A was

written in the BASIC language due to the precision attainable

through its use, the program itself would not be under-

standable without the comment statements and extra

documentation.

Specifically, there are primarily two high level

languages available to the microprocessor programmer;

BASIC as implemented at the Naval Postgraduate School and

PLM. BASIC, as the name implies, provides for the basic

needs of a programmer. BASIC has subroutines, iterative

and logical capability, the full range of mathematical

manipulators and limited I/O. A quick glance at the program

in Appendix A provides the evidence of a major drawback:

lack of variable scope and identifiers. There are no local

variables; all variables are global. This property coupled

with the limited identifier schemes causes a programmer of

a large program to run out of variables quickly. His atten-

tion is turned to efficient use of identifiers instead

of efficient programming techniques.

PLM, on the other hand, provides for scopal variables

and identifiers that allow for self-documentation. The

following statements are equivalent; however, the second

connotes more meaning:

LET Jl = G(Q) - G(R)

DIFF = GHA1 - GHA2.

The array used in the determination of the three

intersections used to calculate the fix (subroutine 0600 . .

ARRAY V(6,6)) is a temporary array. In BASIC the array is

permanently allocated space. Using PLM and scopal variables

the array would be created by the program during execution

(indeed, could be of variable size) and be destroyed or

written over upon exit from the subroutine. There are a

few drawbacks with the use of PLM. The primary drawback

in the execution of the program in Appendix A is the word

size. Sixteen bits do not provide the accuracy needed for

the celestial navigation problem. Though this problem can

be solved, it is not easily solved.

Special mathematical routines like trigonometric func-

tions are not available in PLM, yet they can be programmed.

The point is that PLM can be tailored to the needs of the

programmer with a little extra work while the BASIC language

cannot be tailored to the user at all. PLM provides a

much more versatile language yet the detail required in

programming is greater than that of BASIC.

A final comment on the selection of a language deals

with the multiplicity of processors on an information

distribution system. If each processor were programmed at

a different level with a different language the maintenance

and design problems would be horrible. For example, suppose

one processor is to provide a second processor information.

If the first processor is programmed in BASIC then it would

probably transmit its data in 32 bit floating point form.

The second processor (programmed in PLM) would have to have

an I/O routine to convert that processed data to a local

format. If there were a third language then the PLM-

programmed processor may need yet another I/O processing

routine. This situation is the grounds for selection of a

single programming language for a system of microprocessors.

VIII. CONCLUSIONS

Currently, the proposed computer is capable of developing

a navigational fix (without use of the Nautical Almanac and

H.O. Publications) utilizing only the 57 navigational stars.

Because of this limitation it is obvious that numerous and

known applications are yet to be incorporated. Among these

include methods which employ the attributes of the sun, moon

and planets so that positioning with these bodies can be

performed. Considering functional aspects for future

development of programs, suggested programs are closest

point of approach (CPA),great circle calculations, star

location utilizing estimated altitude and azimuth and fix

triangulation routines.

The sun, moon and planets present special problems

because of their proximity to earth. They do not appear

fixed in the sky as do stars. Stars do move across the

sky due to the earth's rotation but their great distances

impart a constant relationship to their neighboring stars.

The planets and moon, being closer to earth, possess no

fixed relation in the evening sky with the stars.

The size of the sun and moon requires a special con-

sideration termed semi-diameter. More accurate sight reduc-

tions can be performed by aiming the sextant at the upper

and lower limb of these bodies; corrections for the radius

of the body can be programmed.

For lunar observations horizontal parallax is a

parameter required to be considered. It is the apparent

difference in the position of a body when viewed from two

different locations. Horizontal parallax is significant

for the moon because it is the closest body to earth.

The celestial lines of position are included to give

the navigator the option of plotting LOP ' s . This method

should provide the navigator with an azimuth, a distance

and a toward/away indication in reference to the assumed

position of the observer with which the LOP should be

plotted. This is the backup routine to the fix calculation

algorithm.

The proposed celestial navigation computer was used as

a vehicle for the approach to a design of a dedicated micro-

computer. Other devices of similar construction used as

peripherals in the information distribution system would be

approached in the same manner. Approaching the design of

each device on its own merits will allow for the system to

grow in a manner that "fits'* the situation, i.e., a single

"ivory tower" system would not result.

Indeed, the development of the central processor

(assuming enough ports are planned for) would grow with the

system as each new unit would simply add length to the polling

routines and interrupt structures. Following along with

Weir's natural growth concept, each processor's programs

would be designed and built (or at least the algorithms be

provided for) as needed by cognizant individuals, from

current literature, as done in the case of the celestial

navigation computer. The only restraint placed on the

design/designer would be that of language and interface

specifications. As delineated earlier, the authors believe

that of the two languages examined PLM would be the most

efficient language and would provide for much needed

self- documentation.

The central processor in the information distribution

system may very well be a minicomputer or a microcomputer

depending on its functions. It need only be a distribution

device designed along the same lines as the peripherals

it supports. The level of computation provided by the

central processor must be established early in the design

phase because the peripherals would need to "take up the

slack" for the computational capabilities not provided by

the central processor. For example, the averaging of the

revolutions per minute may be accomplished at the peripheral

(which is recommended) or at the central processor on the

request of the inquirer. Again, keeping this device

simple (only the necessary switching and monitoring routines)

will provide for more independence and faster information

transfer

APPENDIX A

CELESTIAL FIX PROGRAM LISTING

<to a:\~ <

-^ <t inm i~ -r-~ to i—

•- O O— CJ f~i-O Z«- Q •-.

X Z«-.~<r to

mmto 2«~ ~UJ <io C\J "J I—••—_) O0

-~tO<t 2••O • > o •-« *^ ov

,•* r*~ sC i-i oo

»•*•

L) >j-if\OcÔHin-j-^MON ifimHff'iAvcsmooco vONOcor»-r\ivOCr, c\j<t-cn<\!vi-r->3-v£> rvi ~j r<*. in m <n r-- co vj-o cmo vOo rf"i o ooo cm co —* —ic co f—<m i—< co soO in »-< rsj oo ô in in «d- r\io— ~' <r rY'Olnô^^^vd-ou^f^:(û>coOs C^âr^cofû^LnLn^ôôcO(^J>tcOr^(û^^\lL~r^^ô^H>0O ^tOvOOOOÔcu^-OCÔO^rvi^î^cOvtÔâivÔOinO^rrttÔcninr^v+vtsOOriiCvtr^.•• .._ t\i k-toOnC f^^-ôo^ô<x>^^(>«^vO-^co^~o^~l^l<>Ôrvoôoc^l ,o^'">oolnlo^•r) r-ô^^•^0—.—CO r~in.^^toa^rnint^(^r^vX)vOOv0.î^r~cOv^cccc^r^rf'>vCro,OvOr^vfimO OfMinin orr>rovt(N;a^r<')0^rof>--i'-oor\ivO.-irOf\i«xi<NioOi'<>oiv-r\ji—tcc(PCD*& •—(•—irui—o«J"f--coo—«<-- _j rnc^GÔajroor^mrsi^r^cococ^vJOf— ^^vn^t-f^sOtvo^rMC^co.^

•- c ;; j rri \-| h-iJ 1 t~ • •«••••••• .•«•••»<>••»••*«•<••»»•<,•••.«.—. «—^ i—im ir, in oooooonro-'r-,r-)-^i---i^^i^^(MM(\i(MMMrofiimpf>t<iMrf' llfn--.,-oinm«Ora>- r<-)sf O^^-iO ll II II II II II II II II i! H II II li ii il II ii il II H II li II II H II II II II n n II ii II II II II

_jt--juj <\j—< •—*o»-<fMro înv0ôoo~0'^^ i^<t- invOh-ccc>0'^(NjroînvOfôoaô>—'c\ifo»*'-nv0^co•» »-0 •or— •_

p-<^^r^^'^r^»^^f-4(\j:\i(\JC\Jr\j(\jr\ir\|iNjr\irnrnf^c^^ror^'n^—.»-. o .mm »-•.».•..«••.«.•.•.»•.».•.••.•.».•.•.•.«.-•.•>.•.•>..«.•.•.•.».•.•.•.•.COO^S:—'O II II II II SHH^H^^H-JH-,-IH^K-<HH-IH^^^^-IH^rtH-(H^^HH^H-IHw— UJ || || MIMrO>j-Ulw«wwww«^.ww^«w^ •—'^-ww——w^«~—^w~w__^,__^.^.^CQoafH-U-OOOO0'l/1t0t0t0t')'yit0t000l/)t0t0t0t')(^t')i0t0l/)t0t0t0t0u0t0t0t0

SIX hHI-t-h-l- KI-hHHI-l-hl-l-HHI-Kh-l-l-f-l-l-t-hhhl-l-hHI-l-l-l-l-h'HI-l-l-!-<-< LUUJUJlliUJLU U^UJUJLLJLUUJLUUJLIJIIJUjLL'UIUJUJUJUJUJUJIUUJUJIIjWWr~\C* „j_j„j_i_j_j _j_j_j_j_!_j_j_j_j_i_j_j.j_i_i_j_j_j_i_)_i_j_i_j_j_j_j_i_i_j_j_i_j_j_j_j_j_j

r-m co

vj-r\i—<cocMcosoooofOI»-f—<o—

—IvOl'OOOcocor— .—icococoororo

in ro cooocr——<<}- 00coooon- in

ocoooinirivO

vproro

—"sOvOvOCOr~-OOVvO•—)vO "J

vOr-CO —I—iin—(CMr-r—.-^cruninin o cmo ro«* o <f cm v0

st-coocNJ-0otTvroir, co0"0—<coco—I CO V+- vO r-

r~-coinCO CM -J"

ccr-oCMn.—

—ir-inmoooo •

r~ invOcmomm—

ro—ic\i

f-inr"-*tr~—<

r— I'oro

<f"CO-<f—Oro

rovDOrOOinr-ooojomr*-co <r co

.-ir-tnoooo<f-r-

r-cor—

OMOlfl

CM CM LA —<CO—JUD.T)vOr^cxivC

vOvOCO<fO CO C\ I —I

ojsOr~mOm—I COro<}-0<f

cm—<

(M—i—

OCMsOOvt vO

O Ocomro—

OfMCMCO—10sOCVICM

inccor— covOCO rri r*-

vf-—iO

Ocmos ro-*

<J"CO^tco<t-mcmcmcmcocmcm(\JOh-OGm-Oo*±o

—i CMO —lOroc\JOro^OCOvj-CO

cmo<mo>s-om<-H<hr-cM—*

en r-vt—icoroocvinrOvi-cc. r— co —

Or— en roC—<^o<}-O—tr-r——lOOro•—icomo(\lC(\iro

ro ro v.+ ^j- <f- <f-^-vj-v-t-<t-xr-ininmininsOvOII II II II II II II M II II II II II II II II II II II

I I I I I

II II II II II II It II II II

I III I I I I I

II II II II II II II II II II II II II II II II

OO—-<CMro<nnor— cooo —<f\irn\tinoN—io\jro<i-inor— coo>o—«r\jro-4-ins0r— cooo —4C\irnNj-mvOr--cooro-J"vt<hvj--4--t^«d-vJ--J-mmmmmmmiPi .-h—<—<—!—<—<—*—!—<—<cmcmcmcmcmcmcmcnjcmcm

i cm rv! r\i cm cm rj r\ . cm r\j c\i r\ir\! cm r\i ro r\i r\j r\i c\i c\j eg r\i cm r\j cm r\i r\i cm cm

cOi/^i>0(yicyioOc/5U;oot^c/icy^ooc/5cX)ooi/5c/)OOoOiyic>ocyiooc/iU)i/)cO

I— I— I— l— I— I— I— V-l— I— I— I— !— I— I— I— I— I— I— h- I— hi— I— t— h-y—h- 1— *— 1— •— I— I— t— I— I— i— hi- 1— I— 1— I— I— t— I— »

LLi U-l i_L» t-LJ l_LJ l_LI LLJ U_l l_U U_) LJU UU i_LJ LXJ l_U U_) LJ_i ULJ Ll_! Ll_l U_i UJ U-J U_i LLI U_J LLJ U_l LJ-J "_LJ U_) LL I LLJ LU LLJ LU U_! LLJ IJJ LU LU U_J LXJ l_U U_! LLJ t-l-J U-J

inromr-< 00 >—i coi-o r^-m\cr\i<}-r<">^'>d--H.-<.—<0—<0o>o<M<Nir--co—•oocomO'j- —^fOvomooor^-a^fM^-j-rof^o -

C^î-r-l^âDO^f)lr^f^",. -or^cvjLoh- NMvCÔOiriOinr-icooina: lu

Ocot— CTN <%ir-<)-«^-f>'~cor-vOt*-r~-i -J- co coo r\im co r*- coo n- co ^- Q- I—ONvOr-tCMnr-iS^rriOmC^OO .—i rJ r\i cc roO i—< f- <—

•O CT^ -J- 0^ LLJ

vor^-jrr, <j-r-<v.tir ir\ co ~t r-*<*~ s a .-< cma ro m ^-i

(ni <f- st r\t r\i x _jcorooirico -OvOOC^-'Of^coO <m in sL'wr, >f in o vO r--m r^ enO >—

• a.

co vfo c\j f\i r-* (\j p- 0" co vo r»-o co r-o^roOvDo^r<->.-<coo.-tCM*<"iu_ Soo^r^-CT^sDu'smivunr— cr>vfW)o v*-—ic^ONininDcoSM^>o oooNO^—<coovOi ,or3(\!(Nixi-vf(^j voojcOvOsO<t---<o^r-'-'a">Lr\rMac: o• •••••••• . . e . * - ...... .<!H l-»

|— 3£i I i i i i i I I O | i I i i oo <rII n n ll ii II il n II m ti n it n it i: n n it ii n u n ii u ii II n cc

., , ,.-. . ,.-., . z o

0>^c\jro<finsOr^cooÔ^CNiro«d-ir>vOfs~cocrO'--<{\J^vt-invOl*~!DOOrricnfororornror^^ro<f-^^vts^^^<f<^îû~'^îniriL'"\irvaiooi•.•.•.•.•.•.•...•.»•.•.«»«.•.•.•.«•.•.•.•.».»»•.•. c\jO-

(\i c\j r\i ro cnj cm (\i cv c\j cm f\i <\j c\j c\j <v r\i <\j c\j cni (\i r\j e\i <nj <ni ro c\j <ni (\i 5."o -

co co co co co co tS) u. co co go c 1 co co co oo oo oo co oo oo oo oo oo co oo oo oo ci. co I—

h- 1— I— I— h-J—— I— hi- K- 1— I— 1— I— >— I— I— h- I- I— I— I— I— I— I— I— I- oO>-«

UjLUUJUJmLUmUJUJUJLULUmUJUJUIL^lUjLiJLJUUJUJLULUUJLLll-UUJ OC£_j_j_j_j_j-j_j_i_j^_j_j_j_i_j_i_j_i_i_i_j_j_j_u_j_j—i cdo.

ft -ft ft -ft ft -ti ft ft ft -ft ft «- ft -5:- •ft* :- -ft ft ft ft

si- Si- ft ft •ft »- ft

ft ft ft ft ft 2T -ft

*- £. ft ft ft Ul ^f•ft CC • ft ft ft ft SI •ft

ft QUI •Si- ft o -ft -ft LU ft-ft a; ft a- LU %- ft CC ft.M. t/>X ft «• OOO -V.

ft _o H.

•ft Z ft ft UJZ ft •ft O0 •ft

ft <rn ft •» l/)t- ft ft < «r•Si- •hH •ft ft Z5T JJ ft LU ft

ft O •51- ft t—i • i:- .^. ST ft.£- <ro ft ft •?rm ft ft ftJt.

OT. LU ft ft •CC J;. ft •z. •ft

ft OO ft •Jc ox ft ft <. ft.>;- O^ ft V IU •>' <:- H-l ^**

Si- k-»-i ft •Si- oc ft ft O it.

ft «l. -ft ft f- ft Si- < ftft o • Si- ft Ci ^4. ft rt: frSi- LUOO ft •}t 1— • ft •ft ft

ft too: Si- ft oo ft ft _i •Jr

ft zx ft ft ooo: ft ft _j -ft

ft -< ft ff zx ft ft < .;}.

ft STZ s:- ft <r ^<. };- ft

ft • in -K- -«- t-<!^ -,;- ft OO K-

Si ol -S<- ^j. Duj ^J- ft LU -::-

.j<. LUl— a «• <X ft ft r>j ft-;<- o li- ti- ccv- -!;- ft l—

ft »"» ft O ft ft ft _J ^.

ft OOI— • ft o ft o0— ft ft <r ft

ft 1- II-» ft o oO ft l-l- -::- ft •SL •ft

# o: «—it—

*- a z ft a: ii ft ft CC j*.

•ft IU_|CL Si- i—

<r » UJ—( ft o -;;- o {(,

* >-^~ ft s;- HH ft > _j ^. o li- z •ft

ft Z -ft t—

oo ft Z— -ft o ft ftft- OhW Si- —

o< »< C ft o ft ^. ft

ft DliJ"-! K- i ndo: •Ji- OH- r-t ft i-M ft o ft

si- 00 •li- om !*• ujo. i/. *v. ft m .x.

ft- -~ LU ft o^a JL ^~00 ft «""* Jr o >c

ft Ooo_l ft r-H—»h- ft o OO 5'r ro ft o •ft

ft —(•—•cQ ft ft —

ft fMOOt—

ft t—

ft «— •ft

Si- C -i Si- c\j t-iUJ ii O UJ ft OO ft LU # ^-1

•s:- —oo: ft »—

wlil {'- ~-a:_J •>r oo •ft z ft O* H-< ft 0~l-a: ft oca ft ft f-l ^<- 1—

i'.•ft

a Ul<T> ft OhZO •ft LUl— <I ft t—I — •ft K- Koo Ji- *m.

ft ZO « -iZwUJ ft z<.*-* ft CNJ —i^. ft oz *;- ~-

Si- t—it—"(0 Si- ft t_ -* Q —< .»{. t-iLJor' •« O ONM M- o<r >;, <-4

ft- 1—OZ ft --( 1 O —

ft \— t-H<r 5I- O vOt—<—

»• a:^-i •ft CX.

Si- DT-i- Si- t-OvOK-O ft 1Q> ft <{• — >-- ft coo •ft wft O 1—"00 ft *- 1 O + 0CO -K- 2 ft Z ——h-l— ft r>< % i-•s:- o: oO ft —iO Om LU j,(. a:^co >f IU r-

r-x'z !(- 00 CC •ft "P

ft ooo£ZN )'<• co z j:- Xl'OCL —II—!—

ft -ft l II 1

* doo- ft —>•—i—

-ZUJO ^{. XJa—" ^j. H-O w-1 1^ ft -Jt-t ft O I

* ooo -;;- 1— -ft ft + OX -ft ft O0Z5O0 ft »;- H- r-((NJ + -ft <Q- ft "V-Hft X ft z-<i-<—It^'l— r-< .jj. Ooo ^_ i-'-i z: a. -<,-< -if Qi^i- ^5- r-IQ.ft _J •Si- .— ClQ. t—

a u_ -li- -JT< •»!- Q-M ^-—•-•LL ->> LUf^J •ft CLwSi- <ru_ ft II II II II £Tl- ii ii ft <t Q- ft II II II II II II II ft z ^j. II II

ft Q->-i ft '-(CM CO —<LU II r-liH ZTft CXU- ft 1—

C\j «) ,-i_i 2:, LUO •ft^^-<

•ft LU ft Ml-lMCLCX—

a_.ja: LUi—

ft ^a i-i —it—< Ql .JQ.» Or- ft Q.Q.•ft Z ft -J =)ft z ft _j O ft ft^j. LU «

1— 1

1— H- 1— ft LU ft h-l— h-Kh-H-l-ft *lH-h-* o ftLULULULU U-LULULUft o •Ji- LJL U 1 LU U-i LU LU LU LU ft ft LULUft ft 1 • • _l l-H _i_j CC-H- ft —i_J-J_J_J_i_lc£-ft ft -i-lZ•ft -ft ft {;- St ft « -ft

• ft -ii * ft ft ft a:o ^-i O r—

o Ds: s:^ s: s: s:£ —< ^h 5:5:5:i:s:5;s.rNJ r\i s: s: s: s: s: 5:o h-LULLILULLIUJaiLUO O UJ LULIJUJ Ii; U ILUO O LULUUJ IU U J L!JO LUcccccccc^cccco o cccctx-ccccccixo 0:0^0:0:0:0:0 CC

* ft ft ft $: ft ft ft # ft

* •K-

# • ft

# Q ft

•a LU ft

# 1— ft

£- z ftj;- O 11J -V.

ii ZLUSOO s:-

•ft <_|LULLILLI >;.

# co -J 2: 2: ft«• 2<tOU>-4»-H ft

* mhJ s:?: .v.

K- 00 r* -• rv c: • -*•

» <f LULUOO ft-8- iu>lui~i— u ft

* OO CD IU LU IU ft

# 0£LU QCtt ft8- IUIJ CO ft

* >l— .JOOOOLU -;;-

-M. ^ _,_._0 ft

.{{. - .3 .>;-

*- ~~ !— »— ft

* UJ—i s'T'ycr) ft

* laCtuai-1 ft

Jf" t—"—?r?- 1 .;;-

* I-3DO .><.

* t/)f-OOtD ft

ft UJZZnoCUJ •ft

ft Za)D<i<o >;•

M- h5!u. Z •><•

ft X~} UJLU<I ;;-

ft aiCTIIii >t

ft LUGiOt— t— -;;-

ft 1— «3" >—• LU ft

ft LU -TLLLL-> J/r —

^+* OOSQCm •Si- ~* —

ft LU 1— ft G. (\i

ft OWUjZoOm ft ^v .»<.

ft <K^Z«-<OW ft im. 4ft o<r—ii/iun .}<. (NJ r—

ft oaruon ^c-;;- Ql

ft araroi ft •—) •!$ (\i OJ 1

•li- LU LLi LU <r <t LU ft <f r-< <$ <f--<

ft zrt- x ft O Q. O o~-» 1—<l— lUUJLUf— •!! O 1 O oa:ft >~ OXT .};. —J orft r>LL V-\—O ft Z— Z ZoOft OOO t- ft LU CC LU LU^ft ct: y-y*Z> ft IT"OT X—

ft moo ujum ft 1— OO i— <*" !— O-

* Dnoxiiu ft ^> —ft 00 1 _> LLI !—(—-. >:- MZO 4-^Zft 00 _J Si- h- —< 1—

•Si- -JLUD—'POO- ?;- uj <r >— Q-UJ<lOft <Ioo 11 11 0. K-Z II O tl Z II II

ft a: q^ <./) (nj r\j< -X- ^-« ^-* «—1 r\j

ft lu lu -« a. a. -:; cm cl ~ Cl-lslO-CLft s:> -;«• Q- a. CX.j;- IUZ <V LL U_Z };- t— (— H t—ft O >—< CL •—1 1—1 t «^ <t-H-luLLllUUMiJU iUJUJlUUJO O OLUoroLQiQrarctaiaCQiaio O oa:

K- tt -J!" «• *- # #x -a-

a- •*

* * l-l ^* o ** * > >* 1-2: # 00K- Um # ^K- »-k- *- v1- C oK- LlJ-eT -K- •_< • •

M- 2 «• ~ O 00 O* u.>-< # 00 Z C\J UJ <\)K- 0_J ^ ^ _ UJ•« O "Jr <C 00 UJ a'. UJ•K- ctuj *- «-t * 1— o KK- 00 #00 in ~ < uj <r* 1- * <r o f^-2-

.t> o a ofr Ljr> # Or' CT> O O ITi .—

-> uj^ -» .—1 ,—« —1 r~ -~- tu n uj

•»• X *- O LO 00 O 5f 00 \D (/)

•if- • -if- 1— u' x Is- Z 2T f-i i-t < m <r« UJ<<— •{{ O LPi ooujo w CO co

-><• xxo •«- lu 2: r- o —* <j> >— x « oW- t—OO -K-t— hhO a. 00 (— o «-> O h- O-X- r<", {{• <r 00 —• LuX<r<TooO*--Lr\»— h-K-oOulO-IJ-Qt: —1 O 2! -h QuLH o UlK- ujX ?'<• 00 z: ,-, >. O I— *-> "s* ill U w **• 0C ITi

* t-i-uj t-z uj < * n a- x _j —

— 00 h- X) r-*<2-M-(D>-i-5>t oujoo— z: 00 o 00}{• LULU 1—

.>;. _, fy- _< _i m pp c—. UJ <f OO O Z <t •p'

Vr Cl.v~\— -};-»— TD o vo r- >- c£ O .—• «-, lj i * <r l— a <> U_ O -^ I- tt —.— -0 5T ->•tt- -JO •»!•»— 2!OOi-HOCjU_U. 7- <r ^——^.j- —W or)cy -k-Oluoo co O O * ooco # a: o o o X ;?: 1— uj i-^i-,-:}-^— t-*<- < •

* —'—tX> ->> (\J OOOOLLUJUJ-H-COcO ——- -H- 00 ? <t- -k- -h ok- o<ioo -is-xo;? • a »-< o OfJ) — >— <r ^zcrr)" —< Q —-* <_>•— -f

s- 1— -«^ .—< 00 1 a. 00 2: zr m^ Of-iwocosrn <r o.'— -~ sk-uj -}<-oi:LP lucouj^:^<< I-,—. Li_moi/>+ ^- ^;- o + cc 1 o> —• o•K- ZQ> -K-<(ViLa t->sj-r- rouj O X^XvD— to o—<-s:- -\<- c\i—

c^cm cc-< -j rr•» "-••—Q -jr-ujr^-r^- acoco >-ro( 1 >-< dcocjco^*-' v.i-^-^-!< locviu -:( miu o»«v "^ m* l— f~

-« vl- O <Lf1f> KOl/1 h- (XI ini-o- \— (Ntv'f- <}•{!• O 1-1 •}?- •r-j mr^- o•M- DQCQ -ii-H-xJJr-^ m^t i—«<f —2~omos-:i-o <k>w.wm7i/)(j-)Oj r~->- — <_>

-> oiuoO -;{-lucox or— ^(—Ovd-i—o 1—'O r\i dnu kO(/)i/i<-wOui<.'N< r—~ ^ u-M- coxuj -:i->c>o urirvjN^K-i^Hxct:_jcr ujmujou-!!- inooooOa: 0000:0: -;;• s: --hi— i— qc•k- 3 1— »;- 2T »o <r>i- •—4-jo^co »-o i-oi-o + h«zouur?-' oco-^ lt\< f-«<r —n*•K- 00000 ^ GOainxNinofflo>-.rHijj(\)<o<OvOU 1 rjosvi/»i- -s:- Ow^ooO' + 00. + oaai«- t— LU -»• O v£> u_; r«-O tg 11 O^rtwD-aOcrroo 11 Ou •coco II cocoo II — 2rm »fXJfri 11 (\iro. 11 o{} —l^-J -W- ro • ^-<m,^ • 00 00 • «^»— f--

I oo-~c )0 —O Ovf ->o-——)C —

« <<uj -M- 5: 11 2: 11 s: 11 11 —<s: 11 s: 11 s: 11 s: 11 2: 11 11 vd- 11 x 11 11 n r- 11 11 s:^ 11 so 11 11 00 11 ocnjs:m- on— 00 ii- LuOuj^-iUjfvicc«—LULOLumuj vj-Lu v0 u.r— in—' vD ui cot— ct>«^0'-«uj—»>—<uj ro-^ ^.^< »—lu* luoo *iiMrY«ti>HwUixuaw^MrxuQ.u i-u^yuwMO^^iyL) fXQ:cnniXffloacouQ;* ZZai ^. X> 3 X>«• LUOX -;<• >>- I— 1—1—1— h- h- I— »- I— K-h-l— )— I— 1— I— I— 1-- I— h- OTr-h- oOJ— i~OOI—•{< OOr— -K- UJ UJ LUUJLU LU UJ UJ UJ UJUJUJUI UJUJUJUJUILIJ UJUI OU-'UjOUJUJ OUJ* -K- _J _J _I_J_J _J _J _l _J I I I—I _J_I_I_J_J_I _J_J O_i_'0_J_!0_J* * * * « !;- •»•

osssiszj: oUJUHULLIUjUJLLI —4c(Toia:a:a_a:(x o

UJI-<QUJi/>

o or—

COo STfM

a-<7? of—«

rOLU a tf

hTi-i «—

1 h-O h-<t-CO ^ + _|o—ro ao~uUjU-* l co i a: i

<—i <\juj>-'s0a:-4'* O'-'OO^C~vOro II II ii O II

>—(O-— —•»—•— —2

ii occcoco-osiLnQ^t—< >_>w>w>.wr uj— r>ClcDOuUUaOI-3 UJ

H-OOt- (— 0- t-QCUJOUJLLUIUJ UJ_ICjj_J—'—'_J _l

#•«-•«• -K- «•-::• * Vr ### *a- M-

•Jr *-

# -* LL•* K- UJ* •fr CfK- if

* O fr UJK- UJ »- ( )

* CrT # Z*• —

•* »—

fr 3 •M- CO•H- o a-»:- LU •K- CO# a: # ,^-»• K- <r•M- <r *- Qfr t- -tt LU•K- <r * D UJ* o *- a: X# *h- t-5* _i >> —.K. <r » n LLI _»*• •—

< (V ^o •» >- Z7 LUK- ^— •• <r » >-H C€ O* •-••^uj X k- "-• 2T <t <r# 2D>- X *- err c*: UJ crfr --J O # < LU > O* _)Q- »—

# LU h- •-s

* _)D< # >- LU a h-$!- -JLLLU CO -"- Cj <. Z* <r _i 1— *• a. LU UJ* CO 1! *—

* <r v+ _j —« i-Z' r m *- uj O 1—

«-•

tt WOh 1—

a _j CM oco _iK- lUw X o H- *^ O f\.l»—

CO UJ# ZD\— ^- tt 2: Q —* O—i 7 o a <nj n UL «_> *-»

•K- UJZ o 3 K- h- ZL<1 h- CO# a:—<or 5: 1— » O r-< UJLU LL UJ 2:* u_< K- < »— r- XV *i—

M- — UJLULU I— M- _J ^o> K- rj O* OQ>X to # a. l—" r-l co UJ >- >—* O (- < * O o«-< O <fr c\ji— cl _J «•_! CL> - X roro r> ct LU* OZ<Ill •w •fr <r O X t» UJl— OO h- UJ CO•M- —"d'nOT •M- O CO?'- I— Orl —.^ fM(NJ <# H-l Cl. cffr 1— _) f-rv •» •-« •-< V P". <r h- N- LU 00 O h- 2! r>M- LUCO II ~>~-?- -» ^--*<r 2:2 — O <I. h-* >-<Cj »DS > •if- _l in 1— r-o LI 1 ti- (NJ

* f-O • • ' 1 • K- 2!U-iQi a: a: + Za: 1-' ll ^ Z Ql CC cfH- Z> • « « > • # h- Oh- LU LU lu :s:r\ira<h t-io-O l-~h- 2: LU 2:uj LU LU

* al<XV- 1— h- •K-h-+ ,«v + K-Z — >i-X + 1— 1— h-

* OCX • • < l » tt 00 U.Q2 2 z 1 or-voz'-. OvJOO -tKOI- -iOZ ^ 2HH- co«-<r\i • < l • # h- LU LU lu 2!po>-ly:q:q^>- « 21 II 2:2:- O- 2:- >- 11 11 11 11 n II 1 2: II UJUJ2wOlL2 M - <- -41- II -* 00 •» LUCMLULU O 5" >- covOf^vor^-vor>-Luc\i_j_j II II It 11 ro < H- w—t

fr c£ •& Cf. —J iV iX h- H-l- h-i— 1— '.r.a:oLCCa:<x.c^u--i ssic f\J 2! Qd h- K-l- »- —It—* O # ZDzzozzoz — 2:2: H- _J ZQ zrz: 02: z8- b_ •fr H _<<—« *_H <J 1—h_(<m|— f~|— |— !

\— t— h-t- — J— 1-4 < _,_<., !—•—

fc # UJ Cf LUI^Cf LUcf (^IUQIUJLUUIUJLLUjLL. LULLU. jjujou. JJUJcrTLUol^LUcrCLua:M- # —1 CL(VClQ.qlClG.(yQ 1 _J I ( 1

_)H IWI-H -i_ICi H-

_j_jo.cx:Q.Q-QrQ la.8- -a- »:- • »• -H--H

C >.—1 CM rO <^misu SISS: 1 O O O

LUUIUJLU.ULUU.IUJU JLU C\ 1 f\l <\J r\i f\j

cCcCccclcccccx. a: aCOl c t O O O O

< ^" 0£ +I-*.

LU O -~Z> 1— tocc v>1— -~ Z?.

oo —00 t—h- ^ h-O — <iz _iV o^;w LU-Jf-

LUf^-LUo D-C05^LLJ 00O -)

UJ ooooQ_ H-COoOCO acxxi

IbOc* >0(XLU Z(MUI

O H- OOk-• ^ UOZ

,-hO—<LU Ouj>-i(ioa - ^S —CX II ^ UJ ||

»—coot— h-o:*h-DZD ZQZ<.>—ii/)l— —<<1— k—<

ujq:oujq;ujq: wet:or a_o_j 0.0:0. _jo_

ooOO<a:LU

001—4

LLOa:UJCO

a: UJ ooU_) •J s:CD CO •

s: < Xr> _l -^;z »—

< oo> > coa <f< Oo -iZCD r\i

*v O ca: oo*s Zi- K-

•—<t— LUZ s:ZOO x< tr>

oa: oo o:h-LLI xJ-Z".-< UJ

.—<ocluj •—ofi—iO-O II - —tO.O II

a. —i q_ c\j

Hccai- h- co ccDZj ZQZD«^>—<o0h->—<<!—io0|—ujct:oaja:u.icr:OUJq.Q-o_jclq:o-0—i

ZQ—<ct: lu

i— vS-O i CM—- —iZ o^oz

UJ OUJ ZCMLU2:- ii •» c>ct:2:» u o- i-i

cc ^ ak— I— iil t— h-O'HZDh-2.Z 2020i2f l-ZQ1—4 (—I Of >—H <l 1—I t~<| —1<1

QiQlOOiUJCrll-LC^UJOQiUJa.Q.LI_CLQic»-<lX_JCD,aOL

uj>200o

2:0LUCcCQo00oCO

(Nil—

CLC11 -

uj—»X^H~ 1

»»^0O

st-Xry+ cf

^olu+ a:h-ro 11 zCtT-^LU11 2- -<aodH-m- q_ 11

11 Octroi— t-ajx2~ ZOZD(—•-I I— t— H-<<»-lO0(—LU CC UL LL LU LU CC LLI Q. O LU_JQ->-Mi~,_j_JQ.ct:CXO_J

* •»*•*# *it •it

•it if

it •it K# it LU Z* * a LUit •it r> 2:* •it 1- _i IUit it t—i :># \- it \- cc O*- O it _l O 2:.jj. UJ i:- <. >• LLit u. it Q 2:* LL •st Q >- ccit UJ -it IU CO O Dit ^<. > O LLit 00 -it c CO CC, K* f—

it LU 1—1 <Ift _l * 00 X C) _)* •it CD »~ 1-4 a.* I—

>t O V Xit CC it CC cc y~ cc•it it < CO Ul n n n* o»- it "? T LL en r-\ LL-it U- it LL. <s y- rfit o<r it a t—t Q 00 <1 00•it Zo it 5- LU 1—

3i LU UJ* <o it 00 < a X O O _jM- ^4. LU CL CC LU h- l~ 3 CO# UJQ it h- u_ LU h- ^—

* CC u_i •it =5 O y CC LU *-H CO•it 3lL it Z H Cu O 1— COit 1— CL .>}. 1—* —

CO LL T _J>t •SCO 4 5u O a \- <c k- a —

LU 1—1 •* s:--" -it LL. co > ^-»

it LUX ii Cl. O y- Z CC X >o it 1— •it—

z Q LU —< <» •H St CC it O CO LU <r z CO LL— + ^j. O it LU LL rvl CD •

00 CO •it IU it f-LU t-roLL LU < O Ul —

—5: X ^J. QK *- 1ox ID COLIJ I X Z X D

II it 3ll •it (Mi- ZCO \- tsj LU y- •^ XQ < •it t-< tt 1 —

00 LU X »—

>— T ^j. •—•re -it LU*~ »

^" OX IU 11

ecu— LU .— LL.k- 1— 1 ) #77<l ' CM— y z y 7 y-

(_) UJ -Jt _Jrv it 1 1 i"— —1— <XI HH —I t—

r\jh- »—

z LL•—

\- it <-< it X2TCCcCOLU i-« SI 2: 2: OO 5! »—

O3 it <!T #ka.Oujc> Cl. CC cc fY UJ CC 1

CC Q. it CC •st LL'CO>00— 1 •» LU UJ UJ ZcC LU ^» LULU 2" * oz it Oh- -it z • sra IP1 • 1— I— rOvM— UJ CC h- —12:H- O a-<-x LLt-H K- <ouur-o -:t lu 1 cc O II OLUOIUOCLQ.LUO XOOUJOC t—

Z r-t o * it (XI 0' • r-nxcoco 11 coc\i«a (M NQOQO 11 II OO -OOQO •m* D-LU _,o»-< t-O it <> a. ccix—ccox—OXO ^ ro—

-* •* LP1 vOO •- naOQ s: ii -it OUJ it

1-2: 11 2: 11 51 11 1! -Z. II O- 11 11 orosozZ2TO —i2IC'2IO II

a. ii u.jco-a lUoo •it (LSLUt-HUJ'—ILUCOLO^' f—i l-H f-4 UJ UJ ^>•^LU Z. II UJ LU r-J

|~ f— COt—"Q_ u:*- CL3 -Ji- cca • aCiXCCCLCCX Q-cOK-Q-ccacacccCQiccjOOaica —1 a. co cc cc a. y—

ZOZD it cc lt < DZ 3 3 3 3 DHZ - 1 3 Z>-i<t>—<0O|— h -it OLL it t-

1— I— h- 1— h- OO 1-. y— ooi— co 00 coi— t— cox CO cot— >—

CC LU Q-O ULI UJ & Dm it U_ LL 1 LU lulululuOcx LUOLUO O OLULU Olull c OLUCCQ-QIO-O-J _J-it it 1-« _i _J _J_l_l-JCJicX-JO_IC0 <J5 C9_J_J OZ hh t: 1 LSjaz

* -i£#»•#* ccl»- O CO 3

2: 21sx s: 21 O h-UJU,(XIUJLUUJ Cv) f\l CM LUa: cc a.' cc cc cc O O CC

ft ft ft 4 r ft ft ft tt ft ft ft ft !* ft

ft *ft ft

ft >- ft

* O ft

ft O -li-

ft CO ft

ft UJ -Jo

ft «» X ft

ft K ft

# «-» *ft X u_ #ft «— «ft o ft

le- z *ft I/) ft 2ft t— *—

* D *»-H- 2: (- ^j. 00 ^» ~.

ft m o^* H- Z ft 2 Q«- —

ft 00 •—

.35. <I OOft z _i * UJ CO + ^t

ft ft ^: —

r^* LU ft 00 a:ft O *- UJ —1 ^^ft or « X T—

>-zft < Q it H- l~sf Qmft t— Z ft *—

Oooft 00 <I it LL LLO cQftft * O Oft —ft to < ft CO 00r^ f—

.& LU X Si- LU 2:0; K-4-~» CI

* 00 Olli ft a D— xo •»

ft Z> I— LU ft 3 I-H + t- 1

* «-» uj<r O li- 1— 1— ^d »ft xo 2 ft •—»

<r arr\i ««i

ft Q 1— Zlu * Z— DS 00* CC LU<J r><v ft "ZL 1—iro u_>d- 00ft < 00OX 00 LU ft O -J—" QC 2:ft O HJ70 LL ft -J OO <tft ^-1 2:ft >- ZUJ ZLU .x. LUft X-H a. •

ft O >-«or <Xr< ft LU o-» OO •• Qft O 2TluZ LU ft X + M _ft CD OTLL UJ SLU ft h- LU LUCO II

ft ^ UJLUX O ft X— xa: > >-* Q \-cfh- U_?" j$ muj j—rvi t—

O n* or LU 7*- ("")>-. ft orz >-• •>« O•H- l- -HUJ ft —.Z—•(- + t——

K- q: LUT'y 1- Q>- ft <|-Qf.r-lDN DO LL LL,

* <c z --< <3 <: ft C\|LU_'(xcc D.+ O O* 1— >-<00 z^o Jt vhur* 2^ft 00 h- 00 •—<»—4 * •4-LU* ozo DCOO^ 0<£ OOft Dtoo. _jO00 Jt or O co •-'

! «-• — r<^, O-^NIO ^CMLLJft o>-r>ljzXO * — a: oooo- 00 11 Q-OOa CLOQft or <oluo<xlu * 11 s: 11 2: II II 2"

II Ovt 11 O- II II O-ft DID_lOOQ .;;. COLL-h-LU^-: OLUrH O. •O —

^fft 00 ft OCcCCCfy-CctXiCCOCCLCO Q.C0I— OlCLCDI—ft -rn^Of^coro.vf « 13 3 I3Z 32li- x a: or or cc or o_ o. * t- h- h— 0OH- t— OOI— t~00i—it— KOOt—

ft h- ft LU LU LUOLU UJOU! LUO cr: LU LUO CC

ft ft _J _J _J(3_I _JO_J_IOQ l—IOQ-* ft ft ft ft ft ft ft ft ft ft ft * ft or

o z>2:2:2:2222:5:2:22:2:2:20 t-LUUJUJUJUJLUUILUUJLU LULU LULU CO UJo'.cccccccc.cccccca.ccccocccaic) or

#*-**-«•«#&#»>«•& -* *•${**#*# • «# a: *-« UJ UJ ## X H- *•«• h- <r -H-

# _j #

•k- DD UJ <j.

•»(• a:i— i/) ^M- U-1 3 #it wi- <:- o•K- ujooooa; # x* ZaQu. * uj ~# <r « q— ~K- l» U. u3 >- # ^5^0 CO# ooo _J * \~cc a:

-K-CJLJjrvJ> # |_2 oo# zr^i— « _ji-i o« Oh t- -M- <tO <_>

^ ZJ<0 O •& -M- >>

# «I Ku. z # o~ —# ni<ra. n «• iu^4 —i•}!• ZIGifl _J » f-iV Q£tt KJ^ IL UJ >- V^ # :_}*- 7—ii COOT. CM <I (— v- O-^" r^itO

# ti-ih——

DO <r -K- S-—' o

•K- X<X~ h- _» -K- Oto UJO# \--JL\-~Z —

uj # 0+ I**# »- w O O O * — K^K- 00 •< Z Z UJ*- UJvO ~-•M- UlLLlO OUJ "ST * Tec u_-»# zqujo _j a: 3 # k— oco -<•«• hduz uj -. to # »-i to qc a# 5It~<< O u_ OOO *- O LLO uj>-# CL*-*-i UJ L'J IU <X * «* OO Z-^j:- ujcoq.—. s: a: o * o # — *-> —

«• h-z 7 3 —- q.< -:;- z-^ onto ooM- UJOUJ- to UJ O O )! Z t-«^0 O-ii-Z to-H- O—'COjvj oo o X> U_ # UJ O0QTX O—M 21m- <r z o # x «- -< s:K- OOOai ^v UJ«-< UJO UJ -K- (— UJOOUJ LUOClJJ •

* ozjo c^ujooo ocdujo «• roi x^x oM- <J"<3I— UJDD r> QD ->> O I— c_> I

H-ZK —tt O OO f-31-tO ^u_3t- #• -H- mK- ailui cot— >—«>- .(Oi—i—

^j. uj uj-»uj UJcoui cm >•

* ujnw> -<>-« t*:<i ^- '—-I

•>! O Z'*? Z I 7 o Q~fr 7-5 Oh70>-jZl-J«: -Jr y-*Ct*-* >-<^.h-i v± 000* «(->< uj<o D«aa«uj -x- "- s + s: sivos: o ccn:if v-t~<o o:_j_ju_o — _j cc *- ^ o-<Njct: ocroCo' 1

•K- DI-OZ OcoOl— OS -K- cc UJQiUj m-UJ 2^-i LLin Oir a<tCD»-< XOO UxrOUJZ) •«• + t— —-I— H-2TI— UJ<X ,-t Oo^— ^O•»• c£_j oujujo:u->7ujk-2 •»• cm ujoouj o uj.-.uj ol 1 oa o >—zo c-::-* CD XUJ H-2I2:LLJOCX»-'2C3 « Qi OOOO -t-iD^QO vtt-'-'rn H C\iZ II —CM r^^H•{( IDOOO <r53cQ UJ_JZ5CLCt -icLL— I— O QC^Od — CCMO LJO—U-O 1^—<Ol-OQ.^ i/>uj<< a:oooo2;<uoooo5:<i « 11 ~z. 11 :c 11 sr n 11 o 11 r 11 x 11 11 01— 11 oz 11 o» 2 11 o 11 o 11

«• SUJ-J O U0 (/) rDX CO LLH/)O I— -x- CO -< CCUJO UJ—iCM COUJOUn-HCM II>—< -*—< ——< —* ~-t

»• toD cl i/i<<zuOo<ow -ii- _joo _i a: q: ccQ-cl co a. cxJtCa: clCl co cr. Q-rQrvi _i cc i— <ia.co _i en <x

* moIq: *. r> 3 -J 3 32 3 3•« xcocjoo o«-<CMr^Nj-iris.cr^-coo ->v^ i— i— 1— 1— 001— i— h-i~co h-oo^ h-io>-<t— i— ooi—ooh-){ i-<u.m cc cc u, oc: q: cc cc cc cc cc -;>uiu_Ui ui ujujouj uj ujujou.ujCujujOq:u)ujOujouj•K- *- Ii—4—1 _j _l_l(J5_J _) —) —IC.D—'-J'J5_J_JOQ-_J-JCD _JCD«J*«•*•*• -K- ie -!t ««• »•

-JS- •){• * -K- # -IV $<•»»•O ^-4 CM

SiSlSmjSJiirjiJ^SlSESO O OUJUJIUUJUJUJU'I.UUJU U'UUJUjIJJUJU HJjUJst n*- >d-

cr-cccccccccCcccCcCcCccnCa:cCcccccxcccCC3 O O

s: »-4

z. o.— »

••

>- —o 00o I/)

CD s:s:

a: o<i —

o ot— XLU zo oZ< ol- LUOO oooHHIX)fM<I- -OcrlOcQ«. II O- - -

^-Q-COh-K h-z DZZi:*—

|— OOl—it-<t—

ciujOo^aa:CL_)OCl-CLQ-Z

=>h-UJoc

•«•

*K-•«

#«•

00I—oUJa:a:

f-5-Do:oo<*u_

t—-J<r<_i«aoUJU.

D-»—

O0I J-'

55- -8 -8 *

OOOmoOinO

UJT'Xui

<r 00(\1 UJ# _J

— ooo h-

UJo<V-00—I

>-oo00

s_5::>:5:UJUJUMJJex a: a: or

sis:UJUJCCCC

r~* OO-fc-mUJ+ QLO I—

I— X f-< «— —- LL! -If- Oa: (— z:oo-~oo>ouiui _i •—w^-zoq;

2 I— il <I II O'-'O —UJ —if-l— *~ II —- CLO^X- —ioo_j—<oo—toos: ii - a. ii

Q || «CLwibH ^I— !—•-<—iO0< iQlllhKQ-zozoo zz>—i<w adl

t—Y— I— •—••—• t

a:ujQ^u_u_oujujuj uiaroiujcxa'Ci.'-"-'U—( i i _jQ_a._i

oooos:s:•

oXoUJI—oUJcc

OCQ—tO- CL»

coi—t— \— cc3ZZZI-DWwmmXI-C a: ex ol uj uiOCL.Q_Q.^or:

ft Z* # 00 •-• _JK- -* -< h- o# LU UJ # O TO Z•K- ujoo<1 IZ o # O h- UJ <ttt _jc£uj y~>— y— -* r«- tok- jic.izu.oo -it o cc c_ _j•K- <3"KX>0—' Luoo Z # _j O UJ <I# »--U_ 0< O -K _J ULh- 2k- <_uj»—: ii.' 5" >— # uj c£« OIHWUjO h- *- Z LU oo -. UJ-* LLJ-_JZC_»--U_ O # •-• _J Z UJ h-K- <OI O UJ * h CD O Q I- Z# oooo m|- Q 00 # ~> *h ~

> 00 -.# - UJ_n_ ujoc c_ # O oouj I- uj# oz<l:>ujooll. uj * oc oo h- _ oo uj# ui^ouil-ih i— #- o <r »— O I* ozoooh- z z * z an: _j_j h--* arujof luiu <- *- O uj < o*- Ouj uj •-a'o >/- «—• i— t— UJB- Zt— U_k-oo< h- #• t— O i-h _J UJ Z<f <LUOZUJ LU OO *- O Z <l X »-H« Q *-"-.mi uj # uj o D I— Zoo* oo oo n_ji— oo <- oo - \- a or^•if- - riujr-,no o # a: vr hi t- ujn#<Z-J3ccQZ-r_j-K-UJ •—. lu o i i—i

# KOI- <tJ O -ic I— LL Z U UJ UJJ—# o a: uj m -jj-z » .-. n _i —.~-> <~o# XiHiOJCr U. # m k- LU OUCU ujfr UJhOOCCmj!; X*- Z Z> LO OO # •«• 0O0O# III ^x_j k • -K- uj o z # -:;- ujoi« h UJ hCu. X * UJ X or O to .—•—• •—.LUM- or>x ooo »»-« * X »- H-i uj c\jr\j qi—# O0<ii—i»—U. XLL •><• t— P=* f— -< (V(V n?* LUl— I— LLOH-UJ •—}<- O OOO O Q|l IDmVt >00O 00_J U.UJ $? O UJ mUJ LL. O •—»-•* -! UJLUUJUJCO X •?<• i— 00 »_•—• OO CO t-HM LULL# ujiiiiiioo_i7Xi-i- ;:- -} oo iv _._. ujoit o:rooi— <i_j<r>-'Q -* o u_in uj o ujlu «r#• LUI-IU O<It-i_.O00 # O OOCQ r- 2 .-— XoOVr CC QCO ZrtT COl-i Vt >- ft" 2 h- + + \-ctif Z H-LL'O0l— UJ tt CO Q UJU. i—

(\jf\l •—# o>-«ui x XOz » uj o y-O u. -jf- -«- u_<xit O T.UJh-UJUJf-ZSO -5:- •-> CD Z LU O it K vj- OCl# vOci-J xx i— •—

t #hq ro^-too x in -~.~o*• OLU CDZl— I— LU t— ftOO LU^w Z rO I— OUJ —I-HnO UJ_)•5J- OOLL**'-* 2<»-< -M- vCCQ ZvO O O <500XctQt:O 00_JK- UJ")OtJ "TU —i u0 « C U.I CDOlli*-" vD LU 0<»-h

i I <I<tK- 7 m •(— f-lLLU.rj * Ol) XI— O r? l)U—'-2 L>•« ,_hgooo_j_»_ luool #z2z >-j7'h-< «-• 2 —irouj z^ h'UZO-XSWO -K-UJk-O -JUJ Z Z 3T LULUlU«-«I t-UUJii- -Tj>-iC:Q->-« UJ LUO » X ZIUJwh UJ (V TITjJh Xll.O# 00— <u_o0o0o0uj -K-l—X> Ot-OOCQH-i x UJ (_h-I—wV H3C1

# ^ni- z«i-<t>: •«• h-_i idz i— ^h- w«—ro«^ —»— h-o•J^ cDOUJ>-ot— OD -K-fv—Z r^ u.rH<oo I ujo r\iZoOa;a:>-(f-H^-<r\jrNjrvjrxiZLjjC>*• _J UJ<rO»-<aQ oo }( 20 O "-• OOH- «-i>J" rvjQO —XIOQI wwr-iww-iH.nJO 1

K- <UjOO<IOJ— UJUJLUOO -^ LU »-<vO'^ + -Ii- I*- UJ O0 oO I— _J UJ v0 _J LU vO CT>

w- "-xa: cco>otx COO LULU-M•K- lu k-<tOoou_j uj -j*. —1 a. or -'O'-* or —<rvaii^JOcx. ctoocr. cti r-~<ct:cx:>-ti-HC\j'—ihO^-<•—<Ocr.0u># q.u.zi2q:iv)zi « z h- z oc z>h-z -< t- y-» ooo'-'t-i— uji— H-.H-.t~ # K- h- c_i— t— y~y- oox k-i— i—i— k-h- t—Vr -}}• LL LUOUJ U_ OUJUJU-UJUJ OUJU- LUUJLL LULUOUJUJO UJ

* K —i —IC-O-J 1—1 U I I'—• —

I OZ—< _J _J— _J_JO —J —IO —I

O —< ru ro <f inJIUIJS^XJSiTIO 00 00UlLUUJLULUUJLLIUJLUUJLLiajUJUJvO vO sD UO vO Oaict-ctlcco^ccccct-ccairtc: cat'-O O O O O O

00UJ_)

— a:— O""

— GiUJ LU

I >-—« 2

vD—l

Coot— CD

in <r i

»- + o I

OOOfNI—<-^ ii ii :

ii n —iroi00->O_O_<

a: a: i— i—OOUiUJU-U--J—I

<Cll-H

<aUJ O._lO UJ2- T<r h-

a: aO 2ct:

UJ UJ\— _i2: o-< z:

ooLU o-J a:<r Lus>oi-0002

LUOX in

UJI—h-Xot— UJuj c£JOO

O UJcri—•J-'-'OO 00OOCL \— C£<S>—>O II ST—IS II II II

OUJ UJ"-1—IC\I

CDCC u. '-* tt >SSZ> >OOh- K— I— J—OUJ U. UJLUU1O _J •—

i _J -J _J

«3H-XooH-LU

_J00 _lUJ<

ID*-oO

llq:OQ.

LUt-_i<r

^i—<T

00OZ—<0_J>~'

tnccLUUI_ii-

i^s:ovOO

ofCOO »• OtMv0OO "iX

Qo- ~a>Lnf— ^-<

crO o0^ r-l> |

o»—

O<r—

oo00<s: oo

LULLOO-"

00a'LUOy~mzri-UJO(_)LU

<M(\!CO

_JLU_Ii i I

•—»»—lr—

h-XUJUJ

J —12

ooo!2LU

LUI— _JX ox<

LUh- O*— Of-*^- </>—7" <X. •> nO> o:>•-hujci ^+ ^o+ +^hsrO"-' lu— lu — z—a<v->q: x-< t^o ujchLU_JU_vCh-5: H-LU »• X •'-Ofh-Of— •> x»-< •— .—••—

• II

uuz^o-nOo^cMH-srcr* s: •*—0>-<>-ihi.w05: —'0(\i«——<crT •—

-.^o —« :> vo£ :> + - +-irsr^r-iLU ii olus ii o ii c^voa: h w •• n o 5-s: n 11 11 11 11 11

00 11 ujujuj 11 c_0>-i O 11 —* 11 —"ww 11 Qr-t 11 O'-i 11 Olulu—4CMro>d-Ln^a cCccccCl OO OO 0>>a. GO— Da! o:ot»-<i-H»-Hi—ii-<i—1

I— Of »— OfO i—Q l— > I-Xi— a. I— l— f— H-l— K-XI— rt i— h-x I— I— h-f-t— h-LULU OU-UJOU_U.UJOU_UJUJLULUUJUJOU_LUUJUJ ujluujujujuj2T—I LL^JO'-w_JC5i-<_I_J_I-JZ_JLLhh_i_j? I I ( —I ( —

LULUXO0I—

UILULU

MlSLV-cC ~UJ ccl-LULUXvOOt-^i-lfM—^

!>S:5-_JI

a- * tt

(MfMCNJI I I

t—,MM

00ovOo

otuon2

— 1/) O0ff) LU I/)- \- 2T— < s:uj ^r t

t >-< . o— Q•—i CL o"-"(NJOvjO z~V.^O olu.-»—.0 _l— v+LA s•$$ t—<l—it— H-(\J | | CC <I

i vor-uj _J<—•(—!—1> ^•»

I-*—»-2 O•-* + +o O O X-<*— vj-m(_KOC\J.—

s c\Ji—1>—• »•

UJ >—1 1—< i-<OC- •-'OQ.LLCOii n ii s: 11 O II II O II - —<

f-coouj,-* 00—• O 2tHWMO. 1Xco>-. Q-aa>-<t— H-a:

3 ID ZZDKHh 1

— OOf— |— CO f_ ,_(-( |—

UJUJLU IJJOUJUJOUJQCQiUJ—I—l-J _j cd _j _jo _i a. n. a:

r\i m-^ —

vO vOo o

K-•«•

*H-.y.

# * *- *- *- # * tt »•«• tt «•«•« «• 8

ni-jcZIH

OOt—« i—

i LU1-tuXUThUJCOUJU-e^XOLUf—t- X•-•a<

UJLUOXLUUh-COO

<ItOCQZUJ o*L\±}>—

r*l— ZLU -.>-'

hl-JUJ_ll )

o_io<or^-oz:oo<i

UJUJ <ZLLX•-•0t—Oco ••

OUJ—a£_joCOt_>IOc£—</)-•

oo_J LU<xo>

<w>|— UJUJ COcull coWOO

UJonZ<OLUI/}

LU_l —

CO<r >-•-• Oa: o< cc

c"5 OZ•-< <l3: XO to_J •

• _j .

ooO •

LULL>—i oOUJ •»-OX oCD!—

*- # # -tf- # * *- #-

LLI UJU. UJ LU LU LUIULUccccccccccvccccccc

*#* *~*

* <— ^» 0-% •-»

•K- (V «—

« »—

ro a: COtt -7 «— cc* «— >— X wM- z «-* CO •^ COH- —

«»» •z.

-X- CO f<~> 1—

CO# H- -0 K- CO K->-*- —

V *— •«• ^~<I* ~ CO —

*^cc-k- CC —» C<cc# ^— —- ct —

<:« •K- X >— O•tt «— **^ ^-^ O •»*

LU-& z ^«. CO «_» COO-K- M a: n Zo-s:- CO •~* •—

+ •-» CO *—

•—<Jf- —

•w •^ + V.O-tt —

CO .— *-» *-»

—.cm Q£ CrO a CO

>->- -J-* «v -O ^-- CCQO # » ^ »-. X w

f-i(\jroo o# co «—

Z «— z.COCO z*- CM l-H CO *—i

>->- <*- —) CO COOOLL.LL 5:- «• -X- -»• vd- *0000 uj-?:- •« ~* »-» O * <^coco Q* •a> ~~. »• r^- ««

00 O-i;- r-H cc CC —

U.UL.UJUJ 1—

M w w cc wMOC» 1-1* r^- O X Z wcCcc H-ifr >w> «a> •»• LU ^«

J-ZZLL'UJ 1— <- CO z Z X *M^ zOOOcooo <>! z fc—

1— CO >—

O^i->COCC —I* UJ CO CO COcOt-H-OO H- X * i 1 1

<3<X n* t— —

^» CM —

•«• --~

U.7ZI-I- »—

^. 1—

.-. O «» LU ^H «—.

OhhxI 5T* CCO -5 O h- O »^ q:

JJOO *-"* *m* w —

O w ror<-i •—

•-«

<1C )L)HM -;;- couj cr> n X —i—3 *•» •^ XXluluulilu X-tt 1 M 2 _ + 1 C\ 1 ^>. co .—

CO—OCOII LU-iS- —» z: UJ z CM CM t—

—1 CCZ.

o# o^« II -H O Xcvi^-i -5-5C »-^ CO 1—

II »-H

z-k- •— r—

r-M sj-r-ICO v±-lh-~5CO v-J- —\ li i 1 *—

CO •4--H 4- — CO•—•-;<• u_ co -> t— a --1O0 -MOO. i -MOO — ^-—

JLO—'O Q. co vO—• »• 11 II — II II 1II II II 1II O II U_ II II II It (\J ,_«,-.

1 II II II 1 1 O II II —> II

QiOQ-Oa. • )! CM "H^ (NJCsJfM rO—)<\l <Ni 1 II t\l—iC\ 1 [a—— 11 CM2 CM r-i CM CO vC «— t—

• };- —J ~D«-h _J -5 Q. CD "O O. Q. CO ~> r\i -0 Q_ 0. co —> CO CO 1-1

!—•

ja q-coq: 3 —JO.OQQII to* CO O _l CO O

*»- h- 1

t— (_ h- CO (- l-l— COH h-H-f-COJ— 1— \-cc\- 1-H-l— COt—t— t—H-K- LUUJU_UJUjLUOUJLULUOUJU- LULULUOLUUJU-/OUJLLUJUJLUOLUUJLUUJ# —I —i—> -J_J_JtO_J_J_JO_j -- _l _l _JO —J -J -J U- Jw.JJJtDU _J -J_J

* -M- it # # *I—

r-j m vj"

2 5 2:5:5:2:5.2:0 OUJtUUJLLJLUUjUJLUr-- r^ t*- r^- r^-

ctctocctaictctQiO O

h-ON-O2:UJvOIO -5

h-f>- -H-

>d- Ooz -W-

ir\ «-» LU CMo or. l-X 1

r- ^ -Jl- r-

o CD O1 '-O —>

LU Q- vOt™ LUOXi-i it ->o II

fMO I vO LU-»^vOII OIL. II -3r-4«— vO I

->ro ii r-*~. it oo-j || «M2a. qd (nj a. l u ~5 it3— ~5 lu a:

ID_j <LU f-ZD(_^ I— I— I— hhXhLUOLLLULUUJLLLLLULULULU_J CD -< -J -J —1 <-"m —I _l2 C£

in •01s- 00o ooot*- r^-r-r-O ooo

APPENDIX B SAMPLE PROGRAM RUN

ENTER DAY20

ENTER MONTH6

ENTER YEAR75

ENTER ALTITJDE (FT MSL)60

EMTER COURSE (D.MS)270

ENTER SPEED (KNOTS TRUE)5

ENTER ASSUMED LAT (N/S) +/-(D.MS)40

ENTER ASSUMED LONG(E/W) +/-(D.MS)15.2224

ENTER NUMBER OF BODIES THIS FIX3

ENTER STAR/B3DY NUMBER1

ENTER GMT 3 = OBS (H.MS).56

GMT (HRS)= .9444+3ENTER HS (D.MS)37.04

ENTER IC (D.MS)

HA= 36.5709GHA OF BODr= 230.043'DEC OF BODY ( D.MMSS)ZN OF BODY (D.MMSS)DISTANCE TOWARD BODY (NM)BASED ON H: (D.MMSS)

28.572883.42 3 1

8.?5D7136.4854

E^TE46

GMTENTE48.

GHADECZNDISTBASE

R STAR/33DY NUMBER

R GMT DF OBS (H.MS)

(HRS)= 1

R HS (D.MS)39R IC (D.MS)

48.3209OF RODf= 19.1425OF BODY (D.MMSS)F BODY (D.MMSS)ANCE TOWARD BDDY (NM)D ON HC (D.MMSS)

12.3+36237.46 230.930349.D3D3

ENT1 .

GMTENT42

HA =GHADECZNDISBAS

ER STAR/BODY NUMBER

ER GMT 3- OBS (H.MS)04(HRS) 1.07778

ER HS (D.MS).11ER IC (D.MS)

42.0409OF BODY= 61.123'+OF BDDY ( D.MMSS)

OF BODY ( D.MMSS )

TANCl I DWARD BODY ( MM

ED ON HZ ( D.MMSS)

74.1533339„ 15314. 4 + 8341.4942

ENTER SHOT DF DESIRED FIX TIME2

CORRECTED DISTANCE TOWARD BODY 1

7.92129BASED ON CORRECTED HO (D.MMSS)36.4834

CORRECTED DISTANCE TOWARD 30DY 2-30.9003BASED ON CORRECTED HO (D.MMSS)49.0303

CORRECTED DISTANCE TOWARD BODY 314.3302

BASED ON CORRECTED HO (D.MMSS)42.0402

FIX (LAT/LONG D.MMSS)=40.3313 15.3354

TIME OF FIX ( ,DAY) =

PROGRAM COMPLETE. 3 41 S 5 66

BIBLIOGRAPHY

1. Weir, Joseph, Interactive Information Systems , BellTelephone Laboratories . Hayden Book Co., Inc. , RochellePark, New Jersey, 1974.

2. Peebles, Richard W. , "Design Considerations for DistributedData Access Systems," Technical Report, University ofPennsylvania

3. Electronics , "C-LAD Steers Ship by Computer," April 18,1974, p. 31.

4. Electronics , "Low Cost LORAN, Transit Developed,"Sept. 11, 1972, p. 32.

5. Rudnick, Steve, "Microprocessors Unmasked," DigitalDesign, June 1974, Benwill Publishing Corp.

6. Wolf, Helmut F., "Microcomputers-Revolution or Evolution,"Digital Design , June 1974, Benwill Publishing Corp.

7. Dejka, W. J., "Navy Opportunities for Microcomputers,"Nav Sea Journal , Jan 1975, Published by Naval SeaSystems Command.

8. Nuese, Carl and Schneider, Dr. Alan, "Celestial NavigationUsing a Hand-held Programmable Calculator," NELC TechnicalNote 2873, 22 Jan 1975 (A tentative and unpublished report)

9. Fox, E. J.s"Proceedings of the Symposium on Computer

Communications Networks and Teletraf fic , " PolytechnicInstitute of Brooklyn, C. R. 1972.

10. The American Ephemeris and Nautical Almanac publishedannually in Washington by the Naval Observatory and inLondon by Her Majesty's Nautical Almanac Office under thetitle The Astronomical Ephemeris , viii, 568 pages.

Explanatory Supplement to the Astronomical Ephemerisprepared jointly by the Nautical Almanac Offices of th

United Kingdom and the United States of America.

12. Intel Corporation, "A Guide to PLM Programming," Rev. 1,Santa Clara, CA, 1973.

13. The Nautical Almanac published annually in Washingtonby the United States Naval Observatory and in Londonby Her Majesty's Stationery Office, xxxvi, A4 , 276 pages.

14. Fricke, W. , and Lederle, T., Apparent Places cfFundamental Stars 1975, Heidelberg, AstronomischesRechen- Institut , 1973, xiiv, 510 pages.

15. Digital Design , Dec 1974, Benwill Publishing Corp.,p. 8.

INITIAL DISTRIBUTION LIST

No. Copies

1. Defense Documentation Center 2

Cameron StationAlexandria, Virginia 22314

2. Library, Code 0212 2

Naval Postgraduate SchoolMonterey, California 93940

3. Chairman, Computer Science Group, Code 72 1

Naval Postgraduate SchoolMonterey, California 93940

4. Asst Professor V. M. Powers, Code 72 Pw 3

Computer Science GroupNaval Postgraduate SchoolMonterey, California 93940

5. Asst Professor G. A. Kildall, Code 72 Kd 1

6. LTJG G. M. Raetz, Code 72 Rz 1

7. LT Jon P. Moore, USN 1

771 Ladysmith DriveEl Cajon, California 92020

8. LT David R. Rainsberger, USN 1

113 Coman StreetClinton, Michigan 49236

1 4 FEB Tf• • • ~ ~ ~

2 FEB79

?U2522 U 9

Thesis

M802c.2

161025

MooreThe design of a

celestial navigation

microcomputer with

thoughts on an integra-

ted information distri-

bution system.

14 FEB 77 JM, 12-78

2 FEB 79

? U 2 5 2

2 4 4 2

161025ThesisM802 Moorec.2 The design of a

celestial navigationmicrocomputer withthoughts on an integra-ted information distri-

bution system.

thesM802

The design of a celestial navigation mic

3 2768 002 04763 1

DUDLEY KNOX LIBRARY

the design of a celestial navigation microcomputer with

Documents

navigation and devices

the celestial sphere in ancient egypt - ankhonline

navigation rules

interpreting celestial simulacra in archaeology

benjamin banneker and celestial navigation

cognitive consequences of microcomputer-based laboratories:...

celestial sphere numericals 2009

the ionosphere, radio navigation, and global navigation...

the role of microcomputer clubs in the education of ... -...

the celestial pebble of san jose, california

a microcomputer-based system for quantitative petrographic...

celestial symbols in european prehistoric art

pic series microcomputer data manual - bitsavers.org

an analysis of the development of celestial navigation -...

a microcomputer solution to maneuvering board problems

interactive volume navigation

celestial newton stone

microcomputer system design - umm al-qura university

post-newtonian celestial dynamics in cosmology: field...

an overview of major terrestrial, celestial, and temporal