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NBS MONOGRAPH 60

iNaiionai Bureau oi Standir^t

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100

Influence of a Sector Ground Screen

1

On the Field of a Vertical Antenna

^/^^^^^^\\

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
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Documents, U.S. Government Printing Office, Washington 25, D.C.
UNITED STATES DEPARTMENT OF COMMERCE • Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS • A. V. Astin, Director

Influence of a Sector Ground Screen

on the Field of a Vertical Antenna

James R. Wait and Lillie C. Walters

Central Radio Propagation Laboratory

National Bureau of Standards

Boulder, Colorado

National Bureau of Standards Monograph 60

Issued April 15, 1963

For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. - Price 25 cents
Library of Congress Catalogue Card Number: 63-60051
Contents

Page

1. Introduction 1 2. Formulation and description of problem 1 3. The circular screen 2

4. The sector screen 3

5. Final remarks 5

6. Appendix 6

6.1. Evaluation of the Fresnel integral 6

6.2. Evaluation of by Gaussian quadrature 6

7. References 6

7.1. Additional references 7 Figures 7 Tables 12

in

Influence of a Sector Ground Screen on the Field of a Vertic 1

I Antenna

i

I James R. Wait and Lillie C. Walters

The field of a short vertical antenna on a homogeneous ground is shown to be modified

by the presence of a metallic screen. The screen is taken in the form of a circular disk and a

concentric sector. The modification of the field is expressed in the form of surface integrals over the disk and the sector. Extensive numerical results for these basic integrals are given

and a number of applications are illustrated.

1. Introduction

The influence of the ground on the fields of antennas has been discussed sporadically in the

literature for many 3'ears. In most propagation

calculations it is assumed that the transmitting

' antenna has a fixed dipole moment and the ground

j is taken to be a perfect conductor or possibly a homogeneous imperfectly conducting half space.

I In practice, however, some kind of ground system

: is used. Usually this takes the form of a metal

screen or radial wire system which is on the

I surface of the ground or ma}' be buried slightly

beneath the surface. The design of such systems

has been typically empirical. Apparently, the

first analytical approach was carried out by Brown

^ et al. [1].^ Later works [2, 3] have dealt mainl}'

with the influence of the ground system on the

impedance. In most cases it has been assumed

Mthat the radiated field for a given current on the

antenna was not appreciably affected by the pres- ence of the ground screen. In fact, an approximate analytical method was given previously by

Wait and Pope [4] which is suitable for estimating

the dependence of the ground wave on the size of a

circular ground screen. Calculations [5] based on

this work supported the contention that a screen has only a small effect on the radiated field provided the radius of the screen is of the order of a wavelength or less. Very similar conclusions have

been arrived at by British workers [6, 7]. In this paper consideration is given to ground

screens which may be large in terms of a wavelength. Since the theory has been treated quite

generally in a previous paper [8], attention wUl be

focused here on the numerical calculations and the

predicted performance.

2. Formulation and Description of Problem

The situation is described as follows. A vertical

electric dipole is located on a flat homogeneous

ground of conductivity a and dielectric constant e. llThe vertical electric field at a distance Rq and

jelevation angle i^o is given as follows

C0S2 rl^oWiRo, Z) (1)

where

Mo=47rX10-^

w= angular frequency

/= effective height of transmitting dipole

/= current at terminals of transmitting dipole

k= 27r/wavelength.

[n the above, W(Ro, Z) is a complex quantity

vhich is a function of the surface impedance Z of

[he ground. Over a perfectly conducting ground,

V would approach unity. In the case of finite

' This work was sponsored by the Electronics Research Directorate of the

ur Force Cambridge Research Laboratories, Office of Aero-Space Research

i-^i'AF), Bedford, Mass., under contract PRO-61-568.

• Figures in brackets indicate tlie literature references on page 6.

ground conductivity [9] WiRo,Z)sl-iiTrpoy'^e-^o Qj-ic (iwl'^) (2)

where

Wo=[l +{r!o/Z) sin i^ofpo,

ikRo

Poland

(3a)

(3b) =1207r.

This result is valid for k i?o» 1 and |Z/7?o|^<<lIf Z=(-i^YTl-4^cos^4" (4)

the expression for W coincides exactly with the

result given by Norton [10] for the same situation. It may be noted that this value of Z is exactly

equal to the ratio of the tangential electric and

magnetic fields for a vertically polarized plane wave incident at an angle 90°— on the homogeneous flat ground.

1
In applications to practical communication

problems it is very convenient to split off the

surface wave portion Ws by writing

W=Wr+W,

where, by definition,

Wr=[l-\-RM]/2

is the radiation or space wave field, and

sin ^0—-Z/rjo

(5)

sin ^o+-Z/7?o

(6)

is the Fresnel reflection coefficient. This decomposition of the total field into space and surface wave was first made by Norton [10] and it is a con- venient procedure in radio engineering since by

definition, is the radiation pattern of the an- tenna in the presence of the ground plane. It may be the dominant term in many cases of practical interest although as \po approaches zero Wr

actually vanishes. Methods for estimating the

relative importance of are given in the papers

by Norton [10]. The central task in the present paper is to in- dicate how a wire mesh or a similar metal screen

lying on the ground will modify the field at the

receiving antenna. The surface impedance is as- sumed to be modified to Z' over the area of the

screen, but remains the same outside the screen. The field in the presence of the screen is then

written

In a previous paper [8] an integral equation for W was obtained by an application of the Lorent^

reciprocity theorem. Although it would be possible to solve this equation directly using a digital

computer it was indicated that a first order itera- tion was satisfactory. In this case it was found

that

W'(R,Z,Z')^WiR,Z) [1 + ^] (8) where is the fractional change of the field due to the presence of the screen. Within the approximations stated, the factor can be regarded as the modification of the effective height of the

transmitting antenna, since it influences Wr and

Ws to the same extent. Before proceeding further it is convenient to introduce a polar coordinate system (p, </>) cen- tered at the source dipole as indicated in figure 1. Thus an element of area of the ground plane is p d<j> dp.

From the analysis in the previous paper by

Wait [8], it was shown that

ik

27r cos ^,

- C C g-ikpg-mR-Rg) ^\

oJJ \ Vo /

X (cos <p)d<t)dp. (9)

where

and

E'-^^^e-^'^^o cos' hW'iRo, Z, Z'), (7)

R =[p^j^(PJ^h?-2pd cos 4>y'^

R,={d'-\-h^y'\ h^Ro sin

d=Ro cos Nowhere W is an unknown complex quantity which

is now a function of Z' in addition to Ro and Z. The quantity W reduces to W if Z' =Z:

The integral may be evaluated when the shape

of the ground screen is specified. In the following,

attention wUl be confined to screens which are in

the form of a sector. A special case is a circular screen and this is considered first.

3. The Circular Screen

Over the range 0<Cp<Cc^ it is assumed that the

surface impedence is Z'=Za. Beyond the screen

(i.e., p^a), Z'=Z. Furthermore, it is assumed

that the receiving antenna is in the far field such

that

" cos ^(

dp, (11)

R—Ro^ — p cos <j) cos <Po. Thus

ik

27r cos J P = 0 J <t>= -TT

If Z'a does not depend on <^ the integration with

respect to <i> may be readily carried out to give

where Ji is the Bessel function of the first type of

order one. When dealing with large screens the

argument kp cos i/'o can be regarded as a large

quantity over the major portions of the integrand.

Thus, JI may be replaced by the first term of its asymptotic expansion. Therefore,

\27r v27r cos^ lAo/ \po/ Jo \ Vo )

g -<Z(1-C08 fo) X(l-'ie-2««<'« ^0) — dx. (12)

2
When Z'a is essentially constant over the range of

integration, fla can be expressed in terms of

Fresnel integrals. After a change of variable it readily follow that

where

^ (2cosVo)"'[sin(./'o/2) Jo

exp [-i(7r/2)i^]rf<-

(4te/n-l'/^ 8ln (^.0/2)

(«a/ir)'/2 cos (i^o/2) cos (i/'o/2) j:J 0

exp [-i{Tr/2)t^]dt~j- (13a)

As ^0 approaches zero the above equation reduces

to

^^'K-^J l'-\ika) Jo

exp [-i(7r/2)/2](^<J (13b)

and, if ^or/>>>l, this may be approximated by

\Ska/ 1

(14)

It is interesting to note that, if the integral in

(12) is evaluated by a stationary phase method,

the second Fresnel integral in the square bracket

term of (13a) is not present. This would corre- spond to the approximation usually employed in the practical theories of mixed-path ground wave

propagation. The value of G corresponding to

this situation is denoted G{1).

Numerical values of the integrals G and G{1)

are given in table 1. The values of ka (denoted

KA) take the values 5, 10, 20, 30, and 100, while

^0 (denoted PSI) runs from 0° to 45°. It is immediately evident that, for small values of i/'o (i.e., near grazing), the integrals G and G{1) are not significantly different. As will be clear from

the following section the integral 6^(1 ) would

correspond physically to the situation where the

^screen is semicircular in shape (i.e., </> extends from

; ir/2 to — x/2 only).

To illustrate the application of the results in table 1, values of the complex quantity 1 + fla have been computed for several values of the

surface impedances of the ground plane,

this purpose it is convenient to write

z-z: 1

Vo N

For

(15)

where A'^ and /3 are real. If the ground screen is a metal sheet Z'a<^<CZ and, consequently, Ne~^^

could be regarded as the complex refractive index

of the ground itself. However, in general, and

/3 have a more general meaning as defined by (15).

-Taking A''=3 and ^=0°, the amplitude and phase

of l+i2„ are shown plotted in figures 2a and 2b,

respectively, as a function of ipo for various values

of ka. It is emphasized that such curves should

not be regarded as radiation patterns but rather

as modifications of the effective height of the

transmitting antenna due to the ground screen.

It is apparent that for the low angles involved in HF communication the ground screen will increase

the effective height of the transmitting antenna

by a significant amount. The value of given

in this example corresponds to a dielectric constant of 3^ or 9 which is typical of very dry ground.

The effect of choosing a large value of is shown

in figures 3a and 3b where A^= 10 and (8 =0°. The

curves are very similar in shape but the overall

effectiveness of the ground screen is reduced

somewhat.

The value of (3, as defined by (15), determines

the phase of the complex refractive index of the

ground. For a very dry or nonconducting ground

(8 is zero as indicated in figures 2a to 3b. However,

when the conductivity becomes important |3 may

be greater than zero. In fact, for a highly con- ducting ground where displacement currents are

negligible, (3 may approach 45°. To illustrate the

influence of finite ^, the amplitude and phase of

1+fia are shown in figures 4a and 4b for ka =20,

N=10, and various values of /3 between 0° and

45°. It is evident from these curves that the

presence of the conduction currents tends to diminish the amplitude but it does increase the

phase.

It is becoming apparent that at the lower fre- quencies and highly conducting ground the pres- ence of the ground screen has a small effect on the

total field (for a given strength // of the source

dipole). To illustrate this point, the amplitude

and phase of 1 + fla are shown in figures 5a and 5b

for ^a =20 and /3=45° for A^=10 and 30. The

modification of the effective height of the antenna

is less than 2 db and here the radius of the screen

is almost 3 wavelengths.

4. The Sector Screen

It is clear from the previous results that a large

circular ground screen will, indeed, improve the

low angle radiation from a ground-based vertical antenna. However, one might ask if any portions

of the circular ground screen could be removed

without materially aft'ecting the performance of the system. This is certainly a valid question.

In the first place it is known [5] that the impedance

of the antenna is not affected by anything beyond

about one-half wavelength from the antenna.

Therefore, to throw some light on the question

posed above, the ground screen is taken to be in

the form of a sector extending from p=a to p =b from the base of the transmitting antenna. From

3
p=0 out to p=a the screen is circular in shape.

The situation is illustrated in figure 6. The

surface impedance over the area of the sector is

Zt,. In terms of the polar coordinate system

(p, the area of the sector is defined by —Ai<

0<^A2 and a<ip'Cb.

It is convenient to express the factor Q. as the

simi of two parts in the manner

(16)

where Oa is the contribution from the circular screen of radius a and fi^ is the contribution from

the sector which extends from a to h. The

portion fl;, can be written

fit 2ir cos i/'o r r , J P=a J <t> = -A^

— ikp

^1+-^^ cos COS ^OXCOS .^(^L^)d^p (17)

where the receiving antenna is assumed to be in

the plane <^=0. The integral for ^„ given above

is sufficiently general to determine the effect of

the sector as a function of elevation and azimuth

angle. Actually, the integral is analogous to (10)

for the circular screen where the limits of <t> extend

from — IT to TT. As before, only first-order phase

terms are retained so that the receiving antenna

must be in the far field.^ The extension to the

near-field case has been considered previously by

Wait [8]. In actual communication circuits the

receiving antenna would always be in the far field. To evaluate the integral in (17) it is convenient

to use the approximation

cos 4>=\—-

for the exponent in the integrand while, in the

integrand, cos <^> is replaced by unity. This is valid since the principal contributions correspond

to small values of 4>. An interesting check on

this statement is given below.

Following the procedure used in the previous

section, a dimensionless function Gt, is introduced

by setting

^6=

Z-Zl

(18)

The integral for may now be written in the

form

Gh=-, -

f

kt> „-ix(l -cos ^o)

where

1/2

F{x)dx (19)

F{x)=-—. exp -i^t'' \dt.

^ "^-Ailci/^) cos ,^oll/2 L ^ J

' This far-field condition can be written

The Fresnel integral F{x) is normalized so that

lim F{x) = \, provided Ai and A2 are both posiJ->co tive. In this limiting case the sector is behaving

essentially as a circular screen. For example, one may note that

=G,{kh)-G,{ka)

where Gi is the integral described by omitting the

second term of (13a).

An interesting special case of (19) is when

i/'o—>0 and Zj can be regarded as a constant. Then

F{x) G

/ 1 r -1/2 dx. (20)

After an integration by parts it readily follows

that

Gb

. /2kbfy{Fm

exp i~ikb^i/2) . exp (--i^6Af/2)

2Ai

-ikaAl/2)

2A,

]

(21)

f

2 WMrexp(-^^

\TrkbJ L 2A2

^expi-^ka^yjy

The integral G;, has been evaluated for a range

of values of kb. To simplify the situation, the

lower limit ka is fixed at 5 and Ai = A2 = A. The

numerical results for Gi, [denoted G(B)] are given

in tables 2 to 8 for A [DELTA] ranging from 5° to 60°. Within each table kb [KB] varies from 10 to 100 and ^0 [PSI] varies from 0° to 45°. As a check on the numerical work, G^ for ^o=0

was calculated using both (19) and (21). Also, it may be noted that

Gbm~\ --GAkb)-G,{b)

where the values of Gi {x) are listed in table 1 and

where x is to be identified with KA.

To illustrate the effect of a finite value of A, some typical cases are shown in figures 7a and 7b

where the amplitude and phase of G^ are plotted

as a function of ^0 for ka =5, ^6=40, and various

values of A. It appears that for these conditions

the total sector angle 2A need not be greater than

about 50° in order to be fully effective. In order to demonstrate the effect of the sector on the total field it is convenient to consider both

Z'a and Z'ft small compared with Z. Thus

z-z:

Vo Vo Z 1

Vo N

where Ne is the complex refractive index of the

4
/

ground. Consequently, it follows from (16), that

g<(/3-7r/4) {Ga-{-G},).

The amplitude of this quantity (expressed in db)

and the phase are shown in figures 8a and 8b for ka =b, H=40, /3=0, and A^=3. This would cor- respond to a relatively dry soil. It is certainly

evident here that considerable improvement re- sults from the presence of the sector. The cor- responding set of curves shown in figures 9a and

9b are for a highly conducting soil characterized

by A^=10 and ^=45°. The sector screen here has

a negligible effect on the performance of the sys- tem. In fact, there is even a slight degradation

for the very low grazing angles.

The marked improvement by using a large

sector screen on a dry ground is indicated in

figure 10. Here ka=b, H=200, iV=3, and |8=0.

At low angles the gain is greater than 12 db even

with a total sector angle, 2A, of 20°. In the preceding discussion it has been tacitly

assumed that the receiving antenna is located in

the vertical plane which bisects the sector. Normally, this would be the optimum location and

for a fixed communication link it would be considered good practice to orient the sector toward

the receiving antenna. However, there may be

certain applications where the receiving antenna

is located off the center line. The formulas given

above are actually valid for this case since Ai and

A2 may take any positive or negative value. However, rather than computing directly from the

general formulas, it is desirable to establish some

simple identities which enable the results in tables 2 to 8 to be used.

It may be readily verified that Gi,{Ai, A2),

defined by (18), has the following property

as

(7»(A„A2) =

6',(A,, A,) +^ft(A2, A,)_GM+G,{A2)

Numerical values of Gt,{A, A) or G^i^) for various

positive values of A are given in tables 2 to 8

inclusive. If negative values of A are encountered

it is useful to note that

G,{A)=-G,{-A).

With this information it is a simple matter to compute (1+fl) as a function of I the azimuth

angle h which is defined by

Thus

1 + fia+fift^l-l6=(A2-A,)/2.

z-z:

z-zi

no e-'"'G{Au A2) (22)

which is an obvious generalization of (18).

To illustrate the azimuthal variation of the

field when using a sector it is again desirable to write z-z:z-z'z\

no Then again denoting the total width of the sector by 2A, the amplitudes of l-f-Qa +flj are shown in

figures 11 and 12 for N=3, /3 =0, ka^5, A =20°,

and various values of ^0 from 0° to 25°. In

figure 11, kb=4:0 whereas in figure 12, ^6 =200.

As expected, the maximum response corresponds

to small values of 5. In fact, as 8 increases the

response decreases quite significantly for the

larger sector.

5. Final Remarks

In the present study, the electrical properties

of the ground are assumed to be characterized

by a surface impedance which is a (complex)

constant Z outside a surface S. Within S, the

impedance Z' is allowed to be variable. In the

case of a radial wire system emanating from Q, it

is appropriate to use formulas which have been

developed for the surface of a wire grid in the

interface of a conducting half space [11]. In

general these are complicated, but recently some

numerical results have been obtained which should

be useful in this problem.* At low radiofrequencies for moderately or well-conducting soils it

is a satisfactory approximation to regard the

surface Z' as the parallel combination of the

' Availal)le from Mrs. T. Larspn. Laboratory of Electromagnetic Theory

Technical University of Denmark, Copenhagen.

surface impedance Z^ of the equivalent grid and

the ground beneath. Thus

Z'i

z,z

'z+z.

wher(

Z^(^MocoM"^

(23)

(24)

and d is the spacing between the radial conductors

and c is the radius of the wires. Such a formula

is strictly valid only if (crMow)*(/<<l everywhere

within the ground system. If there are N radial

conductors, it can be seen that d can be replaced

by 2irp/N where N is usually of the order of 100.

5
6. Appendix

6.1. Evaluation of the Fresnel Integral

The integrals occurring in G (13a), (13b), and

F{x), (19) are of the type

j:

(25)

These Fresnel integrals were evaluated by the

method proposed by Boersma [12]. This method

is based on the r method of Lanczos [13]. The

Fresnel integral defined by Boersma is

(26)

The definition in (25) conforms to the one used by

Boersma [14] in eq (26) if

For values of the argument 0^a:^4 in (26), f(x)

is computed by a finite power series in x; for values

of the argument x^4, /(x) is approximated by a polynomial in 1/x. For 7? = 12, the power series in X vahd for 0 <x< 4 is

The power series in K valid for x^4 is

(27)

-^iS(c.+ «.)(*)" (28)

The numerical values of the coefficients a„, bn, c„, and d„ as developed by Boersma [14, 12] are given

in table 9. With these coefficients the Fresnel

integrals can be computed over the range 0 ^ x ^ <»

, in general, to eight decimal points. The subroutine used in evaluating the Fresnel integral was checked with the tables of Pearcy [15] and

those of Wijngaarden and Scheen [16]. The

former tables, using definition (26), are accurate

to six or seven digits depending on the size of the

argument while the latter, using definition (25), are accurate to five digits.

6.2. Evaluation of Gt, by Gaussian

Quadrature

With a procedure for evaluating the Fresnel

integral, the remaining problem was to compute

the integral in (19). The method used, Gaussian

quadrature, is described briefly below [17]. In quadrature methods a definite integral is approxunated by a weighted sum of particular

values of the ordinate with the abscissas properly

distributed in the limits of integration. Thus,

J'a fix)dx=j: Hjf{a,)+E„. (29)

The abscissas aj are roots of the Legendre polynomials, the weights Hj are functions of these

roots, and is the error term which can, in

general, be made arbitrarily small with increasing

n. The Gaussian roots and weights are tabulated

for various n for limits between —1 and 1 by

Davis and Rabinowitz [18], but other limits can be used by a change of variable as follows:

where

j^f(x)dx=^-^ ^g{y)dy,

h—a . b-{-a

y 2 ^ ' 2

(30)

Furthermore, in the Gaussian quadrature procedure, the integrand is approximated by a polynomial of (2n— 1) degree which has the same

ordinates as the function for n discrete abscissas.

To obtain accuracy for Gt, eq (19) was written

Gt,- [X

10 „ — — cos Fix)

V27rcos3/=^\/'o LJs Vx

-cos ^o' F{x)

dx

+

J 10 dx . yjx

+ r --'—•/•'f(x)^i

(31)

and Gaussian quadrature was used with 7i=16 in

eq (29) for each interval of 5 for kb. This work

was checked against (21) for ^o =0 and various

values of Ai and Ag. The answers agreed to the

five digits asked for in the results.

7. References

[1] G. H. Brown, R. F. Lewis, and J. Epstein, Ground

systems as a factor in antenna efficiency, Proc. IRE 25, 753-787 (June 1937).

[2] F. R. Abbott, Design of optimum buried R. F. ground

systems, Proc. IRE 40, 846-852 (July 1952).

[3] J. R. Wait and W. A. Pope, Input resistance of LF

unipole aerials, Wireless Engineer 32, 131-138

(May 1955). (In eq (9), 1/p should be \pj\)

[4] J. R. Wait and W. A. Pope, The characteristics of a

vertical antenna witlya radial conductor ground

system, Appl. Sci; Research [B] 4, 177-195 (1954).

[5] J. R. Wait, Effect of the ground screen on the field radiated from a monopole, IRE Trans, on Antennas and Propagation AP-4, 179-181 (April 1956).

[6] H. Page and G. D. Monteath, The vertical radiation patterns of medium wave broadcasting aerials, Proc. lEE 102, 279-297 (May 1955).

[7] G. D. Monteath, The effect of the ground constants, and of the earth system, on the performance of a

vertical medium wave aerial, Monograph No.

279R, Inst. Elect. Engrs. (London), pp. 1-15

(Jan. 1958). (This paper contains a valuable and

critical survey of previous work.)
[8] J. R. Wait, The theory of an antenna over an in- homogeneous ground plane, Proc. Symposium on

Electromagnetic Theory and Antennas, Copenhagen, June 1962. (To be published by Pergamon

Press.)

[9] J. R. Wait, Excitation of surface waves on conducting, stratified, dielectric-clad, and corrugated

surfaces, J. Research NBS 59, 365-377 (Dec. 1957)

(In eq (71) (p/w) should be (p/w)5; on page 376,

r2 is defined by r2 = ri + 2hC.)

[10] K. A. Norton, The propagation of radio waves over

the surface of the earth and in the upper atmosphere. Part I, Proc. IRE 24, 1367-1387 (Oct. 1936) ; Part II, Proc. IRE 25, 1203-1236 (Sept.

1937) . [11] J. R. Wait, On the theory of reflection from a wire

grid parallel to an interface between homogeneous

media, Part II, Appl. Sci. Research [B] 7, 355-360

(1959).

[12] J. Boersma, Computation of Fresnel integrals. Math.

of Computation 14, Nos. 69-72, 380 (1960).

[13] C. Lanczos, Applied analysis (Prentice Hall, Englewood Cliffs, N.J., 1956).

[14] J. Boersma, On a numerical method for computation

of Fresnel integrals. Math. Inst., Univ. of Groningen. Report TW2 (1960). (The derivation for

fix) and constants a„, 6„, c„, and d„ are given in this reference.)

[15] T. Pearcev, Table of the Fresnel integral (Cambridge

Univ. Press, 1956).

[16] Adrian van Wijngaardcn and W. L. Schcen, Table

of Fresnel integrals, Amsterdam, Nord-HoUandsche

Uitg, Mij (1949).

[17] F. Kopal, Numerical analysis (John Wiley & Sons,

Inc., New York, N.Y., 1955).

[18] P. Davis and P. Rabinowitz, Abscissas and weights

for Gaussian quadratures of high order, J. Research

NBS 56, 35-37 (Jan. 1956).

7.1 Additional References

T. Larsen, Numerical investigation of the equivalent

impedance of a wire grid parallel to the interface between two media, J. Research NBS 66D (Radio

Prop.) No. 1, pp. 7-14 (Jan.-Feb. 1962).

S. W. Maley and R. J. King, The impedance of a monopole antenna with a circular conducting-disk ground

system on the surface of a lossy half space, J. Research

NBS 65D (Radio Prop.) No. 2, pp. 183-188 (Mar.-

Apr. 1961). A. N. Smith and T. E. Devaney, Fields in electrically short ground systems: An experimental study, J. Research NBS 63D (Radio Prop.) No. 2, pp. 175-180

(Sept.-Oct. 1959).

J. R. Wait, Electromagnetic radiation from cylindrical structures (Pergamon Press, London and New York,

1959). (Includes a discussion of slot radiators on

wedges and half-planes.)

REC.

Figure 1. Vertical electric dipole located over a circular metal screen which, itself, is lying on a homogeneous

ground.

IFigure 2a. The amplitude of 1 + S2a as a function of with parameter ka for nonconducting ground illustrating the

effect of the circular screen of radius a.

i|The ordinate can be regarded as the modification of the effective heiglit of j*e monopole resulting from the pre.sence of the ground screen.] Figure 2b. The phase of l + fia as a function of \f/D with parameter ka for nonconducting ground.
6

5

4 -

3

-1 1 1 1 1

1

1 I r

I I

I I I L J L

0* 2' 10' I? 14* 16* I8' 20*

Figure 3a. The amplitude of l + ^a as a function of with parameber ka and nonconducting ground illustrating the

effect of large N.

Figure 4a. The amplitude of l + fia «s o function of

illustrating the effect of finite /8.

Figure 3b. The phase of 1 + 0^ as a function of with parameter ka and nonconducting ground illustrating the

effect of large N.

1 1 1 1 1 1 1 1 1

/3 =4S» — 35°

. 20f

10°

ka = 20

N = 10

1 1 1 1 1 1 1 1 1 ^

6" 8* 10* 12' 14* 16' 18* 20*

Figure 4b. The phase of l + fia as a function of illustrat- ing the effect of finite /3.

8
Figure 5a. The amplitude of ! + as a function of ypo for

highly conducting ground illustrating the effect of large N.

Figure 6. Vertical electric dipole located over a combination

circular-sector screen which, itself, is lying on a homogeneous ground.

Figure 7a. The amplitude of Gb as a function of <Po Hhistrating the effect of finite A. (These curves are for a

circular screen of radius a and a sector which extends from a to b).

N = 30

Figure 5b. The phase o/ 1 + 0^ as a function of ^ofor highly

conducting ground illustrating the effect of large N.

Figure 7b. The phase of Gb as a function of illusirating

the effect of finite A.

672009 O—€3 2
Figure 8a. The amplitude of l + Oa+fib as a function of \pa illustrating the effect of finite A for nonconducting ground.

(The ordinate can be regarded as the modification of the effective height of the monopole resulting from the presence of the ground screen whicli is in the combined forrr of a circular dislc and a sector.]

30' -

1

-

1

1

ka = 5 kb = 40 0 = 0°

N = 3

1 1 1 1 1 1

-

15° 10°

A=CO ^^^^^

1 1

1

1 1 1 1 1 1 12' 14° 16°

Figure 8b. The phase of l + a^ + Ut as a function of

illustrating the effect of finite A for nonconducting ground.

3.5

1 1 1 1 1 1 1 1 1

3

2.5

ka = 5 kb = 40 0=45°

N= 10 A=CO—

—

2

1.5 20;/ ^

1

0.5

0 A= 10°

-0.5 1 1 1 1 1 1

1 1 0' 2' 4' 6' g. 10. 12. 14. 16* 18' 2

FiGURE 9a. The amplitude of l + i2« + i2i, as a function of vi-o )or highbi conducting ground and' large N illustrating the

effect of finite A.

Figure 9b. The phase of l+li^ + S^b as a function of ^Po for highly conducting ground and large N illustrating the

effect of finite A.

10
11
Table 1

PSKDEGREES) G PHASE I DEGREE S ) G(l) PHASE ( 1 ) I DEGREES

)

0 1. 3887 too 7. 7144 tOl 1 .7841 too 9.0000 tOl

1 1.3891 00 7. 7123 tOl 1 .7845 too 8.9985 tOl

2 I. 3902 *00 7. 7058 tOl 1 .7858 too 8.9942 tOl

3 1. 3921 too 7. 6951 tOl 1 .7878 too 8.9869 tOl 1.3948 too 7. 6801 tOl 1 .7907 too 8.9767 tOl

5 1.3983 too 7. 6608 tOl 1 .7943 too 8.9637 tOl

7 l.'i076 too 7. 6092 tOl 1 .8041 too 8.9288 tOl

10 1.4277 too 7. 4998 tOl 1 .8251 too 8.8549 tOl

15 1.4790 too 7. 2324 tOl 1 .8769 too 8.6747 tOl

20 1.5561 too 6. 8612 tOl 1 .9507 too 8.4246 + 01 25 1.6649 too 6. 3934 tOl 2 .0477 too 8. 1070 tOl

30 1.8143 too 5. 8423 tOl 2 .1699 too 7.7256 + 01 35 2.0161 too 5. 2294 tOl 2 .3201 too 7.2852 + 01 40 2.2849 too 4. 5830 tOl 2.5027 too 6.7927 + 01

'.5 2.6379 too 3. 9340 tOl 2 .7242 too 6.2566 tOl

KA- 20 PSKDEGREES) G PHASE ( DEGREE S ) Gd) PHASE ( 1 ) I DEGRE ES ) 0 3.2088 too 8. 3070 + 01 3. 5682 + 00 9. 0000 + 01

1 3.2101 too 8. 3004 + 01 3. 5691 + 00 3. 9942 01

2 3.2139 too 8. 2807 + 01 3. 5715 + 00 8. 9767 + 01

3 3.2202 too 8. 2478 + 01 3. 5755 + 00 8. 9477 + 01

4 3.2289 + 00 8. 2018 + 01 3. 5809 + 00 8. 9070 + 01

5 3.2400 + 00 8. 1428 + 01 3. 5878 + 00 8. 8547 + 01

7 3.2690 + 00 7. 9862 + 01 3. 6050 + 00 8. 7153 + 01 10 3.3269 + 00 7. 6572 + 01 3. 6362 + 00 8. 4202 01

15 3.4450 + 00 6. 8737 + 01 3. 6817 + 00 7. 7036 tOl

20 3.5403 +00 5. 8358 + 01 3. 6697 + 00 6. 7258 tOl 25 3.5192 + 00 4. 5993 01 3. 5258 + 00 5. 5374 tOl

30 3.2728 + 00 3. 2262 + 01 3. 1724 + 00 4. 2577 tOl

35 2- 7678 + 00 1. 8491 + 01 2. 5782 + 00 3. 1891 + 01 40 2. 1566 + 00 9. 9872 + 00 1. 8936 + 00 3. 1532 + 01 45 1.8859 + 00 1. 8111 + 01 1. 7183 + 00 4. 9660 + 01

KA= 10 KA" 30 (DEGREES) G PHASE(OEGREES) G( 1 1 PHASE! 1) (DEGREES) PSKDEGREES) G PHASE(DEGREES) G( 1) PHASE( 1 ) (DEGREES)

0 2. 2347 too 7.9418 + 01 2 .5231 + 00 9.0000 + 01 0 3. 9966 + 00 8.5080 + 01 4. 3702 00 9. 0000 01

1 2. 2355 too 7.9386 + 01 2 .5237 + 00 8.9971 + 01 1 3. 9980 + 00 8.4983 + 01 4. 3712 + 00 8.9913 01

2 2. 2380 too 7.9292 + 01 2 .5254 + 00 8.9884 + 01 2 4. 0023 + 00 8.4690 + 01 4. 3741 + 00 8.9651 01

3 2. 2420 too 7.9136 + 01 2 .5283 + 00 8.9738 + 01 3 4. 0093 + 00 8.4202 + 01 4. 3789 + 00 8.9215 01

4 2. 2477 too 7.8917 + 01 2 .5323 + 00 8.9535 + 01 4 4. 0188 00 8.3S19 + 01 4. 3852 + 00 8. 8604 01

5 2. 2550 + 00 7.8637 + 01 2 .5374 00 8.9273 + 01 5 4. 0308 00 8.2642 01 4. 3927 + 00 8. 7820 01

7 2. 2743 + 00 7.7892 + 01 2 .5510 00 8.8576 + 01 7 4. 0604 + 00 8.0308 01 4. 4097 + 00 8. 5731 01

10 2. 3148 + 00 7.6322 + 01 2 .5791 + 00 8.7099 01 10 4. 1127 + 00 7.5377 + 01 4. 4306 + 00 8. 1311 + 01

15 2. 4102 + 00 7.2551 + 01 2 .6441 + 00 8. 3499 + 01 15 4. 1757 +00 6.3599 + 01 4. 3932 + 00 7.0654 + 01 20 2. 5325 + 00 6.7426 + 01 2 . 7254 + 00 7.8518 + 01 20 4. 0867 + 00 4.8299 + 01 4. 1355 + 00 5.6486 + 01 25 2. 6670 00 6. 1034 + 01 2 .8118 + 00 7.2242 + 01 25 3. 6387 + 00 3. 1535 + 01 3. 5046 + 00 4.0737 01 30 2. 7920 00 5.3391 + 01 2 .8880 + 00 6.4819 + 01 30 2. 7230 + 00 1.7663 + 01 2. 4964 + 00 2.9776 01 35 2. 8846 + 00 4.4417 + 01 2 .9340 00 5.6499 +01 35 1. 8352 +00 2.0147 + 01 1. 7175 + 00 4.2202 + 01 40 2.9320 + 00 3.4006 01 2 .9260 00 4.7700 + 01 40 2. 1422 + 00 3.4366 + 01 2. 1749 + 00 5. 7104 + 01 45 2. 9472 + 00 2.2358 01 2 .8406 + 00 3.9159 + 01 45 2. 8481 + 00 2.5315 + 01 2. 6110 + 00 4.4159 + 01

KA»100 PSKDEGREES) G PHASE ( DEGREE S ) G(l) PHASE ( 1 )( DEGREE S

)

0 7.6424 00 8. 7479 + 01 7. 9788 00 9. 0000 + 01

1 7.6455 + 00 8. 7177 + 01 7. 9806 00 8. 9709 + 01

2 7.6541 + 00 8. 6269 + 01 7. 9848 00 8. 8837 + 01

3 7.6652 + 00 8. 4757 + 01 7. 9886 + 00 8. 7383 + 01 4 7.6741 + 00 8.2539 + 01 7. 9870 + 00 8. 5350 + 01

5 7.6743 + 00 7. 9919 + 01 7. 9731 + 00 8. 2741 + 01

7 7.6137 + 00 7. 2692 + 01 7. 8714 + 00 7. 5832 + 01

10 7.2068 + 00 5. 7679 + 01 7. 3572 + 00 5. 1585 + 01

15 4.9918 + 00 2. 7524 + 01 4. 8443 + 00 3. 3696 + 01 20 2.5271 + 00 4. 0004 + 01 2. 5377 + 00 5. 2124 01 25 3.2011 +00 2. 8208 + 01 3. 0747 00 3. 9259 01 30 2.3910 + 00 3. 8703 + 01 2. 4284 00 5. 3722 + 01 35 2.0752 + 00 2. 5785 + 01 1. 9458 + 00 4. 4941 + 01 40 2.2996 + 00 1. 9230 +01 2. 0482 + 00 3. 9115 + 01 45 2.4683 +00 1. 7372 + 01 2. 1607 + 00 3. 9056 + 01

12
Table Z KA=5 DELTA(DEGREES)= 5 PSKDEGREESI = 0 PSKDEGREESl = 0.5 PSKDEGREES) = 1 PSIIDEGREES) = 2 KB G ( B PHASEtDEGREESI G( B PHASE(DEGREES) G ( B

)

PHASE(DEGREES), GIB) PHASEIOEGREES

10 1.3888 -01 1.3445 + 02 1 .3889 -0 1 1.3444 + 02 1.3890 -01 1.3439 + 02 1.3897 -01 1.3419 + 02

15 2.7776 -01 1.3427 + 02 2 • 7777 -01 1 .3425 + 02 2 . 7780 -0 1 1.3419 + 02 2 .7792 -01 1.3392 + 02 20 4.1661 -0 1 1.3409 + 02 4. 1663 -01 1 .3406 + 02 4. 1658 -0 1 1.3398 + 02 4.1686 -01 1.3355 + 02

25 5.5545 -01 1.3391 + 02 5.5547 -0 1 1.3388 + 02 5.5 5 53 -0 1 1 .3378 + 02 5.5577 -01 1.3339 + 02 30 6.9425 -0 1 1.3373 + 02 6.9428 -01 1 .3359 + 02 ~n 1 1.3358 + 02 5.9464 -01 1.3312 + 02

35 8.3303 -0 1 1.3355 + 02 8.3306 -0

1

1.3350 + 02 1.3337 + 02 8.3348 -01 1.3285 + 02 *0 9.7176 -0 1 1.3336 + 02 9.7179 -01 1.3332 + 02 9.7189 n 1 1.3317 + 02 9.7225 -01 1 .3258 + 02 45 1 « 1 104 + 00 1.3318 + 02 1 . 1 105 + 00 1.3313 + 02 1 .1 105 + 00 1.3296 + 02 1,1110 +00 1.3231 + 02 50 1 .2491 + 00 1.3300 + 02 1 .2491 + 00 1 .3294 + 02 1 .2492 +00 1 .3276 + 02 1 .2496 + 00 1.3204 + 02

55 1.3877 +00 1 .3282 + 02 1 .3877 + 0 0

1 .3878 + 00 1 .3256 + 02 + 02 60 1.5262 + 00 1.3264 + 02 1 .5262 + 00 1.3257 + 02 1.3235 + 02 1 .5257 +00 1.3151 + 02

65 1.6646 + 00 1.3246 + 02 1.6647 + 00 1.3238 + 02 1 .6648 +00 1.3215 + 02 1 .5552 + 00 1.3124 + 02 70 1.8030 + 00 1.3227 + 02 1.8030 + 00 1.3219 + 02 1 .8031 + 00 1.3195 + 02 1.8035 +00 1.3097 + 02

75 1.9413 +00 1 .3209 + 02 1 .9413 + 00 1.3201 + 02 1 .9414 + 00 1.3175 + 02 1.9417 +00 1.3070 + 02

SO 2.0795 + 00 1.3191 + 02 2.0795 + 00 1.3182 + 02 2.0796 +00 1.3154 + 02 2.0798 + 00 1.3043 + 02

B5 2.2176 +00 1.3173 + 02 2.2176 + 00 1.3153 + 02 2.2177 + 00 1.3134 + 02 2.2178 + 00 1.3016 + 02 90 2.3556 +00 1.3155 + 02 2.3556 + 00 1.3145 + 02 2.3557 + 00 1.3114 + 02 2.3557 +00 1.2990 + 02

95 2.4935 +00 1.3137 + 02 2.4935 +00 1.3125 + 02 2.4935 + 00 1.3093 + 02 2 .4935 +00 1.2953 + 02 100 2.5313 +00 1.3119 + 02 2.6313 +00 1.3107 + 02 2.6313 +00 1.3073 + 02 2.6311 +00 1 .2936 + 02

PSKDEGREES) = 3 PSKDEGREES) = 4 PSKDEGREES) = 5 PSKDEGREES) = 7 KB G( B F>HASE( DEGREES) GIB PHASEIOEGREES) GIB ) PHASE 1 DEGREES

)

GIB PHASEIOEGREES

10 1.3907 -01 1.3387 + 02 1.3922 -01 1.3341 + 02 1.3941 -01 1.3282 + 02 1 .3992 -01 1.3126 + 02

15 2.7813 -01 1.3349 + 02 2.7842 -01 1.3288 + 02 2.7879 -01 1.3210 + 02 2.7975 -01 1.3001 +02

20 4.1715 -01 1.3311 + 02 4.1758 -01 1.3235 + 02 4.1811 -01 1.3137 + 02 4.1945 -01 1.2876 + 02

25 5.5616 -01 1.3273 + 02 5.5559 -01 1.3182 + 02 5.5735 -01 1.3054 + 02 5.5893 -01 1.2751 + 02

30 6.9511 -01 1.3236 + 02 6.9573 -0 1 1.3129 +02 5.9547 -01 1.2992 + 02 5.9812 -01 1 .2626 + 02

35 8.3400 -01 1.3198 + 02 8.3458 -01 1.3076 + 02. 8.3546 -01 1.2919 + 02 8.3595 -01 1.2502 + 02

40 9.7283 -01 1.3160 + 02 9.7353 -01 1.3023 + 02 9.7428 -01 1.2847 + 02 9.7536 -01 1.2377 + 02 45 1.1115 +00 1.3122 + 02 1.1123 + 00 1.2970 +02 1.1129 + 00 1.2774 + 02 1.1133 +00 1.2252 + 02

50 1.2502 +00 1.3084 + 02 1 .2509 + 00 1.2917 + 02 1.2513 +00 1.2701 + 02 1 .2505 +00 1.2127 + 02

55 1.3888 +00 1.3047 + 02 1.3893 + 00 1.2864 + 02 1.3895 +00 1 .2629 + 02 1.3873 + 00 1 .2003 + 02 50 1.5272 +00 1.3009 + 02 1.5275 + 00 1.2811 + 02 1.5274 +00 1.2556 + 02 1.5233 + 00 1.1878 + 02

55 1.5656 +00 1.2971 + 02 1.6557 +00 1.2758 + 02 1.5650 + 00 1 .2484 + 02 1 .6585 + 00 1.1753 + 02

70 1 .8038 +00 1.2934 + 02 1.8035 + 00 1.2705 + 02 1.8022 + 00 1.2411 + 02 1.7929 +00 1.1629 + 02

75 1.9418 + 00 1.2896 + 02 1.9412 +00 1.2652 +02 1.9392 +00 1 .2339 + 02 1.9254 + 00 1.1504 + 02 80 2.0798 +00 1.2858 + 02 2.0787 +00 1.2599 + 02 2.0757 + 00 1.2255 + 02 2.0589 + 00 1.1380 + 02 85 2.2175 + 00 1.2820 + 02 2.2159 + 00 1.2546 + 02 2.2118 +00 1.2194 + 02 2.1903 + 00 1.1255 + 02

90 2.3551 +00 1.2783 + 02 2.3528 +00 1.2493 + 02 2.3476 + 00 1.2121 + 02 2.3207 + 00 1.1131 + 02 95 2.4925 +00 1 .2745 + 02 2.4895 +00 1.2441 + 02 2.4828 +00 1.2049 + 02 2 .4498 +00 1.1005 + 02 100 2.6297 + 00 1.2707 + 02 2.5258 +00 1.2388 + 02 2.6175 + 00 1.1977 + 02 2.5778 + 00 1.0882 + 02

PSKDEGREES) = 10 PSKDEGREES) = 12 PSIIDEGREES) = 14 PSKDEGREES) = 15 KB GIB PHASE 1 DEGREES

)

GIB PHASEIOEGREES) GIB PHASEIOEGREES) GIB PHASEIDEGREE

10 1 .4099 -01 1. 2793 + 02 1.4191 -01 1.2506 + 02 1 .4299 -01 1. 2171 + 02 1 .4360 -01 1.1983 + 02

15 2.8173 -01 1. 2558 + 02 2.8333 -01 1.2177 + 02 2 .8512 -01 1. 1728 + 02 2.8607 -01 1.1477 + 02 20 4.2198 -01 1 . 2322 + 02 4.2380 -01 1.1846 + 02 4 .2553 -01 1. 1284 + 02 4.2630 -01 1.0972 + 02 25 5.6150 -01 1.2087 + 02 5.5284 -01 1.1515 + 02 5 .6339 -01 1. 0841 + 02 5.5320 -01 1.0456 + 02

30 7.0005 -01 1. 1851 + 02 5.9999 -01 1.1185 + 02 6 .9785 -01 1. 0398 + 02 6.9559 -01 9.9508 + 01

35 8.3739 -01 1. 1515 + 02 8.3477 -01 1.0854 + 02 8 .2812 -01 9. 9554 + 01 8.2274 -01 9.4553 + 01 40 9.7329 -01 1. 1381 + 02 9.6574 -01 1.0523 + 02 9 .5340 -01 9. 5124 + 01 9.4337 -01 8.9498 + 01 45 1.1075 +00 1. 1145 + 02 1.0955 +00 1.0193 +02 1 .0730 + 00 9. 0595 + 01 1 .0565 +00 8.4445 + 01

50 1.2398 +00 1. 0910 + 02 1.2205 +00 9.8520 + 01 1 .1861 + 00 8. 5267 + 01 1.1615 + 00 7.9392 + 01 55 1.3700 +00 1. 0675 + 02 1.3414 +00 9.5315 + 01 1 .2921 +00 8. 1840 + 01 1 .2575 +00 7.4340 + 01 60 1.4978 +00 1. 0439 + 02 1 .4579 +00 9.2011 + 01 1 .3903 +00 7. 7413 + 01 1 .3437 + 00 6.9289 + 01 65 1.6230 + 00 1. 0204 + 02 1.5694 + 00 8.8707 + 01 1 .4802 + 00 7. 2987 + 01 1 .4193 +00 6.4239 + 01 70 1.7455 +00 9. 9689 + 01 1 .5755 +00 8.5404 +01 1 .5612 +00 6. 8553 + 01 1 .4839 + 00 5.9190 + 01

75 1.8649 +00 9. 7338 + 01 1.7752 + 00 8.2101 + 01 1 .6328 + 00 6. 4139 + 01 1.5368 +00 5.4143 + 01 80 1.9812 +00 9. 4987 + 01 1 .8709 +00 7.8800 + 01 1 .5947 +00 5. 9717 + 01 1.5778 + 00 4.9098 + 01 85 2.0940 +00 9. 2537 + 01 1.9593 + 00 7.5500 +01 1 .7454 + 00 5. 5297 + 01 1 .6065 +00 4.4054 + 01 90 2.2033 +00 9. 0288 + 01 2.0411 +00 7.2200 + 01 1 .7875 +00 5. 0878 + 01 1.6228 + 00 3.9013 + 01

95 2.3087 +00 8. 7940 + 01 2.1161 +00 6.8902 + 01 1 .8181 +00 4. 5461 + 01 1.5253 +00 3.3974 + 01 100 2.4102 +00 8. 5592 + 01 2 .1839 +00 5.5505 + 01 1 .8378 +00 4. 2045 + 01 1.5172 + 00 2.8938 + 01

PSKDEGREES) = 16 PSK DEGREES ) PSIIDEGREES) = 18 PSKDEGREES) = 18.5

KB GIB) PHASE IDE6REES) GIB PHASEIOEGREES) GIB PHASEIOEGREES)

10 1 .4424 -01 1.1783 + 02 1 .4493 -01 1.1570 +02 1,4555 -01 1.1345 + 02

15 2.8703 -01 1.1211 + 02 2.8802 -01 1.0927 +02 2.8900 -01 1.0527 + 02 20 4.2695 -01 1.0638 + 02 4.2747 -01 1.0284 +02 4.2781 -01 9.9083 + 01 25 5.6260 -01 1 .0056 + 02 5.6152 -01 9,5405 + 01 5.5988 -01 9. 1900 + 01 30 6.9262 -01 9.4937 + 01 5.8849 -01 8.9974 +01 5.8315 -01 8.4718 + 01

35 8.1571 -01 8.9215 + 01 8.0675 -01 8,3543 + 01 7.9567 -01 7.7537 + 01 40 9.3064 -01 8.3494 + 01 9.1485 -01 7,7113 + 01 8.9558 -01 7.0355 + 01 45 1.0363 +00 7.7774 +01 1.0114 +00 7.0583 + 01 9.8150 -01 5.3177 + 01 50 1.1315 +00 7.2054 + 01 1.0952 + 00 6.4255 +01 1.0521 +00 5.5998 + 01

55 1 .2155 +00 6.6335 + 01 1.1552 + 00 5.7828 + 01 1,1051 +00 4.8-821 + 01 60 1.2873 + 00 6.0618 + 01 1.2205 + 00 5.1403 + 01 1.1426 + 00 4. 1545 + 01 65 1.3453 +00 5.4902 + 01 1.2504 + 00 4.4979 + 01 1.1613 + 00 3.4473 + 01 70 1.3918 +00 4.9187 + 01 1.2844 + 00 3.8557 + 01 1.1617 +00 2.7302 + 01 75 1.4234 + 00 4.3475 + 01 1 .2922 +00 3.2137 + 01 1.1439 +00 2.0135 + 01 80 1 .4408 + 00 3.7764 + 01 1.2838 +00 2.5720 + 01 1.1081 + 00 1.2971 + 01

85 1 .4439 +00 3.2056 +01 1 .2592 +00 1.9307 + 01 1.0550 + 00 5.8128 + 00

90 1.4325 + 00 2.5351 + 01 1.2188 + 00 1.2898 + 01 9.8528 -01 -1.3387 + 00

95 1.4069 +00 2.0650 + 01 1.1631 + 00 6.4948 + 00 9.0018 -01 -8.4806 + 00 100 1.3673 +00 1.4953 + 01 1.0927 + 00 9.8482 -02 8.0101 -01 -1.5609 + 01

GIB) 1.4603 -01 2.8950 -01 4.2790 -01 5.5882 -01 5.7997 -01 7.8924 -01 8.8471 -01 9.6472 -01 1.0279 +00 1.0731 +00 1.0996 +00 1.1068 +00 1.0948 +00 1.0637 +00 1.0140 +00 9.4654 -01 8.5281 -01 7.6398 -01 5.5188 -01

PHASEIOEGREES)

1.1228 +02 1.0470 +02 9.7128 +01 8.9655 +01 8.1982 +01 7.4410 +01 6.5838 +01 5.9268 +01 5.1599 +01 4.4131 +01 3.6566 +01 2.9002 +01 2.1442 +01 1.3885 +01 6.3338 +00 -1.2115 +00 -8.7476 +00 -1.5270 +01 -2.3772 +01
Table 2 - Continued

PSKOEGREES) = 19 KB G( B PHASE (DEGREES

)

G( Bl 10 1 .4641 -01 1.1107 + 02 1.4681 -01

15 2.8998 -01 1.0310 + 02 2 .9047 -01 20 4.2793 -01 9.5122 + 01 4.2791 -01

25 5.5759 -01 8.7147 + 01 5.5617 -01

30 6.7644 -01 7.9173 + 01 6.7253 -01

35 7.8218 -01 7.1200 + 01 7.7447 -01 40 8.7278 -01 6.3227 + 01 8.5984 -01 45 9.4647 -01 5.5256 + 01 9.2679 -01

50 1.0018 +00 4.7286 + 01 9.7390 -01

55 1.0378 + 00 3.9317 + 01 1.0002 +00

60 1.0537 +00 3.1351 + 01 1.0050 +00

65 1.0492 + 00 2.3388 + 01 9.8842 -01

70 1 .0244 + 00 1.5428 + 01 9.5067 -01

75 9.7979 -01 7.4721 + 00 8.9260 -01

ao 9.1626 -01 -4.7760 -01 8.1547 -01

85 8.3504 -01 -8.4188 + 00 7.2093 -01

90 7.3772 -01 -1.6347 + 01 6.1103 -01

95 6.2617 -01 -2.4255 + 01 4.8811 -01

100 5.0258 -01 -3.2127 + 01 3.5483 -01

PSKOEGREES) = 19.5 PHASE ( DEGREES I 1.0984 +02 1.0145 +02 9.3064 +01 8.4678 +01 7.6292 +01 5.7907 +01 5.9523 +01 5.1141 +01 4.2759 +01 3.4380 +01 2.6003 +01 1.7629 +01 9.2594 +00 8.9493 -01 -7.4619 +00 -1.5807 +01 -2.4134 +01 -3.2426 +01 -4.0545 +01

PSI(DEGREES) = 20 PSKOEGREES) = 20.5

GIB) 1.4722 2.9095 • 4.2781

5.5455

5.6821

7.5508 • 8.4585 9.0566

9.4408

9.5023

9.5372

9.2472

8.7392 8.0252 • 7.1223

5.0518

4.8391 3.5129

2.1047

PHASEIOEGREES)

1.0857 +02 9.9753 +01 9.0955 +01 8.2147 +01 7.3339 +01 5.4533 +01 5.5727 +01 4.6923 +01 3.8120 +01 2.9320 +01 2.0522 +01 1.1727 +01 2.9379 +00 -5.8449 +00 -1.4518 +01 -2.3374 +01 -3.2100 +01 -4.0750 +01 -4.9220 +01

Gl Bl 1.4763

2.9142 4.2764

5.5274

5.6347

7.5597

8.3080

8 .8304 9.1236

9.1799

8.9979

8.5825

7.9444

7.1005 6.0726

4.8877

3.5764

2.1731 7.1444

-01

-01

-01 -01

-01

-01

-01

-01 -01

-01 -01

-01

-01 -01

-01

-01

-01

-01 -02

PHASEIOEGREES!

1.0728 +02 9.8035 +01 8.8794 +01 7.9554 +01 7.0315 +01 6.1076 +01 5.1839 +01 4.2603 +01 3.3368 +01 2.4136 +01 1.4908 +01 5.6828 +00 -3.5351 +00 -1.2746 +01 -2.1943 +01 -3.1113 +01 -4.0229 +01 -4.9182 +01 -5.6954 +01

PSKOEGREES = 20.75 PSKOEGREES) = 21 KB GIB PHASE 1 DEGREES

)

GIB PHASEIOEGREES

10 1.4784 -01 1 .0652 + 02 1 .4806 -01 1.0595 + 02

15 2.9166 -01 9.7156 + 01 2.9189 -01 9.6256 + 01 20 4.2752 -01 8.7595 + 01 4.2739 -01 8.6583 + 01

25 5.5175 -01 7.8235 + 01 5.5070 -01 7.6900 + 01 30 6.6094 -01 6.8775 + 01 6.5830 -01 6.7219 + 01 35 7.5214 -01 5.9317 + 01 7.4712 -01 5.7538 + 01 40 8.2285 -01 4.9860 + 01 8.1463 -01 4.7858 + 01 45 8.7117 -01 4.0404 + 01 8.5893 -01 3.8180 + 01 50 8.9578 -01 3.0950 + 01 8.7873 -01 2.8504 + 01

55 8.9602 -01 2.1499 + 01 8.7350 -01 1.8831 + 01 60 8.7 188 -01 1.2051 + 01 8.4337 -01 9.1611 + 00

65 8.2404 -01 2.6072 + 00 7.8923 -01 -5.0395 -01

70 7.5380 -01 -5.8300 + 00 7.1253 -01 -1.0162 + 01 75 6.5309 -01 -1.6257 + 01 5.1575 -01 -1.9808 + 01 80 5.5438 -01 -2.5668 + 01 5.0137 -01 -2.9434 + 01

85 4.3064 -01 -3.5045 + 01 3.7275 -01 -3.9016 + 01 90 2.9526 -01 -4.4344 + 01 2.3360 -01 -4.8475 + 01 95 1.5191 -01 -5.3335 + 01 8.7867 -02 -5.7195 + 01 100 5.1376 -03 -3.4545 + 01 6.0385 -02 1.0939 + 02

PSKOEGREES) = 21.75 PSKOEGREES) = 22 GIB) PHASE (DEGREES )' GIB PHASE 1 DEGREES

)

1.4872 -01 1 .0390 + 02 1 .4894 -01 1.0320 + 02 2.9257 -01 9.3536 + 01 2.9279 -01 9.2605 + 01 4.2586 -01 8.3170 + 01 4.2663 -01 8.2008 + 01 5.4720 -01 7.2806 + 01 5.4591 -01 7.1410 + 01 6.4955 -01 5.2442 + 01 5.4654 -01 5.0814 + 01 7.3090 -01 5.2078 + 01 7.2510 -01 5.0218 + 01 7.8827 -01 4.1717 + 01 7.7891 -01 3.9524 + 01 8.1990 -01 3.1357 + 01 8.0513 -01 2.9032 + 01 8.2476 -01 2.0999 + 01 8.0584 -01 1.8442 + 01 8.0269 -01 1.0545 + 01 7.7805 -01 7.8551 + 00 7.5444 -01 2.9440 -01 7.2374 -01 -2.7257 + 00 6.8158 -01 -1 .0049 + 01 5.4476 -01 -1.3301 + 01 5.8650 -01 -2.0382 + 01 5.4380 -01 -2.3863 + 01 4.7232 -0 1 -3.0695 + 01 4.2434 -01 -3.4401 + 01 3.4277 -01 -4.0955 + 01 2.9045 -01 -4.4880 + 01 2.0210 -01 -5.1099 + 01 1 .4672 -01 -5.5122 + 01 5.4915 -02 -6.0002 + 01 2.6595 -03 7.1299 + 01 9.4061 -02 1.0549 + 02 1.5051 -01 1.0232 + 02 2.3983 -01 9.6842 + 01 2.9383 -01 9.2073 + 01

PSKOEGREES) = 23 PSKOEGREES) = 24 PSKOEGREES) = 25

KB GIB PHASE ( DEGREES

)

G( B PHASEIOEGREES) GIB PHASEIOEGREES

10 1.4985 -01 1 .0034 + 02 1 .5082 -01 9.7351 + 01 1.5181 -01 9.4245 + 01

15 2.9353 -01 8.8784 + 01 2.9442 -01 8.4801 + 01 2.9512 -01 8.0560 + 01 20 4.2550 -01 7.7230 + 01 4.2394 -01 7.2252 + 01 4.2190 -01 6.7075 + 01

25 5.4011 -01 6.5678 + 01 5.3319 -01 5.9704 + 01 5.2506 -01 5.3492 + 01

30 6.3281 -01 5.4125 + 01 6.1595 -01 4.7157 + 01 5.9884 -01 3.9910 + 01 35 6.9985 -01 4.2575 + 01 6.7122 -01 3.4511 + 01 5.3909 -01 2.5329 + 01 40 7.3852 -01 3.1026 + 01 5.9340 -01 2.2057 + 01 6.4358 -01 1.2750 + 01 45 7.4725 -01 1.9479 + 01 5.8245 -01 9.5255 + 00 6.1206 -01 -8.2556 -01

50 7.2571 -01 7.9350 + 00 6.3890 -01 -3.0120 + 00 5.4630 -01 -1.4396 + 01

55 6.7475 -01 -3.6044 + 00 5.5484 -01 -1.5543 + 01 4.5000 -01 -2.7956 + 01 60 5.9548 -01 -1.5137 + 01 4.6381 -01 -2.8053 + 01 3.2855 -01 -4. 1495 + 01 55 4.9406 -01 -2.5657 + 01 3.4065 -01 -4.0558 + 01 1.8875 -01 -5.4963 + 01

70 3.7165 -01 -3.8151 + 01 2.0127 -01 -5.2974 + 01 3.8456 -02 -5.7522 + 01

75 2.3424 -01 -4.9572 + 01 5.2330 -02 -5.4536 +01 1.1396 -01 9.7193 + 01 80 8.7397 -02 -6.0547 + 01 9.9076 -02 1.0101 + 02 2.5992 -01 8.3862 + 01

85 6.2957 -02 1 .0574 + 02 2.4556 -01 8.8847 + 01 3.9128 -01 7.0355 + 01 90 2.1065 -01 9.5083 + 01 3.8045 -01 7.6402 + 01 5.0070 -01 5.5815 + 01

95 3.4975 -01 8.3694 + 01 4.9700 -01 6.3908 + 01 5.8205 -01 4.3265 + 01 100 4.7461 -01 7.2218 + 01 5.8975 -01 5.1401 + 01 6.3081 -01 2.9716 + 01

KA = 5 DELTA I DEGREES ) =10 PSKOEGREES) = 0 PSKOEGREES) = 1 PSKOEGREES) = 2 PSKOEGREES) = 3 KB GIB PHASEIOEGREES) GIB) PHASE ( DEGREES 1 GIB) PHASEIOEGREES GIB PHASEIOEGREES

10 2.7760 -01 1.3282 + 02 2.7765 -01 1.3275 + 02 2.7777 -01 1.3256 + 02 2.7798 -01 1.3223 + 02

15 5.5488 -01 1.3209 + 02 5.5496 -0 1 1.3201 + 02 5.5520 -01 1.3175 + 02 5.5560 -01 1.3131 + 02 20 8.3163 -01 1.3137 + 02 8.3175 -01 1.3126 + 02 8.3209 -01 1.3093 + 02 8.3265 -01 1.3039 + 02 25 1.1077 +00 1.3064 + 02 1.1078 +00 1.3051 + 02 1.1082 +00 1.3012 + 02 1.1089 + 00 1.2947 + 02 30 1.3828 + 00 1.2992 + 02 1.3830 + 00 1.2977 + 02 1.3835 + 00 1.2931 + 02 1.3842 + 00 1.2855 + 02 35 1 .6569 +00 1.2920 + 02 1.5571 +00 1.2903 + 02 1.6575 +00 1.2850 + 02 1.6583 + 00 1.2754 + 02 40 1.9298 + 00 1.2848 + 02 1 .9299 +00 1.2828 + 02 1.9303 + 00 1.2770 + 02 1 .9309 + 00 1.2673 + 02 45 2.2012 + 00 1.2776 + 02 2.2013 +00 1.2755 + 02 2.2016 +00 1.2690 + 02 2.2019 + 00 1.2581 + 02 50 2 .4710 + 00 1.2705 + 02 2.4710 + 00 1.2581 + 02 2.4712 +00 1.2510 + 02 2.4712 + 00 1.2491 +02

55 2.7390 + 00 1.2634 + 02 2 .7390 +00 1.2608 +02 2.7388 + 00 1.2530 + 02 2.7384 +00 1.2400 + 02

60 3.0050 + 00 1.2563 + 02 3.0049 +00 1.2535 + 02 3.0045 + 00 1.2451 + 02 3.0034 + 00 1.2310 + 02 55 3.2590 +00 1.2492 + 02 3.2587 + 00 1 .2462 + 02 3.2579 + 00 1.2372 + 02 3.2650 + 00 1.2221 + 02

70 3.5305 + 00 1.2422 + 02 3.5302 + 00 1 .2390 + 02 3.5289 + 00 1.2293 + 02 3.5250 + 00 1.2132 + 02

75 3.7899 +00 1.2353 + 02 3.7893 + 00 1.2318 + 02 3.7873 + 00 1.2215 + 02 3.7633 +00 1.2043 + 02 80 4.0465 + 00 1.2284 + 02 4.0457 +00 1.2247 + 02 4.0430 + 00 1.2137 + 02 4.0376 + 00 1.1955 + 02

85 4.3004 +00 1.2215 + 02 4.2993 +00 1.2176 +02 4.2957 +00 1.2060 + 02 4.2888 + 00 1.1857 +02

90 4.5513 +00 1.2147 + 02 4.5500 +00 1.2105 + 02 4.5455 + 00 1.1984 + 02 4.5368 + 00 1.1780 + 02

95 4.7993 +00 1.2079 + 02 4.7976 +00 1.2036 + 02 4.7920 +00 1.1908 + 02 4.7813 + 00 1.1694 + 02 100 5.0441 + 00 1.2012 + 02 5.0420 +00 1.1957 + 02 '5.0353 +00 1.1832 + 02 5.0223 +00 1.1608 + 02

14
Table 3 - Continued

KB

10

1520

25

30

3540

45

50

5560

6570

7580

8590

95 100

PSI ( G(B 2.7827

5.5616

8. 3343 1.1096

1.3851

1.6591 1.9315 2.2022

2.4708 2.7372

3.0011 3.2624

3.5208

3.7761 4.0282 4.2769

4.5220

4.7632

5.0006

DEGREES) = 4 PHASE ( DEGREES

)

1.3178 +02 1.3070 +02 1.2963 +02 1.2856 +02 1.2749 +02 1.2643 +02 1.2536 +02 1.243U +02 1.2324 +02 1.2219 +02 1.2114 +02 1.2009 +02 1.1905 +02 1.1802 +02 1.1699 +02 1.1597 +02 1.1495 +02 1.1394 +02 1.1294 +02

-01

-01

-01

+ 00

+ 00 +00

+ 00 +00

+ 00 +00

+ 00 +00

+00

+ 00

+ 00 +00

+ 00

+ 00

+ 00

PSI ( G(B

2 .7865 5.5688 8.3441

1.1110

1 .3863

1 .6600 1.9320 2.2020

2.4696 2.7347

2.9969

3.2561 3.5120

3.7644

4.0131 4.2579

4.4985

4.7347

4.9665

DEGREES! = 5 PHASE(DEGREES1

1.3119 +02 1.2992 +02 1.2866 +02 1.2739 +02 1.2613 +02 1.2487 +02 1.2361 +02 1.2235 +02 1.2110 +02 1.1986 +02 1.1862 +02 1.1738 +02 1.1615 +02 1.1492 +02 1.1370 +02 1.1249 +02 1.1129 +02 1.1009 +02 1.0890 +02

PSUDEGREES) = 10

-01

-01

-01

+ 00

+ 00

+ 00

+ 00

+ 00 +00

+ 00

+ 00

+ 00 +00

+ 00 +00

+ 00

+ 00

+ 00

+ 00

PSKDEGREESI = 7 G(B) PHASE (DEGREES) G(B] 2.7965 -01 1.2963 +02 2.8178 -01 5.5875 -01 1.2784 +02 5.6256 -01 8.3688 -01 1.2606 +02 8.4149 -01 1.1136 +00 1.2427 +02 1.1177 +00 1.3886 +00 1.2249 +02 1.3904 +00 1.6614 +00 1.2071 +02 1.6588 +00 1.9316 +00 1.1894 +02 i,9220 +00 2.1988 +00 1.1717 +02 2.1793 +00 2.4627 +00 1.1540 +02 2.4299 +00 2.7229 +00 1.1364 +02 2.6731 +00 2.9790 +00 1.1189 +02 2.9083 +00 3.2307 +00 1.1014 +02 3.1347 +00 3.4776 +00 1.0840 +02 3.3518 +00 3.7195 +00 1.0667 +02 3.5590 +00 3.9559 +00 1.0495 +02 3.7557 +00 4.1868 +00 1.0324 +02 3.9415 +00 4.4116 +00 1.0153 +02 4.1159 +00 4.6303 +00 9.9838 +01 4.2786 +00 4.8425 +00 9.8156 +01 4.4291 +00

PHASE(DEGREES)

1.2632 +02 1.2343 +02 1.2055 +02 1,1766 +02 1.1478 +02 1.1190 +02 1.0903 +02 1.0617 +02 1.0331 +02 1.0046 +02 9.7626 +01 9.4797 +01 9.1980 +01 8.9175 +01 8.5384 +01 8.3607 +01 8.0846 +01 7.8101 +01 7.5375 +01

PSUDEGREES ) 12 KB

10

1520

2530

3540

45

50

5560

65

70

7580

8590

95 100

G(B) 2.8361 -01 5.6566 -01 8.4476 -01 1.1195 +00 1.3886 +00

1.6506 +00 1,9044 +00 2.1486 +00 2.3822 +00 2.6040 +00 2.8130 +00 3.0082 +00 3.1889 +00 3.3541 +00 3.5033 +00 3.6359 +00 3.7514 +00 3.8493 +00 3.9295 +00

PHASEIDEGREES)

1,2348 +02 1,1964 +02 1.1580 +02 1,1197 +02 1,0814 +02 1,0432 +02 1,0051 +02 9,6702 +01 9,2907 +01 8,9122 +01 8.5350 +01 8.1592 +01 7.7848 +01 7.4122 +01 7.0414 +01 6.6727 +01 5.3062 +01 5.9421 +01 5.5807 +01

PSKDEGREES) = 15 GIB) PHASECDEGREESI 2.8696 -01 1.1825 +02 5.7092 -01 1.1267 +02 8.4907 -01 1.0710 +02 1,1186 +00 1,0152 +02 1.3770 +00 9.5961 +01 1.6215 +00 9.0407 +01 1.8499 +00 6.4852 +01 2.0599 +00 7.9330 +01 2.2495 +00 7.3813 +01 2.4172 +00 6.6311 +01 2.5611 +00 6.2829 +01 2.5800 +00 5.7369 +01 2.7731 +00 5.1934 +01 2.8395 +00 4.6528 +01 2.8786 +00 4.1155 +01 2.8908 +00 3.5821 +01 2.6758 +00 3.0531 +01 2.8342 +00 2.5294 +01 2.7667 +00 2.0118 +01

PSI (DEGREES) 16 PSKDEGREESI = 17 0(8) 2.8824 -01 5.7276 -01 8.5012 -01 1.1169 +00 1.3597 +00 1.5056 +00 1.8217 +00 2.0154 +00 2.1845 +00 2.3269 +00 2.4412 +00 2.5260 +00 2.5806 +00 2.6044 +00 2.5975 +00 2.5602 +00 2.4933 +00 2.3979 +00 2.2755 +00

PHASEIDEGREES)

1.1626 +02 2 1.1001 +02 5 1.0377 +02 8 9.7539 +01 1 9.1313 +01 1 8.5097 +01 1 7.8892 +01 1 7.2701 +01 1 6.5527 +01 2 6.0371 +01 2 5,4239 +01 2 4,8132 +01 2 4.2056 +01 2 3,6015 +01 2 3.0018 +01 2 2.4071 +01 2 1.8185 +01 2 1.2375 +01 1 6.5593 +00 1

G(B)

,8960 -01

.7466 -01

,5088 -01

,1141 +00

,3603 +00

,5858 +00

,7874 +00

,9520 +00

,1071 +00

,2206 +00

,3012 +00

,3476 +00

,3595 +00

,3369 +00

,2806 +00

,1915 +00

,0714 +00

,9224 +00

,7472 +00

PHASE (DEGREES

)

1.1414 +02 1.0719 +02 1.0024 +02 9.3303 +01 8.6373 +01 7.9453 +01 7.2547 +01 5.5656 +01 5.8784 +01 5,1935 +01 4,5112 +01 3,8320 +01 3,1567 +01 2,4850 +01 1,8210 +01 1.1531 +01 5.1428 +00 -1.2244 +00 -7.4261 +00

PSKDEGREES) = 18 PSKDEGREES) = 19 PSI (DEGREES

)

19.5

KB

10

1520

25

303540

45

50

5560

6570

7580

8590

95 100

PSKDEGREES) = 20 G(B 2.9104

5.7555

8,5128

1.1101 1.3484

1.5618

1.7463 1.8987 2.0154

2.0974

2.1403

2.1446

2.1105

2.0388

1.9314

1.7903 1.6186

1.4197

1.1978

-01

-01 -01

+00 +00

+00

+00

+00

+ 00

+ 00 +00

+ 00

+ 00 +00

+ 00 +00 +00

+00 +00

PHASE(DEGREES)

1.1189 +02 1.0420 +02 9.6504 +01 6.8818 +01 8.1142 +01 7.3478 +01 6.5829 +01 5.8197 +01 5.0588 +01 4.3005 +01 3.5453 +01 2.7941 +01 2.0478 +01 1.3077 +01 5.7575 +00 1.4536 +00 8.5117 +00

1.5342 +01 2.1808 +01

GIB) 2.9255 -01 5.7842 -01 8.5123 -01 1.1049 +00 1.3338 +00 1.5329 +00 1.6978 +00

1.8251 +00 1.9119 +00 1.9565 +00 1.9585 +00 1.9175 +00 1.6353 +00 1.7137 +00 1.5557 +00 1.3653 +00 1.1471 +00 9.0636 -01 6.4937 -01

PHASE(OEGREES)

1.0953 +02 1.0104 +02 9.2559 +01 6.4085 +01 7.5623 +01 5.7173 +01 5.8740 +01 5.0328 +01 4.1941 +01 3.3585 +01 2.5259 +01 1.7003 +01 8.8034 +00 6.9294 -01 -7.2910 +00 -1.5084 +01 -2,2567 +01 -2,9476 +01 -3,5120 +01

GIB) ,9334 -01 ,7935 -01 .5102 -01 1017 +00 ,3254 +00

,5165 +00

.6706 +00

,7841 +00

,8543 +00

,8796 +00 ,8599 +00

,7957 +00

,5889 +00

,5426 +00 ,3505 +00 .1475 +00 9.0926 -01 6.5223 -01 3.8479 -01

PHASE I DEGREES

)

1.0630 +02 2. 9.9400 +01 5, 9.0509 +01 8, 8.1527 +01 1, 7.2755 +01 1, 6.3898 +01 1, 5.5058 +01 1, 4.5240 +01 1, 3.7450 +01 I, 2.8594 +01 1, 1.9982 +01 1, 1.1328 +01 1, 2.7530 +00 1, -5.7116 +00 1, -1.4010 +01 1, -2.2037 +01 9. -2.9555 +01 5, -3.5991 +01 4, -3.9000 +01 1,

GIB) 9415 -01 8025 -01 5057 -01 0982 +00

3161 +00 4988 +00 6414 +00

7403 +00 7930 +00

7983 +00

7563 +00 5585 +00

5375 +00

3570 +00

1521 +00

2853 -01 7317 -01 0431 -01 4106 -01

PHASEIDEGREES)

1.0704 +02 9.7719 +01 8.8409 +01 7.9107 +01 6.9815 +01 6.0541 +01 5.1284 +01 4.2050 +01 3.2847 +01 2.3682 +01 1.4556 +01 5.5187 +00 -3.4340 +00 -1.2245 +01 -2.0828 +01 -2.8995 +01 -3.6258 +01 -4.0800 +01 -2.6795 +01

PSKDEGREES) = 20.5

KB

10

1520

25

30

3540

45

50

5560

65

70

7580

85

90

95 100

GIB) 2.9497 -01 5.8116 -01 8.5018 -01 1.0942 +00 1.3050 +00 1.4797 +00

1.6101 +00

1.6937 +00

1.7281 +00 1.7127 +00 1.6481 +00 1.5365 +00 1.3815 +00 1.1880 +00 9.5188 -01 7.1032 -01 4.4156 -01 1.7009 -01 1.4608 -01

PHASE I DEGREES

)

1.0574 +02 2 9.5998 +01 5 8.6257 +01 8 7.6525 +01 1 6.6806 +01 1 5.7102 +01 1 4,7418 +01 1 3,7759 +01 1 2,8133 +01 ; 1,8550 +01 1 9,0237 +00 1 -4,2258 -01 1 -9,7513 +00 1 -1.8892 +01 1 -2.7700 +01 7 -3.5804 +01 4 -4.1902 +01 2 -3.6236 +01 9 8.1227 +01 3

PSI I GIB

.9562

,6204

,4952

,0897

.2951

.4591 .5766

.6441

.6595

.5229

.5354

.4002 .2220

,0057 .6156

.9519

.1911

,7219

.6106

+ 01

+ 01

+ 01

+ 01

+ 01

DEGREES! = 21

) PHASEIDEGREES)

1.0442 +02 9.4235 +01 8.4055 +01 7.3883 6,3725

5,3582 4,3461

3.3368 2.3310 +01 1.3300 +01 3.3556 +00 5.4922 +00

1.6190 +01 2.5627 +01 3.4537 +01 4.2051 +01 4.2855 +01 7.1437 +01 9.1045 +01

PSKDEGREES) = 21,5

-01

-01

-01

+ 00

+ 00

+ 00 +00

+ 00

+ 00 +00

+ 00 +00

+ 00

+ 00 -01

-01 -01 -02

-01

GIB) .9668 -01 .8290 -01 .4669 -01 .0846 +00

.2632 +00 .4370 +00 .5409 +00 .5916 +00

.5876

.5291 .4186 +00

.2602 +00

.0597 +00

.2436 -01 ,6294

,8599

,4766

,9581 ,6559 -01

+ 00

+ 00

-01

-01

-02

-01

PHASEIDEGREES)

1.0307 +02 2. 9.2433 +01 5, 6.1802 +01 8. 7.1180 +01 1. 6.0572 +01 1. 4.9982 +01 1. 3.9414 +01 1. 2.8875 +01 1. 1.8376 +01 1, 7.9316 +00 1. -2.4357 +00 1. -1.2684 +01 1. -2.2734 +01 8. -3.2400 +01 6. -4.1128 +01 3. -4.5175 +01 9, 2.8970 +01 2, 9.1407 +01 4, 8.5113 +01 7

PSK

GIB 9757 8374

4768

0795

2704 4133

5030

5352

5121 4315

2982

1171 9568

4255 6810

1228 1606

9105 4785

DEGREES) = 22

I PHASE ( DFGREE S

!

-01 1.0169 +02

-01 9.0590 +01

-01 7.9498 +01

+00 5.6417 +01 +00 5.7349 +01 +00 4.6300 +01 +00 3.5276 +01 +00 2.4283 +01 +00 1.3334 +01 +00 2.4473 +00

+00 -8.3473 +00

+00 -1.8992 +01

-01 -2.9361 +01

-01 -3.9111 +01

-01 -4.6842 +01 -02 -3.3449 +01

-01 9.0972 +01 -01 8.7359 +01

-01 7.8480 +01

15
Table 3 - Continued PSKDEGREES) = 23 psi( KB GIB PHASE (DEGREES I G(B

10 2 .9939 -01 9.8833 + 01 3.0129 -01

15 5.8532 -01 8,6783 + 01 5.8678 -01

20 8.4508 -01 7.4740 +01 8,4162 -01

25 1 .0671 + 00 6.2709 + 01 1.0526 +00

30 1.2417 +00 5.0693 + 01 1 .2089 +00

35 1.3612 +00 3.8697 + 01 1.3024 +00

40 1.4203 +00 2.6730 + 01 1.3286 +00

45 1.4168 +00 1 .4801 + 01 1.2862 +00

50 1.3510 +00 2.9267 + 00 1 .1779 +00

55 1.2262 + 00 -8.8635 + 00 1.0094 + 00

60 1.0461 + 00 -2.0514 + 01 7.8980 -0 1 65 8.2499 -01 -3.1897 + 01 5.3094 -01

70 5.6720 -01 -4.2628 +01 2.4699 -01

75 2.8700 -01 -5.0784 + 01 5.8918 -02

80 3.8617 -02 3.1086 + 01 3.4331 -01

85 2.9971 -01 9.0640 + 01 6.1451 -01

90 5.7313 -01 8.2295 + 01 8.5266 -01

95 8.2016 -01 7.1668 + 01 1 .0454 + 00 100 1.0296 + 00 6.0496 + 01 1.1832 +00

;SI = 24 PSKDEGREES) = 25 PHASE(OEGREESI GIBi PHASE ( DEGREES

)

9.5857 + 01 3 .0327 -01 9 .2753 + 01 8.2816 + 01 5 ,8807 -01 7 .8691 +01 6.9783 + 01 8 .3721 -01 6 .4627 + 01 5.6751 + 01 1.0357 +00 5 .0576 + 01 4.3757 + 01 1 .1716 +00 3 .6544 +01 3.0775 + 01 1 .2369 + 00 2 .2538 +01 1.7827 +01 1 .2278 +00 8 .5704 + 00 4.9250 + 00 1 .1452 +00 -5 .3385 + 00 -7.9049 + 00 9 .9437 -01 -1 .9148 + 01 -2.0613 + 01 7 .8463 -01 -3 .2765 +01 -3.3084 + 01 5.2901 -01 -4 .5891 + 01 -4.4952 + 01 2 .4353 -01 -5.5784 + 01 -5.4119 + 01 6 .1614 -02 8 .0514 +01 7.5317 + 01 3 .5144 -01 8 .5780 + 01 8.8119 + 01 5 .2217 -01 7 .3627 +01 7,7521 + 01 8 .5420 -01 6 .0417 + 01 6.5536 + 01 1 .0337 +00 4 .6951 + 01 5.3203 + 01 1 .1503 +00 3 .3427 + 01 4.0770 +01 1 .1975 + 00 1 .9938 +01

ICA=5 DELTACDEGREES)=15 PSKDEGREES! = 1 PSKDEGREES) = 2 PSKDEGREES) = 3 KB GIB PHASE 1 DEGREES 1 GIB) PHASEIDEGREES) GIB) PHASEIDEGREES) GIB) PHASEIDEGREES

10 4.1534 -01 1.3010 + 02 4.1541 -01 1.3003 + 02 4.1559 -01 1.2984 + 02 4.1590 -01 1.2951 + 02

15 8.2819 -01 1.2847 + 02 8.2830 -01 1 .2838 + 02 8. 2865 -01 1.2812 + 02 8.2922 -01 1.2769 + 02

20 1.2371 + 00 1.2585 + 02 1.2373 +00 1.2574 + 02 1.2377 +00 1.2642 + 02 1.2385 + 00 1.2588 + 02

25 1 .6408 + 00 1.2525 + 02 1.6410 +00 1.2512 + 02 1 .6415 + 00 1.2473 + 02 1 .5423 +00 1 .2409 + 02 30 2.0380 +00 1.2356 + 02 2.0381 + 00 1.2351 +02 2.0385 + 00 1.2305 + 02 2.0392 + 00 1.2231 + 02

35 2.4273 +00 1.2209 + 02 2.4274 + 00 1.2192 + 02 2.4275 + 00 1.2141 + 02 2.4279 + 00 1.2055 + 02

40 2.8077 +00 1.2055 + 02 2.8075 +00 1.2036 + 02 2 .8075 +00 1.1978 + 02 2.8071 +00 1.1882 + 02 45 3.1779 + 00 1 ,1904 + 02 3.1777 +00 1.1882 + 02 3.1771 + 00 1.1818 + 02 3.1758 +00 1.1712 + 02 50 3.5371 +00 1.1755 + 02 3.5367 +00 1.1732 + 02 3.5354 +00 1.1652 + 02 3.5329 +00 1.1545 + 02

55 3.8843 +00 1.1510 + 02 3.8837 + 00 1.1584 + 02 3.8815 +00 1.1508 + 02 3.8775 +00 1.1382 + 02 50 4.2188 + 00 1.1468 + 02 4.2178 + 00 1.1441 + 02 4.2145 +00 1.1359 + 02 4.2087 +00 1.1222 + 02 65 4.5399 +00 1.1331 + 02 4.5384 + 00 1.1302 + 02 4,5339 + 00 1.1214 + 02 4,5258 +00 1.1068 + 02

70 4.8470 +00 1.1198 + 02 4.8451 + 00 1.1157 + 02 4.8391 +00 1.1073 + 02 4.8285 +00 1.0917 + 02

75 5.1397 +00 1.1070 + 02 5.1373 + 00 1.1037 + 02 5.1297 + 00 1 .0938 + 02 5.1151 +00 1.0773 + 02 80 5.4179 +00 1.0947 +02 5.4149 +00 1.0912 + 02 5.4055 + 00 1 .0808 + 02 5.3887 +00 1.0533 + 02

85 5.6814 +00 1.0830 + 02 5.6777 +00 1.0793 + 02 5.6563 +00 1.0583 + 02 5 .5460 +00 1.0500 + 02 90 5.9302 + 00 1.0718 + 02 5.9258 +00 1.0680 + 02 5.9123 +00 1 .0564 + 02 5.8882 +00 1.0372 + 02 95 6.1545 +00 1.0612 + 02 6.1594 +00 1.0572 + 02 6.1436 +00 1.0452 + 02 5.1155 +00 1.0251 + 02 100 6.3847 +00 1.0513 + 02 5.3789 + 00 1.0471 + 02 5.3607 + 00 1.0346 + 02 6.3284 +00 1.0137 + 02

PSI(DEGREES)= 4 PSKDEGREES) = 5 PSKDEGREES) = 7 PSKDEGREES) = 12 KB GIB ) PHASEIDEGREES) GIB) PHASEIDEGREES

)

GIB) PHASEIDEGREES GIB) PHASE ( DEGREES

10 4. 1634 -01 1.2905 + 02 4.1690 -01 1.2848 +02 4.1838 -01 1.2693 + 02 4.2425 -01 1.2081 + 02

15 8.3002 -01 1.2709 + 02 8.3104 -01 1.2632 + 02 8.3370 -01 1.2425 + 02 8.4352 -01 1.1610 +02

20 1 .2395 + 00 1.2513 + 02 1 .2408 +00 1.2415 + 02 1.2440 + 00 1.2158 + 02 1.2539 +00 1.1141 + 02

25 1 .6433 +00 1.2319 + 02 1 .6445 +00 1.2203 + 02 1.6474 + 00 1.1894 + 02 1.6518 + 00 1 .0574 + 02

30 2.0399 +00 1.2125 + 02 2 .0408 + 00 1.1991 + 02 2.0421 +00 1.1631 + 02 2.0337 +00 1.0211 + 02

35 2.4281 + 00 1.1935 + 02 2 .4280 + 00 1.1782 + 02 2.4253 + 00 1.1371 + 02 2.3954 +00 9.7520 +01

40 2 .8064 +00 1.1748 + 02 2.8049 + 00 1.1575 + 02 2.7985 +00 1.1115 + 02 2.7369 + 00 9.2981 + 01 45 3.1737 + 00 1.1553 + 02 3.1702 + 00 1.1372 + 02 3.1572 + 00 1.0852 + 02 3.0526 +00 8.8500 + 01 50 3.5289 + 00 1.1382 + 02 3.5228 + 00 1.1172 + 02 3.5011 +00 1.0514 + 02 3.3416 +00 8.4086 + 01 55 3.8711 +00 1.1205 + 02 3.8615 + 00 1.0977 + 02 3.8291 +00 1.0370 + 02 3.6019 +00 7.9749 + 01 60 4.19 94 +00 1.1031 + 02 4.1858 + 00 1.0785 + 02 4.1403 +00 1.0131 + 02 3.8324 +00 7.5497 + 01

65 4.5132 +00 1.0853 + 02 4.4948 +00 1.0600 + 02 4.4339 +00 9.8984 + 01 4.0323 +00 7.1340 + 01 70 4.8119 + 00 1.0699 + 02 4.7880 + 00 1 .0419 + 02 4.7094 + 00 9.5719 + 01 4.2013 + 00 6.7289 +01

75 5.0952 + 00 1.0541 + 02 5.0650 + 00 1.0244 + 02 4.9664 +00 9.4522 + 01 4.3395 +00 6,3355 + 01 80 5.3629 +00 1.0389 + 02 5.3257 + 00 1.0075 + 02 5.2050 + 00 9.2397 + 01 4.4476 +00 5.9547 + 01

85 5.6148 + 00 1.0243 + 02 5.5700 + 00 9.9131 + 01 5.4252 + 00 9.0350 + 01 4.5268 + 00 5.5877 + 01 90 5.8513 + 00 1.0103 + 02 5.7982 + 00 9.7579 + 01 5.6273 +00 8.8384 + 01 4.5785 + 00 5.2355 + 01 95 5.0724 +00 9.9707 + 01 6.0107 +00 9.5101 + 01 5.8121 +00 8.6505 + 01 4.6048 + 00 4,8991 + 01 100 6.2789 +00 9.8452 + 01 6.2080 +00 9,4699 +01 5.9802 +00 8.4715 + 01 4.6079 +00 4.5796 + 01

PSKDEGREES) = 14 PSKDEGREES! = 15 PSKDEGREES) = 16 PSKDEGREES) = 17 KB GIB! PHASEIDEGREES! GIB

-01 PHASE 1 DEGREES

)

GIB PHASE IDEGREES 1 GIB) PHASEIDEGREES)

10 4.2745 -01 1.1748 + 02 4.2923 1.1562 + 02 4.3113 -01 1.1364 + 02 4.3315 -01 1.1154 + 02

15 8.4839 -01 1.1166 + 02 8.5095 -01 1.0916 + 02 8.5356 -01 1.0654 + 02 8.5619 -01 1.0374 + 02 20 1.2575 + 00 1.0586 + 02 1.2589 +00 1.0277 + 02 1.2599 +00 9.9472 + 01 1.2504 +00 9.5968 + 01 25 1 .5495 + 00 1.0009 + 02 1.6470 +00 9.5389 + 01 1 .6430 + 00 9.2438 +01 1.6375 +00 8.6238 + 01 30 2.0201 + 00 9.4354 + 01 2.0097 +00 9.0053 + 01 1.9955 +00 8.5452 + 01 1.9800 +00 6.0562 + 01 35 2.3545 +00 6.8588 +01 2.3422 + 00 8.3773 + 01 2.3147 + 00 7.8527 + 01 2.2814 +00 7.2951 + 01 40 2.5792 +00 8.3073 + 01 2 .5400 +00 7.7559 + 01 2.5926 +00 7.1575 + 01 2.5362 +00 6.5422 + 01 45 2.9508 +00 7.7529 +01 2 .8995 +00 7.1424 + 01 2.8264 +00 6,4910 + 01 2.7404 +00 5.7990 + 01 SO 3.2068 + 00 7.2057 +01 3.1181 +00 5.5382 + 01 3.0132 +00 5,8250 + 01 2.8909 +00 5.0575 + 01 55 3.4152 + 00 6.6701 + 01 3.2937 +00 5.9446 + 01 3.1512 +00 5.1711 + 01 2.9855 +00 4.3501 +01 50 3.5848 +00 5.1443 + 01 3.4253 + 00 5.3635 + 01 3.2397 + 00 4.5316 + 01 3.0270 +00 3.6495 + 01 65 3.7151 +00 5,5308 + 01 3.5129 +00 4.7966 + 01 3.2793 +00 3.9088 + 01 3.0138 +00 2.9691 + 01 70 3.8055 + 00 5.1313 + 01 3.5571 +00 4.2450 + 01 3.2715 +00 3.3056 + 01 2.9497 +00 2.3131 +01

75 3.8598 + 00 4.5473 + 01 3.5598 +00 3.7142 + 01 3,2189 +00 2.7256 + 01 2.8387 +00 1.6870 +01 80 3.8767 +00 4.1809 + 01 3.5232 +00 3.2036 + 01 3,1251 +00 2.1730 + 01 2.6658 + 00 1.0977 + 01 85 3.8595 +00 3.7340 + 01 3.4507 +00 2.7179 + 01 2.9946 +00 1.6528 + 01 2.4972 +00 5.5504 + 00 90 3.8110 + 00 3.3088 + 01 3.3460 +00 2.2601 + 01 2.8325 +00 1.1717 + 01 2.2800 +00 7.2241 -01

95 3.7345 +00 2.9077 + 01 3.2135 +00 1.8345 + 01 2.5447 +00 7.3762 + 00 2.0421 +00 -3.3154 +00

100 3.5337 + 00 2.5331 + 01 3.0561 +00 1 .4458 + 01 2.4377 +00 3.6124 + 00 1.7925 + 00 -5,2803 + 00

16
Table 4 - Continued

KB

10

1520

2530

35hO

45

50

5560

6570

7580

85

90

95 100

PSI ( G( B 4.3528

8.5883

1 .2503 1.6302

1 .9598 2.2417

2 .4699

2 .6403 2.7501 2.7985 2.7866

2.7169

2.5937

2 .4230 2.2118

1 .9586 1.7033

1 .4275 1.1563

-01

-01

DEGREES! = 18

I PHASE(OEGREES)

1.0931 +02 1.0077 +02 9.2258 +01 8.3792 +01 7.5384 +01 5.7048 +01 5.8802 +01 5.0566 +01 4.2564 +01 3.4825 +01

PSKOEGREES) = 19 PSI (DEGREES! 20 PSI (OEGKEES) = 21

+ 00

+ 00 +00

+00

+00

+ 00 +00 +00

+ 00

+ 00 +00

+ 00

+ 00

+ 00

+ 00

+ 00

2.7189

1.9802

1.2732 5.0710

-4.8177

-5.4208 -9.7184

-1.2383 +01 -1.2419 +01

+ 01

+ 01

+ 01

+ 00 -02

+ 00

+ 00

GIB! .3753 -01 .6144 -01 .2595 +00 .5209 +00

.9354 +00 •1949 +00 .3930 +00 .5254 +00 .5900 +00

.5871 +00 .5190 +00 .3902 +00

.2072 +00

.9781 +00

.7130 +00

.4239 +00

.1259 +00

.4130 -01 .1250 -01

PHASEIOEGREES)

1.0595 +02 9.7532 +01 8.8343 +01 7.9101 +01 5.9921 +01 6.0820 +01 5.1819 +01 4.2942 +01 3.4221 +01 2.5694 +01 1.7415 +01 9.4621 +00

1.9429 +00 -4.9675 +00 -1.0979 +01 -1.5563 +01 -1.7675 +01 -1.5043 +01 -2.9450 +00

GIB) ,3990 -01 .6398 -01

,2581 +00

,5094 +00

,9055 +00

,1404 +00

,3045 +00

,3949 +00

,4103 +00

,3525 +00

,2258 +00

,0372 +00

,7958 +00

,5134 +00

.2040 +00

,8592 -01

,9663 -01

,2309 -01

,9478 -01

PHASE I DEGREES

)

1.0448 +02 9.4334 +01 8.4224 +U1 7.4155 +01 5.4173 +01 5.4258 +01 4.4475 +01 3.4824 +01 2.5355 +01 1.5124 +01 7.2106 +00 -1.2599 +00 -9.0798 +00 -1.5870

-2.0857

-2.2205

-1.4900

1.2012 4.5075

+ 01

+ 01

+ 01

+ 01

+ 01

+ 01

G( Bl .4238 -01 .6543 -01 .2557 +00

.5953 +00 .8726 +00

.0778 +00

,2041 +00

,2485 +00

,2111 +00

,0958 +00

,9097 +00

,5528 +00

,3581 +00

,0421 +00

,0815 -01

.1930 -01

,5317 -01

.6921 -01

,4585 -01

PHASE(DeGREES)

1.0188 +02 9.0875 +01 7.9903 +01 5.8986 +01 5.8143 +01 4.7396 +01 3.6775 +01 2.6317 +01 1.5078 +01 5.1375 +00 -3.3747 +00 -1.2232 +01 -1.9987 +01 -2.5519 +01 -2.5230 +01 -1.1417 +01 3.4597 +01 5.0387 +01 5.3835 +01

PSIIDEGREES! PSKOEGREES) = 22 KB G( B PHASE 1 DEGREES

)

G( B PHASE (DEGREES) G(B)

10 4.4365 -01 1.0054 + 02 4.4497 -01 9.9157 + 01 4.4768 -01

15 8 .6750 -01 8.9084 + 01 8 .6874 -01 8.7254 + 01 8.7089 -01

20 1.2541 + 00 7.7557 + 01 1.2522 + 00 7.5381 + 01 1.2476 + 00

25 1.5872 +00 6.5306 + 01 1 .5784 + 00 6.3567 + 01 1.5585 + 00

30 1.8535 + 00 5.5023 + 01 1.8333 + 00 5.1833 + 01 1 .7862 +00

35 2.0432 + 00 4.3840 + 01 2 .0054 + 00 4.0205 + 01 1 .9258 +00

40 2.1493 + 00 3.2792 + 01 2.0913 + 00 2.8721 + 01 1 .9658 +00

45 2.1593 + 00 2.1920 + 01 2.0851 +00 1.7429 + 01 1 .9031 +00

50 2.1044 + 00 1.1290 + 01 1 .9932 + 00 6.4043 + 00 1.7579 + 00

55 1 .9598 + 00 9.9917 -01 1.8192 + 00 -4.2275 + 00 1 .5257 + 00

50 1 .7443 + 00 -8.7820 + 00 1 .5748 + 00 -1.4241 + 01 1 .2267 + 00

55 1 .4597 + 00 -1.7733 + 01 1 .2741 +00 -2.3167 + 01 8.8049 -01

70 1.1515 +00 -2.5153 + 01 9.3545 -01 -2.9823 + 01 5.1599 -01

75 8.0999 -01 -2.9144 + 01 5.8577 -01 -3.0234 + 01 2.2982 -01

80 4.8145 -01 -2.2815 + 01 3.0180 -01 -5.2151 + 00 3.8397 -01

85 3.0025 -01 1.8334 + 01 3.6189 -01 5.2492 + 01 7.0858 -01

90 4.7090 -01 5.8529 + 01 5.5242 -01 5.5742 + 01 1.0118 + 00

96 7.5941 -01 5.4956 + 01 9.4859 -01 6.3381 + 01 1.2530 + 00

100 1.0377 +00 6. 1804 + 01 1.2070 + 00 5.7030 + 01 1 .4498 +00

PSKOEGREES) = 23 PHASE(DEGREES

9.5330 +01 8.3473 +01 7.0659 +01 5.7908 +01 4.5244 +01 3.2700 +01 2.0319 +01 8.1575 +00 -3.5424 +00 -1.4907 +01 -2.5184 +01 -3.3295 +01 -3.4714 +01 2.4748 -01 5.1795 +01 5.5954 +01

5. 11 54 +01 5.2688 +01 4.3399 +01

PSKOEGREES! = 24 G(B) PHASEIOEGREES)

4.5051 -01 9.3374 +01 8.7283 -01 7.9533 +01

1.2417- +00 6.5738 +01 1.5353 +00 5.2011 +01 1.7370 +00 3.8380 +01 1.8358 +00 2.4882 +01 1.8277 +00 1.1574 +01 1.7151 +00 -1.4520 +00 1.5073 +00 -1.4024 +01 1.2196 +00 -2.5772 +01 8.7274 -01 -3.5681 +01 4.9593 -01 -3.9597 +01 1.8553 -01 -1.2075 +00 3.8496 -01 6.5933 +01 7.2934 -01 6.6692 +01 1.0373 +00 5.8551 +01 1.2821 +00 4.8399 +01 1.4512 +00 3.7702 +01 1.5388 +00 2.7014 +01

PSI lOEGREESl

KB GIB PHASE 1 DEGREES 1 10 4.5344 -01 9.0300 + 01

15 8.7453 -01 7.5436 + 01 20 1.2343 +00 6.0621 + 01 25 1 .5085 + 00 4.5879 + 01 30 1 .5793 + 00 3.1242 + 01

35 1.7352 +00 1.6755 + 01 40 1.6772 +00 2.4938 + 00 45 1.5086 +00 -1.1410 + 01 50 1 .2445 + 00 -2.4672 + 01 55 9.0632 -01 -3.6529 + 01 60 5.2297 -01 -4.3896 + 01 65 1.6973 -01 -1.5124 + 01 70 3.5365 -01 5.7451 + 01

75 7.1385 -01 5.6208 + 01 80 1.0292 +00 5.6319 + 01 85 1.2719 +00 4.4689 + 01 90 1.4279 +00 3.2560 + 01 95 1.4913 +00 2.0749 + 01 100 1.4632 + 00 9.3076 + 00

KA=5 DELTAIDEGREES!

=

KB

10

1520

25

30

3540

4550

5550

55

70

7580

8590

95 100

PSI I GIB 5.5000

1 .0896 1.5132 2.1158 2.5928

3.0405 3.4553

3.8381 4.1851 4.4977 4.7772

5.0262

5.2481

5 .4472 5.6282 5.7955

5.9573 6.1155 5.2754

DEGREES) = 0

! PHASEIOEGREES)

1.2630 +02 1.2344 +02

PSKOEGREES) = 1 -01

+ 00

+ 00

+ 00 +00

+ 00 +00

+ 00

+ 00

+ 00

+ 00

+ 00

+ 00 +00

+00

+ 00

+ 00

+ 00 +00

1.2064 +02 1.1792 +02 1.1529 +02 1.1278 +02

1 . 1040 1.0817

1.0512

1.0427

1.0251 1.0118 9.9979

9.9007 +01 9.8262 +01 9.7732 +01 9.7398 +01 9.7230 +01 9.7194 +01

+ 02

+ 02

+ 02

+ 02

+ 02

+ 02

+ 01

GIB) 5.5008 -01 1.0897 +00 1.6134 +00 2.1159 +00 2.5929 +00 3.0405 +00 3.4559 +00 3.8374 +00 4.1840 +00 4.4961 +00 4.7752 +00 5.0237 +00 5.2451 +00 5.4437 +00 5.5243 +00 5.7923 +00 5.9529 +00 5.1110 +00 5.2708 +00

PHASEIOEGREES

!

1.2523 +02

1.2336 +02 1.2054 +02 1.1779 +02 1.1514 +02 1.1251 +02 1.1021 +02 1.0797 +02 1.0590 +02 1.0403 +02 1.0236 +02 1.0091 +02 9.9593 +01 9.8707 +01 9.7949 +01 9.7407 +01 9.7050 +01 9.5879 +01 9.6831 +01

PSIIDEGREES) = 2 GIB) PHASEIOEGREES!

.5032 -01

,0902 +00

,5139 +00

,1163 +00

.5930 +00

.0401 +00

.4548 +00

.8352 +00

.1805 +00

.4914 +00

.7690 +00 .0159 +00

.2357 +00

.4329 +00

.5123 +00

,7793 +00

,9391 +00

,0968 +00

,2565 +00

1.2604 +02 1.2310 +02 1.2022 +02 1.1741 +02 1.1470 +02 1.1211 +02 1.0965 +02 1.0735 +02 1.0523 +02

1.0331 +02 1.0159 +02 1.0010 +02 9.8836 +01 9.7809 +01 9.7012 +01 9.5431 +01 9.6045 +01 9.5828 +01 9.5739 +01

PSI I gib: 5.5073

1.0909

1.6147 2.1170

2.5931 3.0393

3.4527

3.8314

4.1 747 4.4831 4.7580

0022

2194

4140

5912

7563 9147 0714 5.2306

DEGREES! = 3 PHASEIOEGREES)

1.2572 +02

1.2268 +02 1.1969 +02

1.1678 +02 1.1397 +02 1.1128 +02 1.0872 +02

1.0633 +02

1.0412 +02

1.0211 +02

1.0031 +02 9.8741 +01 9.7407 +01 9.6312 +01 9.5449 +01 9.4805 +01 9.4357 +01 9.4075 +01 9.3920 +01.

-01 +00 +00

+00

+00 +00

+00

+ 00 +00 +00

+00 +00

+ 00

+ 00

+ 00 +00 +00

+00

+00

17
Table 5 - Continued

PSUDEGREES) = 4 PSMOEGREES) = 5 KB G 1 B PHASE (DEGREES

)

G ( B ) PHASE ( DEGREES

10 5.5131 -01 1.2527 + 02 5 • 5204 -01 1.2470 +02

15 1.0919 + 00 1.2206 + 02 1.0931 +00 1.2131 + 02

20 1.6158 +00 1. 1894 + 0? 1.6173 +00 1. 1799 + 02 25 2.1178 +00 1.1589 + 02 2.1188 +0 0 1.1475 + 02 30 2.5932 + 00 1.1294 + 02 ^ "n^^o

1.1161 + 02

35 3 .0380 + 00 l.lOll + 02 3.0360

'"'nn

1 .0860 + 02 40 3.4494 +00 1.0742 + 02 \ *fl

1

7 + 00 1.0574 + 02 45 3.8255 + 00 1 .0490 + 02 3.8172 + 00 1.0305 + 02

50 4.1658 + 00 1.0256 + 02 4.1531 + 00 1.0056 + 02

55 4.4705 + 00 1.0043 + 02 4.4530 + 00 9.8274 + 01 60 4.7416 + 00 9.8520 + 01 4.7186 +00 9.6218 + 01 65 4.9817 + 00 9.6843 + 01 4.9531 + 00 9.4404 + 01 70 5.1949 +00 9.5408 + 01 5.1606 + 00 9.2840 + 01

75 5.3856 + 00 9.4217 + 01 5.3458 + 00 9.1525 + 01 80 5.5593 + 00 9.3262 + 01 5.5144 + 00 9.0453 + 01 85 5.7214 + 00 9.2529 + 01 5.6721 +00 8.9605 + 01 90 5.8774 + 00 9. 1993 + 01 5.8244 +00 8.8954 + 01 95 6.0324 +00 9.1620 + 01 5.9763 +0 0 8.8466 + 01 100 6.1904 +00 9.1373 + 01 6.1318 +00 8.8098 + 01

PSI(DEGREES) = 7 PSKDEGREES) = 10

Gl B PHASE ( DEGREES

)

G { B PHASE 1 DEGREES

5.5401 -0 1 1.2315 + 02 5.5815 -0 1 1.1990 + 02

1 .0965 + 00 1.1927 + 02 1.1032 + 00 1 . 1493 + 02

1 .6208 +00 lil544 + 02 1.6270 1.1004 + 02

2 . 1208 +0 0 1.1171 + 02 2.1222 + 00 1.0525 + 02 2.5915 +00 1 .0808 + 02 2.5825 + 00 1 .0050 + 02

3 .0285 + 00 1 .0450 + 02 3.0031 9.5108 + 01 3.42 88 +00 1.0128 + 02 3.3804 9.1809 + 01

3 . 7906 + 00 9.8145 + 01 3.7126 +00 8.7732 + 01 4.1134 + 00 9.5222 + 01 4.00U2 8 . 3905 + 01

4 . 3982 + 00 9.2530 + 01 4 .2443 + 00 3.0355 + 01 4.6473 + 00 9.0088 + 01 4.4466 + 00 7.7102 + 01 4.8644 +00 8.7909 + 01 4.6180 + 0 0 7.4161 + 01 5.0541 + 00 8.6000 + 01 4.7585 +00 7. 1536 + 01 5.2219 +00 8.4359 + 01 4.8771 +00 5.9220 +01

5. 3740 + 00 8.2974 + 01 4.9609 +00 5.7190 + 01 5.5165 + 00 8.1821 + 01 5.0765 + 00 6.5409 + 01 5.5560 + 00 8.0865 + 01 5.1698 +00 6.3825 + 01 5.7945 +00 8 .0067 + 01 5.2649 + 00 6.2377 + 01 5.9388 +00 7.9375 + 01 5.3642 + 00 5.1002 + 01

K3

10

1520

2530

3540

45' 50

5560

6570

7580

8590

95 100

PSI (D GIB) 5.6174

1.1087 1.5310

2.1201 2.5586

2.9708

3.3228

3.5232

3.8722 4.0725

4,2287

4.3468

4 .4344 4.4994

4.5498

4.5924

4.6326

4.5737 4.7155

1.

EGREES) = 12 PHASE I DEGREES 1 1.1710 +02 1.1120 +02 0539 +02 9699 +01 4156 +01 8797 +01 3557 +01 8772 +01 4174 +01

,9895 +01

,5960 +01

,2385 +01

,91 76 +01

.6316 +01

.3775 +01

.1500 +01

.9423 +01

.7456 +01

,5552 +01

-01 +00

+ 00 +00

+00 +00

+00

+ 00

+ 00 +00

+ 00

+ 00 +no

+00

+00

+ 00

+ 00

+ 00 +00

PSI I GIB 5.5377

1.1116

1 .6328 2.1175

2.5581 2.9481

3.2837

3.5533

3.7875 3.9598 4.0853 4.1709

4.2250

4.2562

4.2728 4.2818

4.2882 4.2946

4.3006

DEGREES

PHAS

-01

+ 00

+ 00

+ 00

+ 00 +00

+ 00 +00

+ 00

+ 00

+ 00 +00

+ 00

+ 00

+ 00 +00

+ 00 +00

+ 00

13

E (DEGREES I ,1551 +02

,0909 +02

,0276 +02

,5546 +01

,0501 +01

,4650 +01

,9034 +01

,3692 +01

,8550 +01

,3975 +01

,9563 +01

,5745 +01

,2222 +01

.9081 +01

.5281 +01

.3751 +01 .1444 +01

.9241 +01

.7068 +01

PSI ( GIB 5.6596

1.1147

1 .6342 2.1138

2.5447

2.9203

3.2364

3.4915 3.5870

3.8265 3.9165

3.9650

3.9809

3.9737

3.9522 3.9234

3.8919

3.6593

3.8244

DEGREES) = 14

) PHASE I DEGREES I -01 1.1380 +02 +00 1.0681 +02 +00 9.9912 +01 +00 9.3149 +01 8.6558 +01 8.0177 +01

PSI IDEGREES) = 15

+00

+00

+ 00 +00

+ 00

+ 00

+ 00

+ 00 +00 +00

+00

+ 00 +00

+00

+00

.4049 +01

,8216 +01

,2721 +01

,7503 +01

,2897 +01

,8623 +01

,4788 +01

,1372 +01

,8331 +01

,5593 +01

,3059 +01

.0659 +01

.8273 +01

GIB) 5.6831 -01 1.1178 +00 1.6352 +00 2.1085 +00 2.5280 +00 2.8855 +00 3.1798 +00 4055 +00

5588 +00 5711 +00 7209 +00 7272 +00

7005 +00 5510 +00 5879 +00

5182 +00

,4460 +00

3720 +00 2938 +00

PHASE(DEGREES)

1.1196 +02 1.0436 +02 9.6661 +01 8.9504 +01 6.2329 +01 7.5360 +01 5.8703 +01 6.2347 +01 5.5351 +01 5.0790 +01 4.5677 +01 4.1047 +01 3.6911 +01 3.3249 +01 3.0012 +01 2.7118 +01 2.4463 +01 2.1939 +01 1.9451 +01

PSKDEGREES) = 16 PSKDEGREES) = 17 KB GIB PHASE 1 DEGREES GIB) PHASE 1 DEGREES

10 5.7061 -01 1.1000 + 02 5.7347 -01 1.0791 + 02

15 1.1211 +00 1.0175 + 02 1.1243 + 00 9.6959 + 01 20 1.5356 +00 9.3604 + 01 1 .6354 +00 9.0143 + 01 25 2.1013 +00 8.5612 + 01 2.0921 + 00 6.1475 +01

30 2.5074 + 00 7.7814 + 01 2.4825 +00 7.3015 + 01

35 2.6461 +00 7.0260 +01 2 .7962 + 00 6.4819 + 01 40 3.1130 +00 6.3000 +01 3.0346 +00 5.5942 + 01 45 3.3072 + 00 5.5090 +01 3.1922 + 00 4.9450 + 01 50 3.4315 + 00 4.9588 + 01 3.2739 + 00 4.2411 + 01

55 3.4917 +00 4.3549 + 01 3.2874 +00 3.5895 + 01 60 3.4965 +00 3.8024 + 01 3.2431 +00 2.9972 + 01 55 3.4567 +00 3.3053 + 01 3. 1534 + 00 2.4697 + 01 70 3.3837 +0 0 2.8653 + 01 3.0315 +00 2.0105 + 01 75 3.2869 +00 2.4807 + 01 2 .8904 +00 1.5197 + 01 80 3.1822 +00 2.1465 + 01 2.7404 +00 1.2927 + 01 85 3.0705 +00 1.8537 + 01 2.5886 + 00 1.0209 + 01 90 2.9573 +00 1 .5908 + 01 2.4380 +00 7.9283 + 00

95 2.8423 +00 1.3456 + 01 2.2877 +00 5.9864 + 00 100 2.7225 + 00 1.1123 + 01 2.1341 + 00 4.3411 + 00

PSKDEGREES) = 18 PSKDEGREES) = 19 GIB) PHASEIDEGREES) GIB PHASE 1 DEGREES

5.7528 -01 1.0570 + 02 5.7925 -01 1.0337 + 02 1.1275 + 00 9.5029 + 01 1.1307 + 00 9.2927 + 01

1 .6344 +00 8.5478 + 01 1.6325 +00 8.2510 + 01 2.0805 + 00 7.7095 + 01 2.0663 + 00 7.2473 + 01 2.4527 + 00 5.7935 + 01 2.4175 + 00 5.2575 + 01 2.7421 +00 5.^050 + 01 2.5771 + 00 5.2985 + 01 2.9445 + 00 5.0534 + 01 2 .8410 +00 4.3779 + 01 3.0604 + 00 4.2433 + 01 2.9110 + 00 3.5049 + 01 3.0950 +00 3.4843 + 01 2.8941 + 00 2.6902 + 01 3.0575 +00 2.7855 + 01 2.8021 +00 1.9454 + 01 2.9605 + 00 2.1565 + 01 2.5501 + 00 1.2876 + 01 2.8167 + 00 1 .5063 + 01 2.4558 + 00 7.2944 + 00

2 .6476 + 00 1.1423 + 01 2.2373 + 00 2 .8744 + 00

2 .4614 + 00 7.6822 + 00 2.0115 +00 -2.4309 -01 2.2719 + 00 4.8329 + 00 1 .7922 +0 0 -1.9519 + 00 2.0867 +00 2.8202 + 00 1.5890 + 00 -2.1821 + 00

1 .9089 +00 1.5732 + 00 1 .4057 +00 -8.6112 -01

1 .7377 +00 1 .0665 + 00 1.2477 + 00 2. 1743 + 00 1.5709 + 00 1.4167 + 00 1.1157 + 00 7.2494 + 00

KB

10

1520

2530

3540

45

50

5560

65

70

7580

8590

95 100

PSI I GIB 5.8237

1.1337 1.6295 2.0490

2.3766

2.6025

2.7237

2.7435 2.6714

2.5222

2.3146

2.0599

1.8100

1.5564 1.3277 1.1394

1.0034

9.2831 9.1945

DEGREES) = 20 PHASE I DEGREES

)

1.0092 +02 8.9553 +01 7.8541 +01

-01

+00

+00

+ 00

+ 00

+ 00 +00

+00

+00

+00 +00

+00

+00

+ 00

+ 00 +00

+00

-01

-01

6.7611 +01 5.6938 +01 4.6598 +01 3.5663 +01 2.7308 +01 1.8512 +01 1.0775 +01 4.0221 +00 1.3610 +00

5.0232 +00 6.5523 +00 5.5115 +00 1.5407 +00

5.4352 +00

1.4861 +0i 2.5400 +01

G I B 8734

1361 6227

0168

3029 4712

5204

4577

2975 2.0610

1.7739

1 .4651 1.1717 9.3078

7.8879

7.7278

6.5901

9.9961

1 .1626

DEGREES) = 20.5 PHASE lOEGREES

)

9.7015 +01 8.4455 +01 7.2052 +01 5.9859 +01 4.7953 +01 3.5438 +01 2.5417 +01 1.5053 +01 5.6057 +00 -2.5150 +00 -9.0756 +00 -1.2937 +01 -1.2838 +01 -6.9048 +00 5.7416 +00 2.1305 +01 3.3448 +01 4.0319 +01 4.3220 +01

-01 +00

+ 00

+ 00

+ 00 +00

+ 00 +00

+00

+ 00

+ 00

+ 00 +00

-01

-01

-01 -01

-01 +00

PSI I GIB 5.8555

1.1367

1.6253 2.0285

2.3292 2.5176 2.5919

2.5575

2.4273

2 . 2 1 97 1.9561

1 .5667 1.3802

1.1233 9.3029

8.3017

DEGREES) = 21 PHASEIDEGREES)PS II DEGREES

)

22 -01

+ 00

+ 00

+ 00

+ 00

+ 00

+ 00 +00

+ 00 +00

+00

+00

+ 00

+ 00 -01

-01 8.3093 -01 9.1131 -01 1.0412 +00

9.8347 +01 8.5238 +01 7.4271 +01 6.2509 +01 5.1023 +01 3.9901 +01 2.9254 +U1 1.9225 +01 1,0009 +01 1.8734 +00 -4.7«34 +00 -9.4197 +00 -1.1160 +01 -8.8547 +00 -1.4188 +00 1.0552 +01 2.3859 +01 3.4339 +01 4.0892 +01

GIB 5.8907

1 . 1 394 1.5197

2 .0043

2 .2749 2.4220

2 .4453 2.3534

2 . 1 ' 3 1

1 .8979 1.5870

1.2648 9.7384

7.7032

7.1125

7.9111

9 .4297 1.1159

1.2885

-01

+ 00

+ 00 +00

+ 00 +00

+ 00

+ 00

; 00

+ 00

+ 00 +00

-01 -01

-01

-0-1 -01

+ 00

+ 00

PHASE ( DEGREES

)

9.5655 +01 8.2654 +01 6.9803 +01 5.7159 +01 4.4834 +01 3.2899 +01 2.1499 +01 1.0623 +01 1.1473 +00 -7.0944

-1.3176

-1.5825

-1.2811

-1.4311

1.5515 +01 3.1720 +01 3.9770 +01 4.2651 +01 4.2555 +01

+ 00

+ 01

+ 01

+ 01

+ 00

18
Table 5 - Continued

KB

10

1520

2530

35

45

50

5560

55

70

7580

8590

95 100

PSl

G I B 5.9265

l.lhl') 1.5126

1 .9751 2.2133

2.3151 2.2837

2.1317

1.8810

1.5614

1.2109 8.7998

5.5030 6.2359

7.7255 9.7550

1.1743

1 .3475

1 .4931

DEGREES) = 23 PHASE ( DEGREES

)

-01 9.2845 +01

+ 00

+ 00

+ 00

+ 00

+ 00 +00

+00 +00

+00

+00

-01

-01

-01 -01

-01

+00 +00

+00

-1.

-2.

+ 01

+ 01

+ 01

+ 01 fOl

1-01

7.8911 6.5137

5. 1 594 3.8374

2.5597

1.3431 2.1315 +00 -7.8830 +00

.5858 +01 .0280 +01 -1.7676 +01 -3.0203 +00

2.1432 +01 3.7315 +01 4.2374 +01 4.2076 +01 3.9387 +01 3.5499 +01

PSl I GIB 5.9637

1 .1442 1.6037

1 .9437

DEGREES) = 24

) PHASE(DEGREES)

,9916 +01

2.1439

2.1957

2.1075

1 .8938

1 .5842 1.2170 8.4555

5.6658 5.4550

7.4820 9.9282

1.2081 1.3775

1 .5008 1.5814

-01 +00

+ 00

+ 00

+ 00 +00

+ 00

+ 00

+ 00

+ 00

-0 1 -01

-0 1 -01 -01

+ 00

+ 00

+ 00 +00

7.5012 6.0275

4.5785

3.1645

1.8000

5.0639 5.8017 +00 1.5925 +01 2.3854 +01 2.3905 +01 7.9255 +00 2.4033 +01 4.0900 +01 4.3413 +01 4.0514 +01 3.5674 +01 3.0124 +01 2.4280 +01

PSl I Gl B 6.0024

1 . 1461 1.5930

1 .9057

2 .0664 2.0556

1 .9170 1.5415

1 .2770 8.7475

5.2800

4.6255

7.0159 9.8257

1 .2162 1.3839

1 .4858 1.5323 1.5275

DEGREES) = 25 PHASE (DEGREES) 8.6870 +01 7.0955 +01 5.6218 +0! 3.9744 +01 2.4651 +01 1.0115 +01 -3.5791 +00 -1.5900 +01 -2.5574 +01 -2.9691 +01 -1.7234 +01 2.2753 +01 4.3082 +01 4.3894 +01 3.8852 +01 3.2099 +01 2.4995 +01 1.8022 +01 1.1323 +01

-0 1 + 00 +00 +00

+00

+00

+ 00 +00

+ 00

-0

-0

-0

-0

-0+00 +00

+00

+00

PSKDEGREES) = 0 PSI(

KB GIB) PHASE I DEGREES ) GIB

10 6.7759 -01 1.2145 +02 6.7770

15 1.3242 +00 1.1712 +02 1.3244

20 1.9249 +00 1.1300 +02 1.9251

25 2.4680 +00 1.0918 +02 2.4681

30 2.9461 +00 1.0572 +02 2.9450

35 3.3565 +00 1.0271 +02 3.3562

40 3.7021 +00 1.0020 +02 3.7015

45 3.9907 +00 9.8257 +01 3.9898

50 4.2344 +00 9.6884 +01 4.2331

55 4.4482 +00 9.5051 +01 4.4458

50 4.6481 +00 9.5714 +01 4.6466

55 4.8484 +00 9.5722 +01 4.8470

70 5.0594 +00 9.5935 +01 5.0580

75 5.2859 +00 9.6202 +01 5.2847

80 5.5270 +00 9.5397 +01 5.5259

85 5.7774 +00 9.6444 +01 5.7754

90 5.0290 +00 9.6316 +01 5.0278

95 5.2730 +00 9.5030 +01 6.2718

100 5.5024 +00 9.5636 +01 6.5008

Table 5 KA=5 DELTAIDEGREES)=25

DEGREES) = 1 PSIIDEGREES) = 2

1 PHASEIDEGREES) GIB) PHASE I DEGR EES

)

-01 +00

+ 00 +00

+ 00

+ 00

+ 00

+ 00

+ 00

+ 00

+ 00 +00 +00

+ 00 +00

+ 00

+ 00

+ 00

+ 00

1.2139 +02 1.1704 +02 1.1290 +02

.0905 +02

.0558 +02

.0255 +02

.0003 +02 .8065 +01 .6679 +01 .5843 +01 9.5482 +01 9.5477 +01 9.5675 +01 9.5925 +01 9.6105 +01 9.6134 +01 9.5987 +01 9.5683 +01 9.5271 +01

6.7800 -01 1.3249 +00 1.9255 +00 2.4584 +00 2.9457 +00 3.3552 +00 3.6995 +00 3.9869 +00 4.2294 +00 4.4425 +00 4.5420 +00 4.8423 +00 5.0537 +00 5.2807 +00 5.5223 +00 5.7728 +00 6.0240 +00 6.2573 +00 5.4953 +001.2120 +02 1.1578 +02 1.1258 +02 1.0868 +02 1.0515 +02 1.0207 +02 9.9499 +01 9.7492 +01 9.6054 +01 9.5188 +01 9.4788 +01 9.4742 +01 9.4897 +01 9.5100 +01 9.5227 +01 9.5201 +01 9.4999 +01 9.4540 +01 9.4176 +01

PSl (DEGREES) = 3 GIB) 5.7851 -01 1.3257 +00 1.9264 +00 2.4688 +00 2.9452 +00 3.3534 +00 3.6963 +00 3.9819 +00 4.2229 +00 4.4348 +00 4.6338 +00 4.8340 +00 5.0457 +00 5.2732 +00 5.5150 +00 5.7654 +00 5.0159 +00 6.2577 +00 6.4838 +00

PHASEIDEGREES)

1.2088 +02 1.1635 +02 1.1206 +02 1.0805 +02 1.0444 +02 1.0127 +02 9.8518 +01 9.6535 +01 9.5038 +01 9.4096 +01 9.3631 +01 9.3517 +01 9.3599 +01 9.3722 +01 9.3762 +01 9.3646 +01 9,3351 +01 9.2902 +01 9.2350 +01

PSIIDEGREES) = 4 PSKDEGREES) = 5 PSIIDEGREES) = 7 PSIIDEGREES) = 10 KB GI'B PHASEIDEGREES GIB! PHASEIDEGREES) GIB) PHASEIDEGREES) GIB) PHASE IDEGREES

10 6.7922 -01 1.2044 + 02 6.8013 -01 1 .1987 + 02 6.8255 -01 1.1836 + 02 6.8772 -01 1.1514 + 02

15 1.3259 +00 1.1578 + 02 1.3284 + 00 1 .1502 + 02 1.3323 + 00 1.1301 + 02 1.3401 + 00 1.0874 + 02 20 1.9276 +00 1.1133 + 02 1.9290 +00 1 .1040 + 02 1.9325 + 00 1.0790 + 02 1.9384 +00 1.0250 + 02

25 2.4593 + 00 1.0720 + 02 2.4698 +00 1 .0508 + 02 2.4704 + 00 1.0312 + 02 2.4584 +00 9.5820 + 01 30 2.9444 + 00 1.0344 + 02 2.9431 + 00 1 .0216 + 02 2.9384 + 00 9.8747 + 01 2.9218 +00 9.1503 + 01

35 3.3507 +00 1.0015 + 02 3.3458 +00 9 .8710 + 01 3.3343 +00 9.4877 + 01 3.2971 +00 8,5741 + 01 40 3.5912 +00 9.7385 + 01 3.5842 +00 9 .5800 + 01 3.5521 +00 9.1575 + 01 3.5997 +00 8.2513 + 01 45 3.9744 +00 9.5198 + 01 3.9640 +00 9 .3477 + 01 3.9315 + 00 8.8893 + 01 3.8414 +00 7.9158 + 01

50 4.2132 +00 9.3502 + 01 4.1995 +00 9 .1756 + 01 4.1573 + 00 8.6837 + 01 4.0390 +00 7.5407 + 01

55 4.4233 + 00 9.2557 + 01 4.4071 + 00 9 .0503 + 01 4.3552 + 00 8.5355 + 01 4.2117 +00 7.4265 + 01 50 4.6212 +00 9.2011 + 01 4.5032 + 00 8 .9928 + 01 4.5456 + 00 8.4375 + 01 4.3775 +00 7.2504 + 01 55 4.8211 + 00 9.1802 + 01 4.8022 +00 8 .9595 + 01 4.7397 +00 8.3712 + 01 4.5497 + 00 7.1236 + 01 70 5.0329 +00 9. 1780 +01 5.0136 + 00 8 .9441 + 01 4.9471 +00 8.3200 + 01 4.7347 +00 5.9957 + 01 75 5.2506 + 00 9.1791 + 01 5.2410 + 00 8 .9306 + 01 5.1700 +00 8.2674 + 01 4.9313 + 00 5.8595 + 01 80 5.5024 + 00 9.1710 + 01 5.4820 +00 8.9069 + 01 5.4045 +00 8.2017 +01 5.1322 +00 6.7049 + 01 85 5.7521 +00 9. 1455 + 01 5.7299 +00 8 .8651 + 01 5.6425 +00 8.1172 + 01 5.3258 +00 5.5285 + 01 90 6.0009 +00 9.1043 + 01 5.9755 + 00 8 .8071 + 01 5.8744 +00 8.0141 + 01 5.5046 + 00 5.3338 + 01 95 5.2401 +00 9.0465 + 01 5.2102 +00 8 .7331 + 01 6.0912 + 00 7.8958 + 01 5.6580 +00 5.1283 + 01 100 6.4527 +00 8.9791 + 01 5.4272 +00 8 .5500 + 01 6.2871 +00 7.7725 + 01 5.7824 +00 5.9211 + 01 105 5.5649 + 00 8.9085 + 01

PSl IDEGREES

)

= 12 PSIIDEGREES) = 14 PSIIDEGREES) = 15 PSIIDFGREES) = 16 KB GIB PHASE 1 DEGREES

]

GIB) PHASE 1 DEOKttS

)

GIB PHASEIDEGREES) GIB PHASEIDEGREES

10 5.9215 -01 1 .1237 + 02 5.9739 -01 1.0911 + 02 7.0030 -01 1 .0729 + 02 7.0340 -01 1.0535 + 02

15 1 .3454 +00 1 .0505 + 02 1 .3534 +00 1.0072 + 02 1 .3571 + 00 9 .8311 + 01 1.3608 +00 9.5735 + 01 20 1.9419 + 00 9 ,8033 + 01 1 .9442 +00 9.2551 + 01 1.9445 +00 8 .9555 + 01 1 .9442 +00 8.5456 + 01

25 2.4529 +00 9 .1399 + 01 2.4520 +00 8.5006 + 01 2.4438 +00 8 .1445 + 01 2.4333 +00 7.7547 + 01 30 2.9005 + 00 8 .5265 + 01 2.8572 + 00 7.7910 +01 2 .8448 +00 7 .3815 + 01 2.8178 +00 5.9444 + 01 35 3.2538 + 00 7 .9737 + 01 3.1893 + 00 7.1480 + 01 3.1473 + 00 6 .5885 + 01 3.0977 +00 6. 1984 + 01 40 3.5292 + 00 7 .4900 + 01 3.4257 + 00 5.5815 + 01 3.3508 +00 6 .0764 + 01 3.2838 + 00 5.5381 + 01 45 3.7407 +00 7 .0806 + 01 3.5957 + 00 6.0970 + 01 3.5033 +00 5 .5511 + 01 3.3958 + 00 4,9703 + 01

50 3.9071 + 00 6 .7448 + 01 3.7177 + 00 5.5929 + 01 3.5973 + 00 5 .1106 + 01 3.4580 +00 4.4925 + 01

55 4.0491 + 00 6 .4739 + 01 3.8149 +00 5.3581 + 01 3.6553 +00 4 .7424 + 01 3.4945 +00 4.0908 + 01 50 4.1849 +00 5 .2513 + 01 3.9057 +00 5.0719 + 01 3.7282 + 00 4 .4233 + 01 3.5234 +00 3.7394 + 01

55 4.3269 +00 5 .0545 + 01 4.0002 + 00 4.8081 + 01 3.7920 + 00 4 .1248 + 01 3.5518 +00 3.4073 + 01 70 4.4785 + 00 5 .8515 + 01 4.0988 + 00 4.5417 + 01 3.8559 + 00 3 .8208 + 01 3.5758 +00 3.0572 + 01

75 4.5358 +00 5 .5545 + 01 4.1933 + 00 4.2559 + 01 3.9098 + 00 3 .4949 + 01 3.5837 +00 2.7037 + 01 60 4.7884 +00 5 .4252 + 01 4.2712 +00 3.9444 + 01 3.9403 +00 3 .1432 + 01 3.5511 + 00 2.3158 + 01

85 4.9245 +00 5 .1729 + 01 4.3197 + 00 3.5115 + 01 3.9348 + 00 2 .7727 + 01 3.4957 +00 1.9151 + 01 90 5.0336 + 00 4 .9044 + 01 4.3299 + 00 3.2582 + 01 3.8860 +00 2 .3980 + 01 3.3855 + 00 1.5214 + 01

95 5.1093 +00 4 .5299 + 01 4.2986 + 00 2.9289 + 01 3.7933 +00 2 .0374 + 01 3.2303 + 00 1.1591 + 01 100 5.1503 +00 4 .3604 + 01 4.2286 + 00 2.5085 + 01 3.5625 + 00 1 .7088 + 01 3.0412

2.8329

+00

+ 00 8.5284

6.2379

+ 00

+ 00
Table 6 - Continued

PSI(OEGREES) = 17. KB GIB) PHASEIDEGREES

10 7,0670 -01 1.0329 + 02

15 1 .3645 +00 9.2998 + 01 20 1 .9430 + 00 8.3057 + 01

25 2.4204 +00 7.3608 + 01

30 2.7857 +00 6.4799 + 01

in

5.6 777 + 01 +00 4.9671

45 3 2721 + 00

5 0 3.2984 + 00 + 01

55 3,2987 + 00 • ^

+ 01

6 0 3 . 2904 + 00

6 5 3 .2793 + 00 2 6628 + 01

7 Q 3.2591 + 00 2.2908 + 01 75 3.2165 + 00 1.6960 + 01 60 3.1372 + 00 1.4820 + 01 85 3.0117 + 00 1.0673 + 01 90 2.8388 + 00 6.8118 + 00

95 2.6261 + 00 3.6005 + 00 100 2.3894 + 00 1.4365 + 00

PSI ( G( B 7.1019

1 .3682

1 .9408 2.4046

2.7479

9725 0924

1313

1178 0782 0295

9757

9083

8129

6762

4921 2649 2.0102

1.7532

DEGREES) = 18

) PHASE ( DEGREES

)

1.0111 +02 9.0099 +01 7.9457 +01 6.9331 +01 5.9881 +01 5.1259 +01 4.3540 +01 3.7081 +01 3.1573 +01 2.5944 +01 2.2881 +01 1.9019 +01 1.5073 +01 1.0946 +01 6.7559 +00

PSI (DEGREES) 18.5

-01

+ 00 +00

+00

+00

+00

+ 00

+ 00

+ 00 +00

+ 00

+ 00

+ 00

+ 00

+ 00 +00

+ 00 +00

+ 00

.8174 +00

,8226 -01

.1955 +00

.8500 +00

GIB)

.1201 -01

.3700 +00

.9393 +00

.3955 +00

.7258 +00

.9352 +00

,0350 +00

,0542 +00

,0195 +00

,9586 +00

,6890 +00

,8130 +00

.7216 +00 5999 +00 4357 +00 2254 +00

.9775 +00

.7133 +00

.4570 +00

PHASE( DEGREES

)

9.9973 +01 8.8589 +01 7.7582 +01 5.7104 +01 5.7321 +01 4.8404 +01 4.0507 +01 3.3728 +01 2.8050 +01 2.3295 +01 1.9139 +01 1.5201 +01 1.1202 +01 7.0752 +00 3.0048 +00 -5.8290 -01 -3.0195 +00 -3.3801 +00 -5.6158 -01

PSI(DEGREES) = 19 G(B)

,1388 -01 ,3716 +00

,9375 +00

,3855 +00

.7040 +00

.8954 +00

.9750 +00

.9725 +00

,9157 +00

,8333 +00

,7421 +00

.5438 +00

.5285 +00

.3814 +00

,1915 +00

,9590 +00

,6975 +00

,4380 +00 2259 +00

PHASE (DEGREES) 9.8807 +01 8.7040 +01 7.5657 +01 6.4817 +01 5.4693 +01 4.5465 +01

3.7298 +01 3.0300 +01 2.4453 +01 1.9504 +01 1.5384 +01 1.1413 +01 7.4205 +00

3.3881 +00 -4.0455 -01 -3.3611 +00 -4.5251 +00 -2.5444 +00 3.9795 +00

PSKDEGREES) = 20 PSKDEGREES) = 21 PSKDEGREES) = 21.5 PSIIDEGREES) = 22 <B G( B PHASE(DEGREES> GIB) PHASE (DEGREES! G(6 PHASE ( DEGREES

]

G(B) PHASE(DEGREES)

10 7.1775 -01 9.5384 + 01 7.2182 -01 9.3843 +01 7.2392 -01 9.2528 + 01 7.2607 -01 9.1164 + 01

15 1.3753 + 00 8.3821 + 01 1.3785 +00 8.0444 + 01 1.3801 +00 7.8696 + 01 1.3816 +00 7.6910 + 01 20 1 .9328 + 00 7.1559 + 01 1 .9267 +00 6.7454 + 01 1 .9229 +00 6.5293 + 01 1 .9188 +00 5.3073 + 01 25 2.3629 + 00 6.0056 + 01 2.3363 + 00 5.5085 + 01 2.3215 + 00 5.2507 + 01 2.3055 +00 4.9871 + 01

30 2.5532 + 00 4.9237 + 01 2.5951 + 00 4.3515 + 01 2.5531 + 00 4.0557 + 01 2.5291 +00 3.7533 + 01

35 2.8076 +00 3.9356 + 01 ,:.7085 + 00 3.2965 + 01 2.6546 + 00 2.9589 + 01 2.5975 + 00 2.5324 + 01 40 2.8450 +00 3.0655 + 01 2.6988 + 00 2.3727 + 01 2.5199 +00 2.0151 + 01 2.5371 + 00 1.5533 + 01 45 2.7953 +00 2.3237 + 01 2.5996 +00 1.5927 +01 2 .4950 + 00 1.2194 + 01 2.3860 +00 8.4198 + 00

50 2.6923 + 00 1.7127 + 01 2 .4485 +00 9.6424 + 00 2.3195 + 00 5.8783 + 00 2. 1862 + 00 2.1253 + 00 55 2.5554 +00 1.2145 + 01 2.2768 + 00 4.7170 + 00 2.1251 + 00 1.0861 + 00 1.9716 + 00 -2.4333 + 00 50 2 .4309 +00 7.9300 + 00 2.1010 +00 7.9395 -01 1 .9314 + 00 -2.5180 + 00 1.7603 + 00 -5.5472 + 00

65 2.2892 + 00 4.0841 + 00 1.9203 +00 -2.4906 + 00 1.7345 + 00 -5.2463 + 00 1.5509 + 00 -7.4356 + 00 70 2.1287 + 00 3.9437 -01 1.7231 + 00 -5.1852 + 00 1.5250 +00 -6.9835 + 00 1.3355 + 00 -7.7265 + 00

75 1 .9351 + 00 -2.9815 + 00 1.5005 + 00 -5.7078 + 00 1.2985 +00 -5.7468 + 00 1.1172 + 00 -4.8753 + 00

80 1.7050 + 00 -5.3945 + 00 1.2599 + 00 -5.5236 + 00 1.0744 + 0U -2.2875 + 00 9.3348 -01 3.9800 + 00

65 : .4496 + 00 -5.5603 + 00 1 .0394 +00 1.0352 + 00 9.1373 -01 9.2931 + 00 8.6653 -01 1 .9805 + 01 90 1.2027 +00 -1.4241 + 00 9.1761 -01 1 .4916 + 01 9.0574 -01 2 .6100 + 01 9.7586 -01 3.4984 + 01 95 1 .0288 + 00 9.0155 + 00 9.5757 -01 3.1010 + 01 1.0671 + 00 3.8687 + 01 1.2093 + 00 4.2149 + 01 100 9.9877 -01 2.3758 + 01 1.1505 + 00 4.0304 + 01 1.3155 + 00 4.3252 + 01 1.4761 + 00 4.2503 +01

PSKDEGREES! = 23 ^^K

KB G(B PHASE(DEGREES) G(B

10 7.3051 -01 8.8407 + 01 7.3614 -01

15 1 .3844 +00 7.3218 + 01 1.3859 +00

20 1.9091 + 00 5.8486 + 01 1 .6972 +00

25 2.2599 +00 4.4427 + 01 2.2293 +00

30 2 .4548 +00 3.1292 + 01 2.3715 +00

35 2.4745 + 00 1.9395 + 01 2.3388 + 00

40 2.3599 + 00 9.1017 + 00 2.1577 + 00

45 2.1553 + 00 7.9103 -01 1 .9095 + 00

50 1 .9081 +00 -5.2361 + 00 1 .5190 + 00

55 1 .5567 + 00 -8.8791 + 00 1 .3414 +00

50 1.4211 + 00 -1.0216 + 01 1.1038 + 00

65 1 .2040 + 00 -9.0796 + 00 9.2027 -01

70 1.0083 + 00 -4.2702 + 00 8.1570 -01

75 8.6552 -01 5.5326 + 00 8.3667 -01

80 8.4582 -01 2.2722 + 01 9.9727 -01

85 9.9074 -01 3.6036 + 01 1 .2441 + 00 90 1.2391 +00 4.1117 + 01 1 .5062 + 00

95 1 .5090 +00 3.9649 + 01 1 .7275 +00

100 1.7422 +00 3.5085 + 01 1.8716 1.9216

+00

+00

! = 24 PSKDEGREES! = 25 PHASE ( DEGREES

)

G( B) PHASE(DEGREES)

8.5513 + 01 7.3995 -01 8.2503 + 01 5.9372 + 01 1.3689 +00 6.5371 + 01 5.3709 + 01 1.8832 +00 4.8739 + 01 3.8754 + 01 2.1834 +00 3.2856 + 01 2.4797 + 01 2.2794 + 00 1.8054 + 01 1.2210 + 01 2.1905 + 00 4.7870 + 00 1.4718 + 00 1.9512 +00 -6.2993 + 00 -6.8432 + 00

1 .6512 +00 -1.4291 + 01 -1.2121 + 01 1.3255 +00 -1.7943 + 01 -1.3833 + 01 1.0422 +00 -1.5754 + 01 -1.1541 + 01 8.4547 -01 -6.5279 + 00 -4.5169 + 00 7.6685 -01 8.3409 + 00 8.1140 + 00 8.2149 -01 2.3565 + 01 2.3805 + 01 9.9112 -01 3.3214 + 01 3.5139 + 01 1 .2275 +00 3.5566 + 01 3.6726 + 01 1 .4748 + 00 3.2770 + 01 3.6449 + 01 1.5813 +00 2.5540 + 01 3.0771 + 01 1.8075 + 00 1.8527 + 01 2.3425 + 01 1.8317 +00 9.9188 + 00 1.5585 + 01

KA = 5 DELTA(DEGREES)=50 PSKDEGREES) = 0 PSKDEGREES) = 1 PSKDEGREES) = 2 PSKDEGREES) = 3 KB G( B PHASE(DEGREES) G(B PHASE(DEGREES) G( B ! PHASE(DEGREES) G(B) PHASE(DEGREES

10 7.5723 -01 7.9230 + 01 7.5750 -01 7.9168 + 01 7.5829 -01 7.8982 + 01 7.5961 -01 7.8572 + 01

15 1 .2694 + 00 8.7185 + 01 1 .2896 +00 6.7103 + 01 1.2910 +00 8.5853 + 01 1.2929 + 00 6.6437 + 01 20 1.8110 + 00 8.6549 + 01 1.6116 +00 6.6448 + 01 1.8132 + 00 8.5145 + 01 1 .8159 +00 8.5640 + 01

25 2.1874 + 00 8.7702 + 01 2.1881 +00 8.7583 + 01 2.1900 + 00 8.7224 + 01 2.1933 + 00 8.6625 + 01 30 2.6073 +00 8.8007 + 01 2.5081 + 00 8.7870 + 01 2.5105 + 00 8.7459 + 01 2.6143 +00 8.5775 + 01 35 2.9259 +00 6.6023 + 01 2.9258 +00 8.7859 + 01 2 .9294 +00 8.7405 + 01 2.9337 +00 8.6532 + 01 40 3.2732 +00 B.8551 + 01 3.2742 + 00 8.6389 + 01 3.2771 + 00 8.7874 + 01 3.2818 + 00 8.7015 + 01 45 3.5681 +00 8.8315 + 01 3.5692 + 00 6.8125 + 01 3.5724 + 00 8.7550 + 01 3.5775 +00 8.6616 + 01 50 3.8588 + 00 8.8780 + 01 3.8600 +00 8.8574 + 01 3.8534 +00 8.7957 + 01 3.8686 + 00 8.6929 + 01

55 4.1410 + 00 8.8591 + 01 4.1422 + 00 8.8369 + 01 4.1459 + 00 8.7701 + 01 4.1516 + 00 8.6589 + 01 60 4.3914 +00 8.8658 + 01 4.3927 +00 8.8619 + 01 4.3966 +00 8.7901 + 01 4.4025 +00 8.5705 + 01 55 4.6594 + 00 8.8629 + 01 4.6608 + 00 8.8573 + 01 4.6649 + 00 8.7805 + 01 4.5711 +00 8.6527 + 01 70 4.8851 + 00 6.8695 + 01 4.8875 + 00 8.8623 + 01 4.8919 + 00 6.7606 + 01 4 .8982 + 00 6.5445 + 01 75 5.1344 + 00 8.9003 + 01 5.1360 +00 8.8714 + 01 5.1405 +00 8.7848 + 01 5.1459 + 00 8.5405 + 01 80 5.3507 + 00 6.8943 + 01 5.3524 + 00 3.8638 + 01 5.3570 +00 8.7723 + 01 5.3535 + 00 6.5198 + 01

85 5.5756 + 00 8.9106 + 01 5.5775 + 00 8.6767 + 01 5.5823 + 00 8.7822 + 01 5.5888 +00 8.6215 + 01 90 5.7887 + 00 8.9018 + 01 5.7905 +00 8.8681 + 01 5.7954 +00 8.7667 + 01 5.6019 + 00 8.5979 + 01

95 5.9918 +00 8.9157 + 01 5.9937 +00 8.8803 + 01 5.9987 + 00 8 .7741 + 01 6.0051 +00 8.5972 + 01 100 5.2015 + 00 8.9110 + 01 6.2035 +00 8.8740 + 01 5.2066 + 00 8.7530 + 01 6.2149 +0U 8.5779 + 01

20
Table 7 - Continued

PSIIDEGREESI = 4 PSKOEGREES) = 5 PSKOEGREESI = 7 KB

10

1520

2530

3540

45

50

5560

6570

7580

8590

95 100

G(B) 7.7145 -01 1.2956 +00 1.8197 +00 2.1978 +00 2.6195 +00 2.9395 +00 3.2881 +00 3.5842 +00 3.8758 +00 4.1588 +00 4.4098 +00 4.6784 +00 4.9053 +00 5.1539 +00 5.3701 +00 5.5950 +00 5.8075 +00 6.0101 +0u 6.2191 +00

PHASE(DEGREESI

7.8239 +01 7 8.5854 +01 1 8.4934 +01 1 8.5789 +01 2 8.5817 +01 2 8.5551 +01 2 8.5815 +01 3 8,5296 +01 3 8.5491 +01 3 8.5034 +01 4 8.5033 +01 4 8.4739 +01 4 8.4541 +01 4 8.4386 +01 5 8.4064 +01 5 8.3968 +01 5 8.3618 +01 5 8.3497 +01 6 8.3192 +01 6

G(B)

,7383 -01

,2990 +00

,8246 +00

,2034 +00

,5260 +00

,9465 +00

,2956 +00

,5920 +00

,8835 +00

,1656 +00

,4172 +00

,5853 +00

,9116 +00

,1692 +00

,3743 +00

,5979 +00

,8087 +00

,0096 +00

,2155 +00

PHASE(DEGREES1

7.7583 +01 8.5105 +01 8.4025 +01 8.4715 +01 8.4586 +01 8.4152 +01 8.4272 +01 8.3500 +01 8.3543 +01 8.3035 +01 8.2885 +01 8.2441 +01 8.2095 +01 8.1793 +01 8.1324 +01 8.1082 +01 8.0586 +01 8.0320 +01 7.9869 +01

PSIIDEGREESI = 10 GIBl 7.8019 -01 1.3082 +00 1.8372 +00 2.2179 +00 2.6422 +00 2.9535 +00 3.3126 +00 3.5084 +00 3.8985 +00 4.1792 +00 4.4267 +00 4.5908 +00 4.9119 +00 5.1537 +00 5.3618 +00 5.5774 +00 5.7792 +00 5.9599 +00 6.1655 +00

PHASEIDEGREES)

7.6201 +01 8.3112 +01 8.1609 +01 8.1853 +01 8.1310 +01 8.0465 +01 8.0156 +01 7.9086 +01 7.8725 +01 7.7717 +01 7.7159 +01 7.5329 +01 7.5591 +01 7.4897 +01 7.4039 +01 7.3410 +01 7.2527 +01 7.1879 +01 7.1045 +01

G(B) 7.9377 -01 1.3273 +00 1.8629 +00 2.2457 +00 2.6707 +00 2.9897 +00 3.3337 +00 3.6217 +00 3.9004 +00 4.1569 +00 4.3951 +00 4.5388 +00 4.8344 +00 5.0470 +00 5.2215 +00 5.4000 +00 5.5599 +00 5.7049 +00

.5.8501 +00

PHASE I DEGREES

)

7.3055 +01 7.8893 +01 7,5491 +01 7.5795 +01 7.4375 +01 7.2540 +01 7.1479 +01 6.9537 +01 6.8330 +01 6.6479 +01 6.5101 +01 5.3434 +01 5.1878 +01 5.0374 +01 5.8711 +01 5,7290 +01 5,5614 +01 5,4192 +01 5,2578 +01

PSIIDEGREESI = IS KB GIBl PHASE IDEGREES

I

10 8.2746 -01 6.5447 +01

15 1.3725 +00 6.8643 +01

20 1.9181 +00 6.4054 +01

25 2.2953 +00 5.1085 +01

30 2.7059 +00 5.7545 +01

35 2.9962 +00 5.3572 +01 40 3.2978 +00 5,0464 +01

45 3.5290 +00 4.5475 +01

50 3.7351 +00 4.3305 +01

55 3.9137 +00 3.9495 +01

60 4.0384 +00 3.6248 +01

55 4.1608 +00 3.2733 +01

70 4.2195 +00 2.9412 +01

75 4.2802 +00 2,5209 +01

80 4,2861 +00 2.2903 +01

85 4.2828 +00 1.9977 +01

90 4.2451 +00 1.5827 +01

95 4.1819 +00 1.4138 +01

100 4.1053 +00 1,1300 +01

PSIIDEGREESI = 16 GIBl

,3590 -01

,3834 +00

,9301 +00

.3035 +00

,7057 +00

,9848 +00

,2695 +00

,4789 +00

,6579 +00

,8044 +00

,8922 +00

,9731 +00

,9858 +00

,9970 +00

,9499 +00

,8919 +00

,7971 +00

,6773 +00

,5437 +00

PHASE IDEGREES

I

5,3572 +01 5,5121 +01 5,0993 +01 5,7468 +01 5,3414 +01 4.9022 +01 4.5327 +01 4.0852 +01 3.7234 +01 3.2978 +01 2.9330 +01 2,5430 +01 2,1771 +01 1,8272 +01 1.4717 +01 1.1626 +01 8.3517 +00 5,7013 +00 2.9568 +00

PSI I GIB 8,4492

1 .3947 1.9420

2.3102

2.7041

2.9671

3.2311 3.4140

3.5508 3.6697

3.7145 3.7478 3.7089

3.5558

3.5517 3.4470

3.2949

3.1221 2.9387

DEGREES) = 17

I -01

+ 00

+ 00

+ 00

+ 00

+ 00 +00

+ 00

+ 00 +00

+ 00 +00

+ 00 +00

+ 00 +00

+00

+ 00 +00

PHASE I DEGREES I 6.1583 +01 6.3444 +01 5.7745 +01 5.3533 +01 4.9034 +01 4.4099 +01 3.9897 +01 3.4919 +01 3.0847 +01 2.5145 +01 2.2114 +01 1.7856 +01 1.3914 +01 1.0201 +01 5.5147 +00 3.4375 +00 2.9423 -01 -1.9875 +00 -4.1658 +00

PSIIDEGREESI = 20 GIBl 8.7552 -01 1,4312 +00 1.9758 +00 2.3184 +00 2.5686 +00 2.8651 +00 3.0411 +00 3.1147 +00 3.1327 +00 3.0954 +00 2.9816 +00 2.8475 +00 2.5391 +00 2.4334 +00 2.1801 +00

1.9511 +00 1.7240 +00 1.5590 +00 1,4519 +00

PHASEIDEGREES)

5,4937 +01 5.4505 +01 4.5901 +01 4.0844 +01 3.4454 +01 2.7767 +01 2.1980 +01 1.5452 +01 1,0118 +01 4,2435 +00 -5.4068 -01 -5.2847 +00 -9.0631 +00 -1.1918 +01 -1.3570 +01 -1.3234 +01 -1.1056 +01 -5.4315 +00

1,7285 +00

PSIIDEGREESI = 21 PSIIDEGREESI = 22 KB

10

1520

2530

3540

45

50

5550

5570

7580

8590

95 100

GIBl 8.8592 -01 1.4441 +00 1.9858 +00 2.3155 +00 2.6451 +00 2,8114 +00 2.9485 +00 2.9753 +00 2.9405 +00 2.8450 +00 2.5744 +00 2.4845 +00 2.2285 +00 1.9903 +00 1.7284 +00 1.5333 +00 1.3897 +00 1.3735 +00 1.4467 +00PHASE I DEGREES I 5.2499 +01 5.1227 +01 4.2928 +01 3.6156 +01 2.9150 +01 2.1837 +01 1.5524 +01 8.5210 +00 2.8558 +00 -3.2473 +00 -7.9532 +00 -1.2358 +01 -1.5195 +01 -1.5406 +01 -1.5318 +01 -1.0722 +01 -3.3798 +00 6.4074 +00

1.4491 +01

GIBl 8.9894 -01 1.4572 +00 1.9947 +00 2.3094 +00 2.5146 +00 2.7460 +00 2.8395 +00 2.8148 +00 2.7237 +00 2.5702 +00 2.3432 +00 2.1055 +00 1.8205 +00 1.5841 +00 1.3731 +00 1.2957 +00 1.3208 +00 1.4788 +00 1.5714 +00

PHASE IDEGREES

I

4.9953 +01 4.7804 +01 3.8779 +01 3.1288 +01 2.3521 +01

1.5687 +01 8.8598 +00 1.4269 +00 -4.4456 +00 -1.0590 +01 -1.4845 +01 -1.8311 +01 -1.9098 +01 -1.7010 +01 -1.0801 +01 -9.7754 -01 9.2129 +00 1,5708 +01 1,9994 +01

PSIIDEGREESI = 25 GIBl PHASEIDEGREES)

9,3872 -01 4.1675 +01 1.4972 +00 3.5580 +01 2.0128 +00 2.5312 +01 2.2542 +00 1,5509 +01 2,4728 +00 5.8502 +00 2.4722 +00 -3.8727 +00 2.4084 +00 -1.1855 +01 2.2090 +00 -1.9916 +01 1.9481 +00 -2.4775 +01 1.6452 +00 -2.8088 +01 1.3429 +00 -2.4859 +01 1.1445 +00 -1.6294 +01 1.1058 +00 -1.2658 +00 1.2584 +00 8,9075 +00 1,4924 +00 1.3715 +01 1.7514 +00 1.2355 +01 1.9530 +00 8.8490 +00 2.1096 +00 3.3214 +00 2.1623 +00 -2.5758 +00

KA = 5 DELTA I DEGREES)!

KB

10

1520

25

30

3540

45

50

5560

6570

7580

85

90

95 100

PSI I GIB

7,3901

1,3051

1 ,7841 2.2053

2.5861 2.9352

3.2621 3.5582

3.8578

4.1331 4.3953

4.5485

4.8915

5.1258 5.3524

5.5720

5.7853

5.9927 5.1947

-01

+ 00 +00

+00

+00 +00

+00

+ 00

+ 00 +00

+00

+00

+00

+00 +00

+00

+00

+00

+00

PHASE IDEGREES

I

9.0000 +01 9.0000 +01 9.0000 +01 9.0000 +01 9.0000 +01 9.0000 +01 9,0000 +01 9,0000 +01 9,0000 +01 9.0000 +01 9,0000 +01 9.0000 +01 9.0000 +01 9.0000 +01 9.0000 +01 9.0000 +01 9.0000 +01 9.0000 +01 9.0000 +01

PSI I GIB 7.3918

1 .3064 2.2058

2.5867

1 .7845 2.9359

3.2629

3.5691 3.8586

4.1341 4.3973

4.6497

4.8925

5.1259

5.3536

5.5732

5.7866 5.9940

6.1961

DEGREES) - 1

1 PHASEIDEGREESl

8.9936 +01 8.9917 +01 8.9880 +01 8.9863 +01 8.9898 +01 8.9845 +01 8.9828 +01 8.9811 +01 8.9794 +01 8.9777 +01 8.9761 +01 8.9744 +01 8.9727 +01 8.9711 +01 8.9595 +01 8.9678 +01 8.9652 +01 8.9546 +01 8.9530 +01

PSKDEGREESI = 2 PSI IDEGREES)

-01

+ 00

+ 00

+ 00 +00

+ 00 +00

+ 00

+ 00 +00

+ 00

+ 00

+ 00

+ 00

+ 00

+ 00

+ 00

+ 00

+ 00

GIBl 7.3968 -01 1.3073 +00 1.7857 +00 2.2073 +00 2.5884 +00 2.9389 +00 3,2551 +00 3.5714 +00 3,8512 +00 4,1368 +00 4,4001 +00 4.6525 +00 4.8955 +00 5.1300 +00 5.3568 +00 5.5765 +00 5.7899 +00 5.9974 +00 5,1995 +00

PHASEIDEGREES!

8.9743 +01 8.9657 +01 8.9593 +01 8,9521 +01 8,9450 +01 8,9381 +01 8,9312 +01 8.9244 +01 8.9175 +01 8.9109 +01 8.9042 +01 8.8975 +01 8.8910 +01 8.8844 +01 8.8778 +01 8.8713 +01 8.8648 +01 8.8583 +01 8.8518 +01

GIBl 7.4053 -01 1.3087 +00 1.7878 +00 2.2098 +00 2.5913 +00 2.9421 +00 3.2685 +00 3.5751 +00 3.8551 +00 4.1408 +00 4.4043 +00 4.6569 +00 4.8999 +00 5.1343 +00 5.3610 +00 5.5805 +00 5.7938 +00 6.0011 +00 6.2030 +00

PHASEIDEGREESl

8.9422 +01 8.9250 +01 8.9084 +01 8.8922 +01 8.8753 +01 8.8507 +01 8.8452 +01 8.8299 +01 8.8147 +01 8.7995 +01 8.7845 +01 8.7596 +01 8.7547 +01 8.7399 +01 8.7252 +01 8.7105 +01 8.5958 +01 8.5812 +01 8.5567 +01

21
Table 8 - Continued PSMDEGREES) = 4 PSI (DEGREES) = 5 KB PHASE(DEGREES) G ( B PHASE(DEGREES

10 *

- 7.4 324 -01 f .8396 + 01

15

J

* + 00 * 8667 + 01 1.3135 . 79 1 7 + 01 20

7 * 7?7^ . 7456 + 01 25 22132 +00 i *8084 * + 01 ,7007 + 01 30 2 • 59 5

1

+ 00 ? 'cqqq . 6 566 + 01

35 + 00 1 *7524 + 01 2*9514 '*"oo • 6 1 3 2 40 3 • 2 7 3

1

+ 00 ' *• 7249 + 01 3,2 784 + 00 £ 45

"*"nn

*

"''ni _

^ .5276 : 50 +00 1 .6706 3.8751

5 5 ^ ' oon

.643 7 4.1505 nn + 01 60 4,4 90 + 00 1 .6170 + 01 4.4132 + 00 £ *4018 + 01

6 5 4 » 6 6 14 +00 £ • 5905 + 01 + 00 8 . 3604 + 01 70 4.9041 + 00 £ ,5641 + 01 4.9067 + 00 8 .3191 + 01

75 5.1382 +00 e ,5378 + 01 5.1396 + 00 8 .2780 + 01 80 5,3643 + 00 £ ,5116 + 01 5.3644 +00 8 .2371 + 01 85 5,5834 +00 £ ,4855 + 01 5,5818 +00 8 .1964 + 01 90 5.7958 +00 e .4594 + 01 5.7925 +00 8 .1557 + 01 95 6.0023 + 00 £ .4335 + 01 5.9969 +00 8 ,1153 + 01 100 6.2032 + 00 £ .4076 + 01 6,1955 +00 8 .0749 +01

PSIIDEGREESI = 7 PSHDEGREES) = 10 GIB PHASE (DEGREES 1 GIB PHASEIDEGREES

7.*731 -01 8 .6858 + 01 7.5599 -01 8.3 596 + 01 1.3205 + 00 8 .5920 + 01 1.3351 + 00 8. 1684 + 01 1.8033 + 00 8 .5018 + 01 1.8215 +00 7.9845 + 01 2.2281 +00 8 .4136 + 01 2.2478 +00 7.8053 + 01

2.611<f + 00 8 .3274 + 01 2.6301 + 00 7.6295 + 01 2.9631 +00 8 .2423 + 01 2.9781 + 00 7.4563 + 01 3.2895 +00 8 .1582 + 01 3.2981 + 00 7.2851 + 01 3.59it9 + 00 8 .0749 + 01 3.5943 +00 7.1158 + 01 3.8827 + 00 7 .9923 + 01 3 . 8696 + 00 4.1552 +00 7.9102 + 01 4 . 1263 + 00 a' 7R?fl + 01 4.4142 + 00 7 .8287 + 01 4.3661 +00 6 6167 + 01 4.6612 +00 7 .7477 + 01 4.5903 +00 6.4529 + 01 4.8974 +00 7 .6670 + 01 4.7999 +00 6.2902 + 01 5.1237 +00 7 .5868 + 01 4.9958 +00 6.1286 + 01 5.3409 + 00 7 .5069 + 01 5.1787 + 00 5.9681 + 01 5^5496 +00 7 .4274 + 01 5.3491 +00 5.8086 + 01 5.7508 + 00 7 .3482 + 01 5.5075 +00 5.6503 + 01 5.9444 + 00 7.2692 + 01 5.6543 + 00 5.4930 + 01 6.1312 + 00 7 .1906 + 01 5.7899 + 00 5.3368 + 01

PSIIDEGREESI = 12 PSIIDEGREESI = 15 PSIIDEGREESI = 16 PSIIDEGREESI = 17 KB GIB 1 PHASEIDEGREESI G 1 B 1 PHASEIDEGREESI GIB PHASEIDEGREESI GIB PHASEIDEGREES

10 7.5353 -01 8.0789 + 01 7.7751 -01 7.5637 + 01 • 7.8290 -01 7.3671 + 01 7.8856 -01 7.1582 +01

15 1.3474 +00 7.8039 + 01 1.3691 + 00 7.1350 + 01 1.3771 + 00 5.8798 + 01 1.3855 + 00 5.5085 + 01 20 1 .8359 + 00 7.5395 + 01 1 .8588 + 00 6.7230 +01 1 .8663 + 00 6.4116 + 01 1 .8735 + 00 5.0807 + 01 25 2.2613 + 00 7.2818 + 01 2.2779 + 00 5.3221 + 01 2.2813 + 00 5.9562 + 01 2.2831 + 00 5.5676 + 01 30 2.5397 +00 7.0292 + 01 2.6415 +00 5.9295 + 01 2.5358 + 00 5.5105 + 01 2.5284 + 00 5.0561 + 01 35 2.9804 + 00 6.7805 + 01 2.9583 + 00 5.5439 + 01 2.9409 + 00 5.0736 + 01 2.9170 +00 4.5749 + 01 40 3.2893 + 00 5.5352 + 01 3.2334 + 00 5.1646 + 01 3.1987 + 00 4.6443 + 01 3.1538 + 00 4.0934 + 01 45 3.5703 + 00 6.2927 + 01 3.4702 +00 4.7912 + 01 3.4132 +00 4.2225 + 01 3.3417 + 00 3.6217 + 01 50 3.8263 + 00 6.0528 + 01 3.5711 + 00 4.4235 + 01 3.5869 + 00 3.8085 + 01 3.4832 + 00 3.1602 + 01 55 4.0593 + 00 5.8153 + 01 3.8378 +00 4.0616 + 01 3.7215 +00 3.4025 + 01 3.5802 + 00 2.7100 + 01 60 4.2708 + 00 5.5802 + 01 3.9718 +00 3.7063 + 01 3.8187 + 00 3.0053 + 01 3.6347 +00 2.2724 + 01 65 4.4619 + 00 5. 3474 + 01 4.0743 +00 3.3574 + 01 3.8797 +00 2.5178 + 01 3.6485 + 00 1.8491 + 01 70 4.5336 + 00 5.1159 + 01 4. 1464 +00 3.0157 + 01 3.9053 +00 2.2412 + 01 3 .5241 +00 1 .4426 + 01

75 4. 7867 +00 4.8888 + 01 4.1892 + 00 2.6819 + 01 3.8999 + 00 1.8758 + 01 3.5538 + 00 1.0555 + 01 80 4.9218 + 00 4.6530 + 01 4.2039 + 00 2.3569 + 01 3.8523 +00 1.5257 + 01 3.4703 + 00 5.9219 + 00

85 5.0394 +00 4.4397 + 01 4.1917 +00 2 .0419 + 01 3.7955 +00 1.1932 + 01 3.3459 + 00 3.5713 + 00

90 5.1400 + 00 4.2190 + 01 4.1539 +00 1.7382 + 01 3.7015 +00 8.7900 + 00 3.1972 + 00 5.6779 -01

95 5.2241 +00 4.0011 + 01 4.0919 +00 1 .4474 + 01 3.5831 +00 5 .6782 + 00 3.0255 +00 -2.0070 + 00

100 5.2921 + 00 3.7850 + 01 4.0074 + 00 1.1714 + 01 3.4428 +00 3.2411 + 00 2.8368 +00 -4.0476 + 00

PSI IDEGREESl 18 PSIIDEGREESI = 19 PSIIDEGREESI = 20 KB

10

1520

2530

3540

45

50

5550

5570

75

80

85

90

95 100

GIBl 7.9479 -01 1.3941 +00 1.8804 +00 2.2830 +00 2.6157 +00 2.8856 +00 3.0974 +00 3.2540 +00 3.3580 +00 3.4120 +00 3.4184 +00 3.3802 +00 3.3007 +00

3.^1837 3.0339

+ 00

+ 00 2.8565 +00 2.5580

2 .4458 2.2293

PHASE ( DEGREES 1 5.9369 +01 5.3215 +01 5.7305 +01 5.1555 +01 4.5953 +01 4.0485 +01 3.5129 +01 2.9901 +01 2.4813 +01 1.9882 +01 1.5134 +01 1.0504 +01 6.3358 +00 2.3897 +00 -1.1548 +00 -4.1915 +00 -6.5781 +00 -8.1250 +00 -8.5865 +00

GIB I .0131 -01

,4030 +00

.8856 +00

.2805 +00

.5981 +00

.8459 +00

,0283 +00

.1487 +00

,2101 +00

,2158 +00

,1695 +00

,0755 +00

,9393 +00

.7667 +00

.5554 +00

,3445 +00

,1154 +00

.8926 +00

.5945 +00

PHASEIDEGREES)

6.7035 +01 6.0185 +01 5.3511 +01 4.7232 +01 4.1015 +01 3.4951 +01 2.9041 +01 2.3299 +01 1.7749 +01 1.2423 +01 7.3594 +00 2.5515 +00 -1.5419 +00 -5.3890 +00 -8,4202 +00 -1.0500 +01 -1.1307 +01 -1.0429 +01 -7.4288 +00

GIB 8.0820

1.4121 1.8920 2.2756

2.5749

2.7967 2.9453

3.0246 3.0384

2.9914

2.8891

2.7383 2.5470

2.3255

2 .0854

1 .8463

1 .6259 1.4551 1.3539

-01

+ 00 +00

+00

+ 00

+ 00 +00

+00

+00

+ 00

+ 00

+ 00

+ 00 +00

+ 00

+ 00

+ 00

+ 00

+ 00

PHASEI DEGREES I 5.4580 +01 5.6999 +01 4.9726 +01 4.2560 +01 3.5824 +01 2.9155 +01 2.2584 +01 1.5437 +01 1.0456 +01 4.8000 +00 -4.4378 -01 -5.1530 +00 -9.1513 +00 -1.2183 +01 -1.3881 +01 -1.3732 +01

-1..1115 +01 -5.5539 +00 2.5160 +00

PSI I GIB 8.1549

1.4213

1.8955 2.2674

2.5455 2.7373

2.8475

2.8808 2.8426

2.7396

2.5802

2.3748 2.1354

1 .8820

1 .5348

1 .4258

1 .2938 1.2705 1.3574

DEGREESI = 21

I PHASEIDEGREESI

-01 5.2003 +01

+00 5.3657 +01 +00 4.5655 +01

+00 3.7911 +01 +00 3.0394 +01 +00 2.3108 +01 +00 1.5078 +01 +00 9.3494 +00

+00 2.9951 +00

+00 -2.8775 +00

+00 -8.1093 +00

+00 -1.2461 +01 +00 -1.5573 +01 +00 -1.6903 +01 +00 -1.5567 +01 +00 -1.1076 +01

+00 -2.6499 +00

+00 7.3393 +00 +00 1.5308 +01

PSIIDEGREESI = 22 PSIIDEGREESI = 23 KB GIB) PHASEIDEGREES GIB) PHASEIDEGREES

10 8.2316 -01 5.9307 + 01 8.3127 -01 5.5492 + 01

15 1.4307 +00 5.0159 + 01 1 .4400 + 00 4.6508 + 01 20 1 .8998 + 00 4.1397 + 01 1.9016 +00 3.5955 + 01 25 2.2557 + 00 3.2929 + 01 2.2401 + 00 2.7739 + 01 30 2.5092 +00 2.4733 + 01 2 .4554 +00 1.8848 + 01 35 2 .5658 + 00 1.6824 + 01 2.5844 +00 1.0318 + 01 40 2.7339 + 00 9.2475 + 00 2.6039 +00 2.2253 + 00

45 2.7158 +00 2.0833 + 00 2.5325 +00 -5.2958 + 00

60 2.6231 +00 -4.5440 + 00 2.3815 +00 -1.2031 + 01 55 2 .4528 + 00 -1 .0442 + 01 2.1653 +00 -1.7529 + 01 50 2.2485 + 00 -1.5311 + 01 1.9033 +00 -2.1512 + 01 65 1 .9964 +00 -1.8575 + 01 1 .6218 +00 -2.2720 + 01 70 1.7283 +00 -1.9787 + 01 1 .3593 + 00 -1.9806 + 01 75 1 .4747 + 00 -1.7570 + 01 1.1709 +00 -1.1427 + 01 80 1 .2783 +00 -1.0951 + 01 1.1166 +00 1.0771 + 00

85 1.1862 +00 -3.6135 -01 1.2112 +00 1.2338 + 01 90 1 .2304 + 00 1.0734 + 01 1.4054 +00 1.8529 + 01 95 1.3807 + 00 1.8454 + 01 1.5355 +00 1.9978 + 01 100 1.5678 + 00 2.1855 + 01 1.8558 + 00 1.8279 + 01

PSHDEGREES) = 24 PSMDEGREES) = 25 GIBl PHASEIDEGREES) GIBl PHASE IDEGREES

)

8.3977 -01 5.3559 + 01 8.4859 -01 5.0509 + 01 1.4494 +00 4.2705 + 01 1.4587 +00 3.8752 + 01 1.9021 + 00 3.2330 + 01 1.9007 + 00 2.7526 + 01 2.2201 + 00 2.2344 + 01 2.1953 +00 1.6750 +01 2.4133 +00 1.2749 + 01 2.3525 + 00 6.4482 + 00 2.4894 + 00 3.6101 + 00 2.3615 + 00 -3.2723 + 00 2.4574 +00 -4.9451 + 00 2.2944 + 00 -1.2204 + 01 2.3292 + 00 -1.2595 + 01 2.1081 +00 -1.9976 + 01 2.1209 + 00 -1.9264 + 01 1 .8460 +00 -2.5922 + 01 1.8543 + 00 -2.4002 + 01 1.5413 + 00 -2.6807 + 01 1.5500 + 00 -2.5770 + 01 1.2445 +00 -2.6447 + 01

1 .2832 + 00 -2.2728 + 01 1 .0354 +00 -1.5307 + 01

1 1.0922 + 00 -1.3079 + 01 1 .0049 + 00 -6.8880 -01 1.0595 +00 1.0308 + 00 1.1574 + 00 1.1109 + 01 1.1910 + 00 1.2345 + 01 1 .4008 + 00 1.5260 + 01

1 .4144 + 00 1.7251 + 01 1.5509 + 00 1.4031 + 01

i 1.6567 + 00 1.7159 +01 1.6597 + 00 9.8426 + 00

;l 1.8725 + 00 1.4084 + 01 2.0016 + 00 4.1581 +00 2.0350 +00 9.3540 + 00 2.0643 + 00 -2.1418 + 00

•1;

22

.i
Table 9

a

-

o

+ 1 595769140 ^

= - 0 000001702

- 6 808568856

^3 = - 0 000576361

+ 6 920691905 ^

= - 0 016898657

3 050485662 ^

= 0 075752420

+ 0 850663781 N

= 0 025639041

0 150230960

^1 = + 0 034404779

b =

o

- 0. 000000033 \

- + 4. 255387524

= - 0. 000092809

"3 = - 7. 780020406

''4 = - 0. 009520896

"5 = + 5. 075161301 \

= 0. 138341946

1. 36372912 5 \

- 0. 403349276 \

- + 0. 702222017 ho = 0. 216195929

^1

= + 0. 019547031

c = 0

0

= 1 = - 0. 024933975

= + 0. 000003936

= 3 = + 0. 005770956

^4 = + 0. 000689892

^5 ^ - 0. 009497136

^^6 ° + 0. 011948809

= 7 = 0. 006748873

"=8 = + 0. 000246420 S

= + 0. 002102967

=^10 = 0. 001217930

=^11 = + 0. 000233939

d = 0

+ 0. 199471140

+ 0. 000000023

^z

- - 0. 009351341

"^3 = + 0. 000023006

^4 = + 0. 004851466

+ 0. 001903218

0. 017122914

^7 = 0

.

02906406

7

^8 = 0. 027928955

=^9 = 0. 016497308

''10 = 0. 005598515

'^ll = + 0. 000838386

U. S. GOVERNMENT PRINTING OFFICE : 1963 O - 672009

23

U.S. DEPARTMENT OF COMMERCE

Luther H. Hodges, Secretary

NATIONAL BUREAU OF STANDARDS

A. V. Astin, Director

THE NATIONAL BUREAU OF STANDARDS

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In general, each section carries out specialized research, development, and engineering in the field indicated by

its title. A brief description of the activities, and of the resultant publications, appears on the inside of the front

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