Tl-fE
1
Dl~S IG- 1\!
01~~
•'
A thesis submitted in partial satisfaction of the
requirements for the degree of Master of Science in
, .• ,
"
J~r1g;l11e
Vli.lliarn
erJ_ tl{~
h
o~Neil
Price
__-/
c t
Calif
JS
of
~illiHm
o•Neil Pri.ce
I~
approveds
a State University, Northrid
].,
'
Il1ustrations
.'
lll
v
Introduction
:l
Chapter
I.
II.
fllAXIlvlUf/1 POiiEH DENSI'l'Y ON W\.D/i.H HEAl\!
"(
A'l"l'ENUA'I'ION OF HADIATION BY /.!, WIHE
20
•
III.
i~5
EX.FEHHiiEN'I' •
IV.
~
V.
':PHE DBSIG.l'; Of' HADIATION
PROTECTION FENCES
:35
L~6
?0
Heferences
'73
( .
1•
Hadars and magazines
2
2.
A typical magazine .
J
A radar antenna aperture •
8
J.
..
An approximation for
10
Helative nower densitv versus
distance along the radar beam
unif;rm illumination
17
7.
The wire mesh model with parameters
used in Ghent s formul<::ttion • • • . •
21
8.
Transmission coefficient. T, versus
dimension of square aperture 1n
•
u
2J
9.
Wire mesh and frame used in
..
..
10.
An over~ead view of the
experiment arrangement .
11~
Arrangement of wire mesh, anechoic
bloeks u a.nd receiving antenna u.sed
in experiment • • • • ~ • . • • • •
12.
A cylindrical wavefront incident
on
lJ.
half plane
~
• • . •
...
Transmission of radiation over
.......
Relation of transmission point
to observation point • • . . .
a half p1a.ne
16.
1?.
zine and radiation protection
f·er1ce
s1'1()\v:Lr1f~
s·hadovi
J~ers.io_rl
iii
~·,
/
)0
38
An approximation for r • .
Cornu spiral •
15.
• • • •
ze
~
~
~
~
ILLUSTRATIONS (continued)
n
1. o.
<
0
L /
~
20.
The shadow region
Four transmission coefficients
and related areas
The re~at~onship ~~t~een the
transmlss1on coefilClent of
a radiation protection fence,
~P, 1 , s
ElT1d
.50
.
vvavt~]_ent~·tl1
.J_
..
VtH'I::iUS
ca.ses
• •
Table
1. •
Description of wire meshes and
equipment used in experiment • . • •
2.6
Experimental results . .
Comparison of experiment results
with equc_1.tions (50) and (51) • • • •
...
Distance from each rcu1ar to
each magazine
JJ
60
J(aximum r;owr::r density at each
magazine due to all radars . •
6.
The electric field attenuation
'(.
OOesh attenuation factors .
8.
Hequ.ired atte:nuation by fencf::; 1
Optimum dimen::::ions of :fer:..ce
for (~aeh mesh
•
10.
~
•
ey
5.55
Area of the fences •
'1 c:0 .
Cost of alternative designs
f?
•
..
•••
• •
iv
6:t
•
em~
11.
<
•
Attenuation of radiation of fence
an.d mes:r-t~ T~i', at A."'"
•
0
..
66
6'?
68
4·
Figure J ,
The AN/FPS-16 radar
I'H;E DESIGN OF
RADIATION PROTECTION FENCES
by
William O'Neil Price
~aster
of Science in Engineering
August~
In the last
decads~
:L 976
several high power radars
were installed near the ordnance magazines at the
Pacific tlli ss.ilr:; 'I' est
Center~
Faint t·;,Uf!;u, California"
The radars were built several hundred feet from the
end of a long row of the magazines.
Recently? radiation power density measurements
revealed that hazardous conditions might exist at
the ordnance handling <lreas. Naval r<J.dia tion hazard
must be less than 1.2 milliwatts per square centimeter
wherever ordnance is stored or handled.
A fence of wire mesh was suggested as a way of
attenuating radiation incident on the magaz1nes. Similar
fences have been successfully used 1n other military
and industrial environments around microwave aevlces.
Using modern radiation theory the power density
along tlte beam axis of a radar antenna was determined.
Diffraction of
iation over a fence edge was also
characterized, and the attem1ating properties of wire
mesh were measured. Pinally, the dimensions and position
of a radiation attenuating fence were determined for
each magazine.
vi
Il'PJ:RODUC'l'I OH
In the early nineteen sixties, four
radars werr::; instalh.:d near the
the
~acific ~issile
ordnancE~
Test Center, Point
AN/F~S-16
mag:<::tzlnes at
California.
~ugu~
'I'he radars were bu:'Ll t about fi 'le hundred feet from
the r:md of the magazine row, ;:1s shown in Figure 1 ,,
Recently, radiation power densities were
measured at the magazines as they were illuminated
by the radars. In some cases the measured power densities
exceeded the hazard level for ordnance stored in the
magazines.
radar is a monopulse tracking system
that radiates 640 watts average power between 5.4 and 5.9
GigaHe:etz through a para.bolic reflector t¥velve feet in
diameter. The four radars are synchronized so that
pulses from each are not coincident in time
~]
•
r.rhe rad,SJ.r antennas <:n..,e forty feet above mean se<.:I.
and have a mechanical elevation capability down to ten
degrees below the horizQn. Most often only two radars
are used to track an object, but it is possible that
all radars could transmit in one direction.
1
le\rE~1
2
1 (~
"11
I I ~l
I
I
L~/
(])
:
I II~
I
\
Q""J
OJ
;fl
\
\\
\
I
r-o
L3
[]]
\
I
/
[[]
Irr
I
I~
Ii
.I I
[~l
~_j
II)
[]]
I
I 'I
J
~I
I li
I iI)
r-J
t-!_
Magazines
f1J
ITIJ
11
J
II~~
1
[ill
! r
I
rrn
I ;J
I
!14'
,_____j
Jj
'/1'
//
[ill
II
i
/
?Y
7
X
1--
11
I
a---~
[)]
\I
;~
\
I
I
Radars
[!lJ
I. I;l
I
Figure
l
~
}{ctd;1t"t;3
ClYlCl rn;:1g:e~ ~~ir1es
J
~...--.---;--_:.·:;::-_:.:.~~· ....=;:._;;'-
Figure 2-
.
··-
nlr:-t.tsa. zir1e
5
Naval radiation hazard specifications
require that
radiation power densities must be less than 1.2 milliwatts
per square centimeter at the magazines, and are determined
by the type of ordnance and the frequency of incident
radiation.
When a radiation power density greater than the hazard
level is incident on ordnance, heating of the explosive
is caused by excitation of the electrons. Current may also
be induced in the wires of electro-explosive devices. It is
possible that ordnance could be ienited by incident
radiation. however, no case of destruction or deterioration
of ordnance has been noted at FMTC although several
magazines were emptied until power densities could be
lowered.
l'ilr. Frank Steptoe of the Ordnance a.nd Launching
Branch, Ha.nge Operations
Department~
Pl\'i'l'C, has suggested
the use of a metal fence to attenuate energy radiated
from the radars. Subsequent research has shown that
radar fences are the most practical way to attenuate
radiation over large areas. Installation of fences at
SlJCCessful [J J •
r
-r
1!-~J
•
The design of a radar fence requires knowledge in
the following areasz
1.
The power density along the beam axis of a
radar antenna
6
')
£,.,.
~
').
.,)•
Attenuation of radiation by a wire mesh
Diffraction of radiation over an edge
The rest of this paper explores these three items·
theoretically, includes the results of an experiment
to measure attenuation of radiation by a wire mesht and
outlines the design process of radar fences. The
dimensions and position of a radar fence are calculated
for each magazine so that power dens1t1es will be
below hazard levels under all conditions.
ON HADA.H BEAti
To determine how much hazardous radiation exists
at the
magazines~
S\~veral
fo:ernulas v>lil1 be derived
describing the max1mum power density on the beam axis
of a radar antenna.
The plane containing the edge of a parabolic reflector
is the aperture of the antenna. Hadiation from the focus
is reflected by the parabolic mirror and arrives in phase
at the aperture. If the radiation intensity in the aperture
is known, then the aperture fields may be considered as a
two dimensional arra.y of Huygen' s sou.rces [5] , each
contributing to the radiated beam. In this analysis, the
s.hown in
as
i='
'-0
E(r')
(
~r r-")
-· ''rio
7.5
\.'1 )
(.....-X.
-o-
(2)
vy
'J'he aperture fields are replaced by equivalent
sheet~l}
. D.nd magnetic current
e.'l~Hctr·J..c
7
.J {f') and
j·~, (f'}
y
'\,
\,r--r"
'
~',
F'igure lt-.
....
A r<Jda.r antenna ap•2rture
(j
/
J ( f') --
H ( r')
n X
---
-·- Ho e_x
( 3)
and
J-:::m (F') =n-where
-I1 1.8
.
X
E (f') ·- - [D
e~..~
0
the unit vector normal to t.hH aperture plane [6).
The circular aperture is shown in Figure 4 centered
at the origin in the x-y plane, with the beam axis
coincident with the z axis. The vector,
F~
describes the
'
observation point, P, on the beam axis, and f' specifies
a source point, Q.
't'he dista.nce be-t:vteen
the
source
::1nd ob~:;erver
points
lS
and will be approx1mated by an easily integrated form.
the angle
~
in Figure 5 is small, then
/r-
r·'l
:::::::
'('
+
j __
)._
'Y"'
I I
and
~
--
1
l ' Sin¢
'('I
C::::
so
-r;·- r~' I
~
Y'
l
-t
tq (\ ¢
---
' ? )
\0
1"'':!:
"("
e
;t'!'
The radiated electric field on the beam axis is
found. by solving the i.ntegral C:ceen' s functio.n equationr
(?)
(B)
10
T
1
If' I
I
I
I
~----··---------
rlgure
·n •
r
~·
Ir I -----------·--·--1
A
•
+•
f'
An
approx1maulOD
_or
1-r- ·--·
=.;:;'
~ 11
l.L
are the dyadic and scalar free
space Gr(?en' s fcmctions for th(; wave equation, and
.L_k l. r--. -r-1
-,•
e
( 1. 0)
a:nd
(ll)
"''U'"'l''
+hq·t
·~~ ~-v
v.~. Ct
!.
gradie:nt
,-l
'--·
·ic
k~J
•p--;
v.J.l.l.-. .....
l.J
"'·"hVJ1b
dyadic~
~
k
and
v "7
'y
<:;/
where xi.
-.f
f
' V7 \7:.8
·t'•o
V .l.l....
],\....._,.
r<nubl-8
....l......, ;;
and k is the wave numbc.::r expressed by
.~
u
,<va.-(1~c·
...... w&..
U,.J
I
Tr1::: I
·-·
3
~~
emen6mn
n"'\
(12)
).TI
-;:-
-t f
( 13)
'
c)
e m e n 3X rn. oXh'
( 1=1, 2, 3) are the cartesian coo:cdin.<:l.teB r
the
e l ( i="1 t 2, 3) a.re the uni. t
Kronecker delta
~] •
All operators fun.ction with
rE~spect
to tha
unprinH~d
coordinates only, and integration is with respect to the
primed coordinates.
The first integrand of equation (9) is
~
...
_,._,.,
-~
C,cr,t') J(r') ex
f'(r,f') · J(i~'J ~
() ).
J ('f')
(}x 2
c_; Cr ,i<:') e X
+
( 1. .5 )
and the second integrand of equation (9) 1s
'\
\7
c; tr, f
--
1
)
~n ( f') ~ ~n('f'')
X
d
ax G(r/r') (~ ~
( 16)
The radiated electric field becomes a sum of integrals,
-
4
b
1 '---)= t&JJ.J\1
Lt!
L . n _L\__T
. i...,
n=t
n~~
•l
1
where
T
_L!
( 1 ,., )
\ ... f
lj
I\ 2',.,.
i )
and
·:>'1)
( ;~,.,.
..) I
Now? m..:tb;::;titt1ting equations (3) and (10) into (18),
the first integral becomes
T
...L
·-~
I
a per-tv re.
Since an accurate approximation of l~-~1 is more
necessary in the exponent than in the denominator of the
Green's
function~
equa"C:ton
I
i1
{
Q
\
;,b)
will be substituted into
the exponent. and the approximation
{.25)
will be used in the denominator? yielding
1 ,,
,.. . , d
l
Y'"'
1
e--X
(26)
where a is the radius of the aperture.
When all terms are dropped that vary
n
2
<J..
s r
-n
r
where
1, equations (19) through (22) tend to zero 1 however 1
equation (23) becones
I
Je
i_kr'
(27)
Substituting equations (26) and (27) into (17) yields
(2B)
Now, radiated power is proportional to the square of the
electric
where TJ
field~
and
15
l i, F
- \1 r:J.
· expancea
l ' ruy use o f hu~er
..' " ' s· lden
· t.1~y.
''
1s
e
LO<
- COS<X +LSina
TL),
( -"'-
then
and
(JJ)
Now, the magnitude of the squared electric field is
<>n<i •
(_,
f)"
.,y
<~u·b·s····{.c.!
+1\f•l' 11::::,
vn
'"
{, ..L,".-~..,
e>nna·
.. 01~l
't"' +~J
v .•
,
( _.•))JJ,.)
·irlt:n
--
{,
?.9)., tl1e
....
}Jr)wer
is
(35)
In the aperture
f)
r ( 0) ·-
1 L- 2
["
0
(Je))
16
and the power density
l
lS
l .,;::
lA-o
where A is the aperture area.
LJ Cr)
(J8)
Substituting equation (34) into (38) gives the
power density along the beam axis
rJ
ko 1
LJ (f,:;) ~ 11.lJ c ~J--=--~- 0 £___}. Y' l
p.\
\'J-Y;\
Since
( l~O)
and
A'""TTq
1
then
(h2)
The radiation power density can be divided into a near
field and a far field. The near, or Fresnel, region
contains a series of maxima and minima as shown in Figure
6.,
~Phe
far field extends from near the last maxi:mum to
Figure 6.
1oL
i
!~!
o:;!
j
I'
.:::::
!
-
''e
ill»>
lI
m
=
<W
I
I
1
e>..
(I)
I
l
I
I'
I
\
=
il
II
l'
d
I'
I
II
~
~
foe field
•o~mula
---~~I
~
iJ
\ i
-20 f·--
~
~
'I
,
i
<:;,!
i
\
I
l.'lJ
0
1
\. I
\ I
\I I
!
>
;
I
i
I
I
e
olmoximc
l
~
"
-t----=-+---1-·---:-------~~----
1
1
®
""'
~
-~
~
-1\--- ~,---_locus
I \ I
~~
-10}-.
"':::J!
Relative power density versus distance
the radar beam axis for uniform
illumination
I
0
~~~
\
-3u
!HiS
OJ
J__L_j________J______________l______L _____l.__j__
0.6 0.8 1.0
2
4
6 8 10
__l, _ _ _ _
1
0.2
0.4
.i\r
It
,....
--.,j
infinity
3
~
Simple expressions of the maximum
powf~r
density
for each region will be developed. By inspection, the
maxima in the near field are
(hJ)
The power density in the far field can be approximated
by expanding the cosine function in equation (42) as a
power series and truncating the series after the second
cos x.
x.:L
M
1 --
·-z-·
Substitutin,g equation (l4-h) into (4·2) gives tl1e power
density as
The simple express1ons for power density in both reg1ons
intersect at r 0
~
where
\ '+ 6')
'I
19
'l'he error betw·een the approximate and re::::tl
expressions for power density is greatest at r 0
less than
~ost
,
but
1.5 db.
radar antenna apertures do not have uniform
illwninations~
but are tapered so that the electric
field is greatest at the center and decreases at the
edge of the <:tperture. rv:umford [:3] has shmvn that the
approximate expressions for the near field and far field
apertures.
CHAP1'ER II
ATTENUATION OF RADIATION
When electromagnetic radiation strikes in irregularly
shaped object? it is scattered in many directions. If
the object has a pattern or symmetry t the sea ttering:
can often be described mathematically.
Radiation propagating in a symmetrical object
often travels in field configurations. or modes,
that are easily defined.
I\iode~3
in a waveguide exist
as either propagating or evanescent. An evanescent
mode cioes not travel, but dissipates energy into the
waveguide
v
and the PJ'.~opaga t:Lng mocie ra.dia tc~s energy [5] •
If the apertures of a wire mesh are considered
as short waveguides side by side, as in Figure 7,
then the radiation going through a mesh will be modal.
Also} if the fields entering each aperture are similar,
thenthe fields radiated from each aperture will be
s1m1lar. In fact. the total radiated field will be
periodic in space and can be described as modal
20
//~-"'
////
\.
. ~;Y5~f1
/
~/~
~YA'1
/0~;>'
.~
r-1
~~\
·~
j
r'
·
V
I
I
[/
~t-/.
~1~
~
,- ~ /1
/
J
:)J
v;
( 1\
//
_,./
Pic:ru
._,, re .7.
.1
'he .~ wirE~
Tl!"
. . vL•~ .rtl"')Sh
~I '·"'l
.r>
b, u ~ •O. ·--r"'
,'
•
•.•
•'-·- ..._,
(,n
"._.-~r";ime'~~'"·r
rlldde
1
I ormul···
·t .·
.:o<:::-0. ln C'1en's
· ct.~on
22
When the Floquet modes near the mesh are
matched with the waveguide modes in the mesh. the
nature of each mode is defined. Some modes are found
to be evanescent, and the transmission coefficient
of the mesh is the ratio of power in propagating modes
to power incident on the mesh.
Using this method. Chen lli] found the transmission
coefficient for a metal plate perforated periodically
with apertures. Though a perforated metal plate and
a wire mesh are only roughly
similar~
Chen's equations
are
(h?)
(48)
(50)
where a. d» and 1 are the dimensions of the mesh shown
in Figure '?. and Tm is the transmission coefficient.
d.{
l~~umford
[J] has derived an empirical equation
fror:1 the works o:f ,'3helkunoff Hnd SharplesD [12] ~ and
fi':arkuvitz
0.:31
vvhich prediets within j: 1 db the
.L
I
I
Jf"..!
I
co
-
-~
1
.....
----·
~~------------
d
---·---~
transmission coefficient of a wire mesh.
~umford's
equation is given below in modified form•
(51)
T·m
where c is the radius of the wire in the mesh.
Table
3 compares values of atterulation predicted
by equations
(50) and (51). Mumford's equation gives
lovver value[:i o:f
<:1 ttic;;nu,a tion
than Chen' : : ~
To determine the usefulness of each equation
in designing a radiation protection fence. an experiment
was conducted to measure attenuation of radiation by
several meshes. The results of this experiment are
from equations (50) and (51)
in tht3 next chapter.
CH.APTEH III
The most useful theoretical and empirical equations
describing attenuation of radiation by wire meshes are
those of Chen
(8} and.
they give
;~lightly
different results for the same mesh. To determine
which formula is most valuable in designing radiation
fences 1 me::1surements were made on three wire ;r:eshElS
on December J, 197.5 at the Frequncy lYlanagenH:?nt
Division~
PfVlTC t Point Mugu, California.
The three wire meshes were purchased at People•s
Lumber Company in Oxnclrd t California, in November t 197 5 1
and are described in Table 1.
Each wire mesh was stretched and stapled to a
frame, :fou:r' ::feet
square~
of two inch by one hEtlf ineh
lumber as shown in Figure 9.
Equipment used in the experiment is listed in
Table
1~
and Figure 10 shows the physical arrangement
of the equipment. One mesh was set on two anechoic
blocks so that the mesh plane was perpendicular to
the ground. A frame of 'J.nechoic blocks 'nas added
until the mesh was surrounded. as in Figure 11.
2.5
26
Table 1.
Description of wire meshes and
equipment used ln experiment
Mesh 1:
One half inch galvanized steel wire
mesh. not wove~; wires are spaced at
one half inch intervals1 wir~
·-·rr'"•t·-·r
(~l· dxc JV
Mesh J:
r>\.. o 0.. 1' ')
l. <'
,..:.'
.
A
'""'t·t::.,.
l. r'c'~,...;.,
,l
Iu::::~>
One eighth inch galvanized steel wire
mesh, woven; wires are spaced at one
eighth inch intervals; wire diameter
o ~ Ot-~()
is
1. •
.ir1ci1es
·')'if1c·cr Stodda.,..·t \•!J'P-6c;T n~,dj o L!'.J·,c:.y•J·.,er·eneP
vc
.
Analyzer-Receiver, Serial No. 19
...
-.-
"~'_)-,..,...
~
•
.1.,..
...
'i. j
,./
"'-<--\.
...
}
~
1
-~
._.r ' " '
EMC Instrumentation Inc. [;lodel 1001, 12.
inch reflector, and .Model 1 OJO rectangular
horn (receiving antenna)
J,
4-.
Singer Instrumentation 18 inch
5.
reflector~
n18'9?
'l. 1 cc.
anc~
~+n~c~a-~
_,D_,_l·.r_(~r~...~+.
- - -·
•. .... ..,
"...., -,4 ,tc
Co. rectangular horn, Model 91890-1
·l~oclal
•, •. < '·' ••••
:1
J.
;...
,
• _ •'·' _ ,
two feet square by one foot
anechoic blocks
Eighteen~
.•R~~l.'J'
, ,:;, ~'
2'7
Figure 9.
Wire mesh and frame
used in experiment
v
w\ \
\V
\ \
\\ \ I
~\ \ I
;p \ \
v\ I 1
r , Ii \
I. II
I
I .
II
\IV ,I
\
I
I
I
I
I
I / II
I
I
I
l I I
1
I
~
I I
~( ( ~
r 1\ \
Figure 10.
An overhead view of the
experiment arrangement
~
~\\
I\II\
lj
!
I
I
I
I
J
I
29
WIRE
MESH
IHHEMiU
Figure 11.
Arrangement of wire mesh,
anechoic blocksa and receiving
antenna used in the experiment
~30
The focus of the rece.1Vlng antenna v;:1s eight
inches :from the center of the screen? and the antenna's
beam axis was perpendicular to the mesh plane. Four
anechoic blocks were placed between the receiving
antenna and the receiver. which was next to the mesh.
'l'he transmitting antenna
from
waG
sixty five feet
rne sll so that the beam axes of both antennas
were coincident. The transmitter was set on a table
behind the transmitting antenna.
Transmission of the 5.9 GigaHertz beam was
continuous, .s.nd the beams of both a:ntennas were
a.ligrH~d
by moving them until maximum received power was
indicated at the receiver.
Since the diffracted field of a finite periodic
array of apertul'es differs from that of ::;_n in:fini te
array only at the edges
[lL~] , Eill radiation
received
was considered as propagating through an infinite
mesh.
The anechoic blocks around the mesh minimized
radiation diffracted over the screen edge. Measurements
were made with and without the top row of blocks and
no significant change in received power was noticed.
Accordin.g to equation ( l.J,o) in Chapter I
6
the far
field of each antenna begins sixty four inches along
the 1;eam .s-tx.is frmn
the~
apertu.re plane. The transmitting
and receiving antennas were sixty five feet apart, so
near field effects did not interfere with measurements.
Behind the receiving antenna was a large body
water which offered very little surface that could
reflect energy back to the mesh and receiving antenna.
'l'he receiver has a meter that may be
adjustr~d
to read relative received power in decibels. The range
and position of t1H:; meter needle was set to u.se tvro
thirds of the full meter range during measurement.
With no wire
5. 9 GigaLertz
v1as
mesh~
the transmitted power at
set to a reference leve1 of .fifty
decibels. The transmitter was then turned off and the
background and internal noise level of the receiver
was noted. Next, the transmitter was turned on and
the reference level checked again. One wire mesh was
installed and the received power level recorded. This
procedure was repeated until each mesh had been tested.
The received power levels with and without each
mesh were corrected by subtracting the power due to
noise. The difference between the corrected received
power with and without the mesh was taken as the
attenuation of rnicrovm.ve radiation at that frequency
by the mesh. The me:::wured resu1 ts of this experirnent
arE:c shovm in 'I'ab1e 2.
I!ieasured attenuation of radiation by the three
meshes are compared in Table J with values calculated
'.!'able 3.
Comparison of experiment results
with equations (50) and (51)
·t.•l,q.~.·
, - ••. l~l.£.'.·.·
. ,
c'q11'-:.
~ fl[l
t.'"'
'·; .. A C.\. +
v .i.
~' •. ~'
{\
t;(l)
_, V
formulas of Chen and
..P
:> ·-
J\':Um.J.
oru.
-~
Chen~s
formula gives
values of attenuation greater ttilln those measured,
but applies to a perforated flat plate and not to a
mesh of round wires.
cause of galvinization, the
'
apertures of the wire mesh tended to be oval and not
square.
Since [\:urnford'
~3
formula was derived frorn the
l1. 2] , and
earlior 1..vorks of Shelkunof:f' a.nd Sharpless
J\arcuvi tz
U- J]
~ and ad.apted to empiric:al data 1 it was
in very good agreement with the results of this
experiment. The differences between Rwnford's prediction
than 1. 5 db. lVuuford has st<.l ted that the accuracy of
~-'~0,-L'at::"J..ODl
·- _
-1
....-_
·t- 1 ~ 0 ,.l,
,-'lb
-~
(\ _.,~
t:;·)......
F
l
.r
H
·~rrJe··:~r·r·•
C.,.l...'_;:·L.,,
0
,J·,,,l,..,·irl·~
<.·< .. f.'j-·
b
measured data "
f'J~'J''"'
- ... ' 1d
--t:o
v
o..., .
"c>'"
~....._,
<.•l
...._)~
s:r'ltl~''
.._.Y
J... t.;:.j
C"'r"''"'l'3rJ.·
~o1·1
. u ".L·'· ... ;:)
_
]-,o+·+·or
:v'-" v ... ,...
~
',-"J.t'·t
, __ . ! t.,·h_,:_.,,
. ,
+ll"''D
V4
>;,...-.,.
"
1 .. ~:'l'\ff'!_l·
~
~-- -.l,r_:l.>)l'"
[J] .
The empirical formula of Mwnford will be used
to calculate values of attenuation
for future applications.
wi:cc meshes
DIF~{ACTION
OF
EL~CTROMAGGETIC
Since the radar £ences to be built at PfuTC have
edges, it will be necessary to describe the diffraction
of radiation over a straight edge.
Figure 12 shows a cylindrical wavefront arriving
normally at a conducting :half
of transmission-
~
plane~
1' is the point
1
the source point on the wavefront,
The segment Y is the
distance between the source and observation points,
and RK is a vertical line containing the observation
point
[5] .,
An expression for r will be derived, so
(
I~')
~-· £.~
)
(53)
and
(Sf+)
and
(55)
35
,."'f.,/
j()
Figure 12.
A cylindrical wavefront
incident on a half plane
so
ir\
~.
Define a variable, w, such that
(
r~?
_J!
\
I
y
r \ d J ,.
I} (d -r cL~) d ld
(lt1d_
.
-r
,2.,
_A
__
~
'-..LC,)
I
du
1
distance
v·c-lr·j_eE~
,
..1
in the x' direction
as shown in Figure 1). Substituting equation (57)
into (56) yields
(60)
The total expression for
:;.,-..,-1
1
~
i
·j-
ql.
lrl
JL
lk
is
w2
( 61)
where
1l'
"
X'.l
-·2.k v·.. ""'
-·' 2<fo
and
I
dx'
Now the differential area element on the wavefront
i6~\')
\
,J , / ~
I
_.L
Figure
:LJ~
An approximation for r
J9
SLlr·face is
l A'
0 t\
I
-=:
\
d U 0 X'
-
1 dg
2
Using the method in Chapter I to find the radiated
electric field at the observation
integral, 1 1
•
point~
the first
can be formed. The cylindrical wavefront
is considered as a set of sheet currents, J(r~ and
at the wavefront 9 where
on the wavefront surface, so
(f
-
;)
(66)
A'
SubstitutinG equation (61) into the exponent of !
1 •
and the approximation
(6?)
in·t0
~
""
~h-e
lJ
a·e~c,~l·rlq·to~
I... "'.l ~... '-·
" _,_
ofT
/-~1.
I
g1.ves
?
(
Q)
(}(;
I.ro
where
. (?0)
Using Eulerfs identity.
e
If
LO(
- COS IX
-t
l 5 \ na::
( ''H )
\ ( ..!.
bE;CtJD18S
(72)
Since
. ro
__
·rr .
cos :tv'- dv ·/
·-co
(74)
and
(7.5)
lr (
j
··
Wo
)
"::c
l. +· '-.,.\.!_)c)
~'(
\
),
(. >Jt::.\
( U I
::1nd similarly
""7)
I\ (
(
(?8)
When integrals 1 1 through
I~
are evaluated,
only I& contributes significantly to the radiated
(?9)
The relative forward transmission, T? is
and is shown in Figu.re 15 [11]
~:'he
quantity in equation (80), P(v..l,), involving
the Fresnel integrals 9 where
( Bl)
can be neatly represented as a graph known as the Cornu
spiral. The spiral is shown on the complex plane
'
in Flgure
I
1Ll
•
Wlth
C(
\
WoJ
D.S the
•
ElbSClSSa
•n(
a.nd J.w
Wo;\
Cornu spiral
Figure 15. Transmission of radiation
over a half plane
between the coordinate (-*,-*) and some point on the
spiral corresponding tow ••
simplifying the original integral.
l_,r:;t
P( wo) be
If 1' is la.rge E:uch that
( nt.~)
then
()-\
........ .5)
.
\
(66)
and
1'his approximation implies the observation point is
in the shadow region.
"
'
•
•
'n•·) lrJ.GO
• .._
Subst1tut1ng
equat1on
ld7
(('·1\
0L; fSl ves
{aa)
Now~
u. and
W0
can be written in terms of y and d 0
as shovm i.n f'igure 16 so that
( PQ\
";,.} ..... 1
and 1 uslng equation (70),
(90)
gives the
expression for forward transmission over the screen
edge in the shadow region
( 91)
so
(92)
This equation agrees well with the results of Becker
and is, in fact, more accurate and
much simpler.
Figure 16.
Helation of transmission point
to observation point
CHAP'l'EH V
'r:HE DESIGN OF
IIf and
IV, and the experimental results of Chapter III, radiation
protection fences can be designed for each magazine
at PMTC. An expression for the total transmission of
radiation through and around a fence will be described,
and techniques will be used that minimize the amount
of wire mesh used in each screen. while satisfying
atterrnation requirements. A design is made at each
cost ;::malysis allo'vs one design to be chonen for ea.ch
magazine.
Radar fences are most effective when the radiation
is normally incident on the wire mesh ~] • so the
fences should be perpendicular to the access road, as
shown in Figure 17. The access road must not be
blocked, so the fence will be built some distance. do ,
from
thE~
magazine. As do increases
g
the size of the
a smaller fence built next to the magazine.
4-6
Figu:ce 1. 7.
zine and radiation protection
fence showing shadow region
<.--
_____
./
----~---
·----------~--
A shadow region. behind the fence, will be defined
as the ;.:;ma.llest right rectangular prism contain.ing: the
magazine ordnance handling area, hav1ng one face on
the fence and one on the ground. The shadow region
is described by three
in F:if;ure 1. 8,
whE?.re
d0
-
the length of the shadow region1
the distance from the
fE.~nce
to
the opposite face of the prism
a
-
the width of the shadow area
along the base of the fence
b
the height of the shadow region
The greatest power density in the shadow region is
at the upper corners of the prism opposite the fence.
There are four sources of radiation that contribute
to the total electric field in
shadow region.
Radiation can go through the mesh, and diffract over the
transmission coefficient can be calculated for the mesh
and the three edges. The electric fields from each
region are summed as follows:
'>Nhere
Em -
the electric field transmitted
through the mesh
,~1
L;
.
l{~tlr-~e
The
rec:i 011
/
/
/
/
/
/
/
/
/
/
T2
F
ure 19.
Four transmission coefficients
and related areas
51
E1
the electric field transmitted
-
over the top of the fence
~
..l.,..ll
-
the electric field transmitted
around a side of the fence
the maximum electric field allowed
T{-,
.uma~
The electric fields represented by the above express1ons
are present at the rear corners of the top of the
shadow regH.m. Dividing both sidE::s of t:;qua tion ( 9J)
by the incident electric field g1ves
(
I ,
9·+·)
or
Tm
-r
T· I
t
1T.
- ).
~
T'i'YHi X
where
TT -
the total relative transmission
at the upper rear corners of the
S}1EiClOVJ
Tm
=
the transmission coefficient of
the
'1' 1
r~ef~.i<)J1
m.1:~sh
th(:3 transmission coef:ficient oi'
.._
the top edge of the fence
T1
the transmission coefficient of
-
a
~: 'Y'Mx
-·
side edge of the fence
the maximum forward tn:-ulSmission
allowed
( 0
\ 7
c;)
_r.
The expressions of the forward transmlsslon
coefficients are listed below:
(96)
Tm
1
~, r{LAd_
(97)
L
(- n9)
j';
(100)
If TF is the transmission around the fence where
( 101)
then, by substituting equations (98) and (99) into (101)
r _I_+2J
l~
where
b+y
a+2x
-- the fence height
~-
t.he
( 102)
xj
~
and
fence l.ength, or
(10.3)
where
(104)
~ow,
an expresslon for the fence area can be wri·tten.
(L05)
Substituting equation (103) into (105) yields
( 1 06)
Differentiating both sides
Now, the minimwn area 1s found
lu
J
+
:::.-0
and
( l 09)
How x is de:fi.rwd by eoua1;1.on (lOJ)
the fence
p
and. the area of
Y 9 and A should be
found for each mesh, and the cost of each alternative
weighed. A first order estimate of cost 1s to multiply
the mesh area by the cost per unit area of mesh.
Since the fence must attenuate radiation over a
small range of freque:rtcies, 5.Lr to
behavior of Tf and Tm , as
5.9 GigaJLertzi the
~varies,
should be studied.
The express1on for TT is
(l:LO)
'l'he graph of T 1
1.s
shown in Figure 20 and has one
minimum. Over a range of
r;-~
1
-" T w1.'
.. J---·
OCC1'~"'
'""·-
;:]
-
t
frequency~
the maximum vaJ.ue
.p
O'
one en,d of' thf!, range 1 therefore it is
necessary to check the value of Trat both extremes.
Initiallyf
the smallest
'I'T may or may not exceed
the fence is
r<e
c;
i crr'ec'l C-·~
"'+ A,
'\
u
\,....'..-{:~
wavelengths~
1. .._..
·-
I.J
1
the largest and smallest
respectively.
it will be necessary to redesign
and
A step by step procedure for designing radar fences
follows, and all parameters are shown in Tables 4
through
1:3~
.5.5
1. 0 ~----------··--------------·---·-----·-·-------·-------l
I
o.s
I
I
1
0.6 _
0.4,I \ \
1
~/
~
------~------
0.2 .
f
.---~------
I
!
I
I
o L-·---·-------..--·-----·---~--------J
Figure
20~
The relationship between the
transmission coefficient of
a radiation protection fence.
TT• and wavelength
(c)
l."ig11.r~e
2:L •
versus wa vt.dength
for several cases
57
1.
Determine
thE~
c1ist:JJ'We :from. each magazine to each ·
density at r~ach mr:~.gazine
using
Pqua tions
9
:for both
A.,
and A.~.
,
( 1.} 3) and ( L1·6) • 'J'he maxi. mum
power density is expressed as PT , where
(111)
Vsximum power densities are given
2.
1n
Table
5.
Calculate the electric field attenuation required
at each magazine for both wavelengths (Table 6).
The required attenuation is
J.
Calculate the mesh transmission coefficients for
coefficients for
thE:~
thrt:~e mesht3S
experiment are given in Table 7.
used in the
~ ... .l.Lv\...-.~c--v
,..,.,,J·· c~+p....,
(.Ja
'I'.. F
.f'O'Y'
.1.--
\
/\.,
nsing thE: equation b;low ~ wht?ro
( 113)
rp
A.
5.
f
ble 8.
are
Specify the shadow region parameters, d
b. For the example the values are:
a
30 feet
~
e
b
6.
Calcu1a te
tht:~
feet
OIYtirnum fence height and width using
equations (103). (104)
1
(109). and the express1ons
he.,qh-\·
·-
b+~
(l·•i+)
.•. .1..
WHj,.J,-h
·-
G. \·lY.
(lt.5)
and
Values for width and height are given in Table 9.
'7
I
using
•
the attenuation required at that waveleneth. If TT
Tma~•
then redesign the fence at
by repeating steps 4.
5, and 6. Redesign was not
1s greater than
necessary in the example. Values of TT are eiven
in 'I'abJJ:?. 10.
8.
Perforw a cost analysis of each alternative fence
design and choose a final design on the basis of
lowest cost. Tables
design step.
11~
12i and 13 show this last
Table 4$ Distance from each radar to each magazine
61.
The electric field attenuation
.
., a,t eacn
' m~:tgaz.lne
.
requ.1ren
~
-<.max
!1'\
6J
Table 7.
Mesh attenuation factors
,;;"J!E;U ~~:;~ 0 I-~~~~
~~..-----------------~----~~~- --~~~-;:l~I
I
I
rv: I;;~~j·;
'I
!I
"
-u:., '1'''~' nJ"'l
,L...•, (,
~;.
~
.k. .. ,-!.
r c:.1 1I
\
)
II:---- -=--~~. \) --T,·--::-5·~-----·1
~~~,~~~~--~-=-=--=-==~----~~-~~~~~~~::=-J:· ~:~~ ~~~:lJ
I
1
II 0 ,if 58 I 0 • I<[ 9 i
;~
II 0 . 1 9LI- l 0 . 1 7 8 l
")
IIli 0 •07 )'7
d(' •.06'''~
) j__, I
1
L-·---------------JL ________________________ j
61!
Table 8. Required attenuation by fence,
T~
1-
(])
0
66
Attenuation of rad tiCJtl.
fence and mesh. T0 , at u~. .5 ~ 5.5 ern ~
ea
fable 12.
Cost of alternative designs
Final design characteristics of each fence
CCJl\I (ji,tJS I Q_f'i
Through the use of electromagnetic theory involving
C~rt:;e.rl • ~1
d.y2;.zlic
:ttrrtcti.o11s
J
iation from a radar
tl1B
antenna. and diffraction of radiation over a fence edge
were described. Several theories of transmission of
radiation through wire meshes were considered and one
chosen through experimental verification. These results
were all utilized in a fence design method that was
outlined in the last chapter. In addition. a systems
amone several
costs
oJ~
~r.11e
se,Jer~(::tl
altern~tives
by considering rraterial
a.
des
of each fence is conservative 1n that
a.sstnttl)t:i.c)l"'1S v1e:ce rn~id.(:;1
th-r'Ol1gh_(Jl.:t·t ·tl1e n.rlaly·sis
and are listed below:
1.
all four radars were considered to be
radiating in the same direction
to be illuminated by
<:-1
plane wave with a
power density eq ua1 to the rnaxirnurn powc:::r·
density along the radar beam. so all
fence edges diffract radiation
71
J.
the radar antenna aperture was asswned to
be one hundred
l; . •
1s more conservative than more r1gorous
5.
the electric field contributions from
direction
6.
the power densities in the shadow region
will be less than those calculated at the
rear upper corners of the region
Several tu1controlled factors tend to increase
the possible power density in the ordnance handling
1.
ground reflection of the radar beam could
increase the power density by a factor of
:fot:tl'i,
increase incident power density
J.
degradation of the wire mesh due to
corrosion could increase the transmission
coefficient of
thE~
screen
Further work should be done on estimating the
useful lifetime of a wire mesh fence. Corrosion effects
seem to limit the lifetime to about ten
• A study
of the physical construction of a fence should be
conducted.
After one fence is built near the radars, power
density measurements should be made and compared with
the results of this paper.
dio Cornoration cf
:L
[
.J..
~-~ • :'"~ .}... {.."'I
1. \..1 <...{ Ll \,_.,.- 0 ~-..> :-
.,.. -, ;-"\
•.
~~ ..
i ,.,, ('~
1~, ~
~
] ;
ca. Defense Electronic
~:;urfacc
o ~:) l.~ ~ E::
2
.3
1,,,
1
"Sorn;::;
t~Lor:
:tia.
li\':chn.:Lca1
~r l~
L; (~ e J~ e r~
Environment by Use of Fences,n
f
?1
<it
l\;-. :i e r· o ~N a. \'l e
1 ~J6l)! l~2'?--
:\;'3
~-~
..
/--.,- :"'"·--·
6
Wrtve
o c;k~~~·-·c ()
8
w
~
Densities in the Fre
(December 1959):2119.2120.
f;
(~ ~
C
li
(Jfl~:~r:t
y
·~ ·~;_':C'ElX1Sfni
SSiorl o:C
l'v~ic~y~c~vvrl·\r~_::.
1
T\tli'\Oll{:?;11
~_C1ti. c }:rl.e. E:~ s
Analysjs of 1er1a
"
J,
l--; 0 ~~
11
ff
? H
il
12
rr)}_(;?;--~s
;:::;y·~;·tern~:":
;\ l.~£~1J. ;_; t:
rr..
l~.
T;e(:Ylrt
•t
~;
1J
~ ~3
"
l' -·-J
1
\~}{t~_f]~cctil1f~
r:~. ·t
I\. o .,
;?,
~ ;:~:
1 ~
t
J·.a_r~:JEY1
U-r·ici~3 ~
::: ,
fo~c
1
q)\
St1x.~·ve~/
-.· -----·-·: : - ·
o~f
t1te
iJ,l'lt~ol~:'{
o_f~
~Ni:ee
I(L£E:QI?5l~) ~)!{-§f.i J~:J::;i