Note: Descriptions are shown in the official language in which they were submitted.
~ 3~
The invention relates to radar re1ectors and more
particularly but not solely to such reflectors for use on sea
vessels.
Radar reflectors are.employed to improve the radar
echoing properties of objects or land formations with a view to
improving the detection of such objects or formation by radar
scanning equipment. Radar reflectors of this type to be fully
efficient should reflect radar waves back parallel to their
initial direction.
In many applications it is advantageous if the reflector is
capable of providing reflection of radar signals in any direction
and in applications such as in sea vessels it is advantageous if
this capability is not badly affected upon heeling of the vessel,
Corner reflectors, constructed o three sheets of reflective
material which are mutually perpendicular, i.e. orthogonal re-
entrant trihedrals, are known to provi.de effective reflection
over a,range of angles of incidence, with the signal strength
decreasing as the obliquity increases, forming a lobe.
This invention ha~ heen arrived at by consideration of the
above mentloned requirements and seeks to provide a radar
reflector which provides effective reflection of signals received
from any direction in a horizontal plane.
According to the invention there is provided a radar
reflector comprising at least six corner ref'lectors directed
outwardly of and disposed 'helically about a major axis of the
reflector along two successive hel~cal paths one of which paths
is sinistrorse and the other o which paths is dextro~se.
The corner reflectors are preferably evenly distributed to
cover the full 360 of horizon,
In one advantageous :form of the invention ten corner reflec
tors are employed.
A reflector in accordance T.~ith the invent.ion mav be formetl
from a strip of radar reflective sheet material folded i.n
alternate directions along fold axes spaced apart on the strip
2 ~
~ V35
and extending tr nsversol~ across tne str;p with t-~o consec~ltl~te
ones of the '-OlCI axes d 1 sposed intermediately being substantially
parallel and the remaining folds being alternately convergent and
divergent in a direction from one edge to the opposite edge of
the strip the folds dividing the strip into sections adjacent
sections being disposed at right angles and a separator plate
being provided between and at right angles to each pair of adja
cent sections to form therewith two corner reflectors. The
separator plates may be rectangular but rectangular plates naving
one point cut off are to be preferred, the plate being positioned
such that the edge where the point ha~ been removed is remote
from the adjacent sections. This cut away avoids interaction
with reflections from other ones of the corner reflectors.
The edge of the strip and/or the cut away point of the
separator plates can be profiled such that they have an edge
profile conforming to part of the internal surface of a cylind-
rical housing to permit slidable and secure location of the
reflector within the housing.
.
In order that the invention and its various other preferred
features may be understood more easily, an embodiment thereof
will now be described, by way of example only9 with reerence to
the drawings, in which:-
Figure 1 is an elevational view of a radar reflector
constructed in accordance with the invention,
Figure 2 shows a blank strip for bending to form the reflec-
tor of Figure 1 illustrating the bending axes,
Figure 3 shows horizontal projections of two adjacent
sections of the target radar reflector of Figure 1 illustrating
angle of twist,
Figures 4a and 4b are circular and elliptical sections of a
stepped helix,
Figures Sa and 5b are schematic elevational views of oppo-
site sides of a stepped helix,
Figure 6a is a schematic elevational view of a corner
reflector 9
Figure 6b is a schematic plan view of the corner reflector
~ 35
of Flgure 6a,
Figures 7~. and 7b are schematir tilted corner views in plan
and perspective respectively,
Figure 8 is a polar diagram showing schematically the con-
struction viewed from above,
Figure 9 is a predicted polar diagram showing the response
of the radar reflector, and
Figure 10 is a side view of a demountable reflector con-
structed in accordance with the invention and folded into a flat
condition.
In the drawings Figure 1 shows a particularly advantageous
form of the invention hauled up to the cross tree of a mast. The
radar reflector indicated generally at lO is formed of a
strip of radar reflective material e.g. 18 s.w.g. sheet duralum-
inium or stainless steel. The strip is folded along axes which
extend transversely across the strip in concertina fashion. The
folds divide the strip into a series of sections 11, 12 and 13
adj~cent ones of which are disposed at right angles.
A flat strip suitable for folding to ~orm in this case
triangular divislons is shown in Figure 2. The chain lines
indicate axes at which the fold is to be forwards and the dot
and chain lines indicate axes at which the fold is to be back-
wards. It will be apparent from the drawing that the fold axes
in this case are all of the same length.
The folds defining the centre ~ection 12 of the strip are
parallel, the centre section being of parallelogram form. The
other folds are alternatPly convergent and divergent in a direc-
tion from one edge to the opposite edge of the strip and divide
the strip into triangular sections 11 and end sections 13 of
basically trapezium form which end sections are cut away to one
side of an axis extending at right angles to their adjacent fold
axis to leave only the portion with the shorter side at the edge
of the strip.
The folded strip forms a spine having seven sec~ions adjac-
ent ones of which are disposed at right angles. Each pair of
adjacent surfaces of the sections is provided with a sheet metal
~ 35
divider 14 which is afixed thereto 'oy ~or e~amp'le rive~Lting Ot
welding at righr, ang~es to both surfaces to ~orm a pair of cor~
ner reflectors ln the form of ortllogonal re;-entrant trihedrals
which are capable of acting as elementary reflectors.
The radar reflector can be hung from one end from a
point adjacent the axis at which the end section is cut away or
can be hoisted by a similar connection at each end as shown in
Figure 1. The reflector hangs normally by its own weight with
the surfaces of the sections inclined alternately at 45 above
and below the horizontal.
, The maximum reflecting capability of a corner reflector
occurs along an axis extending equiangularly between the faces
of the corner and this axis may be,termed the directional axis
of the reflector. When the reflector is hung as previously des-
cribed the directional axes are inclined above or below the
horizontal at a constant angle.
The folding of the strip to form the spine results in an
effective twist or change in azimuth of each fold relative to
its adjacent one. Figure 3 shows only two adjacent
sections to facilitate illustration of the twist which occurs.
It will be seen that bisectors of the two sections are disposed
at horizontal angles 2~o to each other. It has been discovered
that if the twist is arranged such that the reflectors on
adjacent olds are directed with an azimuthal displacement of
about 36 then a most efficient "all round" reflection coverage
results. The reflected signal strength at a lobe width or 36,
i.e. ~ 18 from the directional axis, is sufficiently low that
overlap of the lobes of diferent ones of the reflective corners
at this level have been found to introduce an acceptably narrow
deterioration of the polar response of the radar target reflec-
tor due to phase cancellation. Accordingly ten elemental
reflectors evenly disposed ar~und a polar axis have been found
to give a particularly good polar responseO To provide this
displacement the angle "~ o" should be about 1 8o It will be
, appreciated that in view of the twist the solid ang~es of the
elemental reflectors all diver~e radially from 'cwo helical axes
one of which is sinistrorse and the ot'her of which is dextrorse.
~ 3~
The sections 11 need nct be trl~ngular but can be oL trun-
cated trian~ul-~r iorm t~at is of trapezium shapeO
There now ~ollows a mathematical analysis of the const~lc-
tion.
The circle in Figure4a represents a right section of a
cylinder in which are contained the stepped helices of a
reflector. The trapezium shown is the pro~ection of an actual
trapezium of construction on to the circular plane which is
normally horizontal. All intersections, dimensions and angles
in this plane will bear a zero suffix. The actual trapezium of
construction is at 45 deg to the circular plane. Its plane will
be an ellipse. O, W and W' are in both planes because ~hey are
on the axis of rotation.
Note QOPo is para~lel to SoNo (and parallel to OVO)
, ~ ~
OV T , OU S , Q T S are constructed right angles
Let Q S = P N = P
-o o o o o
QoPo qO
S N = s
- o o o
~0 OU = x
Q T = t
o o o
Q O = OS = r
o o o
SoQoTo = ~o, the half-twist angle
O Q T = ~
o o o o
Problem : Given r , ~ and x
. o o o
(i) Calculate pO, qO~ sO, to etc 9 then
(ii) Calculate p9 q9 ~, t etc In t'ne tilted plane
formed by a 4' deg rotation abou~ axis T,~W~.
Because 0U bi.sects Q S
o o o
P = 2 ¦ r 2 _ x 2 .,...... ,.~... ~,... (1)
In ~ 0Q V
o o
qO 2 rO sin ~ O~O~ (2
In ~0Q U
o o
tan ( ~O + ~ O) = 2 xO .. O... ..~... ,.... (3)
Po
Combining (2) and (3)
q = 2 r sin (tan 2 xO ~ ~ ) ..................... (4) (the
brackets con~
pO tain ~ O)
In ~ S Q T
o o o
sin ~ - s - q
o o o
~ Po
ie sO - 2 pO sin ~ O ~ qO ~I~DO~ (5)
Now, in the tilted plane,
q = q ~2
(see Figure Sa)
s sO ~2
: Therefore, from (4) and (5)
q = 2 ~2 rOsin (tan 2 xO - ~ O~ o - - ~ (6)
pO
and s = 2 ~2 p sin ~ O ~ J2q ~O~ (7)
In ~ S Q T
o o o
tan ~ O (sO qO~ r ~ ~ ~ e ~ ~ o ~ 8 )
2t
~ 35
And in ~ SQT
tan ~ ~ ........... (9)
2t
( O qO~ ~2
2t
= J2 tan ~ O
Therefore ~ = tan (J2. tan ~ .O.~..... (10)
Because planes QQOPOP and SSoNoN are parallel
QoTo = t c QT
Examining the plane SS N N (Figure 5b), Q will be directly above
T, distance t
SST = ST - TST = ~ - q2
~ 2
QST PO S QOSO
Consider ~ SQST
`SST = tan SQST
.' T
ie SQST - tan ~ ........... (11~ (call
2 ~2 pO , see
later)
also QST = COS S~ST = PO
.: p= P
O
cos tan 1~ s - q
__
2~po
~ O~ 12)
cos tan 1 sin ~
,:
Finally note in ~ SoQoTo ~Figure 4a~
Po Y o
and in ~ OQWQ
= tan~ tan ~ _9L___ \ ......... ,... (14
OWQ ~rO cos ~
Definition of the unit trapezium is now complete.
The position of the separator plates must now be definedO In
the circular plane of Figure 4a each is defined by the line
U O Y . U is at the apex of the two reflecting corners. (Note
however U - UO, because both are in the circular and tilted
planes~. O is on the cylinder axis (midway) between the inter-
sections of the axis with adjacent trapezia. YO is located
arbitrarily on the U O axis at some point within the cylinder
envelope.
Because QS is tilted at angle from the horizontal, so the
plane of the separator plate will be tilted at angle from the
vertical. Thus the separator plate will be situated on the.
tilted.plane QSNP a~ UX where X is on PN (see Figure 4b~, On
the next PN ~old above XYZ9 ~N~ say, there will be another
point X9 where the plane of the separator i.ntersects P/N'~ How
ever, P9N~ will not be in the vertical plane of PN~ but another,
also vertical. but rotated through the tWlSt angle, In fact UX
= U~' by symmetry.
Also SUX = QUX = SUX' = QUX' = 90 deg.
Now calculate the dimensions of the individual reflectors. They
are QXX' which has edges UQ9 UX9 UX' and SXX9 which has edges
US, UX, UX~
: Of these edges UQ = US ~bisected chord Qk an ellipse~ and so
an~ UX = UX' (see above) constructed)
UO~ US ........................... ~. J A ,.. 0 (15)
Consider ~ XJP in Figure 4b
q + -~ . ux ~ p
2 sin`~ - 2 tan ~ 16)
sin (90-2~) sin (90
.~. UX = ~ (q ~ ......... (17
sin 90 + 2Y 2 sin ~ 2 tan ~
= cos ~ (q + ~ ......... (18)
cos 2 ~ 2 sin ~ ~ 2 tan ~
A hypotenuse length can now be calculated using -the smallest of
the edges (15) or (18) and multiplying by ~2.
10 ~Z~:
It has been assumed this far that the stepped helix has been
constructed of trapezia with sides QP and SN straight and para-
llel. In fact they could be extended to the wall of the
enclosing cylinder when they would assume an elliptical curva-
ture.
It can be simply shown that the smaller semi-diameter is on the
axis WW' and is rO~ the radius of cyl:inder~ The major semi
diameter is then J~ rO.
~C~
Let be the angle of tilt of the fold to the horizontal. This
is angle ~ST described in association with Figure 5b.
From (11) ~ = tan (s - q) = sin (s - q)
2 ~po 2v~ p
sin /sin ~ o~(l9)
~ J .
Thus, in Figure 4a direction US is inclined upwards at deg
" UQ " " downwards at deg
UOO " Horizontally
Each lobe wlll therefore be inclined at a characteristic eleva-
tion, between 0 and deg, up or down as appropriate, as
determined by its azimuth between the face and edge of the corner
(see Figure 6a).
~ 3 ~
Reca]l tha~ the lo~e a~imuth is at tan y~ )from the face of the
corner,
Recall that the lobe ~zimuth ls at tan ~ from the ~ of the
corner,
the plane of edge-to-face-centre is in the plane of the
incident radiation (ss Figure 6b). But it is not, S is ~ilted
upwards deg about axis FU (and Q is tilted down), see Figure
7a.
If S is the projection of S in the horizontal plane, note
(i) FUS being 90 deg, FUS C 90 deg,
(ii) the angle between the lobe peak and the fold US (LUS in
Figure 7b)~ which was formerly tan 1 J 2 must now be less. Call
this angle ~ (= L US in Figure 7b).
First calculate the lobe elevation. As it is a concomitant of
heel (~ ) it can usefully be calle~ ~ (= LUL in Figure 7b).
~ "~ ~ o ~ ~_~
Note in Figure 7b th~t SUF, SLU, SSoF, SS U, LL U and LL F are
all 90 deg.
Thus in ~ s LL F and SS F
o o
sin LFL ~ LL = SS
o _ _
20LF FS
LL - SS LF
o o
FS
Because sin ~O = LLo
UL
sin ~ = SS I.F
o o .
FS UL .O~ (20)
But SS = US sin ~
LF = US sin tan ( ~ )
~ 2
30FS = US
cos tan ~2)
~1
~ 33~
and UL = rJs eo5 t~n 1(~2~
Therefore sin~ = sin sin tan 1 ( - ) v~ o~(21)
Now find ~ - 1, USO, the angle between the azimuths of the direc-
tional axis of the lobe and the fold.
cos ~ = rJL
USO
=~
- US cos ~
~ ~ (22)
- -- - O .. , . O ~ ~
l 2 co~ ,~
Considerlng the construction of Figures 1 and 2, which I
call an ambiorse construction, with the sinistrorse folds Nos:
1, 2 and 3 on top, and No: 1 topmost, The spine before folding
i9 shown in Figure 2, Let U9 start at fold No: 3 for (ultimate)
simplicity. Fold No: 3 define~ the azimuth datum) 09 in the
horizontal projection ~hown in Figura ~9 where the construction
i9 viewed from above. Each foid i9 tangential to the circle,
radius x which is the locus of the corners U, The face of the
o
plate shown in Figure 2 is defined as its 'front' face, and the
odd-n~mbered folds (which are shown as chain lines in Figure 2
and dotted in Figure 8~ and which have reference numerals en- -
2~ circled in Figures 2 and 8) are produced by folding the plate
forwards for example see fold No: 3, i.e. the front is the face
on whlch the corners 3L ~nd 3R will be situated. The other
face is the 'back', and the (even~numbered) backwards folds are
; shown as do~ and chain lines in Figure 2 and as solid lines in
Figure 8 and with reference numerals not circled in Figures 2 and 8.
Adjacent fol~s are folded in opposite senses (Figure 2), i.e, the
plate is folded rom top t~ bottom f~ rn~tely for~ff~rGs and
backwards9 wif~h odd~numbered folds forwards (encircled) and even-
numbered folds backwards.
Going from ("start" in F~gure 8) Fold No: 3 to Fold No: 2
up thefsinistrorse he~ix causes a ~ hand turn throu~h the
~2
L03S
twist angle ~2~ 35.8 in ChiS examp1e). Similarly going from
Fold No: 2 to Fold No: 1 causes the same 35.8 right handed turn.
These are shown in Figure 8~
Fold No: 4 is parallel to Fold No: 3, and is of opposite
sense. It is the uppermost of the three ~Nos 4, 5 and 6) dex-
trorse folds forming the bottom half of the whole construction.
Going from Fold No: 4 to Fold No: 5 down the dextrorse helix
causes a ~ -hand turn through the twist angle, and similarly
again from Fold No: 5 to Fold No: 6 ("Finish")O
The horizontal projection of each pair of corners for each
fold is shown in Figure 8 following the construction described
above. In the following Table 1 are shown the fold azimuths
(left and right, when viewing from behind the reflector, i.eO
towards the central axis). Hence the lobe azimuths (left and
right) for each fold are given9 being ~ degrees (see Eqn. 22)
into each corner from each fold azirnuth. The lobe azimuths for
the de~xtrorse helix are exactly at 180 to those for the
enantiomorphic sinistrorse helix. The lobe azimuths are shown
around Figure 8.
TABLE 1
. . ~.
Fold . Lobe Azimuths Lobe
Fold Azlmuths9 deg ~. .
No: deg. ~levatlon*
. . , _ . ~ . ~ ~ .. _.
1 (L) 71.69 251.6 (R) (L 125.1) (-)
R 198.1
2 (R) 35.8, 215.8 (L) R 342 3
3 (L~ 0 , 180 (R) L 53.5
_ R 126.5
4 (R) 0 , 180 (L) L 233`.5 +
'~ R 306.5 _
, 5 (L) 35.8, 215.8 (R) L 89.3 +
R ]62.3
6 (R) 71.6, 251.6 ~L) (L 305~1) (~)
R 18.1
, ...... . _ ~_ _.,, .. _ . __ . . ~_
~ 9.77 deg above (~ or below ~) the horiæon.
Thus the whole 360 degrees of azimuth are covered by 12 corners
with two overlapping pairs 7 o~e corner of each of which can be
eliminated as they are at GppOslte ends of ~he construction (lL
~3
3~;
and 6L, bracketted in the Table), leaving 1.0 lobes.
So the azim~thal sequence of the remain.ing lobes is as in Table
2.
TABLE 2
__ .
Lobe No: 6R 3L 5L 3R
Elevation - - + +
Azimuth, deg. 18.1 53.5 89.3 126.5
Spacing, deg. 35.4 35~8 37.2
Deviation from 36.0 -0.6 -0.2 +1.2
Lobe No: 3R 5R lR
Elevation + - ~
Azimuth, deg. 126.5 162.3 198~1
Spacing, deg~ 37.2 35.8 35.8
Deviation from 36.0 +1.2 -0.2 -0.2
Lobe No: lR 4L 2L
Elevation ~ ~ -
Azimuth, deg. 198.1 233.S 269.3
Spacing, deg. 35.8 35.4 35.8
Deviation from 36.0 -0.2 -0.6 -0.2
Lobe No: 2L 4R 2R
Elevation ~ ~ +
Azimuth, deg. 269.3 306.5 342.3
Spacing, deg. 35O8 37.2 35.8
Deviation from 36.0 -0.2 ~1.2 -0.2
; Lobe No: 2R 6R etc
Elevation ~ -
Azimuth, deg. 342.3 18.1
Spacing, cleg. 35~8 35.8
Deviation from 36.0 -0.2 -0.2
That is to say, the 10 corners are disposed substantially evenly
around the azimuth, as indicated in Figure 9.
14
~ 35
Arl ait2;rat~;~ oollaps-ole ~ers~on of a refiector in
accordance ~i.C~ e Inventlorl is shown in Figure 10. In this
embodiment sections 21 and 22 of radar reflective sheet material
are hingedly interconnected in edge to edge relationship to form
a strip by means of hinges 23. The portions 21 are of similar
shaping to the portions 11 and the portion 22 is of similar
shaping to the portion 12 of Figure 2. The hinges permit the
strip to be folded back~ards and forwards in concerting fashion
into a small space. The opposite edges of the portion 22 which
are hingedly connected to adjacent portions 21 are substantially
parallel~ The hingedly connected edges of the other portions 21
are alternately divergent and convergent in a direction from one
edge to the other edge of the sectional strip.
Each of the portions 21 and 22 except the top portion is
provided with a separator plate 24 which are hingedly connected
to their respective por~ion ~l~ernately to opposite faces of the
plate. The separator plates are shaped and positioned so as to
be movable into a position at right angles to their respective
portion and to permit the adiacent portion to be hinged into
contact therewith at which ~osition the adjacent portions are
mutually ac right anglesO A cl~p 25 is provided w~ich engages
the edge of the separator pla~e and secures the plate in posi-
tion. The two adjacent portions and the separator plate form a
? pair of orthogonal re-entrant trihedrals in the same form as
Figure 1.
It will be appreciated that this version of the reflector
can be folded down for storage in a confined space yet is quickly
reassembled for use.
It is believed that the constructions described fully meet
the stringent performance requirements of the Department of
Trade ~larine Radar Reflector Performance Specification 1977. In
particular, since the response for the vertical plane is also
extremely good the vertical angle response~ so imporcant to
main~ain reflectio-n d~.lr,ng hee~ing -;n ro~gh seas9 meets the
requirement thaL the vert c~i coverage 7 t l5 to t'ne norizontal,
shali not remaîn ~e~ow ~6dB relat-Lve to the LOm vaLue over any
single angle of more than ïO~;CO
3~6~35
It will be appreciated that more o~ less reflective corners
could be employed and that provided at least six are distributed
around a 360 arc, a useful construction may be obtained.
Refl~ctors employing more than 10 reflective corners in which
overlapping of lobes at higher signal strengths occurs may well
provide useful constructions and such constructions are at pres-
ent being analysed as their usefulness is influenced by their
response at diferent heeling angles as well as by several
other complex factors.
Although the spine and dividers of the described reflector
are formed from a single sheet of material the invention is not
restricted to such a construction and any other radar reflective
material can be employed~ For example, the whole could be
moulded in plastics e.g. by injection moulding. Such a moulding
could be effected with a moulding material containing particles
of radar reflective material so that these particles are embedde~
in the moulded reflector. Another possibility is the provision
of acings of radar reflective material on a plastics moulded
construction e.g. by metal plating or metalization.
A radar reflector as previously described may be encapsul-
ated or hermetically sealed in a container of for example glass
reinforced plastics material~
It will be understood that the above description of the
! present invention is susceptible to various modification
changes and adaptations,
16
