ANALYSIS OF CHAFF CLOUD RCS APPLYING FUZZY CALCULUS

A. D. Macedo F. DSAM - Brazilian Navy Weapon Systems Directorate

Rua 1' de Marqo 118 - 2@ andar - Centro Rio de Janeiro -RJ, Brasil, CEP: 20010-000

ABSTRACT

This work provides an insight to the application of fuzzy theory to evaluate chaff cloud RCS, i?. First, it describes a model for 6 , and then some of the parameters are taken as fuzzy. It also indicates how the efectiveness of a chaff system a m specific threaths can be assessed by means of a Belief function. Futhermore, before the conclusions, it comments a technique to evaluate 6 when only fixed frequency radars are available.

1. INTRODUCTION

It is well known that sea-skimmhg missiles are the most critical challenge to a Naval Force 111. The defense against such weapons is difficult and expensive. Among the defensive measures, chaff is probably the oldest, yet still &&Ave. Besides, comparing to other countermeasures, chaff is quite inexpensive. It is used since 1937, when the british discovered that a radar would detect a strip of wire hr;! long, suspended from a balmn, at ranges up to 30Km. Chaff can be made of alu" strips, zinc coated fiberglass, oooper wire, and album coatedf2mglaq which is the most popular material. Chaff clouds act as decay targets or can saturate an area to confuse radar systems. Therefore, to defend &ce ships, chaff clouds must present a Radar Cross Section, 6, at least around io4 m2.

However, the nature of the chaf€ cloud makes it hard to qwnw crisp parametres, while fuzzy numbers [2] describe more realistically the uncerta&ies of the equivalent radar cross section, blooming and collapsing time. The aim of this work is to inkroduce the fuzzy techniques to describe the chaff cloud RCS and & m e s s .

2. RADAR CROSS SECTION OF CHAFF CLOUDS

The RCS of an object is definedas :

I Power returned to radar receiver / unit solid angle Incident power density / 4.n

A simple dipole reflector is a straight element of contittctk material which behaves as an antenna when illu"ted by an incident RF wave. In theoq-, the shortest length of such antenna would be U2. Nevertheless, in real dipoles, depending on their physical Properties, the velocity of propagation is less then c. Fmthermm, since the current induced along the length of the chaff dipole is proportional to the projection of the electrical field along its axis, the response depends on the signal polarisaton.

The chaff dipole RCS near the resso~liince region is 00nsiW as [31:

As Grequency drifts away from the resonant point, the RCS will decrease, with smaller peaks at multipies of W2. Nonetheless, in practice, the skirt around 2 1 is the upper limit of the chaff response, since beyond this point it is insignifirrmt and usually outside the bands of interest. Fig 1 shows a typical chaff dipole response. Note that the curve shiqmess depend cm the aspect ratio AR= Vd, (lengtb/diameter) [4].

0-78034165-1/97/$10.00 0 1997 IEEE. 724 SBMOBEEE MTT-S IMOC'97 Proceedings

Til- Normalised response of cJ@rtipoles with A=200 and 2000

Concerning the behaviour of chaff clouds, effectiveness factors q~ q, ancl qpl are used to descnlae its deviatioos [5] such as: a)"birdnesting'', that is, depending on the dispensing and packing techniques, sets of CM dipoles can cling togheter providing a less effective response; b)dipoles within two wavelengths from each other don't behave like isolated dipoles because there is energy couplin% among adjacent dipoles; c)dipoles near la the radar can shield the far side ones fkom the full enerm, and d)as vertical attitude dipoles fali fister, the chaff (cloud RCS significsantly depends on the radar signal polarisation.

If qpl, the cloud RCS, 6 , is N times the single dipole RCS, oaiP where N is the number of chaf€ dipoles in the payload. However9 qf may range from roughly .8, for I-band dipoles, to .4, for D-band dipoles. Usually, 0.4< qf < .5, and is typically a finzv number. Factor qc model the effectiveness of the dqxmion technique appliedl For pptecWcaUy ejected &@ due to damage caused by the ejection forces and heat, qe.8, while for mechatlcally ejected chaffqel. Finally, qPl, takes into account the signal polarkation. As socm as chaff is deployed it is wrbject to a great deal of turbulence, when any orientation for each individual dipole is q d y likely. However, as time

Dipoles with horizonxal auitude descends more slowly than dipoles with verIical athtude. Thus, the lower partion of the ChafFCld becomes V-pol, while the whole cloud is mainly H-pol. Here, it will be Consicked

Moreover, after blooming, not all of the chaff dipoles contained in the payload wil l be inside the radar's resolution cell, as in Fig 2. The larger the resolution cell, the largr will be the "A cloud RCS. The volume *by such cell depends on the radar guise width (z), the slant range to the poimt in space in which the cell is centered (R) and the horizontal (e) andvertical (+) beawi&hs, and is given by [6]:

passes, the dipoles orientation tend to &bike under the influence of gravity andl aerodyIlarm -c characteristics.

. qp01=. 6 for H-pl, -4 fbr V-pol and .5 for circularlly polarized waves.

'where ki Herea,b

z 500 fvps andkz a 106 ftp NM. Here z is in p, andR is inNM, and Care also given in ft.

while both 0 and +arein

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It is important to distinguish the clouds produced through the two basic blooming techniques. In pyrothecnical ejection systems, the cloud is approxhatelly spherical, while the plume cloud, produced by mechanical ejection techniques, resebles a “croissant” shaped cigar. The W ones are more evenly dispersed and allows a short blooming time with equaI screening effect in all directions. In the other han6 the plume type cloud usually has one very long dimension. Therefore, such clouds presents a far worse screening effect in one direction than in the other. Besides, plume clouds are more likely to unfold beyond the radar resolution cell being more inefficient. FurthermoIe, the signal attenuation in a chaff cloud makes a chaf€ element located inside the cloud to receive less energy then an isolated element at the same location. Thus, if L is the chaff clouds dimension in the sense of the radar propagatioq then according to [6], the simplified expression of the c M - cloud RCS is:

Where o d is the response of a single chaff dipole. This expression contains many values which are tvpicaUy fizzy: qf, qe qPl, and L. Such statement agrees

with the common sense opinion that 5 must be also fuzzy. The next item provides an insigth to chaff cloud RCS anatysis through fuzzy theory.

3. CE€AFF CLOUDS W A R CROSS SECTION Fuzzy PARAMETERS

First, it is necessary to model the chaff dipole fkpency response. This response can be seen as the composition of four triangles as shown in Fig 3a). Furthermore, the three effectiveness factors are also modeled as triangles as in Fig 3b). These fixtors are estimated computing the data measured from several chaff launchings in Merent conditions. Wind speed and direct io~ humidity and rocket settings impose important constraints to these values. A more accnrate model would use gaassian curves instead oftriangles

I

0.9

3 0.8

g- 0.7

2 0.6

- 0.5 9 5 0.4

v 8.3

a U) A

U

2f

Q. 0

.-

CD g 0.2

0.1

0 0

a) fkpency (0 relative to resonant fi-equency (fr) m

2 4

’I 0.9f

0.7 1 Y- a

4

CJ a,

.- “iij 0.6 -

0.5. U-

L

# “0.4 - U :li. 0.1 0

8 0.5 1

b)efiienessparametersvalues

A more coIllplicated guess is to define the chaff cloud size and shape. A pyrothecnical ejection system produces a rather spherical cloud, but its diameter depends on the strength given to the ejection itself, on the chaff

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payload weigth, and on the altitude where the chaff is deployed For naval purposes, the chaff cloud is usually deployed so near to the sea surface, that the difference between the air density froin where the cloud blooms to the sea surface is negligiile. This size and shape may only be possible to model impirically after a great number of launchings in different meteorological conditions. The plume type cloud can be ii bit more easy to model as it is usually larger than the radar resolution cell. Thus, if L is mnsidered to be the c M cloud depth length at its maximum, while eff'e number of dipoles in the cell is assumed to be around (V=~/Vdouk)N. Thus, eqmsion (6) can be evaluated as.

Where the W! means a "ordered weighed average" operator [7].

Therefore, the application of fuzzy theory produces a simple method to evaluate chaff system &fecltiveness and also to prospect the improvements obtained in di€€erent tactical situations. It can also be defined a Belief function, &&-I( 5, $, [m] and [c]), to estimates the defense ef€ixtivens of Ihe chaff system. Here, J< is the threath fresuency and [m] and [c] are the set of meteorological and cinematic conditions of the ship ;and the missile. One must note that, as the enemy data are in principle unknown, they are also fuzzy numbers, or f k z y measures [SI.

Moreover, when no wideband instrumental radar [9] is available to measure the chaff cloud RCS, fuzty theory can also be useful. Ifthere are at least 2 fixed low frequency radars andthei chaffpayload is set for ;a single frequency, then two fuzzy points are lrnown in the curve response. These fizzy points must fall in a curve imilar to the one in Fig 3a). Thus the straigth lines joining the peaks from these responses and the one passing lby their meanvalues, limits the uncertainty arouudthe chaffresponse curve. The projection of these lines canbenmade up to the point corresponding to the chaff payload central fkquencyfobtaining RCS values al and a;?. The belief fanction defining the x" RCS is:

Amnlti-~cypayloadisestimated -the individual responses..

4. CONCLUSIONS

This work introduced the use of fuzzy numbers to chaff clouds RCS malysis. The of such approach is that it takes into accoullt the "I -es that are intrinsical to this ,problem. It'& provides a good methodto infer the effectiveness ofthe chaf€launching system against specific ttureatbs. Unfortunately, as most of the data and saidiesbeingamductedintbis area are classijiedthey were omitedhlere. However, this wok exposes an entkly novel approach which is being consideredby soe in the Brazilian Navy.

5. REFERENCES

[l] Handbook 1981 Edition; p~ 338-344. [2] ~ C S and lo@'; CRC Press, Boca -XI, 1987 Fl., p ~ - 3-39. [3] Cauntermeasares Handbook 1980 Edition; p ~ - 3 16-324. [4] 197-201 [5] Hancibook 1976 edition; p ~ . 512-517. [6] 1979 Editioq pp- 383392; [7] IEEE Trans. on Systems, Man and cybennetiff, vol. 18, January/Februa~y 1988; pp 183-190.

Wps Elecktro m e r , " C M for ships: operational amsi&rations''; Internatonal Couaxenrteasures

D.D~bois & €LPrade; "Fuzzy numbers: an overview''. In J.C.BQ&k, "Analysis offuzzy informaticon-vol I:

Mitchell, P.K. & Short, RH.; " C M basic c h a " h . 'cs and applications detailed"; Intennational

Butters, B.C.F.; " C W ; IEE PrOceeQn gs, Vo1.129, R.F; Ng 3, Jime 1982; pp-

Maha&fiq7 U; "Electrical fimQmentals of cauntermeauge chaff"; Internatonal (buntenmeasure

Mitchell, P.K & Short, RH; Haw to plan a chaff comdor"; Internatit>nal- Handbook

RRYageq "On the ordered weighted averaging -on operators in multicriteria decisiomlaking";

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181 N.York US& 1988. 191

Klir, G.J & Folger, TA; “Fuzzy sets, uncertainty, and information”; Prentice-Hall International Inc.,

DyW, RB; “Radar cross section measurements”, EEE Proceedings, Vol75, N“- 4, April 1986.

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