Aerospace Science and Technology 15 (2011) 511–518
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Aerospace Science and Technology
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A new assessment method for the comprehensive stealth performanceof penetration aircrafts ✩
Ying Li a, Jun Huang a, Sheng Hong b,∗, Zhe Wu a, Zhanhe Liu a
a School of Aeronautic Science and Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, Chinab School of Reliability and System Engineering, Beijing University of Aeronautics and Astronautics, Beijing 100191, China
a r t i c l e i n f o a b s t r a c t
Article history:Received 6 April 2010Received in revised form 12 July 2010Accepted 22 July 2010Available online 1 February 2011
Taking the limitations of existing stealth performance assessment methods into account, a new methodfor the evaluation of the comprehensive stealth performance of penetration aircrafts is proposed. Thispaper investigates the various characteristics of target Radar Cross Section (RCS), and integrates theparameters needed for building up target RCS numerical simulation model. The circumferential RCScontrolling parameter and the RCS curve peak controlling factor are respectively introduced to controlthe changing trend of circumferential RCS characteristics and RCS curve peak characteristics of the model.During the whole penetration course, a dynamic assessment model as well as a series of comprehensiveassessment rules is proposed according to the dynamic detecting characteristics of radar and radarnetwork. This new assessment method can enhance the integrality and confidence degree of aircraftstealth performance assessment conclusions. The relations between the RCS scattering characteristicsand the comprehensive stealth performance of penetration aircrafts are summarized. The rules indicatedby these relations can be used as the reference for the design of new stealth aircrafts and specificpenetration tactics making.
In modern electronic warfare, advanced stealth technology isthe main method used to reduce radar detecting probability andenhance the survivability of aircrafts. Due to the importance ofstealth technology, it is necessary to get comprehensive and rea-sonable conclusions about the effects of different target scatteringcharacteristics on the comprehensive stealth performance of air-crafts. These conclusions can be important reference for modifyingthe design parameters of new type of stealth aircraft, and makingeffective RCS reduction plans.
Existing stealth performance assessment method just uses theaverage RCS of target circumferential area, or that of some criticalradar detecting areas, under some important radar frequencies asthe basis. In fact, the target with the same average RCS can havecompletely different RCS characteristics. Therefore, the conclusions,derived from the existing assessment methods, can just reflect onlypart of the target RCS characteristics. Besides, the conclusions donot have enough high confidence degree, for not taking into ac-count the actual combat missions and detecting environment.
✩ Supported by National Basic Research Program of China (61320) and Fundamen-tal Research Funds for the Central Universities (YWF-10-02-023).
To overcome these disadvantages, this paper presents a newmethod for the assessment of the comprehensive stealth perfor-mance of penetration aircrafts. In this new method, the target RCSnumerical simulation model is built up. This model can reflect dif-ferent target RCS characteristics, and can satisfy various stealthperformance assessment requirements well. This new method tak-ing into account the characteristics of radar (or radar network)detecting during the whole penetration course, develops a dynamicassessment model. Based on the new method, the effects of differ-ent target RCS characteristics on the comprehensive stealth perfor-mance of penetration aircrafts are discussed in the present paper.
2. RCS numerical simulation model
2.1. Model parameters
There are four requirements for the model [1]: (1) quantifyingthe overall and local target RCS characteristics, (2) setting up therelations between each different radar detecting area, (3) control-ling the circumferential RCS changing trends of model, through in-troducing several model circumferential RCS scattering controllingparameters, (4) controlling the RCS curve peak changing trends ofthe model, by introducing the RCS curve peak controlling factors.
As the RCS can reflect the quantified target scattering charac-teristics, the average RCS of the target circumferential area δave isintroduced as the overall circumferential RCS controlling parameter
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Nomenclature
δave Average RCS of target circumferential areaδ̄0, δ̄i Average RCS of target forward critical and another crit-
ical radar detecting areaskδi Ratio of δ̄i to δ̄0La, Lb Long and short side length of numerical simulation
modelKL Ratio of La to LbA F Angular region of target forward critical radar detect-
ing areaK A Ratio of A F to 360 degreeδMax Peak value of RCS curve peakϕWidth Azimuth-width of RCS curve peakϕ j Azimuth-location of RCS curve peaksδmin RCS of the coordinate originϕ j(Left), ϕ j(Right) Left and right azimuth boundary of jth RCS
curve peakpfa Radar false alarm
y0 Threshold of radar false alarmn0 Radar accumulated scanning numberPd, P D Radar and radar network detecting probabilityTFind Time aircraft first found by radar (or radar network)NFind, NLose Total number of target being found and lost by
radar (or radar network)T f (Find), T(l)Lose Duration of aircraft in continuously radar (or
radar network) found and lost situation
Subscripts
i Sequence of radar detecting areasj Sequence of RCS curve peakk Sequence of R valuesn Single radar numberf Target found by radar (or radar network) numberl Target lost by radar (or radar network) number
of the model. Considering that the differences among RCS in dif-ferent target azimuth may up to the magnitude order, we choosedBsm as the unit of δave [9].
The existing assessment methods do not take into accountthe change to the comprehensive stealth performance caused bychanging the relations among different critical radar detecting re-gion. For example, the aircraft could be excellent in depth pene-tration mission, if it has lower RCS at its front azimuth, but higherRCS at other azimuths. Moreover, if the aircraft has lower RCS atits two side azimuths, compared with another azimuth, it can carryout penetration mission with a smaller horizontal distance to theenemy bases [4,17]. To describe the relation between different crit-ical radar detecting areas, the average RCS of target forward criticalradar detecting area, and that of another critical radar detectingareas, are introduced into the model as the target local circum-ferential RCS controlling parameters. Their corresponding symbolsare δ̄i (i = 0,1,2, . . .), and the subscript i represents the sequenceof radar detecting areas. Furthermore, the model defines a set ofrelational parameters kδi (i = 1,2,3, . . .), they can be expressed bythe equation:
kδi = δ̄i/δ̄0 (1)
(where δ̄0 represents the average RCS of the target front criticalradar detecting area).
X-45 and X-47 are the stealth unmanned combat air vehicle be-ing developed for strike missions such as suppression of enemy airdefense, electronic warfare and associated operations. They bothhave a subsonic cruise speed. As it is shown in Figs. 1 and 2,due to different stealth design parameters, the shape of these twoRCS curves differs much from each other. Therefore the same setof circumferential RCS controlling parameters cannot describe thedissimilar RCS curve patterns and control the circumferential RCSchanging trend of model well.
The circumferential RCS controlling parameters should satisfytwo requirements: First, there should not be too many circum-ferential RCS controlling parameters; second, the model should beable to satisfy all kinds of comprehensive stealth performance as-sessment requirements [8]. For example, besides δave , building upthe model with triangle pattern character (see Fig. 2) needs an-other two circumferential RCS controlling parameters, K L and K A ,which can be defined by Eqs. (2) and (3) respectively:
KL = La/Lb (2)
K A = A F /360 (3)
Fig. 1. The RCS curve of UCAV X-45.
(where La and Lb are, respectively, the long side length and shortside length of model, and A F is the forward angular region of tar-get critical radar detecting area).
Fig. 3 shows three models with different target circumferen-tial RCS characteristics, built up by changing the values of KL
and K A , when δave = −10 dBsm. The requirements for the assess-ment on the effect of the change between the target head and thetail stealth performance can be satisfied by changing K L . Similarly,changing A F can meet the requirements for the assessment aboutthe effects on comprehensive stealth performance, which is causedby different forward angular region of target critical radar detect-ing area.
As schematically illustrated in Fig. 4, the peak value and theazimuth-width of RCS curve peak are two main factors for control-ling the changing trends of RCS curve peaks scattering characteris-tics. Therefore, the peak value controlling factor δMax and the peakazimuth-width controlling factor ϕWidth are introduced. It also de-fines a series of RCS curve peaks azimuth-location parameters ϕ j
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Fig. 2. The RCS curve of UCAV X-47.
Fig. 3. RCS curves of different numerical simulation models.
( j = 0,1,2, . . .), where the subscript j represents the sequence ofRCS curve peaks on the target RCS curve.
When δave = −20 dBsm, two models are built up by changingδMax and ϕWidth . As shown in Fig. 5, these two models have thesame target circumferential RCS characteristics, but with differenttarget RCS curve peak characteristics.
2.2. Modeling method
The method to build up model with rectangle pattern character(see Fig. 1) is described in this section.
(1) δave (the average RCS of target circumferential area) and KL(the ratio of long side length to short side length) are defined as
Fig. 4. Schematic illustration of different RCS curve peak.
Fig. 5. Models with different RCS curve peak scattering characteristics.
the overall and local circumferential RCS character controlling pa-rameter respectively.
(2) Determine the values of δMax,ϕWidth and ϕ j ( j = 0,1,2, . . .)according to the target RCS curve peak characteristics.
(3) Divide the RCS curve into several parts based on the tar-get RCS characteristics and azimuth-location of RCS curve peaks,and then use different curve functions to describe these parts re-spectively. In the curve function, angle ϕ is the variable and itscorresponding function value is coordinate length value R , how-ever for the target RCS curve, corresponding value of ϕ is thetarget RCS. Therefore, a transform between R and RCS is needed,which can be expressed by Eq. (4)
δ(ϕ) = δave +(
R(ϕ) − 1
N
N∑k=1
Rk
)× δave + δmin
1N
∑Nk=1 Rk
(4)
where R(ϕ) and δ(ϕ) denote the value of R and RCS in any targetazimuth respectively, Rk is the kth R value in the target circum-ferential radar detecting area (and δmin is RCS of the coordinate
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origin). Based on this transform, the RCS curve function of the cir-cumferential radar detecting area can be written as:
δ(ϕ) = R(ϕ) × (δave + δmin)
1N
∑Nk=1 Rk
− δmin (5)
The function of the target RCS curve peak for the jth RCS curvepeak ( j = 0,1,2, . . .) can be defined by Eq. (6)
δ j(ϕ) = δ j(Max) − δ j(Max) − δ j(Left)
ϕ j(Width)
× |ϕ j(Max) − ϕ|(ϕ j(Left) < ϕ < ϕ j(Right)) (6)
where δ j(Max) and ϕ j(Width) , respectively represent the RCS andazimuth-width of the jth target RCS curve peak. (ϕ j(Left) andϕ j(Right) are respectively left and right azimuth boundary of thejth RCS curve peak.)
Therefore, the RCS curve functions of the target circumferentialradar detecting area and target RCS curve peak can be respectivelydefined by Eqs. (7) and (8)
The dynamic assessment model includes two elements: one isthe radar (or radar network) dynamic detecting model [6], and theother is the dynamic integrated assessment criteria.
Emphases of building up a dynamic detecting model includetwo points: one is to simulate the changing process of radar (orradar network) detection [5], the other is to calculate the changingdetecting probability of radar (or radar network) at different time.The radar detecting probability Pd can be defined by Eq. (11):
Pd = 1 − B
∞∫e−1ϕ
{y0 − n0[1 + (S/N)t]
n0[1 + 2(S/N)t]}
dt (11)
0
where:
ϕ(x) = (√
2π)−1
0∫−∞
e−t2/2 dt (12)
(with pfa as the radar false alarm, y0 as the threshold of pfa andn0 as the radar accumulated scanning number) [7,18].
The radar network dynamic detecting model is built up basedon the single radar dynamic detecting model and complex char-acteristics of radar network detection. Two aspects should be in-cluded in the model: (1) the total number and positions of eachkind of radar in the radar network, (2) the detecting characteris-tics and operational performance of each kind of radar. The radarnetwork detecting probability P D can be defined by Eq. (13):
P D = 1 −N∏
n=1
(1 − Pdn) (13)
with Pdn as the detecting probability of the nth single radar inradar network.
3.2. Dynamic integrated assessment criteria
Two factors must be taken into account for making the assess-ment criteria [3,15,20]. First is the occurrence sequence of eventsduring whole the penetration process. These events include tar-get being found (or lost) by radar (or radar network), the enemylaunches missiles to attack the target and so on. Second is the ef-fects of radar (or radar network) with different detecting resultson the aircraft survivability [12]. Therefore, five aspects are cho-sen as the basis of the criteria [16]: (1) The first time (TFirst) whenthe penetration aircraft is found by the radar (or radar network).TFirst can determine how many times the aircraft would be at-tacked by enemy firepower. (2) NFind and NLose are respectively thetotal number of the aircraft being found and lost by radar (or radarnetwork) during the whole penetration period. They also directlyaffect how many times the aircraft would probably be attacked.(3) The series notations T f (Find) ( f = 1,2,3, . . . , NFind) and T(l)Lose(l = 1,2, . . . , NLose) respectively represent the duration of the pene-tration aircraft in continuously radar (or radar network) found andlost situation. Their effects on the integrated stealth performanceof aircrafts are similar to the influences of TFirst , NFind and NLose
[2,13,19]. (4) The phenomenon that aircraft is found or lost byradar (or radar network) from time to time, defined as the tar-get “flashing signal”, is an important index for the comprehensivestealth performance of penetration aircraft. (5) The recorded de-tecting probability of single radar Pdn (n = 1,2, . . .) and that ofradar network P D , since the first time aircraft found by radar (orradar network). These values can describe dynamic comprehensivestealth performance of penetration aircrafts in another viewpoint[10,11,14].
4. Simulation cases
4.1. Influences of circumferential RCS characteristics
In this example, two serial target RCS numerical simulationmodels are built up according to Figs. 1 and 2 respectively. Thevalues of the circumferential RCS controlling parameters of thesetwo serial models are:
• Serial one models: δave = −10 dBsm, 0 dBsm; KL = 0.5,1.0and 2.0.
• Serial two models: δave = −10 dBsm; KL = 1.5,2.0; K A =1/12,7/72 and 1/9.
Y. Li et al. / Aerospace Science and Technology 15 (2011) 511–518 515
Fig. 6. Comparison of radar detecting probability of the serial one models (δave =−10 dBsm).
Simulation conditions of this example are:
• Flight condition: flight altitude H = 1000 m; flight velocityV = 204 m/s, flight azimuth relative to enemy base ϕ f = 90degree.
• Condition of radar network: azimuths (relative to enemybase) of every single radar in radar network are ϕri =0,30,45,60,90,120,135 and 180 degree.
A comparison is made between the comprehensive stealth perfor-mances of serial one models.
Figs. 6 and 7 compare the average radar detecting probability ofevery single radar in the radar network, when δave are, respectively,equal to −10 dBsm and 0 dBsm. According to the existing stealthperformance assessment methods, targets with same average RCSof their circumferential area have the same stealth performancein their circumferential area. However, as shown in Fig. 6, whenδave = −10 dBsm, the comprehensive stealth performance of thesethree models differs much from each other. Among these models,the one corresponding to KL = 0.5 has the highest average radardetecting probability. When KL = 1.0, the model has much loweraverage radar detecting probability. When K L = 0.5, radars locatedin the two sides of the enemy base have much higher detectingprobability than that for KL = 1.0. Therefore, when δave is around−10 dBsm, the condition KL = 1.0 can not only lead to excellentsidewise stealth performance of the penetration aircraft with rect-angular RCS curve pattern, but also can make the aircraft carryout penetration mission with a small transverse distance arrivingat enemy base. Moreover, the average radar detecting probabilityrises remarkably, when δave goes up to 0 dBsm.
Figs. 8 and 9 show the comparison of average radar detect-ing probability of the serial two models. Fig. 8 shows that whenδave = −10 dBsm and KL = 1.5, the model with K A = 1/9 haslower radar detecting probability than the models correspondingto K A = 1/12 and 7/72. The radar detecting probability curves inFig. 9 show that when KL = 2.0, the average radar detecting prob-ability decreases with the increase of K A . Especially for K A = 7/72,the range of decrease is the maximum one. Both the two models
Fig. 7. Comparison of radar detecting probability of the serial one models (δave =0 dBsm).
Fig. 8. Comparison of radar detecting probability of the serial two models (δave =−10 dBsm, KL = 1.5).
corresponding to K A = 7/72 and 1/9 have lower radar detectingprobability in their two sides than that of their heading direction,especially when K A = 7/72.
4.2. Influences of RCS curve peak characteristics
For evaluating effects on the integrated stealth performanceof penetration aircraft, caused by different target RCS curve peakcharacteristics. According to Fig. 1, this section builds up seriesof models, with the same circumferential RCS characteristics, butdifferent RCS curve peak characteristics. The circumferential RCScharacteristics controlling parameters of these models are: δave =−10 dBsm, KL = 1.0, and the RCS curve peak azimuth-location
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Fig. 9. Comparison of radar detecting probability of the serial two models (δave =−10 dBsm, KL = 2.0).
• Flight condition: flight altitude H = 1000 m; flight velocityV = 200 m/s, flight azimuth (relative to the enemy base)ϕ f = −40, −20, 0, 20 and 40 degrees; the distance to pen-etration destination L = 400 km.
• Condition of radar network: Table 2 lists the positions of everyground to air radar (GR) in the network and the location of thepenetration destination (basement).
Table 3 lists the radar network detecting results of this serialmodels when ϕ f = −20 degree.
Table 3Radar network detecting results of serial models.
TFirst N( f )Find T f (Find) N(l)Lose T(l)Lose
Model 1 209.4 1 150.5 1 559.12 281
Model 2 173.6 1 222.3 1 523.12 281
Model 3 173.6 1 258.3 1 475.12 293
Model 4 209.4 1 186.5 1 523.12 281
Model 5 173.6 1 258.3 1 487.12 281
Model 6 137.7 1 330.2 1 427.12 305
Model 7 209.4 1 186.5 1 523.12 281
Model 8 137.7 1 294.2 1 487.12 281
Model 9 101.8 1 366.1 1 427.12 305
From Table 3 we find that, ϕWidth and δMax have different effectson the comprehensive stealth performance of penetration aircrafts.First, if ϕWidth takes a fixed value, TFirst will decrease and the target“flashing signal” will weaken (T f (Find) increases and T(l)Lose de-creases) with the increase of δMax . Furthermore, when ϕWidth hasa bigger fixed value, the effects caused by increase of δMax wouldbe more obvious. Adversely, if ϕWidth takes a small value, namely,the azimuth-width of target RCS curve peak is narrow, δMax wouldhave little effect on the comprehensive stealth performance of pen-etration aircrafts. Second, if δMax takes a fixed value, TFirst willdecrease and the target “flashing signal” will weaken with increaseof ϕWidth . Similarly, when δMax has a bigger fixed value, the effectscaused by the increase of ϕWidth would be more obvious. Lastly,when one of δMax and ϕWidth takes a big fixed value, and the otherincreases, TFirst would be more obviously put off, which is causedby the increase of ϕWidth .
Accordingly to the analysis above, the rules for reducing air-craft scattering sources and improving the comprehensive stealthperformance of penetration aircrafts can be obtained:
(1) In order to put off TFirst, δMax should be firstly reduced.(2) To strengthen the target “flashing signal”, we should reduce
δMax firstly and ϕWidth secondly, when δMax takes a big value.However, when δMax is small, we should reduce ϕWidth firstly.
(3) It is not needed to reduce δMax too much if the azimuth-widthof RCS curve peak is narrow.
4.3. Influences of superposing RCS curve peaks
Because of the stealth design plan: “parallel leading-edge” and“parallel trailing-edge”, the RCS curve peaks created by wing edges,could be located on the same azimuth. Two models, correspond-ing to “before superposing” and “after superposing” respectively(see Figs. 10 and 11), are established to evaluate the effects of theplan. The circumferential RCS controlling parameters of these twomodels are: δMax = −20 dBsm, KL = 1.0, and the RCS curve peakcontrolling factors are:
Simulation conditions are the same as the example in Sec-tion 4.2.
Y. Li et al. / Aerospace Science and Technology 15 (2011) 511–518 517
Fig. 10. RCS curve of model one (“before superposing”).
Fig. 11. RCS curve of model two (“after superposing”).
Table 4 lists the radar network detecting results correspondingto ϕ f = −20◦ , 0◦ and 20◦ , respectively. These results show that,due to superposing RCS curve peaks, not only TFirst is reduced alittle, but also the target “flashing signal” is strengthened. Namely,the comprehensive stealth performance of penetration aircrafts canbe enhanced by superposing RCS curve peaks.
5. Conclusions
The conclusions about the comprehensive stealth performanceof penetration aircrafts, based on a reasonable assessment method,are meaningful for both the design of new-type stealth penetra-tion aircrafts and efficient penetration tactics making. This paper
Table 4Radar network detecting results of the two models.
ϕ f TFirst N( f )Find T f (Find) N(l)Lose T(l)Lose
proposes a new comprehensive stealth performance assessmentmethod for penetration aircrafts, which consists of the target RCSnumerical simulation model and the dynamic assessment model.This method can assess the effects of different target circumferen-tial RCS characteristics and RCS curve peak characteristics on thecomprehensive stealth performance of penetration aircrafts. As afruit, three examples in this paper show that:
(1) The target RCS numerical simulation models, performing dif-ferent circumferential RCS characteristics or RCS curve peakcharacteristics, could satisfy various assessment requirementsfor the comprehensive stealth performance of aircraft.
(2) Better configurations, which can improve the comprehensivestealth performance of penetration aircrafts, could be obtainedfrom the laws on the effects of different target RCS character-istics.
As a new method, it can be applied in the comprehensivestealth performance of aircraft assessment field. To get more cred-ible assessment conclusions, the more accurate target RCS numer-ical simulation model and dynamic assessment model should beintroduced.
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