DING Hong-yan(丁红岩)，DONG xiao-ming(董晓明)，JIAN Ming-yu(蹇明裕)

(1.College of Marine Engineering，Northwestern Polytechnical University，Xi’an 710072，Shaanxi，China;2.Dalian Naval Academy，Dalian 116018，Liaoning，China;3.Unit No.91526，Zhanjiang 524064，Guangdong，China)

Introduction

In the process of using air-drop torpedoes to attack a submarine by a single helicopter，the helicopter need to draw in the airborne dunking sonar and fly towards to drop the torpedoes after the sonar detects and tracks a target.If the sonar loses the target，it may maneuver to avoid to be attacked.Therefore，two helicopters need to coordinately attack a submarine to improve the hit probability.When two helicopters coordinately attack，they often fly towards to drop the torpedoes.Theory and practice indicate that the coordinated attack of two helicopters with the dunking sonars and air-drop torpedoes is a high-effective of approach of antisubmarine.

During the actual combat，the submarine’s countermeasures may influence the attacking effect of torpedo.The submarine may take the countermeasures such as maneuvering and noise jammer when it discovers the signal from dunking sonar or torpedo.When the submarine uses the noise jammer，the interference succeeds if the jamming noise spectrum received by the torpedo sonar array achieves a certain level.Therefore，it is of a great importance to research the coordinated attack of two helicopters.

1 Anti-submarine Process of Two HelicoptersCoordinatedlyFlyingTowards to Drop Torpedoes

1.1 The Organization and Implementation

When two helicopters coordinatedly fly towards to drop the torpedoes，the one is a guidance helicopter which is in a position to keep detecting，and the other is a helicopter which performs an attacking mission.The guidance helicopter which keeps the sound contact with submarine measures the bearing and distance of target constantly，calculates the course and speed of the submarine，and sends these data to the attack helicopter.And then，the attack helicopter flies to the submarine and drops the torpedoes to the scheduled point rapidly after the corresponding tactical datum are calculated.

1.2 Calculating Model of Submarine Position Parameters

As shown in Fig.1，when the attack helicopter receives the submarine data and starts to attack，the position of guidance helicopter is taken as the coordinate originO，the positive east direction asxaxis，the positive north direction asyaxis，and then the Cartesian coordinate system is established.

In Fig.1，Ais the position of attack helicopter，the submarine course isCm，and its speed isVm.The bearing of which guidance helicopter is measured by the radar on the attack helicopter isB0，the distance isD0.Based on the submarine bearingB1and distanceD1provided by guidance helicopter，the attack helicopter can calculate the submarine bearingB2and distanceD2(the method is omitted).

Fig.1 Sketch map of coordinated attack

1.3 Selection of Drop Point of Torpedo and the Calculation of Flight Parameters

When the attack helicopter drops the torpedoes expect to improve the hitting probability of torpedo.Therefore，the selection of drop point of torpedo should take into account the highest discovering probability of torpedo.After the course and speed of the submarine are calculated，the advanced position of the target(PointI)is usually taken to be an aiming point.Considering that the homing device of torpedo need a certain time to startup after a torpedo goes into water，and the different hydrology conditions make the detecting distances of torpedo different，the dropping leadRof torpedo should be calculated.The torpedo dropping circle is confirmed with PointIand radiusR.When the attack helicopter enters the torpedo dropping circle，it can drop the torpedoes.

According to the submarinebearingB2，distanceD2，courseCmand speedVm，the distanceDqof submarine’s advanced dot can be calculated to derive the flight course and time of attack helicopter before dropping(the method is omitted).

2 Model of Submarine Countermeasures

2.1 The Maneuver Model of Submarine

The submarine usually takes the evading action when it detects the torpedo.The mainly maneuvering methods include speed change，depth change and turning.The most common and effective method is turning or turning while accelerating.There are two kinds of turnaround methods:“point totorpedoand turn around”and“turn in reverse”.Submarine usually adopts”turn in reverse”when it finds a torpedo at long range or bigger relative bearing，and then leaves the torpedo behind it.So the torpedo will chase submarine to consume its voyage.

Generally，the turning radiusRmand the turning angular rate ωmofsubmarine are calculated by Eq.(1)［3］.

To discuss the submarine evasion，the point which torpedo goes into the water is taken as the coordinate originO，the positive east direction asxaxis，and the north direction asyaxis.The Cartesian coordinate sys-tem(Fig.2)is then calculated.The position of the submarine at momenttcan be got as follows.

Fig.2 Sketch map of submarine maneuver

1)The straight leg of submarine:

wherexm0andym0are the coordinates of submarine position points when the torpedo goes into water，which can be calculated according to the bearingBand distanceDof submarine;t0is the time when the torpedo goes into water.

2)The turning segment of submarine:

wherexmkandymkare the coordinates of submarine position points when it starts to turn，βmis turning angle，tkis the time when submarine starts to turn.

3)The end segment of submarine turning:

wherexmdandymdare the coordinates of submarine position points when it completes its turning，tdis the time when submarine completes its turning.

2.2 Interference Model of Noise Jammer for Sub-marine

The noise jammer is used to lower the homing distance of torpedo［4］.The interference effect of the noise jammer on the active sonar can be analyzed by sonar equation.When the noise is concealed，the sonar equation is

When the torpedo is interfered，the sonar equation is

whereSLis the torpedo acoustic radiating level，TLis the transmitting loss，TSis the reflecting intensity of target，NLis torpedo interference noise level，DIis the exponent of torpedo receiving direction，DTis the examination threshold of torpedo，DI(θ)is the acoustic receiving direction function，NLjis the interference noise level of torpedo when the noise jammer operates.

When an noise jammer doesn’t operate or is located out of homing sector of torpedo，the torpedo can detect the submarine if Eq.(5)is effective;when the noise jammer operates and is located in the homing sector of torpedo，the torpedo still can detect the target if Eq.(6)is effective，otherwise the interference is successive.

3 Simulation Results and Analysis

Simulation conditions:the initial bearing of submarine is 0°，the homing range of torpedo is 1 500 m，the homing sector of torpedo is 90°，the torpedo speed is 45 knots，the ring search angular speed of torpedo is 10°/s(if the submarine falls into the torpedo homing search sector，we consider that torpedo succeed in acquiring and hitting the target);the torpedo alerting distance of submarine is 30 cab;the course and speed errors of torpedo obey the normal distribution;the simulation times are 2 000.

3.1 Simulation Results

1)Supposing that the initial distance from attack helicopter to submarine is 4 000 m，the initial speed of submarine is 6 knots，the submarine adopts the eva-ding way of acceleration and“turn in reverse”.After turning，the submarine travels at 20 knots.Taking the ways to attck the submarine is the torpedo attack from single helicopter and the coordinated torpedo attacking from two helicopters.The variation in hit probability of torpedo with different target courses is shown in Fig.3.

Fig.3 The variation in hit probability with different target courses

2)Supposing that the relative bearing of submarine is 30°，and two helicopters are used for coordinated attack.The submarine can evade after it delivers a noise jammer.The submarine speed is 20 knots after it changes its direction.The variation in hit probability of torpedo with different initial distances is shown in Fig.4.

Fig.4 The variation in hit probability with different initial attack start distances

3)Supposing that the initial distance between attack helicopter and submarine is 4 000 m，the initial speed of submarine is 6 knots.Two helicopters are used for coordinated attack.The submarine can evade after it delivers a noise jammer.The submarine speed is 20 knots after it changes its direction.The variation in hit probability of torpedo with different relative bearing of submarine is shown in Fig.5.

Fig.5 The variation in hit probability with different relative bearings

3.2 Result Analysis

Fig.3 shows that the hit probability of torpedo is obviously influenced by submarine course when the submarine evades.If the course of submarine is 50°～150°or 300°～340°，the attack effect is not ideal.In addition，if the course of submarine is 220°～ 260°，the attack effect of single helicopter is not ideal.As a whole，the hit probability of two helicopters is higher than using a single helicopter.The reason is that the time of attack is shorten by using two helicopters to attack to leave out the recovering process of sonar.Even though the submarine maneuvers，the attack helicopter also can obtain the submarine information in time and the attacking parameters to fulfil the purpose of attack.Consequently，two helicopters should be used for coordinated attack.

Fig.4 shows that the hit probability of torpedo descends clearly with the increase in initial distance from attack helicopter to submarine;if the initial distance from attack helicopter to submarine is 2 000－3 000 m，the change of torpedo hit probability is smaller when the submarine maneuvers purely or maneuvers while using the noise jammer.The hit probability of torpedo changes greatly at 3 000 m.It indicates that the purely maneuvering submarine can not avoid the coordinated attack of double helicopters.Consequently，two helicopters are used for coordinated attack，and the initial distance from attack helicopter to submarine should be shorten.

Fig.5 shows that the hit probability of torpedo is influenced clearly during the coordinated attack of two helicopters and the maneuver of submarine with the noise jammer.The variation in hit probability of torpedo is comparable to that during the pure maneuver of submarine when the initial relative bearing is 0°～30°，130°～140°，－20°～ －50°or －160°～ －180°etc.It indicates that the hit probability of torpedo depends on the initial relative bearing when the submarine maneuvers and uses the noise jammer.Therefore it is important to choose an initial relative bearing to attack.

As mentioned above，it is better to use two helicopters coordinately to attack under the condition of countermeasure.The conditions of using two helicopters to attack are relaxed for the same combat effect.Therefore，the coordinated attack of two helicopters is an effective way of shipboard helicopter antisubmarine.

［1］SUN Ming-tai.Military tactics of aviation antisubmarine search［M］.Beijing:Military Science Publishing，Company 2003.(in Chinese)

［2］XIAO Feng.An interference of noise resists the voice from lead the torpedo result to imitate the true research［J］.The Warship Ship Argument Reference，2007，(4):45－48.(in Chinese)

［3］MENG Qin-yu，ZHANG Jing-yuan，SONG Bao-wei.The torpedo battle effect analyze［M］.Beijing:National Defence Industry Press，2003.(in Chinese)

［4］CHEN Chun-yu.Antitorpedo technique［M］.Beijing:Defence Industry Press，2003.(in Chinese)