helicopter antisubmarine operations

Helicopter Antisubmarine Operations

by

for

SA367, Mathematical Modeling

09 November 2000

Summary

The purpose of this report was to determine whether the effectiveness of the antisubmarine

Helicopter Antisubmarine Operations

by

for

SA367, Mathematical Modeling

09 November 2000

Summary

The purpose of this report was to determine whether the effectiveness of the antisubmarine

warfare helicopter would be enhanced if an additional torpedo would be added to its

payload. As of now, the helicopter carried two torpedoes for its missions.

It was found that in developing the model, an estimate of the probability of killing a

submarine was based on the distance to contact datum and the number of torpedoes carried.

Limiting the size of the problem to fifty and seventy-five nautical miles, the question

became how many torpedoes should the helicopter carry.

It was found to be more effective for the SH-60 anti-submarine helicopter to carry two

torpedoes. Simply put, the kill probability drops too significantly at long ranges with

three torpedoes. An 87% drop in kill probability between two and three torpedoes is

undoubtedly very significant. However, kill probability at short ranges differ by only

17%, and remain high while carrying both two and three torpedoes.

Unfortunately, our naval forces cannot always count on enemy submarines appearing within

the fifty nautical mile range, so it's important to have an anti-submarine platform that

retains its mission outside of this range. If an SH-60's payload could be increased to

carrying three torpedoes and twenty sonobuoys, the SH-60 loses this mission

ineffectiveness.

Introduction

payload. As of now, the helicopter carried two torpedoes for its missions.

It was found that in developing the model, an estimate of the probability of killing a

submarine was based on the distance to contact datum and the number of torpedoes carried.

Limiting the size of the problem to fifty and seventy-five nautical miles, the question

became how many torpedoes should the helicopter carry.

It was found to be more effective for the SH-60 anti-submarine helicopter to carry two

torpedoes. Simply put, the kill probability drops too significantly at long ranges with

three torpedoes. An 87% drop in kill probability between two and three torpedoes is

undoubtedly very significant. However, kill probability at short ranges differ by only

17%, and remain high while carrying both two and three torpedoes.

Unfortunately, our naval forces cannot always count on enemy submarines appearing within

the fifty nautical mile range, so it's important to have an anti-submarine platform that

retains its mission outside of this range. If an SH-60's payload could be increased to

carrying three torpedoes and twenty sonobuoys, the SH-60 loses this mission

ineffectiveness.

Introduction

Anti-submarine warfare is becoming an integral part of the protection of our naval forces

in foreign seas. The proliferation of extremely quiet, diesel engine submarines has

proved to be a deadly threat particularly in the littoral areas.

To combat this silent threat, the United States Navy developed the most capable

anti-submarine helicopter forces in the world. Today's SH-60 helicopter, equipped with

technically advanced sonobuoys, detection equipment, and torpedoes, are a great asset to

protecting our surface forces from the threat of foreign submarines.

Initially, submarines were spotted by long-range airborne antisubmarine units that patrol

continuously in the assigned operational area. Once sighted, the patrol relayed the

contact's range and bearing from the task force. The helicopters then deployed and began

their search using sonobuoys. After locating the submarine, the SH-60 helicopter attacked

using the highly capable ADCAP torpedoes.

Problem

The purpose of this study was to determine whether or nor it is more effective for the

helicopter to carry an additional torpedo.

Measure of Effectiveness

The measure of effectiveness (MOE) used for this problem was the probability that the

submarine was detected and killed by the SH-60.

in foreign seas. The proliferation of extremely quiet, diesel engine submarines has

proved to be a deadly threat particularly in the littoral areas.

To combat this silent threat, the United States Navy developed the most capable

anti-submarine helicopter forces in the world. Today's SH-60 helicopter, equipped with

technically advanced sonobuoys, detection equipment, and torpedoes, are a great asset to

protecting our surface forces from the threat of foreign submarines.

Initially, submarines were spotted by long-range airborne antisubmarine units that patrol

continuously in the assigned operational area. Once sighted, the patrol relayed the

contact's range and bearing from the task force. The helicopters then deployed and began

their search using sonobuoys. After locating the submarine, the SH-60 helicopter attacked

using the highly capable ADCAP torpedoes.

Problem

The purpose of this study was to determine whether or nor it is more effective for the

helicopter to carry an additional torpedo.

Measure of Effectiveness

The measure of effectiveness (MOE) used for this problem was the probability that the

submarine was detected and killed by the SH-60.

Goals

The problem was addressed through the following steps:

1. Using the supplied data, determine how much weight was available for sonobuoys and torpedoes.

2. Determine whether it was more effective to carry type A or type B sonobuoys.

3. Determine whether it was more effective to carry two torpedoes or carry three torpedoes.

Assumptions

The testing of our model was based on the following assumptions:

1. The initial contact datum was obtained from fleeting visual periscope detection by a

long-range airborne anti-submarine unit patrolling continuously within the operational

area of the task force.

2. Information on the contact datum was not be updated during the passage of the helicopter.

3. The submarine was submerged and heading in an unknown, but constant, direction from the contact point.

4. Once the helicopter reached station, it was assumed that the submarine had no further significant movement.

5. The helicopter scattered the sonobuoys in a uniform random pattern over the area

defined that the submarine could possibly be in.

6. The total distance traveled by the helicopter during the deployment of the sonobuoys

and torpedo kill phase was defined as eight times the radius of the circle defining the

maximum area that the enemy submarine could be in.

7. Maximum submerged speed of the submarine was 20 knots.

8. The submarine had an initial contact range from the task force of fifty or seventy-five nautical miles.

Data

The following figures give the performance data that was used in creating the model.

ASW Helicopter Performance Data

Cruising Speed (knots) 100.00

Fuel Consumption (lbs per nm) 5.00

Maximum Payload 2850.00

Emergency Fuel Reserve 50.00

Maximum Sonobuoy Rack Capacity 10.00

Existing Torpedo Rack Capacity 2.00

Typical Time Into Action 5.00

8. The submarine had an initial contact range from the task force of fifty or seventy-five nautical miles.

Data

The following figures give the performance data that was used in creating the model.

ASW Helicopter Performance Data

Cruising Speed (knots) 100.00

Fuel Consumption (lbs per nm) 5.00

Maximum Payload 2850.00

Emergency Fuel Reserve 50.00

Maximum Sonobuoy Rack Capacity 10.00

Existing Torpedo Rack Capacity 2.00

Typical Time Into Action 5.00

Figure 1

Torpedo Performance Data

P(Kill given detection and location) 0.50

Weight per Torpedo Rack (lbs) 400.00

Sonobuoy Performance Data Type A Type B

Detection Radius (nm) 3.50 4.00

Detection Area (nm^2) 38.47 50.24

Weight of Sonobuoy Rack 30.00 40.00

Maximum Speed of Enemy Submarine (knots) 20.00

Figure 2

Model for probability of detection

To determine whether carrying an additional torpedo would enhance the kill probability of

the SH-60 helicopter, the critical factor proved to be the allowable payload. We

recognized that at some distances, the weight of carrying three torpedoes would somewhat

limit our number of available sonobuoys, thereby reducing the probability of detection and

ultimately, kill probability. In analyzing this problem, our first step was to create a

model that could calculate the weight available for sonobuoy use. Since our data assumed

both constant speed of the submarine and an approximation of the detection radius in which

the submarine may be operating, we could determine the exact poundage of fuel needed as a

function of the distance to contact datum. From there, we simply added in the weight of

the fuel reserve, sonobuoys, and torpedoes. This gave a working model for the available

weight for sonobuoys, which can be seen in figure 3.

Figure 3

Distance to Contact (nm) 50.00

Time of Flight (min) 35.00

Radius of Detection (nm) 11.67

Total Search Distance (nm) 93.33

Total Distance Traveled (nm) 193.33

Fuel Needed (lbs) 966.67

Circular Area of Detection (nm^2) 427.39

# of Torpedoes 3.00

Weight of Torpedoes 1200.00

Weight Available for Sonobuoys 633.33

However, our next step towards our ultimate goal of determining the probability of kill

was to develop a model that could tell us the probability of detection. This depended

model that could calculate the weight available for sonobuoy use. Since our data assumed

both constant speed of the submarine and an approximation of the detection radius in which

the submarine may be operating, we could determine the exact poundage of fuel needed as a

function of the distance to contact datum. From there, we simply added in the weight of

the fuel reserve, sonobuoys, and torpedoes. This gave a working model for the available

weight for sonobuoys, which can be seen in figure 3.

Figure 3

Distance to Contact (nm) 50.00

Time of Flight (min) 35.00

Radius of Detection (nm) 11.67

Total Search Distance (nm) 93.33

Total Distance Traveled (nm) 193.33

Fuel Needed (lbs) 966.67

Circular Area of Detection (nm^2) 427.39

# of Torpedoes 3.00

Weight of Torpedoes 1200.00

Weight Available for Sonobuoys 633.33

However, our next step towards our ultimate goal of determining the probability of kill

was to develop a model that could tell us the probability of detection. This depended

solely on the available sonobuoys and the search area. In the end, it was decided to use

a model that was admittedly optimistic. This model assumed that the sonobuoys would be

placed in the area of absolute efficiency. In other words, no overlap of detection area

was accounted for in the model. However, this was not a limiting factor in the accuracy

of our testing, since the model tested the same for both two and three torpedoes. Even

though the model inflated the actual kill probability, it did so proportionally with each

variable, so that the choice of carrying two or three torpedoes was not affected by this

inaccuracy. This is seen in figure 4.

Figure 4

(Using the #s from the above example)

Type A Type B

Sonobuoy Capacity 6.00 4.00

Max Area of Detection 230.79 200.96

Probability of Detection 0.26

From this probability of detection, determining our kill probability consisted of the

simple task of including the probability of kill of each torpedo. In our model, the kill

probability of a single shot was 50%. Therefore, to estimate kill probability, we took

a model that was admittedly optimistic. This model assumed that the sonobuoys would be

placed in the area of absolute efficiency. In other words, no overlap of detection area

was accounted for in the model. However, this was not a limiting factor in the accuracy

of our testing, since the model tested the same for both two and three torpedoes. Even

though the model inflated the actual kill probability, it did so proportionally with each

variable, so that the choice of carrying two or three torpedoes was not affected by this

inaccuracy. This is seen in figure 4.

Figure 4

(Using the #s from the above example)

Type A Type B

Sonobuoy Capacity 6.00 4.00

Max Area of Detection 230.79 200.96

Probability of Detection 0.26

From this probability of detection, determining our kill probability consisted of the

simple task of including the probability of kill of each torpedo. In our model, the kill

probability of a single shot was 50%. Therefore, to estimate kill probability, we took