Kill Probability Of The Sh 60 Helicopter example essay topic

Helicopter Antisubmarine Operations by for SA 367, 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 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 AD CAP 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 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 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 the probability of detection and multiplied it by 1- (1-P (Kss) ^n), where n reflected the number of torpedoes carried. Figure 5 (Using the #s from above example) Probability of Kill 0.23 In the end, the model developed an estimate of the probability of killing a submarine based on the distance to contact datum and the number of torpedoes carried. Our final step was to put our model to use and analyze which option for torpedo carriage was preferable. Analysis In analyzing our model for kill probability, we recognized that the distances to contact would range from very short distances of 30 nautical miles, all the way up to very long distances of over 100 miles.

However, for purposes of simplicity, the range was limited to contact distance of 50 to 75 nautical miles. It was also concluded that as a normal distribution, the majority of contact distances would occur within this range. The analysis of each range and torpedo carriage is listed below: Distance to Contact (nm) 75.00 Time of Flight (min) 50.00 Radius of Detection (nm) 16.67 Total Search Distance (nm) 133.33 Total Distance Travelled (nm) 283.33 Fuel Needed (lbs) 1416.67 Circular Area of Detection (nm^2) 872.22 # of Torpedoes 3.00 Weight of Torpedoes 1200.00 Weight Available for Sonobuoys 183.33 Type A Type B Sonobuoy Capacity 6.00 4.00 Max Area of Detection 230.79 200.96 Probability of Detection 0.26 Probability of Kill 0.23 Distance to Contact (nm) 75.00 Time of Flight (min) 50.00 Radius of Detection (nm) 16.67 Total Search Distance (nm) 133.33 Total Distance Travelled (nm) 283.33 Fuel Needed (lbs) 1416.67 Circular Area of Detection (nm^2) 872.22 # of Torpedoes 2.00 Weight of Torpedoes 800.00 Weight Available for Sonobuoys 583.33 Type A Type B Sonobuoy Capacity 10.00 10.00 Max Area of Detection 384.65 502.40 Probability of Detection 0.58 Probability of Kill 0.43 75 MILES TO CONTACT 75 MILES TO CONTACT 3 TORPEDOES 2 TORPEDOES Figure 6 From the above data, it is perfectly clear that, at long ranges, carrying two torpedoes is more effective than carrying three. In fact, the kill probability increases by a full 87% when the added weight of an extra torpedo can be used for sonobuoys. This was perfectly consistent with expectations. It was expected that at the longer distances, the maximum weight capacity of the helicopter would limit the available number of sonobuoys.

This problem was magnified when a third torpedo was added. However, the analysis of the shorter ranges differs: 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 Travelled (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 Type A Type B Sonobuoy Capacity 10.00 10.00 Max Area of Detection 384.65 502.40 Probability of Detection 1.00 Probability of Kill 0.88 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 Travelled (nm) 193.33 Fuel Needed (lbs) 966.67 Circular Area of Detection (nm^2) 427.39 # of Torpedoes 2.00 Weight of Torpedoes 800.00 Weight Available for Sonobuoys 1033.33 Type A Type B Sonobuoy Capacity 10.00 10.00 Max Area of Detection 384.65 502.40 Probability of Detection 1.00 Probability of Kill 0.75 50 MILES TO CONTACT 50 MILES TO CONTACT 3 TORPEDOES 2 TORPEDOES Figure 7 At this shorter range of fifty nautical miles, it becomes evident that carrying three torpedoes has some advantage over carrying only two. Since in both cases, sonobuoys do not limit the area of detection, the kill probability depends solely on the number of available torpedoes. In this case, probability of a kill increased by 17% when a third torpedo was carried.

Sensitivity Testing Several variables in this model proved to be sensitive, but only one variable was sensitive enough to possibly change the conclusion. That variable was maximum payload, or total weight available for carriage. Our initial estimate of maximum payload was 2850 lbs. However, it was found that if this payload was increased to 3100 lbs, our recommendation changed: Distance to Contact (nm) 75.00 Time of Flight (min) 50.00 Radius of Detection (nm) 16.67 Total Search Distance (nm) 133.33 Total Distance Traveled (nm) 283.33 Fuel Needed (lbs) 1416.67 Circular Area of Detection (nm^2) 872.22 # of Torpedoes 3.00 Weight of Torpedoes 1200.00 Weight Available for Sonobuoys 433.33 Type A Type B Sonobuoy Capacity 10.00 10.00 Max Area of Detection 384.65 502.40 Probability of Detection 0.58 Probability of Kill 0.50 Distance to Contact (nm) 75.00 Time of Flight (min) 50.00 Radius of Detection (nm) 16.67 Total Search Distance (nm) 133.33 Total Distance Traveled (nm) 283.33 Fuel Needed (lbs) 1416.67 Circular Area of Detection (nm^2) 872.22 # of Torpedoes 2.00 Weight of Torpedoes 800.00 Weight Available for Sonobuoys 833.33 Type A Type B Sonobuoy Capacity 10.00 10.00 Max Area of Detection 384.65 502.40 Probability of Detection 0.58 Probability of Kill 0.43 MAXIMUM PAYLOAD = 3100 LBS MAXIMUM PAYLOAD = 3100 LBS Figure 8 We can see here that even at the longer range of 75 nautical miles, the probability of kill remains higher while carrying three torpedoes. The reason for this change is simple. The added payload of the helicopter takes away the disadvantage of being unable to carry maximum sonobuoys.

If the payload can be increased up to 3100 lbs, our recommendation will be to increase the torpedo carriage. Conclusions From our analysis, we have come to our final decision. It will be more effective for the SH-60 anti-submarine helicopter to carry two torpedoes.