.

. wo 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. 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.

Mathematics.