FOOTNOTES

1.	The term U-boat is used to refer to any enemy submarine (German, Italian, Vichy French, or Japanese) with a displacement of 200 tons or more.
2.	The estimates given here for U-boat sinkings are based on Allied assessments. Incidents assessed A or B are considered to have sunk the U-boat. Justification for this assumption is given in Appendix 1.
3.	Four more Japanese U-boats were sunk in the Indian Ocean.
4.	The figures given in this summary are based on CNO records as of November 1945. They do not agree exactly with figures given in other chapters which were prepared earlier. Assessments of attacks, in particular, have been changed somewhat on the basis of intelligence gained from German sources after the German surrender. As is shown in Appendix 1, however, the earlier assessments as they existed at the end of the war were in good general agreement with German records of submarine losses and therefore provide a fairly reliable basis for the discussion given in the other chapters.
5.	Visual detection of a submerged submarine is possible only in very rare cases. Magnetic detection is effective only at very short ranges, much shorter than those of underwater sound.
6.	This type of comparison can be made most clearly on the basis of sinking rates, as in Chapter 13.
7.	The sweep rate Q is defined in Volume 2B, Search and Screening. Q gives the effective area which the searcher is able to inspect completely in a unit of time.
8.	Total flying hours were: November, 933; December, 1833; January, 2167; February, 2120.
9.	See Chapter 2 of Volume 2B, Search and Screening, for a complete exposition of contact phenomena.
10.	This figure depends on a number of factors, such as type of ship, distance from land, roughness of sea, etc. The experience of United States submarines has been that about 40 per cent of the ships hit by one torpedo sink. This would lead to 1.76 x 0.40 = 0.71 ships sunk per salvo. Thus the estimate of 1 to 1½ ships sunk is probably too high, if anything, though it may be about correct for rough weather in mid-Atlantic.
11.	As a corollary it may be concluded that for attack on very large convoys, a long-range torpedo would be very effective because it would have good chances of success when fired into the convoy as a brawning shot.
12.	A figure analogous to the five to one ratio found for independent versus convoyed ships can be obtained by comparing sinkings before and after convoying in certain regions. The Capetown and Trinidad areas (both regions of high U-boat activity) give ratios of about six to one and ten to one.
13.	For comparison, the data on convoys which spent more than half their time south of the Great Circle are shown. Losses for convoys on southerly routes   Number of convoys Percent sighted Percent attacked Ships sunk per convoy sailing SC and ONS (7 kt) 8 88 88 2.9 HX and ONF (9½ kt) 7 86 86 3.7 The numbers here are small and actually the fast convoys suffered more heavily than the slow. It is of great interest that they were attacked twice as often as those on northerly routes, particularly since the number of U-boats on patrol in the southerly zone was less than a third of the number further north.
14.	This contrasts strongly with the experience of United States submarines in attacking Japanese convoys, for their ability to sink ships has not been affected by the number of convoy escorts present; the only possible conclusion is that Japanese detection equipment and procedure have been highly ineffective.
15.	Standard doctrine presented in FTP 223A for the use of cut-on technique and range recorder is an example of an implicit tracking procedure. Range rates, recorder traces, and changes in bearing are used to give rules for carrying out the attack. The antisubmarine attack plotter, on the other hand, is a device for explicit tracking, since it presents a geographic plot of submarine motion.
16.	The rule of combination of errors used in equation (1) is consistent with the normal usage of the term probable error, but Figures 6 and 7 are not. They should be considered as illustrations only, not exact diagrams.
17.	A slight correction must be made to take account of charges that either hit glancing blows on the sides of the submarine and fail to explode or hit and explode in some position too far from the pressure huff to be lethal.
18.	The interpretation of these figures is open to some question, however, because incidents have normally been classed as coordinated only when several ships actually attacked the submarine. Cases in which several ships were on hand but only one released depth charges are not usually counted as coordinated. This type of selection introduces a bias such that coordinated incidents may be credited with values of C (and of lethality) which are higher than those actually obtained in operations.
19.	During the course of World War II, this assessment was based on visible evidence of damage, survivors from the U-boat, if any, and supporting intelligence. After the German surrender, however, captured documents have become available to supplement this information, and assessments have been revised. The data presented here are based on the earlier wartime assessments. See the Appendix and Chapter 8 for further discussion of this question.
20.	The figures given are for United States attacks from July 1942 to July 1943 assessed A to G, for which the information necessary to estimate sound conditions from oceanographic considerations was given.
21.	In the analysis, attacks thought to have been made on the U-boat's wake or made after a kill had already been assured are not counted. Hence the figures are a fairly pure measure of weapon effectiveness.
22.	This effect may be somewhat exaggerated by the method of designating coordinated incidents. If two ships make attacks a few hours apart on what was probably the same submarine, the actions involved will be likely to be considered a single coordinated incident if damage is done, two independent incidents if there is no damage.
23.	See Chapter 13 for a further discussion of this point.
24.	Use of Schnorchel by the submarine will, of course, greatly reduce the searching effectiveness of the aircraft but will not change the basic attack problem except to the extent that it increases the average degree of submergence of submarines when attacked.
25.	Blind time has been defined in Chapter 11.
26.	See Chapter 14.
27.	It should be noted that line errors varied noticeably with angle between aircraft course and target course. The MPI was on target for track attacks and 10 or 20 ft right for beam attacks, according to whether approach was from port or starboard. Probable error about the MPI was about 15 ft for track attacks and 40 ft for beam attacks.
28.	Angle of attack is angle between aircraft course and submarine course.
29.	This is not strictly true of course, since there are bound to be fluctuations; some bombs will explode under the lethal area and fail to destroy the target, while others somewhat outside this area will succeed. The assumption of a fixed lethal area can, however, give us the correct average expectancy for a large number of cases.
30.	Penetration of the pressure hull by a rocket may not always cause immediate sinking, but the resulting damage should normally be sufficient to keep the submarine on the surface and permit follow-up attacks to sink it. Hence the term lethal may reasonably be used.
31.	These errors, considerably greater than those quoted earlier for practice drops, are still rather small for operational errors.
32.	While the accuracy of intelligence is of great importance in deciding on the plan of any search operation, since it determines the area that should be searched, analysis of the accuracy of different types of intelligence is beyond the scope of this discussion.
33.	See Chapters 4 and 5 of Volume 2B, Search and Screening.
34.	Special gear in the form of sonobuoys or magnetic anomaly detectors [MAD] are available for detection of submerged sub-marines. They will be discussed later, since the sweep rates are very small.
35.	Operations Research Section--Coastal Command, Report No. 204, Air Offensive Against U-Boats in Transit, December 10, 1942.
36.	Plans are presented in FTP 223A. The mathematical basis upon which such plans are constructed is given in Volume 2B, Chapters 3 and 7.
37.	At the end of the war German U-boats of high submerged speed (10-15 knots for Type XXI, 15-25 knots for the proposed Type XXVI) were approaching operational status. They were designed to operate effectively when submerged and would have been able to stay submerged using Schnorchel to escape radar detection, yet retain potent offensive capabilities because of their special propulsion for high submerged speed. Conclusions drawn from operations involving old-style U-boats may be completely inapplicable to these new types. Their development shows, however, that the Germans had realized that the other types were not satisfactory for completely submerged operation.
38.	United States submarine crews have to some extent shared the Germans' suspicion of aircraft warning radar and convinced themselves that the Japanese were homing on SD radar transmissions from a number of individual incidents which seemed to indicate such homing. Many of them ceased to use SD radar. Statistical data showed, however, that no effective homing was taking place as late as December 1944, as can be deduced from the table below.   Aircraft contacts per 100 days (in Luzon Strait) Percentage of aircraft (all areas) that detected subs Day Night Day Night SD nonusers 84 23 12 10 SD users 86 24 9 8
39.	See Volume 2B, Chapter 5, for detailed discussion of radar ranges.
40.	Noise generated by the torpedo itself, particularly its propellers, makes a substantial contribution to the background noise heard by the acoustic mechanism. This contribution is called self noise.
41.	An acoustic torpedo could not be sensitive to a lower frequency because a hydrophone system small enough to fit in a torpedo would not be sufficiently directional, that is, could not tell the side on which a noise was heard.
42.	Trajectories of this type are discussed on page 168.
43.	Much of the early information concerning the German acoustic torpedo was obtained from interrogation of prisoners of war. Unfortunately they did not, in general, know anything of its actual operation, so that it was necessary to deduce its method of operation from fragmentary observations which they had happened to make of its construction and use.
44.	Thirty-nine warships were sunk by U-boats between January 1942 and August 1943 in contrast to 1541 merchant ships.
45.	Information in the fall of 1943 continued to confirm the fact that the enemy had enlarged the rudders of their G7e torpedo to give the acoustic torpedo a minimum turning radius of 80 to 100 m.
46.	A listening arrangement would be much simpler than one involving echo ranging and less subject to failure. It Would probably have a greater homing distance. A torpedo would have little use for range information. The enemy had had much more experience with passive detection equipment. Most important, none of the intelligence information suggested echo ranging.
47.	In the initial trajectory studies, an attenuation of 0.1 db per foot was taken as a conservative assumption, even at lower frequencies.
48.	This pattern is essentially that assumed in the earliest United States studies mentioned in Section 15.2.1, this chapter.
49.	A pattern of this sort was decided upon in the fall of 1943 on the basis of United States experience in the design of hydrophones and acoustic torpedoes.
50.	It was once thought that there was it good chance that the D required to take the torpedo off gyro would be greater than that needed for the later steering. Using this "gate" would sacrifice some homing range in order to prevent a temporary peak in ship noise from taking the torpedo off gyro course and leaving it circling at such a distance that the normal ship noise could not be heard. However, the gate was assumed not to exist since its presence was found to be if anything an aid to countermeasure.
51.	Various estimates were made of the actuation range of the German torpedo, ranging from 100 to 1000 yd for a typical ship target. Later tests suggest the higher figures to have been the better.
52.	Allowing a margin of safety, a directive was issued specifying that when possible any submarine be kept more than 10 degrees off the bow of a ship towing FXR.
53.	Since accurate detailed knowledge of the German acoustic torpedoes sensitivity pattern has not been available, there has always been doubt on the subject of safety from stern chases. This has, in fact, been the crux of the countermeasure problem.
54.	The British even proposed a complicated hypothetical rudder control for T-5 which would be able to make a stern chase hit over one NM despite the 30-db) restriction. The phasing system between the hydrophones was sufficiently complicated to be able to distinguish between loss of contact when the torpedo passes over a noise source and loss of contact when the torpedo passes beside the source. In the first case the rudder would straighten until differential was again obtained, so that having made a stern chase on an NM the torpedo continues toward the ship without circling. In the second case the rudder locked over in the direction of the source, thus assuring more than one pass at a ship by a shot from ahead. This proposal seemed too complicated to be practical. In addition, the slight weave of the torpedo oil a stern chase would often cause it to pass somewhat to one side of the NM, possibly causing the rudder to lock over.
55.	Sonar interference from Mk 4 was at times so troublesome that a device was developed to turn it off completely when desired, designated as Harp. The noise output of Harp can be turned off or on by quick slackening of the towing cable. It should be kept in mind, however, that stopping the NM exposes the ship not only to torpedoes fired during the quiet period but also to torpedoes fired within 10 minutes prior to its stopping, which may have been pursuing the NM. Most WS torpedoes which had been trapped by the NM would then hear and attack the ship.
56.	The British double Foxer always had serious practical difficulties, but a simple light diverter (Scate) had been developed in the United States by the end of World War II which should make a two-NM scheme feasible.
57.	The hydrogen peroxide required was expensive to produce and the majority of the supply was used by the German Air Force, especially in the V-bomb program.

 

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