The Loss of HMS Hood

A Re-Examination

by William J. Jurens

Part 2


Sinking of HMS Hood

Sinking of H.M.S. Hood
 Painting by J.C. Schmitz-Westerholt
U.S. Naval Historical Center Photograph # NH 50741-KN

.

no21987-Exhibit_M_Sketch.jpg

Exhibit M of the Second Board of Inquiry, which the court used as a general guideline to the geometry of the stern portion of the ship.  Note the notations added by the board during the course of their investigation.

Click on this sketch for a larger image.

Events After the Explosion:


The Admiralty announced the loss of Hood at 9 P.M. on the 24th of May in the form of the following simple communiqué:

"British naval forces intercepted early this morning off the coast of Greenland German naval forces including the battleship Bismarck.

"The enemy were attacked, and during the ensuing action H.M.S. Hood (Captain R. Kerr, C.B.E., R.N.) wearing the flag of Vice-Admiral L.F. Holland, C.B., received an unlucky hit in the magazine and blew up.

 "The Bismarck has received damage and the pursuit of the enemy continues."


Adding in a final poignant sentence:

"It is feared there will be few survivors from H.M.S. Hood."37


Thousands of British sailors and citizens recalled receiving the news as the single greatest shock of the war.  Several officers recalled decoding the message again and again, in the absolute certainty that an error must have been made.  The story hit the papers the next day.  NAZI BATTLESHIP BISMARCK SINKS THE HOOD IN NORTH ATLANTIC DUEL; BRITISH GIVE CHASE; RAF FLIES TO CRETE, BLASTS 14 AIR TRANSPORTS read the verbose headline in the New York Times for Sunday the 25th.  Describing Hood as a symbol of British naval power and the ". . . show ship of the British Navy," the paper called the action the greatest naval victory of the war since the River Plate.  The Times of London carried the story matter-of-factly on page 4 of the edition of Monday the 26th, calling it ". . . the heaviest blow the navy has received in the war," and in an editorial entitled "The Price of Sea Power" characterized it as a ". . . heavy calamity." German communiqués, which were remarkable for their lack of self-congratulation, stated simply that Hood had been sunk in a five minute engagement between a German flotilla and heavy English naval forces, and that the Germans had received no damage worthy of mention in return - a not unreasonable assessment at the time.

It wasn't long before British recriminations began.  A writer to the Times of London, in a letter entitled "DESIGN OF THE HOOD NO MISCALCULATION -The Handicap of Age" stated the Hood had not been destroyed by a "lucky hit" but because ". . . she had to fight a ship 22 years more modern than herself.  This was not the fault of the British seamen.  It was the direct responsibility of those who opposed the rebuilding of the British Battle Fleet until 1937, two years before the second great war started.  It is fair to her gallant crew that this should be written."38  The Admiralty, still reeling from the shock of the loss, chose to file the letter as part of the official record.

It is clear that the Admiralty responded to the loss about as rapidly as circumstances allowed.  In a letter to the Controller and the First Lord, Sir Dudley Pound wrote on 28th May:

"The loss of HOOD from internal explosion after a few minutes' action at 23,000 yards is disturbing, as we thought that the defects in construction which led to the similar loss of three capital ships at Jutland had been eliminated.  . . . Now, after the lapse of 25 years, we have the first close action between one of our capital ships and that of the Germans since the Battle of Jutland and the HOOD has been destroyed in what appears to the onlooker to be in exactly the same manner as the QUEEN MARY, INDEFATIGABLE and INVINCIBLE, in spite of the action which was taken subsequent to Jutland to prevent further ships being destroyed as a result of 'flash'.  . . . In the light of this experience, will you please have the whole matter re-opened, going back to the records of the last war and see whether any theory can be evolved that would explain the loss of all four ships from some cause other than 'flash'."39


Sir Dudley's letter set in motion the activities of the first inquiry to investigate the causes of the loss, convening on 30 May 1941 and headed by Vice Admiral Sir Geoffrey Blake.40  The results of the board, a two page report signed by S.V. Goodall, and classified "SECRET," were made available to V.C.N.S. and First Sea Lord on 2 June, 1941, only nine days after the loss and only a week after Prince of Wales returned from Hvals Fjord.41  The report began:

"This report contains the findings of the Court, but not the evidence on which these findings are based.  Hence, some of the points raised in the following remarks may have been dealt with in the evidence and the Court's conclusions reached after full consideration of such points."


With some qualifiers, the report found that ". . . a 15-in shell fired from 'Bismarck' at the range and inclination of the fatal fifth salvo could, if lucky and if possessing sufficient delay, reach the after magazines," noted that the explosion seemed to originate at the base of the mainmast, and stated, "It is extremely difficult to associate this observed fact with the explosion of the 4-in magazines, the forward bulkhead of which group is 64 ft abaft the center of the mainmast."  Almost unbelievably, as an alternative, the board felt that even a single torpedo head exploding in its confined box ". . . would most probably break the ship's back and result in rapid foundering."  The report concluded:

"It is important the doubts concerning the loss of this ship should be cleared up if possible at a very early date, as although action is being taken to implement the lessons of both explanations, it is impossible to do this quickly for all our old capital ships if the true explanation is found by the Court.  Moreover, it will never be possible to give these ships such protection to their magazines as to ensure certainty [sic] that modern shells and bombs under all circumstances that may exist in modern actions cannot reach their magazines."


Not surprisingly, when one considers the speed with which it was prepared, the report was rather incomplete.  Although Goodall made this clear in the introduction, it was nonetheless criticized quite severely by some of the recipients.

In a memo dated 18 July 1941, V.C.N.S. wrote:

"D.N.C. in his minute on this paper raises a point of great importance, i.e., as he points out the report contains the findings of the Court, but not the evidence on which those findings are based.  . . . it unfortunately transpired that no shorthand notes of the evidence were taken.

"This matter of the blowing up of the HOOD is one of the first importance to the Navy.  It will be discussed for years to come and important decisions as to the design of ships must rest on the conclusions that are arrived at.  This being so, it seems to me that the most searching inquiry is necessary.  . . . I regret to state that in my opinion the report as rendered by this Board does not give me confidence that such a searching inquiry has been carried out; in particular the failure to record the evidence of the various witnesses of the event strikes me as quite extraordinary.  . . . I also note that of the three survivors from the HOOD one only was interviewed.  This strikes me as quite remarkable.

". . . I propose, therefore, that a further Board of Inquiry should be assembled as soon as possible and that the necessary witnesses should be made available.  At this enquiry every individual in every ship present who saw the HOOD at or about the time of the blowing up should be fully interrogated."42


To that end, a second board of inquiry, headed by Rear Admiral H.T.C. Walker R.N., began hearings in August of 1941, delivering its final report on 12 September.  Not surprisingly, the second report was much more thorough than was the first, taking evidence from a total of 176 eyewitnesses to the disaster, including 71 from H.M.S. Prince of Wales, 89 from H.M.S. Norfolk, 14 from H.M.S. Suffolk, and 2 from H.M.S. Hood, the third survivor, Midshipman W.J. Dundas being ". . . not available to give evidence to us."43  In addition, evidence was taken from two officers who had recently served aboard Hood, and from a number of other technical witnesses nominated by the Director of Naval Construction, the Director of Naval Ordnance, the Director of Torpedoes and Mining and the Chief Superintendent of the Research Department.  In summary, the general findings of the second hoard of inquiry were as follows:

a) The signal for the final turn 20° to port was flying at the time of the blast, but never executed.

b) The fire was started on the port side of the boat deck of Hood by the 3rd or 4th salvo from Bismarck.  The preponderance of evidence suggested that it was a cordite fire from U.P.44 and possibly 4-in ammunition in the vicinity.  The fire on the boat deck had nothing to do with the final explosion.

c) Evidence as to the seat of the explosion was divided between before and abaft the mainmast with a bias towards the former.  The large explosion, which was visibly similar to magazine explosions aboard World War I battlecruisers, was due to the explosion of the after magazines.

d) A large majority of witnesses heard little or no noise of the explosion.

e) Very few witnesses could be very definite about the debris from the explosion, and 'a large number of small pieces' best described the general impression.

f) The ship sank in three minutes or less.

g) Evidence generally indicated that the salvos from Bismarck in the order they fell could be described as:  1) ahead, 2) astern, 3) straddle with hit, 4) close short, 5) probable hit.  One salvo of 8-in H.E. was also noted astern of Hood.

h) The explosion or detonation of torpedo warheads was of low probability, and at any rate could not have been the cause of the loss.

i) If the muzzle velocity of Bismarck's guns was between 830 and 930 meters per second then a 380mm penetration to the main magazines was "quite possible"; if over about 930 meters per second, then the probability was "considerable." [The actual initial velocity of Bismarck's guns was c. 820 mps.]

j) An effective underwater hit was relatively unlikely due to the c. 75 foot [23 meter] fuze delay required to reach the magazines.


The nineteen page report concluded:

"(1) That the sinking of the HOOD was due to a hit from BISMARCK's 15-in shell in or adjacent to HOOD's 4-in or 15-in magazines, causing them all to explode and wreck the after part of the ship.  The probability is that the 4-in magazines exploded first.

(2) There is no conclusive evidence that one or two torpedo warheads detonated or exploded simultaneously with the magazines, or at any other time, but the possibility cannot be entirely excluded.  We consider that if they had done so their effect would not have been so disastrous as to cause the immediate destruction of the ship, and on the whole we are of the opinion that they did not.

(3) That the fire which was seen on HOOD's boat deck, and in which U.P. and/or 4-in ammunition was certainly involved, was not the cause of her loss."45
 

A Re-Evaluation:

There are a number of possible explanations that might account for the loss of the Hood.  A projectile from Bismarck may have penetrated her main belt and reached a magazine.  Alternatively, a shell may have gone over the main belt instead, or reached the magazines by passing underneath.  Some authors have suggested that it was a projectile from Prinz Eugen which caused the loss, or advanced the hypothesis that Hood was destroyed by the explosion of her port or starboard torpedo tube nest.  Still others have proposed that it was an uncontrollable spread of the fire on the boatdeck that lead to her loss, that perhaps a loading accident was to blame, or that the blast was caused by unsafe or unstable propellant.  Was the loss caused by one of these causes, several working together, or some entirely unrelated circumstance?  I have begun by assuming that any reasonably credible explanation of the loss must meet most or all of the following criteria.  First, it must be consistent with the observations of the eyewitnesses.  Second, it must be physically plausible, in the sense that it is consistent with the normal laws of physics.  Third, it should be of such a nature as to have had a reasonable probability of actually taking place.  To that end, in order to reach my conclusions, I have undertaken both a careful and critical re-reading of the entire minutes of both boards of inquiry into the loss of the Hood, and re-assessed these observations as seen in the light of information unavailable to the original investigators.

Any discussion on the loss of the Hood must make it clear at the outset that there are important inconsistencies as to the range and target angle of Hood at the time she was hit.  Published statements of the range, for example, range from an apparent low of 14,500 yards [13,260 meters], given in Raven and Roberts, to an apparent high of 19,685 yards [18,000 meters] given in Müllenheim-Rechberg.46  Although in more elementary treatments some of this is no doubt due to confused reading of accounts by writers making no distinction between "gun range," i.e. the range set on the sights of the guns to obtain a hit, and "navigational range," the geometric distance between the firing ship and the target, discrepancies in more knowledgeable presentations are difficult to explain.  Even official track charts have proven inconsistent and unreliable.  The track chart shown below, which was developed with the aid of a computer, has been redrawn from information taken from a large number of British and German sources and is, so far as I know, the first to reconcile all of these outstanding discrepancies.  Geometric reconstruction of the various accounts indicates that the most probable range at impact was in the vicinity of 18,100 meters.  Given this information, accurate figures for the appropriate terminal conditions of Bismarck's shells can be inferred from contemporary German range tables.
 
 

no21987-Track_Chart.jpg

Track chart of the action of 24 May 1941, adapted from British and German sources.  The letter "A" represents the British estimate of the course of the Bismarck and Prinz Eugen, "B" represents the planned future course of Hood and Prince of Wales after 0600, and "C" indicates the British estimate of the German position at 0600.  The sinuous course of Prince of Wales after 0600 is from the British track chart, whilst the more regular turn is taken from German accounts.

Click on this picture for a larger image.

There are also major difficulties in determining Hood's exact target angle at the time of the blast.  Some descriptions of the action suggest that Hood was either in the midst of completing her turn of 20 degrees away or that she had in fact completed it when the fatal explosion occurred.47  Witnesses in Prince of Wales, including Captain Leach and Cdr. Rowell, were consistent however in affirming that although a 2 blue was flying, it had yet to be executed when Hood blew up.  The boards of inquiry specifically found that the final turn was never executed.  The turn would have only taken about twenty seconds to complete, however, and there is at least circumstantial evidence that Hood might indeed have at least begun to turn when she exploded.  Numerous witnesses confirmed that Prince of Wales had to alter course to starboard to avoid wreckage of Hood as she steamed past.  It is very unlikely that such a maneuver would have been required unless Prince of Wales had already commenced a turn of 2 blue herself.  Assuming that Hood and Prince of Wales maintained the normal practice of turning together and recalling that Hood was flag and thus controlled the movements of both British ships, it is clearly unlikely that Prince of Wales would have begun the turn without receiving an 'execute' signal from Hood.  In my own opinion, the most probable explanation is that Hood had just begun the final turn, perhaps without yet sending the execute signal to Prince of Wales, and that Prince of Wales began the turn by reflex, in effect completing Hood's intention at the exact moment she exploded.  In fact, both of Hood's surviving witnesses who gave detailed testimony stated that a turn to port had just begun when the explosion occurred.  In describing the final seconds of Hood, Able Seaman Tilburn stated ". . . we started turning round to port and we were hit somewhere, and the whole ship shook and a lot of debris and bodies started falling all over the deck." Briggs confirmed this, stating ". . . it was either just immediately after or whilst we were doing this turn to port that the explosion took place."  When asked if the execute signal had been made before the explosion, Briggs replied "I am not certain but I think it had."48
 
 
 

no21987-Robert_Tilburn.jpg

Able Seaman Robert Tilburn, R.N., one of three survivors of Hood's action with Bismarck and Prinz Eugen.  He was lying down adjacent to Hood's forward funnel when the ship disintegrated around him.  HU 50191.

A Technical Analysis:

Although the testimony of eyewitnesses can give an overall picture of the circumstances leading up to the loss of Hood, such evidence cannot hope to establish the cause of the loss in detail.  Not only was the incident itself rather poorly - almost casually - observed, but the dynamics of the event itself necessarily took place so quickly or in such locations that they were literally beyond the grasp of human perception.  In such circumstances, the anecdotal accounts of witnesses can be used only to narrow down the range of possibilities, and to form a rough guide as to the most likely routes for further investigation.  The final explanation must of necessity be technical in nature, and be reached via a scientific approach.  The remainder of this paper will devote itself to a technical evaluation of the evidence available.
 

Vulnerability of the Armor System:

Initial data concerning the details of German guns and the armor of Hood has been relatively easy to obtain.  Reference to Hood's cross section (see Part 1) shows that her belt armor was made up of three main sections, an upper belt 127mm thick, a middle belt 178mm thick, and a lower belt 305mm thick.49  Each was sloped 10° from the vertical with the bottom edge inboard to further increase its effective resistance.  The deck armor is also shown in the cross sectional view.  A range table for Bismarck's 380mm main battery over the ranges of interest is shown in Table II and a drawing of one of Bismarck's 380mm projectiles50 is shown further below.
 
 
Table II
Range Table for 38cm SK C/3451

Projectile Weight 800 kg      Initial Velocity = 820 mps

Range
(meters)
Angle of Fall
(deg.)
Time of Flight
(sec)
Striking Vel.
(mps)
Prob. Error
(meters)
14,000
  9.9
20.7
581
49.5
14,500
10.0
21.7
575
50.0
15,000
10.5
22.4
569
50.4
15,500
11.0
23.3
561
50.9
16,000
11.5
24.2
556
51.3
16,500
12.2
25.0
550
51.8
17,000
12.8
26.0
544
52.3
17,500
13.3
27.0
537
52.7
18,000
13.9
28.0
532
53.2
18,500
14.5
29.0
527
53.6
19,000
15.0
30.0
520
54.1
19,500
15.8
31.0
515
54.5
20,000
16.4
32.0
510
55.0
20,500
17.0
33.0
507
55.5
21,000
17.8
34.0
502
56.0
21,500
18.3
35.0
498
56.5
22,000
19.0
36.2
492
57.0
22,500
19.9
37.3
489
57.5
23,000
20.7
38.4
485
58.0
23,500
21.3
39.5
482
58.5
24,000
22.0
40.6
478
59.0

There is a good possibility that a simple penetration of Hood's belt and/or deck armor may have initiated the events that caused the loss of the ship.  The arrangement of the armor dictated that even if Hood had been engaged directly from abeam, the minimum obliquity of impact would have been c. 24°, equal to the 14° angle of fall plus the 10° slope of the armor. An analysis of the track charts of the action indicates that at the fatal moment, assuming she had not begun the final turn, Hood's target angle would have been approximately 53°.52  For this angle, corresponding to a shot approaching from 37° forward of the beam, the resolved obliquity would have been approximately 43.85°.53  German armor penetration curves, redrawn below,54 indicate that at the predicted striking velocity of 530 meters per second, the penetration for an intact projectile into face-hardened armor would have been approximately 240mm.  An intact penetration of the 305mm main belt would therefore have been improbable, although either of the thinner sections would have been easily perforated.  Calculations yield an exit velocity of about 450 meters per second from the 127mm plate and 365 meters per second from the 178mm plate.55  The impact would have certainly decapped the projectile and forced it to exit closer to the normal than its impact angle, meaning that the projectile might well have been traveling nearly horizontal and nearly athwartships, as it left the plate.

Depending upon the exact location of the hit, a shot perforating the 127mm belt would still have to penetrate approximately 160-180mm of deck armor in order to reach the magazines.  If the hit went through the 178mm belt instead, only about 130mm of deck penetration would have been required, but in compensation the shell would have been traveling much more slowly.  In either case the trajectory of the projectile, its velocity, and its high obliquity would have rendered useful penetration to the area of the magazines highly unlikely.56  Even assuming the projectile were not rejected or deflected by Hood's deck armor, the fuze delay of the German projectiles would have probably detonated the shell before it could reach a magazine.  Assuming that the required deck penetrations reduced the projectile's average velocity to half of the plate exit velocity, a nominal fuze delay of 0.035 seconds corresponds to a travel of only eight meters at best, not enough to reliably reach a magazine.57  The German penetration diagrams are reproduced below.
 
 

no21987-AP_curves1.jpg

Armor penetration curves for the German 38cm projectile against face hardened armor.  The shaded area indicates the probable limiting conditions at impact, with the figures "73" and "53" at the top referring to the probable target angles at the beginning and the end of the final turn and the figures "570" and "530" representing the probable range of striking velocities.

no21987-AP_curves2.jpg

  Armor Penetration curves for the German 38cm projectile against homogenous (deck) armor.  Note that at angles of fall less than about 20 degrees penetration of any sort was considered problematical.  These curves were adapted from those given in "Unterlagen."

no21987-Ballistic_Angle_vs_Target_Angle_sketch.jpg

The German penetration curves redrawn in another form.

no21987-German_38cm_apc.jpg

Cross-section of one of Bismarck's 38cm projectiles.  Note the relatively flat front of the armor-piercing cap, which may have greatly enhanced its diving capabilities.

Sketch by William Jurens with additional work by Tony DiGiulian


 

......
To Part 1     To Part 3


Footnotes for Part 2:

37 Bradford, pp. 186.

38 Letter to the editor The Times, 28 May 1941, reproduced in ADM 116/4351 pp. 17.

39 ADM 116/4351 pp. 14.

40 The other members of the board were Capt. C.F. Gammel of H.M.S. President and Capt. C.H.J. Harcourt of H.M.S. Duke of York.

41 The entire first report is given in ADM 116/4351 pp. 6-7.

42 ADM 116/4351 pp. 10-11.  The last three paragraphs of the memo have obviously been "patched on" from text prepared using a different typewriter.

43 ADM 116/4351 pp. 89 et. seq.  It is worthy of note that Norfolk was fifteen miles distant at the time of the blast, and Suffolk was nearly twice as far, so the evidence of the witnesses from these ships is rather general in nature.

44 The abbreviation 'U.P.' stood for Unrotated Projectiles, i.e. rockets.

45 The entire final report is given in ADM 116/4351 pp. 89-108.  As a matter of interest, the board also listed their estimates of 90° immunity zones for British ships against German 15-in shell.  In rounded metric units, these were:  KGV class 13,700 - 31,000 meters, Nelson class 13,700- 32,000 meters, Queen Elizabeth class 16,450 - 25,150 meters, Royal Sovereign class 16,450 - vulnerable (18,750 meters with 25mm deck armor addition).  Renown's immune zone was negative, with the belt limit at 25,600 meters and the deck limit at 21,950.  The immune zone is the area far enough away from the enemy to prevent penetration of the belt armor, yet close enough in to prevent plunging  fire from penetrating the deck.

46 Other values are 16,500 yards [15,087 meters] quoted in both Roberts and Bradford, and 21,130 yards [19,300 meters] scaled from a track chart in Grenfell.  Whitley [German Cruisers of World War II, U.S. Naval Institute, 1985] gives the ranges from Prinz Eugen to Prince of Wales as 24,500 meters at 0553 and 16,000-17,000 meters at 0559.  Dulin and Garzke [Battleships - Axis and Neutral Battleships of World War II, U.S. Naval Institute, 1985] give the range from Bismarck as decreasing to 18,300 meters after the fatal shells had been fired, which implies the range was higher before that  time.  A track chart in Schmalenbach yields a range of c. 18,000 meters at the time of the blast.  The official British track chart gives the range as 16,300 yards, i.e., 14,900 meters.

47 E.g. Bradford pp. 184 and Kennedy pp. 86.  Statements that Hood's 'A' arcs were closed up until that time were false.  Drawings of the ship show that Hood's after turrets could train and fire within 30° of the bow, although her starboard turret rangefinder optics would have been 'wooded' by the after superstructure until an angle of 43° had passed.  Official drawings of Prince of Wales show her after turrets could have engaged up to 45° from either bow.  As Bismarck was bearing approximately 53° off the bow during the final run in, it is evident that both Hood's and Prince of Wales' 'A' arcs had in fact been well clear since the turn at 0555, provided one would  have been willing to accept some damage from muzzle blast.  Captain Leach's statements that Y turret would not bear probably mean that 'Y' turret would not bear comfortably.

48 ADM 116/4351 pp. 360-365.  Perhaps significantly, however, Briggs was equally positive that the turn was one of 40° instead of the 20° it actually was.

49 These values have been converted and rounded to metric units, in Imperial units the thicknesses were 5-in, 7-in, and 12-in., respectively.

50 As an aside, in the process of reviewing preliminary drafts of this manuscript, several readers took me to task for using "bullets" as a synonym for "shells" or "projectiles."  Although I have thus deleted this noun from the paper, readers should note that it is not entirely unknown.  For one example, see S.E. Morison, History of United States Naval Operations in World War II, Vol. XII. pp. 190 et. seq., "The proportion of 8-inch bullets in the heavy cruisers was 66 per cent."

51 All range tables in this paper are derived from "Unterlagen" described in the bibliography.

52 Strictly speaking the target angle is defined as the angle between the firing ship's bow and the line of sight to the target, an angle which is used to develop the lead angle used in surface gunfire.  In the absence of a better term, I have used it here to describe the angle from which the projectiles from Bismarck actually arrived on the Hood. Hood and Bismarck would not have moved significantly with respect to each other during the approximately 28 second time of flight of Bismarck's projectiles.

53 The equations to determine the resolved obliquity for a sloped armor plate are basic but are rarely reproduced.  In simple terms Oo = Arcos [Cos(Fd)Cos(Id)Cos(Bpd - Rd)Sin(Fd) Sin(Id)], where Oo equals the resolved obliquity, Bpd equals the target angle, Id equals the inclination angle of the armor, Rd equals the rotation angle of the armor, basically its horizontal orientation within the ship, and Fd equals the angle of fall.  Vide, Okun, Nathan "Frames of Reference," unpublished manuscript in the author's collection.

54 Vide "Unterlagen und Richlinien . . ."

55 As a first approximation, Yr = (V2 - VI2)0.5, where Yr equals the residual velocity, V equals the striking velocity and VI equals the limit velocity for the plate in question.  These exit velocities were obtained directly from the German data, and thus do not exactly match the (more accurate) values given in Table II, and derived from more modern computations.

56 Note that all the figures for armor thicknesses given here ignore the roughly 38mm thick backing plates and teak cushion behind the face hardened armor, a not insubstantial barrier that would reduce the penetration of impacting projectiles even further.  Thus the penetration values given here, are, if anything, somewhat optimistic.

57 When examining Hood's cross sections, an eight meter travel along the line of flight corresponds to an athwartships distance of only about 6 meters.  Assuming a target angle of 53°, and that the projectile was undeflected by its passage through the armor, the ratio of actual travel to projected travel when superimposed on the ship's cross section is equal to cos 37°, or 0.7981.  Of course, the projectile would have been deflected athwartship during penetration, so this may be looked upon as a minimum value.  It is worth noting that the angle of fall would have been greatly reduced at the same time, which would have tended to keep the flight line above the crowns of the magazines.
 



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