Ph = 10(E-TX)
Ph = Percentage of hitsIn which we express X as a percentage of maximum range in order to render the equation dimensionless. In the formulation above, 100% hits occur at 0% range and a variable number of hits occur at 100% range. That 100% hits occur at 0% range is true almost by definition, but the percentage of hits occurring at maximum range (i.e., at 45° elevation) is somewhat more difficult to define. For most normal situations, the equation is most accurate when T is selected as being equal to 0.023, equivalent to 0.5% hits at maximum range.80
K = Percentage of hits at maximum range of gun
E = 2.00
T = 0.02 - (0.01 Log K)
X = Percentage of the maximum range of gun
The maximum range of Bismarck's guns taken from published range tables is normally approximately of 35,500 meters. This figure corresponds to only a 30° angle of elevation however, as Bismarck's guns could not elevate any higher. Computer simulations however, show that the 45° maximum range would have been in the immediate vicinity of 41,700 meters. Taking this figure as the maximum range of Bismarck's guns would mean that Hood was at about 36% of maximum range when she exploded. At that range, the equation would yield approximately 15% hits.81
U.S. Navy fire effect tables from 193582 give 0.235 hits per gun per three-minute period for the 14-in/50 gun at 16,000 yards [14,630 meters], a roughly equivalent situation. Assuming one round per gun per minute, this is equivalent to a hit percentage of 0.235/3 = 0.078, or 7.8%.
Other official figures83 give average four-gun pattern sizes for U.S. 14-in and 16-in [350mm and 406mm] guns as approximately 190 meters at our range of interest. A very simple approximation, giving Hood a beam of 30 meters, would render a hit percentage in the vicinity of 30/190, or 15%.84
Bismarck's actual performance was in fact in rough agreement with these estimates. Up to the time Hood exploded, Bismarck fired five, four-gun salvos, and achieved between one and three hits, giving her a raw hit percentage of about 2/20 or 10%. In viewing this figure, however, we must remember that the five salvos she fired included at least two and possibly three to find the range, and also that Hood and Prince of Wales were making rather frequent course changes during the action, so that her hit percentage in aimed, well-ranged fire would probably have been somewhat higher.
Taking this and other factors
into account, once Bismarck had found the range it would appear
reasonable to grant Bismarck about a 10% - 15% hit probability during
the final salvos she fired at Hood. A statistical analysis
of four-gun salvos with a 10% single shot hit probability shows that about
64% of such salvos would result in no hits, 31% would result in one hit,
5% would result in two hits, and only about 0.27% would result in three.
For a 15% hit probability, the figures are about 5%, 40%, 9%, and 0.8%
respectively. Thus the chance of two simultaneous or near simultaneous
hits on Hood leading to the visible effects accompanying the blast
seem only to be about one in fifteen or twenty. The probability of
more than two simultaneous hits causing the blast is negligible.
It is interesting to note that more than a third of the witnesses aboard Prince of Wales actually missed the fatal explosion itself. Further, of the approximately forty-five witnesses who observed the explosion directly, less than a quarter associated it with a specific fall of shot from the enemy. A further 22% associated the explosion with the firing of one of the after turrets, and fully 55% of the observers did not associate the explosion with anything at all - to them the ship just blew up. There is therefore at least a minor possibility that the final explosion had nothing to do with Prinz Eugen or Bismarck at all.
Several witnesses noticed - and chose to mention unusual events aboard Hood during the action. P.O. George Henry Goff, a layer-rating in the port battery in Prince of Wales' port-after director, testified that he saw the third salvo fall ". . . on the starboard side of the 'Hood,' very close. The next thing I remember was seeing flames from 'X' turret. 'A,' 'B,' and 'Y' were firing at the time and I noticed that 'X' turret was not firing. . . . The next thing I noticed was that the 'B' turret was firing but belching out flames. After that 'Y' turret fired on its own and 'Hood' went up." When queried in detail about the belching flames, he replied, somewhat opaquely, "When a gun fires the flash licks slowly round the muzzle of the gun. But there was no straight flash and the flames licked slowly round." The board dismissed his testimony with the statement "This witness is rather inclined to be imaginative."85
But others had noticed a similar phenomenon. Through his periscope, Petty Officer James Crowley, captain of Prince of Wales' P.4 turret, noted ". . . when I looked through the periscope again I saw a flame come from 'B' turret through one of the guns. Not many moments after that she blew up."86 P.O. Edgar Holt saw the same thing through the periscope of P.5. turret. ". . . a fire broke out abreast 'X' turret on 'Hood' [sic] port side," he said. "About two minutes later I saw a flame about 10 feet long shoot out of 'B' turret muzzle and about a half to one minute later 'Y' turret on 'Hood' fired her first salvo. About a second later, 'Hood' blew up."87
Others also observed something unusual with 'Y' turret. Petty Officer Lawrence Sutton saw the action from the port side of the Admiral's shelter deck on Prince of Wales. ". . . Hood was firing with her foremost turrets," he said. 'Y' turret had been trained fore and after during this time. 'Y' turret then trained towards the enemy and before firing there was a flash abaft the mainmast of the 'Hood' which appeared to be a fire on the boat deck. 'Y' turret then fired," he continued, "and at the same time a huge flash came up all around 'Y' turret. The flash rose to well above the mainmast of the ship and all I heard was a tremendous roar and I could not see anything until the smoke had cleared away. That was all I saw of the 'Hood'." The court considered the memory of what he saw "very confused."88 A number of other witnesses confirmed Sutton's observations. At least one clearly saw Y turret train toward the enemy, return again to its fore-and-aft position, and train upon the enemy again.
To what can we ascribe this
unusual performance? Could Hood have been encountering internal
difficulties with her supply of powder and shell? Could some failure
have disrupted the notoriously complex and often unreliable sequence of
anti-flash mechanisms installed after British experience at Jutland?89
In the urgency of combat, might someone in the turret have over-ridden
a balky anti-flash interlock in order to bring the turret back into operation?
Might there have been something wrong with Hood's propellant?
Could a failure of her gas ejection system have caused a flare back into
'Y' turret which thence blew up the ship? Are these scenarios all
merely wild speculation? These possibilities, though unlikely, cannot
be positively excluded.
Given the conflicting and confusing evidence that has been presented, is there nonetheless a "most probable" explanation for the loss of Hood that reconciles the observations of witnesses with the geometry of the ship, and with the course of the action? I believe there is. The first significant bit of evidence is that to most witnesses the blast was essentially noiseless, or at least lacking a noticeable "bang." The "bang" of an explosion is caused by the creation of a supersonic shockwave, and is necessarily absent when burning occurs, even very rapid burning indeed. The noiselessness of the explosion constitutes strong circumstantial evidence that the fatal blast was caused not by the detonation of Hood's shells or torpedoes but by the more or less rapid combustion of her propellants. It is probably no coincidence that a very similar noiselessness was associated with the explosion of USS Arizona's propellant magazines at Pearl Harbor. This conclusion is in accordance with the findings of the original boards. Assuming that a shell or shells from Bismarck precipitated the disaster, this also explains the short delay that witnesses noted between the arrival of Bismarck's fatal salvo and the first evidence of the blast, and may in fact explain why many did not causally connect the two events. The burning rate of typical gun propellant is closely related to the surrounding pressure and temperature, and except in a very tightly enclosed space - such as the breech of a gun - take a considerable time to "build up steam." In fact, if venting is adequate, most gun propellants are surprisingly hard to ignite and unspectacular in their combustion.
In the absence of any other possible energy source, like the boards, I have concluded that it is most probable that Hood was relatively slowly rent apart over a period of perhaps a second by the uncontrolled burning of the propellants in her after magazines. Although the actual position of the hit and the subsequent path of the projectile through the ship are problematical, it is clear that there are several routes by which one of Bismarck's 380mm shells might have reached the after magazines. Again, like the boards, I have also concluded that the most probable cause of the final blast was a hit from a single 380mm projectile from Bismarck.
The general consensus of witnesses was that the explosion seemed to originate in the vicinity of the mainmast, some distance forward of the after magazines. The orthographic diagram shows that there is one place where a shell falling slightly short could have passed through the after engine room and detonated in or near the magazines located immediately adjacent to its after bulkhead at station 280. Yet another possibility is that it passed through the 178mm belt before detonating in essentially the same place. If this occurred, and ignition of the propellant in the magazines followed from it, then a large part of the rapidly expanding gas bubble would have taken the path of least resistance and vented into the engineering spaces immediately forward of this area. For a time the sheer inertia of Hood's structure would have slowed expansion in any other direction. Once the expanding gasses had reached the engine rooms, the quickest exits to the outside would have been the series of massive exhaust vents located on the centerline immediately forward and aft of the mainmast. These huge ducts, changing in size and shape as they rose through the ship ended in roughly square vents 1.8 meters on a side on the boat deck. It was as spectacular, near-vertical columns of flame from these vents near the mainmast, foreshortened to observers on surrounding ships, that the explosion first became visible. Shortly thereafter, the entire stern of the ship exploded.90
At the time of the blast,
the Boards of inquiry calculated the "X" 15-in magazine contained about
49 tons of cordite, "Y" magazine contained 45 tons, and the 4-in magazines
contained about 18.5 tons. The uncontrolled burning of this quantity
of propellant in the after magazines might have slowed briefly as the volume
of the engineering spaces served as a space into which the gasses could
expand, and as the vents directed much of the combustion products outboard.
But although this expansion and venting could temporarily relieve the pressure,
it could never be enough to prevent an explosion from eventually tearing
the ship apart.91 Ironically,
the chemical energy stored in the battlecruiser's after magazines - enough
to lift her enemy over a kilometer in the air had it been employed to do
so - had instead destroyed the Hood herself.
Photograph of a model of Hood showing the engine room exhausts through which the final explosion probably first vented itself. The model is Tamiya kit no. 7827-950.
Click on this sketch for a larger image.
This program, which I have developed myself, and which is still in the developmental stages, analyzes the entire gunfire problem from the muzzle to the post impact behavior of the projectile on the target. The program uses a series of complex and accurate algorithms to compute the percentage of hits to be expected on the target at various ranges, the proportion of hits on each exposed surface of the target's armored box, and the number of penetrations based on the U.S. Navy's WW II armor penetration equation given in ORD SK78841 [More details on this equation and its derivation are given in Nathan Okun's article '"Armor and Its Application to Warships - Part III," Warship International No. 2, 1979, pp. 284 et. seq.]. At this preliminary stage, the program assumes the armor suit of the target to be a simple box with single plate sides, ends, and deck.
Assuming the initial values
for Hood's armor to have been 200mm, 178mm, and 127mm, respectively,
it is easy to vary the thickness of the deck armor and compute equivalent
values for the thickness of the belt and ends while keeping the overall
displacement the same. This results in the values shown below in
Computing the hit percentages
and the number of penetrating hits that Bismarck might be expected
to score on Hood over the range band from 15,000 - 25,000 meters
at 1,000 meter increments, using optical fire control, and target angles
from 0° to 90° in 30° increments, results in the graph shown
below. What is important here is not the absolute number of penetrations
that are scored, but the relative number of penetrations that occur as
deck thickness varies.
The graph clearly shows that
in this particular situation the minimum number of penetrations occurs
with deck thicknesses between about 125 and 150mm. It is also interesting
to note that increasing the deck thickness beyond this value is actually
counterproductive. Even though the algorithms used for armor penetration
are admittedly approximate, they do indicate that rather than being too
thin, Hood's decks might have been just about ideal for the situation
in which she found herself on the 24th of May. Incidentally, the
program also predicts that Bismarck would have been expected to
score approximately 10.1% hits on Hood at a nominal range of 18,000
meters and a target angle of 60°.93
To Part 3
Many thanks are also due
to Mr. Harry Purdue, Chairman of the Hood Association, and to Mr. James
Brown of Cheshunt, Herts, who were able to answer many questions, and who
supplied, amongst other things, a complete list of those lost in the tragedy.
ADM 116/4352. A continuation of the above record, primarily comprised of duplicate illustrations and the actual shorthand notes of the court reporters. 467 pp.
Bradford, Ernie, The Mighty Hood, Hodder and Stoughton, 1959, 224 pp. A readable, if popularized, account emphasizing the operational history of Hood from her construction to her loss.
D'Eyncourt, E., H.M.S. Hood, Engineering, March 26, 1920. Detailed technical description, with many interesting illustrations, but dated when compared with modern sources.
Grenfell, Russel, The Bismarck Episode, Faber and Baber, 1960. A well-written, basic account of the entire sortie of Bismarck and Prinz Eugen.
Kennedy, Ludovic, Pursuit - The Sinking of the Bismarck, William Collins Sons & Co. Ltd., 1974. Probably the best "all round" account for the hunt for the Bismarck.
Müllinheim-Rechberg, Baron Burkhard Von, Battleship Bismarck - A Survivor's Story, U.S. Naval Institute, 1980. An interesting personal narrative of the German side of the action [Transcriber's Note: This book was revised and re-issued by the U.S. Naval Institute in 1990].
National Maritime Museum, Greenwich, England. "As Fitted" drawings of H.M.S. Hood 1/8 in = 1 ft 0 in (1/96) scale, corrected to c. 1931. Extremely expensive to obtain, drawings from the N.M.M. tend to be of inconsistent scale and are often poorly reproduced and incomplete. Sadly, in spite of the greatly increased quality of service which would result from such a move, the N.M.M. still refuses to supply microfilm copies of drawings in their collections.
Newton, R.U., Practical Construction of Warships, Longmans, Green and Co., London, 1939. A top-notch descriptive textbook describing the nuts and bolts detail of British construction methods between the wars. Although never specifically mentioned, many of the illustrations describing capital ship construction are actually of Hood.
Northcott, Maurice, Hood: Design and Construction (Ensign Special), Bivouac Books, Plaistow Press, London, 1975. Main focus on design and construction of Hood. Includes a separate eight page compilation of abstracts from the official boards.
Oberkommando der Kriegsmarine, Unterlagen und Richtlinien zur Bestimmung der Hauptkampfentfernung und der Geschoswahl ("Basis and Guidance For the Determination of the Best Range and the Choice of Projectiles"), Berlin, 1940. Enclosure (A) to U.S. Naval Technical Mission to Europe report No.37245. Operational Archives Branch, U.S. Naval History Division.
Raven, Alan, and Roberts, John, British Battleships of World War II, U.S. Naval Institute Press, 1976. Chapter 4 deals specifically with the design of Hood, with many other references throughout. An excellent source of design information
Roberts, John, Anatomy of the Ship: The Battlecruiser Hood, U.S. Naval Institute Press, 1982. 127 pp. A comprehensive technical description, with many outstanding illustrations.
Schmalenbach, Paul, Kreuzer Prinz Eugen . . . unter 3 Flaggen, Koehlers Verlagsgesellschaft MbH, Herford, 1985. An excellent account by the Assistant Gunnery Officer of Prinz Eugen. In German.
Vielica, Ron, "Who Sank the Hood?" Sea Combat magazine, Spring, 1979, pp. 16-23 et. seq. Highly speculative and technically weak account which investigates the possibility that a shell from Prinz Eugen actually caused the sinking.
Weldon, D.G., "H.M.S. Hood,"
International, No.2, 1972, pp.114-157. An excellent overall account
with a good mixture of technical and operational details.
81 Copies of the official German tactical gunnery manual Unterlagen und Richtlinien [Basis and Guidance for the Determination of the Best Range and the Choice of Projectile], secret at the time, give us a check on this figure. The necessary computations are too complex and voluminous to reproduce here, but give an estimated 45% hit percentage. This is obviously too high when compared to Bismarck's observed gunnery on the day in question. This is likely because the German manual implicitly assumes that the Mean Point of Impact (MPI) of the salvo is centered on the target. This is rarely the case in real life, and results in a considerable overestimate of the hit percentage, especially at longer ranges. For those readers who might be interested, the probable error for single gun fire for the guns of Bismarck and Prinz Eugen is given in the range tables reproduced in this paper. Multiply these values by about 1.5 to give probable errors for salvo fire.
82 "FIRE EFFECT TABLE - BLUE 14-in/50, 2577/6-31, Department of Operations, Naval War College, Newport, R.I., c. June 1935.
83 U.S. Navy, Bulletin of Ordnance Information 2-45, pp. 29-30.
84 I have assumed in this computation that the Hood would normally lie at least somewhere in the pattern, and that the average displacement of the MPI is roughly compensated for by the effect of the substantial danger space.
85 ADM 116/4351 pp. 205-206.
86 ADM 116/4351 pp. 207.
87 ADM 116/4351 pp. 216. Petty Officer Harold Pickard in the port forward H.A. Director saw it too. "The 'Hood' was still firing with all turrets," he said, narrating the action, ". . . when a peculiar thing happened, it seemed to me. It appeared as if 'B' gun had opened her air blast. Flames came out of the muzzle and instead of stopping like an ordinary air blast they carried on." Other witnesses described the delay as from one to five seconds.
88 ADM 116/4351 pp. 212-213.
89 One author lists no fewer than thirty-seven safety interlocks controlling the operations of the 15-in Mk I. See Hodges, Peter, The Big Gun, Conway Maritime Press, 1981 pp. 133 et. seq. In fairness, the British 15-in twin mount was considered one of the most reliable in service, however, and most difficulties seemed to revolve around other installations.
90 A similar phenomenon was noted in the loss of U.S.S. Arizona, which was also marked by an obvious vertical venting of gasses through the engineering spaces while the decks directly over the magazines remained substantially intact. For more details, see the survey of Arizona recently completed as a joint project of the Arizona Memorial Museum Association, the U.S. National Park Service, and the United States Navy, and published in 1985 a series of drawings prepared for the Arizona Memorial Museum Association.
91 From a series of tests using cordite, the British developed a rough formula for the non-explosive venting of powder fires, making A = (W0.666)/8 where A is the vent area in square feet, and W equals the weight of exposed powder in pounds. Assuming the total area of the vents to have been approximately 140 square feet, therefore, indicates that they could have handled some 37,500 pounds or 17,000 kg of burning powder before overloading. These tests are reported in N.A. London Serials 558-1940 and 678-1940. In metric units the formula is A = (W0.666)/50.84 where A is the area in square meters and W equals the weight in kilograms.
92 Prince of Wales cut in front of Hood after she exploded, and turned away to port shortly thereafter, and her courses after disengaging, first 160 then 250 degrees, would not have brought her around behind the Hood again from the German point of view. The black smoke usually attributed to Prince of Wales in photographs is in fact most likely from Norfolk, which was in the appropriate position during the action.
For further details on all weapons carried by Hood, Prince of
Wales, Bismarck, Prinz Eugen, Norfolk and Suffolk
please see Naval
Weapons of the World.