Difference between revisions of "Dreyer Fire Control Table"

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Dreyer Fire Control Tables were early mechanical computers ("calculating workbenches" might be a better term) meant to process data to permit a ship to engage a distant target with heavy artillery.  They were fairly involved pieces of equipment, and grew more intricate between the invention of the first prototype table in 1911, their first deployment on dreadnoughts in 1912 (?) and the creation of the Mark V table in 1918.  The dreadnoughts of the Grand Fleet relied on Dreyer equipment at Jutland to convert sporadic and imprecise estimates of range and bearing into workable firing parameters.  Sadly, the level of success was spotty, as visibility conditions made such systematic data collection too occasional for performing the sort of graphical analysis on which the Dreyer relied.
 
Dreyer Fire Control Tables were early mechanical computers ("calculating workbenches" might be a better term) meant to process data to permit a ship to engage a distant target with heavy artillery.  They were fairly involved pieces of equipment, and grew more intricate between the invention of the first prototype table in 1911, their first deployment on dreadnoughts in 1912 (?) and the creation of the Mark V table in 1918.  The dreadnoughts of the Grand Fleet relied on Dreyer equipment at Jutland to convert sporadic and imprecise estimates of range and bearing into workable firing parameters.  Sadly, the level of success was spotty, as visibility conditions made such systematic data collection too occasional for performing the sort of graphical analysis on which the Dreyer relied.
  
The Dreyer FCTs were literally sturdy iron tables fitted with a number of fire control devices tied together by rotating shafts, bicycle chains and other linkages, worked by 7 or more men simultaneously as a corporate endeavour.  In the earlier and smaller versions, the mechanical integration of the components was less complete and required manual interaction.   
+
The Dreyer FCTs were literally sturdy iron tables fitted with a number of fire control devices tied together by rotating shafts, bicycle chains and other linkages, worked by seven or more men simultaneously as a corporate endeavour.  In the earlier and smaller versions, the mechanical integration of the components was less complete and required manual interaction.   
  
Dreyer tables were housed deep within the ship in the [[Transmitting Station]] (T.S.) located beneath the armoured deck.  By the time the [[Dreyer Table Mark V|Mark V table]] was fitted in [[H.M.S. Hood (1918)|H.M.S. Hood]], as many as 30 people might occupy the T.S., working the table and its many ancillary devices or serving as liaisons to the fighting positions of the ship.  It is fair to suggest that the Dreyer and its environment and attendants resembled a premonition of the Mission Control centres of the Apollo program 50 years later: a human/machine system on a broad scale to factor down a torrent of real time sensory data to create a manageable environment for exerting command at a rate tolerable to humans.
+
Dreyer tables were housed deep within the ship in the [[Transmitting Station]] located beneath the armoured deck.  By the time the [[Dreyer Table Mark V|Mark V table]] was fitted in [[H.M.S. Hood (1918)|H.M.S. Hood]], as many as 30 people might occupy the TS, working the table and its many ancillary devices or serving as liaisons to the fighting positions of the ship.  It is fair to suggest that the Dreyer and its environment and attendants resembled a premonition of the Mission Control centres of the Apollo program 50 years later: a human/machine system on a broad scale to factor down a torrent of real time sensory data to create a manageable environment for exerting command at a rate tolerable to humans.
  
 
==Dreyer Table as CPU in a Ship/Computer==
 
==Dreyer Table as CPU in a Ship/Computer==
  
It is not possible to study the Dreyer tables without developing a familiarity with the ship-wide art of fire control, the process of calculation and articulation by which the shells can be made to rapidly and continually fall in a pattern around a distant maneuvering enemy.  The Dreyer's role was akin to that of a CPU within a modern computer system, and its "socket" was the T.S.
+
It is not possible to study the Dreyer tables without developing a familiarity with the ship-wide art of fire control, the process of calculation and articulation by which the shells can be made to rapidly and continually fall in a pattern around a distant maneuvering enemy.  The Dreyer's role was akin to that of a CPU within a modern computer system, and its "socket" was the TS.
  
Examining a dreadnought as a computer system is the best way to develop this understanding.  Just as a CPU processes input received via keyboard, mouse, and network adapter, the Dreyer table was given data on what the enemy ''appeared'' to be doing.  And, just as a CPU might generate output on a screen or printer, the Dreyer's output peripherals were powerful naval guns.  Without paying too much attention to the input and output devices, let's examine the T.S.'s role in the system by drawing a circle around it and observing which inputs and outputs crossed this membrane.
+
Examining a dreadnought as a computer system is the best way to develop this understanding.  Just as a CPU processes input received via keyboard, mouse, and network adapter, the Dreyer table was given data on what the enemy ''appeared'' to be doing.  And, just as a CPU might generate output on a screen or printer, the Dreyer's output peripherals were powerful naval guns.  Without paying too much attention to the input and output devices, let's examine the TS's role in the system by drawing a circle around it and observing which inputs and outputs crossed this membrane.
  
 
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Revision as of 14:34, 15 August 2011

<video id="iZZ7wdnRLsE" height="300" width="400" frame="false" position="right"/> The Dreyer Fire Control Table was the Royal Navy's highest-level Fire Control instrument during World War I.

Mark III Dreyer Fire Control Table as it appeared by 1918, front
Bearing plot, deflection drums and deflection totaliser on left (Wind Dumaresq obscured behind this equipment), Mark VI* dumaresq with integral range and bearing clocks beneath gyro-compass repeater and Forbes log in centre, and range plot, gun range counter and spotting corrector on right.
Dreyer Fire Control Table Mark III as it appeared by 1918, back
Spotting Corrector, Range plot and range plot grid on left, emergency manual drive hand-crank and stop-watch governor housing in centre (dumaresq, etc in rear), axle and chain drive to actuate bearing plot is prominent, and the wind dumaresq is visible here with the bearing plot, bearing grid, and deflection drums beyond. Though the Mark III table was introduced in 1912, this image depicts it after it had ripened through the addition of several accessories, most notably by the addition of deflection drums, deflection totaliser, wind dumaresq, and an improved range plot typewriter. These improvements typified the continual refinement process the Dreyer tables' open-faced nature seemed to welcome.

The tables existed in various Marks, though they were not developed in the order of their Roman numeral Mark numbers (Mark III was first). The Dreyer tables were based on semi-automated plotting of range cuts and bearings versus time on separate sheets of paper and employing a dumaresq and other appliances to relate these data, guess their derivatives, and compute a continuous range and deflection for use at the guns and/or the director.

For many decades, Dreyer tables have been a scapegoat for poor shooting by the Royal Navy. A technical evaluation suggests that this criticism is misdirected.

Overview

Dreyer Fire Control Tables were early mechanical computers ("calculating workbenches" might be a better term) meant to process data to permit a ship to engage a distant target with heavy artillery. They were fairly involved pieces of equipment, and grew more intricate between the invention of the first prototype table in 1911, their first deployment on dreadnoughts in 1912 (?) and the creation of the Mark V table in 1918. The dreadnoughts of the Grand Fleet relied on Dreyer equipment at Jutland to convert sporadic and imprecise estimates of range and bearing into workable firing parameters. Sadly, the level of success was spotty, as visibility conditions made such systematic data collection too occasional for performing the sort of graphical analysis on which the Dreyer relied.

The Dreyer FCTs were literally sturdy iron tables fitted with a number of fire control devices tied together by rotating shafts, bicycle chains and other linkages, worked by seven or more men simultaneously as a corporate endeavour. In the earlier and smaller versions, the mechanical integration of the components was less complete and required manual interaction.

Dreyer tables were housed deep within the ship in the Transmitting Station located beneath the armoured deck. By the time the Mark V table was fitted in H.M.S. Hood, as many as 30 people might occupy the TS, working the table and its many ancillary devices or serving as liaisons to the fighting positions of the ship. It is fair to suggest that the Dreyer and its environment and attendants resembled a premonition of the Mission Control centres of the Apollo program 50 years later: a human/machine system on a broad scale to factor down a torrent of real time sensory data to create a manageable environment for exerting command at a rate tolerable to humans.

Dreyer Table as CPU in a Ship/Computer

It is not possible to study the Dreyer tables without developing a familiarity with the ship-wide art of fire control, the process of calculation and articulation by which the shells can be made to rapidly and continually fall in a pattern around a distant maneuvering enemy. The Dreyer's role was akin to that of a CPU within a modern computer system, and its "socket" was the TS.

Examining a dreadnought as a computer system is the best way to develop this understanding. Just as a CPU processes input received via keyboard, mouse, and network adapter, the Dreyer table was given data on what the enemy appeared to be doing. And, just as a CPU might generate output on a screen or printer, the Dreyer's output peripherals were powerful naval guns. Without paying too much attention to the input and output devices, let's examine the TS's role in the system by drawing a circle around it and observing which inputs and outputs crossed this membrane.

Inputs to a Dreyer Table Mark III, c1918
Information Received Source Input Mechanism Nature of Data
Estimates of Target Heading/Speed Visual estimates Manually sporadic, authoritative
Range Rates from Rate Officer, aloft Verbally sporadic, authoritative
Estimates of Target Range Optical rangefinders Manually sporadic, imprecise
Observations of Target Relative Bearing Optical device Automatically sporadic, granular
Spotting corrections Verbal reports Manually fairly often, authoritative
Own ship's heading Gyro-compass Automatically continuous, fairly precise
Own ship's speed Forbes Log (a speedometer) Manually continuous, fairly precise
Apparent wind speed Anemometer Manually continuous, fairly precise
Apparent wind direction Wind vane Manually continuous, fairly precise
Adjustments to range (for Wind Along, etc) Dreyer Calculator Verbally occasional, consistent

A Dreyer table delivered the only 2 outputs a gunner with a modern gun sight needed to hit a target he could see.

Outputs from a Dreyer Table Mark III
Output Generated Source of Data Nature of Data
Gun range Range clock + accrued spotting corrections continuous, 25 yard granularity
Gun Deflection Computed totals + accrued spotting corrections continuous, "1 knot" granularity

Development and Introduction to Service

Dreyer Tables (Roughly Sorted by First Installation)
Mark Installed Installed in Notes
Original Dreyer Table 1911 only one built very much a proof of concept
Dreyer Table Mark III 1912-1913 new and late-model BBs and BCs helm-free, derived from Original
Dreyer Table Mark II 1913-1914 new and late-model BBs and BCs tested Argo Clock Mark IV
Dreyer Table Mark IV 1914 new construction electric dumaresq
Dreyer Table Mark I 1915-1916 old ships with small TSs compact but hand-worked
Dreyer Table Mark IV* 1915-1918 new construction Mark IV mod for longer ranges
Turret Control Table 1914- big-gun turrets and light cruisers helm-free Mark I variant
Dreyer Table Mark I* 1918- cruisers and monitors helm-free Mark I variant
Dreyer Table Mark III* 1918-1921 new light cruisers more mature Mark III type
Dreyer Table Mark V 1922 Hood the final edition

Dreyer tables did not get built in the order implied by their Mark numbers; the Mark III table was the first developed for regular service in the fleet, being installed in a few vessels in 1912-13. A smaller and simpler Mark I table was created for older ships with smaller TSs, and a Mark II table was created to test the Argo Clock Mark IV in place of the customary dumaresq and Dreyer clock combination used in the other models. The Mark IV and IV* tables were based on the best aspects of the Mark III table, using an electrical dumaresq to automatically update the range rate and deflection to ease the workload.

A small range-only table for local control in large gun turrets and small cruisers was developed alongside the major tables. Mark III* tables appeared late in the war for use in the latest light cruisers which had to have large TSs indeed. The Mark I* table came so late that most installations in cruisers occurred post-war.

Some ships had their first tables swapped out for later models (Lion and Princess Royal went from Mark III to Mark IV* some time after Jutland), but generally installed tables received only refinements that were deemed unworthy of a new designation, though study of their particulars often makes it clear that substantial improvement in capability resulted from these initiatives.

Primary Components

Dreyer tables differed in their particulars by model and by refinements applied to each over time (which were seldom heralded and are difficult to track reliably), but they generally had 4 primary components and some number of ancillary subsystems.

Range Plot

The range plot was a semi-automated scatter plot of optical range estimates versus time. A wide expanse of paper (46-in wide paper in a Mark IV* table[1]) scrolled away from the observer on a flat surface at a constant speed, and as range cuts from rangefinder topside arrived, he plotted them on the paper at the appropriate position as measured by a graduated range scale arranged horizontally across the paper at its near edge. The means of plotting these points evolved over time[2]:

  • In Mark III tables prior to around 1918, the plotting from a single rangefinder was entirely automated.
  • In early 1914, Lieutenant Patrick Macnamara's plotter was tested unsuccessfully. It was capable of plotting cuts from several rangefinders pneumatically.
  • In mid 1914, Commander John Brownrigg's eponymous keyboard passed testing and was deployed to see use through Jutland on Mark IV and IV* tables. While it could plot data from any number of rangefinders, they were all represented by holes punched in the paper.
  • Soon after Jutland, a range typewriter was tested which could allow up to 9 rangefinders to have their data plotted, each with a distinctive mark. It was deployed in 1917 and even to the Mark III tables by 1918.

A range rate grid positioned over the plot could be moved over the recent range data samples and a skein of wires within it deflected to what the operator perceived was a linear trend suggested by their alteration over time. In this way, the range plot was a means for allowing the operator to visually see through the errors in the rangefinder data while also taking the derivative over time. This linear correlation provided a workable instantaneous range rate to establish on the table's range clock.

Also marking the face of the range plot's sheet was a pencil in a carrier on a worm screw that could be moved to any position near the range scale under the influence of the table's range clock. This range pencil could trace a continual hypothesis of the clock range (the current range to the target). The operator was able to manually position the pencil so it would be within the recent ranges being reported should the hypothesis and observational data diverge significantly. On some Dreyer tables (or added to some after their initial installation), a second pencil could be offset laterally from the first (often from a device called the Spotting Corrector) by the accrued spotting corrections and the corrections of a separate Dreyer Calculator so it would plot the gun range.

Bearing Plot

The bearing plot was similar to the range plot, but generally smaller in size (16-in wide paper in a Mark IV* table[3]) and it plotted bearings corrected for yaw versus time. In most of the pivotal battles, the bearing plots in use were widely criticised and seems to have been a true shortcoming in the Dreyer tables[Citation needed].

The shortcomings of the bearing plot used through Jutland seemed to be these:

  • it was large, with paper 16-in wide, requiring a means to move the bearing rate grid
  • the relative bearings taken were transmitted in coarse 1/4 degree steps[4].
  • the gyroscopes and the relays conveying their indications were prone to wander[5].
  • the paper plotted 120 degrees across its width (7.5 degrees per inch)[6], producing for moderate bearing rates subtle angles difficult to measure confidently[7]. The operator might have to reposition a pencil in a carriage if it got near the edge of the paper.
  • a lack of integration to automatically pass gun deflections onward

A solution to at least some these issues appeared in the form of the compact and well-integrated Standard Bearing Plot documented in the 1918 Dreyer Table handbook, which

  • had paper just 6.5-in wide (41% as wide as the original), allowing the rate grid to be in a fixed position[8].
  • the paper recorded just 10 degrees across its width, a scale more effective for modest rates, at 1.5 degrees per inch width. Additionally, the design did not require the operator to ever reposition a pencil[9].
  • was to exploit a change-over to finer 4 arc-minute steps for transmitting relative bearing[10].
  • included a Deflection Totaliser which acted for deflection like the Spotting Corrector did for range by permitting corrections to be added in and finally provided a proper mechanism for outputting the aggregate gun deflection

The "Standard Bearing Plots" never lived up to the ubiquity implied by their name, being deployed in perhaps just Ramillies before Gyro Director Training Gear was tested in Emperor of India in July 1918 and ordered widely early in 1919[11]. The weakest aspect of the Dreyer tables, then, received its makeover too late to count.

Dumaresq

A dumaresq situated on the table could relate range rate, speed-across, target bearing, and the speed and heading of the two vessels in a manner that permitted the operators to divine the data they lacked from those they had in hand, or to judge the plausibility of the data they were receiving. The dumaresq might convert an initial assessment as to enemy bearing, speed and heading into a range rate for initial use. Taking the indicated speed-across and a range estimate could allow the operators to reference special charts or deflection drums and arrive at an initial gun deflection.

Most vitally, the relationships a dumaresq modeled could permit a good firing solution against a non-maneuvering enemy to be maintained even while one's own ship maneuvered and range and bearing reports slacked off. The more feature-rich Dreyer tables automated the way in which the dumaresq could fulfill these purposes.

Range Clock

A clock-work or electrically driven range clock was an essential tool for reducing the workload for fire control and to permit a reasonable representation of the firing scenario to persist during temporary interruptions in visibility. All Dreyer tables possessed a range clock of some kind, and the better tables increased the ease with which the clock was kept in agreement with the dumaresq's configuration or even allowed an electric dumaresq to set the clock's range rate automatically.

The range clock's output was directed toward a Spotting Corrector which in turn drove the plotting pencils.

Bearing Clock

Most Dreyer tables also had a bearing clock which would help keep the target bearing updated on the dumaresq. In a simple installation such as a Mark III table, this clock applied a constant bearing rate to the present bearing, and the operator would periodically update this rate by hand. In a fancier installation, when the bearing rate grid was correctly aligned with the bearings visible on the plot below, the bearing clock was automatically set by the same action and the corresponding gun deflection entered into the first column of the deflection totaliser. As ever, the later and larger Dreyer tables smoother out the edges progressively while the smaller and earlier designs generally needed more attention to meet the task.

Spotting Corrector Gear

The range clock drove this differential gear, and through it, the red clock range pencil drew on the range plot. A dial and differential within this box, however, permitted incremental spotting corrections for range to be applied to this figure, along with a separate little addend from a Dreyer Calculator found on the transmitting station's bulkhead. In later Dreyer tables, a second gun range pencil was added to the range plot. A digital gun range counter similar to an old odometer sat on the table and provided a continuous display of the gun range. On a very late model Dreyer table, the clock range might also be brought to the standard bearing plot to rotate the deflection drums as needed and to set the change of bearing gear for gun range.

Installation of Dreyer Fire Control Tables

Information as to which ships had Dreyer tables, and of which type and from which date are incomplete and at times unreliable for a variety of reasons.[Citation needed] Each time a reference is discovered to a ship having a Dreyer table (or a particular type of table), the following aspects of the citation must be considered:

  • Is the writer speaking of an intended installation, or an existing one?
  • Is the installation written of the first for the ship?
  • Is the data current as of the date of promulgation of the document?
  • What can be inferred about entries found missing? Crossed out by hand? Written in by hand? When might they have been made and by whom?

And, for any table in any ship, one must also consider its level of refinement within its nominal Mark at any point in time:

  • Are ranges being plotted by a single Argo RF in an automated way, by Brownrigg keyboard, or by range typewriter?
  • Does the table have an elegant means of outputting deflections? With spotting corrections easily added in?
  • Does the table have a gun range pencil?
  • Is there an extended range scale?
  • Are any of the appointments jury-rigged or so recently installed that the crew might have chosen not to use them?

The Admiralty's Gunnery Branch promulgated the Handbook for Capt. FC Dreyer's Fire Control Tables. in June 1918, and a table on page 3 provides a "List of Ships carrying Dreyer Fire Control Tables".[12] This is the single most complete source for such data, but even a glimpse shows its value as a reference resource to be problematic.

Some ships listed as "carrying" Mark V tables were never completed:

  • Howe (crossed out by a light stroke)
  • Rodney (crossed out by a light stroke)
  • Anson (perhaps not crossed out, or maybe very faintly so)

Some Gunnery Schools are written in for Mark V table, but may never have received them:[Citation needed]

  • Chatham
  • Portsmouth
  • Devonport

Of the 15 ships listed as carrying Mark I tables:

  • 14 old 12-in ships are heavily crossed out
  • Marlborough is not only not crossed out — her name is prominently circled

We can sanely infer that someone crossed out ships that had been or were about to be scrapped (as the 14 12-in ships were soon after the war), and felt Marlborough's singular exception to this extinction was important enough that emphasis was required to drive home the fact. I would take this as a strong indication that Marlborough retained her Mark I table to her final days.

These examples illustrate the perils of reading a document in a naively trusting manner. A loose analysis of the page suggests that many of the editorial marks were made around 1922-6, as Ajax was decommissioned in 1924 and scrapped in 1926 and its name is left in place, while Princess Royal was sold for scrap in 1922. Interpretation can be sound or simply an exercise in self-deception; such possible pitfalls are certainly worth footnoting.

To keep the complexity of this article at a minimum and to allow sufficient detail for each specific ship carrying a Dreyer table, please refer to the articles for the ships in question. Of particular interest is trying to sort out which ships carried which equipment at Jutland, which we catalogue in the article: British Fire Control Systems at Jutland.

Evaluation and Review

In late 1918, the Grand Fleet Dreyer Table Committee was formed to look specifically at how the tables were being used, and to study individually crafted and implemented enhancements to mechanism and method of use so that best practices and common implementations made for use on all suitable tables.

The Royal Navy had been continually refining its Dreyer tables during and after the war. The basic feature set varied between Marks, and once in the hands of the gunnery officers (whose cleverness and daring seemed to vary considerably), individual tables were adapted in a customised manner to suit the ideas of its individual users.

Some of the tables' greatest common faults — coarsely quantised bearings, clumsy manual range plotting, input from gyroscopes prone to wandering, a lack of automation in tallying deflections, reliance on range cuts taken from rangefinders of insufficient base length for the battle ranges — were not addressed until after its greatest test at Jutland had come and gone, but were well met by replacing 15 arc minute bearing circuits with 4 arc minute quantisation, Brownrigg keyboards giving way to range cut typewriters, Sperry gyroscopes replacing Anschutz models, adoption of the deflection totaliser and GDT gear, and the increased use of longer base rangefinders in the Fleet. By war's end, most of the Dreyer tables (excepting perhaps the Mark Is) and their supporting appliances offered mature and reliable implementations of the dual-rate plotting design.

The Admiralty was not complacent, but its general satisfaction that it was not going astray with the Dreyer system is evident in the nature of the changes applied to the tables during the war, which took the form of refinement and improvement rather than any alteration which suggested a move away from the foundation of dual-rate plotting. As to whether the basis itself were suspect or deficient is answered by the nature of some of the improvements made to the Dreyer tables to which the Argo system was wholly unable to benefit from, such as plotting gun ranges alongside geometric ranges, or allowing a large number of rangefinders and from consort ships to inform the fire control solution.

Between 1918 and 1919, the Dreyer Table Committee concentrated its suggestions along the lines of how best to plot consort range cuts on the range plot, and how to remove clutter from the range plot to enhance its visibility. The suggested changes it prompted in each case kept the basic nature of the pre-existing function unchanged as it refined or extended it: a third pencil was to be added, a second typewriter to permit external range and spotting observations to be plotted, and removal of the range rate grid to a model on the overhead which would cast a shadow of rate lines onto the plot below, a better means of applying corrections from the Dreyer Calculator onto the table, concentration of fire, and so forth.

But not every aspect of the tables was stellar, even when optimised. As they were initially envisioned, the Dreyer tables were intended to permit range rates to be quickly perceived from a range plot richly speckled with timely range cuts conforming to regular and reasonable errors about the true geometric range to the target. But by 1919, the consensus taken from experience was clear: the latency, paucity and reliability of range cuts was not sufficient to allow the trend and thus the range rate to be taken from the plot. This did not completely nullify the value of the range plot, the biggest single element of the Dreyer tables' footprints, but it prompted the idea that it should be demoted to serve as a fall-back to verify ambiguity in inclinometer-supplied indications of enemy heading. In pursuit of this vision, new plots of multiple inclination source indications versus time were to be added.

Even within this renovation of the principle were some comforting aspects:

  • the open nature of the Dreyer tables' mechanical design tolerated the change in thinking better than would Argo systems
  • the system's character of plotting individual data independently versus time before inter-relating them provided a ready, common basis for adding inclination into the recipe: they would be on separate plots

See Also

Footnotes

  1. Captain F.C. Dreyer's Fire Control Apparatus, Mark IV., sheet 11.
  2. Brooks, John. Dreadnought Gunnery and the Battle of Jutland, pp. 171-4.
  3. Captain F.C. Dreyer's Fire Control Apparatus, Mark IV., sheet 11.
  4. Brooks, John. Dreadnought Gunnery and the Battle of Jutland, p. 171.
  5. Brooks, John. Dreadnought Gunnery and the Battle of Jutland, p. 171.
  6. Captain F.C. Dreyer's Fire Control Apparatus, Mark IV., sheets 44-5 & Fig. XII.
  7. Brooks, John. Dreadnought Gunnery and the Battle of Jutland, p. 171.
  8. Handbook of Captain F.C. Dreyer's Fire Control Tables, 1918., p. 35.
  9. Handbook of Captain F.C. Dreyer's Fire Control Tables, 1918., p. 35.
  10. Brooks, John. Dreadnought Gunnery and the Battle of Jutland, p. 174.
  11. Brooks, John. Dreadnought Gunnery and the Battle of Jutland, pp. 174-5.
  12. Handbook for Capt. FC Dreyer's Fire Control Tables. p. 3.

Bibliography