# Dumaresq

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A Dumaresq (sometimes the initial D is capitalised, though the practice subsided) is an mechanical analog fire control instrument helpful in related the relative motion of one's own ship and a target ship to the corresponding range rate and speed-across. It was designed and patented by Lieutenant John Saumarez Dumaresq between 1902 and 1904.[1]

There were a considerable number of dumaresq Marks, but all answered to the same underlying geometric principles.

## Geometric Principle

It is often easiest to apprehend mechanical devices through visual means, such as this online video.

A dumaresq functions by mechanically implementing a flexible means of working the geometry of two independently moving ships with a relative bearing from one of the other and being able to relate this to motion along and across the line of bearing (range rate and speed-across, respectively). Specifically, it permitted you to subtract the motion vector of your own ship from that of a target ship to yield the target's relative motion vector which could then be projected onto a Cartesian coordinate graph oriented along the line of bearing, permitting the range rate and speed-across to be read off as a coordinate pair.

Users commonly set up a dumaresq in this manner:

1. set their own ship's speed and heading
2. set the target ship's speed and heading (by estimation)
3. rotate a pair of coordinate axes along the line of bearing to the target
4. read the range rate off one axis of the graph and the speed across off the other

However, the dumaresq was not a modern computer which used a given set of inputs to a given set of outputs. It was wholly indifferent to which of the variables it represented in its workings were inputs and which were outputs. Altering one variable by rotating a knob or by positioning a slider caused other variables to change to continually satisfy the relationship between two ships moving around and the range rate and speed-across their relative motion would imply. This meant that the sequence of use described above which derives range rate and speed-across from the speed and heading of both vessels and the target bearing could be worked flipped on its head to find the enemy speed and heading from a given range rate and speed-across. This was called a "cross-cut".

## Cross-Cut

When making a cross-cut, a dumaresq operator would manually move the indicator stem expressing the difference of own ship's and target ship's motion and permitting the enemy heading ring and speed slider to re-orient and slip as needed to follow your demands. Upon placing the indicator at the range rate and speed-across you thought proper, the dumaresq would then indicate the enemy speed and heading that would be implied by your hypothesis of range rate and speed across (own ship's speed and heading and the target bearing being held unchanged in this case).

Steps to make a cross-cut on a dumaresq:

1. set their own ship's speed and heading
2. rotate a pair of coordinate axes along the line of bearing to the target
3. drag the relative velocity indicator stem to the estimated range rate and speed-across
4. observe the enemy speed and heading which are then indicated

## Dumaresq Marks

Dumaresqs existed in a variety of Marks, differing in their features and in some odd particulars.

## Obsolesence

The dumaresq was first eclipsed from service when its integrated application within the Dreyer Fire Control Table was not succeeded by an appearance with its heirs and cousins such as the Royal Navy's Admiralty Fire Control Table or the American Navy's Ford Rangekeeper. Both these evolutionary paths of development features "rate solvers" similar in mechanical design to the one found in the Argo Clocks. The rate solvers in the Argo clocks were much more compact and intrinsically supported the Argo's inventive visual display which clearly represented the relationship of own ship, target ship, and the relative bearing. The functionality was largely the same between these two designs, but the dumaresq looked and felt clumsy relative to the alternative.

The Wind Dumaresq continued to have a role in at least some Royal Navy transmitting stations well into World War II, as one can be seen in the cruiser H.M.S. Belfast, situated on a bulkhead alongside its AFCT.

The dumaresq enjoyed a longer reign in aloft positions for moderately equipped ships which paired simple dumaresqs with a standalone range clock. The Mark VII was likely one of the models used in this manner, owing to its appearance in a postwar handbook[2].

The extremely Spartan dumaresqs Mark XI and Mark XII suitable to armed merchant ships likely also saw service throughout World War II[3]. These were so reductionist in their design that the speed of own ship was fixed at 12 knots. Moreover, the Mark XI model did not even have markings on its dial plate for seeing range rate — it indicated a speed-across only. In both cases, the speeds-across obtained were intended to be used directly as the gun deflections, as the short ranges such vessels were expected to fight at produced times of flight roughly proportional to range.

## Footnotes

1. Brooks, Dreadnought Gunnery and the Battle of Jutland: The Question of Fire Control, p. 42
2. B.R. 1534 (1), Handbook on Minor Fire Control Instruments
3. B.R. 1534 (2 & 3), Handbook on Minor Fire Control Instruments