Naval Anti-Aircraft Guns and Gunnery. Norman Friedman
direct course for long enough at a time.
A drawing from a US Navy handbook shows the two kinds of levelling, level in the direction of the line of sight and cross-level across it. Trunnion tilt is a failure to cross-level. As the ship rolls and pitches, and as the director or gun is trained in some direction other than straight ahead or abeam, it is subject to a combination of errors in level and cross-level. The third dimension of stabilisation is yaw: the ship swings back and forth as it moves ahead. A tri-axially stabilised mounting cancels out all three kinds of error.
This diagram from a US Navy manual shows why stabilisation was so important in anti-aircraft fire. Although it was intended to show the effect of a ship’s roll on surface fire, the reader can easily imagine that there would also be errors in altitude. An anti-aircraft system had to compensate for roll, pitch and yaw. All of them caused the deck to tilt away from the horizontal. An anti-aircraft fire-control system tracked an aircraft as it moved in the sky, not as it was seen from the pitching, rolling ship. The motion through the sky was relatively simple (and in many cases system designers made further simplifying assumptions, such as that the aircraft was flying straight and level). Once its motion was measured, the system could project where it would be in the sky a few moments later, when shells should arrive. The same system ideally had to cancel out the ship’s motion, both in interpreting what was seen of the aircraft, and in aiming guns.
The livelier the ship motion, the more effort it takes to stabilise guns and directors, particularly those high in a ship (the distance from the waterline increases the linear motion, which is associated with the angular motion of the ship – this effect is used in inverse synthetic aperture radars). The Royal Navy approach, for small lively ships with primarily anti-aircraft batteries, was to stabilise the whole ship. The ‘Hunt’ class destroyers (originally called fast escort vessels) and the Black Swan class sloops (originally called escort vessels) were given fin stabilisers, a radical new technology at the time. Some of the ‘Wair’ conversions of ‘V&W’ class destroyers may also have been so fitted. Cleveland is shown in 1942, with a 2pdr in her bows to deal with E-boats (German MTBs) in the Channel.
A synthetic system could be considered tachymetric, in the sense that its outputs could include generated bearing and elevation. As in the much simpler Vickers approach, gunners would make adjustments (in this case, to assumed target course and speed) to cause generated data to match reality. This is the sense in which US synthetic systems such as Mk 37 can be considered tachymetric. They never measured rates directly, but they generated solutions which made the motion of the angle-measuring director match actual angles, hence the rates at which the director moved matched actual rates.
The two approaches largely correspond to the sort of co-ordinates the system uses. The gunner sees the situation in polar form: as a distance (slant range) and elevation and bearing (azimuth) angles. The rectangular approach concentrates on what the aircraft is actually doing. At the core of the calculation is assumed simple target motion – straight and at a constant speed. That motion is easy to project ahead. The aircraft’s steady motion is best expressed in rectangular co-ordinates (up and down, in and out, sideways). For example, in a system of rectangular coordinates centred on the aircraft, it is flying along one co-ordinate (dimension). The complicated part is to transform the solution so as to express that motion as a gunner sees it, first so that the gunner can correct the estimated target motion and then so that he can fire his guns.
An aircraft flying straight and level (the simplest situation) traces a corresponding straight course over the ground, what the British called a course in plan or a plan course. That was the course at which it proceeded at a steady speed. It could be deduced by cancelling out the sight angle. For an aircraft flying straight and level, the angular rate across (ultimately giving horizontal deflection) gave the speed across in plan. The vertical angular rate gave the speed along in plan. The ratio of the two gives inclination, the angle between the aircraft’s course and the line of sight.6 That is, inclination – enemy course – could be measured without knowing enemy range and speed. Similarly, given enemy speed and course (inclination), speeds along and across could be calculated without reference to range. The plan part of the aircraft’s motion could be treated like the motion of a ship along the surface, albeit at much higher speed.
If the aircraft could be seen far enough away, its speed could be estimated from observation. It would remain a long time at a low sight angle, so slant range would not be much different from plan range. Plan range gave the desired speed along the line of sight. The aircraft would also be flying more or less directly towards the observer; its speed across the line of sight could be neglected. A series of ranges would provide a reasonable estimate of its speed, until it rose far enough above the horizon that angle of sight made much of a difference. That is why, as described below, British systems were designed for rangefinding at low angles of sight (which meant long range) and for heightfinding (height could be calculated from slant range and angle of sight). Speed estimated at long range could be fed into a computer as an initial estimate. Another initial estimate might be that the aircraft was flying directly at the gunner. These estimates could be refined as the aircraft approached.
How good initial estimates were depended on the sensors available to the gunner. Although in theory the British could estimate the speed of an approaching aircraft based on a series of observed ranges, in fact their horizontal coincidence rangefinders were ill-equipped for this purpose. They relied instead on an estimate by the control officer, based on the type of aircraft involved. To the extent that speed was measured, that was by feeding assumed speed into the prisms of the rangefinder (which they called a height finder) and seeing whether the ‘cut’ stayed on the target. That was analogous to estimating a rate and checking the estimate against observed target motion, tuning the assumed rate until the two matched. In both cases the problem was that speed towards the gunner (the ship) would vary over time if the aircraft was not headed directly towards the ship (not to mention variation of measurable [slant] range due to changing sight angle). The US Navy was in a very different position once it adopted stereo rangefinders in its Mk 28 system in the early 1930s.
Imagine the enemy’s movement as a vector (an arrow) pointing along his course, its length corresponding to his speed. Any vector can be expressed as the sum of components, such as speed along and speed across, each at right angles to the other. As the target moves, the line of sight also moves, so the relationship between the speed along and the speed across changes. That is why, except in the unusual case in which the target is moving towards or directly away from the shooter, the range rate varies. A mechanical device can split a vector into the desired pair of components. The US Navy called its means of splitting a vector a component resolver. It and similar devices split motion into two rather than three dimensions, i.e., in a flat plane of some kind. The simplest solution to the problem was to divide the aircraft’s path into horizontal and vertical components, and to divide horizontal (plan) motion into along and across components.
A rectangular-co-ordinate computer worked in co-ordinates centred on the aircraft, in which rates along the different directions were fixed.7 It also traced the position of the ship, which gave changing angles of sight at which the aircraft was viewed. It used component resolvers or their equivalents to translate into ship co-ordinates. The resolvers worked in linear terms (such as knots), never in terms of angles.8 However the fire-control problem is handled, the gunner works in polar co-ordinates. In order to lead his target, for example, he needs to know how fast the enemy’s bearing is changing. In effect that is the speed across divided by the range.9 The fire-control computer can integrate the bearing rate to find the enemy’s future bearing.
Feedback: Spotting
The core of the synthetic approach is feedback while the target is being tracked, before opening fire. The initial set-up is a guess as to target course and speed in three dimensions. On that