Both in the Royal Navy and in the US Navy, and probably in others, there was considerable argument before the war as to whether all shells should be fired at the point indicated by the fire-control system, or whether they should be spread deliberately to make up for random errors. During the First World War the Royal Navy developed the ladder. Instead of firing one salvo, observing, and correcting, the British fired a quick series of salvos distributed in range (later also in bearing), the idea being that the different salvos or shots represented alternative possibilities which the spotter could then interpret. The usual delay between salvos was dramatically reduced, the gunner fixing much more quickly on the target. The technique was called laddering, because the salvos or shots at a series of ranges formed the rungs of a ladder. Laddering made it possible to get a few hits on a fast-moving, often manoeuvring, target. The Royal Navy developed it intensively between wars against fast surface targets.
Laddering seemed to be a way of overcoming uncertainties in anti-aircraft fire. At least the Royal Navy and the US Navy tried it. The US Navy tried ladders in aim and also in fuse timing (sometimes called mechanical fuse spotting). The US Navy found that laddering made it more likely that a target would be hit at least once, but much less likely that it would be shot down. Unfortunately individual shells turned out to be much less lethal than had been hoped. It took multiple hits to bring down an aircraft. Laddering badly diluted anti-aircraft shellfire. It worked much better in surface fire because the target was much larger, and because a single hit was much more likely to be effective.
Solving the Fire Control Problem
The gunner sees an aircraft moving up and down and from left to right – a pair of angular movements. He can measure the range to the aircraft. The basis of nearly all fire control was to measure or calculate the rates at which these key parameters changed. For example, speed is the rate at which range changes. Given known rates, range, bearing, and elevation could be calculated for a later moment, say when shells were to arrive at the target. The predicted bearing and elevation were the deflections a gunner had to use to lead the target so that it could be hit.
The only way to measure a rate is to see how something changes over time: that measurement takes time. The longer the time, the more accurate the measurement – if the rate is constant. If it is not constant, there is a premium on reducing the time of measurement (the rate is said to become stale) – but that makes for reduced accuracy. All of this is aside from the fact that a ship rolls and pitches (and moves ahead) while angles are being measured. The Royal Navy suffered because when its high-angle control system was being designed its scientists felt that directors could not be well enough stabilised to cancel out roll and pitch so as to isolate the aircraft’s motion.
An integrator fed with changing (or constant) rates calculated their total effect over time.1 It was said to generate future values of whatever it calculated. For example, integrating speed over time gives the predicted range.
Unfortunately neither angles nor range (slant range up to the aircraft) change at a constant rate, even if the aircraft is moving straight and level at a steady speed. For example, imagine the line pointing up at the aircraft (the angle up: sight angle or, in US parlance, position angle). As the aircraft approaches, that angle steepens, even if the aircraft is not climbing. Unless the aircraft is heading directly for the observer, the way in which the angle steepens depends on the changing bearing of the aircraft. Things become much more complicated if the aircraft is diving or climbing, because in that case the gunner sees is a combination of motion due to the approach of the aircraft and a separate component due to diving or climbing.
The angles and the slant range are all entangled. However, for short intervals the rates at which they change are nearly fixed. They can be measured, and they can be used directly for predictions (which become less and less accurate over time). Systems based on measured angular rates were called tachymetric, after the Greek word for speed, tachys.2 The simple multiplying approach might be called analytic, because it deduces what it needs by direct analysis of what the gunner can see. An analytic system can overcome the fact that the rates are not constant by measuring the way in which they change and using that data, too, but that involves a delicacy of measurement which is probably impractical.3
Tachymetric systems measured angular rates in various ways. For example, in the Vickers system sold to the Imperial Japanese Navy an operator set an estimated rate into an integrator, which generated angles on that basis. If the generated angle did not match what the operator saw, he changed the estimated rate until estimate matched reality. A more sophisticated technique employed a gyro forced to follow the target. The gyro would resist that movement. The force required to keep it on target was proportional to the rate at which the gyro was being forced to turn. In both approaches vertical and horizontal angles were handled separately.
Cancelling Ship Motion
Somehow the ship’s motion must be separated from that of the aircraft. The angle approach demands a stabilised line of sight, against which angles can be measured. Angles and rates had to be measured from a stabilised position. Otherwise the rates were entangled with the motion of the ship carrying the gyros. The higher the shooting angle, the worse the problem. The US Navy seems to have enjoyed great superiority due to its development of the stable vertical, a gyro motion sensor.
Post-1918 discussions of anti-aircraft fire control frequently refer to trunnion tilt. A gun or other pointing device elevates or depresses on trunnions. If it is pointed directly on the broadside, the ship’s roll simply changes elevation or depression. This motion can be cancelled out by elevating and depressing the gun as the ship rolls. However, if the gun points away from the broadside, then rolling tilts the trunnions, so that as the gun elevates or depresses not only does it not point up or down at the desired angle, it points to one side. The motion of the ship entangles the two key angles, elevation and bearing (azimuth). Some way has to be found not only to move the device up or down as the ship moves, but also from side to side. It must have been obvious fairly early that bombers tended to attack along the ship’s axis, just where trunnion tilt was worst, because that minimised timing errors which could cause bombs to fall long or short.
Synthetic Systems
If just multiplying rates was not good enough, what was? The alternative, adopted by the US Navy during the First World War and by the Royal Navy after it (and then by all other major navies) for surface warfare was to create a mechanical model of the engagement, based on assumed enemy course and speed.4 This analog computer could predict (generate) the bearing and range of the target based on the assumptions. Conversely, gunners could compare generated with actual bearing and range to correct their assumptions. Once the assumptions had been confirmed, the fire-control system would continue to predict range and bearing correctly until the enemy changed either. This technique had the incidental advantage that the ship could manoeuvre freely without losing the target.5 The US Navy and the Royal Navy both adopted this analog approach to air defence, albeit in very different forms. This form of control might be called synthetic, because its basis is a model created (synthesised) by the gunner. The system design problem is to make it possible for a gunner to correct for what he sees in such a way that the course and speed inside the system come closer to reality. The more direct the translation from what can be seen (in this case, rates) to prediction, the shorter (in theory) time to arrive at a fire-control solution. At least in theory, a quick solution might make it possible to deal with a manoeuvring