The presentation used to calculate deflections graphically, from the 1945 Gunnery Pocket Book. (Photograph by Richard S Pekelney, Historic Naval Ships Association, courtesy of Mr Pekelney)
The computer did not calculate these future ranges. Instead, an operator extrapolated a range plot, using a grid of lines which could be rotated to match the estimated slope of the plot.25 The technique may have been intended to allow for estimates to correct errors of calculation. Unfortunately the range plot was not a straight line, because the range rate along the line of sight varied. Only at very long range could motion across the line of sight be ignored, hence only at long range was the plot more or less straight. The chosen fuse setting was called out by the plot reader. An operator set a transmitter which drove receiving pointers at the guns. Fuses were set manually.
The integrator worked, not in terms of range itself (as in a low-angle system), but instead in terms of the logarithm (log) of range, log R.26 The system had to keep translating back and forth between plan range and plan inclination the slant range (usually angle of sight) measured by the height finder. That required frequent multiplication by trigonometric functions, a complicated process in mechanical terms. Using logarithms simplified it, because the logarithm of a product is a simple sum of the logarithms of the quantities involved – adding is a simple process, mechanically. Working with log R made it possible to combine in a single plot long-range low-angle target motion (for which sight angle was difficult to measure, so the heightfinder worked as a rangefinder) and closer-in motion for which sight angles were used (the Hill fuse predictor was modified to work with range rather than sight angle). It was sometimes also claimed that the log R plot might be easier to extrapolate than a simpler plot of range against time, but even the this plot curved so sharply that the HACS sometimes produced too short a fuse range for an approaching target.
At first there seems not to have been any attempt to use feedback to check and improve the initial set-up. At the outset, the only source of feedback appears to have been spotting. The prisms of the heightfinder were moved at an average rate of sight angle change derived from a plot of sight angle. As the HACS developed, the device was integrated more fully (as in the change from HACS I to I* described above) and the operators learned to use feedback to correct the initial set-up. As experience was gained and the HACS was better integrated internally, range and inclination were used for feedback, as a means of detecting errors in set-up so that they could be corrected (this function was barely, if at all, mentioned in early accounts of the HACS). Range was fed back by moving the prisms in the heightfinder electrically (which is why it was called an electric heightfinder). If the range prediction was correct, the ‘cut’ would stay on the target. Angle of inclination was fed back by moving a graticule in the control officer’s binoculars. The control officer in the director tracked both forms of feedback and communicated observed errors to the HACT team below decks.
The Royal Navy distrusted purely mechanical solutions to gunnery problems. It knew that input data were often riddled with errors: although it did not use the phrase, it understood ‘garbage in, garbage out’. Thus the HACT incorporated feedback and correction mechanisms. In addition to range, angle of presentation was fed back via a graticule in the control officer’s binoculars controlled by the computer below decks. The main data correction mechanism was the ability to choose data, sometimes on the basis of a plot. A human plotter could average a run of data by eye, in effect drawing a line through the scattered points of a plot. For example, one operator was assigned to keep track of the observed log H (the logarithm of height). Initially he set target height based on the control officer’s estimate (from the director). Once rangefinder data began to come in, he used the average reading or followed directions from the plot reader. Together with rangefinder angles, the chosen height gave a series of ranges for insertion into the computer.
Generated range was plotted alongside range from the rangefinder. Even if there was a systematic error, the generated range plot was expected to parallel the plot of rangefinder data, and an operator could use the generated plot to spot errors in the rangefinder data.27 In addition to range, the computer plotted angle of sight (which was equivalent, given fixed target height). The angle of sight plot seems to have been set by the mean observed rate of change of angle of sight, not by any analysis of target motion. It was used to set the angle of sight motion driving the rangefinder prism.
The HACS based its calculations on the motion of the aircraft relative to the ship. Corrections for own-ship motion, drift and (in later versions) convergence were all added to the calculated deflection. There was no wind corrector. It was assumed that wind would affect aircraft and shell more or less equally, but by 1931 it was clear that was not so; that was much of the reason that fictitious target course and speed had to be introduced. Given the estimated course and speed of the aircraft (assumed to be flying level), and estimated height, the computer generated range (and, therefore, sight angle, which was a simple function of range if the aircraft was flying straight and level).
Fleet exercises with HACS I began in 1930. The results seemed promising. Both with HACS I and with the earlier STS, time between first sight of the enemy and first range or height was 31 seconds. Average time to open fire was similar, 53 seconds for HACS I vs 50 seconds for STS. However, the percentage of shots within 100 yds for both range and line was 16.1 per cent for HACS I vs 6.9 per cent for STS. The superiority of HACS I was somewhat exaggerated because it included shots for which data were imprecise. As experience was gained, the gap between the new and the old system widened considerably. Of 148 shots against sleeve targets fired by Nelson in six firings in 1930, 50.7 per cent were within 100 yds for range and line, and 92.5 per cent within 200 yds. In 1931, HACS I got 15 per cent of bursts within 100 yds for range and line, compared to 7 per cent for the STS, and the figures for between 100 and 400 yds were 54 per cent vs 34 per cent.
However, it was already clear that fuse prediction by extrapolation was not working well enough.28 At this time spotting was the major way of correcting for a bad set-up. It was not at all clear whether a control officer could disentangle bursts at long range and at high rates of fire. Was a burst the result of the most recent correction, or a previous one? If a fuse was predicted wrong, meaning that range was in error, then the wrong average projectile velocity would be applied to the deflection unit, and deflection would also be wrong. Delays in reporting spots (bursts) could cause the bursts to appear astern of the target (but expected lags in transmitting spots did not seem large enough to explain the errors).
In 1930 it was reported that HACT teams often had to use entirely false set-ups to bring bursts into line with the target.29 That happened even when range was approximately correct. That spotting was needed to correct for line (direction) pointed to a need for some means of measuring rather than estimating the relative course and speed of the aircraft, rather than guessing both. That was never possible.30
The HACT Mk IV as shown in the 1940 handbook. Fuse number is the fuse setting in fractions of a second. The fuse range crank above it is a typical follow-up. In analogue computers like this one, the result of a calculation was typically displayed on a dial, and it had to be read off and cranked back in for a second calculation. In theory using follow-ups made it possible for operators to smooth data and to correct obvious errors during computation.
HACS I was conceived to control 4in and 4.7in high-angle guns, but in the 1920s the Royal Navy was interested in using heavier-calibre guns. HACS IA and IB were associated with this project. Due to their calibre, hence weight of shell, these guns were considered to possess considerable anti-aircraft potential. That was why the 8in guns of the new cruisers were given 70° elevation, and the 6in secondaries of the Nelsons were given 60° (although the ships had dedicated 4.7in anti-aircraft guns).31 Initially there was hope that these heavier guns would have anti-aircraft control on a par with HACS. However, as of 1926 design work had not yet begun, so none of the ships