In addition, there would be a continual yawing, pitching and rolling as a result of the action of the sea. If the target were on the beam, these motions would have the following effects. Yawing (left/right) would affect the target bearing and thus the necessary traverse. Pitching would change the height of the gun, if it weren't on the pitch axis, and therefore the proper elevation to account for ballistic drop at the target range, unless the gun happened to be on the pitch axis. And rolling would change the target elevation and thus the required gun elevation. Pitching down when heeled away would create forward traverse and lower effective elevation.
A typical rate of roll would be one degree a second. If the target range were 3,000 yards, the line of sight would sweep across 15 vertical feet in less than one-tenth a second. But early-twentieth-century German warships were "stiff," rolling at a rate of three degrees a second. (Friedman 163).
Moreover, the target didn't necessarily cooperate by remaining abeam. If it were fleeing, and your ship trying to cut off its escape, chances are that your guns are firing obliquely rather than perpendicularly to your ship's centerline. If so, roll changes not only elevation, but also bearing—the latter was called "cross-roll." In the sailing ship era, when ships would be heeled over by the wind, Stevens (26) warned that in a chase, the guns would be inclined to leeward, and the bow or stern guns should therefore be pointed at the "weathermost" part of the enemy's hull.
Timing the Roll
In the 1630s, and indeed for more than two centuries thereafter, gunners only took roll into account. A ship rolled with a pendulum motion; fastest (but at constant speed) at mid-roll, paused (but accelerating or decelerating) at the top and bottom. Therefore, some gunners favored firing at the top or bottom of a roll. This had several consequences. First, it limited to the rate of fire to the period (or half-period) of the roll. Secondly, the gunner had to anticipate when the top or bottom of the roll was approaching, and whether this was possible or not depended on the regularity of the roll.
For this reason, British and French nineteenth-century naval practice favored firing only on the rising motion, so that a shot intended for the hull would at worst hit the rigging (as opposed to missing altogether). (Douglas 235 ff). I must note that the bottom of the roll was sometimes impractical, as that meant that the ship was in the trough of the waves, so the shot might be delayed until later in the rise. The Americans, in contrast, fired at the top of the sea, or on the falling motion. (245). The rising motion was slowest on the lee side, and the reverse was true on the weather side, but it wasn't always possible to take advantage of this. (Stevens 21).
Firing Interval
Moreover, the ideal would be for the projectile to leave the muzzle at that point, but there were several delays: from observing the roll to the decision to fire; from making the decision to lighting the fuse; from that moment to the ignition of the powder; and finally the time for the projectile to travel down the barrel. Overall, this lag was called the "firing interval," and Alger reported that under the best circumstances it was 0.25–0.30 seconds in the late-nineteenth century. Chances are that the gunner wouldn't take all this into account and the projectile would emerge a little late.
We may try to reduce the firing interval as much as humanly possible. Alger conducted an experiment comparing seven different methods of actuating the firing device. The fastest involved biting on (0.198 seconds to the striking of the primer) or puffing air from the cheeks (0.214) into a mouthpiece. These also had the least variation. The classic lanyard pull was slower (0.268 spring lock; 0.354 hammer).
Roll Compensation
The nineteenth-century British Captain Brooke used a pendulum to correct gun elevation for the normal heel of a ship. One might take this a step further and use it to detect the true angle of elevation during a roll, i.e., the sum of the gun's elevation from the deck and the ship's roll angle. For this to work properly, two criteria must be met.
First, the pendulum must have a long period relative to the roll period of the ship. If it has a short period, it will indicate the apparent vertical, perpendicular to the wave surface, not the true vertical, as discovered by Froude.
Secondly, the pendulum must hang from the center of oscillation (Atwood 252); the pendulum would then indicate the true vertical and the angle between that and the bore would be the true elevation plus 90 degrees. Unfortunately, the guns are distant from the roll axis, which should pass near the center of gravity. Brown (62) says, "one might expect an error of about 20% from a pendulum on the upper deck on an ironclad and of some 50% on a wooden battleship."
There are two choices, then. We can have a master pendulum at the proper location, with a gauge that reads off its angle with the "ship vertical." This angle could be communicated, perhaps electrically, to the gun stations.
Or, we accept the inherent inaccuracy and hang the pendulum near the gun. It's been suggested that the tilt sensor could be as crude as a cannonball hung from a nearby spar. The gunner would ignite the gun when "just before it was parallel to the mast." (NAVORD 15A2). If this was in fact done, it wouldn't have been easy to judge. Sometime before 1855, the French "used a reflector to compare the indication of the pendulum with the real horizon; this combination was called L'Horizon Ballistique." (Friedman 292).
In 1872, Froude designed an automatic roll recorder that featured both short and long period pendula. The long period one was robust, an eccentrically mounted wheel "three feet in diameter and weighing 200 pounds," with a half-period of 34 seconds. The roll recorder was used in sea trials of Inflexible (1882), Revenge (1895) and the Vivien gyrostabilizer (1925). It was not used in a firing mechanism. (Brown 62ff).
Bessemer proposed (1873) a firing device that featured a "tumbling bob," a slender triangular element positioned with wide end up, resting against one of two flanking arms. One arm was insulated, the other had an electrical contact, as did the bob. The whole assembly was itself mounted on a graduated quadrant, so it could be inclined at a specified angle to the frame of the quadrant, which corresponded to the desired true elevation at the time of firing. The idea was that with the bob resting against the insulated arm, the gunner would close one switch by pressing the firing button. When the ship rolled enough in the direction of the electrified arm so that the bob would fall over against it, the second and last contact would be closed and a firing signal delivered to the primer. Bessemer recognized that it would require a finite amount of time for the bob to change position, and that the launch of the projectile was also delayed by the "firing interval," so he provided a secondary movement for adjusting the neutral inclination to allow for this. It appears that Bessemer demonstrated a table model at the Royal Naval College, but his offer to fit a British warship with it at his own expense fell on deaf ears (Vincent 507).
Continuous Aim
In the late-nineteenth century, if telescopic sights were available, they were used just to make the initial estimate of the range. The gunner dialed in the elevation but still waited for the roll to bring the aiming point into open sights. Accuracy was poor. Firing for five minutes each at a hulk 1600 yards away, five British warships managed to score a grand total of two hits. (Morrison).
In 1899, Percy Scott stunned the Royal Navy when his cruiser Scylla achieved an accuracy of 80% in a prize firing, about six times the normal performance. Rather than set a fixed elevation for the estimated range and try to time the roll, his gunners continuously aimed (i.e., adjusted the elevation) of their guns (Friedman 19).
While this was a procedural rather than a technological change, it was of course made possible by technological improvements, such as breechloading, rifling, elevating gears, and telescopic sights.
Moreover, Scott did some technological fine-tuning, too. He changed the gear ratio on the elevating gear so that the gunner could follow the target during the roll. And he modified the mounting of the telescope sight so it wouldn't be pushed back (into the gunner's eye!) by the recoil. (Morison).
Scott's methods r
evolutionized naval gunnery; in 1905, a gunner "made fifteen hits in one minute at a target 75 by 25 feet at 1600 yards; half of them hit in a bull's eye 50 inches square." (Id.)
However, the bigger the gun, the more difficult it was to move it fast enough to achieve "continuous aim." (Friedman 20). Also, that 1600 yards was about the practical limit without improved range estimation and prediction of target motion (22).
Gun Platform and Ship Stabilization
In 1889, Beauchamp Tower constructed and tested an apparatus for providing a steady naval gun platform. The position of the gyroscope affected the flow of pressurized water into four hydraulic cylinders on which the gun platform rested. The Admiralty tested it on two gunboats; it worked, but the weight was considered excessive. Thornycroft's pendulum, which hyrdraulically shifted a weight within the hold to stabilize the entire ship (1892), had the same problem. (Bennett 97). Still, in 1906 Schlick showed that an 1100 pound steam-driven gyroscope could reduce a torpedo boat's roll from 15o each way to 1.5o. (Airey 49).
There are two modern approaches to ship stabilization. Fin stabilizers have an angle of inclination that is gyroscopically controlled; they are effective only when the ship is traveling. A tank stabilizer operates even when the ship is at rest. One version used a single partially filled tank; others featured two wing tanks connected in some way, but with constricted flow between them. Care must be taken with tank stabilizers to ensure that they decrease rather than increase roll, and of course the tanks take up space and add to the weight of the ship.
Fire Control Systems
The pre-WW I increase in torpedo range to 1500 yards at high speed and 3500 at reduced speed provided considerable incentive for further increasing effective gun range, as "it was widely understood that a line of battleships would be a virtually unmissable target... [with] little or no underwater protection." (Friedman 22). That meant that further improvements in fire control were necessary for the gun to regain primacy.
Until the gun is fired, and during the "firing interval," the combined motion of the firing ship and the target ship cause the range and bearing of the target ship to be continuously changing. When the projectile leaves the muzzle, its velocity is the vector sum of the velocity imparted by the gun and the velocity of the ship (and the wind, if any). When the projectile is in flight, the firing ship's further motion is irrelevant, but the target's motion during the "time in flight" must have been anticipated, in order for the projectile to strike it.
Friedman (22) says, "Only once a ship's motion had been cancelled out did it really matter whether the range to the target was known." As a result of the relative motion of the ships, and late-nineteenth-century warship speeds, the range could change at a rate of "200 yards or more per minute." (Friedman 23).
The range to look up in the range tables is not the geometric range at the time the decision is made to fire, but rather the range the target is expected to be at when the projectile descends low enough to strike it. If the firing ship and the target ship are moving at constant direction and speed, the range will be changing at a nearly (Friedman 41) constant rate, and the range to set is the sum of the geometric range and the product of the "range rate" and the sum of the firing interval and the time of flight. But the time of flight is itself a function of the range.
The problem of the combined motion of the gun and target could be solved by hand using the same traverse tables that were used for navigation. These were essentially pre-computed trig tables for a converting a distance on a course to a latitude and longitude change; you replaced "distance" with "speed," and interpreted "latitude" as rate of change parallel to the line of fire and "longitude" as the perpendicular rate.
During the early-twentieth century, crude analog mechanical computers were used to take into account the effect of gun and target motion on the proper range and bearing setting. One such device was the "Dumaresq," invented 1902–4 and variations of which were used in WW I.
The Dumaresq subtracted the firing ship's velocity (direction and speed) from the enemy ship's velocity, resolving the difference into components along the line of bearing (the range rate) and perpendicular to it (the deflection rate). First, the inner ring was rotated to the enemy's bearing relative to your bow. Then the outer ring was rotated to your own heading. A slider was mounted on an overhead bar supported by the outer ring, and this slider was moved "aftward" to show your speed forward—thus subtracting it. A ring hung down from the slider and it was rotated to show the enemy heading. And this ring had a slider bar, and the slider was moved to show the enemy speed. A pointer hung down from that slider, marking a point on a graph that indicated the corresponding range and deflection rates (yards/minute).
Of course, to use the Dumaresq, you needed data:
Target Bearing. With experience, target bearing can be estimated by eye within 5–10o (BMR). The down-timers already use an "azimuth compass" to determine the bearing of an object close to the horizon, for navigational purposes, and that's accurate to 0.5–2o.
Own Speed and Course. To determine the "range rate," we must know our own ship's speed and course. Prior to RoF, sailors determined speed by the "common log" (tossing a log attached to a knotted rope behind the ship and timing how fast the knots passed over the rail) . A continuous log using some sort of rotating element was invented by Humfray Cole and published by Bourne in 1578, and another was constructed by Hooke in 1668. However, rotatory logs didn't come into common use until the nineteenth century, under the name "patent log." (EB11/Log; Robinson 53).
Early-twentieth-century naval fire control systems used a pitometer log; this measures the total pressure of seawater in the direction of motion and perpendicularly to it, and either measures the pressure difference or generates an equalizing pressure. The side pressure is just the static pressure of the water whereas the forward pressure is augmented by the motion, including a dynamic pressure proportional to the squared velocity. The pitometer log is analogous to a pitot tube airspeed indicator on an aircraft; the tube is used on the Belle built in NTL 1633. (Flint, 1633, Chapter 11).
Down-timers read their heading (approximately equal to the course) by comparing it to their magnetic compass, which points to magnetic north (or south). The magnetic compass reading requires correction for magnetic variation (caused by changes in the Earth's magnetic field) and deviation (caused by ferromagnetic materials on board). A gyrocompass finds true north; the first practical one was invented in 1908 (Wikipedia). It requires electric power. See "Gyro Sights," Part 2.
The heading differs from the course by the leeway angle. This will be affected by the ship speed and the wind and sea conditions; you can determine a typical leeway angle by maintaining a set heading from one known reference point to another in smooth water with a known current and known steady wind and see how far off course you go.
Target Speed and Course. Friedman (30) states that "at short ranges ... it was relatively easy to guess enemy course by how foreshortened the target looked, and speed might be estimated form the appearance of the enemy bow wave." Observers trained themselves to estimate course by studying models of enemy ships, and might be aided by instruments that measured the angular width of the enemy ship and calculated the angle it made to the line of bearing if the range and ship length were known.
In turn, ships were given dazzle camouflage (sometimes including a fake bow wave) to make it difficult to judge course and speed. But even without camouflage, course was estimated by eye only to about a point (11.25o), and speed was typically 15–30% off. (45).
The Dumaresq could also be operated in reverse, inputting the range rate (determined by successive rangefinder measurements) and the deflection rate. (The latter was not directly observable; what you saw was the rate of change of target bearing, which could be divided by the range to get the deflection rate. Some Dumaresqs were inscribed with bearing rate curves to make this easier.) That caused the elements to move to indicate the corresponding target speed and course.
Unfor
tunately, period rangefinders were not sufficiently accurate to make good estimates of range rates, which after all were the differences between range measurements made at short time intervals. (Id.) As for bearing rates, the trouble was that ships yawed back and forth a great deal, so the bearing rate was very messy. (44).
What you could do, instead, was use the Dumaresq to calculate the range and deflection rates, use them to estimate a later target range and bearing, and see how good the estimate was. If it was off, you adjusted the rates accordingly until you were happy with the prognoses.
Integrator. On the Vickers "range clock," a wheel spun at constant speed, and a spherical roller connected to an output shaft was held against it; the closer to the rim it was, the faster it turned. The roller was set to a position based on the computed range rate, and the outputs were the current true range (black hand) and the adjusted range for targeting (red hand). The latter would be entered into the range tables. I'm not sure how they adjusted the range for targeting without pulling the time of flight from the range tables, but perhaps it was a successive approximation method.
Unfortunately, the range rate wasn't constant even if speeds and courses were maintained. Changing the roller position was a bit awkward, unfortunately, so it was only changed at set intervals and there were "lagging errors." Ideally, you would be able to change the roller position continuously and instantaneously without interfering with the wheel rotation.
Communication. All the number crunching doesn't do you any good if the results aren't timely communicated to the gunners. This could be done by voice, through a sound pipe or phone, or purely electronically, by wire or radio. The concerns were to transmit the data accurately and without disruption by enemy action.
System Evolution. Initially, fire control systems were a "kludge." There would be a large number of operators, some reading off data from gauges and others inputting the data into the Dumaresq or a similar device or transferring the Dumaresq's range rate into a range clock.