Update: We are resurfacing this feature from 2014 for your reading pleasure on this holiday weekend.

The USS Zumwalt, the latest destroyer now undergoing acceptance trials, comes with a new type of naval artillery: the Advanced Gun System (AGS). The automated AGS can fire 10 rocket-assisted, precision-guided projectiles per minute at targets over 100 miles away.

Those projectiles use GPS and inertial guidance to improve the gun’s accuracy to a 50 meter (164 feet) circle of probable error—meaning that half of its GPS-guided shells will fall within that distance from the target. But take away the fancy GPS shells, and the AGS and its digital fire control system are no more accurate than mechanical analog technology that is nearly a century old.

We're talking about electro-mechanical analog fire control computers like the Ford Instruments Mark 1A Fire Control Computer and Mark 8 Rangekeeper. These machines solved 20-plus variable calculus problems in real-time, constantly, long before digital computers got their sea legs. They were still in use when I served aboard the USS Iowa in the late 1980s.

There were a few efforts to marry these older systems to or replace them with digital technology during my tour, one of which (called the Advanced Gun Weapon System Technology Program) was remarkably like the AGS’s 100-mile shell: a GPS and inertially guided 11-inch dart-shaped shell wrapped in a 16-inch peel-away jacket, or sabot, that would have been able to fly nearly as far without the rocket assist thanks to the battleship’s big guns.

So why did the Navy never follow through with digitizing the battleship’s big guns? I asked retired Navy Captain David Boslaugh, former director of the Navy Tactical Embedded Computer Program Office, that question. And if anyone would know, it's Boslaugh. He played a role in the development of the Navy Tactical Data System—the forerunner to today’s Aegis systems, the mother of all digital sensor and fire control systems.

“At one time, my office was asked to do a study regarding upgrading the Iowa-class battleship fire control systems from analog to digital computers,” Boslaugh replied. “We found that digitizing the computer would improve neither the reliability nor the accuracy of the system and recommended, ‘Don't bother.’” Even without digital computers, the Iowa could fire 2,700-pound “dumb” shells nearly 30 miles inland with deadly accuracy, within a circle of probable error of around 80 meters. Some of its shells had circles of destruction larger than that.

Just how can a box of gears, cams, racks, and pins handle ballistics calculations based on differential equations with dozens of variables in real time? How does it manage to put a hunk of metal weighing as much as a Volkswagen Beetle on top of a target over the horizon in the first place? And how did this metal and grease out-calculate digital systems for so long? Let's start with a little bit of a history on battleship ballistics—complete with vintage Navy training films to show precisely how mechanical analog computing works.

Going ballistic

Shooting things with a gun from a ship is not exactly easy. In addition to the usual problems faced by ballistics—calculating how much bang to apply, how high to aim to reach a target at a certain range, how much to compensate for wind and the Coriolis effect—you have to take into account the fact that you’re shooting from a platform that has constantly changing pitch, yaw, and position. If you’re lucky enough to have a stationary target, the variables are still comparable to trying to hit something with a water balloon from the back of a hopping kangaroo.

Shooting things within sight of a ship is a feedback loop. Aim at the target, calculate its relative movement and other ballistic conditions, shoot, watch where the shot falls, and adjust. Shooting targets over the horizon is even trickier. It requires a forward observer who can give a precise geographic fix and then give corrections based on where shells land to walk them onto target.

In the days before turrets, ships fired guns in broadsides. Adjustments were generally made by where the shells fell and by waiting to fire until the side facing the enemy was on the upward side of a roll. But with the arrival of dreadnoughts and battle cruisers at the beginning of the 20th century, the range and lethality of ships’ guns both rose dramatically. There was now a greater need for accuracy, too.

That need corresponded with the rise of analog computers. Mechanical analog computers were used by astronomers for centuries to predict star positions, eclipses, and the phases of the moon—the earliest known mechanical analog computer, called the Antikythera Mechanism, dated to 100 BC. But nobody got around to using computers to try to kill people until much later.

Analog computers use a common set of mechanical devices to do their calculations—the same sorts of devices that convert the torque created by a car’s engine into turning wheels, lifting valves, and moving pistons. Data is “entered” into analog computers continuously, usually by the rotation of shaft inputs. A mathematical value is assigned to one full 360-degree rotation of the shaft.

In the days of the ancient Greeks, data entry was performed by turning a wheel. In more modern analog computers, variables from sensor data such as speed, direction, wind speed, and other factors were passed by electromechanical connections—synchro signals from gyrocompasses and gyroscopic “stable verticals,” tracking systems, and speed sensors. Constants, like passing time, were input by special constant-speed electrical motors.

Connecting all the shafts together to turn them into a continuous set of calculation outputs is a collection of gears, cams, racks, pins, and other mechanical elements that translate motion into math through geometric and trigonometric principles. This is also done through “hard-coded” functions that store the results of more complex calculations in their precisely machined shapes. Working together, these parts instantaneously calculate a very precise answer to a very specific set of questions: where will the target be when the giant bullet I push out of a 68-foot long rifled barrel gets there, and where do I need to aim to get it there?

When assembled precisely, analog computers can be much more accurate than digital computers on these types of questions. Because they use physical rather than digital inputs and outputs, they can represent curves and other geometric elements of calculations with an infinite level of resolution (though the precision of those calculations is based on how well their parts are machined, and loss from friction and slippage). There are no least significant digits dropped, and answers are continuous rather than dependent on “for-next” clock-driven computing cycles.