The Kerrison Predictor was developed after it had been realized that modern aircraft on the attack flew too quickly for existing traversal systems on medium-sized guns to work. Smaller guns could be aimed by hand due to the short ranges at which they operated, and larger guns shot at targets so far away that the speed that the angle changed at was low enough to calculate the required "lead" using a simple slide rule device in the gunsight.
However there was a middle range, served by the British Army's 37mm and Bofors 40mm guns, where the range was too far to "guess" the required lead, but at the same time short enough that the angle changed fast enough that the gunners were hard pressed simply turning the traversal handles, let alone trying to operate a calculating gunsight at the same time. Making matters worse was that these ranges were exactly where the Luftwaffe's dive bombers were attacking from, which were quickly proving to be a decisive weapon in the Blitzkrieg.
The Predictor solved the problem by doing all of the calculations mechanically through a complex system of gears. Inputs included wind speed, gravity, ballistics of the gun and the rounds it fired, angle to the target in azimuth and altitude, and a user-input estimated speed. All of these inputs were fed in via dials, which turned gearing inside the Predictor to calculate the range (from the change in angle and estimated speed) and direction of motion, generate the correct lead needed based on that calculation, and the "output" the result by moving a small pointer mounted on the gun. The gunners simply kept the pointer in the middle of the gunsight and loaded, while the gunnery operators simply had to point the Predictor, mounted on a large tripod, at the target.
The Predictor proved to be able to hit practically anything that flew in a straight line, and it was particularily effective against dive bombers. However it was also very complex, including over 1,000 precision parts and weighing over 500 pounds even though much of it was aluminum. With the demands of the RAF for almost all light metals and machinists, the Predictor was far too difficult for the Army to produce in any number.
Meanwhile in September 1940 the US Army's Coast Artillery Corps had become unhappy with their existing 37mm guns, and General Marshall asked the British to loan him four of their Bofors guns and Predictors for testing. They were more than impressed, and they asked the Sperry Corporation to adapt it to US manufacturing systems. Sperry was currently starting production of their own system, the M7, but sent back plans for such a version of the Predictor as the M5. To produce the M5 the Singer Corporation was brought in in in December 1940 to produce 1,500 a month to equip their existing 37mm guns. However in February 1941 the US Navy decided to use the Bofors gun as well, and the Army then agreed to in order to simplify production. Singer required massive changes in the company, including building new factories and the switching of a foundry from steel to aluminum, that production didn't start until January 1943. Nevertheless the production line proved to be sound, and the order was filled for their Director, Antiaircraft, M5 by the middle of 1944.
With aircraft speeds increasing dramatically during the war, even the speed of the Kerrison Predictor proved lacking by the end. Nevertheless the Predictor demonstrated that effective gunnery required some sort of reasonably powerful computing support, and in 1944 Bell Labs started delivery of a new system based around an analog computer. The timing proved excellent. Late in the summer the Germans started attacking London with the V-1 flying bomb, which flew at high speeds at low altitudes. After a month of limited success against them, every available anti-aircraft gun was moved to the stripe of land on the approach to London, and the new sights proved to be more than capable against them. Daytime attacks were soon abandoned.
Long after the war, US M5's started appearing in surplus shops in the late 1950s. John Whitney purchased one (and later a Sperry M7) and connected the mechanical outputs to servos controlling the positioning small lit targets and light bulbs. He then modified the "mathematics" of the system to move the targets in various mathematically controlled ways, a technique he referred to as incremental drift. As the power of the systems grew they eventually evolved into what is today known as motion control photography, a widely used technique in special effects filming.