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Gun Balance for Late Turret
Like most German tanks, the Tiger had its gun out of balance and a large spring was used to keep it level. The photographs of the early Tiger at Bovington (number 250122) are widely known and they show the recoil spring housed in a large black cylinder at the right side of the turret. The rear end is firmly attached to the turret ring's top plate, and the front is linked to the gun mantlet through a couple of levers attached to the turret roof.
This arrangement mustn't have worked very well, because when they redesigned the turret they moved the spring balance unit to a completely different location. It was put beside the commander's seat, there was room for it because the commander and his new cupola were moved to the left, but I don't know if that's the reason.
This diagram from the Tiger Turret Manual shows a profile of the turret and a few items within it. The gun balance is labelled "Federausgleicher" and I have labelled a few of the other items myself. You can see the cylinder housing the recoil spring; as far as I know it was identical to the original cylinder in size. The top of it is anchored in a solid rectangular steel block that has its rear face angled so it fits snugly against the turret wall (this diagram draws only the left, shorter face of it).
The bottom of the cylinder is attached to a large cam, and a chain (much like a bicycle chain) attaches the cam to a protruding arm welded to the gun's housing. You can see that this cam has a strange shape, intended to apply the correct force at each angle of elevation of the gun. (The middle of the cam outline drawn here is hollow.)
This side profile cannot show it, but most of the cam is only about an inch thick and is offset far enough to the right that it just clears the cylinder. The thin part curves smoothly out into the bottom part, which is about 3 inches thick and centered under the cylinder. I can't really describe this shape without building a 3D model for you. The cam's shape is shown clearly in a single photograph, taken in the Tiger at Saumur, that is published in the "New Vanguard" series on the Tiger I. Naturally I cannot reproduce it here.
The cam's hinge is mounted in a sort of clumsy box-girder made from a few metal plates. The rear part consists of two 10mm steel plates; one is slanted and runs down to the turret floor, and the other is L-shaped and is bolted to the turret wall. The sides of the box-girder are made of thinner steel and serve to prevent buckling. Both sides are the same shape but one is further forward than the other because of the turret's curvature.
Here are my own diagrams of the box girder. You can see that it's squeezed in very tightly beside the seat, and its shape is distorted to fit the curvature of the turret. The small items on the turret wall are just welded squares of steel with bolt holes - the manufacturers were reluctant to drill the armour plate itself..

The bottom of this box girder is a metal plate bolted to the top of turret floor. As far as I can determine, there was no change made to the webbing on the underside of the turret floor. This second diagram is from the front; the box girder is 17cm wide at the top and the steel box on the turret roof is 100mm wide.

Sources
[1] Survey of vehicle 250122, Bovington, by David Byrden
[2] Survey of vehicle at Saumur, by Hilary Louis Doyle
[3] Factory drawing: Turmgehause 2AKF31861U1B11 (overall turret armour)
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