Tanks with multiple turrets were designed to engage multiple targets at the same time. For example, the Vickers Mk.E Type A with two machine gun turrets was designed for trench sweeping. A tank could drive up on a trench and fire in two directions at once so enemy troops had nowhere to run. This sort of approach fell out of favour quickly since the most you could fit into one of these turrets was a very small gun (low velocity 37 mm) or a machine gun. It was also difficult to communicate with the other turret. Interestingly enough, the idea of one main turret and a small machine gun turret persisted for quite some time. The German Neubaufahrzeug, Canadian Ram, and British Crusader all had this solution. This merely gave the hull gunner more range when engaging enemy infantry. All three nations dropped the idea, since the machine gun turret turned out to be very cramped.
Double barreled tanks also existed but they were much rarer. The idea behind these tanks was to increase the density of fire when engaging a single target rather than engaging multiple targets like the multi-turret tanks did. The gunner could also correct his aim and make a rapid follow-up shot. This also got rid of the problem with communication, since both weapons were aimed by the same crew and they were not separated into different turrets.
One such vehicle was the KV-7. This vehicle was classified as an assault tank and first actually had *three* guns (one 76 mm and two 45 mm) and later modified to fit two 76 mm guns. Trials showed that volley fire didn't quite work all that well when the faster firing 45 mm guns were restricted to the lower rate of fire of the 76 mm gun. The dual 76 mm gun variant had low priority to begin with and later it turned out that the guns were difficult to operate and fire.
The Australians built a Sentinel tank with two 25-pounders, although it was never meant to fight. The idea behind this tank was to simulate the recoil of a 17-pounder gun (as one had not yet been delivered to Australia).
The most successful double barreled tank design was the Marmon-Herrington MTLS-IGI4. 145 units were built and they even saw battle. The tank was armed with two semiautomatic 37 mm guns fed with 5 round clips.
There were plenty of designs that remained on paper. The T-34-3 tank was a proposal similar to the KV-7 with two 45 mm and one 76 mm gun. The SU-2-122 was an SPG on the T-34 chassis with two M-30 122 mm howitzers. There was also the ST-II tank pitched in 1945. Here the rate of fire was increased by having not only double the guns, but also two loaders. These are only the ones I'm aware of and I'm sure this is not an exhaustive list.
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