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There were many versions of the Mosquito chiefly bomber, recon and fighter bomber, this was only an option for the fighter bomber version. Many were flying alone and duking it out with rear facing guns was not an option. For a lone aircraft 5 or 10MPH on maximum or cruising speed is huge. A single engine fighter climbing to 30,000 feet only has an advantage in speed (if at all) when it gets up to 30,000 ft and when it gets there it has maybe 30 minutes on full power.Mosquito's often outran the opposing fighters and when they didn't they often reduced the closing speed significantly giving the Mosquito valuable time to find cover or for any escort to help out. One tactic I read was for the FBVI version. If spotted in time the rear most section would drop their bombs and execute a 180 degree turn, then attack the fighters head on and keep going for home. Normally the fighters would lose time speed and energy making a turn and the Mosquito's who had attacked would have a very healthy lead and be almost impossible to catch in a tail chase. Those still 'bombed up' would be well gone by the time the attacking fighters sorted themselves out.
So why were streamlined pods not fitted to the rear fuselage say four in each quarter containing a small machine gun (the Browning .50 AN/M2 would be good ) that could fire tracer . Operated by the co pilot and sighted through enhanced rear facing wide and narrow mirrors .
Tail turrets were investigated for the DH.98 before the prototype was built; DH staff calculated the impact that various configurations of tail armament would have on it - a simple two gun tail turret would have added 500lb in weight and cost 20 to 30 mph in speed. A single traversing gun under the belly was considered also in conjunction with a tail turret. In November 1939, Arthur Tedder and William Sholto Douglas stated that the proposal would be of value if it had a tail turret, and instructed de Havilland to build two prototypes with a four-gun tail turret, although de Havilland was reluctant to relinquish the unarmed prototype and it was Freeman, that saviour of the type to gamble that the four-gun tail turreted prototype would be built some nine months after the unarmed prototype had been built, knowing the unarmed prototype's performance would be excellent and might dissuade supporters of the tail turret idea. Naturally, it was never built as the unarmed prototype's performance was. I've never found drawings of what a Mossie would have looked like with a tail turret. Probably ghastly. I don't think the company took a tail turreted Mosquito very seriously.
The People's Mosquito holds copies of outline sketches for both the proposed 4 x .303 rear turret (designed by Bristol) and the underlying turret ring and support structure.