To reduce the errors in testing from dropping from aircraft;
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The original 4000lb cookies tended to tumble in flight which makes predicting the path a little difficult. Some had a hollow drum attached to the back which was supposed to help but I don't know if the flat front and hollow drum rear gave as steady a flight path as a pointy front ( or semi-pointy) and regular fins.
The USAAC used very few 1600lbs. They get listed a lot as they make an airplane
sound like it has a very impressive bomb load. The have a much thicker casing than a "normal" GP bomb and are actually smaller in diameter than a 1000lb bomb. They carried less explosive than a 500lb GP bomb ( here is one example of weight of bomb vs weight of explosive) but fit rather nicely in small bomb bays. Unless attacking armoured ships or concrete they really weren't much good.
Planes do have an effect on accuracy. Some bombers were known to "snake" or yaw a bit from side to side as they flew which affects not only the bomb aimer but the drop it self.