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Why would you calculate the climb gradient for the second segment in the event an engine failure at V1 if there were no obstacles?
Because the regulations require specified minimum gradients, engine-out, in the first, second and final segments.
The WAT curves, referred to above by Blind Pew, show the Weight permissible at Altitude and Temperature when meeting the required net gradient. You don't have to calculate the gradient as we who published the WAT curve did it so that you only had to input T and A and then not exceed the Weight you read from the graph.
Oh and there can indeed be different regulations for what you refer to as tiddly aircraft, if by that you mean those of sub-airliner size.