What would cause a 15.5HP Briggs and Stratton OHV Engine to Idle fine but run rough and blow black smoke at any speed over an Idle?

Black smoke is an indication that not all the fuel that is entering the combustion chamber is being detonated. Three things to look for: (1) spark plug; (2) air filter; (3) carburetor adjustment. If the spark plug and the air filter are clean and in good condition but the problem persists, rotate the carburetor needle valve clockwise 1/8 turn for a slightly leaner air.fuel mixture.