During the 1950s, Dunning was often consulted on nuclear technology matters by President Dwight D. Eisenhower and Rear Admiral Hyman G. Rickover, the head of the Navy's nuclear powered ships project. Dunning was elected to the United States National Academy of Sciences in 1948, and the Phi Kappa Tau Hall of Fame. Over the years he served as Chairman of the New York City Board of Education Advisory Committee on Science Manpower, the President's Committee on Supersonic Transport and the Science Advisory Council to the Legislature of the State of New York. He was a Member of the Board, of the American Association for the Advancement of Science and the Science Advisory Committee of the Department of Defense.