Robert Ingalls Simpson (May 25, 1892 – November 10, 1974) was an American hurdler and track and field coach. Simpson set several world records in the 120 yd hurdles, equaled the world record in the 220 yd hurdles, and won two gold medals at the 1919 Inter-Allied Games. He served in the United States Army in both World Wars, rising to the rank of major by 1944. He was track and field head coach at first the University of Missouri and then Iowa State University, and later in Hungary; he also coached Army athletes.