Inspired by the example of his glider flying brother Edgar, Dittmar took an apprenticeship at the German Institute for Gliding (DFS). In 1932, flying his self-built glider Kondor, he won a first prize at the Rhön Glider Competition.
Dittmar then became a research pilot. In 1934, he, Hanna Reitsch and Wolf Hirth were members of the German glider expedition to Argentina, where he achieved a new world gliding altitude record (about 4,350 metres (14,270 ft)). Later the same year, he achieved a new world record for long-distance using a Fafnir II and was awarded the Hindenburg Cup. In 1936, he achieved the first crossing of the Alps in a glider. He then crowned his career as a glider pilot by becoming the first Gliding World Champion after his victory at the first Rhön International Gliding Competition in 1937.
During and after the Second World War, Dittmar worked as an aircraft designer and test pilot. On 2 October 1941, flying the Messerschmitt Me-163 A V4 KE+SW, he became the first human to fly faster than 1,000 km/h (620 mph). This record was achieved over the FAI-specified 3-km distance and was measured using an Askania theodolite. Later, on 6 July 1944, he reached a speed of 1,130 km/h (700 mph) in the Me 163B V18 bearing the Stammkennzeichen code of VA+SP.