I read that von Braun & his team at ABMA had started to work upon a big rocket in April / May 1957, which was to have a thrust of 1500000 lbf (1.5 Mi. lbf). It is said that Saturn I was started to fulfill US DoD's need for a heavy lift vehicle, to launch A): 20,000 to 40,000 pounds (~9,100 to ~18,200 kg) into orbit, or B): accelerating 13,200 to 26,200 pounds (6,000 to 11,900 kg) to trans-lunar injection. However the ARPA order based on which work on Saturn I started, was issued on 15th Aug. 1958. The question is: Does this ARPA order,and DoD's expression of need to have a heavy lift vehicle, and work by von Braun, which he started in April/May 1957, have any common link? If yes, what is their chronology?