Nagel died Jan. 15 in San Antonio, according to the University of Iowa, where he had been head coach from 1966 to 1970. No cause was given.
A Los Angeles native whose father owned a bakery at the Farmer's Market, Nagel was a star quarterback at Los Angeles High School.
He played at UCLA from 1946 to 1949, first as a quarterback in a T-formation, and in 1948 broke the Bruins' single-season pass completion record held by Bob Waterfield. His last season was the first for Coach Red Sanders, who installed a single wing formation offense, which forced Nagel to switch to a new position, tailback. He also played safety on defense.
Sanders, who went on to lead UCLA to its only national title in 1954, said of Nagel, "He isn't fast. He isn't big. He isn't what you'd call a great passer. But he's a smart field general. He picks up the team. He's what you have to call a winner."
After finishing his playing career at UCLA, Nagel stayed on as the freshman team's coach. He was a varsity assistant in 1951 and 1952 while earning his law degree. He played one season for the Chicago Cardinals in the NFL then worked as an assistant coach for Bud Wilkinson at the University of Oklahoma but by 1955 was back at UCLA as an assistant to Sanders.
He got his shot at a head coaching position in 1958 at Utah and after eight years moved on to Iowa. His rocky tenure there included a public feud with the athletic director, Forest Evashevski, and a walkout by 16 black players during spring workouts in 1969, part of a protest by black students demanding reforms on campus.
Nagel left in 1971 to become athletic director at Washington State University. Among his hires was George Raveling, who later coached basketball at USC. Nagel was hired as Hawaii's athletic director in 1976 and remained there until 1983.
That year Rams owner Georgia Frontiere hired him as executive vice president to handle general manager duties. Overshadowed by coach John Robinson and John Shaw, vice president of finance, Nagel left the team in 1984.
He returned to Hawaii, where he took an executive position in public relations with the Bank of Hawaii and served as executive director of the Hula Bowl.
Nagel and his wife, Shirley, had five children.