Jaroslav Drápal was born in Moravská Huzová, from where his family had to relocate to Olomouc after the annexation of the Sudetenland by the German Reich. After studying at Brno University of Technology under Bohuslav Fuchs, Bedřich Rozehnal, and Miloslav Kopřiva, Jaroslav Drápal received a placement in the Olomouc Stavoprojekt in 1959. In 1961, he applied for an assistant position at the Department of Architectural Development and Monument Reconstruction, led by Prof. Antonín Kurial, and returned to Brno University of Technology. He based his teaching method on the knowledge of Prof. Curt Siegel from Stuttgart, who focused on teaching principles of load-bearing structures and authored the book "Strukturformen der modernen Architektur" in 1960. Drápal further developed Siegel's method and adapted it to the conditions and framework of Brno architecture, publishing it with students in the prestigious review L'architecture d'aujourd'hui in 1967.

In addition to his academic career, Jaroslav Drápal worked as a practicing architect and realized several buildings, primarily in collaboration with his wife, Olga Drápalová. Their constructions emerged in the context of European architecture, maintaining a parity with what was being created west of the Czechoslovak borders. This is evidenced especially by the residential house on Pellicova Street in Brno (1976–1979) or the commercial building in Tišnov (1982–1983). From 1977 to 1980, he collaborated on the Brno-Slatina housing estate project, designed a complex of buildings for the postal and customs office in Královo Pole, and contributed to numerous reconstructions and adaptations of historical and sacral buildings. After 1989, he established his own architectural firm, AADD, with his wife, Olga.

Jaroslav Drápal earned respect among his colleagues and the affection of students not only as an educator and architect but also as a morally steadfast individual. He refused to express consent for the occupation of Czechoslovakia in 1968 during the normalization examinations and despite pervasive pressure, never joined the Communist Party. This aspect of his professional life was a reason for the City of Brno to award him the Prize for Lifetime Artistic and Pedagogical Achievement, presented by the city's mayor in 2006.

Jaroslav Drápal stands among the most significant educators who have ever worked at the Brno Faculty of Architecture. His expertise, life story, passion, and dedication continue to inspire future generations of teachers and their students.