Sergey Alekseevich Chaplygin was born on April 5, 1869, in Ranenburg, located in the Ryazan province. His father worked as a shopkeeper, while his mother managed the household. The family was close-knit, but happiness was short-lived: when Sergey was two years old, his father passed away due to a cholera epidemic.

His maternal grandparents insisted on her remarrying, and Anna Petrovna moved with her son to Voronezh, where her new husband lived. Sergey was a serious boy, learned to count and write early, and helped his mother a lot. His stepfather treated him well and invited a seminary student to prepare Sergey for admission to the gymnasium. Thanks to his excellent memory and academic abilities, he passed the exams brilliantly.

However, his stepfather turned out to be a poor family man and left Sergey’s mother with five children. All responsibilities fell on the shoulders of the eldest son. After school, Sergey helped his mother and gave lessons. He studied excellently, so he was often invited to tutor struggling children. At 13, Chaplygin became the breadwinner of the family.

In 1886, Sergey graduated from the gymnasium with a medal and enrolled in the Faculty of Physics and Mathematics at Moscow University. He attended all lectures and continued to give private lessons, sending most of his earnings to his mother in Voronezh. He lived modestly but did not complain and diligently studied physics, mathematics, mechanics, and astronomy. Among his teachers were A.G. Stoletov, N.E. Zhukovsky, and F.A. Bredikhin.

Zhukovsky's lectures sparked Chaplygin's interest in mechanics, and on the professor's advice, he began working on a scientific paper on hydrodynamics, which became the basis of his diploma thesis and was awarded a gold medal.

Remaining at the university, Chaplygin worked on his dissertation and taught. From 1894, he became a privat-docent at Moscow University. In the autumn of the same year, he married the landlady, Ekaterina Arno. In 1897, they had a daughter, Olga.

Sergey actively engaged in research in hydrodynamics and studied the motion of bodies on rough surfaces. His works became classical, and he wrote two textbooks on mechanics for universities. Later, Chaplygin defended his doctoral dissertation and became a professor.

After the October Revolution, he continued his scientific research and teaching. When the Central Aerohydrodynamic Institute was established, Zhukovsky invited Chaplygin to head the branch of TsAGI near Moscow. After Zhukovsky's death in 1921, Chaplygin became the scientific director of TsAGI.

Sergey Chaplygin gained recognition as a scientist and was elected a member of the USSR Academy of Sciences in 1929. The workload affected his health, and in 1931 he requested to be relieved of his leadership at TsAGI, but continued to collaborate with the institute until the end of his life.