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Which Western aircraft was the An-40 compared to?
Short answer
The Lockheed C-5 Galaxy. The An-124, called An-40 in the West during its development, broadly resembled the American strategic transport, though with improvements such as more carbon fibre and titanium. Antonov began the design in 1971. NATO gave it the reporting name Condor.

A need for strategic airlift
In the 1970s, the command of the Soviet Air Force's Military Transport Aviation (VTA) suffered from a shortfall in heavy strategic airlift capacity. Its largest aircraft was the An-22, of which it operated about 50 turboprops that were heavily used in tactical roles.
The West's "An-40"
Design work began in 1971 at the Antonov design bureau, with Viktor Tolmachev as chief designer of the An-124 and of its enlarged derivative, the An-225. Internally the program was known as Izdeliye 400 (product No. 400), while in the West it was called the An-40. NATO assigned it the reporting name Condor.
Similarities and differences with the C-5 Galaxy
The resulting design broadly resembled the Lockheed C-5 Galaxy, the American strategic transport, though it incorporated numerous improvements: among them, greater use of carbon-fibre composite materials — around 5% of the aircraft's total weight — and more extensive use of titanium. By that comparison, the An-124 has a somewhat shorter fuselage, a somewhat greater wingspan, and can carry a payload 17% larger.
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