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rat rod

n. A style of hot rod or custom car that imitates or exaggerates the hot rods of the 1940s, 1950s, and 1960s. It is distinct from the "traditional" hot rod, which is an accurate re-creation or period-correct restoration of a hot rod from the same era.

Wikipedia
Rat rod

A rat rod is a style of hot rod or custom car that, in most cases, imitates (or exaggerates) the early hot rods of the 1940s, 1950s, and early-1960s. The style is not to be confused with the somewhat closely related "traditional" hot rod, which is an accurate re-creation or period-correct restoration of a hot rod from the same era.

Most rat rods appear "unfinished", regardless of their status, as only the vehicle's bare essentials are driven. These are built to drive, not exclusively for show.