In Pixar's Cars, Doc Hudson wears the number 51 during flashbacks to his racing career.
Doc is revealed to be the Fabulous Hudson Hornet, a celebrated racer who won three Piston Cups in the early 1950s. His racing number, 51, appears on the blue Hudson Hornet shown in the film's historical material.
The character is based on the real Hudson Hornet, a car that became famous in stock-car racing. Real Hudson Hornets competed successfully in the early NASCAR era, and the film adapts that history into Doc's fictional career and later life in Radiator Springs.
The number is easy to mix up with other Cars racers. Lightning McQueen is number 95, The King is number 43, and Chick Hicks is number 86. Number 51 specifically belongs to Doc's racing identity.