Why were tanks more effective on open plains than in mountains, forests, swamps, or cities?

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Kuwait: U.S. 1st Armored Division M1A1 Abrams tanks — tank M1A1 Abrams main battle tanks of the U.S. 1st Armored Division moving across the desert in northern Kuwait during the Persian Gulf War, February 1991.

Tanks are most effective on broad, open plains because these environments provide the necessary space for armoured forces to maneuver and deploy fully.1

In contrast, tanks face significant limitations in mountainous, forested, swampy, or built-up (urban) terrain due to two primary factors:

Diminished Trafficability: The physical characteristics of these environments often restrict the movement and speed of heavy vehicles.1
Lack of Deployment Space: These terrains lack the open area required for tanks to operate as a cohesive force, often forcing them to be relegated to a secondary role supporting infantry.1

While there have been rare exceptions, such as the German maneuver through the Ardennes in 1940, tanks in restricted terrain are frequently rendered ineffective or are used inefficiently as makeshift artillery. Because tank turrets must absorb recoil, their guns are typically smaller than standard field cannons, making them a costly and suboptimal substitute for dedicated artillery units.1