Why are high heeled shoes so damaging to floors?

Why do high heels worn by a lady walking on a wooden floor leave impressions on the floor? — AK, Abbottabad, Pakistan

High heeled shoes can produce enormous pressures on a wooden floor and dent it permanently. To understand why that happens, let’s start with a pair of flat-heeled shoes and consider the forces and pressures in that situation.

When a women stands on the floor, the floor must support her weight. Specifically, she isn’t accelerating so the net force on her must equal zero. That implies that the floor must exert an upward force on her that exactly cancels her downward weight. She is motionless and stays motionless because there is no overall force on her.

Because the floor is pushing upward on her shoes, her shoes must be pushing downward on the floor. It’s an example of the famous “action and reaction” principle known as Newton’s third law: if you push on something, it pushes back equally hard in the opposite direction. Anyway, her shoes are pushing down hard on the floor.

Now for the pressure part of the story. Because she is wearing flats, her shoes are pushing against a large area of the floor and the pressure—the force per area—she produces on the floor is relatively small. For example, if she weighs 130 pounds (580 newtons) and her shoes have a contact area of 10 square inches (65 square centimeters), then the pressure she exerts on the floor is about 13 pounds-per-square-inch (9 newtons-per-square-centimeter or 90,000 pascals). That’s a gentle pressure that won’t permanently dent most woods. It might dent cork or balsa, but that’s about it.

But when she wears high heels, most of her weight is supported by a very small area of flooring. If the heels are narrow spikes with a contact area of 0.1 square inches (0.65 square centimeters) and she puts all of her weight briefly on one of the heels, she may exert a pressure of 1300 pounds-per-square-inch (9000 newtons-per-square-centimeter or 90 million pascals) on the floor. That’s an enormous pressure that will permanently dent most wooden floors.