The Thermodynamics of Running Shoes

For my final project in Thermodynamics, we could analyze anything thermodynamically. I chose running shoes. I run cross country and track, I'd been curious about how super shoes actually worked, and it seemed like a good excuse to find out. My usual approach to gear is whatever's on sale or the brightest color, so this was a step up.

Shoes as Thermodynamic Systems

Every stride involves mechanical work, friction, and heat — and the shoe has to manage all of it. The midsole foam compresses under your foot, stores some energy elastically, and releases it as you push off. The part it doesn't return gets lost as heat through internal damping. So energy return and heat generation are directly linked: a more efficient foam loses less energy as heat and gives more back to you as forward motion. Your body isn't great at this either — only about 20–25% of your metabolic energy actually goes toward moving you forward.

Why Your Shoes Feel Different in the Cold

This one I found satisfying because it confirmed something I'd already noticed: shoes genuinely do feel harder in cold weather and softer when it's warm. Turns out there's a real physical reason for it.

The three main foam materials — EVA, TPU, and PEBA — each have different molecular structures that determine how they respond to temperature. EVA, the most common midsole material, has a partially crystalline structure. Those ordered molecular regions restrict how freely molecules can vibrate, so in cold conditions, EVA gets significantly stiffer — up to 70% by some measurements. Less molecular motion means less cushioning. TPU and PEBA are mostly amorphous (disordered) at the molecular level, so they stay soft and responsive even when it's cold. PEBA, which Nike uses in the Vaporfly, is especially stable — its alternating soft and hard molecular segments give it both high elasticity and consistent performance across temperatures.

Where Heat Goes During a Run

Heat moves through a shoe via conduction through the foam, airflow through the upper, and evaporation of sweat. Conduction follows Fourier's law:

EVA and PEBA are chosen in part because they have relatively low thermal conductivity — EVA typically measures about 0.18 W/m·K, while PEBA can reach around 0.35 W/m·K. This means that these foams act as insulators, helping to shield the foot from cold surfaces. However, this same insulating quality can become a drawback during long runs. When heat generated by the foot cannot escape efficiently, the result is a buildup of internal temperature.

Evaporation is a very efficient mechanism for removing heat. As human sweat vaporizes at the foot's surface, it removes about 580 kilocalories per liter of thermal energy. However, its effectiveness depends on airflow and humidity within the shoe. When fabrics such as socks and linings become saturated, evaporative heat loss drops sharply, causing heat to build up where sweat cannot escape. The shoe you're wearing at mile 20 is mechanically a little different from the one you started in.

Researchers measured foot temperature at the heel, arch, and forefoot during running at different speeds. At 4 km/h, the heel showed the greatest temperature increase, about 2°C. At 16 km/h, the highest temperature shifted to the toes, reaching approximately 6°C, which corresponds to the forward movement of plantar pressure at higher speeds. After exercise, the heel cooled faster than other areas because heat was conducted through the sole into the ground. The heat distribution is basically a map of where your foot is working hardest, and it shifts with pace. I'd never thought about it that way before. But I thought it completely checked out.

What the Carbon Plate Actually Does

The carbon plate in super shoes is often described as "giving you energy back," which is a little misleading. What it really does is reduce energy loss. It acts as a stiff spring that limits forefoot deformation, reducing the energy lost to internal damping in the foam. Less heat generated per stride means more energy returned to propulsion. From a thermodynamics perspective, these shoes reduce entropy generation per stride, resulting in lower metabolic energy expenditure and improved running economy.

I got Vaporflys for track last year and they're genuinely different. I wish I'd had them for Grandma's Marathon, but they were a bit spendy and I didn't know I'd end up on a varsity team. It was still a good investment.