The team led by Rodger Kram discovered that, for either running or walking, slopes between 20 and 30 degrees require the same amount of energy to climb at the same vertical velocity. In other words, there’s an optimal range of slope angles where the degree of incline doesn’t matter, and where the same rate of ascent requires the same rate of energy expenditure. The researchers are calling it the “Goldilocks Plateau.”


It’s a strange, and even unintuitive result. Kram used an analogy to describe his team’s findings:

Imagine that you are standing in Colorado at a trailhead where the base elevation is 9,000 feet. Your friend challenges you to race to the summit of the mountain, which tops out at 12,280 feet, i.e. 1,000 meters of elevation gain. There are several different trails that go to the summit. They are all pretty steep and some are extremely steep. One trail averages 10 degrees incline and the sign says it is 3.6 miles long. A second trail averages 30 degrees, but is only 1.25 miles long. A third trail averages 40 degrees, but only 1 mile long. To get to the summit the fastest, which trail should you choose and should you walk or run?

Based on our research, we now know that choosing the second trail (30 degrees) and walking as fast as you can within your aerobic capacity is the fastest way to go.

Cool right? The experiment might seem frivolous, but it’s important for runners who participate in vertical kilometer (VK) races, which are becoming quite popular in mountainous regions. In these races, athletes run or walk up steep slopes ranging between 10 and 30 degrees, and often to heights approaching an entire kilometer, or 0.6 miles, over a distance less than 3.1 miles (5 km).

Read the entire study at the Journal of Applied Physiology: “Energetics of vertical kilometer foot races; is steeper cheaper?”.


Email the author at and follow him at @dvorsky. Top image by University of Colorado