Comparing Steepness of Ski Trails

outer-limitsAbove, staring down Outer Limits, Killington VT


The math and reasoning is sort of explained below. If you want to skip that stuff and just get to the facts, scroll down the page…

The claims are ubiquitous: “Steepest in the east!” or “Longest and steepest in the midwest” or “Longest sustained pitch in Colorado” and of course the always popular, “If you can ski here you can ski anywhere.”

Ski areas are notorious for making claims. They exaggerate almost as much as skiers. In fact, the ski area spokesman’s propensity to enhance and embellish the treachery of a steep trail is second only to those of us who ski them. We lobby for our favorites, dismiss those at lesser mountains, and generally have no clue about the facts. As for the ski resorts, they often speak in terms of “percent of grade” or some other obscure measure that is only understood by engineers. You can ask an engineer to explain it, but chances are you’ll nod off during their ensuing discourse.

How then, to honestly compare and categorize steepness, and dumb it down so the rest of us can understand it?

The angle of the slope, expressed in degrees, is probably the best method for a moderately educated person. Most of us know that if a cliff goes straight up, it’s a 90° angle. That’s too steep to ski. Cut that down quite a bit, say, to the angle of a modern staircase, which is about 38°. Still too steep for most people to ski. If you cut even that in half — less than 20° — you’d say that’s a very low angle staircase. But put on a pair of skis, and even most advanced skiers will pause at the top of a 19° slope to pick their route.

Regardless of whether or not you can ski it, chances are that you can understand the steepness of a slope if someone tells you what the angle is when expressed in degrees. The question then becomes, how to determine the “degrees” of a ski slope?

Thanks to NASA, the US Geological Survey, the Google, and a dead guy named Pythagoras, we can come pretty darn close to accurately measuring the angle of any given ski slope. Because elevation data is now available at the click of a mouse, we can measure the altitude at the top and bottom of a slope and be accurate to within a few feet. The difference between the numbers is the vertical drop, and we can start to sketch out a right triangle. If we use the measuring tool on a map program to find the actual distance between those same points — specifically, “ground distance,” like pulling a tape measure down the hill — we now have the hypotenuse of our right triangle:

slope-angle

What we’re trying to find, of course, is the angle indicated in yellow in the diagram above. Armed with the length of the slope (the hypotenuse) and the length of at least one other side (the vertical drop) of this theoretical right triangle, we thank that old Greek dude for providing us with the math. I sat next to a cute redhead in geometry class, so I really can’t be much help here. It’s something about the square of the other sides equals the square of the hypotenuse, then you divide the “b” side by the hypotenuse, invert something, take the sine of that, and you get the angle. Yeah yeah, whatever. Ask an engineer.

This won’t solve all of our arguments, however, because the reality is that most hills are shaped like this:

slope-angle2

In which case, you cannot measure the length of the ground slope because it is no longer a triangle. You could measure the theoretical hypotenuse, or measure side “b”, but then you’d have an “average” angle. The average on a consistent slope like Outer Limits at Killington is meaningful, but the average on a slope like Shay’s Revenge at Snowshoe — with a long lead in and run out — gives no indication of how steep the headwall is. So what we’ve done on a slope like that is measure just the crux of the trail, kind of like the red line in the diagram immediately above.

In this manner we’ve selected the most fearsome section of each trail. In some cases, that’s a very short headwall. In others, it’s virtually top-to-bottom for 1,000 feet of white knuckle skiing. To put these in perspective, we’ve segregated the trails by the length of the steepness. In other words, the half mile on Sugarloaf’s Gondy Line at 30° shouldn’t take a backseat to 100 yards on Mount Snow’s Ripcord at 35°. So we compare apples to apples.