The Existential Terror of Steep Friction and Some Physics Thereof by Bill Atkinson
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I can guarantee you that any roped free climber, regardless of experience or ability, on a serious and committing friction lead has known the fear to which my title refers. This subject comes to mind in the wake of Daniel Duane’s brilliant piece in the New York Times [1] on Alex Honnold’s free solo ascent of the Free Rider on El Cap. In it are evocations of the primal fear of having to trust the shoes while the hands are essentially useless, and the fatal urge to lean-in toward the cliff face is sometimes irresistible.
According to the Web, the coefficient of friction of climbing shoe rubber in contact with various rock surfaces varies from 0.9 to 1.1 and even higher if the surface is particularly rough. For my purpose here, I will use a coefficient value of one—a force normal to the rock surface produces an equal friction resistance parallel to the surface.
This means, for example, that a shoe vertically loaded on a forty-five degree slope has a friction resistance equal to its tendency to slide. In this case there is no margin for error and to lean-in from the vertical without slippage is impossible. Slopes steeper than this are theoretically unclimbable simply by stepping up, although I’m sure there are steeper ones (on the Big Stone and elsewhere) that could yield to unusual roughness, dynamic technique, or raw courage.
More commonly one is on a lesser slope, say one of thirty degrees as is typical of our own White Horse Ledge in New Hampshire. Here the geometry is better although it takes real conviction to believe it. In this case one need lean-in from the vertical only fifteen degrees for the feet to give way. And in the steeper places—even less than that.
Evidently Alex learned to control a reluctance to stand free and tall. In effect occasionally putting his hands in his pockets and just walking upstairs to the next landing. Two-thousand feet in the air! Without a rope! Wow!
References:
1. New York Times, Daniel Duane: