Rock Climbing Friction Lab: Edging on Real Rock

Rock Type

Surface Conditions

Moisture 0% (dry)

Foothold Geometry

Foothold slope θ 18°

Lean-out from wall 0°

Result

FOOT HOLDS

μ available

0.85

μ required

0.32

Safety margin (μ_avail − μ_req)

+0.53

How it works

A climbing shoe edging on a sloped foothold is a classic angle of repose problem. Resolve the climber's weight into components along and perpendicular to the hold surface:

Along surface:  F = m g sin(θ_eff)
Into surface:   N = m g cos(θ_eff)
No slip requires: F ≤ μ·N
   → tan(θ_eff) ≤ μ_available

where θ_eff is the foothold's slope plus how far the climber leans their hips out from the wall (leaning out steepens the effective angle the foot must resist). So the foot holds exactly when:

μ_required = tan(θ_eff)
μ_available = μ_base(rock) × (1 − 0.65·moisture) × (chalk ? 1.10 : 1.00)
Grip ⇔ μ_available ≥ μ_required

Rock type sets the dry rubber-on-rock base friction: granite's coarse crystalline grain grips best (μ≈0.85), sandstone is intermediate (μ≈0.65), and fine-grained limestone polishes smooth fastest (μ≈0.50).
Moisture is the single biggest grip-killer on real rock — a film of water can cut available friction by more than half.
Chalk dries sweat off skin and shoe rubber, giving a modest but real friction boost.
Slope + lean-out raise the required friction the same way a steeper ramp does; the cone drawn from the foot is the friction cone — its half-angle is atan(μ_available). Whenever the effective slope points outside that cone, the foot slides.

Real-world relevance: this is exactly how climbers, route-setters and shoe manufacturers reason about "smearing" and "edging" — and why routes graded fine on dry granite become desperate after rain, or on polished limestone after years of traffic.

Friction cone (μ_available) Required slip direction

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