Wedge Splitting Force and Self-Locking

a splitting maul or log-splitter wedge, a wedge jack, a machine-leveling wedge, or a shim. A driving force along the centerline of a symmetric wedge of included angle alpha (half-angle b = alpha/2) becomes a spreading force on each face; with dry friction the advantage is (cos b - mu sin b)/(sin b + mu cos b). Frictionless that is cot b - a sharp wedge multiplies hugely - but a wedge lives on friction: much of the drive is spent overcoming it (a 30-degree wedge at mu 0.3 gives 1.6x, not 3.7x), and that same friction is what lets a driven wedge or shim STAY put. It self-locks when the half-angle is under the friction angle, b < atan(mu): a 15-degree half-angle holds under mu 0.3 (friction angle 16.7 degrees) but backs out under a slicker mu 0.2. A blunt wedge can multiply less than 1 or jam entirely. Ideal rigid wedge, dry friction, quasi-static; the material's splitting resistance and impact driving are separate. A planning aid; Machinery's Handbook and the tool maker govern.

b = alpha/2; MA = (cos b - mu sin b)/(sin b + mu cos b); spreading = P x MA; frictionless MA = cot b; self-locks when b < atan(mu).

Wedge statics - spreading force (cos b - mu sin b)/(sin b + mu cos b) and self-locking at b < atan(mu) (standard mechanics; Machinery's Handbook), by name.

Wedge statics is a standard published result; the driving force, wedge angle, and friction coefficient are the user's inputs.

Estimate. AHJ and licensed professional govern.

Field names used by the API: driving_force_lb, included_angle_deg, friction_coefficient, spreading_force_lb, ideal_mechanical_advantage

• Advantage MA = (cos b - mu sin b)/(sin b + mu cos b), b the half-angle; frictionless cot bMachinery's Handbook
• Self-locking self-locks (stays driven) when b < atan(mu); backs out otherwisefriction mechanics
• Scope rigid wedge, dry quasi-static friction; splitting resistance, impact driving, wedge strength are separatescope of this tile