Wedge Splitting Force and Self-Locking
The splitting, lifting, or shimming force of a wedge.
Example
You enter
- Driving force along the wedge (lb) 100
- Included (total) wedge angle (deg) 30
- Friction coefficient mu 0.3
You get
- Spreading force (lb) 80.96
- Ideal mechanical advantage 1.866
No published worked example is on file for this calculation. It is checked against a hand-worked derivation of its method and an independent reference test.
Details, formula, and sources
Scopea 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)/(2 (sin b + mu cos b)). Frictionless that is 1/(2 tan 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 0.81x, not 1.87x), 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.
Formula or tableb = alpha/2; P = 2 N (sin b + mu cos b); per-face spreading N (cos b - mu sin b), so MA = (cos b - mu sin b)/(2 (sin b + mu cos b)); spreading = P x MA; frictionless MA = 1/(2 tan b); self-locks when b < atan(mu).
Source and editionWedge statics - spreading force per face (cos b - mu sin b)/(2 (sin b + mu cos b)) and self-locking at b < atan(mu) (standard mechanics; Machinery's Handbook), by name.
Free accessWedge statics is a standard published result; the driving force, wedge angle, and friction coefficient are the user's inputs.
What governsEstimate. AHJ and licensed professional govern.
API field namesdriving_force_lb, included_angle_deg, friction_coefficient, spreading_force_lb, ideal_mechanical_advantage
- Advantage MA = (cos b - mu sin b)/(2 (sin b + mu cos b)), b the half-angle; frictionless 1/(2 tan b)Machinery'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