Recovery Winch Lab: Mechanical Advantage, Snatch Blocks, Anchors and Stuck Vehicles

Blender 5.2 + Three.js

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T_in - F_out - R_break - v -

line load / WLL

01.0

Scenarios

Live numbers

Graph

Weakest-link check

Experiments

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Safety. This is a physics-teaching model of a generic recovery truck, not an operating manual. Winch lines, chains and straps store large elastic energy: when a component fails the line can whip back along its length. Real recoveries use rated gear, a damper blanket over the line, a clear zone and trained crews.

The science

Teaching model. Generic, unbranded equipment; numbers are textbook-order and illustrative, not data for any real winch, rope or vehicle.

Mechanical advantage. A tackle with n rope segments on the moving block gives ideal F_out = n F_in; the line must be hauled s_in = n s_out (work in = work out). With sheave efficiency eta (about 0.90-0.95 per sheave, approximate) the segment tensions are T_j = T_in eta^j, so F_out = T_in (1 - eta^n)/(1 - eta) and eta_tot = F_out/(n T_in).
Line stretch. Rope stiffness EA/L; the haul-end compliance of the system is sum a_j^2 L_j / EA (Castigliano), which sets how fast tension builds while the winch takes up line.
Winch drum layers. Constant drum torque T_m = F_1 r_1, so the pull on layer k is F_k = T_m / (r_1 + (k-1) d) and line speed v = omega r_k; power P = F v = T_m omega stays constant. Hydraulic pressure p = 2 pi T_shaft / (D eta_m) (illustrative gearing and motor size). At relief pressure the drum stalls.
Stuck vehicle. Resistance per axle W_i f (1 + 1.2 z / D_w) with mud rolling coefficient f = 0.3-0.5 plus the slope term W sin(theta) from the rut ramp; breakout needs beta R_roll + S + W sin(theta) (beta = 1.3, suction S fades after a few centimetres of travel). Illustrative, not a validated terramechanics model (see Bekker for that).
Snatch recovery. Rope as spring k = EA/L with hysteresis damping: 1/2 m v^2 = 1/2 k x^2 gives T_peak = v sqrt(m k) against an immovable load; for two free masses use the reduced mass. A steel chain or wire rope (high k) reaches several times the strap's peak for the same speed; a kinetic strap (low k, long stretch) spreads the load over time. Dynamic load factor DLF = T_peak / static breakout pull.
Snap-back. Stored energy E = T^2/(2k) is released if a link fails; the free end can be thrown back with speed of order sqrt(2 eps E / m) (eps about 0.3 assumed). A damper blanket adds mass and weighs the line down; it does not remove the energy. Numbers only, no scenes of harm.
Anchors. Deadman (buried log): Rankine passive pressure p = gamma z K_p + 2 c sqrt(K_p) with K_p = tan^2(45 + phi/2), resultant F_h = 1/2 gamma (H_b^2 - H_t^2) L K_p + 2 c (H_b - H_t) L sqrt(K_p); with an upward pull at angle psi the allowable load is limited by F_h / cos psi and by uplift U / sin psi. Screw anchor: helix bearing A_h (c N_c + gamma H N_q) plus shaft friction, reduced when the pull is not aligned with the shaft (lateral soil resistance). Vehicle anchor: mu W with brakes on. Soil values are typical textbook figures.
Block on an anchor. Two legs with tension T and angle alpha between them load the anchor with 2 T cos(alpha/2): 2T for a hairpin (0 deg), T sqrt(2) at 90 deg, about T at 120 deg, 0 for a straight run.
Weakest link. Each component's working load limit is WLL = MBS / SF (typical design factor 5, shown as practice, not a rule); the system fails at the lowest MBS_i / g_i, where g_i is the share of the haul tension that reaches component i.
Simplifications. Quasi-1D axis motion, rigid vehicles, no rope bending or sheave wrap loss beyond eta, no soil strain-softening, line angle effects other than the redirect case are neglected. Not affiliated with any equipment maker.