Also in: Disaster Response and Recovery
Rope Rescue Mechanical Advantage
Theoretical and actual MA across rig types with pulley losses, tracking the tension through each pulley.
Example
You enter
- Rig 4:1
- Pulley efficiency (0-1) 0.9
- Load (lb) 600
You get
- Theoretical MA 4
- Actual MA (after pulley losses) 3.439
- Haul force 174 lb
- Pulleys 3
Checked against published worked examples from: CMC (CMC Rescue); Rescue Dynamics (Cyril Shokoples).
Details, formula, and sources
Scopea 3:1 Z-rig at 90% pulleys is 2.71:1, at 70% 2.19:1. Simple rigs; the rescue team's rigging governs.
Formula or tableActual MA by tension tracking for a simple rig: 1 + p + p^2 + ... + p^n for n pulleys of efficiency p (Rescue Dynamics: 3:1 = 2.71 at p 0.90, 2.19 at 0.70, 1.65 at a 0.45 carabiner). Haul force = load / actual_MA. Rigs 1:1, 2:1, 3:1 (the Z-rig), 4:1, 5:1; the T_method and 5:1_piggyback options compute a simple 5:1 (the T-method is a way to analyze any rig, and a complex or piggyback rig needs its own tension tracking).
Source and editionNFPA 1006 / NFPA 1670 by name; CMC Rope Rescue Manual + Rigging for Rescue training materials by name.
Free accessNFPA standards read-only at nfpa.org/freeaccess; NFA rope-rescue materials free at usfa.fema.gov.
What governsEstimate. AHJ and licensed fire protection engineer govern.
API field namesrig, efficiency, load_lb, theoretical_ma, actual_ma, haul_force_lb, pulleys
- Pulley efficiency 0.90 prussik-minding pulley / 0.95 ball-bearing pulley unless user suppliesmanufacturer typical