Pulley System Mechanical Advantage
Theoretical and actual MA across fixed/movable/block-and-tackle rigs.
Example
You enter
- Rig block_3
- Pulley efficiency (0-1) 0.95
You get
- Theoretical MA 3
- Actual MA 2.71
- Pulleys 3
Checked against published worked examples from: Naval Education and Training Professional Development and Technology Center (US Navy).
Details, formula, and sources
Formula or tableTheoretical MA = number of supporting rope segments. Actual MA = theoretical × pulley_efficiency^n_pulleys. Fixed pulley redirects but does not multiply force; movable pulley × 2; the block_n options are an n-part tackle (MA n) reeved over n sheaves, the haul line leaving the fixed block. The p^n friction model is a simple approximation: tension tracking (1 + p + ... per sheave) gives a somewhat higher actual MA, and the Army FM 5-125 rule (add about 10% of the load per sheave: 5,000 lb on a 4-part, 4-sheave tackle takes a 1,750 lb pull, MA 2.86) a lower one than p^n at 0.95.
Source and editionClassical mechanics; NFPA 1006 / 1670 by name for rescue context.
Free accessMechanics texts free at university OCW.
What governsEstimate. AHJ and licensed professional govern.
API field namesrig, efficiency, theoretical_ma, actual_ma, pulleys
- Default pulley efficiency 0.95 ball-bearing / 0.90 prussik-mindingmanufacturer typical