A two fixed and one movable pulley combination is a block and tackle arrangement where two sheaves sit fixed to an overhead anchor and one sheave rides on the load, giving a theoretical mechanical advantage of 3 to 1. Unlike a single movable pulley which only doubles your input force, this layout supports three rope segments under the load so each one carries a third of the weight. You pull more rope per unit of lift, but you only feel a third of the load at your hands. Riggers use it to lift 200 to 400 kg drops by hand without a winch.
Two Fixed and One Movable Pulley Combination Interactive Calculator
Vary the load, lift height, and sheave efficiency to see haul force, rope travel, and real mechanical advantage for a 3:1 pulley tackle.
Equation Used
This calculator uses the worked example relationship for a two-fixed, one-movable pulley tackle: three supporting rope falls give an ideal mechanical advantage of 3:1, so each fall carries W/3 and pulling 3 m of rope lifts the load 1 m. Reducing sheave efficiency lowers the effective mechanical advantage as 3 * eta^3.
- Three rope falls support the movable pulley and load.
- At 100% sheave efficiency the theoretical mechanical advantage is 3:1.
- Efficiency is applied once per sheave, matching the article note that three inefficient sheaves reduce real MA.
- Load W is entered in consistent force units.
How the Two Fixed and One Movable Pulley Combination Actually Works
The geometry is straightforward. Three rope segments share the load: two run between the fixed sheaves and the movable block, and the third is your hauling line coming off one of the fixed pulleys. The load hangs from the movable block. Because the load is supported by three parallel rope falls, each fall carries roughly W/3, so the force you apply at the hauling end is also W/3 — minus friction. That is the line pull ratio in action. The trade is distance: to raise the load 1 metre you must pull 3 metres of rope through your hands.
Why two fixed and one movable instead of one fixed and two movable? Both arrangements give 3:1 mechanical advantage on paper, but a two-fixed configuration keeps the heavy hardware up at the anchor and the lighter movable block down on the load. That matters when you're lifting overhead — less mass swinging around at head height, and the hauling line exits at the anchor where you can route it cleanly to a belay or cleat. The compound pulley system is also easier to inspect because both fixed sheaves stay at eye level when you're on a ladder.
Tolerance and condition matter more than people expect. Sheave diameter should be at least 8× the rope diameter — if you crowd a 12 mm rope onto a 60 mm sheave you crush the lay and rope efficiency drops from around 95% per sheave to under 88%. Stack three sheaves at 88% and your real mechanical advantage falls from 3.0 to about 2.05. The rigging hoist feels heavy and you'll swear someone added weight to the load. Common failure modes: a seized sheave bearing (rope slides instead of rolling — efficiency collapses), a fouled fall where two ropes cross over each other inside the block, and undersized becket attachment on the movable block letting the lifting block twist under load.
Key Components
- Upper (fixed) double block: Houses the two fixed sheaves on a common axle, anchored to the overhead beam or hook. Sheave-to-rope diameter ratio should be 8:1 minimum for fibre rope, 16:1 for wire rope. The block must be rated for the full load — not a third of it — because all three rope tensions sum at this anchor.
- Lower (movable) single block: Carries the load on a single sheave plus a becket (a fixed eye where the dead-end of the rope ties off). The becket is what makes this a 3:1 instead of a 2:1 system — it adds the third supporting fall. Becket strength must match sheave strength; cheap blocks often skimp here.
- Sheaves: Grooved wheels that turn on bushings or sealed bearings. Groove radius should be 1.05 to 1.10× rope radius — too tight pinches the rope, too loose lets it jump the groove. Bronze bushings give 92–95% efficiency per sheave; sealed ball bearings give 96–98%.
- Hauling line / rope: Typically 10–14 mm three-strand polyester or double-braid for hand-hauled work. Working load limit should be at least 5× the per-fall load (so 5 × W/3). For a 300 kg lift that means each fall sees 100 kgf and the rope WLL needs to be ≥ 500 kgf.
- Becket attachment point: Where the rope dead-ends onto the lower block. Use a bowline or a proper thimble-and-shackle termination — never a clove hitch, which slips under cyclic load. The becket carries one full fall of tension, identical to the other two falls.
- Anchor hook or shackle: Connects the upper block to the structure. Must be rated for the full load plus a dynamic shock factor of 2× for hand-hauled lifts. A 300 kg static load needs a 600 kgf-rated shackle minimum.
Industries That Rely on the Two Fixed and One Movable Pulley Combination
This configuration shows up wherever you need to lift a few hundred kilos by hand and a winch is overkill or unavailable. The 3:1 ratio is the sweet spot for human-powered hoisting — a fit adult can sustain about 25 kgf on a hauling line indefinitely, so 3:1 puts you comfortably in the 75 kg lift range, and short bursts get you into the 200–300 kg territory. Below 3:1 you run out of arm strength fast; above 4:1 the rope length and friction stack-up make the system sluggish.
- Theatre rigging: Counterweight fly systems on Broadway-style stages use 3:1 tackles for spot-line cues — lifting a 180 kg lighting truss above the proscenium during scene changes at the Stratford Festival Theatre.
- Marine / sailing: Mainsheet tackles on cruising sailboats — a Harken 57 mm triple/double block setup gives 3:1 purchase to trim a mainsail on a 35-foot Catalina against 250 kgf of sheet load.
- Arborist tree work: Lowering large limbs during removal — a Petzl Maestro plus a 3:1 mechanical advantage rope tackle controls a 200 kg oak limb descent at a residential takedown in Asheville NC.
- Warehouse / small workshop: Hand-hauled hoists for engine pulls — lifting a 270 kg small-block Chevy out of a project car at a backyard restoration shop without buying a chain hoist.
- Heritage construction: Lifting timber framing components — a traditional gin-pole rig with a 3:1 lifting block raised oak top plates on a timber-frame barn raising in Vermont.
- Film and TV grip work: Raising lighting and rigging hardware on set — grips use 3:1 tackles to position a 150 kg Condor truss arm extension above a soundstage at Pinewood Toronto.
The Formula Behind the Two Fixed and One Movable Pulley Combination
The formula tells you how much force you need at the hauling line to lift a given load, accounting for sheave friction. The clean theoretical answer is W/3, but real rigging never gives you that. At the low end of typical sheave condition — old bronze bushings, dirty grooves — per-sheave efficiency drops to around 88% and your effective mechanical advantage falls below 2.1. At the high end with sealed ball-bearing blocks like Harken or Ronstan series, you get 97% per sheave and your effective MA reaches about 2.83. The sweet spot for hand-hauled work sits around 92–94% per sheave, which is what well-maintained Garhauer or CMI blocks deliver in normal service.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Fhaul | Force required at the hauling line | N (or kgf) | lbf |
| W | Weight of the load being lifted | N (or kgf) | lbf |
| η | Efficiency per sheave (0.88 to 0.98 typical) | dimensionless | dimensionless |
| n | Number of supporting rope falls (3 for this configuration) | dimensionless | dimensionless |
| MAreal | Real mechanical advantage = ηn × n | dimensionless | dimensionless |
Worked Example: Two Fixed and One Movable Pulley Combination in a museum specimen mount install
You're rigging a 3:1 hand-hauled tackle from a steel I-beam above the central atrium of a regional aquarium in Halifax to lift a 285 kg fibreglass orca model from the floor up to a 7 m display height. The upper block is a Harken 75 mm double; the lower is a Harken 75 mm single with becket. You want to know what force a single rigger has to sustain on the hauling line, and how that changes if the blocks are dry and dirty versus freshly serviced.
Given
- W = 285 kgf
- n = 3 rope falls
- η (nominal, serviced sealed-bearing block) = 0.96 per sheave
- Lift height = 7 m
Solution
Step 1 — compute the theoretical (frictionless) hauling force at nominal condition:
Step 2 — apply the real per-sheave efficiency at nominal serviced condition (η = 0.96 across 3 sheaves):
That's the nominal answer with fresh blocks. 107.5 kgf is more than one rigger can sustain — you need two haulers on the line, or a tail-wrap on a cleat to hold between pulls.
Step 3 — at the low end of the typical operating range (dirty bronze-bushed blocks, η = 0.88), efficiency collapses:
That's the difference between a manageable two-rigger lift and a three-rigger lift. You can feel the system bog down — the rope drags, sheaves squeal, and the load creeps up in jerks rather than smoothly.
Step 4 — at the high end of the typical operating range (premium sealed ball-bearing blocks like Harken Black Magic, η = 0.98):
Going from low-end to high-end shaves nearly 40 kgf off the rigger's effort — a 28% reduction. That's why serviced blocks earn their cost on any lift over 200 kg.
Result
Nominal hauling force is approximately 107. 5 kgf with serviced sealed-bearing blocks. In practice that means two riggers on the line, or one rigger with a cleat hitch to belay between hauls — a single person cannot sustain 107 kgf for the duration of a 7 m lift. At the low end of typical operating condition (dirty blocks) you climb to 140 kgf which forces a third rigger; at the high end (premium serviced blocks) you drop to 101 kgf which is on the edge of two-person territory. If your measured haul force runs higher than the predicted 107.5 kgf, look for: (1) a fouled fall where one of the three rope segments has wrapped over another inside the upper block, instantly cutting effective MA by roughly a third; (2) a seized sheave on the movable block — spin-test it before lifting, you should get at least 3 free revolutions from a hand flick; (3) the rope diameter mismatched to sheave groove radius, pinching the lay and bleeding force into rope deformation rather than lift.
Two Fixed and One Movable Pulley Combination vs Alternatives
The 3:1 with two fixed and one movable competes against a single movable pulley (2:1) and a 4:1 double-and-double tackle. Each one trades off differently on hauling force, rope length, friction stack, and hardware cost. Pick based on the load, the lift height, and how many hands you have on the line.
| Property | 2 Fixed + 1 Movable (3:1) | Single Movable Pulley (2:1) | Double + Double Block (4:1) |
|---|---|---|---|
| Theoretical mechanical advantage | 3:1 | 2:1 | 4:1 |
| Real MA with serviced blocks | ~2.65–2.82 | ~1.88–1.96 | ~3.39–3.69 |
| Practical load range (hand-hauled, single rigger) | 75–200 kg | 50°125 kg | 100–280 kg |
| Rope length pulled per metre lifted | 3 m | 2 m | 4 m |
| Hardware cost (quality blocks) | $180–400 | $60–150 | $260–550 |
| Friction-loss per added sheave | 3 sheaves total | 2 sheaves total | 4 sheaves total |
| Lift speed at fixed haul rate | Moderate | Fast | Slow |
| Best application fit | 200–300 kg overhead lifts, theatre, marine sheets | Light loads, simple direction-changers | Heavy hand lifts above 250 kg |
Frequently Asked Questions About Two Fixed and One Movable Pulley Combination
Almost always it's a fouled fall — one rope segment has crossed over or under another inside the upper block, pinching against the cheek plate. The friction spikes, sometimes by 40–50%, and you lose roughly a full unit of mechanical advantage.
Diagnostic check: lower the load slightly, look up into the gap between the two fixed sheaves, and trace each rope segment from haul end to becket. All three should run in clean parallel lines with no twist. A second cause is a swivel head on the upper block that's seized — if the block can't rotate to align with the haul direction, the rope enters the sheave at an angle and you bleed force into side-loading.
Put the heavier hardware where it doesn't have to travel. The two-fixed configuration keeps the double block stationary at the anchor and only the lighter single block rides up and down on the load. That means less mass to lift (the movable block is part of the load you're hauling), less swing risk overhead, and the haul line exits at the anchor where you can belay it cleanly to a cleat or hitch.
Use one-fixed-two-movable only when the geometry forces it — for example, when the anchor point is too narrow to fit a double block, or when you need the haul line to come off the load end (rare, but happens in some hauling-from-below cave rigging).
Rope stiffness. The formula assumes the rope flexes freely around each sheave, but stiff rope — especially new double-braid before it's broken in, or any rope colder than about 5 °C — resists bending and that resistance shows up as added haul force. Bend losses can add 3–5% per sheave on top of the bearing efficiency, so across 3 sheaves you can easily see 10% extra.
Fix: flake the rope out and run it through the system 5–10 times under light load before the real lift. For cold-weather work, store the rope warm until you're ready to rig.
You can, but understand the cost. A rope running over a steel carabiner has an efficiency of roughly 50–60%, compared to 95%+ for a proper sheave. Drop one sheave for a carabiner and your effective MA on a 3:1 falls from about 2.7 down to 1.6 — barely better than a single movable pulley, and you've added the work of pulling more rope.
For a one-time light lift under 50 kg it doesn't matter. For anything over 150 kg, the carabiner shortcut means you're working harder than you would with a 2:1 from quality blocks. Buy or rent the proper hardware.
You're feeling the cube of the rope friction working backward against you. When you stop pulling, the load wants to fall, and the rope tries to run backward through the system. Bearing friction now helps you (it resists backward motion just like it resisted forward motion), but it's not enough by itself → under static hold you still need to apply roughly W / MAreal at your hands.
For a 285 kg load that's still over 100 kgf of grip force. Always belay the haul line to a cleat or use a progress-capture device (a Petzl Micro Traxion or a simple prusik) between pulls. Hand-holding is for the active haul phase only.
You need clearance equal to the lift height plus the stacked length of both blocks plus rope termination space. For a 7 m lift with 75 mm Harken blocks, the upper block plus shackle eats about 250 mm, the lower block plus the load attachment eats another 300 mm, and you want at least 200 mm of clear rope above the lower block at full lift to keep the becket from jamming into the upper sheaves.
So 7 m of lift needs roughly 7.75 m of clear vertical space from load attachment to anchor point. Run out of clearance and the lower block crashes into the upper block — called "two-blocking" — and you either jam the system or shock-load the anchor. Plan the geometry before you rig.
References & Further Reading
- Wikipedia contributors. Block and tackle. Wikipedia
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