Sovereignty Module: Multiply the Force
Multiply the Force
Complete Mechanical Advantage: Pulleys, Levers, Inclined Planes, and Lifting Systems
Complete Mechanical Advantage: Pulleys, Levers, Inclined Planes, and Lifting Systems
Simple machines multiply human strength. This campaign covers every mechanical advantage system for construction, logging, and heavy lifting without powered equipment.
Chapter 1: Simple Machines Overview
| Machine | Mechanical Advantage | Formula | Example |
|---|---|---|---|
| Lever (Class 1) | Distance from fulcrum ratio | MA = effort arm / load arm | Pry bar, seesaw, crowbar |
| Lever (Class 2) | Load between fulcrum and effort | MA = effort arm / load arm | Wheelbarrow, nutcracker |
| Lever (Class 3) | Effort between fulcrum and load | MA < 1 (speed advantage) | Fishing rod, tweezers |
| Pulley (single fixed) | 1:1 (direction change only) | MA = 1 | Flagpole, well bucket |
| Pulley (single movable) | 2:1 | MA = 2 | Basic block and tackle |
| Block and tackle | Number of rope sections supporting load | MA = number of lines | Crane, ship rigging |
| Inclined plane | Length / height ratio | MA = slope length / rise | Ramp, loading dock |
| Wedge | Length / thickness ratio | MA = length / width at base | Axe, splitting wedge, chisel |
| Screw | Circumference / pitch ratio | MA = 2πr / pitch | Jack, press, vise |
| Wheel and axle | Wheel radius / axle radius | MA = R(wheel) / r(axle) | Windlass, capstan, winch |
Chapter 2: Block and Tackle Systems
| Configuration | Mechanical Advantage | Rope Needed | Friction Loss | Practical Lift |
|---|---|---|---|---|
| Single fixed pulley | 1:1 | 1× height | ~5% | Direction change only |
| Gun tackle (1 fixed + 1 movable) | 2:1 | 2× height | ~10% | 100 lbs effort lifts 180 lbs |
| Luff tackle (1 double + 1 single) | 3:1 | 3× height | ~15% | 100 lbs effort lifts 255 lbs |
| Double tackle (2 double blocks) | 4:1 | 4× height | ~20% | 100 lbs effort lifts 320 lbs |
| Triple tackle (2 triple blocks) | 6:1 | 6× height | ~30% | 100 lbs effort lifts 420 lbs |
| Compound (tackle on tackle) | Multiply MAs | Varies | High (40%+) | Extreme loads |
Friction rule: Each sheave (pulley wheel) loses approximately 5-10% efficiency. A 4:1 system with 4 sheaves actually delivers about 3.2:1 in practice. Use well-greased bronze or nylon bushings to minimize friction.
Chapter 3: Gin Pole and Derrick
| System | Capacity | Height | Materials | Best For |
|---|---|---|---|---|
| Gin pole (single pole + guy wires) | 500-2,000 lbs | 15-30 feet | Pole, rope, stakes | Lifting to height (construction) |
| A-frame (two poles, apex joined) | 1,000-5,000 lbs | 10-20 feet | Two poles, rope | Heavy lifting, no guy wires needed |
| Tripod (three poles) | 2,000-10,000 lbs | 10-25 feet | Three poles, rope | Very stable, well drilling, heavy |
| Shear legs (two poles, spread base) | 1,000-3,000 lbs | 15-25 feet | Two poles, rope | Moderate loads, easy to build |
| Derrick (mast + boom) | 2,000-20,000 lbs | 20-60 feet | Mast, boom, guy wires | Large construction, rotating |
Gin pole rules: 1. Pole length = 1.5× desired lift height. 2. Minimum 3 guy wires (4 preferred), equally spaced. 3. Guy wire angle: 45° from pole (minimum). 4. Anchor stakes driven 3+ feet deep. 5. Load line runs through pulley at top. 6. Never stand under suspended load.
Chapter 4: Winch and Capstan
| Type | Mechanical Advantage | Construction | Capacity | Speed |
|---|---|---|---|---|
| Simple windlass (hand crank) | R(handle)/r(drum) = 4-8:1 | Drum + crank handle | 200-800 lbs | Moderate |
| Geared winch | Gear ratio × handle ratio = 10-50:1 | Drum + gear train + handle | 500-5,000 lbs | Slow |
| Capstan (vertical drum) | R(bar)/r(drum) × number of bars | Vertical drum + push bars | 1,000-10,000 lbs | Slow |
| Spanish windlass (toggle) | Stick length / rope diameter | Rope loop + toggle stick | 500-2,000 lbs | Very slow |
| Come-along (ratchet) | Internal gear ratio | Purchased or fabricated | 1,000-6,000 lbs | Very slow |
Spanish windlass: Simplest high-force tool. Loop rope around load and anchor. Insert stick through loop. Twist stick to shorten rope (enormous force). Pin stick to prevent untwisting. Used for: pulling stumps, straightening frames, emergency vehicle recovery.
Chapter 5: Inclined Plane and Ramp Systems
| Application | Slope Ratio | Mechanical Advantage | Example |
|---|---|---|---|
| Loading dock ramp | 1:6 to 1:8 | 6:1 to 8:1 | Rolling barrels up ramp |
| Earth ramp (pyramid building) | 1:10 to 1:15 | 10:1 to 15:1 | Dragging stone blocks |
| Screw jack | Circumference:pitch | 50:1 to 200:1 | Lifting buildings, vehicles |
| Wedge (splitting) | Length:width | 4:1 to 10:1 | Splitting logs, quarrying stone |
| Archimedes screw | Pitch × turns | Variable | Lifting water uphill |
Chapter 6: Practical Applications
| Task | Best System | Setup | Capacity Needed |
|---|---|---|---|
| Raising roof beams | Gin pole + block and tackle | Pole at ridge, 4:1 tackle | 500-2,000 lbs |
| Lifting well bucket | Simple windlass | Crank over well | 50-100 lbs |
| Moving boulders | A-frame + chain hoist | Straddle boulder | 2,000-10,000 lbs |
| Pulling stumps | Come-along or Spanish windlass | Anchor to standing tree | 2,000-5,000 lbs |
| Raising walls (timber frame) | Pike poles + gin pole | Multiple helpers + mechanical | 500-3,000 lbs |
| Loading logs onto wagon | Ramp + peavey + rope | Skid ramp at wagon height | 500-2,000 lbs |
| Tensioning fence wire | Spanish windlass | Loop + toggle | 200-500 lbs |
| Hoisting hay to loft | Fixed pulley + rope | Pulley at loft door | 50-200 lbs |
Reference Card
- Block and tackle MA = number of rope lines supporting the load. Count lines at the moving block.
- Each pulley sheave loses 5-10% to friction. A 4:1 system delivers ~3.2:1 in practice. Grease bearings.
- Gin pole: 3+ guy wires at 45°, pole 1.5× lift height, NEVER stand under suspended load.
- Spanish windlass: simplest high-force tool. Rope loop + stick. Twist for enormous pulling force.
- Inclined plane: longer ramp = less force needed. 1:10 slope means 100 lbs of push moves 1,000 lbs.
- Tripod: most stable lifting frame. Three poles, lashed at apex. No guy wires needed. Great for wells.
- Windlass MA = handle radius ÷ drum radius. 12-inch handle on 2-inch drum = 6:1 advantage.
- Safety: always use rated rope/chain. Working load = 1/5 of breaking strength (5:1 safety factor).
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