BIZOMAT MAKEOS · Mechanics
Windlass, Gear Hoist and Differential Pulley Effort
What effort lifts this load with a windlass, geared winch, rope block or differential chain pulley?
Effort and mechanical advantage for the handbook’s simple lifting machines: wheel and axle, a windlass driven through up to two gear pairs, a block and tackle with several parts of rope, a differential chain pulley and a Chinese (differential) windlass, with an overall efficiency.
Open the calculatorRuns in your browser. No account needed.
How this tool works
Inputs, units and where to find them
| Input | Unit | Typical source |
|---|---|---|
| Machine | choice | Choose the lifting machine. |
| Load to lift | N | Weight to be lifted. |
| Crank, hand-wheel or large sheave radius | mm | Wheel-and-axle wheel or crank radius; for the differential pulley and Chinese windlass, the larger sheave or drum radius. |
| Drum or small sheave radius | mm | Drum radius; for the differential pulley and Chinese windlass, the smaller sheave or drum radius. |
| Gear ratio, first pair (driven ÷ driver) | Speed reduction of the first gear pair. | |
| Gear ratio, second pair (1 = none) | Speed reduction of the second gear pair. | |
| Parts of rope supporting the load (block) | Number of rope parts carrying the moving block. | |
| Crank radius (Chinese windlass) | mm | Radius of the crank turning a Chinese windlass. |
| Overall efficiency | % | Overall efficiency from friction (differential pulleys are low, which keeps them self-sustaining). |
What each input means
Open an input to see what it is, its units, the worked example and the common mistakes, with a small diagram.
What this means: Machine
- What it is
- The kind of lifting machine. Each one uses only the radii, gear ratios or rope parts that apply to it; the other inputs are ignored.
- Units and format
- Choose one of 5 options from the list: Wheel and axle; Geared windlass (up to two gear pairs); Block and tackle; Differential chain pulley; Chinese windlass.
- Example
- The form opens with “Differential chain pulley” selected as a worked example. Choose the option that matches your case.
What this means: Load to lift
- What it is
- The weight to be raised, including the hook, slings and any moving block.
- Units and format
- Enter a number in N: newtons. The form accepts 0.000001 N or more. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 10000 N as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The effort rises in proportion.
- Get it right
- Enter a force in newtons: multiply a mass in kg by gravity.
What this means: Crank, hand-wheel or large sheave radius
- What it is
- For the wheel and axle and the geared windlass, the radius of the crank or hand-wheel where the effort is applied; for the differential chain pulley and Chinese windlass, the radius of the larger sheave or drum.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 150 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Drum or small sheave radius
- What it is
- For the wheel and axle and the geared windlass, the radius of the drum the rope winds on; for the differential chain pulley and Chinese windlass, the radius of the smaller sheave or drum.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 135 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Get it right
- For the differential machines the effort depends on the small difference R − r, so measure both radii carefully to the rope or chain centre line.
What this means: Gear ratio, first pair (driven ÷ driver)
- What it is
- The speed reduction of the first gear pair of a geared windlass: teeth on the driven gear divided by teeth on the driving gear.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 1000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The effort falls in proportion to the product of the two gear ratios.
What this means: Gear ratio, second pair (1 = none)
- What it is
- The speed reduction of a second gear pair in a geared windlass, driven teeth over driver teeth; 1 when there is only one pair.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 1000. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 1 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
What this means: Parts of rope supporting the load (block)
- What it is
- The number of rope falls holding up the moving (lower) block of a block and tackle; a rope end tied to the moving block counts as one.
- Units and format
- Enter a plain number with no unit. The form accepts 1 to 40. Use a whole number. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 4 as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The ideal effort is the load divided by this number.
- Get it right
- Do not count the hauling part where it leaves a fixed block, because it does not support the moving block.
What this means: Crank radius (Chinese windlass)
- What it is
- For a Chinese (differential) windlass, the radius of the crank handle that turns the two drums.
- Units and format
- Enter a number in mm: millimetres. The form accepts 0.000001 mm to 100000 mm. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 300 mm as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The effort is inversely proportional to the crank radius.
What this means: Overall efficiency
- What it is
- The share of the input work that reaches the load after friction in the sheaves, gears and bearings, taken for the whole machine; the ideal effort is divided by it.
- Units and format
- Enter a number in %: percent: the number is read as a percentage, so type 8 for 8 %. The form accepts 1% to 100%. Required: the tool does not calculate until every input is valid.
- Example
- The form opens with 35% as a worked example. It is an illustration, not a recommended value: replace it with your own figure.
- Effect on the result
- The effort is inversely proportional to the efficiency.
- Get it right
- Type the percentage itself, not a fraction; take it from the maker’s data or a test lift.
Method and formulas
- Wheel and axle: F = W r ÷ R. Geared windlass: F = W r ÷ (R × gear ratios).
- Block and tackle: F = W ÷ n.
- Differential pulley: F = W (R − r) ÷ 2R. Chinese windlass: F = W (R − r) ÷ 2 × crank; the load rises half the difference of the drum circumferences per turn.
- Effort with friction = ideal effort ÷ efficiency.
- Example: a 10000 N load on a differential pulley of 150 and 135 mm needs 1,428.6 N.
Limitations
- Static lifting; acceleration and rope stiffness are excluded.
- Use certified lifting equipment within its rated load.
- Example values are illustrations. Replace them with values for your actual task.
Typical uses
- Check the hand effort on a chain block or winch
- Compare hoisting arrangements for a lift
- Estimate hook travel per turn of a hand wheel
Who it is for
- Rigging supervisors
- Maintenance fitters
- Machine designers
What you get
- Effort required
- Mechanical advantage
- Load travel per turn or per unit of effort travel
Interpreting the result
- A differential pulley with low efficiency holds the load without a brake; check that the chosen machine is self-sustaining if it must be.
References
- Machinery’s Handbook, 29th edition (Industrial Press, 2012), printed pp. 170–171. Topic reference; no source tables or recommended settings are reproduced.
BIZOMAT tools are screening and decision-support utilities. Verify important financial, engineering, safety, legal or operational decisions using appropriate professional standards and your organisation’s approved data.
Open the Windlass, Gear Hoist and Differential Pulley Effort calculator