A horse-powered hoisting drum converts the motion of an input sweep into winding-rope travel. Hiscox’s example includes two selectable gear speeds and a disengaging clutch. The calculator below is a separate direct-coupled comparison: it assumes the sweep and drum turn together and calculates circumference and ideal force ratios without those gears.
Horse-power Hoisting Drum Interactive Calculator
Explore one-turn input path, first-layer rope travel and the ideal reciprocal force/path ratio for two rigidly coupled radii.
Equation Used
- Input sweep and drum share one rigid shaft and complete the same angular turn.
- Drum effective radius remains constant as if on the first layer or an ideal zero-thickness rope.
- Tangential input and rope forces are compared quasistatically with no losses.
- No payload, acceleration, braking, rope, shaft, bearing, frame, foundation, control, guarding, human-hoisting, animal-welfare or safety calculation.
Abstract geometry only. The model does not size or approve a drum, rope, brake, shaft, structure, drive, animal-powered system or any device that lifts people or loads.
Two rigidly coupled radii
An input point travels around radius Rs while a drum of effective radius Rd turns through the same angle. One full turn gives path lengths 2piRs and 2piRd.
Equating ideal work gives Finput(2piRs)=Frope(2piRd), so Frope/Finput=Rs/Rd. This is an ideal static ratio, not available capacity.
Use as a geometry and work check
The identities illustrate how a larger input radius trades longer input travel for a larger ideal output-force multiple at a smaller drum radius. They can expose reversed ratios in a concept sketch, but cannot approve a hoist or restoration.
Radius and circumference identities
For equal angular motion, the linear travel ratio equals the radius ratio. In an ideal lossless quasistatic comparison, the force ratio is reciprocal to travel: Frope/Finput=Rs/Rd while srope/sinput=Rd/Rs.
The calculator assumes a fixed drum radius. Real wound rope changes the effective radius layer by layer.
Worked example
With Rs=4.0 m and Rd=0.75 m, one input turn covers 25.13 m and ideal first-layer rope travel is 4.71 m. Their ratio is 5.33, so the lossless static rope-force multiple relative to tangential input force is also 5.33.
Scope and limitations
Real systems require verified loads and duty; rope construction, termination, fleet angle and bending fatigue; multilayer winding; drum shell and flange design; shafts, keys, bearings and frames; brakes and redundant load holding; overspeed and end limits; guarding, controls, inspection and applicable hoisting law. Human lifting has additional requirements and is never addressed by this calculator.
Questions
Is the ratio a safe load multiplier?
No. It is an ideal force ratio with no strength, loss or dynamic model.
Why say first-layer travel?
Additional rope layers increase effective drum radius and change both travel and force ratio.
Does it include gears?
No. The two radii are assumed to share one shaft.
Historical source and calculation basis
Gardner D. Hiscox, Mechanical Movements, Powers, Devices and Appliances, entry 1210, describes a two-speed horse-power hoisting drum with selectable driving gears and a gear clutch.
The calculator instead assumes direct 1:1 angular coupling. Its circumference and ideal-work identities do not specify the historical gearing, available pull, load capacity or braking performance.
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