The Chinese shaft derrick illustrated by Hiscox uses a differential windlass below two overhead guide sheaves. The guides route the rope above the shaft mouth, allowing the bucket’s moving block to rise above the opening.
Chinese Shaft Derrick Interactive Calculator
Set the handle radius, the two effective drum radii and the applied tangential effort. One drum takes in more rope than the other pays out, lifting the bucket block by half the net rope difference.
Equation Used
- Rigid shared drum shaft and constant effective winding radii.
- One rope winds onto the large drum and off the small drum.
- Upper guide sheaves are fixed; the bucket sheave moves with the load.
- All entered effort is tangential at the handle radius.
- R must exceed r for the depicted lifting direction. Equal radii produce no differential lift.
Ideal differential-windlass calculation with two supporting rope legs. Upper guide sheaves redirect the rope above the shaft mouth. Numerical results are force and travel relationships, not safe working load ratings.
A differential windlass below overhead guides
Hiscox figure 41 shows the shaft derrick beside the ordinary Chinese windlass in figure 40. Its added upper sheaves redirect the rope so the bucket can rise above the pit opening.
The larger drum winds rope in while the smaller drum pays rope out. Both turn on the same shaft. The net reduction in free rope is shared by the two legs supporting the moving bucket block.
The animation makes the rope route explicit: up from one drum, over the left fixed guide, under the moving block, over the right fixed guide and down to the second drum. The two guides change direction; they do not create an additional load-multiplication stage.
Raising a bucket above a shaft mouth
Placing guide sheaves overhead separates the position of the winding shaft from the highest attainable bucket position. The resulting arrangement can be studied as a differential hoisting mechanism.
This calculator describes its ideal force and distance relationships. It does not specify a lifting installation, personnel hoist, brake or structural rating.
Deriving the lift and force ratio
In one shaft revolution, the large drum takes in 2 pi R of rope and the small drum releases 2 pi r. Net take-up is 2 pi (R-r). Because the load block has two supporting legs, its rise is pi (R-r).
A tangential effort at handle radius a moves through 2 pi a per turn. Equating ideal input work with load times rise gives the force ratio 2a/(R-r). Total effort is the number of equal contributors multiplied by force each.
The input torque is total effort times handle radius. Force is entered in lbf; the displayed torque converts radius from metres to feet using 0.3048 m/ft. These expressions assume constant effective drum radii and exclude losses.
Default differential pair
With a 0.5 m handle, 0.25 m large drum and 0.20 m small drum, the ideal force ratio is 20:1. One 30 lbf tangential effort corresponds to an ideal supported load of 600 lbf.
The bucket rises about 0.157 m for one shaft turn. Input torque is about 49.2 lbf·ft. Making the drum radii closer together increases ideal force multiplication while reducing rise per turn.
When the radii are equal, net rope take-up is zero. The calculator marks that pair invalid because it gives no differential lifting travel.
Ideal multiplication does not establish capacity
Rope and bearing losses alter the required effort, while winding layers alter effective drum radius. Frame, shaft, sheave, rope and attachment strengths place separate limits on use.
The illustration scales vertical travel and the handle for readability. It reverses after one shaft turn to demonstrate raising and lowering. It does not simulate load dynamics, braking or a complete winding-layer arrangement.
Calculator questions
Why are two drum radii needed?
The net take-up comes from the difference in their circumferences. A single-radius capstan calculation describes a different mechanism.
Do the upper guides double the force again?
No. They are fixed direction-changing sheaves. The moving bucket block has the two supporting rope legs used in the calculation.
Why does a smaller radius difference increase the force ratio?
It reduces load travel per handle revolution. In the ideal work balance, less output travel corresponds to greater force multiplication.
Can I treat ideal supported load as a rated lifting capacity?
No. The model does not evaluate losses, braking or the strengths of the lifting components.
References & Further Reading
- Hiscox, Mechanical Movements, Powers, Devices and Appliances, printed page 25, figures 40–41: Chinese differential windlass and shaft derrick with overhead guides.
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