Historical sources document vertical water-raising wheels with buckets around their rims. This calculator evaluates only an explicit ideal bucket-delivery count and an assumed lift height—not a site or wheel-performance model.
Vertical Bucket Paddle Wheel Interactive Calculator
Enter wheel diameter, bucket count and volume, rpm and an assumed usable-fill fraction. Results are an ideal one-delivery-per-bucket calculations; they do not predict a stream-driven wheel or actual pumping performance.
Equation Used
- Every entered bucket completes one delivery per wheel revolution.
- Usable delivered volume per bucket equals entered bucket volume multiplied by entered fill fraction.
- Wheel rpm is prescribed rather than predicted from current, head, paddles or load.
- Lift height is defined as 0.85 times wheel diameter.
- Water density is 1000 kg/m³ and gravitational acceleration is 9.81 m/s².
- Leakage, spillage, incomplete pickup, bucket residence time, trough geometry, backwater, torque, drag, bearings, efficiency, structure and safety are omitted.
Historical Water-Raising Topology
A Smithsonian historical bulletin identifies current wheels used for raising water as Persian wheels, norias and tympanums. A National Park Service record for the Captain Stoffel Waterwheel documents a large river-driven wheel fitted with steel buckets and used for irrigation. These references support the topology, not the calculator's ideal performance assumptions.
What This Calculator Represents
The tool counts one assumed delivery per bucket per revolution, applies an entered usable-fill fraction, converts the rate to a daily volume and evaluates ideal water power at an assumed lift height of 0.85D.
Ideal Bucket-delivery Calculations
rim speed=pi D rpm/60
daily volume=86.4Q
assumed H=0.85D
ideal water power=rho g (Q/1000)H
Q is in litres per second before conversion to cubic metres per second in the power equation.
Worked Idealized Example
For D=6 m, N=24, Vb=15 L, 3 rpm and eta=0.75, the ideal carried-volume rate is 13.5 L/s, rim speed is about 0.94 m/s, daily volume is 1,166 m³/day and ideal water power at H=5.1 m is about 675 W.
Model Boundary
- Calculated: ideal delivery count, rim speed, daily-volume conversion and rho g Q H at an assumed height.
- Illustrated: vertical bucket wheel, lower pickup region and upper delivery trough.
- Not calculated: driving current or head, actual rpm, bucket filling and discharge, spillage, leakage, drag, torque, efficiency, required shaft power, backwater, structure, foundations or safety.
Frequently Asked Questions
Does the calculator predict wheel rpm?
No; rpm is entered.
Is fill percentage an efficiency prediction?
No; it is an assumed usable delivered fraction.
Is 0.85D a measured lift?
No. The calculator assumes lift height is 0.85 times wheel diameter.
Is the reported power required shaft power?
No; it is ideal rho g Q H water power.
Are leakage and spillage included?
No.
Can this size a real irrigation wheel?
No; site flow, load, losses, structure and safety require separate engineering.
References
- U.S. National Museum Bulletin 119: historical water-raising current wheels, including Persian wheel, noria and tympanum.
- National Park Service, Captain Stoffel Waterwheel nomination: bucket count, water-lifting use and documented operating context.
- U.S. Department of Energy pump test procedure: hydraulic output power relation P=rho Q H g.
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