A Pelton runner receives a free water jet in a sequence of split buckets. A central ridge divides the incoming flow between two curved cups, turning it back to either side. Explore that geometry in the enlarged cutaway, and use the calculator to estimate force and power at the ideal half-jet-speed condition.
Buckets of a Pelton Water Wheel Interactive Calculator
Change jet speed, flow, relative turning angle and an assumed additional loss multiplier. The ideal model fixes bucket speed at half jet speed. The large view follows the bucket; the inset shows runner context.
Equation Used
- One steady water jet; density 1000 kg/m³.
- Bucket speed fixed at u=V/2, the ideal optimum for this model.
- Two equal streams; relative turning angle measured from the incoming relative-flow direction.
- No relative speed loss in the momentum calculation; an entered multiplier reduces power afterward.
- Force is runner-average tangential force, not a bucket impact or strength calculation.
- Manufactured bucket dimensions, runner diameter, RPM and transient water behavior are not solved.
The enlarged split-cup view shows how the central splitter divides the jet and the two cups turn the flow. Turning angle is measured in the bucket frame; the loss multiplier is an assumption, not measured turbine efficiency.
Recognizing a Pelton bucket
The distinctive feature is a double cup separated by a central splitter. The incoming jet divides and follows the two curved inner surfaces before returning toward either side. The enlarged view is a simplified cutaway in the moving bucket frame. Flow markers show the direction, while the inset places buckets around a runner.
The drawing is informed by Voith’s photographs of finished bucket heads and runners. It is not a dimensioned reconstruction of one manufacturer’s profile. Actual jet interaction changes as each bucket crosses the nozzle stream; that transient behavior needs more than this steady momentum model.
Where Pelton buckets are used
Pelton turbines use free jets to drive a runner and are particularly suited to high-head hydropower. Water arrives through one or more nozzles; each bucket divides and turns the jet as it crosses the stream. Voith’s Gerlos 1 description shows this principle in a six-nozzle installation.
The arrangement serves both large and small hydropower plants. Bieudron in Switzerland has three Pelton turbines rated at 423 MW each, according to operator Grande Dixence. Voith also offers Pelton turbines for small hydropower.
Those installations do not set a universal head threshold, turning angle or bucket size. Selecting a runner requires the site head, available flow and manufacturer performance data; the calculator below compares an ideal momentum model.
Force and power at the ideal speed point
Let V be nozzle jet speed, Q the full jet flow in m³/s, u the bucket speed, and β the relative turning angle measured from the incoming flow direction. This calculator fixes u=V/2. With equal relative inlet and outlet speed magnitudes, the tangential runner force is F=ρQ(V−u)(1−cosβ).
The ideal transferred power is Fu. The entered additional loss multiplier η gives the displayed shaft estimate P=ηFu. This multiplier is not a prediction of turbine losses and is not the relative-velocity coefficient sometimes used inside the momentum equation. The full jet kinetic power is ρQV²/2; the displayed estimate cannot exceed it within the allowed inputs.
Changing the turning angle affects force and power. Changing η affects the power estimate alone. Speed ratio remains 0.5 because that condition is built into the model, rather than being a separately optimized result.
Worked example using the default inputs
At V=100 m/s and Q=50 L/s, the calculator converts Q to 0.05 m³/s and sets u=50 m/s. For β=165°, the ideal tangential force is 1000×0.05×50×(1−cos165°)=4914.81 N, or 4.91 kN.
Ideal transferred power is 245.74 kW. Applying the assumed 92% multiplier gives 226.08 kW. For comparison, the full jet kinetic power is 250 kW. The jet diameter implied by these flow and speed inputs is 25.23 mm. No runner diameter is entered, so this calculation does not supply an RPM.
What this comparison can show
At the fixed half-speed condition, force increases with flow and jet speed, and power increases with flow and the square of jet speed. Turning the relative flow further toward 180° increases the ideal tangential momentum change. Real bucket clearance and water discharge limit how closely a manufactured runner can follow that idealization.
This tool compares explicit inputs; it does not select bucket count, verify a runner design or size a generator. The drawing deliberately avoids treating its illustrative runner rotation as a calculated operating speed.
Questions about the calculator
Why does speed ratio stay at 0.5?
The calculator assumes the ideal half-jet-speed condition. It does not optimize a real turbine’s operating point.
Is the displayed force the load on one bucket?
It is the steady tangential force from the full jet acting on the sequence of runner buckets. Individual impact loads and structural stresses are not calculated.
What does the loss multiplier do?
It reduces ideal transferred power after the momentum calculation. It is a user assumption, not a measured efficiency or a prediction of bucket friction.
Why is there no RPM result?
Bucket speed is a linear speed. Converting it to RPM also requires the runner pitch diameter, which is not an input here.
References and visual basis
- Voith, Pelton turbines — finished bucket and runner photographs, especially page 5.
- NPTEL Fluid Machinery: Pelton wheel — split-cup geometry and momentum analysis.
- NPTEL: ideal efficiency and speed ratio — ideal half-jet-speed result.
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