---
title: "Pelton turbine: Design in 13 steps"
description: "Pelton turbine design in thirteen steps: from head and discharge to jet, runner, speed, generator, buckets and housing. With calculator."
author: "Erlach & Erlach GmbH"
language: en
canonical: https://www.erlach-erlach.com/en/pelton-turbine/design/
translation:
de: https://www.erlach-erlach.com/pelton-turbine/auslegung/
license: CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/)
source: Generated at build time from the HTML page; same text, same sources.
---
# Pelton turbine: Design in 13 steps
From head and discharge to the machine in thirteen steps, by the textbook. The calculator works through the chain, six pages go deeper into single steps. Where the textbook ends, System Erlach begins.
This page holds for **every Pelton turbine**. Where a section is about System Erlach, the horizontal Pelton turbine with up to six nozzles designed by Josef Erlach, its heading says so. The difference is explained in the overview [Pelton turbine](https://www.erlach-erlach.com/en/pelton-turbine/) System Erlach.
## Designing a Pelton turbine: two numbers, three decisions, thirteen steps
At the start are two numbers the plant provides: the head and the discharge. Then come three decisions of the designer: the number of nozzles, the speed and the position of the shaft. Everything else follows in a fixed order, as taught in hydropower engineering courses and worked through here.
How nozzle, jet and bucket work together is explained under [Pelton turbine working principle](https://www.erlach-erlach.com/en/pelton-turbine/working-principle/). For the same head and discharge there are always several solutions, as the table in the calculator shows.
## Pelton design from A to Z: the thirteen steps
1. **Head and discharge are given.** The plant supplies both. The power follows. The head is referred to the inlet of the distributor, the reference section of IEC 60193. More under [Pelton turbine nozzle](https://www.erlach-erlach.com/en/pelton-turbine/design/nozzle/).
2. **Set jet and bucket velocity.** For the first estimate the jet is calculated with the full velocity √(2gH); the roughly 2 per cent loss up to the jet stands in the loss balance as in Veselý. The buckets run at 47 per cent of it, just under half the jet velocity. More under [Pelton turbine nozzle](https://www.erlach-erlach.com/en/pelton-turbine/design/nozzle/).
3. **Choose the number of nozzles.** More nozzles mean thinner jets, higher speed, a smaller machine. Conventional: horizontal up to two, vertical up to six; System Erlach: horizontal up to six. More under [Horizontal Pelton turbine](https://www.erlach-erlach.com/en/pelton-turbine/design/horizontal/).
4. **Jet diameter.** From discharge per nozzle and jet velocity, by continuity. More under [Pelton turbine nozzle](https://www.erlach-erlach.com/en/pelton-turbine/design/nozzle/).
5. **Bucket width.** About 3.1 times the jet diameter for one nozzle, 3.2 for two, 3.3 for four to five, more for six. Manufacturers deviate according to production and experience.
6. **Runner diameter from the head.** The higher the head, the larger the runner in relation to the jet: 10 times at 400 metres, 15 times at 1400 metres. Below 9.5 water is lost. More under [Pelton turbine specific speed](https://www.erlach-erlach.com/en/pelton-turbine/design/specific-speed/).
7. **Speed.** From peripheral velocity and diameter. More under [Pelton turbine specific speed](https://www.erlach-erlach.com/en/pelton-turbine/design/specific-speed/).
8. **Generator pole pairs.** The speed must match the grid frequency. The number of pole pairs is rounded to the nearest whole number; only if the runner would then fall below 10 times the jet is it rounded up.
9. **Recalculate the speed.** With the whole number of pole pairs the speed is fixed, slightly above or below the value of step 7.
10. **Recalculate the diameter.** The runner gets slightly smaller or larger accordingly. The specific speed per nozzle is now a result, not an input. More under [Pelton turbine specific speed](https://www.erlach-erlach.com/en/pelton-turbine/design/specific-speed/).
11. **Number of buckets.** At least 17, empirically. As an estimate 15 plus runner diameter over twice the jet diameter.
12. **Housing.** With a vertical shaft, runner plus 8 to 9 bucket widths in diameter. With a horizontal shaft about four bucket widths of pit width, and the splash water decides how many nozzles are possible. More under [Horizontal Pelton turbine](https://www.erlach-erlach.com/en/pelton-turbine/design/horizontal/).
13. **Heights.** Runner to tailwater about 3.5 bucket widths, runner centre to ceiling 2 to 2.5 bucket widths.
Two things belong to the design and are not in the chain, because the textbook does not put them into numbers: the distributor, which should bring equal water to every nozzle, see [Pelton turbine distributor](https://www.erlach-erlach.com/en/pelton-turbine/design/distributor/), and the behaviour at low discharge, see [Pelton turbine efficiency](https://www.erlach-erlach.com/en/pelton-turbine/design/efficiency/).
**Source:** lecture slides “Design of Pelton turbines”, NTNU Trondheim (Kvaerner/GE Hydro), steps 1 to 13 with the examples Jostedal and Khimti; [H. Brekke, Hydraulic Turbines, NTNU 2015](https://www.ntnu.no/documents/381182060/1267681377/HYDRAULIC+TURBINES_Hermod+Brekke+-+2015.pdf), pp. [40](https://www.ntnu.no/documents/381182060/1267681377/HYDRAULIC+TURBINES_Hermod+Brekke+-+2015.pdf#page=45), [41](https://www.ntnu.no/documents/381182060/1267681377/HYDRAULIC+TURBINES_Hermod+Brekke+-+2015.pdf#page=46), [106](https://www.ntnu.no/documents/381182060/1267681377/HYDRAULIC+TURBINES_Hermod+Brekke+-+2015.pdf#page=111) and [137](https://www.ntnu.no/documents/381182060/1267681377/HYDRAULIC+TURBINES_Hermod+Brekke+-+2015.pdf#page=142)–[138](https://www.ntnu.no/documents/381182060/1267681377/HYDRAULIC+TURBINES_Hermod+Brekke+-+2015.pdf#page=143); jet and bucket velocity after Josef Erlach, 3 and 12 October 2026.
## The Pelton calculator: the thirteen steps worked through
The calculator goes through the chain for the head, discharge and number of nozzles entered and shows each step with its number. The two examples come from the lecture; their results are recalculated every time the website is built. Below, the same calculation is shown for one to six nozzles side by side.
1. **Head and discharge are given:** H = 1,130 m, Q = 28.50 m³/s. From these the power P = ρ · g · Q · H · η = **284.3 MW** (η = 0.90).
2. **Set jet and bucket velocity:** Jet c1 = √(2gH) = **148.9 m/s**, periphery u1 = 0.47 · √(2gH) = **70.0 m/s**.
3. **Choose the number of nozzles:** z = **5**, per nozzle Qnozzle = Q / z = **5.700 m³/s**.
4. **Jet diameter from continuity:** d0 = √(4 · Qnozzle / (π · c1)) = **221 mm**.
5. **Bucket width:** B = 3.30 · d0 = **729 mm** (factor by number of nozzles).
6. **Runner diameter from the head:** D1 / d0 = 0,005 · H + 8 = 13.65, so D1 = **3,014 mm**.
7. **Calculate the speed:** n = 60 · u1 / (π · D1) = **443.5 rpm**.
8. **Generator pole pairs:** p = 60 · f / n = 6.76, rounded **p = 7** (14 poles, f = 50 Hz).
9. **Recalculate the speed:** n = 60 · f / p = **428.6 rpm** (slightly below step 7, the runner gets larger).
10. **Recalculate the diameter:** D1 = 60 · u1 / (π · n) = **3,119 mm**, D1 / d0 = 14.1, nq per nozzle = 5.2.
11. **Number of buckets:** zB = **22** (rule of thumb 15 + D1 / (2 · d0) = 22.1, at least 17).
12. **Housing:** Vertical: DG = D1 + K · B = **9.31 m** (K = 8.5). Horizontal: pit width about 4 · B = 2.91 m; the splash water decides, see System Erlach.
13. **Heights:** Runner to tailwater about 3,5 · B = **2.55 m** (vertical); runner centre to ceiling 2 to 2,5 · B = 1.46 to 1.82 m. Runaway speed, guide value: 771 to 814 rpm.
Calculated for the first estimate with the full jet velocity √(2gH), the losses up to the jet stand in the loss balance as in Veselý; after Josef Erlach the buckets run at 47 per cent of it. The lecture uses 48 per cent; the text output below shows what that changes.
### The same head and discharge with one to six nozzles
| Nozzles | Jet d0 mm | Bucket B mm | Runner D1 mm | Speed n rpm | nq per nozzle | Buckets | Shaft conventional |
| --- | --- | --- | --- | --- | --- | --- | --- |
| 1 | 494 | 1,530 | 6,683 | 200 (30 poles) | 5.5 | 22 | horizontal |
| 2 | 349 | 1,117 | 4,901 | 272.7 (22 poles) | 5.3 | 22 | horizontal |
| 3 | 285 | 926 | 4,010 | 333.3 (18 poles) | 5.3 | 22 | horizontal with narrow nozzle spacing, or vertical |
| 4 | 247 | 815 | 3,564 | 375 (16 poles) | 5.1 | 22 | vertical |
| 5 | 221 | 729 | 3,119 | 428.6 (14 poles) | 5.2 | 22 | vertical |
| 6 | 202 | 675 | 2,673 | 500 (12 poles) | 5.6 | 22 | vertical |
**For engineers:** First estimate, not a design. The number of pole pairs is rounded; the speed therefore deviates slightly from step 7, and the diameter follows in step 10. The two lecture examples are recalculated at every build; for Khimti the lecture rounds the jet to 0.15 m and chooses 22 buckets, the rule of thumb gives 20 to 21 depending on the coefficients. The rule of thumb, the rounding of pole pairs and the minimum of two pole pairs are assumptions of this page, not of the lecture. Not included: bucket shape, needle and nozzle tip, the distributor in detail, strength, control, model test.
**Formulas as text:** P = rho · g · Q · H · eta; c\_1 = sqrt(2 · g · H); u\_1 = k\_u · sqrt(2 · g · H); Q\_nozzle = Q / z; d\_0 = sqrt(4 · Q\_nozzle / (pi · c\_1)); B = 3.1 · d\_0 for one nozzle, 3.2 for two, 3.3 for four to five, above 3.3 for six; D\_1 / d\_0 = 0.005 · H + 8, at least 10 (10 at 400 m, 15 at 1400 m); n = 60 · u\_1 / (pi · D\_1); p = 60 · f / n, rounded to the nearest whole number; rounded up if D\_1 / d\_0 would then fall below 10; n = 60 · f / p; D\_1 = 60 · u\_1 / (pi · n); n\_q = n · sqrt(Q\_nozzle) / H^0.75; z\_B ≈ 15 + D\_1 / (2 · d\_0), at least 17; D\_G = D\_1 + K · B (vertical machine); horizontal machine: pit width ≈ 4 · B; n\_R ≈ 1.8 to 1.9 · n (guide value). **Quantities:** P power in W; rho density of water in kg/m³, equal to 1000; g gravitational acceleration in m/s², equal to 9.81; Q discharge of the turbine in m³/s; H head, referred to the high pressure reference section of IEC 60193, here the inlet of the distributor in m; eta turbine efficiency, no unit; c\_1 jet velocity in m/s; u\_1 peripheral velocity at the pitch circle in m/s; k\_u share of the theoretical jet velocity at which the buckets run, no unit, typically 0.45 to 0.48; Q\_nozzle discharge per nozzle in m³/s; z number of nozzles, no unit; d\_0 jet diameter in m; pi the number pi, no unit, equal to 3.1416; B bucket width in m; D\_1 pitch circle diameter of the runner in m; n rotational speed in rpm; p number of generator pole pairs, no unit; f grid frequency in Hz; n\_q specific speed (n in rpm, Q in m³/s, H in m) in rpm · (m³/s)^0.5 / m^0.75 (unit-dependent); z\_B number of buckets, no unit; D\_G housing diameter of the vertical machine in m; K housing factor, 8 to 9, rising with the number of nozzles, no unit; n\_R runaway speed in rpm.
## Pelton turbine and System Erlach: where the textbook ends
The thirteen steps lead to the runner, the speed and the housing of a vertical machine. They leave three questions open, and these are exactly where the [Pelton turbine System Erlach](https://www.erlach-erlach.com/en/pelton-turbine/) starts.
- **How does the water reach the nozzles?** The textbook names the ring distributor. In System Erlach an axial distributor gives every nozzle the same inflow, see [Pelton turbine distributor](https://www.erlach-erlach.com/en/pelton-turbine/design/distributor/).
- **How many nozzles can a horizontal shaft take?** Conventionally two, because otherwise the splash water falls back onto the runner. In System Erlach two guide rings lead the water away, up to six nozzles, see [Horizontal Pelton turbine](https://www.erlach-erlach.com/en/pelton-turbine/design/horizontal/).
- **What happens at low discharge?** Switch nozzles off instead of throttling all of them, with the same inflow for every nozzle, see [Pelton turbine efficiency](https://www.erlach-erlach.com/en/pelton-turbine/design/efficiency/).
**Source:** [J. M. Erlach, New Pelton Concept, Viennahydro 2012, Full Paper](https://www.erlach-erlach.com/downloads/2012_Viennahydro_Erlach_New-Pelton-Concept_Full-Paper.pdf), sections [2.2](https://www.erlach-erlach.com/downloads/2012_Viennahydro_Erlach_New-Pelton-Concept_Full-Paper.pdf#page=2) to [2.5](https://www.erlach-erlach.com/downloads/2012_Viennahydro_Erlach_New-Pelton-Concept_Full-Paper.pdf#page=6); [leaflet for Viennahydro 2012](https://www.erlach-erlach.com/downloads/2012_Viennahydro_Erlach-und-Erlach_Faltblatt.pdf).
## Pelton design, further quantities: jet deflector, water hammer, runaway speed
- **Jet deflector.** If the generator suddenly loses its load, a deflector turns the jet away from the runner at once.
- **Water hammer.** The needle may only close slowly. Otherwise water hammer occurs in the penstock. This is why the deflector is needed.
- **Runaway speed.** If the load is lost and the jet is not deflected, the runner accelerates towards its runaway speed. As a guide value, 1.8 to 1.9 times the rated speed; the value verified by the manufacturer governs, up to about twice the rated speed according to Zhang. Runner and generator must be designed for it.
**Formula as text:** n\_R ≈ 1.8 to 1.9 · n (guide value). **Quantities:** n\_R runaway speed in rpm; n rotational speed in rpm.
**Source:** [energie.ch, Peltonturbine](https://energie.ch/peltonturbine/) (runaway speed); Josef Erlach, 3 October 2026 (guide value); [Z. Zhang, Pelton Turbines, Springer 2016](https://link.springer.com/chapter/10.1007/978-3-319-31909-4_17), chapter 17 (runaway speed up to about twice the rated speed).
## Limits of the Pelton calculator: a preliminary design, not a machine
The chain works with textbook relations and usual values from experience. It gives the order of magnitude of a machine: jet, runner, speed, generator, number of buckets, housing. What makes a turbine is not in it: the shape of the buckets, needle and nozzle tip, the distributor in detail, strength, cavitation and abrasion, control, and the model test. The chain replaces neither the work of a design engineer nor the model test.
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Erlach & Erlach GmbH, Ravensburg. Web page: https://www.erlach-erlach.com/en/pelton-turbine/design/ · License for this text: CC BY 4.0 · Overview for assistants: https://www.erlach-erlach.com/llms.txt