Pelton Wheel

What a Pelton wheel is — and why it is an impulse turbine

A Pelton wheel is a hydraulic turbine that turns the kinetic energy of a fast water jet directly into rotation. It is the canonical impulse turbine: the working water is not under pressure as it passes through the machine — instead, a nozzle has already converted all the available pressure into the velocity of a free jet, and the runner extracts energy purely from the momentum of that jet striking the buckets. There is no pressure drop across the buckets, the runner spins in open air at atmospheric pressure, and the only thing touching the buckets is a coherent stream of water moving fast enough to peel the skin off your hand.

That distinction matters. A Francis or Kaplan turbine is a reaction machine: it sits fully submerged, water flows through it under pressure, and the runner extracts energy from both the change in pressure and the change in velocity as the flow passes through curved blades. A Pelton wheel does none of that. The penstock delivers high-pressure water to a nozzle; the nozzle does all the pressure-to-velocity conversion; and the runner just catches the jet. This is why a Pelton is the natural choice for high-head hydropower — when you have a 600- or 1200-metre vertical drop available, you would rather convert that head to a clean high-velocity jet and fire it at buckets than try to contain enormous pressures inside a submerged casing.

The machine is named for Lester Allan Pelton, a Gold Rush millwright who, around 1878, noticed that a misaligned water wheel whose jet struck the edge of the cups rather than their centre ran faster than one hit dead-on. He realised the splitter ridge — dividing each cup into two halves and turning the water back on itself — was the key. His double-cup bucket, patented in 1880, is essentially unchanged in geometry today; modern runners are CNC-milled from forged stainless steel, but the shape Pelton drew is still the shape that spins.

The mechanism — splitter, double cup, and 180° deflection

Walk the energy through the machine. Water is stored at a reservoir at a height H (the gross head) above the powerhouse. It runs down a long pipe — the penstock — losing a little to pipe friction, arriving at the nozzle with a net head H_n. The nozzle is a converging cone with a streamlined needle (the spear valve) inside it. As the water accelerates through the shrinking annulus between needle and nozzle wall, its pressure falls to atmospheric and its velocity rises. The jet leaves at:

V = C_v · √(2 · g · H_n)

where  C_v ≈ 0.97–0.99   (nozzle velocity coefficient)
       g  = 9.81 m/s²
       H_n = net head at the nozzle (m)

At a net head of 600 m, that is V = 0.98 · √(2 · 9.81 · 600) ≈ 106 m/s — a jet of water moving at nearly 240 mph, perhaps 100–200 mm in diameter, coherent enough to hold its shape across the gap to the wheel. That jet strikes the rim of the runner, where 16 to 26 buckets are bolted or forged in place.

Each bucket is a double cup: two ellipsoidal half-cups joined by a sharp central ridge, the splitter. The splitter cleaves the incoming jet into two equal sheets. Each sheet flows around the inside of its half-cup and is turned through almost 180°, exiting sideways and backwards, off the outer edges of the bucket, at low speed. By splitting the jet symmetrically, the bucket cancels the axial thrust that a single deflected sheet would otherwise dump into the shaft bearing — the two halves push sideways in opposite directions and balance out, leaving only the useful tangential force that turns the wheel.

Each bucket also has a notch — the cutaway or lip — cut into its outer edge. As the runner turns, the leading edge of each incoming bucket would otherwise slice the root of the jet and rob the bucket ahead of the last slug of water it was still receiving. The notch lets the bucket swing past so the jet enters cleanly at the splitter and is fully captured before the next bucket cuts in. Getting this notch geometry and bucket spacing right is one of the unglamorous reasons real Pelton runners reach above 90 percent while a naive build struggles past 75.

Why the bucket should run at half the jet speed

This is the single most elegant result in turbomachinery, and it falls out of one momentum balance. Work in the reference frame of a bucket moving at speed U while a jet of speed V and mass flow ṁ strikes it. In that frame the water arrives at relative velocity (V − U), is turned through an angle close to 180°, and leaves at relative velocity −(V − U) (a perfect 180° turn reverses it). The force on the bucket is the rate of change of momentum, and the power delivered is force times bucket speed:

Force on bucket:   F = ṁ · (V − U) · (1 + k·cos β)
Power:             P = F · U = ṁ · (V − U) · U · (1 + k·cos β)

where  β = bucket exit angle from the incoming direction (β ≈ 165°, so cos β ≈ −0.97)
       k = friction factor for the water sheet over the bucket (k ≈ 0.85–0.9)
       (1 + k·cos β) ≈ 1.8 for a near-180° turn

Maximise P over U:   dP/dU = 0   →   U = V / 2

The physics is intuitive once you see the two limits. If the bucket stands still (U = 0) it feels the full jet force but travels no distance, so power is zero. If the bucket runs as fast as the jet (U = V) there is no relative velocity, the water cannot catch the bucket, force is zero, and power is again zero. The product F·U peaks exactly halfway between, at U = V/2. At that operating point, with an ideal 180° turn, the water leaves the bucket with essentially zero absolute velocity — every joule of kinetic energy it carried in has been transferred to the wheel.

Real machines cannot quite hit it. The buckets deflect the jet only about 165–170° (so the outgoing sheet clears the back of the following bucket), and sheet friction takes a bite, so the practical optimum speed ratio U/V lands around 0.46 to 0.48. That is why the dimensionless coefficient φ = U/√(2gH) used in design charts is quoted as roughly 0.45–0.48 rather than the textbook 0.5. The diameter of the runner is then chosen to put the bucket pitch-circle velocity at that value when the generator is locked to grid frequency:

Runner speed:   U = π · D · N / 60       (D = pitch diameter, N = rpm)
Set U = 0.47 · V, then solve for D given N fixed by grid:

  N = 500 rpm (10-pole, 50 Hz),  V = 106 m/s,  U = 49.8 m/s
  →  D = 60·U / (π·N) = 60·49.8 / (π·500) ≈ 1.90 m

Multiple jets, specific speed, and runner sizing

One nozzle on a vertical-shaft runner is the simplest layout, but big stations use up to six nozzles arranged radially around a single horizontal-axis or vertical-axis wheel. Adding jets increases the flow — and therefore the power — without enlarging the runner or slowing it down, because the bucket still only ever sees one jet's worth of velocity at a time. Multi-jet machines also let the operator throttle load jet-by-jet, which is the source of the Pelton's famously flat part-load efficiency.

The number that governs all of this is specific speed, N_s, a dimensionless-ish similarity parameter that collapses head, flow, and rotational speed into one figure that says which turbine type fits:

N_s = N · √P / H^(5/4)      (metric form, P in kW, H in m, N in rpm)

Single-jet Pelton:   N_s ≈ 8–30
Six-jet Pelton:      N_s ≈ 25–70   (jets add √n_jets to effective N_s)
Francis:             N_s ≈ 60–400
Kaplan:              N_s ≈ 300–1000

Low specific speed means high head and low flow — exactly the Pelton's home. The jet-to-runner diameter ratio m = D/d (pitch diameter over jet diameter) is kept above about 10, and ideally 12–15, so each bucket is large relative to the jet and the geometry stays clean; pushing m below 10 crowds the buckets and erodes efficiency. The number of buckets is set so the jet is always caught — a common empirical rule is Z = D/(2d) + 15, giving 18–26 buckets for typical machines.

Real-world machines — Bieudron and the high-head record holders

The headline example is the Bieudron power station in the Swiss Alps, part of the Cleuson-Dixence scheme. Its three Pelton units run on a net head of 1869 metres — water dropping nearly two vertical kilometres — and each unit produces 423 MW from five jets, at the time the most powerful Pelton wheels and the highest-head Pelton installation in the world. The jet velocity there is about 190 m/s. (A penstock rupture in 2000 shut the scheme for years and is a sober reminder of what 1869 m of head means in pipe pressure: roughly 185 bar.)

Other touchstones: the Mont-Cenis and Grande Dixence schemes in the Alps; the Walchensee plant in Bavaria; and countless small alpine and Himalayan run-of-river plants where a modest flow falls a long way. At the small end, micro-hydro Pelton wheels the size of a dinner plate power off-grid cabins from a mountain stream with 30–100 m of head. The geometry scales across more than four orders of magnitude of power, from a few hundred watts to nearly half a gigawatt, because the underlying impulse physics is scale-independent.

Flow control — spear valve, deflector, and water hammer

Controlling a Pelton is a study in not breaking the penstock. The spear valve (needle valve) slides axially inside each nozzle to change the jet diameter, and therefore flow, while keeping the jet velocity fixed by the head. That is exactly what you want: throttle the flow but never the speed, so the runner stays at its optimum speed ratio U/V across the whole load range. This is why a six-jet Pelton can shut five jets entirely and run one at near-peak efficiency.

The catch is that you cannot slam the spear valve shut to reject load, because suddenly arresting a long, fast-moving column of water in the penstock produces a water-hammer pressure surge — a transient spike that can be several times the static head and is fully capable of bursting the pipe (this is the same physics as the bang in household plumbing, scaled to megawatts). So the Pelton separates the two jobs. A curved jet deflector swings into the jet within a second or two and flicks it sideways off the buckets, instantly removing torque from the runner during a load rejection; meanwhile the spear valve closes slowly, over many seconds, so the water column decelerates gently and the surge stays bounded. Large units also carry a small brake jet aimed at the back of the buckets to stop the runner after shutdown, since with no deflector torque and no bearing brake the wheel would otherwise coast for a long time.

Pelton vs Francis vs Kaplan — picking the turbine

The selection is driven almost entirely by head and flow. The comparison below is the chart every hydro engineer carries in their head.

Property	Pelton (impulse)	Francis (reaction)	Kaplan (reaction)
Head range	50–1800 m	40–600 m	2–70 m
Flow regime	Low flow, high head	Medium flow & head	High flow, low head
Specific speed N_s	8–70	60–400	300–1000
Working principle	Free jet impulse, atmospheric	Pressure + velocity, submerged	Pressure + velocity, submerged
Peak efficiency	90–92 %	93–96 %	90–94 %
Part-load efficiency	Excellent (jet-by-jet)	Poor below ~50 %	Good (adjustable blades)
Flow control	Spear valve + deflector	Guide vanes (wicket gates)	Adjustable runner blades + vanes
Cavitation risk	Essentially none (runs in air)	Significant	Significant
Sediment / silt tolerance	Buckets erode but easy to replace	Sensitive — runner erosion	Sensitive

Two things stand out. First, the Pelton concedes a point or two of peak efficiency to a good Francis but wins decisively on the flatness of the part-load curve — independent jets let it hold above 88 percent from a fifth of rated flow to full load, which makes it the turbine of choice for grid-following duty and frequency regulation. Second, because the runner spins in air rather than submerged in flowing water, a Pelton has essentially no cavitation problem — the failure mode that haunts Francis and Kaplan designs. Its erosion instead comes from sediment in the jet sandblasting the buckets, which is a maintenance problem (replace or hard-coat the buckets) rather than a hydrodynamic one.

Failure modes — where Pelton wheels actually break

• Sediment erosion of buckets. Glacial and Himalayan rivers carry suspended quartz and silt that act like a sandblaster at 100+ m/s. The splitter ridge and bucket entry edge erode first, rounding the sharp splitter and ruining the clean jet split, which drops efficiency by several points. Cure: tungsten-carbide or ceramic hard-coatings (HVOF spray), desilting basins upstream, and scheduled bucket replacement.
• Fatigue cracking at the bucket root. Each bucket is struck by the jet once per revolution — at 500 rpm that is over 250 million load cycles a year — so the bucket-to-disc junction sees high-cycle fatigue. Cracks initiate at the root fillet. Cure: forged one-piece runners (no bolted joints to fret), generous root radii, shot-peening, and periodic dye-penetrant inspection.
• Splitter wear and jet interference. A worn or chipped splitter no longer divides the jet symmetrically; the two sheets become unequal, axial thrust returns to the bearing, and the wheel runs rough. Caught by vibration monitoring on the shaft bearings.
• Nozzle and spear-valve erosion. The needle and seat see the same abrasive water at full velocity; a worn seat lets the jet spray and lose coherence, fattening and slowing the effective jet. Replaceable hardened needle tips and nozzle inserts are standard.
• Water hammer from mis-sequenced shutdown. If the deflector fails to deploy or the spear valve closes too fast, the penstock surge can exceed the pipe's design pressure. The 2000 Cleuson-Dixence penstock rupture, though triggered by a manufacturing flaw in the pipe, is the cautionary tale of what high-head water columns can do.
• Windage and casing flooding. The housing must keep spent water from piling up around the runner; a flooded casing makes the buckets plough through standing water and bleeds power to windage. Tail-water level control and adequate casing drainage are part of the design.

Common pitfalls when designing or specifying a Pelton

• Running at the wrong speed ratio. The optimum is U/V ≈ 0.47, not 0.5. Size the runner diameter to the real value at locked grid speed, or you leave several points of efficiency on the table.
• Jet-to-runner diameter ratio too small. Pushing D/d below 10 to make a more compact runner crowds the buckets and forces too sharp a jet split; keep it above 10, ideally 12–15.
• Ignoring the assembly and notch geometry. If bucket spacing and the cutaway notch are not matched to the jet, the leading bucket interrupts the jet early and efficiency falls toward the 70s. This is geometry, not horsepower.
• Under-deflecting the jet. Designers sometimes deflect the jet far less than 165° to keep the outgoing sheet clear, sacrificing the (1 + k·cos β) term. The exit angle is a careful trade between energy capture and back-splash onto the following bucket.
• Forgetting the deflector in the control logic. A spear-valve-only control scheme cannot reject load without a water-hammer surge. The deflector is not optional on any machine with a long penstock.
• Specifying a Pelton outside its head band. Below ~50 m of head the jet is slow, the runner large, and a Francis will simply do it better. Match the turbine to the specific speed before drawing anything.