Wilkinson's Steam Turbine is a pure reaction turbine where steam exits tangential nozzles fixed to the rim of a rotating disc, propelling the disc by jet reaction in the same way an aeolipile spins. Small surviving examples run at 3,000 to 8,000 RPM on a few bar of saturated steam. The design exists to convert steam pressure directly into shaft rotation without reciprocating parts, valves or eccentrics. You will see Wilkinson-pattern rotors driving demonstration dynamos, model boat propellers, and lecture-bench rigs at heritage sites like the Internal Fire Museum of Power in Wales.
Wilkinson's Steam Turbine Interactive Calculator
Vary rotor diameter and speed to see the rim tip speed for a Wilkinson reaction steam turbine and compare it with a larger rotor.
Equation Used
The article's worked comparison uses rim speed to show why rotor diameter matters: for the same RPM, tip speed rises directly with diameter.
FIRGELLI Automations - Interactive Mechanism Calculators.
- Rotor diameter is the outside nozzle path diameter.
- Speed is steady shaft RPM.
- Calculation is mechanical rim speed only, not steam flow or power.
- Comparison rotor uses the same RPM.
How the Wilkinson's Steam Turbine Actually Works
The principle is the one Hero of Alexandria worked out two thousand years ago — steam fed through the centre of a free-spinning rotor, ducted out through nozzles aimed tangentially at the rim, and the reaction force of those jets spins the disc. Wilkinson's contribution was to refine the geometry into something practical: a balanced rotor, properly profiled convergent nozzles, and a steam gland at the centre that lets pressurised steam in without bleeding the bearings dry. Steam enters the central hollow shaft at supply pressure — typically 2 to 7 bar gauge for a small demonstration unit — flows radially outward through internal passages, and accelerates through the nozzle throats. The exit velocity sets the jet reaction force, and that force times the rotor radius gives you torque.
The geometry has to be right or the rotor never makes its rated speed. The nozzle throat area sets steam mass flow, and if you oversize it you flood the rotor without ever reaching choked-flow exit velocity — the jets become lazy and the rotor windmills. Undersize the throat and you starve the turbine at full pressure, choking the inlet and dropping shaft power. Tip speed is the other limit. A typical brass or bronze Wilkinson rotor of 150 mm diameter at 8,000 RPM sees a tip speed around 63 m/s — fine for the material — but push diameter to 250 mm at the same RPM and you are at 105 m/s, where centrifugal stress on the nozzle bosses starts to matter and you need careful balancing or the bearings will sing.
Failure modes are mechanical, not thermodynamic. Bearing wear from poor steam-side lubrication is the first one — the central gland leaks superheated steam onto the inboard bearing and the grease cooks. Out-of-balance from a partially blocked nozzle is the second — one nozzle scales up with feedwater deposits, the rotor goes one-sided, and you get vibration that telegraphs straight through to the dynamo or whatever the turbine is driving. The third is rotor erosion from wet steam — if the supply is not properly dried, water droplets sandblast the nozzle exits and the throat area drifts open over a season of running.
Key Components
- Hollow Central Shaft: Carries supply steam from the inlet gland into the rotor passages. Bore is typically 8 to 16 mm on small units. Concentricity to the rotor disc must be within 0.05 mm or vibration above 5,000 RPM becomes unmanageable.
- Tangential Nozzles: Convergent brass or bronze nozzles, usually 2 or 4, screwed into rim bosses and aimed tangentially. Throat diameter typically 1.5 to 3.0 mm and the nozzle axis must lie within ±1° of true tangent - off-axis nozzles waste reaction force on radial component and cost you RPM.
- Rotor Disc: The reaction-mass flywheel. Bronze or brass on heritage units, 100 to 250 mm diameter. Static and dynamic balance to within 2 g·mm at the rim is the practical minimum for clean running above 6,000 RPM.
- Inlet Gland and Bearings: Carbon-graphite or stuffing-box gland sealing the rotating shaft against the static steam supply. Bearing pair straddles the gland — usually plain bronze on the steam side and a sealed ball race on the dry side.
- Casing and Exhaust: Surrounds the spinning rotor to direct exhaust steam to a single outlet and to keep your fingers out. Casing clearance to rotor tip is typically 3 to 5 mm — tight enough to control windage, loose enough to clear thermal growth.
Where the Wilkinson's Steam Turbine Is Used
You see Wilkinson-pattern reaction turbines wherever someone wants high RPM from steam without the complexity of a multi-stage impulse machine, and where shaft power demand is modest — from a few watts on a lecture bench to a few hundred watts on a heritage demonstration. The mechanism shines at low power, low cost, and high speed. It struggles when you ask for efficiency, because a single-stage reaction rotor wastes most of the available enthalpy in exhaust kinetic energy.
- Heritage demonstration: Reaction-rotor demonstration unit driving a small lighting dynamo at the Internal Fire Museum of Power, Tan-y-groes, Wales
- Education and lecture bench: Cambridge Engineering Department teaching aeolipile-derivative rotor used in undergraduate thermodynamics demonstrations
- Model engineering: Stuart Models small reaction turbine kits driving model launch propellers in 1/12 scale steam launches
- Steam fairs and rallies: Portable Wilkinson-style rotor running off a portable boiler at the Great Dorset Steam Fair driving a brake dynamo for crowd display
- Industrial museums: Bench-mounted reaction turbine in the steam hall at the Kew Bridge Steam Museum demonstrating the Hero principle
- Amateur power generation: Hobbyist micro-turbines built to ABMA-style codes driving 12 V alternators from solar-concentrator boilers
The Formula Behind the Wilkinson's Steam Turbine
What you actually need to size is the shaft power available at a given supply pressure and rotor RPM. Power comes from jet reaction force times rotor tip speed, and the jet reaction force is steam mass flow times nozzle exit velocity. At the low end of the typical operating range — say 2 bar gauge — exit velocity is modest and the rotor lopes along at 3,000 RPM with a few watts of useful shaft power. At the high end — 7 bar gauge with dry saturated steam — exit velocity climbs past 600 m/s and the rotor wants to spin at 8,000 RPM or more, but practical tip-speed and balance limits cap you well below the theoretical optimum. The sweet spot for a 150 mm rotor with 2.5 mm nozzles sits around 4 to 5 bar gauge and 5,000 to 6,000 RPM.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| Pshaft | Useful shaft power delivered by the rotor | W | ft·lbf/s |
| ṁ | Steam mass flow rate through all nozzles combined | kg/s | lb/s |
| vjet | Steam exit velocity at nozzle throat (isentropic) | m/s | ft/s |
| utip | Rotor tip linear velocity (— × D × N / 60) | m/s | ft/s |
| ηr | Reaction-stage efficiency factor accounting for nozzle losses, windage and bearing drag | dimensionless | dimensionless |
Worked Example: Wilkinson's Steam Turbine in a heritage demonstration Wilkinson rotor driving a lighting dynamo
You are confirming useful shaft power across three steam supply pressures on a recommissioned 1894 Wilkinson-pattern reaction turbine being returned to demonstration running at the Internal Fire Museum of Power in Tan-y-groes, west Wales, where the rotor drives a small Crompton 24 V lighting dynamo and the trustees want shaft power verified at slow trial running of 2 bar gauge, nominal demonstration of 4 bar gauge, and a brisk full-display burst at 7 bar gauge before the open weekend. The rotor is 150 mm diameter with 2 tangential nozzles each 2.5 mm throat, and reaction efficiency is taken as 0.18 based on prior brake-test data.
Given
- Drotor = 0.150 m
- dthroat = 2.5 mm
- nnozzles = 2 —
- ηr = 0.18 —
- Nnominal = 5,500 RPM
- Psupply (low / nom / high) = 2 / 4 / 7 bar gauge
Solution
Step 1 — total nozzle throat area for the pair of 2.5 mm holes:
Step 2 — at nominal 4 bar gauge (5 bar absolute, dry saturated steam), the choked-flow mass rate through the throats works out to roughly 0.0095 kg/s and the isentropic exit velocity is approximately 540 m/s for the available enthalpy drop to atmosphere:
Step 3 — rotor tip speed at the nominal 5,500 RPM:
Step 4 — nominal shaft power:
That is roughly 40 W at the dynamo terminals before electrical losses — enough to keep two festoon lamps glowing on the demonstration board.
At the low end of the operating range, 2 bar gauge supply, both mass flow and jet velocity drop. Mass flow falls to around 0.0055 kg/s, jet velocity to about 440 m/s, and the rotor will only pull about 3,500 RPM under load (utip ≈ 27.5 m/s):
At 12 W the dynamo is barely lighting one lamp — enough for the trustees to confirm the rotor spins clean and the gland is sealing, but not a public-display result.
At the high end, 7 bar gauge, mass flow climbs to roughly 0.0152 kg/s, jet velocity to about 605 m/s, and the rotor accelerates toward 7,200 RPM (utip ≈ 56.5 m/s):
At 93 W you are running the entire lamp board bright, but you are also pushing tip speed past 56 m/s on a 130-year-old bronze rotor — vibration from the inlet gland will start to climb and you should not hold this rate for more than a few minutes.
Result
At nominal 4 bar gauge and 5,500 RPM the rotor delivers roughly 40 W of useful shaft power. To the watching public this looks like a steady glow on a pair of lamps and a clean whistle from the casing — convincing demonstration without drama. Comparing the three points: 12 W at 2 bar feels lazy and the rotor sounds breathy, 40 W at 4 bar is the genuine sweet spot, and 93 W at 7 bar is loud, fast, and short-duration only. If your measured power is well below predicted, check three things in order: nozzle throats partially blocked by feedwater scale (clean with a 2.5 mm reamer to bring the throat back to spec — even 0.2 mm undersize halves mass flow), inlet gland leaking past the carbon ring (you will see steam plume from the rear bearing housing and the inboard bearing will run hot), and rotor unbalance from one nozzle running heavier than the other (vibration peaks at the rotational frequency rather than at twice it).
Wilkinson's Steam Turbine vs Alternatives
A Wilkinson reaction rotor is one of three small-steam-power options a museum or model engineer realistically considers. The other two are a single-stage impulse turbine of the De Laval pattern and a small reciprocating engine like a Stuart 10V. Each has its own envelope.
| Property | Wilkinson Reaction Turbine | De Laval Impulse Turbine | Reciprocating Engine (Stuart 10V class) |
|---|---|---|---|
| Typical operating speed | 3,000-8,000 RPM | 10,000-30,000 RPM | 300-1,500 RPM |
| Stage efficiency | 10-20% | 30-50% | 5-12% indicated |
| Build cost (small unit) | Low — simple turning and drilling | Medium — profiled nozzles and blading | Medium-high — castings, valves, eccentrics |
| Reliability over 1,000 running hours | Good if dry steam supplied — gland is the weak point | Good — but high RPM stresses bearings | Excellent — proven topology |
| Useful shaft power range | 1 W - 500 W | 100 W - 50 kW | 5 W - 5 kW |
| Sensitivity to wet steam | High — nozzle erosion within a season | High — blade erosion | Low — tolerates wet steam well |
| Best application fit | Heritage demos, education, micro-power | Industrial small-power, marine auxiliaries | Model engineering, low-RPM direct drive |
Frequently Asked Questions About Wilkinson's Steam Turbine
This is the classic single-stage reaction problem. The rotor only develops useful torque when tip speed is well below jet velocity, but a free-running rotor accelerates until windage and bearing drag balance the jet thrust — which can be at 70-80% of jet velocity. As soon as you load it, the operating point shifts to where torque is produced, and that point is much further down the speed curve.
If the speed under load is unworkably low, your nozzles are undersized for the dynamo's torque demand. Either open the throats by 0.2-0.3 mm, raise supply pressure, or accept that a single-stage Hero-pattern rotor is a poor match for a stiff electrical load and add a belt reduction.
At 100 W the choice comes down to manufacturing capability and the speed your driven load wants. A Wilkinson rotor is two tangential nozzles screwed into a turned brass disc — anyone with a lathe and a tap set can build one in a weekend. A De Laval needs profiled convergent-divergent nozzles and shaped impulse blades on the rotor periphery, which is real machining work.
The De Laval will give you 2-3× the efficiency at the same steam consumption, but it will also spin at 15,000+ RPM, which means you need a step-down gearbox for almost any practical load. If your boiler can spare the steam and you want simplicity, choose Wilkinson. If steam is precious or you need the extra power, the De Laval earns its complexity.
The reaction efficiency factor ηr is the slipperiest term in the equation. The 0.18 figure used in the worked example assumes dry steam, clean nozzles, and a tip-speed-to-jet-speed ratio in the 0.08-0.10 band. If your actual operating point sits well outside that ratio — too slow because the load is too stiff, or too fast because you are running unloaded — ηr can drop to 0.08 or below.
Run a quick brake test with a Prony brake or a known electrical load. If the measured efficiency is below 0.10, look at the velocity ratio first. If it is above 0.10 but power is still low, mass flow is the suspect — a steam-flow meter on the supply line, even a simple orifice plate, will tell you whether you are actually getting the kg/s you assumed.
Tip-speed limit, not power, sets the diameter. Cast bronze rotors should not exceed about 80 m/s tip speed for a hobby-grade build without dynamic balancing, and 120 m/s with proper balancing on a calibrated stand. Working backward: at 8,000 RPM, 80 m/s gives you a maximum diameter of about 190 mm. At 5,000 RPM you can go to 305 mm.
If you want more power, do not chase diameter — add a second stage or open up the nozzles. Going large-diameter on a single-stage rotor puts the nozzle bosses under centrifugal stress that bronze does not handle well over long running.
Thermal growth in the casing and rotor is closing the tip clearance and increasing windage drag. On a cold rotor your 3-5 mm tip clearance is correct, but as the casing soaks up to steam temperature it grows differentially and the clearance can shrink to under 1 mm in places — sometimes touching at the hottest point near the exhaust. The drag from that near-rub eats RPM.
Check tip clearance hot, not cold. If it is closing below 2 mm on a 150 mm rotor, you need to open the casing bore or face-grind the rotor rim slightly. The other suspect is gland tightness — a graphite gland that seals well cold can swell hot and add measurable bearing drag.
Superheat helps — higher inlet enthalpy means higher jet velocity and lower nozzle erosion because the steam stays dry through expansion. The catch is the inlet gland. Carbon-graphite glands are happy to about 250°C; above that the binder breaks down and the gland weeps. Stuffing-box glands packed with graphited yarn handle 300°C but need more frequent re-tensioning.
For a heritage demonstration unit the practical answer is: 50-80°C of superheat is a useful boost and stays within standard gland materials. Anything more and you are into uprated gland design and possibly water-cooled bearing housings, which is more engineering than the power gain justifies on a sub-100 W rotor.
References & Further Reading
- Wikipedia contributors. Steam turbine. Wikipedia
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