A Form 2 windmill is a horizontal-axis sail mill — the classic European post or tower mill — where four cloth-covered sails rotate on a near-horizontal wind shaft to drive a vertical millstone shaft through wooden gearing. It solves the problem of converting low-density wind energy into rotary shaft power without electricity, using swept area and gear-up ratios to lift millstone speed to useful values. A typical 4-sail mill with 10 m sails sweeps roughly 314 m² and delivers 5-15 kW at the stones in a 7 m/s wind, enough to grind 100-200 kg of grain per hour.
Windmill Form 2 Interactive Calculator
Vary sail speed and gear step-up ratios to see the runner stone RPM and second-stage gearing.
Equation Used
The calculator multiplies the sail RPM by the total gear step-up to estimate runner-stone speed. It also divides the total ratio by the first-stage brake-wheel/wallower ratio to show the second-stage spur-wheel/stone-nut ratio required.
- Gear train is treated as an ideal speed step-up with no slip.
- The low and high ratios represent the worked example runner-stone speed range.
- Stage 1 is the brake-wheel to wallower ratio; stage 2 is the spur-wheel to stone-nut ratio.
How the Windmill (form 2) Works
The Form 2 windmill captures wind on four sails set at a pitch angle, typically 12-18° at the tip and 25-30° at the root, so the sail behaves like a long twisted aerofoil rather than a flat paddle. Wind hits the sail at an angle of attack, generates lift, and that lift component along the plane of rotation is what drives the wind shaft. The whole cap or buck must point into the wind — that's what luffing means — because if the sails sit more than about 15° off-wind, power drops by half and the structure starts shaking from cyclic side loading.
Inside the cap, the wind shaft carries the brake wheel, a large cogged wheel 2-3 m in diameter that meshes with the wallower on top of the vertical upright shaft. The wallower drives the great spur wheel further down, which in turn drives one or more stone nuts on the millstone spindles. Step-up ratios of 6:1 to 8:1 are standard, so a sail turning at 12 RPM in a working wind drives the runner stone at 80-100 RPM — the right speed for grinding without scorching the flour.
Get the sail twist wrong and the mill misbehaves in named ways. Too much pitch and the sails stall in light wind — they never start. Too little pitch and the mill runs away in a gale, which is why every working post mill has a striking gear or a brake wheel rope to choke off the millstones before the sails self-destruct. The 1779 collapse of several Norfolk smock mills in a single storm came down to brake-wheel failure, not sail failure.
Key Components
- Sails (whips and bays): Four wooden lattice frames covered with canvas, typically 9-12 m long, set at a twisted pitch from root to tip. The sail catches wind, generates lift, and converts it to torque on the wind shaft. Cloth coverage is reefed by hand on common sails — a miller climbs the sails with the brake on to roll cloth in or out depending on wind strength.
- Wind shaft: A massive oak or cast-iron shaft, usually inclined 5-15° above horizontal so the sails clear the body of the mill. It carries the sails on its outer end and the brake wheel on its inner end. Bearings are bronze or lignum vitae thrust pads — the inclination matters because a level shaft would let the sails strike the mill body in flex.
- Brake wheel: A 2-3 m diameter cogged wheel keyed to the wind shaft. It transmits drive to the wallower and also serves as the friction surface for the brake band, which is the only way to stop a runaway mill. Wooden cogs are sized to mesh with the wallower at a 1:6 to 1:8 step-up ratio.
- Wallower: A smaller cogged wheel mounted on top of the vertical upright shaft, meshing horizontally with the brake wheel. It transfers drive from the horizontal wind shaft to the vertical drive train. Tooth count typically 30-40 cogs against the brake wheel's 60-80, giving the first step-up.
- Great spur wheel: Mounted lower on the upright shaft, this large gear drives one or more stone nuts. Diameter 2-3 m, hardwood cogs running against cast-iron stone nut pinions. This stage provides the second step-up to bring runner-stone speed up to 80-120 RPM.
- Tail pole or fantail: The mechanism that keeps the cap pointed into the wind. A tail pole is manually pushed by the miller; a fantail (added on English mills after Edmund Lee's 1745 patent) is a small auxiliary windmill at right angles that automatically luffs the cap when the wind shifts. Without it, the mill loses 50% power on a 30° wind shift.
Where the Windmill (form 2) Is Used
Form 2 windmills powered the pre-industrial economy of northern Europe for 600 years and remain in working order at dozens of heritage sites today. They drive millstones, scoop wheels, sawmill cranks, and oil-seed presses — anywhere a steady rotary shaft is wanted and a fall of water isn't available. The horizontal-axis sail mill has the highest power coefficient of any pre-electric wind machine — common sails reach Cp around 0.17, patent sails 0.20-0.25, well below the Betz limit of 0.59 but more than enough for grain milling.
- Heritage grain milling: Jill Windmill in Clayton, Sussex — a working post mill grinding stoneground wholemeal flour for local bakeries on weekends when wind exceeds 4 m/s.
- Land drainage: Dutch polder mills like the Kinderdijk group, where 19 Form 2 mills lifted water 1.5 m per stage from polders below sea level into the Lek river, each scoop wheel moving 40-60 m³/min in a working wind.
- Oil-seed pressing: De Zoeker oil mill at Zaanse Schans, a working octagonal smock mill crushing linseed and rapeseed using stamper hammers driven off the great spur wheel.
- Sawmilling: Het Jonge Schaap paltrok mill in the Zaan region, driving a reciprocating frame saw via a crank off the upright shaft to cut oak planks for traditional Dutch boatbuilding.
- Education and demonstration: Bembridge Windmill on the Isle of Wight, run by the National Trust as a static educational mill showing the full gear train from sails to stones.
- Craft distilling and malting: Heritage malting mills in Holland and East Anglia historically cracked malted barley with windmill-driven stones at 60-80 RPM, slow enough to avoid scorching the husk.
The Formula Behind the Windmill (form 2)
The shaft power a Form 2 windmill delivers depends on swept area, wind speed cubed, and the power coefficient of the sails. Wind speed dominates because of the cube — doubling wind speed gives eight times the power, which is why millers wait for the right day rather than work in a breeze. At the low end of useful wind (around 4 m/s) a typical mill barely turns the stones; at nominal working wind (7 m/s) it grinds at full rated output; above 12 m/s the miller starts reefing cloth or risks tearing the sails apart. The sweet spot for steady milling sits between 6 and 9 m/s.
Variables
| Symbol | Meaning | Unit (SI) | Unit (Imperial) |
|---|---|---|---|
| P | Shaft power delivered at the wind shaft | W | ft·lbf/s |
| ρ | Air density (≈1.225 at sea level, 15°C) | kg/m³ | lb/ft³ |
| A | Swept area of the sails (π × R2) | m² | ft² |
| v | Free-stream wind speed at hub height | m/s | ft/s |
| Cp | Power coefficient of the sail set (0.15-0.25 for traditional sails) | dimensionless | dimensionless |
Worked Example: Windmill (form 2) in a working heritage rapeseed-oil mill on the Danish island of Bornholm
A small heritage rapeseed-oil cooperative on Bornholm wants to restore a four-sail post mill to drive a stamper press for cold-pressed rapeseed oil. The sails are 10 m long (so radius R = 10 m, swept diameter 20 m), the sails are patent-type with a power coefficient of 0.22, and the local wind atlas gives a mean working wind of 7 m/s with a usable range of 4-12 m/s. The press needs about 8 kW at the input shaft to crush 60 kg/hr of seed. You need to know if the mill produces enough power across the working wind range.
Given
- R = 10 m
- ρ = 1.225 kg/m³
- Cp = 0.22 —
- vnom = 7 m/s
- vlow = 4 m/s
- vhigh = 12 m/s
Solution
Step 1 — compute the swept area. The sails sweep a full circle of radius 10 m:
Step 2 — at nominal 7 m/s working wind, compute shaft power:
That gives plenty of margin over the 8 kW press demand. The miller can run at part load or run two stamper sets in parallel.
Step 3 — at the low end of the working range, 4 m/s, recompute. The cube of wind speed dominates:
That's well below the 8 kW press demand — in a 4 m/s breeze the sails turn but the press won't lift its hammer fast enough to do useful work. The miller would either disengage the press and let the sails freewheel, or wait for stronger wind. This is why traditional millers worked to a wind threshold, not a schedule.
Step 4 — at the high end, 12 m/s, the cube law turns brutal:
That's nearly five times the rated load. No traditional mill is built to handle that — the brake wheel cogs would shear, the wind shaft journals would overheat, and the sails themselves would tear at the bays. The miller must reef the cloth back to roughly half-coverage before wind reaches 10 m/s, or the mill destroys itself. This is exactly the failure mode that took out several Lincolnshire mills in the 1894 storm.
Result
At nominal 7 m/s wind the mill delivers about 14. 5 kW at the wind shaft, comfortably above the 8 kW press demand. At the 4 m/s low end the mill produces only 2.7 kW — the sails turn but the press starves, which is why a miller waits for working wind rather than fighting a breeze. At 12 m/s the theoretical power balloons to 73 kW and the mill must be reefed or braked or it self-destructs. If your measured shaft power runs 30%+ below the predicted 14.5 kW at nominal wind, check three things in this order: (1) cap luffing — if the sails sit more than 15° off-wind the cosine loss alone wipes out a third of your power; (2) sail cloth coverage — patent sails with shutters stuck partly closed cut Cp from 0.22 down toward 0.12; and (3) brake-band drag — a partly-engaged brake band on the brake wheel can swallow several kilowatts as heat without the miller noticing until the wood smokes.
Windmill (form 2) vs Alternatives
The Form 2 horizontal-axis windmill competes against vertical-axis sail mills (the older Form 1, like the Persian Sistan mill) and modern small wind turbines for off-grid mechanical work. Each makes different compromises on power coefficient, build complexity, and what happens in a storm.
| Property | Form 2 horizontal windmill | Form 1 vertical-axis sail mill | Modern small HAWT (3-blade) |
|---|---|---|---|
| Power coefficient Cp | 0.17-0.25 (patent sails) | 0.08-0.12 | 0.40-0.45 |
| Typical shaft RPM (10 m sails / equivalent) | 10-18 RPM at sail, 80-120 RPM at stone | 20-40 RPM | 150-300 RPM at rotor |
| Yaw / luffing requirement | Yes — fantail or tail pole required | No — accepts wind from any direction | Yes — active yaw drive |
| Build cost (heritage / restoration) | £250k-£800k full restoration | £50k-£150k | £3k-£20k off-the-shelf |
| Storm survivability | Requires manual reefing above 12 m/s | Self-limiting in high wind | Auto-feathering or furling above 15 m/s |
| Maintenance interval (working mill) | Sail cloth annual, cogs every 5-10 yrs | Reed mats every 2-3 yrs | Bearings 5 yrs, blades 20 yrs |
| Best application fit | Direct mechanical drive — millstones, presses, scoop wheels | Low-power continuous pumping | Electrical generation |
Frequently Asked Questions About Windmill (form 2)
The cube law on wind speed is unforgiving and most working sites measure wind at the wrong height. Anemometer readings taken on the ground or on a nearby roof routinely under-read the hub-height wind by 20-30%, so what you call 7 m/s might actually be 5.5 m/s at hub height — and 5.53 versus 73 is roughly half the power. Get a proper hub-height reading before you blame the gearing.
Beyond that, check sail twist. Old patent-sail shutters that have been re-canvased without preserving the original twist distribution often end up running closer to a flat plate than a twisted aerofoil, and Cp drops from 0.22 to around 0.14 — about 35% less power for the same wind.
More sails do not give proportionally more power — swept area is what matters, and adding sails inside the same diameter actually adds drag without much extra lift. Five and six-sail mills (like Heckington in Lincolnshire) were built for a different reason: redundancy. Lose one sail in a storm and a 5-sailer is still balanced as a 4-sailer with reduced output, while a 4-sailer with one sail down is dangerously unbalanced and must stop.
For new restoration work, four sails are simpler to build, easier to reef, and cheaper to re-canvas. Choose five or six only if the original mill had them — keeping the historical configuration matters for listed-building consent.
The rule of thumb among working millers is reef before 10 m/s on common sails, before 11 m/s on patent sails. The reason is structural, not aerodynamic — at 10 m/s the bending moment on each sail whip is roughly four times what it is at 5 m/s (force scales with v²), and the timber whips, the canvas attachment points, and the brake-wheel cogs all start operating near their fatigue limits.
Above 12 m/s on full sail, expect to hear the cogs grumble and the wind shaft journals heat up within minutes. That heat is the warning sign — bronze bearings smelling hot is the cue to apply the brake immediately.
Brake band slip is the usual culprit, and it almost always traces to the brake band lining being glazed or oil-contaminated. The traditional band is wood or strap iron lined with leather or a hardwood block running against the iron rim of the brake wheel. Once that surface glazes, the coefficient of friction drops from around 0.4 to 0.15, and the band cannot dissipate the wind input in a working breeze.
The fix is to dress the band — file or sand the glazed surface back to fresh material, and check that no grease has migrated from the wind-shaft bearing onto the brake wheel rim. If you're still slipping after dressing, the band tension lever geometry has likely shifted with timber shrinkage and needs re-pinning.
You can, but you have to match the load curve. Millstones are forgiving — they accept whatever power the wind gives and grind faster or slower accordingly. A generator with a fixed electrical load will stall the mill in light wind and overspeed it in strong wind unless you put a governor or a dump load between them.
The practical answer for heritage sites is a permanent-magnet generator with a resistive dump load that absorbs excess power as heat. Sized correctly, it lets the mill run at roughly constant tip-speed-ratio across the working wind range, which keeps Cp near its peak rather than collapsing to zero in stalled or runaway conditions.
Fantail hunting is almost always a gear-ratio issue between the fantail and the curb. Edmund Lee's original 1745 design used a worm-and-wheel drive with a step-down on the order of 3000:1, so a wind shift of 30° at the fantail moves the cap maybe half a degree per fantail revolution — slow enough to never overshoot.
If your restoration cap turns visibly during a fantail rotation, the gearing has been shortened somewhere in the chain — often a lost intermediate gear replaced with a direct coupling. The cure is to restore the full reduction; without it, the fantail will oscillate every time wind direction shifts more than a few degrees, and the cap bearings will wear out within a season.
Yes — usually around 3-3.5 m/s for a 10 m sail set, depending on sail pitch and bearing friction. Below that, the lift generated at the sail tips can't overcome static friction in the wind shaft bearings plus the disengaged drag of the wallower. The mill sits stationary even though the cloth fills.
Two things move that threshold down: cleaning and oiling the wind shaft bearings (good lignum vitae bearings can drop the cut-in wind by 0.5 m/s), and disengaging the stone nuts so the sails only have to spin the brake wheel and wallower at startup. Engage the stones only once the mill has spun up to 8-10 RPM at the sails.
References & Further Reading
- Wikipedia contributors. Windmill. Wikipedia
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