MY SIMULATOR

English Watermill: Overshot Wheel

Water fills the buckets. Its weight turns the wheel.

INTERACTIVE 3D

Power vs wheel speed

Classroom-scale model of a traditional wheel — not a hydro-site design tool; real output depends on the site. Values are model values.

Sluice gate

Board hook-back

Millstone load

Lab & science

Drag to orbit, wheel / pinch to zoom. P = pause, R = reset.

Setup

Pond head above the flume floor

Number of buckets

Time scale (the real wheel needs a minute to settle)

Presets

Camera

Graphics (High on every device; Low = smaller shadows, no spray)

Live readout (model values)

Experiment: how far should the boards hook back?

Sweeps the hook-back angle with the current gate and head, finds the best wheel speed for each, and compares the full model with the textbook closed form.

Missions

Mission 4: head 0.7 m and gate 100 mm: what is the flow Q in litres per second?

The science

What you see

An overshot wheel: the flume drops water into buckets on the top of the wheel. Each bucket carries its water down the far side; the weight of that water, acting at a horizontal lever arm, gives the torque. The buckets spill as they tilt, so how long they hold the water decides how much of the available height is used. The stones load the wheel; the wheel settles where driving torque equals load torque.

Equations

Gate flow          Q = Cd a b sqrt(2 g h)        Cd = 0.62, b = 1.0 m
Jet speed          v = 0.9 sqrt(2 g h)           [flume losses: model]
Water per bucket   A_f = Q p / (w BW)            p = 2 pi / N, w = angular speed
Bucket held area   A(beta) = min(A_f, min over the path of A_r)
Retained area      A_r = area( bucket polygon  cap  y <= y_lip )   (free surface horizontal)
Torque of water    tau_w = sum_k rho g BW A_k x_k    (x_k: horizontal centroid distance)
Jet impulse        tau_j = rho Q (v - w R) R cos(beta_in)
Shaft power        P = (tau_w + tau_j) w
Available power    P0 = rho g Q H_gross          H_gross = flume + head - tailwater
Efficiency         eta = P / P0
Wheel dynamics     J dw/dt = tau_w + tau_j - tau_fric - s (T0 + T1 w)
Closed form check  P = rho g Q R_c (1 - cos theta_s)   (point buckets held to theta_s)

Assumptions & honest simplifications

The bucket is a flat (2-D) quadrilateral; the free surface is horizontal and the water never sloshes. Real buckets are curved and the water lags and splashes.
All water is captured at the entry point except the overflow of a full bucket; real wheels lose some water to splash at the entry.
Friction, the stone load and the gear ratio (12:1, stone speed = 12 x wheel speed) are illustrative constants, not measured from a real mill. Flour output uses a typical specific energy of about 55 kWh per tonne [typical value, verify before use].
Head and discharge are held constant; the millpond does not drain in this model.

Independent numerical checks

Also in node: node check.js.

Sources

Standard hydraulics texts for the orifice (Torricelli) discharge equation and overshot-wheel efficiency (typical well-built wheels reach roughly 60-85 percent [typical, verify]); bucket-retention geometry is derived here from first principles. No real mill, brand or drawing is reproduced.

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