A 1.2 m granite runner about 25 cm thick weighs about 733 kg, stores about 7.4 kJ of rotational energy at 100 rpm, and carries about 296 N-m of drive torque when 3.1 kW reaches the stone. Centrifugal stress at that speed is only about 85 kPa, far below the strength of any millstone rock, so a runner is made safe by balance, by sound stone and by a known stopping time rather than by fear of bursting.
Part of Community Grain Mill
The mechanics of the turning stone and its fixed partner: mass, inertia, torque, centrifugal stress, balance, and how the working gap is set and checked.
The Numbers Behind A Runner Come From Its Mass And Speed
The disc is a cylinder with a central hole. Take a 1.2 m runner (outer radius 0.6 m) of granite at 2,650 kg/m3 (a typical value, recalled), 0.25 m thick, with an eye 0.175 m across (radius 0.0875 m). These dimensions follow the sizes in Millstone Selection, which gives an eye of 15-20 cm for a 1.2 m stone.
| Quantity | Working | Result |
|---|---|---|
| Face area | pi x (0.6^2 - 0.0875^2) | 1.107 m2 |
| Volume | 1.107 x 0.25 | 0.277 m3 |
| Mass | 0.277 x 2,650 | 733 kg |
| Weight | 733 x 9.81 | 7.19 kN |
| Speed | 100 rpm = 100 x 2 x pi / 60 | 10.47 rad/s |
| Rim speed | 10.47 x 0.6 | 6.28 m/s |
| Moment of inertia | 0.5 x 733 x (0.6^2 + 0.0875^2) | 134.8 kg-m2 |
| Stored energy | 0.5 x 134.8 x 10.47^2 | 7.39 kJ |
The 733 kg lies inside the 500-800 kg that the corpus gives for a loaded millstone (Bearing Replacement).
Drive Torque Passes Through The Rynd And The Eye
Torque is power divided by angular speed. For the 3.1 kW at the stone worked out for a 3 m head and 0.2 m3/s (Water Wheel Design and Siting), 3,099 / 10.47 = 296 N-m. If the rynd bears on the eye wall at 0.0875 m radius the total push on the stone is 296 / 0.0875 = 3,382 N, about 1.7 kN on each of two ears. That is 47% of the runner’s own weight acting sideways on the eye edge, so a cracked or chipped eye fails first under drive load. Fit the rynd snug but not tight, and check the eye for cracks at every dressing.
Centrifugal Stress Is Small; Cracks And Imbalance Are Not
For a thin disc with a small central hole, the textbook peak hoop stress at the hole edge is about (3 + v) / 4 x density x angular speed^2 x outer radius^2, with Poisson’s ratio v about 0.25 (a standard formula, recalled). At 100 rpm:
- density x speed^2 x radius^2 = 2,650 x (10.47 x 0.6)^2 = 2,650 x 39.5 = 104.7 kPa
- peak stress = 0.8125 x 104.7 = 85 kPa
Stress rises with the square of speed: at 2 times the design speed it is 0.34 MPa, at 5 times 2.1 MPa and at 10 times 8.5 MPa. Stone tensile strength is a few MPa for sandstone and tens for hard granite (a recalled range, not a measurement), so a runner fed by a wheel or sails that run away to a small multiple of design speed does not burst from rotation alone. What breaks runners is flaws, a dropped stone, a mallet blow on the eye or an iron band that shifts, not speed. That is a reason to ring-test the stone at every dressing, not a reason to relax about overspeed.
Balance Sets How Hard The Stones Hammer
If the runner’s center of mass is offset from the spindle axis by e, the rotating force on the spindle is mass x e x speed^2.
- 1 mm offset: 733 x 0.001 x 10.47^2 = 80 N
- 5 mm offset: 733 x 0.005 x 10.47^2 = 402 N
That force revolves once every 0.6 s, shaking the thrust bearing and making the gap vary around the circle, which grinds some parts too fine and others coarse. To correct a 5 mm offset with lead at a radius of 0.5 m takes 733 x 0.005 / 0.5 = 7.3 kg. Traditional runners have cavities in the back for such weights.
Method: Balance And Gap
Step 1: Balance the runner on its seat. Support it level on a central pivot or on the spindle point with the drive disconnected. Note where it settles low, and add weight opposite until it stays level whichever way it is turned.
Step 2: Mount, clear the eye and set a wide gap. Run the stones empty for a minute and listen for a steady note.
Step 3: Set the gap by feel and sound. The corpus gives a coarse-meal gap of 1-2 mm and a fine-flour gap of 0.1-0.5 mm (Watermill Design); the mill-construction page puts the working gap at 0.5-2 mm overall. A rumble means the stones are too close; a hiss means too open. Meal at the spout should not exceed 40 degrees C by hand.
Step 4: Re-set after each dressing, because the lands have worn.
Step 5: Measure the coast-down. Cut the drive and time how long the stones take to fall from 100 rpm to 50 rpm with the gap open and no grain. The stored energy falls by 75% of 7.39 kJ, 5.5 kJ. If that takes 30 s, the average friction loss is 5.5 / 30 = 185 W. A longer coast than before means freer bearings; a shorter one means rising friction (Bearing and Shaft Maintenance).
The Bedstone Never Moves, So Its Support Must Not Either
The bedstone sits fixed and level on the timber frame, checked with a straightedge and a water level. Any rocking is ground into the face as unevenness and shows up as a changing gap around the circle. Bed it on mortar or wedge it on three points, never loosely.
Common Mistakes
- Trusting a fall-from-speed fear. A runner that runs away to 2 times the design speed sees 0.34 MPa; the real risks are cracks and imbalance.
- Balancing by eye. A 5 mm offset puts 402 N on the bearing; use the pivot test.
- Setting the gap once. Re-set after dressing, after a change in feed and as the wind or flow changes.
Stopping a 730 kg wheel of stone
The runner stores 7.4 kJ at 100 rpm and is driven through a gear train that cannot be halted by hand. The stop is the disengaged stone nut or the closed sluice or sail brake, and the coast time depends on friction: if friction at the stones and bearings absorbs 300 W the runner turns for about 7.39 / 0.3 = 25 s, and if grain is still being ground at the normal 3.1 kW only about 7.39 / 3.1 = 2.4 s. Never reach into the vat or the eye until the runner is dead still, and never lift it with the spindle engaged. Flour dust ignites if a bare stone strikes sparks or a hot bearing heats it: keep the hopper fed, sweep dust, allow no open flame in the mill and never test for dust with a flame.
What’s Next
- Learn next: Bearing and Shaft Maintenance - the footstep that carries the weight
- Combine with: Feed Mechanism - the shoe and damsel that keep the stones fed