Output Calculations
Part of Mill Construction
Calculating expected mill output lets you match mill capacity to community needs, size the water wheel correctly, and plan operational schedules.
Why This Matters
Building a mill is one of the largest capital investments a rebuilding community will make. Getting the size wrong in either direction has serious consequences. An undersized mill creates bottlenecks at harvest time when grain is plentiful and must be processed quickly. An oversized mill wastes scarce labor and materials, and a water wheel larger than the stream can reliably support will run intermittently and frustrate everyone who depends on it.
Output calculations also drive downstream decisions: how large to build grain storage, how many people a single miller can serve, whether a second mill is justified, and when to schedule maintenance shutdowns that won’t conflict with peak demand. These are planning questions that a community leadership needs answered before breaking ground, not after the mill is already running.
The math is not complicated, but it requires honest assessment of three things: the available water power, the grinding characteristics of the stones, and the actual demand from the community being served.
Power Available from Water
Water power is calculated from two variables: the flow rate (how much water passes through) and the head (how far it falls). The formula is:
Power (watts) = Flow (m³/s) × Head (m) × 1,000 × efficiency
Efficiency for a well-built overshot wheel is about 70–85%. For a breastshot wheel, 50–70%. For an undershot wheel, 25–35%.
Example: A stream with a flow of 0.2 m³/s (200 liters per second) and a head of 3 meters:
- Raw hydraulic power: 0.2 × 3 × 1,000 = 600 watts
- With an overshot wheel at 75% efficiency: 600 × 0.75 = 450 watts delivered to the millshaft
To convert watts to practical terms: grinding wheat requires roughly 0.3–0.5 watts per kg/hour of throughput for a well-designed stone mill. So 450 watts available could support 900–1,500 kg/hour of grinding capacity — far more than the stones can actually process. In practice, stone capacity is often the limiting factor, not water power.
Measuring Stream Flow
Before calculating anything else, you need to know how much water is available — and critically, how that flow varies across seasons.
Float method: Choose a straight section of stream 10–15 meters long with a relatively uniform cross-section. Measure the cross-section area at three points (width × average depth) and take the average. Release a floating object (a small stick or cork) at the upstream point and time how long it takes to reach the downstream point. Average velocity = distance ÷ time. Flow = average cross-section area × average velocity × 0.8 (the 0.8 corrects for the surface float being faster than the average current).
Weir method (more accurate): Build a temporary dam across the stream with a rectangular notch of known width cut into the top. All water flows through the notch. Measure the depth of water flowing over the notch (call it H, in meters). For a notch W meters wide: Flow (m³/s) = 1.84 × W × H^1.5. This formula works for a sharp-edged notch with water approaching slowly.
Measure flow at least monthly for a full year before building, or ask long-term residents about dry-season minimums. Design for the minimum reliable flow, not the average.
Stone Speed and Grinding Rate
Millstones have an optimal running speed — fast enough to grind efficiently, slow enough not to overheat the grain.
The peripheral speed of the runner stone (the speed at the outer edge) should be between 5 and 7 meters per second for most grains. Too slow and grinding is inefficient; too fast and the flour overheats.
Converting peripheral speed to RPM: RPM = (peripheral speed × 60) ÷ (π × diameter)
For a 1.2-meter diameter stone running at 6 m/s peripheral speed: RPM = (6 × 60) ÷ (3.14159 × 1.2) = 360 ÷ 3.77 = 95.5 RPM
The gearing between the water wheel and the millstone must achieve this RPM from the wheel’s slower rotation. A typical overshot wheel turns at 4–8 RPM. To reach 95 RPM at the stone from a 6 RPM wheel requires a gear ratio of about 16:1.
Grinding output depends on stone speed, stone diameter, furrow pattern quality, and grain type. Empirical values for wheat:
| Stone Diameter | Speed (RPM) | Output Range (kg/hr) |
|---|---|---|
| 0.75 m | 120 | 20–40 |
| 1.0 m | 100 | 40–70 |
| 1.2 m | 90 | 60–100 |
| 1.5 m | 80 | 100–160 |
| 1.8 m | 70 | 150–240 |
These ranges reflect variation in stone condition, grain moisture, and miller skill. Use the lower end for planning purposes.
Calculating Community Demand
Human flour consumption varies significantly based on diet, but practical planning figures:
- Minimal ration (survival): 300g flour per person per day
- Adequate ration (reasonable diet including other foods): 450–500g per person per day
- Full ration (flour as dietary staple): 600–700g per person per day
For a community of 500 people on an adequate ration: Daily flour demand = 500 × 0.45 kg = 225 kg/day
With a 1.2m stone at 80 kg/hour (conservative estimate) running 8 hours/day: Daily output = 640 kg/day — nearly three times demand.
This suggests one small mill can support a community of around 1,400 people on an adequate ration (640 kg ÷ 0.45 kg/person). But this assumes the mill runs every day, which it doesn’t. With maintenance days, stone re-dressing, and the seasonal nature of grain supply, effective capacity is about 70% of theoretical. Revised estimate: one 1.2m mill adequately serves 1,000 people.
Planning for harvest surge
At harvest time, you need to process the year’s grain supply in a limited window (6–8 weeks) before it deteriorates. This may require 3–4× normal daily throughput. Either build extra capacity, or plan to run the mill double shifts during harvest, or maintain large storage bins for un-milled grain.
Efficiency Losses to Account For
Extraction rate: Not all grain weight becomes flour. Whole-grain extraction is 80–95% by weight; fine white flour requires sifting and has an extraction rate of 60–70%. If your stones produce whole wheat flour (no sifting), your output numbers match the grinding rate. If sifting, expect 20–30% of output to be bran that doesn’t count as usable flour.
Downtime: Allow 20–30% downtime across a year for maintenance, re-dressing, repairs, and bad weather that reduces water flow below operating minimums.
Grist loss: Some grain and flour escapes during handling and milling — typically 2–3%. Not large, but worth accounting for in tight supply situations.
Combined efficiency: Multiplying these factors: 0.70 (uptime) × 0.85 (extraction, whole grain) × 0.97 (grist loss) = 0.58 overall. A mill rated at 100 kg/hour delivers about 58 kg/hour of usable whole flour to the consumer over a full year of operation.
Matching Wheel Size to Mill Demand
Once you know the power needed to drive the stones at the required output, work backwards to size the wheel:
Required power at millshaft = stone diameter factor × output rate
A rough rule: grinding 100 kg/hour of wheat at optimal stone speed requires about 50–75 watts at the millshaft. For 80 kg/hour output, call it 50 watts needed.
Working backwards from 50 watts needed, with an overshot wheel at 75% efficiency: Required hydraulic power = 50 ÷ 0.75 = 67 watts With 3 meters of head: required flow = 67 ÷ (3 × 1,000) = 0.022 m³/s = 22 liters/second
This is a modest stream requirement — many small streams exceed this year-round. The wheel diameter determines the head; a 2.5m diameter wheel on a 3m head site is practical and will easily exceed this power requirement.
Always build slightly more wheel than you calculate needing. The penalty for an oversized wheel is minor (slightly more material); the penalty for an undersized wheel is a mill that never reaches full capacity.