How SprinklerMap works: calculation methodology

Design principles adopted

SprinklerMap applies the principles of professional irrigation design defined by ASABE (American Society of Agricultural and Biological Engineers) and the technical guidelines of Rain Bird, Hunter Industries and the Irrigation Association.

The three core principles built into the tool:

1. Head-to-head coverage: the distance between adjacent sprinklers never exceeds the coverage radius. This is the spacing criterion recommended by manufacturer guidelines and by the IA (Irrigation Association) Best Management Practices, which set a target Distribution Uniformity (DU) of 75–90% for turf. Overlap favours uniformity but does not guarantee it on its own: the DU you actually measure also depends on the nozzle's distribution profile, operating pressure, wind, arc and installation quality.
2. Matched Precipitation Rate (MPR): sprinklers on the same circuit must have the same flow rate per unit area. A 180° sprinkler must deliver exactly twice the flow of a 90° sprinkler of the same model, at the same radius.
3. Hydrozone separation: plants with different water needs, or incompatible distribution systems (pop-up vs. drip), are never placed on the same circuit.

Sprinkler coverage calculation

Distribution model

SprinklerMap uses a simplified radial distribution model, consistent with the flow profiles published by sprinkler manufacturers. Precipitation rate (flow per unit area) is highest in the central zones and decreases toward the periphery following an approximated non-linear function.

Theoretical precipitation rate formula for sector sprinklers:

PR (mm/h) = (60 × Q) / (π × R² × (arc/360))

Where: Q = flow rate in L/min, R = radius in meters, arc in degrees. The constant 60 is nothing but the minutes-to-hours conversion: 1 L/min spread evenly over 1 m² for 60 minutes is 60 L/m², i.e. 60 mm/h. No external source is needed — it is a dimensional identity, and the denominator is simply the wetted sector area.

Distribution Uniformity (DU)

The coverage simulation computes the low-quarter Distribution Uniformity (DU_LQ) over the grid of irrigated cells:

DU_LQ = mean of the driest 25% of cells / mean of all irrigated cells

This is not Christiansen's CU, which measures something different (the mean absolute deviation from the mean) and is not computed here. Cells that never receive water are excluded: including them would measure coverage, not uniformity. DU_LQ ≥ 0.75 is generally considered adequate for residential use and ≥ 0.85 is the professional target, but this figure comes from the model, not from a measurement: on a built system, uniformity is verified with a catch-can test.

Head loss calculation

Head loss along the pipes is calculated using the Hazen-Williams formula, the hydraulic industry standard for polyethylene pipe (coefficient C = 140–150 for PE):

h_f = 10.67 × L × Q^1.852 / (C^1.852 × D^4.87)

Where: L = pipe length in m, Q = flow rate in m³/s, C = Hazen-Williams coefficient, D = internal diameter in m.

Local losses in solenoid valves, filters and fittings are estimated from the figures published in the manufacturers' data sheets (Hunter, Rain Bird, Bermad). One note on terminology, because the two are often quoted as if they were one: the resistance coefficient K (h = K · v²/2g) and the equivalent-length method (each fitting replaced by a length of pipe causing the same loss) are two distinct approaches, not the same method under two names.

Zone count calculation

The number of zones (independent hydraulic circuits) is determined by three constraints:

1. Flow constraint: the sum of the sprinkler flows on a circuit is kept within about 78% of the available flow. That 78% is a design margin adopted by SprinklerMap, not a standard or a legal requirement: it leaves room for mains pressure variation and for losses the model does not represent. A designer may reasonably adopt a different margin.
2. Pressure constraint: the pressure available at the farthest sprinklers on the circuit must be at least equal to the minimum operating pressure of the chosen sprinkler.
3. Compatibility constraint: pop-up sprinklers and drippers can never share the same circuit, due to incompatible operating pressures (2–3 bar vs. 0.5–1.5 bar).

Materials list calculation

Pipe runs are calculated by measuring the shortest path between all sprinklers in each zone (an approximated spanning-tree algorithm), plus a 10% margin for fittings, measurement error and routing changes during installation.

T-fittings are counted based on the branches along the route. Outlet fittings (saddle clamps or direct fittings) are counted one per sprinkler.

The main pipe size (25 mm, 32 mm or 40 mm) is selected based on the circuit's flow rate to keep flow velocity under 1.5 m/s (the recommended limit to reduce water hammer in PE pipe, source: Plastics Pipe Institute TR-4).

Sources for the numeric claims used on the site

The figures shown on the site are indicative and represent typical scenarios under normal conditions. Actual savings depend on specific local factors.

Stated limitations of the tool

• SprinklerMap does not account for steeply sloped terrain (>15%), which requires elevation-differentiated pressure calculations.
• The water distribution model is simplified: it does not simulate the effect of wind on sprinkler throw.
• Prices in the materials list are indicative and based on 2024 price lists. Actual prices vary by retailer and country.
• The tool is designed for residential systems (gardens up to about 2,000 m²). For larger or agricultural systems, a certified irrigation designer or agronomist engineer is recommended.

Questions about the methodology? Contact us. To use the tool: open SprinklerMap →

Deep dives on the algorithms

Two pages on how the app's automation works, with the same worked examples on the same garden: