Variable-Rate Fertilization Simulator

Application Mode

Field & Economics

Grid resolution 12 × 8

Nitrogen price $1.10/kg

Grain price $0.22/kg

Soil Test Nitrogen

Low N (needs more) → High N (needs less)

0 ppm40 ppm

Live Readouts

Total N applied

0 kg

Fertilizer cost

Est. yield

0 t/ha

N surplus (runoff risk)

0 kg

Net return

vs. uniform-rate

+$0

How it works

Every field cell is a soil-test sensor reading (N₀, ppm of plant-available nitrogen, generated with layered value noise so nearby cells are correlated like a real field). Crop response to nitrogen follows the classic quadratic Mitscherlich-type yield curve:

Yield(N) = Y0 + b·N − c·N²
Economic optimum: dYield/dN · Pgrain = Pnitrogen
  → N_opt = (b − Pn/Pg) / (2c)

The variable-rate applicator solves N_opt per cell, using each cell's own soil-test level to shift the curve — a cell already rich in soil N needs less added fertilizer to reach the same economic optimum, a depleted cell needs more. The uniform-rate mode instead applies the single field-average N_opt everywhere.

Total N applied / cost — sum of the applied-rate map × cell area × nitrogen price.
Est. yield — the quadratic response evaluated at each cell's applied rate, averaged over the field.
N surplus — nitrogen applied beyond what the crop can take up (over-application in already-rich cells), the main driver of nitrate runoff and leaching.
Net return — grain revenue minus fertilizer cost, compared directly against the uniform-rate baseline.

Real precision-ag rigs (John Deere, Trimble, Raven) do exactly this: a soil-sampling grid or on-the-go optical sensor feeds a prescription map to a rate-controller that pulses the boom's flow valves in real time as the applicator drives the field.

Hover a cell for soil-N & applied rate

⚠ Couldn't load the 3D engineThree.js failed to load from the CDN. Check your connection and reload.