Smart Irrigation Engineering – ESP32-S3 Waveshare 6CH Relay

In agrometeorology and irrigation engineering, the industry standard for calculating crop water requirements is the FAO-56 Penman-Monteith model (or its simplified variants tailored for microcontrollers, such as the Hargreaves-Samani equation).

For the ESP32-S3 microcontroller, the irrigation coefficient $ K_{\text{irrig}} $ (run-time multiplier for each zone) is calculated as a water balance relative to evapotranspiration and precipitation:

Where:

$ \text{ET}_c $ – actual crop evapotranspiration (water depleted from the soil via plant transpiration and surface evaporation).
$ P_{\text{eff}} $ – effective precipitation (rainfall that actually infiltrates the root zone).
$ \text{ET}_{\text{base}} $ – baseline daily water demand (the reference value for which the user set the default runtime in minutes, typically $ 4.0\text{ mm/day} $).
$ \text{clamp}(x, 0.0, 1.5) $ – saturation function restricting the coefficient within a safe operating range.

1. Formula Breakdown

A. Actual Crop Evapotranspiration ($ \text{ET}_c $)

$$\text{ET}_c = \text{ET}_0 \times K_c$$

$ K_c $ – crop coefficient (e.g., turf grass = $ 0.8 $–$ 0.9 $, shrubs = $ 0.6 $).
$ \text{ET}_0 $ – reference evapotranspiration [mm/day].

On the ESP32-S3 microcontroller, using data from Open-Meteo (temperature and relative humidity), reference evapotranspiration $ \text{ET}_0 $ is computed using the simplified Roman-Turc formula:

Under typical conditions, using only ambient temperature $ T $ [°C] and relative humidity $ RH $ [%]:

When the air is dry ($ RH < 40\% $) and hot, the $ C_h $ coefficient automatically increases soil evaporation losses.

B. Effective Precipitation ($ P_{\text{eff}} $)

Plants cannot utilize all precipitation—heavy rainfall exceeding the soil infiltration capacity results in surface runoff or deep percolation below the root zone. According to USDA (Soil Conservation Service) guidelines:

Where:

2. Vector Implementation on ESP32-S3

The heuristic algorithm implemented in smart_irrigation.c is a first-order Taylor series expansion of the governing equations centered around the equilibrium point ($ T = 20^\circ\text{C} $, $ RH = 60\% $, $ P = 0\text{ mm} $):

$$K_{\text{irrig}} = 1.0 + \Delta T + \Delta RH - \Delta P$$

Linear sensitivity weights derived from differential evapotranspiration models:

$$K_{\text{irrig}} = 1.0 + 0.03 \cdot (T - 20) + 0.008 \cdot (60 - RH) - 0.20 \cdot P_{\text{eff}}$$

Subject to hard safety thresholds:

$$\text{If } \left( P_{\text{now}} > 0.5\text{ mm} \quad \text{or} \quad P_{\text{tot}} \ge 5.0\text{ mm} \right) \implies K_{\text{irrig}} = 0.0$$

3. Solenoid Valve Runtime Calculation

The target duration written to registers and hardware countdown routines in RAM (relay_countdown_timers[zone]) is determined by:

$$t_{\text{runtime}} = \lfloor t_{\text{base}} \times 60 \times K_{\text{irrig}} \rfloor \quad [\text{seconds}]$$

For a baseline schedule of $ t_{\text{base}} = 10\text{ minutes} $ and a calculated multiplier of $ K_{\text{irrig}} = 0.47 $:

$$t_{\text{runtime}} = 10 \times 60 \times 0.47 = 282\text{ seconds}$$

Edge AI Implementation Summary

Deploying vector heuristics directly onto the ESP32-S3 microcontroller eliminates cloud dependencies by executing full microclimate analytics at the edge:

Autonomous Decision-Making: The $ K_{\text{irrig}} $ factor is calculated entirely in RAM based on the real-time weather telemetry vector from Open-Meteo ($ T, RH, P $).
Resource Conservation: Dynamic zone runtime scaling prevents overwatering, while the hard rain interlock ($ P_{\text{tot}} \ge 5.0\text{ mm} $) instantly closes all solenoid valves.
Core Process Isolation: Mathematical modeling running on Core 1 does not affect GPIO hardware register operations or AES-128-GCM encrypted UDP communications handled by Core 0.

Architecture deployed on a Waveshare 6CH relay module within the ProPresta IT Home Automation platform.

1. Formula Breakdown

2. Vector Implementation on ESP32-S3

3. Solenoid Valve Runtime Calculation

Edge AI Implementation Summary

Hello, I'm Andre Stepniewski