How pool heat-up time is estimated

Energy Balance Equation

The core model solves a first-order ordinary differential equation (ODE) representing the net energy flux into the pool water mass: Q_net = Q_heater − Q_evap − Q_radiation − Q_convection − Q_conduction The rate of temperature rise (dT/dt) equals Q_net divided by the thermal mass of the water (mass × specific heat capacity, 4.186 kJ/kg·°C). This is solved numerically using adaptive time-stepping to account for the temperature-dependent loss terms.

Heater Performance Modelling

Different heater types deliver energy at fundamentally different rates and efficiencies: • Gas heaters: Rated in MJ/h with thermal efficiency typically 80 to 85% for modern condensing units • Heat pumps: modelled using Coefficient of Performance (COP) curves that vary with air temperature and humidity. A unit rated at COP 5.0 at 25 degrees may be much lower at 10 degrees. • Electric resistance: Near-unity efficiency (>99%) but limited by element wattage • Solar: Collector area, orientation, and hourly solar irradiance data for Melbourne (Bureau of Meteorology TMY dataset)

• Heat pump COP degradation curves modelled from manufacturer performance data
• Gas heater efficiency accounts for flue losses and cycling penalties
• Solar thermal gain uses Melbourne-specific hourly irradiance profiles
• Defrost cycles for heat pumps below 7°C ambient are factored into net output

Heat Loss Mechanisms

A pool loses heat through four primary mechanisms, each modelled independently: Evaporative loss dominates in most conditions (40 to 70% of total loss). It depends on water surface temperature, ambient humidity, and wind speed via the Penman evaporation equation adapted for pool surfaces. Radiative loss follows Stefan-Boltzmann law, exchanging longwave radiation between the water surface and the sky dome (effective sky temperature is typically 10 to 20°C below ambient). Convective loss is driven by the temperature differential between water surface and ambient air, modulated by wind speed using empirical convection coefficients. Conductive loss through pool walls and floor is typically minor (5 to 10%) but included for completeness using thermal resistance values for common construction types.

Pool Cover Effects

Pool covers dramatically alter the heat loss profile by suppressing evaporation (the dominant loss mechanism). Our model applies cover-specific reduction factors: • Bubble/solar covers: 85 to 95% evaporation reduction, minor solar gain contribution • Thermal blankets: 90 to 98% evaporation reduction, higher R-value insulation • Liquid covers: 30 to 50% evaporation reduction (molecular monolayer) • No cover baseline: Full exposure to all loss mechanisms The calculator assumes the cover is on when the pool is not being used, unless you enter uncovered hours.

Melbourne Climate Integration

Rather than using generic climate assumptions, our model incorporates Melbourne-specific meteorological data including typical diurnal temperature swings, seasonal humidity patterns, prevailing wind conditions, and solar irradiance profiles. This gives a closer estimate than using a generic climate setting, but wind, shade, cover use and equipment condition can change the result.