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+
+## Heating Water Pool Model
+
+For a pool of a given size (liters/gallons), with given insulation (R-value or
+U-value), at an external air temperature, with/without a cover, with a given
+input of electrical heating power, at a given initial temperature:
+
+- how long to heat to a given temperature
+- power needed to maintain temperature
+- how much energy to heat
+
+Assumptions/constraints:
+
+- atmospheric pressure
+- water stays between freezing and boiling
+- humidity?
+
+Overall refs:
+
+- [Energy Smart Pools Software](http://www.rlmartin.com/rspec/software.htm)
+
+### Units
+
+A BTU (Britich Thermal Unit) is the amount of heat (energy) which will increase
+the temperature of one pound of water by one degree Fahrenheit.
+
+A calorie (SI) is the amount of heat (energy) which will increase the
+temperature of one gram of water by one degree Celsius.
+
+1 BTU ~= 1055 Joule
+1 BTU ~= 0.2931 watt hours
+1 BTU ~= 252 calories
+
+Refs:
+
+- [Wikipedia: BTU](https://en.wikipedia.org/wiki/British_thermal_unit)
+
+### Heating
+
+heat capacity of water: 4200 Joules / Kelvin / gramm
+
+T: temperature
+P: power (Watt)
+t: time (second)
+C: heat capacity (Joules / Kelvin)
+m: mass (gramm)
+
+dT/dt = P / (C * m)
+
+### Conductive heat loss
+
+Conductive loss (walls, floor):
+
+theta: "heat flow rate" (Watt)
+A: surface area (meter^2)
+deltaT: temperature difference (Kelvin)
+R_val: R-value (Kelvin * meter^2 / Watt)
+
+assertion: T >= T_env
+
+deltaT = T - T_env
+theta = (deltaT * A) / R_val
+
+Refs:
+
+- [How To Calculate Heat Loss?](https://industrialheatingsystems.com/How-calculate-heat-loss.html)
+
+### Evaporative heat loss
+
+This part is trickier, lots of factors could be included.
+
+k_s: heat loss factor
+deltaT: temperature difference (Kelvin)
+A: surface area (meter^2)
+
+TODO
+
+- [Measurement and Analysis of Evaporation from an Inactive Outdoor Swimming Pool](http://www.rlmartin.com/rspec/whatis/studies_outdoor_inactive.htm)
+- [How to Calculate Water Evaporation Loss in a Swimming Pool](https://dengarden.com/swimming-pools/Determine-Evaporation-Rate-for-Swimming-Pool)