## 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)