How an engineer looks at kiddie pools: tensile strength of curved walls, thermal conductivity, evaporative cooling, blackbody radiation, Sun ephemerides, and water sanitation techniques.

1. Introduction Nowadays you can get a 4,400 liter, 3 meter wide, metal frame above ground swimming pool for 99 EUR. Inflatable models with the same capacity sell for less than 60 EUR - and that includes filtration ! But it is easy to spend a lot more on add-ons than on the pool itself, for the sake of doing a bit of applied science in one's backyard. This article is a collection of back-of-the-envelope calculations about mechanical design, thermodynamics and chemistry in relation to garden swimming pools.



3. Assumptions For numerical calculations we will assume: Overall diameter: 3.05 m

Water quantity: 4,400 kg

Water surface: 6.5 m²

Water height: 0.68 m

Ambient temperature: 20°C (293 K)

Target water temperature: 30°C (303 K)

Heat capacity: Cp = 4180 J/kg/K

Latent heat of vaporization: L = 2260 kJ/kg

4. Tensile strength The side wall of these pools is typically made of two layers of PVC laminated to an inner polyester mesh. It must be strong enough to resist hydrostatic pressure. Thin-walled cylindrical pressure vessels are dimensioned according to the formula S=P*r/t where S is circumferential stress, P is inner relative pressure, r is radius of curvature, and t is wall thickness. Here r = 1.5 m, P = 6800 Pa at the bottom, and t = 0.71 mm. So the tensile strength of the liner should be at least 14 MPa. This is consistent with polyester having a tensile strength of 55 MPa. According to the same formula, the largest model in the product range should have a liner about 5 times as thick, i.e. between 3 and 4 mm, for a diameter of 7.92 m and a water height of 1.17 m.

5. Resistive heating



3 kW pool heater



3 kW pool heater



3 kW pool heater

Affiliate links It takes 184 MJ (51 kWh) to raise the water temperature by 10 K. Assuming 0.15 EUR/kWh, a 3 kW pool heater can do the job in 17 hours for 8 EUR. Afterward, the heater still needs to compensate for losses. For comparison, the cost of filling the pool with tap water is 19 EUR.



7. Solar cover vs. evaporative cooling



Solar blanket 3.05 m



Solar blanket 3.05 m



Solar blanket 3.05 m



Solar blanket 3.05 m

Affiliate links A solar cover (a.k.a. solar blanket) is a sheet of plastic material that looks like bubble wrap and floats on the surface of the pool. The name suggests that its purpose is to capture sunlight, possibly like a greenhouse would. But this does not make much sense, as water itself is very good at absorbing infrared radiation. Presumably the actual function of these covers is to reduce heat loss: The air inside the bubbles creates an insulating layer against heat loss by conduction.

The cover acts as a barrier against evaporation. Evaporative cooling is a very significant phenomenon: Whenever 1 % of the water evaporates, the temperature drops by 5 K.



9. Vertical solar collector There are several motivations for installing solar collectors vertically: Not enough space available on the ground

Ground is shaded by trees or buildings

Capturing heat in the morning when the sun is low on the horizon. Here are the issues that need to be addressed: Filtration pumps generate only about 1 meter of head. Therefore air must be flushed and prevented from re-entering the circuit. Otherwise the flow will be interrupted and the pump may overheat.

Air is best flushed by injecting water at the bottom of the circuit, e.g. by connecting a garden hose, but care must be taken to avoid over-pressurizing the collectors; their rated maximum pressure is about 1 bar.

Pressure at the top of the circuit will be below atmospheric pressure. This may cause problem with plumbing connectors that are designed for positive pressure. For example, the quick connect fittings which are commonly found on garden hoses are not watertight under negative pressure. And here is one way to implement a vertical collector: Attach a transparent bubble trap and a one-way valve at the highest point of the circuit.

Attach a ball valve and fitting for a garden hose at the bottom.

Install the bypass valve at the egress of the collector, rather than at the ingress.

Add a one-way valve at the ingress of the collector. With this configuration, it is possible to disconnect the collector from the filtration circuit, and safely flush air by injecting water at the bottom.



10. Ground insulation



60x60 cm foam mat x4



60x60 cm foam mat x4



60x60 cm foam mat x4



2'x2' foam mat x6

Affiliate links Presumably a significant portion of heat losses is caused by conduction to the ground. Suppose the pool is installed on a 13 mm thick EVA foam mat. Assuming the ground is at ambient temperature and EVA foam has the same thermal conductivity as polyurethane foam (0.02 W/m/K), this reduces losses to 15 W/m² (0.02 K/h). Assuming instead that the weight of the pool compresses the foam into a 5 mm layer with the same thermal conductivity as solid EVA (0.34 W/m/K), heat loss would be 680 W/m² (0.9 K/h). In practice, dry soil would provide additional insulation. The foam mat also protects the pool liner from sharp rocks and other debris which are hard to find until the pool has been filled.



11. Sun ephemerides The pool and solar collector should be positioned optimally after taking into account Sun ephemerides for the specific location and time of year, statistical climate data, and 3D models of surrounding trees and buildings. But maybe this would be going too far into over-engineering territory. Institut de Mécanique céleste et de calcul des éphémérides (IMCCE)

JPL HORIZONS on-line solar system data and ephemeris computation service