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This section provides basic formulae and equations for calculating a spa's energy consumption. Although the given equations are valid for most of the spas, our calculations and assumptions are based on the popular and energy efficient Sovereign model from Hotspring.

There are lots of energy calculations presented on the internet. However, most of them are based on a limited spa usage of approx. once per day and between 20 and 30 minutes open of which then the jet pump(s) are on between 10 and 20 min each use! For the rest of the time the spa just 'sleeps' in standby-mode, with its cover fitted, of course.

The energy calculations do not really inform the user how their spa's energy consumption will change if they don't follow the above mentioned usage pattern.

How will the costs be affected, when

• the cover is off for a longer period?
• the user enjoys soaking longer than 30 minutes a day?
• the jet pump(s) are on all the time?
• the spa is exposed to wind and precipitation?
• ...?

The quoted costs in this study are based on average electric power rates in Germany for 2008 of 0,20 €/kWh which represents approx. 0,30 US$/kWh (depending on exchange rate!).

Heating up of the freshly filled spa

According to water sanitation manuals the 39°C hot spa water should be renewed about four times a year. Assuming the spa will be filled with fresh water from the mains which temperature varies between 6°C and 16 °C with respect to the season the water will have to be heated up by approx 28°C.

Heating a volume of 1000 liter spa water (or 264 US gls) by 1°C requires an energy 'Q' calculated by equation (1)

Q = 1000 kg * 4,182 kJ/kgK * 1 K  = 4182 kJ or 1,163 kWh (factor 2,78 10^-4 kWh/kJ)

Heating up the Sovereign with 1200 ltr from 11°C to 39°C therefore consumes an energy of 39 kWh or 7,81 € if heated electrically. Renewing the spa water four times a year amounts to 156 kWh or 31 €.

If non-electrically heated domestic water is available, users should use this to refill their spas, since this is more efficient than using electrical energy (unless produced by renewable resources such as water power).

(1) Q = m c ΔT_W

with

• m = water in kg
• c = thermal capacity of Water in kJ/kgK
• ΔT_W = temperature change of water in Kelvin

Standby

Most of the time the spa will be in its standby mode (hopefully covered) and filtering the water using a pump either permanently operated (24/7) or frequently operated. It could be a dedicated circulation pump or the 1st stage of a jet pump employed for this task.

Our test model has a standard own circulation pump which operates 24/7 hardly noticeable (means neighbourhood friendly!). Its power consumption depends on the filter condition. Additionally there is energy required for operating the ozonator and the spa control unit which are also on for 24/7. For our model the circulation pump, ozonator and spa control unit amount to 47 W.

Their energy consumption 'E' calculates by

E = 47 W x 24 h/d = 1,13 kW/d (or 7,9 kWh/wk or 34 kWh/m or 412 kWh/a)

Operating costs are 0,23 €/day.

How long the pump has to be 'on' per day is a question of water sanitation. The manufacturer will recommend a minimum operation time for keeping the water 'clean'. Be aware when the circulation of your spa consumes more than 100 W (try to get an explanation from the dealer)!

In standby mode the spa's heater will switch on frequently in order to maintain the set water temperature within a tolerance. Heater wattage can be as little as 1500 W as for our model or up to 6000 W. The circulation pump will have to work while the heater is operated.

According to equation (1) the 1200 ltr spa water are heated up by 0,96°C per hour using the 1500 W no-fault heater (assuming 100% efficiency).

The heater has to compensate the heat loss of the spa through its insulation. We have estimated from published Hotspring data a specific spa standby efficiency of U_spec = 7,5 W/K for the model Sovereign.

For an ambient temperature of 8,2°C and a spa temperature of 39°C the heat loss 'P_HL' of the spa calculates by

P_HL = 7,5 W/K x (39,0 - 8,2)K = 231 W or 5,54 kWh per day incl. the circ pump

It has to emphasised that this assumed 'U_spec' represents a very good energy efficiency which is unsurpassed by most of the other spas.

CLEAN cycle before using the spa

Prior to using the spa it is recommended to add some sanitizer and run the jet pump on a specific CLEAN cycle (which is approx. 10 min.). There is only one jet pump in the Sovereign, which however, we feel sufficient enough. The jet pump operates simultaneously with the circulation pump, ozonator and the spa control and draws approx 2100 W.

The 10 min CLEAN cycle before each usage consume additionally 0,35 kWh  (2100 x 10min/60min/h)

Using the spa

For using the spa the cover will have to be removed, exposing the hot water to ambient air. The heat loss of the uncovered spa is significant and is a summary of

• heat transfer between water surface and ambience
  
  
• evaporation of spa water (under investigation)

The heat transfer via the unmoved water surface alone can be calculated by equation (2)

(2) Q = α A ΔT_LW

with

• α, the heat transfer coefficient for an unmoved water surface:
• α = 10,7 W/m²K (wind shielded) or
• α = 12,7 W/m²K under wind exposure
  
  
• A, the exposed area of water surface: A = 3,2 m²
  
  
• ΔT_LW, the temperature difference between ambience and spa water:
• ΔT_LW = 31 K (from spa temp 39°C minus average ambience 8°C)
  
  

For our test model a "αA"-value of 37,44 W/K can be calculated, resulting in an average heat loss of 1086 W assuming unmoved water and ΔT_LW = 31 K!

At an ambient temperature of -10°C the heat loss amounts to 1835 W!

At an ambient temperature of +25°C the heat loss amounts to 524 W!

First measurements have revealed an energy loss of approx. 3 kWh for a 30 min usage (AT approx 0°C).