Ideal heating cycle for winter outdoor spas?

Lee In VT · Feb 27, 2014

I'm wondering how regular users of hot tubs, kept outdoors in winter up North, manage their heat/cool down cycle most efficiently. Our tub is new, a basic model but spray insulated to current industry standards (or to Nordic's standards) with a nice fitting cover. My wife and I soak most days, usually afternoon/eve. Thereafter I've been setting the temp to 85 and let it fall till next use. Typically the temp has fallen all the way to 85 deg by the next day (especially this frigid winter) implying it may have demanded some heat to maintain, or will before our next use preheat. I could set it lower (needing a longer preheat prior but less interim heat). Or I could set it higher to avoid the longer preheat, but with an obvious tradeoff in interim heating. Is there an ideal breakpoint, the goal being the least use of electricity? What about when the outdoor temps moderate?
Lee

chem geek · Feb 27, 2014

The least amount of heat required would be to let the temperature drop after use to as low as possible but obviously starting heating long enough before the next soak so that you will get to the desired temperature in time. The reason this is the most energy efficient is that heat loss is proportional to the temperature difference between the spa water and the outside air temperature. So the longer period of time with a lower spa water temperature, the less heat loss so that much less heat needed to be replaced. If you were to constantly maintain a high spa temperature, you would be losing heat more quickly and therefore replacing (heating) it more as well.

There are diminishing returns for this if the temperature drop is smaller, the outside air temperature warmer, and the time between uses shorter. Here are two examples to give you a rough idea of the differences. For simplicity I assume that the rate of heat loss and therefore temperature drop (since water volume is constant) is exactly proportional to the temperature difference between the spa water and the air temperature and I assume a constant proportionality.

dT/dt = -k*(T - Tair)
T = Tair + (T₀ - Tair)*exp(-k*t)

Let's assume that k = 0.5 so that with Tair = 40ºF and T₀ = 104ºF, then after one day so t=1 we have
T = 40ºF + (104ºF - 40ºF)*exp(-0.5) = 78.8ºF
If we had the spa heating set to 85ºF, then the temperature would get to that temperature at
t = -ln((T - Tair)/(T₀ - Tair))/k = -ln((85-40)/(104-40))/0.5 = 0.70 days
so you would be maintaining an 85ºF temperature for 1-0.70 = 0.30 days with a heat loss dT/dt = -0.5*(85-40) = 22.5 so this is a total energy proportional to 0.30*22.5 = 6.75 (I'm using degrees as a proportional unit of energy).
You then need to heat up the spa from 85ºF to 104ºF which in these same proportional units (where heat is proportional to temperature deltas) is 19 where we assume near instant heating for simplicity. So that's a total proportional heat of 6.75+19 = 25.75

If instead you were to maintain a 104ºF temperature for the entire day, then this is a total energy proportional to 1*(104-40) = 64 so around 2.5 times more energy needed.

If the outside temperature were only 70ºF, then we have
t = -ln((T - Tair)/(T₀ - Tair))/k = -ln((85-70)/(104-70))/0.5 = 1.6 days so the spa temperature wouldn't drop from 104 to 85 over just one day. Instead, the temperature would drop to
T = 70ºF + (104ºF - 70ºF)*exp(-0.5) = 90.6ºF
so we just have heating to 104ºF so 13.4 proportional units of heat.

If instead you maintain 104ºF temperature, then the total energy is proportional to 0.5*(104-70) = 17 so around 1.3 times as much energy is needed.

Lee In VT · Mar 1, 2014

I see. So even holding it at 85deg is worse than say 80 (the lowest the spa will go I think), to avoid any maintenance heating.
My spa in on an automatic twice a day filtering schedule. I can set each cycle to last from 2 to 12 hours but not the time of day (as far as I know) currently set at 3 hours. It occurs to me that, if at all possible I should use the daytime filtering cycle as the time to reheat the tub, since the circulator pump is running anyway. What is the relative power consumption of the circulator pump compared to the heater in general? We tend to use the tub at inconsistent times but occasionally, if I hear the tub running, I'll turn on the heat then, even though it might mean reaching and maintaining the target temperature for several hours before use.

dsime42 · Mar 2, 2014

Not an expert on this and your question is about heating cycles so this is somewhat Off-Topic, but.

If I lived where it was somewhat cooler, I'd get a big piece of plastic. One large enough to cover the tub in all directions right down to the ground and 2-3 feet beyond. The I'd get some 4x4s to keep the plastic OFF the tub's cover. The tub would lose heat to the surrounding air, but the plastic would retain that air and the "warmer air" would change the "Tair = " part of the equation.
It would be more hassle to move and replace plastic and separators but you wouldn't have to drop the water temp as much or at all.
Of course your tub would look like a construction area during the winter and there is the possibility that I am just all wet on this.
As I said "If I lived where it was somewhat cooler"

chem geek · Mar 3, 2014

To reduce heat loss, you want more insulation. If it's just a thin piece of plastic, that won't insulate that well and there will still be heat loss from the air on one side of the plastic to the other side. Trapped air does insulate on its own (R value is 1.0), but not nearly as good as additional insulating material (EPS foam in standard spa covers is an R value of roughly 4, fiberglass batts is around 3-4, etc.). You also want to make sure the seal from the cover to the sides of the tub is relatively air tight.

Lee In VT · Mar 3, 2014

Our tub has spray on foam insulation, directly adherent to the tub itself. Great stuff. It's probably the industry standard for quality tubs. There is also a plastic curtain around the tub, enclosing all the guts, which helps keep wind drafts out, but has no 'R' value per se. I think it would help if I did loosely pack in fiberglass insulation where I could, to bolster the effective R value. I'm impressed with how well the tub holds heat after use, despite cold cold temps. But this is our first season and I have no comparison. Predicted lows tonight -5 to -10F. Good time to have a well insulated tub.

GuinnessPhish · Mar 3, 2014

Not sure if your spa is the same, but my spa's factory setting is to filter (and heat) twice a day for two hours at a time. I can control when it starts by switching the breaker off, and then back on again. Once I turn it on again, the spa starts the two hour filter and heating cycle. My spa has a economy heating setting where it only heats during the filter cycle. I set the spa to 100 degrees. We typically use it around 9 pm, so by setting turning the breaker off and then on again once at 7pm, the spa is always the desired temperature by the time we use it.

If we want to use the spa in the afternoon or some other time, we'll switch the economy heating off to regular heating and heat it up if need be.

Lee In VT · Mar 5, 2014

Mine is set to filter twice a day too and I can control how long each cycle lasts (you probably can too). I realized I could use the circuit breaker to alter the filtering start time but didn't know if the cycle would necessarily begin when I first power up, which makes sense. Despite the very detailed calculation from Ralph about temperature control vs energy consumption, I realized that not using the filtering cycle as the time to heat the system too (e.g. your economy heating setting) would increase the energy use significantly (i.e. if the heating cycle isn't concurrent with the filtering cycle). Unfortunately the time use the tub varies day to day, some days not used at all. So I do my best to coordinate the two cycles.