Physics/engineering/heating question

I have three electric baseboard heaters in this room, all of equal size. They are not connected to a central thermostat but each have manual thermostats on them (kind of a pain, I know–but cheaper to install). Over the years I have determined that to heat the room to a comfortable 68 degrees, on all but the very coldest winter days it only requires the efforts of two of the three heaters. However, on most other fairly cold days, if just one heater is turned up, it will struggle and lag in the mid-50s while running continuously.

So here’s my question: Let’s say on one of those “fairly cold days” (and let’s assume for the sake of discussion that the outside temperature, wind, sun, etc. stay constant for several hours), I enter the room and all three heaters are turned down to save energy, and the thermometer reads 60 degrees. If I turn one of the heaters up to where I’d normally turn two of them to get to 68 (or higher than that for that matter), will anything happen? My suspicion is that other than perhaps an initial jump to 61 or so, there would ultimately be no effect. I haven’t tested this experimentally, but it is complicated by the fact that outside temperatures around here tend to fluctuate wildly.

If the room 60 degrees I would expect it to raise some. To many unknowns to guess how much.

But as soon as it goes to say 61, the other two heaters will stop kicking on, and we’ve established that one heater is not sufficient to make it warmer than about 55. But maybe since having it at 60 gives the one heater a “head start”, that somehow helps? I don’t know though: my impression is that if I had all of them (or two of them at least) set at 68, and turned down all but one, it will not be able to maintain the temp.

I an not an engineer, but surely it is no saving to turn any of the heaters off. If you set all three thermostats to the same temperature (and they are reasonably accurate) all three heaters will cut out when that temp is reached. If one is off, it will just take longer unless the remaining two were unable to overcome the heat loss from poor insulation.

IF you use 2 or 3 to warm up to 60, but only set one to 68, that means if the room heats up to above 60, the other two heaters will turn off… one heater probably won’t be enough to maintain 60, but even if it is , it will never warm the room to 68

The reason is that rate heat flow (outward, through the glass and walls ) is related to the difference in temperature from outside to inside.
So the each degree of difference is requiring more power to maintain.

Its takes less power from the heaters to maintain the first 5 degrees of warming (above outside) than the second 5 degrees… (that is, if it takes X kW to maintain 5 degrees of difference, it takes more than X kW EXTRA to maintain 10 degrees of warming… )

IF you use all three heaters to go up to 68, and turn off 2, you may find the one remaining won’t keep it at 68.

If you want to save energy, upgrade the insulation. This need not be all that expensive - curtains and draught excluders are a cheap start.

The advantage of running fewer heaters is that the temperature will be more stable. Imagine if you had one heater that was the perfect size to maintain temperature while on 100%…there would be no cycling so the temp would be constant.

Of course the problem is then if it gets colder outside, you lack the power to maintain comfort.

What you can do is set one heater to maintain desired temperature on mild days. Set second and third heaters (for example) 3 and 6 degrees cooler. On cold days the first heater will run continuously, and the second heater will cycle on and off. On bitter cold days the third one will cycle on and off, while two run steady.

Line voltage thermostats often have lots of hysteresis, so 3 degree offset between may not be enough.

With electrical resistance heat, it is going to require nearly the same KWh to maintain a given temperature regardless how many heaters you run. Less cycling may improve comfort, and slightly reduce heat loss during peaks. Unless you have peak demand or off-peak metering though, it really doesn’t matter if you run 3 heaters at 33% duty cycle or 1 at 100%.

Probably the most logical and simplest configuration is to set one thermostat at 68, another at 65 and another at 62. Then when the room is cold all three are on and as the room heats up they successively switch off. This assumes good air circulation so that all three thermostats sense the same temperature so it may require some adjustments.

Just to clarify, I am not asking this for any practical purpose. It is kind of a thought experiment.

This would be correct with perfect air mixing. What would actually happen is that you’d have the room somewhat warmer near the one set to 68, with the room close to 60 near the other two. How much warmer is impossible to say.

If all three heaters are on outside walls, but one of the heaters is on a wall that gets more Sun, if that’s the one set to 68, you might see a larger effect, since the other two are on colder walls, and will tend to be on more even with the third one set to a higher temp.

Conversely, if one is on a colder wall, and that is the one is turned up, the other two might never turn on. You may have already been in a situation where that heater was doing most of the room heating, since it would cool down below its temperature setting before the other two.

If it’s a cold day, this won’t get you to 68 degrees. When you get to 62 degrees, one heater will stop. If two heaters are still enough to heat further, then the temperature will increase further, perhaps up to 65, but if they’re not, then the temperature will stay at 62. If you get to 65, then another one will stop. If the lone heater is enough to reach 68, it’ll do so, but if it’s not, then it’ll stay at 65.

Seriously, the simple solution really is to just set all three to 68, or whatever other temperature you want the room at. This probably won’t even result in much temperature fluctuation: The temperature equalization of the room isn’t going to be perfect, so the three heaters will probably be cycling on and off at different times. On average, you’ll have exactly as many heaters running as you need, to get exactly the temperature you like.

Yes, it depends what you want. With the configuration I mention on a very cold day one heater will stay permanently on while one cycles and the third stays off. On an even colder day two would stay on and one would cycle. And on an even colder day all three would stay on. The temperature will be a bit lower inside the colder it gets outside but I consider this a feature, not a bug, because it saves heating costs.

If that lower temperature is acceptable, though, then you should just keep it at that temperature all the time, and save even more.