To understand how this works it's important to know that temperature loss is linearly proportional to the temperature difference. Insulation reduces the ratio independently of temperature.
As an approximate example, suppose if takes one hour for the tank/building to reduce to a thermostat set-point 10% lower than the 'high' set point. Further assume you could use that lower set point for 11 hours, so the tank/building temperature is 10% lower for a full 10 hours. Finally, assume increasing the temperature of the tank/building by 10% takes one unit of energy.
In order to maintain the low set point, the first hour is free since we are losing temperature. The middle 9 hours need (190%) = 0.9 units per hour for a total of 8.1 units. In the 10th hour the low-set point scenario needs to warm up to the high set point and overcome heat loss so that individual hour requires more energy than the high set-point scenario: (1110%) = 1.1 units for that single hour to return to the high set point.
In total the low-set point needs 0 + 8.1 + 1.1 = 9.2 units of energy over the 11 hours.
For the full 11 hours the energy required to maintain the high set point is 11 units (1 unit per hour to make up for 10% loss).
Insulation is worthwhile, but has nothing to do with what you are asking.
If you are heating a house, or a water tank, or anything, it requires much more energy to keep it at a constant temp 24x7 than it does to let it cool down when you don't need it hot, and then just heat it back up again later.
That is why "smart" thermostats like the Nest became so popular. No need to heat your house while you are away during the day. So let it cool down a bit, then just warm it back up again soon before you come home.
Much less energy used.
That fully depends on the level of insulation. Newly build houses here in The Netherlands rarely cool down when heating is off, and the temperature stays generally stable, even when you are out (and the heating is off).
My Quooker is so well insulated, that you should only turn it off if you aren’t home for a week. Otherwise is exactly counter to what you say: more energy efficient to keep it at temperature instead of letting it cool and heating it again [0].
No, that is still not true, no matter how good the insulation.
> That fully depends on the level of insulation. Newly build houses here in The Netherlands rarely cool down when heating is off, and the temperature stays generally stable, even when you are out (and the heating is off).
Even if it's a few days, and it does drop a few degrees, you still spend less energy bringing it back up to whatever temperature than you would have to keep it there the entire time.
Do you have anything to support that claim? Because in my belief this follows normal thermodynamics, which means that if the energy dissipation over an amount of time is less than the energy cost to heat, it makes sense to do it.
Do you think there is no relation between the thickness of the insulation and the time it takes before reheating is more energy efficient?