It takes 7kw at 17ºF to provide 48k BTU. There are 0.293W/hr per BTU so 7,000W = 25k BTU "in" and 48k BTU "out" or a COP of 1.9. At -15ºF, it's using 5.9KW but can only produce 28,500. So a COP of ~1.4. Still better than electric resistive heating but not by much. At 40ºF, the COP is more like 3.3 which is in line with the very efficient numbers.
Fortunately my 99% design temp is ~8ºF and my area only sees 20hrs below zero per year, so this will work just fine for me.
Heat pumps might make sense when you have a well-insulated house, like the kinds in Northern Europe, to trap heat and reduce the power required to heat the room. American houses in most places are far too drafty.
If you need significant heating or cooling in a home, the first thing you need is to deal with is insulation, otherwise nothing you do is going to work well.
The idea that indoors needs to be between 72° (F) and 75° at all times is unsustainable.
The other problem is that if you do decide to insulate the house, then you may end up needing to use A/C because the house can no longer be wind-cooled to an acceptable temperature, and you will need to update the heating system as traditional methods of heating (fireplace, stove, simple furnaces) depend on external air circulation.
> The idea that indoors needs to be between 72° (F) and 75° at all times is unsustainable.
The WHO recommends a general minimum household temperature of 64°F for all populations for health reasons, with a higher minimum for sensitive groups including children and the elderly; maximums are more regionally variant because acclimitization (which takes years) plays more of a factor in high-heat health risks, but even in extreme regions seems to top out at about 90°F for the general population.
Lots of the US spends lots of time significantly out of at least one end of that range (and, especially given that the top gets lower in colder regions, lots of the US spends lots of time significantly out on both ends of the scale.)
> The other problem is that if you do decide to insulate the house, then you may end up needing to use A/C because the house can no longer be wind-cooled to an acceptable temperature
If you have a house that is insulated well and also lacks doors and windows that can be opened, sure.
But... that presents other problems, too.
So even if per unit of energy gas is way cheaper, heat pumps can still come out ahead.