Stretch wrote:
A couple of things to mention.

1) The COP of the heat pumps I normally install is greater than 3.5
when the outdoor temperature is 47 degrees when heating and greater
than 2.5 at 17 degrees outdoor temperature when heating. The COP of
strip heat is ALWAYS 1.0. In my area it does not often get below 20
degrees outside temperature. Even at 0 degrees the COP of air to air
heat pumps manufactured in the last 20 years will be at least 1.5.
More efficient units will have a COP of 1.7 to 2.0 under the same
conditions. Look it up in your engineering data guys.

2) The heat output of air to air heatpumps drops as it gets colder
outside while the heat load of the house goes up under the same
conditions.

3) The balance point of most properly sized heat pumps is around 35
degrees outdoor temperature. That means that most properly sized heat
pumps without heat strips cannot heat the house to 75 degrees indoors
when it is below 35 degrees outdoors. Therefore when it is below 35
degrees outdoors, such as at night, the compressor will run constantly
and the heat strips will cycle on & off to maintain comfort.

4) As an experiment, I installed a setback thermostat in my house 10
years ago. I locked out the strip heat and programmed the
temperatures at 68 degrees setback at 11:00 PM and 75 degrees setup
at 5:00 AM. The heat pump started running constantly at 5:00 AM and
did not bring the temperature back up to 75 degrees till after 5:00
PM. The day time temperatures were in the mid 50s and the nighttime
temperatures wewre in the mid 20s.

5) Setback thermostats were originally designed to save money
operating oversized fossil fuel furnaces. If your heat pump is
properly sized by the cooling load, it will not be able to recover in
a reasonable amount of time whithout using the strip heat. Therefore,
you will either be cold much of the time in the winter or your
electric bill will INCREASE with a setback thermostat. NOTE: If
your heat pump is oversized the setback penalty will be reduced, but
the fact it is too big will reduce the effective efficiency all year
long. NOTE also that setback thermostats WILL save money in the
cooling season, even when the heat pump is properly sized.

One obvious approach would be to have two,
use one in the summer and both in the winter.

For what it is worth. Measured data, not guesses.