This is a simple calculator using the Carnot efficiency equation. It uses the refrigerant temperatures to estimate the approximate COP. The actual real-life COP is usually around 50% of the theoretical Carnot COP. (see further info at the bottom). Note – This is only an estimate for one point in time. Various things affect the actual daily or annual result. SPF or SCOP should be used to assess expected annual averages. [Celsius version]
The Refrigerant condensing temperature is likely to be a few degrees (F) hotter than the flow temperature.. maybe 3.5° to 7°F warmer. The evaporating temperature might be 9° to 15°F colder than the outside air temperature.
The two ‘offset’ values at the bottom are approximate estimates to correct for the above temperature differences.
In general, these offsets will be lower at minimum compressor speed and greater at maximum speed. flow-return dt of about 9 degrees F is assumed.
Carnot COP = TH / ( TH-TL ) Using absolute Rankine temperatures, where TH = condensing (hot) temperature and TL = evaporating (low) temperature. The actual COP is about 50% of the Carnot COP
Be mindful that the COP result is for any one moment. Below 40 or 45°F there can be defrosts, and this will reduce the COP. This could be very variable, but often somewhere in the region of up to 10% during periods where defrosts happen. I have also added the option to add a percentage to allow for the power used by fans and pumps.
Uses for the comparator
It can be good for making comparisons… e.g. to see the likely percentage improvement in COP if you increase the radiator size, or to estimate the reduction in COP due to a poorly ventilated ASHP (where air is several degrees colder due to re-circulation). It can help extrapolate COP readings from data sheets.
You can change the Carnot Efficiency from 50% to help align estimated to your values, then leave this percentage whilst changing the temperatures.
Be mindful that there are many factors that contribute to the actual resulting COP over the day.
Other calculators
The below is an attempt at ‘spelling out’ the dt issue.
‘A’ is a standard condition with flow-return dt of 9F. If we consider ‘B’ with dt of 18F, the flowrate must have halved to achieve this (assume heat output is the same). The radiators etc have less flowrate, so whilst the condensing pressure is lower (better COP), the heat is delivered at a lower mean temperature. To get a ‘level playing field’ (as in C) we have adjusted the flow temperature up so that the average flow-return is about the same. This raises the refrigerant temperature The most energy-efficient option here is A.
Note, the condensing temperature is guessed from my experience taking readings from heat pumps. Also, the ‘flat’ condensing line is not quite flat due to pressure drops. CO2 heat pumps are quite different, there is no actual condensing temperature with them.