- Keep the installation spacing in the bathroom at 5cm, if possible add some wall area (let’s see what’s possible) and lower the target temperature in the calculation to 22/23°C.
- This should reduce the supply temperature and thus also reduce the installation spacing in the rest of the house (20°C design temperature in living areas)
I would suggest the same, to use 20 cm throughout the entire house, arguing that needing 40°C supply temperature anyway to heat the bathroom is absurd. This blocks all optimization options afterward, or the possibility to be satisfied with 21°C in the bathroom, possibly with an infrared mirror or bathroom radiator.
Regarding efficiency: the 40°C is the supply temperature in the peak load case, i.e., at -12/14/16 °C outside temperature. This temperature is not maintained continuously, but only 1-2 weeks per year. Therefore, the electricity consumption will not be twice as high, but only slightly higher.
A recent Swiss study (Quality monitoring of small heat pumps and statistical evaluation 2018 – Mick Eschmann, Interstate University of Technology NTB) examined measurements from small heat pumps in operation with 35°C in the design case (surface heating) and 55°C in the design case (radiators) and determined average SCOP values of 4.2 for 35°C and 3.2 for 55°C.
40°C would then (assuming a linear relationship) result in approximately 3.95, i.e., about 6-7% increase in electricity consumption for the same heat demand compared to a 35°C design.
In fact, the relationship is likely not linear, since the physical process (compression) does not require energy in a linear way. Therefore, temperature changes in the lower range are less relevant than at the high end. -> reducing from 55°C to 50°C is more important than from 40°C to 35°C.
Much more important than the last °C in the supply temperature is a proper balancing and operation of the system to operate the heat pump properly without short cycling and buffer tank (which require higher supply temperature). Nevertheless, the approach to reduce the required supply temperature as much as possible is correct.