Yes I was working on 16A for the air con, 10A for the UFH and 2A for the lighting. This left only 4A for what ever else you might want to use. Before we knew what you we planning to use the garage for, 4A is not normally sufficient for normal garage power use.
Now we know a bit more and realising the air con and the heating won't be on at the same time, you supply is probably ok.
I still think that underfloor heating is not the correct form of heating for what you are trying to achieve.
Both can be true.
The A/C may only pull 500W, but it is "rather too common" for manufacturers to simply specify an oversized supply to avoid having to specify what the supply requirements actually are. So they'll be working on the basis that their startup loads won't trip a type B 16A beaker. The fact that it might well run from a 5A fuse is irrelevant - they don't want the complication of having to deal with supply considerations. The result is that users are completely confused by wildly overstated supply requirements - especially if they are installing lots of machines (anyone recall the thread that involved a load of treadmills that all "needed a 16A supply" ?)
The term is Coefficient of Performance (COP). As a ready reckoner, you can assume about 3 for cooling systems (the electrical energy put in is lost outside), and 4 for heating systems (the electrical energy ends up inside where you want it). It varies a lot with operating conditions and any half decent manufacturer will give tables showing capacities (plural !) for a variety of temperature and humidity combinations - a 3 variable table, indoor temperature, outdoor temperature, and humidity. In addition there are two capacities (with or without taking into account the latent heat from condensing water from the air that's being cooled).
For heating, COP decreases as the outside gets cooler and/or the inside gets warmer - and most ASHPs will revert to an immersion heater at something like -5˚C or so outside as the COP will have dropped below 1 ! For cooling, COP drops off with decreasing internal and increasing external temperatures. And for cooling a space that doesn't have people in it, make sure the system can cope with dry air - a lot will freeze up and stop working if the air is too dry (now work that one out !)
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