Air Source Heat Pump limit of Coefficient Of Performance being less than one?

The coefficient of performance can certainly be less than 1, as you will see from any thermodynamics text book. The COP is directly related to the ratio of input and output temperatures, as this becomes bigger the COP falls dramatically. The whole heat pump thing is driven by misconceptions and assumptions, because mechanical and heat losses in the compressor are rarely taken into account and as the COP becomes smaller  become very important. The easiest way to understand this is to examine any engine that depends on combustion, how efficient is your car engine, or a jet engine or anything similar. All of these use exactly the same thermodynamics, and you will find that the efficiency of an engine rises as the temperature differential across it gets larger. This is why power stations use super-heated steam at a very high temperature and operate into cooling towers to make the exhaust temperature as low as possible, the same for gas turbines, the fuel is burnt at as high a temperature as possible (given practical materials for combustion chambers and turbine blades) and operate into as much of a heat sink as possible, typically a low temperature combined cycle boiler.

For heat pumps the input and output temperatures are critical to the COP, given underfloor heating as the output and a warm day as input the COP can be very high, 10 or maybe more. BUT if the cold end temperature is -10C and the output to radiators at 60-70C (less than normal CH BTW), the COP will be less than 2 with practical working fluids. This is another point, the best fluids tend to be ammonia (very explosive) or flourinated hydrocarbons (banned as being greenhouse gases!). This also reduces the temperature range available and the COP.

Another way of looking at it is that it is difficult to extract heat from cold air. So when it is near to freezing in winter, the COP is worst. Granted, a COP of > 1 is better than conventional heating, but what is the payback time compared with say fan heaters?

In the same way that banks will lend you an umbrella when the sun's shining but want it back when it starts raining ASH work best in warm weather . . .

A COP >1 might be better that conventional electric heating but it's certainly not better than oil or gas. And electric heating is instantaneous and silent and not some great box whirring away outside!

For heat pumps the input and output temperatures are critical to the COP, given underfloor heating as the output and a warm day as input the COP can be very high, 10 or maybe more. BUT if the cold end temperature is -10C and the output to radiators at 60-70C (less than normal CH BTW), the COP will be less than 2 with practical working fluids. 

That's why nobody with any sense would run a heat pump that hot.  Something like 40C is more sensible.  If it's for space heating, run it at a lower temperature for a longer time.  If it's for hot water, give the hot water tank a boost to 60C with an immersion heater perhaps once a week to kill off any bugs that live at 40C.

But do you realise how big a conventional radiator needs to be to be useful at 40C or less? It is monsterous! In other words it is completely unsuitable unless it is a new build and can have underfloor heating throughout. Now look and see what the Government says, because they haven't even considered any of these things. The downside of underfloor is that it has a high thermal capacity and takes a long time to heat up. Thus it needs to operate for long periods, even 24/7 to work. All this means that the only useful heat pump system is air to air, meaning real aircon.is the only proper option if it must be reasonably silent.

I stayed in a hotel recently with an air to air system in an older building. The room was cold for more than an hour until the miniscule heat input managed to heat the room, probably 1kW, and that was it on a not very cold day and the fan was quite noisy.

We have a local swimming pool and can heat pump a stream that runs 5 metres behind the plantroom.

Now if the stream is 10 degrees cooler than the 27 degree pool will it be economical to install a heat pump or better to run on gas??

The heat pump is probably a bit cheaper but the capital cost is more. With a 17 degree differential the COP could be 7 or 8 and electricity is about 6 times as expensive, so a long payback period. Good luck. Ask the manufacturer for an accurate figure and actual electricity consumption. Assume a gas boiler is 90% efficient,(although probably a bit more) and compare.

You're thinking about it like gas central heating.  You don't say "it's a bit chilly" and turn the heating on.  Because you turned the heating on in the Autumn, and it's staying on until Spring.  It may run 24 hours a day if needed.  The controller decides when it needs to run to keep the house warm.

I haven't got rose tinted spectacles on this one.  My existing heating system is totally unsuited to conversion to a heat pump, and would need to be entirely ripped out and replaced.  The radiators are old, and not the modern high efficiency ones.  And microbore plumbing is no use at all for high flow low temperature operation.  It's only barely adequate as a gas fired heating system.  So all the figures of how much it would cost for me to switch to a heat pump are likely to be far too optimistic.

The problems are solvable.  But it may need a lot of money thrown at it.

Simon Barker said:

The problems are solvable.  But it may need a lot of money thrown at it.

Anything at a price!

To get a meaningful payback period a COP of 3 or 4 is needed.  To get high COP needs the heat source to be warmer than the output temperature like geothermal which is ideal.

Logic tells me that in my case that a compressor that pumps warm refrigerant into a cold stream where it expands may come back to the plantroom cooler than it went out because of the losses on the insulated pipes [which are not perfect] and the mechanical heat losses that make the compressor housing warm are excessive 

These losses combine to make the COP less than 1 which means it is much cheaper to use an immersion heater and obviously better still to use gas heating despite the negative publicity it is receiving at present.