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I have been told that ASHP's do not work well when run for short bursts, as the startup uses more energy. Does anyone know (or can point me where to find out) roughly how many hours of steady running equals the extra cost of starting?
No heating equipment works well in short bursts except pure electrical resistance heating. A heatpump contains an evaporator, condenser and compressor and these have to reach a steady state to be operating efficiently - something of the order of at least five minutes. Rather similar to a car engine in as much as an engine is not running efficiently when cold. There is an initial inrush of current when the compressor starts, but this is only for a few milliseconds and doesn't really affect the efficiency at all.
To cut a long story short, it's important that your heating system is properly sized according to the design load and that requires some software to perform the calculation. Anyone who just calculates based on the area of the rooms of your home is not doing a proper job and the result is usually an oversized (and hence inefficient) system.
As Paul states, short running times and frequent start/stops is not the most efficient way to run any piece of equipment that uses the vapour compression cycle. Also, it is the stop/starts that are the most wearing for the compressor and will shorten the compressor's life. Long running times are what you are after and ,to some extent ,many heatpumps be they ASHP or GSHP, are limited to 4 starts in an hour.