Thanks for your comments folks, they have given me some better ideas of how to make this comparison.

If we assume a three or four person household, twenty tubes sounds like it's not enough in Melbourne, so from here on I’ll use 30 tube systems.

Water heating requirement (4 people, 50 litres each, heat rise from 15 to 60oC) is 37.63 MJ per day…

4.1813 joule per gram per degree C

X 200 litres

X 1000 grams per litre

X 45 degrees C temp rise

= 37631700 Joules

= 37.6317 MJ per day to heat hot water

According to http://www.energymatters.com.au/climate-data/

Melbourne has an annual average of 4.12 kwh/m2 per day, dropping to a low of 1.5 kwh/m2 in June and rising to a peak of about 6.5 kwh/m2 in December.

Apparently an Apricus 20 tube collector has an actual collector area of 1.6m2. So a 30 tube system presumably has 2.4m2 area. So a 30 tube system should harvest, assuming three months of winter at 1.75kw/m2/day, six months at the annual average of 4.12, and three months of summer at 5.75….

Which gives us winter, spring-autumn and summer collectors potential yields of 4.2, 9.9 and 13.8 kwh/day…if we assume collectors are only 80% efficient then we have 3.5, 7.9 and 11 kwh day harvested from the sun.

In MJ this is;

12.1 in winter, giving us a daily deficity of 25.5 MJ

28.5 in spring-autumn, giving us a daily deficity of 9.1 MJ

39.7 in spring-autumn, giving us a daily excess of 2.1 MJ

So, over the year, these deficits work out to be

91 days require 25.5 MJ boost = 2320.5

182 days require 9.1 MJ boost = 1656.2

91 days require no boost at all.

Total boost heat required annually = 3976.7MJ

…..so annually we are getting about 71% of our hot water heated by the sun.

If we assume gas burner (Rinnai or the like) is 80% efficient we need to burn about 4970.9MJ worth of gas annually to get our heat. Which, according to this site;

http://www.abc.net.au/tv/carboncops/calculator.htm

results in CO2 emissions of 348kg, and costs about $0.015 per MJ (According to http://www.originenergy.com.au/priceguide), so around $75 per year.

So to compare the above NG boosted solar system with an air source heat pump (ASHP)......

As far as I can tell the typical COPs of ASHP these are around 2, and not 3 or 4 as some manufacturers suggest.

This Canadian reference suggests ASHP have COPs for hot water heating of 2 to 3, but they use low ambient air temps;

http://dsp-psd.pwgsc.gc.ca/Collection/M92-251-2002E.pdf

The last post on this topic suggests COP of 3 is unrealistic;

http://www.ata.org.au/forums/topic/2165

However a few anecdotal reports state bigger savings. One user on;

http://forums.whirlpool.net.au/archive/740793

reported old resistance heating electricity use of 13.8KW/day and then 3.7KW/day with a ASHP system, which would seem the new machine has a COP of around 3.7 – pretty impressive, and there are others around reporting similar savings. Siddons and Stiebel Eltron claim savings electricity savings of 75% and 70% respectively.

So if we assume we are heating 200 litres per day (four person household, 50 litres each) from 15 C to 60C we require a total of;

4.1813 specific heat per gram x 365 days x 200 litres x 1000g per litre x 45 degrees rise = 13735570500 = 13735.57 MJ of electricity per annum, which equals about 3815kwh per annum (if we were using resistance heating, and assuming 1 kw electric = 1 kw thermal – accurate enough for this).

If we are using an ASHP…

…with a COP of 2, the required electric power would be 1908kwh, which is apparently about 1908kg of CO2 (coal fired electricity), and at 20c/kwh costs $381,

…with a COP of 3, electric power would be 1272kwh, about 1272kg of CO2, costs about $254,

…with a COP of 4, electric power would be 954kwh, about 954kg of CO2, costs about $190.

Of course, with greener power the CO2 emissions of the ASHP would drop.

So if we pick the middle ground, and assume an ASHP COP of 3, then I calculate;

ASHP have an annual heat source cost of $254, annual CO2 emissions of 1272kg (assuming coal fired electricity), system cost of $3,660 and a pretty low install cost, say $500, and give 31 RECS in zone 4.

Evac Tubes + Nat Gas have an annual heat source cost of $75, annual CO2 emmissions of 348kg, system cost of $5615 + $240 for mount frame and an install cost of say $1,500, and give 30 RECS in zone 4.

Installed, excluding RECS we are looking at around $4,000 for ASHP c/w around $7,000 for evac tubes.

The $3,000 difference goes quite a long way towards a 1.5kw PV array…and in Melbourne a well installed 1.5 kw array will supposedly produce around 2000 kwh per year….so an ASHP with PV would have similar cost, and less CO2 than solar thermal + NG boost. I think.

It looks to me like ASHP is the winner...I am surprised at that result.

Any comments? Silly assumptions here? Am I on the right track?