AP Efficiency -
Part 1 Performance Basics
Solar water heater performance
is often presented as a graph, or set of three performance
variables. Values may be provided based on gross area,
aperture area or absorber area. In Europe, aperture or
absorber is often used, in the US, gross area is often used.
It doesn't really matter which values is used, as long as
you use the correct value. ie. Don't use absorber area when
using performance values based on gross area.
To adjust from one to the other, multiply by the size
ie. Absorber area = 0.6m2, gross area = 1.1m2. If
performance variables are provided for gross area, multiply
by 1.83 (1.1/0.6 = 1.83) to obtain absorber area values. The
smaller the area used, the higher the performance variable
The three performance variables for the AP solar collector
as provided by the
testing laboratory in Switzerland (SPF report C632LPEN) are
as follows (for metric calculations - absorber area):
h0 = 0.717
Loss Coefficient: a1 = 1.52 W/(m2K)
Loss Coefficient: a2 = 0.0085 W/(m2K2)
As well as the three
performance variables shown above, insolation level (G) in
ambient temperatures (Ta) and average manifold temperature
(Tm) must be know. These values give the value x,
also sometimes presented as T*m, used in the formula below.
different forms of this formula are used, but provide the same
How to use the formula?
Based on the ambient temperature, average manifold
temperature and insolation level firstly calculate the value
Eg. At 2:00pm, the ambient temperature is 25oC
(77oF), and the average water temp [(Tin+Tex)/2]
is 50oC (122oF). The insolation level
is 800Watts/m2 (252Btu/ft2).
x = (50-25)/800 =
Now enter all the
values into the formula:
h(x) = 0.717 -
(1.52*0.03125) - (0.0085*800*0.031252)
h(x) = 0.717 - 0.0475 - 0.0066 = 0.663
The solar conversion
efficiency for that specific point in time and set of
environmental conditions is 66.3%. That is: 66.3% of the
energy provided by the sun is actually used to heat the
Based on the assumption that those three environmental
factors (G, Tm and Ta) are stable for a period of one hour,
then 800 x 0.663 = 530.4 Watts of energy per m2
of absorber area will be used to heat the water (168Btu/ft2)
530.4Watts is equivalent to 456kcal, which could heat 100L
of water by 4.56oC
(20 Gallons by 10.9oF)
Below is a graph showing the performance curves for the AP
solar collector at three different insolation levels, from 0
Delta-T. In most cases the Delta-T values will be in the
range of 20-50oC,
with higher values present for high temperature heating such
a for absorption cooling applications, or during very cold
weather. As can be seen conversion efficiency is highly
dependent on solar insolation levels, with higher insolation
yielding greater levels of solar conversion.
In reality ambient temperature
will fluctuate, and the manifold temperature will gradually
increase as the water is heated. Furthermore insolation
levels may fluctuate with intermittent cloud cover. In order
to more accurately calculate energy output per
day/month/year a more complete set of environmental data
must be considered and many (hourly) performance
calculations throughout the day taken. Your local Apricus
distributor can provide estimates of average monthly and
annual performance, heat output and thus solar contribution
for your location.
One factor which is not considered in the straight
performance calculations outlined above, is the affect of
transversal IAM values (Incidence Angle Modifier) on solar
collector output throughout the day. Please read the
following section to
learn more about IAM.
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