Why a percentage will not do
Every collector datasheet in the world carries the same three numbers, and almost nobody uses them. The curve is efficiency plotted against (mean fluid temperature minus air temperature) divided by irradiance, and it is a downward parabola: an intercept where the fluid sits at air temperature and the panel is only fighting its own optics, then a straight-line loss term, then a small squared term that bends the tail down. Enter a0, a1 and a2 and the page reports what the panel returns at the point it will actually run at.
With the defaults — 1,600 BTU per square foot gathered over six hours, so 267 BTU/h per square foot; fluid at 120 °F, air at 70 °F — the reduced temperature is 0.187. The intercept of 0.72 loses 0.150 to a1 and another 0.023 to a2, and what is left is 0.547. A panel somebody would describe as "seventy per cent efficient" is delivering just under 55 per cent, and if the tank is already hot on a cool afternoon it delivers a good deal less than that.
The draw is the input worth measuring
Sixty gallons a day lifted 70 °F is 35,028 BTU: 60 × 8.34 lb per gallon × 70 °F. That arithmetic is exact and it is the only exact thing on the page. Everything else — insolation, the curve, the mean fluid temperature, the losses between the collector and the tank — carries real uncertainty, so it is worth spending the effort on the one input you can pin down. A cheap meter on the cold feed to the water heater, read for a week, will tell you more than any table of gallons per person.
The two households that use the same total often have very different loads anyway, because the delivery temperature differs. The same 60 gallons at 105 °F instead of 125 °F is 25,020 BTU, a 29 per cent smaller load, and the array shrinks with it.
What the mean fluid temperature does to the answer
The table on the page runs the same panel from 20 to 120 °F above air, and the area moves by more than a factor of two across that range. This is the mechanism behind the advice that a bigger tank collects more: a bigger store runs cooler for the same heat, the fluid returning to the collector is colder, the reduced temperature falls and the panel sits higher on its curve. It is also why a system that has been sitting idle since Thursday collects poorly on Friday morning — it starts the day hot.
The mean fluid temperature is genuinely hard to know in advance. It moves through the day, it depends on the flow the pump actually delivers and on the heat exchanger, and it is the input on this page most likely to be wrong. Running the page at two or three plausible values and looking at the spread is more honest than picking one.
Which area, gross or absorber
Certification sheets quote the coefficients against one of gross area, aperture area or absorber area, and the three differ by ten to twenty per cent on the same panel. Whichever basis the coefficients came from is the basis the answer comes back in, and the panel area field has to match it. Mixing an aperture-based a0 with a gross panel size is a quiet ten per cent error that nothing downstream will catch.
What this page does not know
It does not know your weather. It does not know how the array is shaded at nine in the morning in November, what angle the sun strikes the glass at, or how many days in a row are cloudy. It applies no incidence angle modifier and treats a day as a flat block of average irradiance. And it makes no judgement about whether an array is correctly sized, adequately protected, or safe — a collector array is a roof load, a roof penetration and, on a still summer day with the pump off, a very hot object.
Questions people ask
How many square feet of solar collector do I need for hot water?
It falls out of your draw, your insolation and the curve, and the honest answer is that it moves a long way with all three. With the defaults — 60 gallons a day lifted 70 degrees, 1,600 BTU per square foot per day, and a 0.72 / 0.80 / 0.0025 curve running at 50 degrees above air — 70 per cent of the load takes about 32 square feet. Change the mean fluid temperature to 100 degrees above air and the same load takes closer to 53.
What are a0, a1 and a2 on a collector datasheet?
They are the three coefficients of the efficiency curve. a0 is the intercept, the share of incident sun the panel returns when the fluid inside is at air temperature. a1 is the linear loss, in BTU per hour per square foot per degree of difference. a2 is a small squared term that bends the curve down at high temperature differences. Efficiency is a0 minus a1 times the difference over irradiance, minus a2 times the difference squared over irradiance.
Why does my collector do worse when the tank is hot?
Because the loss terms scale with how far the fluid sits above the surrounding air, and a hot tank sends hot fluid back to the collector. The panel is losing heat to the air the whole time it is gaining it from the sun, and the hotter it runs the more it loses. This is the single biggest reason a real system underperforms a flat-percentage estimate, and it is why storage volume and collector output are not independent of each other.
How do I convert kWh per square metre per day into BTU per square foot?
Multiply by 317. One kWh is 3,412 BTU and one square metre is 10.764 square feet, so 3412 divided by 10.764 gives 317. Five kWh per square metre per day, a common summer figure, is about 1,585 BTU per square foot per day. Take the number for the plane your collector actually faces, not the horizontal figure, because tilt and azimuth move it substantially.
Should I size for the worst month or the average one?
That is the design decision the page deliberately leaves to you, through the solar fraction field. Sizing for the worst month means a large array that spends the summer making heat nobody draws, and heat with nowhere to go is where stagnation comes from. Sizing for the average leaves a backup doing real work in winter. Run the page twice with winter and summer numbers; the gap between the two areas is the question.