The same three numbers, read the other way
An efficiency curve is normally used to answer "how much do I get out of this". Set the output to zero and it answers a different question: how hot does the plate have to get before it is losing everything it takes in. That is stagnation, and it is a property of the collector rather than of the system attached to it.
The algebra is a quadratic. Efficiency is a0 − a1·ΔT/G − a2·ΔT²/G, and setting it to zero and multiplying through by G gives a2·ΔT² + a1·ΔT − a0·G = 0. With the defaults — 0.72, 0.80, 0.0025 and 300 BTU/h per square foot — the positive root is 174.7 °F, and on 95 °F air that puts the absorber at 269.7 °F. The page reads the curve back at that rise and reports the residual, so you can see the root is genuinely a root and not an arithmetic slip.
Why the answer barely cares about the air temperature
The table at the bottom of the page runs three air temperatures against four irradiances, and the pattern is that the rise hardly moves with the air temperature at all — it is fixed by the curve and the sun — while the absolute temperature moves one degree for every degree of air. That is a useful thing to know: the worst case for stagnation is not the hottest day but the hottest day that is also clear and still, and the two ingredients contribute very differently.
Irradiance is the input the answer is sensitive to, and it is the one people take from a horizontal annual average rather than a peak in the plane of the array. A steeply mounted panel in a cool climate can see more in its own plane on an April afternoon than a horizontal figure ever suggests.
What a1 does, and why vacuum tubes are different
a1 is the linear loss to the surroundings, and it is the term that stops the temperature climbing. Halve a1 and the stagnation rise roughly doubles at small a2. This is why an evacuated tube collector, whose entire design purpose is to remove convective loss, reaches temperatures a flat plate does not. The property that makes it collect well on a cold morning is the same property, unchanged, on the afternoon the controller stops the pump.
If your sheet publishes only a straight line, enter zero for a2 and the answer comes back as a0·G ÷ a1. It will read high, because the second-order term exists precisely to bend the curve down in this region, and the page says so on the field hint rather than quietly using it.
Pressure at the top of the loop
A gauge in a basement is not reading what the collector sees. Water loses 0.4335 psi per foot of height, and a glycol mix at 1.04 specific gravity loses 0.4508. Twenty five feet of that is 11.3 psi, so a 30 psig cold fill reads 18.7 psig at the collector — and the collector is the hottest point in the loop as well as the lowest pressure in it, which is why it is the point that matters.
The page will not interpolate a vapour pressure curve for your fluid, because doing so would mean stating a fluid property as fact. Instead it asks for one boiling point and the pressure it is quoted at, straight off your data sheet, and puts the two pairs of figures side by side. What lies between them is for the fluid manufacturer to say.
Stated plainly, and then left alone
A stagnating collector is hot enough to destroy things attached to it, to cook a heat transfer fluid, and to burn on contact. A closed loop whose contents pass their boiling point stops being a liquid circuit. Water stored by such a system scalds. Those are facts about the physics and they are stated here so nobody is surprised by them. How a particular system is arranged so that none of it becomes a problem — where the heat goes, what shades the array, what relieves what — is a design question for whoever specifies and installs it, and no procedure for any of it appears on this site.
Questions people ask
What temperature does a solar collector reach at stagnation?
Whatever temperature makes its efficiency curve cross zero, which the certification sheet already tells you. With a 0.72 intercept, an a1 of 0.80 and an a2 of 0.0025, on 300 BTU per hour per square foot, the rise above air is 174.7 degrees F. On a 95 degree afternoon that is 269.7 degrees at the absorber. Change the collector and that number moves a long way, which is the point of solving the curve rather than quoting a figure.
Why do evacuated tube collectors stagnate hotter than flat plates?
Because the loss coefficient a1 is what stops the temperature climbing, and removing convective loss is the entire design purpose of a vacuum. A collector that cannot shed heat to the surrounding air has to get much hotter before it sheds as much as it absorbs. The property that makes it collect well on a cold morning is unchanged on the afternoon the pump stops, and it is the same number in the same equation.
How much pressure do I lose to the height of the collector?
0.4335 psi per foot for water, multiplied by the specific gravity of whatever is actually in the loop. A glycol mix at 1.04 loses 0.4508 psi per foot, so 25 feet costs 11.3 psi. A 30 psig cold fill at a basement gauge is therefore 18.7 psig at the collector, which is both the hottest point in the loop and the lowest pressure in it.
Does this tell me whether my loop will boil?
No, and it deliberately does not try. It gives you the stagnation temperature from your curve, the cold pressure at the collector from your gauge reading and your height, and it puts those next to the one boiling point and pressure you copied off your fluid data sheet. It interpolates no vapour pressure curve and issues no verdict. What happens between those figures is for the fluid manufacturer and the system designer to answer.
How long does a collector take to reach stagnation?
Less time than people expect, because there is not much mass in a flat plate absorber. Tens of minutes on a clear day rather than hours. The page gives a steady state answer and says nothing about the approach to it, and it also assumes the fluid is still wetting the absorber. Once a fluid has left the plate the plate runs hotter still, and that regime is outside anything a certification curve describes.