Collector efficiency reference

A solar thermal collector's datasheet headline number — the peak optical efficiency η₀, typically quoted at 0.70–0.82 for a good flat-plate panel — is the maximum possible fraction of incident sunlight converted to useful heat at one favourable instant: sun normal to the glazing, fluid entering at ambient temperature.

The annual delivered fraction — useful heat at the tank, divided by sunlight incident on the panel over a whole year — is much lower because of a cascade of physical losses, each modest on its own, that compound through the year. This page lays the cascade out explicitly, shows the Hottel–Whillier–Bliss equation that drives the biggest term, and lists published references that bracket the real-world range.

If you're trying to size a collector array, this page is the "what fraction of the sun do I actually get?" input to the /resources/sizing calculator. If you're trying to orient an existing array, head to the /resources/tilt-optimizer.

From peak η₀ to annual delivered: the cascade

Typical residential drainback flat-plate, mid-latitude site
Stage	Factor	Running
Peak η₀ (SRCC / Solar Keymark nameplate, ΔT = 0, normal incidence)	0.78	78 %
× Temperature derate (collector hotter than ambient — Hottel–Whillier–Bliss)	0.85	66 %
× Cosine-of-incidence averaged across the day (sun isn't normal except at one moment)	0.85	56 %
× Pump / control losses + morning warm-up of cold pipe	0.93	53 %
× Stagnation periods (tank full, collector idle, no useful collection)	0.95	50 %
× Pipe loss to surroundings (worse for long outdoor runs)	0.93	47 %
× Soiling, dust, partial shading over the year	0.97	45 %

A reasonable starting point for seasonal-average delivered efficiency in the /resources/tilt-optimizer or /resources/sizing calculators:

0.40–0.45 — typical residential drainback flat-plate
0.50–0.55 — well-designed short-pipe / low-delivery-temperature install
0.45–0.55 — evacuated tube in high-ΔT applications (the vacuum jacket gives a much lower temperature derate, but optical η₀ is lower to start with)

Hottel–Whillier–Bliss: the temperature-derate term

The single biggest loss after the headline number is the temperature derate. A collector running hotter than ambient leaks heat out of the same absorber that's collecting it; the hotter it runs, the worse the leak. The standard SRCC / ASHRAE-93 single-line model:

η = η₀ − a₁ · (ΔT / G) − a₂ · (ΔT)² / G

η — instantaneous collection efficiency [0–1]
η₀ — peak optical efficiency (datasheet Y-intercept, dimensionless)
a₁ — first-order heat-loss coefficient, W/(m²·K)
a₂ — second-order coefficient, W/(m²·K²) — small for flat-plate, important for high-ΔT evacuated tube
ΔT — T_collector_inlet − T_ambient, K
G — solar insolation on the collector plane, W/m²

In practice for flat-plate panels at moderate temperatures the second-order term is small and can be dropped, giving the linear form:

η ≈ η₀ − a₁ · (ΔT / G)

Worked example — flat-plate at solar noon

Using a flat-plate panel with η₀ = 0.78 and a₁ ≈ 4 W/(m²·K), operating at ΔT = 30 K (collector 30 °C above ambient) and G = 600 W/m² (good but not peak sun):

η = 0.78 − 4 × 30 / 600
  = 0.78 − 0.20
  = 0.58  (instantaneous, solar noon)

So 20 percentage points lost to the temperature-derate term alone, before any of the other cascade losses kick in. The cosine factor, control losses, pipe losses, stagnation, and soiling then drag the annual average down from there.

Crossover: when evacuated tube starts to win

Two collectors with different (η₀, a₁) pairs have their efficiency lines cross at a particular ΔT:

ΔT_crossover = (η₀,FP − η₀,ET) / (a₁,FP − a₁,ET)

Using representative SRCC-certified collector parameters — flat-plate AET AE-32 (η₀ ≈ 0.71, a₁ ≈ 4.9 W/(m²·K)) versus a typical evacuated tube (η₀ ≈ 0.46, a₁ ≈ 1.6 W/(m²·K)) — at G ≈ 250 W/m² (80 % full sun), the crossover sits at ΔT ≈ 34 K. For domestic hot-water duty (T_inlet typically 5–40 °C, ΔT modest), flat-plate always wins. Evacuated tube only pays back its higher cost when the operating ΔT is large (winter space heating in a cold climate, process heat above 60 °C, or stagnation-prone undersized stores). Both parameter sets above are published in the public SRCC OG-100 collector database.

What the rest of the cascade is

Cosine of incidence (×0.85) — averaged across the solar day, the sun is rarely normal to the collector face; the panel collects the projected component cos(θ). Even with perfect tilt and orientation, half the day's hours are at θ > 45° from normal.
Pump / control losses + morning warm-up (×0.93) — the controller waits until the absorber is warmer than the tank before starting circulation, then the cold pipe loop has to warm up before any useful heat lands at the tank. Both bites come off the morning yield.
Stagnation (×0.95) — for installs sized to deliver useful shoulder-season output, summer at noon often finds the tank already at its hi-limit cut-off and the controller stops pumping. Any further clear-sky energy is simply not collected (drainback systems) or is dumped via a bypass valve (closed glycol systems).
Pipe loss to surroundings (×0.93) — every metre of pipe between collector and tank, especially outdoor runs, leaks heat proportional to (T_pipe − T_ambient) × pipe_UA. Short, well- insulated, indoor runs minimise this.
Soiling, dust, partial shading (×0.97) — accumulates over the year; an annual hose-down recovers most of it.

References & sanity benchmarks

Hottel, H. C., Whillier, A., & Bliss, R. W. (1958). Evaluation of flat-plate solar collector performance. The original heat-balance derivation behind the η = η₀ − a₁·(ΔT/G) form still used on every collector datasheet today.
Klein, S. A., Beckman, W. A., & Duffie, J. A. (1976). A design procedure for solar heating systems, Solar Energy vol. 18, pp. 113–127. The F-Chart paper.
Duffie, J. A., Beckman, W. A., Blair, N. (2020). Solar Engineering of Thermal Processes, Photovoltaics and Wind, 5th ed., Wiley. Ch. 6 (collector performance) and Ch. 21 (F-Chart sizing). Canonical textbook reference.
SRCC OG-100 / Solar Keymark collector certification databases — public source for individual collector η₀ and a₁ values (including the AET AE-32 numbers used in the worked example).
Fraunhofer ISE long-term monitoring of European residential installs: 35–50 % annual delivered efficiency typical.
IEA SHC Task 26 (small DHW systems benchmarking): 38–42 % annual delivered, median across European participants.
Typical per-m² yield benchmark widely reported in Fraunhofer ISE / IEA SHC monitoring: 400–600 kWh/m²/yr of net energy delivered to the store is the band a well-sized mid-latitude flat-plate install lands in. Below ~350 = something is wrong (over-sized array, undersized tank, high delivery temperature, heavy shading). Above ~650 = either the climate is exceptional or the model is being too optimistic.