The 17/47 trap: why two numbers can't predict a heat pump in a Quebec winter

To justify replacing equipment with a heat pump, almost everyone quotes the same two numbers: the COP "at 47" and the COP "at 17." They are convenient, they are printed on the spec sheet, and they feel like a fair summary of how the unit performs.

The problem: a heat pump's performance is a curve, not a straight line between two points. In Quebec, where we design for −23 to −25 °C, trusting the 17/47 line paints a picture that is consistently too optimistic: it overstates capacity, overstates COP, understates backup, so it overstates savings and shortens the payback period you present to the client.

Where "17" and "47" come from

They aren't arbitrary: they're the AHRI 210/240 standard rating points, the North-American standard for rating heat pumps.

• 47°F (8.3°C): the "mild" point. This is where the heat pump is most efficient.
• 17°F (−8.3°C): the official "cold" point of the rating.

For reference, Optima's default heating dataset (reference unit) is built on exactly those two points: COP 2.40 / 184,000 Btu/h at 17°F and COP 3.54 / 225,000 Btu/h at 47°F. Capacity at 17°F is only ~82 % of the nominal capacity at 47°F.

The standard itself isn't the problem; it lets you compare units. The problem is what many tools and proposals do next: they take those two points and draw a straight line to estimate performance at every other temperature.

Two points only define a straight line

It's basic geometry: exactly one straight line passes through two points. If 17°F and 47°F are your only data, your model can only be a linear interpolation, a constant slope. But real heat-pump performance is not linear:

• COP and capacity fall faster as it gets colder;
• the curve sags in the defrost range (around 0 °C);
• on a variable-speed (inverter) unit, COP also depends on the modulation level, not just outdoor temperature.

As engineers put it on GreenBuildingAdvisor: "the relationship between COP at 47°F, 17°F and −13°F isn't linear, making prediction unreliable." Drawing a line between two points is exactly that unreliable prediction.

In Quebec, we heat below the 17 °F point

This is the heart of the matter for our climate. The standard's "cold" point, 17°F, is −8.3 °C. But heating design temperatures (National Building Code / ASHRAE) are far lower:

City	Heating design temp	In °F
Montreal	≈ −23 °C	≈ −9 °F
Quebec City	≈ −25 °C	≈ −13 °F

In other words, the hours that matter most (the coldest, when the building demands the most heat) sit 15 to 17 °C below the coldest rating point. There, you're no longer interpolating between known points: you're extrapolating beyond your data. And an extrapolated straight line drifts further from reality the further you push it.

The chart below is a real case exported from Optima. The blue dots are the manufacturer's real data; the blue line is the curve Optima fits through them; the orange line is the 2-point estimate drawn from the two rated points alone (in red).

Look at the left edge: −13°F is exactly Quebec City's design temperature. At that point, the 2-point line claims ~205,000 Btu/h, while the real curve gives ~122,000 Btu/h: the line overstates capacity by ~68 %, right at the most critical condition of the year. And the line only errs one way: optimistic.

Defrost: a real dip, invisible to the line

Below freezing and in humid weather, frost builds on the outdoor coil. The heat pump must periodically reverse its cycle to melt it: during those minutes it doesn't heat the building and it draws energy. The result is a real loss of capacity, concentrated near 0 °C, precisely the most frequent temperature range of a Quebec winter.

A 2-point line is structurally unable to represent this: a straight line can't dip and recover. It simply ignores part of the backup heat that will actually be needed.

Optima does not ignore it. And, crucially, it handles defrost on top of the COP curve, not instead of it. The engine starts from the real capacity and COP curve, then applies a defrost correction computed from the conditions, and it also estimates the uncertainty around it. That penalty is then folded into the hour-by-hour calculation, so into the energy, the cost and the final payback period shown to the client. The exact method is part of our know-how; what matters here is that defrost is computed on top of the COP and accounted for, not ignored.

Falling capacity, rising demand: the balance point

This is where the error truly costs money. As temperature drops, the heat pump's capacity falls while the building's demand rises. The two eventually cross: that's the balance point. Below it, the heat pump can't keep up and backup heat (electric resistance or gas) must make up the difference.

The whole economic story lives here: backup is the expensive part of heating (COP of 1 for resistance heat). And how much backup you need depends entirely on the accuracy of the capacity curve. A too-optimistic line, overstating capacity by 68 % in deep cold, as above, pushes the balance point colder and understates backup. You then promise a payback period shorter than reality.

What Optima does instead

Optima doesn't just connect two dots. The simulation engine:

1. accepts multi-point data (beyond 17/47: 5 °F, −13 °F, and the full extended performance table when available);
2. fits a non-linear curve rather than a line, following the manufacturer's data with excellent correlation;
3. models defrost (a calibrated correction curve and its uncertainty) instead of ignoring it;
4. handles backup and switchover explicitly;
5. bounds extrapolation within physically plausible limits, so it never produces nonsense at the extremes.

All of it runs hour by hour against the site's real weather data, then converts to energy, cost and payback period. That's the difference between a "drawn-with-a-ruler" estimate and a simulation that respects the physics of cold.

Takeaways

• 17°F and 47°F are rating points (AHRI), not a performance curve.
• Two points = a straight line. Real performance is a non-linear curve.
• In Quebec we heat below 17°F: we extrapolate, where the line is least reliable, up to +68 % capacity overstated at Quebec City's design temperature.
• Defrost creates a capacity loss around 0 °C, invisible to the 2-point method, and that's where most hours are. Optima computes it on top of the COP curve and folds it into the result (with its uncertainty); the line ignores it.
• The error is always optimistic: too much capacity, too much COP, not enough backup, so an understated payback period.
• Optima uses the real curves (multi-point, defrost, backup logic), hour by hour.

Methodology: curve reused from a real case exported from Optima, capacity (°F, Btu/h) fitted to the manufacturer's data with excellent correlation. Defrost is modelled by Optima (proprietary model, not shown). References: AHRI 210/240; Optima default values (ASHRAE 90.1-2019 Tab. 6.8.1-2); NBC/ASHRAE design temperatures.