Heating loads

When the Novaks first asked about a heat pump, the quote they received from another contractor had sized the system by floor area: 2,600 ft² at 18 Btu/h per square foot, a four-ton unit. Northfield's quote was for a three-ton cold-climate heat pump, because Dana had insisted on a calculated heat loss, and RAC-320 lesson 7 followed that decision. In January, with the house running well, Irene asked Theo to show her how the calculation worked. "I'm an engineer," she said. "I'd like to see the numbers, not just the answer." Theo was glad of the excuse to go through them properly.

This lesson explains how a heating load is calculated: the design temperatures, heat loss through each part of the envelope, air leakage, below-grade losses, and how ACCA Manual J organizes the work. Lesson 6 does the same for cooling.

What a heating load is

The design heating load is the rate at which a building loses heat on a cold day near the coldest of a typical winter, with the inside held at the design indoor temperature. It is the capacity the heating system must supply. It is not the coldest day ever recorded, and it is not the energy used over a season, which depends on the whole winter's weather and is estimated separately, as RAC-320 lesson 12 did with degree-days.

Heat leaves a building in two main ways. It is conducted through the walls, windows, doors, roof, basement and floor, at a rate proportional to the area of each part, its thermal transmittance and the temperature difference across it. And it is carried away by air: outdoor air that leaks in through cracks and is heated, and indoor air that leaves through exhaust fans, chimneys and ventilation. In houses, the two are often similar in size; in a leaky older house the air can be the larger.

Design temperatures

The outdoor design temperature comes from published climate data. In the United States, ACCA Manual J's tables and ASHRAE's climate data give the 99 % heating design temperature: the temperature that the hourly outdoor temperature stays above for 99 % of the hours in a year. For Louisville it is about 10 °F. Colder spells happen, and the house cools slightly during them or the supplementary heat makes up the difference, but sizing to the extreme would oversize the equipment for every other day.

The indoor design temperature is set by the standard: 70 °F in Manual J for heating. It is a design value, not the setpoint the family will choose.

Conduction through the envelope

Each part of the envelope has a U-value, its thermal transmittance, the heat flow through one square meter or square foot for each degree of temperature difference. It is the inverse of the total thermal resistance, R, in ft²·°F·h/Btu (RSI in SI units, where R = RSI × 5.678). The resistance of a wall is the sum of its layers' resistances, including the air films on each surface, but framing members, which conduct heat much better than insulation, form thermal bridges through it. The effective resistance of a wood-framed wall is therefore noticeably lower than the nominal value of the insulation in it, and calculation standards use effective values.

Windows and doors use the manufacturer's rated U-value, or a typical value for the type and age when no rating is available. A 1960s double-glazed window in a wood or steel frame might be 0.45 to 0.55 Btu/h·ft²·°F; a modern triple-glazed unit under 0.20; so windows, though a small part of the area, are often a large part of the loss.

Areas are measured from the drawings or on site: gross wall area, minus windows and doors, for each orientation; ceiling area under the attic; and the below-grade parts of the basement. Manual J calculations are normally done room by room, because the room loads set the airflow to each room, which lesson 9 uses to size ducts. For the whole-house total, a single calculation for each component type is enough.

Below-grade losses

Basement walls and floors lose heat to the soil, which is warmer than the outdoor air in winter and cooler deep down than near the surface. Heat flow through the upper part of a basement wall is much higher than through the lower part, and the floor loses relatively little, mostly near its edges. The standards handle this with tables or formulas that give effective U-values for below-grade walls by depth and insulation, and for floors by their size and edge insulation, against either the outdoor design temperature or a ground temperature. The Novak basement walls had R-10 insulation on the upper half only, added when the basement was finished in the 1990s.

Air leakage

Air leakage is the hardest part of the load to estimate, because it depends on the size and location of the leaks and on the wind and the stack effect, the tendency of warm air to rise out through the top of a heated house and draw cold air in at the bottom. There are two common approaches.

• Estimate leakage from the construction quality, using the standard's tables for tight, average or loose construction.
• Measure it with a blower door, a calibrated fan in an exterior doorway that depressurizes the house to 50 pascals and measures the airflow needed. The result is expressed as air changes per hour at 50 Pa, ACH50. A rough rule divides ACH50 by a factor of about 10 to 20, depending on the climate, the number of stories and the exposure, to estimate the natural air change rate on an average winter day. More detailed methods use the measured leakage area and the design wind and temperature difference.

The heat needed to warm the leaking air is the airflow times the sensible heat factor times the temperature difference. For a natural air change rate in air changes per hour, the airflow is that rate times the house volume.

Q_{\text{air}} = 1.08 \times \frac{\text{ACH} \times V}{60} \times \Delta T \quad \text{Btu/h (V in ft}^3)

The Novaks had had a blower door test before and after the air sealing, as part of their energy audit. Before: about 9.0 ACH50. After sealing the attic hatch, the top plates, the old chimney chase and the rim joists: about 4.5 ACH50. Theo used a factor of 14, a typical value for a one-story house in a sheltered suburb, and labeled it as an estimate.

The Novak calculation

The script follows the calculation Theo had done in the office, one line for each component type, with the areas from the house drawings and effective U-values from the standard's tables and the window ratings. It then compares the leakage before and after the air sealing, and checks the heat pump's capacity at the design temperature, from RAC-320 lesson 6.

T_IN, T_OUT = 70.0, 10.0           # Manual J indoor design and Louisville's 99 % heating design temperature
dT = T_IN - T_OUT
V = 2600 * 8                        # ft3 of heated volume, main floor and finished basement
def infiltration_ua(ach50, n=14):
    """Natural air change rate from a blower-door result, then Btu/h per deg F (1.08 x cfm)."""
    ach = ach50 / n
    cfm = ach * V / 60
    return 1.08 * cfm, ach, cfm
parts = [
    # name, area ft2, U-value Btu/(h ft2 F)
    ("walls above grade", 948, 0.142),
    ("windows and doors", 226, 0.46),
    ("attic ceiling (after upgrade)", 1300, 0.050),
    ("basement walls below grade", 947, 0.060),
    ("basement floor", 1300, 0.014),
]
ua_total = 0
for name, area, u in parts:
    ua = area * u; ua_total += ua
    print(f"{name:32s} {area:5d} ft2 x U {u:5.3f} = {ua:5.1f} Btu/h F -> {ua * dT:7,.0f} Btu/h")
ua_inf, ach, cfm = infiltration_ua(4.5)
ua_total += ua_inf
print(f"{'air leakage (4.5 ACH50)':32s} {ach:.2f} ACH, about {cfm:.0f} cfm  = {ua_inf:5.1f} Btu/h F -> {ua_inf * dT:7,.0f} Btu/h")
loss = ua_total * dT
print(f"total UA {ua_total:.0f} Btu/h F, design heat loss {loss:,.0f} Btu/h at {T_OUT:.0f} F")
before = infiltration_ua(9.0)[0]
print(f"before air sealing (9.0 ACH50) the leakage alone was {before * dT:,.0f} Btu/h")
hp = 25750
print(f"heat pump at design {hp:,} Btu/h covers {hp / loss:.0%}; the rest comes from the heater kit")

walls above grade                  948 ft2 x U 0.142 = 134.6 Btu/h F ->   8,077 Btu/h
windows and doors                  226 ft2 x U 0.460 = 104.0 Btu/h F ->   6,238 Btu/h
attic ceiling (after upgrade)     1300 ft2 x U 0.050 =  65.0 Btu/h F ->   3,900 Btu/h
basement walls below grade         947 ft2 x U 0.060 =  56.8 Btu/h F ->   3,409 Btu/h
basement floor                    1300 ft2 x U 0.014 =  18.2 Btu/h F ->   1,092 Btu/h
air leakage (4.5 ACH50)          0.32 ACH, about 111 cfm  = 120.3 Btu/h F ->   7,221 Btu/h
total UA 499 Btu/h F, design heat loss 29,936 Btu/h at 10 F
before air sealing (9.0 ACH50) the leakage alone was 14,441 Btu/h
heat pump at design 25,750 Btu/h covers 86%; the rest comes from the heater kit

The total UA came to about 500 Btu/h·°F and the design heat loss to about 30,000 Btu/h at 10 °F. The walls and the air leakage were the two largest parts, each about a quarter of the total, and the windows came next. The air sealing had cut the leakage load from about 14,400 Btu/h to 7,200, which on its own was the difference between a three-ton and a four-ton heat pump. At the design temperature the cold-climate heat pump's 25,750 Btu/h covered 86 % of the load.

Irene checked the attic line and asked why it was so modest, since the attic had been insulated. Theo explained that the low roof over the eaves limited the insulation depth near the walls, and the effective value included the framing and the less-insulated areas around the hatch and the old chimney; about R-20 effective over the whole ceiling was a fair estimate. Irene also asked about the floor-area rule. Theo showed her that 18 Btu/h per square foot would have given about 47,000 Btu/h, half again as much as the real loss, because the rule assumes an average house and the Novaks' was now tighter and better insulated than average.

CSA F280 and Manual J

ACCA Manual J, Residential Load Calculation, is the US standard method for house heating and cooling loads, and the International Residential Code, as adopted in Kentucky and most states, requires heating and cooling equipment to be sized from a Manual J calculation and selected with Manual S. Manual J specifies the design conditions, the U-value and below-grade methods, the infiltration estimate, and the room-by-room procedure; Manual S sets how closely the equipment capacity must match the calculated load.

Both are normally done with software, which applies the tables and adds up the rooms. The technician's job is to give the software good inputs: measured areas, real window ratings, the insulation actually found in the walls and attic, a blower door result when there is one, and the correct design temperatures. Most errors in load calculations are not errors in arithmetic but guesses about the building: assuming insulation that is not there, or ignoring a large basement window.

Ventilation and other gains and losses

If a house has mechanical ventilation, the heat needed to warm the ventilation air is part of the load, reduced by the heat recovery of an HRV or ERV, as lesson 11 shows. Duct losses add to the load when ducts run through unheated spaces such as a vented attic or crawlspace; the Novaks' ducts were all inside the heated basement, so their losses stayed in the house. Internal gains from people, lighting and appliances reduce the heating needed on most days, but heating calculations usually ignore them, because the design day might be a night with nobody home.