Heating and cooling · Pascal Architecture

The reference house's forced-air system threaded through its frame: the furnace and the heat pump outside, a supply trunk along the girder, branches between the joists to registers under the windows, and the return that brings the air back. Change the climate and the walls and the heat loss follows; switch to a ducted heat pump, radiant floors or ductless heads to see what each asks of the house.

A house in winter is a warm box leaking heat: through its walls, windows and ceiling by conduction, and with every cubic foot of air that slips out through a crack or is pushed out by a fan. A heating system puts the heat back as fast as it leaks. So the system is sized from the leak, not from the floor area, and it has to be threaded through a structure that was framed first, without weakening it. That is what the figure follows: the reference house’s forced-air system, from the furnace beside the girder to the registers under the windows, and the three other ways the same house could be kept warm.

How much heat leaves

Heat flows through an assembly at a rate set by its U-factor (the inverse of its R-value), its area and the temperature difference across it. Designers work from the design temperature: the outdoor temperature that is colder only 1 percent of the winter’s hours. For the reference house, in a climate like Chicago’s, that is −4 °F (−20 °C) against 70 °F (21 °C) inside, a difference of 74 °F.

Q = U × A × ΔTQ heat flow (Btu/h) · U U-factor (Btu/h·ft²·°F) · A area (ft²) · ΔT inside minus outside (°F)

Where the heat goes	Area	U-factor	Loss at −4 °F
Windows, 25	363 ft² (33.7 m²)	0.30	8,100 Btu/h
Walls, 2×6 with R-21	1,773 ft² (165 m²)	0.059	7,700 Btu/h
Air leakage, 3 ACH50	65 cfm	—	5,200 Btu/h
Ventilation, 89 cfm through an ERV	—	—	2,100 Btu/h
Basement walls and slab	1,800 ft² (167 m²)	to the ground	2,100 Btu/h
Ceiling, R-49	864 ft² (80 m²)	0.026	1,700 Btu/h
Front door	21 ft² (2.0 m²)	0.30	500 Btu/h
Total	—	—	27,400 Btu/h (8.0 kW)

Two things stand out. The windows, a sixth of the wall, lose more than the rest of the wall put together: a good window is still a poor wall. And air, leaking in or brought in on purpose, is a quarter of the load. That is why the stage after rough-in is spent sealing every gap, and why a tight house needs a fan to bring fresh air in, through a heat exchanger so that most of the heat stays. Change the walls, the airtightness or the climate in the figure and every number below follows. The walls and their four control layers are drawn in Wall assembly.

Sizing the equipment

Bigger is not safer. A furnace twice too big reaches the thermostat’s setting in a few minutes, shuts off, and starts again: short cycles that waste fuel, wear the parts and leave the house swinging between too warm and too cool. An oversized air conditioner is worse: it cools the air before it has run long enough to pull the moisture out, and the house feels cold and clammy. So the load comes first, room by room (the Manual J calculation the figure simplifies), and the equipment is chosen to match it (Manual S): a furnace between 100 and 140 percent of the heating load, a cooling unit close to its load.

Here the smallest common furnace, 40,000 Btu/h in, gives 38,400 out at 96 percent efficiency: 1.4 times the loss, and its modulating burner turns down to about a third of that on mild days. Cooling needs about 21,000 Btu/h on a 88 °F (31 °C) afternoon, mostly sun through the glass, so a 2-ton (24,000 Btu/h) air conditioner.

A heat pump is sized differently, because its output falls as it gets colder outside while the house’s loss rises. Where the two lines cross is the balance point: above it the heat pump carries the house alone, below it electric strips make up the difference. A 3-ton cold-climate unit holds this house to about −2 °F (−19 °C); on the design day it still delivers nearly 26,000 Btu/h, and 5 kW of strips cover the last 1,500. Its coefficient of performance, the heat it delivers per unit of electricity, is about 1.9 on that day and over 3.5 in mild weather.

Moving the air

A furnace warms the air about 50 °F (28 °C) on its way through, so each cubic foot per minute carries about 54 Btu/h. Cooling sets the larger flow: 400 cfm for every ton, so 800 cfm for this house. The blower pushes it through the supply: a plenum on the furnace, a trunk, and a round branch to every register. It comes back through the return, a few large grilles and ducts that bring the air to the filter and the blower again. A house with supplies and no returns pressurises the rooms with closed doors and starves the furnace.

Registers: Under the windows, on the outside walls: warm air rising across the coldest surface stops the cold draft that would fall from the glass onto the floor. About 40 cfm each here, more upstairs, where the ceiling adds its loss.
Returns: In the middle of the house: one in the hall floor, one high on the upstairs hall wall. Closing a joist bay or a stud bay with sheet metal (panning) makes the bay itself the duct: allowed for return air, never for supply.
Sealing: Every seam, takeoff and boot is sealed with mastic. Ducts that leak 20 percent of their air are common, and leaks on the return side pull in dust and, near a furnace, flue gas.
Inside the envelope: All of this ductwork is in the basement and the floors, inside the insulated house, so whatever it loses still heats the house. Ducts in a vented attic or a crawl space lose it to the outdoors.

Through the structure

The frame comes first, and the ducts must fit it without cutting what carries load. The rules are simple and strict, and they shape the whole layout.

Joists: A hole may be no more than a third of the joist’s depth, 3 in (78) in a 2×10, kept 2 in (50) from either edge; a notch no deeper than a sixth, never in the middle third of the span. A 6 in (150) branch fits neither rule. So branches run in the bays, parallel to the joists, and the trunk hangs below them beside the girder, where they all come together.
Subfloor: Cut only for the boots: a 4¼ × 10¼ in (108 × 260) hole between two joists, the boot sealed to it.
Bearing wall: Second-floor air goes up stud bays of the 2×4 bearing wall in 3¼ × 10 in (83 × 255) stacks. The stack takes the full depth of the wall, so both top plates are cut through, and the code asks for a steel strap 1½ in (38) wide across the cut, eight 10d nails each side. Each stack has to land in a bay that is clear of the lapped joists below and the floor joists above: four such bays exist in this house, and the stacks are in them.
Fire: A wall cavity open from basement to attic is a chimney. Where ducts and pipes pass the plates, the gaps are sealed with fire-rated sealant, and the outside walls are kept free of ducts so their insulation is whole.
Combustion: A sealed, condensing furnace draws its air from outside and sends out cool, wet exhaust, so two PVC pipes run out through the rim, 12 in (305) above grade and above the snow. An older furnace needed a masonry or metal chimney and drew its air from the basement.

The other three

A heat pump is an air conditioner that can run backwards: in winter it pulls heat out of the outdoor air and pumps it in. It uses the same ducts, with an air handler where the furnace stood. Its supply air is cooler, about 95 °F (35 °C), so it moves more air for the same heat, and the outdoor unit stands on a stand above the snow because in winter it frosts and defrosts. Radiant floors heat the floor rather than the air: water at about 105 °F (41 °C) runs through PEX tubing stapled under the subfloor in every joist bay and laid in the basement slab. Nothing blows, the floors are warm, and there are no ducts at all, but it cannot cool. Mini-splits are small heat pumps whose outdoor units feed heads on the walls through refrigerant lines no thicker than a thumb: no ducts, room-by-room control, but each head heats only the room it hangs in.

Why this, not that

How is the house heated and cooled?

Decided by the winter design temperature · the fuels on the street and their price · whether the house needs cooling too · room for ducts · first cost against running cost · carbon

Gas furnace and air conditionerThis house
A condensing furnace blows heated air through ducts; an outdoor condenser and a coil on the furnace cool the same air in summer.
Choose it when gas is on the street and cheap against electricity; winters are long and very cold, where a furnace's output never falls with the weather; the house needs cooling too and has room for ducts in the basement and the walls.
The catch two machines, two fuels and two service lines; it burns fossil fuel on site: a flue, a gas line and carbon monoxide to guard against; ducts lose heat and leak unless sealed and kept inside the insulated house.
The furnace in the basement No. 20 →
Ducted heat pump
An outdoor unit moves heat into the house in winter and out of it in summer, through the same ducts a furnace would use, with electric strips for the coldest hours.
Choose it when there is no gas, or the owner wants none; winters reach about −15 °F (−26 °C) or warmer, within reach of a cold-climate unit; one machine should both heat and cool; the house is tight and well insulated, so a modest unit carries it.
The catch capacity and efficiency fall as it gets colder: below the balance point the backup strips run, at a third of the efficiency; cooler supply air, about 95 °F (35 °C), feels less warm at the register and needs more airflow, so larger ducts; the outdoor unit needs a stand above the snow and room for its defrost water.
The heat pump outside No. 20 →
Radiant floors and a boiler
A boiler heats water that runs through PEX tubing under or in the floors; the floors warm the room and everything in it, with no moving air.
Choose it when comfort comes first: warm floors, no drafts, no blowing dust, silence; floors are tile, stone or concrete that store and spread the heat; the house needs little or no cooling, or will get a separate system for it.
The catch no cooling at all: summer needs a second system; slow to respond: a cold room takes hours to warm, so setbacks hardly pay; the highest first cost, and carpet or thick wood floors smother it.
The boiler and manifold No. 20 →
Ductless mini-splits
Small heat pumps whose outdoor units feed wall-mounted heads in the rooms through thin refrigerant lines, with no ducts at all.
Choose it when there is nowhere to run ducts: an addition, an old house, an open plan; the house is very tight and needs little heat, so a few heads carry it; rooms want their own control, and the owner accepts a unit on the wall.
The catch a head heats only the room it is in: closed bedrooms without one run several degrees cooler; no filtration or fresh air for the whole house: ventilation needs its own ducts; each head has a filter to clean, a condensate drain, and a box on the wall.
A head and its line set No. 20 →

Here A condensing gas furnace with an air conditioner: gas is in the street, Chicago-like winters reach −4 °F (−20 °C), and the basement gives the ducts an easy home. The same ducts would take a cold-climate heat pump later, which is why they are sized generously.

How the figure decides

Design temperatures	Mild: 25 °F (−4 °C); cold: −4 °F (−20 °C); very cold: −16 °F (−27 °C); inside 70 °F (21 °C)
Walls	Whole-wall U-factors with framing at 25 %: 0.085, 0.059, 0.035
Windows and door	U-0.30; window area from the plan, 363 ft²
Below grade	Basement walls U-0.05 and slab U-0.025 against the ground’s winter temperature
Air	Natural leakage = ACH50 ÷ 17; ventilation 89 cfm (ASHRAE 62.2) through an ERV recovering 70 %
Cooling	Conduction, 30 Btu/h per ft² of glass for sun, people and appliances, and moisture
Heat pump	Capacity 100 % at 47 °F, 80 % at 5 °F, 72 % at −4 °F; strips in 5 kW steps
Air to rooms	Blower flow split by each level’s share of the loss, over its registers

These are the simplifications of a first pass. A real design runs the load room by room with each wall’s orientation and shading, sizes every duct from the friction it can afford, and checks the equipment’s published capacity at the design temperature.