Heat flow and insulation

Lavoie begins the second week with two wall samples on the table, each about three feet square. One is a wood stud wall, the other a steel stud wall; both have the same batts in their cavities, the same sheathing and the same gypsum board. 'The insulation label on both says the same number,' she says. 'One of these walls loses heat nearly twice as fast as the other. Which one, and why?' Joon-ho guesses the steel wall, correctly. Callum asks how much difference a few thin strips of metal can make. The answer, which this lesson calculates, surprises everyone: the steel studs cut the effective resistance of the insulated cavity by more than half. The environmental systems course introduced conduction, thermal resistance and the parallel path method. This lesson goes further: into the different insulation materials and their real performance, into steel framing and cladding attachments, which defeat the parallel path method, and into the question every client eventually asks, how much insulation is enough.

Insulation materials

Insulation works by trapping still gas in small cells or between fibers, because still air conducts heat poorly. Each family of materials has its own strengths. Mineral wool, made from rock or slag spun into fibers, is noncombustible, tolerates high temperatures, drains water and allows vapor to pass, and comes as batts for cavities and as rigid boards for continuous exterior insulation. Glass fiber batts are the cheapest cavity insulation and similar in performance to mineral wool batts. Cellulose, made from recycled newsprint treated with fire retardant, is blown into cavities and attics; it has low embodied carbon and buffers moisture, but must be kept from bulk water. Expanded polystyrene, the white bead board, is cheap, comes in several densities and is often used below grade and in insulated concrete forms. Extruded polystyrene, usually pink or blue, is denser and more resistant to water absorption. Polyisocyanurate boards, faced with foil or glass mat, have the highest resistance per thickness of common boards. Spray polyurethane foam fills irregular cavities and seals them; closed-cell foam is dense, vapor-retarding and adds stiffness, while open-cell foam is light and vapor-open. Wood fiber boards, common in Europe and increasingly available in North America, are vapor-open, have low embodied carbon and add thermal mass.

The values in tables are measured at a mean temperature near room temperature. Two materials behave differently in a cold climate. Polyisocyanurate loses part of its resistance when its mean temperature falls below about 50 °F, because the blowing agent in its cells begins to condense; on a cold night on a Minneapolis roof, its resistance may be a quarter lower than its label. Designers in cold climates often combine polyisocyanurate with a layer of mineral wool or polystyrene outside it, which keeps it warmer, or simply derate it. Foam plastics also lose some resistance over years as the blowing agent diffuses out of the cells and air diffuses in; the standards in both countries require manufacturers to report a long-term value that accounts for this aging. The blowing agents themselves have changed: the hydrofluorocarbons that replaced ozone-depleting gases had high global warming potential and are being phased out in both countries in favor of agents with much lower impact.

How insulation fails

An insulation layer performs as tested only if it is installed as tested. Batts must fill their cavities completely, touching the studs on both sides and the plates top and bottom, without being compressed behind wires, pipes or electrical boxes; gaps of an eighth of an inch around a batt can reduce the cavity's effective resistance by a tenth or more, and a batt that does not touch the back of the sheathing leaves an air space in which convection loops carry heat around it. Rigid boards must be tight to each other and to the substrate, with joints staggered in two layers where possible. Loose fill in attics settles and must be installed above its rated depth. Wind washing, cold air blowing into the edges of attic insulation at the eaves, can make the outer part of a ceiling almost worthless unless baffles protect it. And wet insulation conducts heat much better than dry insulation, which is one more reason the water, air and vapor control layers matter.

Steel framing and the zone method

The parallel path method, used in the environmental systems course for wood stud walls, assumes that heat flows straight through each path, the insulated path and the framing path, without moving sideways between them. That is close enough for wood, which conducts heat only about three times as well as insulation. It is badly wrong for steel, which conducts heat about four hundred times as well as wood. Heat flowing through the sheathing toward a steel stud spreads sideways to the stud, runs through its web and spreads again into the gypsum board, so that the stud's influence extends far beyond its own thickness. Engineers use the isothermal planes method, the zone method or tables derived from hot box tests and computer modeling to find the effective resistance of steel-framed walls. The tables published with the energy standards give effective values directly: a 6 in steel stud cavity at 16 in spacing, filled with batts of R-19, performs as if it had only about R-7.1, little more than a third of the label.

This is why steel stud walls in cold climates need continuous exterior insulation, and why the way that insulation is attached matters so much. Cladding must be fastened to the structure through the insulation. If it is hung from continuous steel girts running across the insulation, the girts form a new thermal bridge and the exterior insulation may perform at less than half its nominal value. Intermittent steel clips do better, and clips made of stainless steel, fiberglass or with thermal isolators do better still. Some systems use long screws through the insulation into the studs, with the cladding fastened to strapping held by the screws. Published research and manufacturers' tests give the effective resistance of each system; the following calculation uses typical factors to compare the options for a Minneapolis office wall.

# Effective thermal resistance of wood and steel stud walls (R)
films = 2.8        # inside film, gypsum board, sheathing, cladding with cavity, outside film
batt = 19          # batt in the stud cavity, nominal
wood_stud = 6.9       # a wood stud through the cavity depth
steel_cavity = 7.1    # effective value of the same batt between steel studs (tables)
board = 12           # exterior insulation board, nominal
framing = 0.23         # fraction of the wall that is wood framing

def wood(ci):
    u = (1 - framing) / (films + batt + ci) + framing / (films + wood_stud + ci)
    return 1 / u

cases = [
    ("wood studs, cavity only", wood(0)),
    ("wood studs + exterior board", wood(board)),
    ("steel studs, cavity only", films + steel_cavity),
    ("steel + board on continuous girts", films + steel_cavity + 0.45 * board),
    ("steel + board on steel clips", films + steel_cavity + 0.75 * board),
    ("steel + board on isolated clips", films + steel_cavity + 0.90 * board),
]
for name, r in cases:
    print(f"{name:36s} R {r:5.1f}   U = {1 / r:.4f}")
print(f"nominal label of batt + board: R {batt + board:.1f}")

wood studs, cavity only              R  16.9   U = 0.0590
wood studs + exterior board          R  30.0   U = 0.0334
steel studs, cavity only             R   9.9   U = 0.1010
steel + board on continuous girts    R  15.3   U = 0.0654
steel + board on steel clips         R  18.9   U = 0.0529
steel + board on isolated clips      R  20.7   U = 0.0483
nominal label of batt + board: R 31.0

The steel stud wall without exterior insulation, films and finishes included, reaches only about half of the label on its batts. The same wall with exterior board on continuous girts is still worse than a wood stud wall with no exterior insulation at all. The clip system matters almost as much as the thickness of the board: moving from girts to isolated clips adds as much resistance as an inch and a quarter of extra board. For this reason, many designers of steel-framed buildings now leave the stud cavities empty, which avoids condensation in the cavity and simplifies the wiring, and put all the insulation outside the sheathing on well-isolated clips.

Thermal mass and the direction of heat flow

Thermal resistance describes steady heat flow. Real envelopes see temperatures that change through the day, and materials with high heat capacity, such as concrete, masonry and water, absorb heat as the temperature rises and release it as it falls. A heavy wall therefore delays and damps the peak of heat flow through it, which helps in climates with large daily swings and in buildings with large solar gains. In a cold continental climate with long cold spells, mass does little to reduce the total heating load, but mass inside the insulation stabilizes indoor temperatures, as the passive heating lesson of the environmental systems course showed. Mass outside the insulation, such as a brick veneer, contributes almost nothing to the thermal performance of the wall.

The direction of heat flow also matters for some layers. An air space conducts heat differently up, down and sideways, because warm air rises: a horizontal air space under a floor resists downward heat flow better than upward flow through a ceiling. Reflective foil facings reduce radiant transfer across an air space next to them, and a reflective layer facing a ventilated attic can reduce summer heat gain through a ceiling. But a reflective surface works only if it faces an air space, it loses its effect when dusty, and it adds almost nothing in a cold climate where conduction dominates. Claims of very high resistance for thin reflective products usually refer to an assembly with air spaces, under ideal conditions, not to the product itself.

How much insulation is enough

Each added layer of insulation saves less energy than the one before, because the heat loss is inversely proportional to the total resistance. Doubling the resistance halves the loss; doubling it again saves only a quarter of the original. The following calculation shows the annual heat loss through one square foot of wall in Minneapolis, with about 7,500 heating degree-days, as exterior insulation is added in steps to a wood stud wall.

# Diminishing returns: annual heat loss through a wall as insulation is added
hdd = 7500             # heating degree-days (F-days)
base = 17.6           # effective resistance of the stud wall alone (R)
step = 6.0           # resistance of each added layer of exterior board
prev = None
for n in range(0, 6):
    r = base + n * step
    loss = 24 * hdd / r / 1000            # kBtu per year through one ft2
    saved = "" if prev is None else f"saves {prev - loss:6.2f}"
    print(f"{n} layers  R {r:5.1f}  loss {loss:6.2f} kBtu  {saved}")
    prev = loss

0 layers  R  17.6  loss  10.23 kBtu  
1 layers  R  23.6  loss   7.63 kBtu  saves   2.60
2 layers  R  29.6  loss   6.08 kBtu  saves   1.55
3 layers  R  35.6  loss   5.06 kBtu  saves   1.02
4 layers  R  41.6  loss   4.33 kBtu  saves   0.73
5 layers  R  47.6  loss   3.78 kBtu  saves   0.55

The first layer of exterior board saves several times as much as the fifth. Whether the fifth layer is worth adding depends on its cost, the price of energy over the life of the building, the carbon in the insulation itself, the floor area lost to a thicker wall and, often decisively, the details: a thicker layer of insulation needs longer fasteners, deeper window returns and heavier cladding supports. In a cold climate, the point of diminishing returns for walls usually lies somewhere between R-23 and R-40 effective, higher for roofs, where insulation is cheap to add, and highest in buildings aiming for Passive House levels of performance. Beyond that, the money is better spent on windows, airtightness, thermal bridges and heat recovery, as the environmental systems course concluded.

The carbon in insulation

The materials course showed that insulation products differ greatly in embodied carbon. For thick layers, the difference matters: a wall insulated with a high-impact foam can embody more carbon in its insulation than the building will save by its reduced heating over decades, especially where the heating comes from a low-carbon grid such as Minnesota's increasingly clean grid. Mineral wool, cellulose and wood fiber usually carry the least embodied carbon per unit of resistance; polystyrene and polyisocyanurate sit in the middle and depend on their blowing agents. The optimal design weighs both: enough insulation to make operating energy small, of materials whose own carbon does not outweigh what they save.

Exercise 2: effective resistance

This exercise takes about one week.

• Calculate the nominal and effective resistance of the main wall and roof of your mixed-use building.
• For any steel-framed assembly, use the published effective values for the cavity and the attachment system you have drawn.
• Draw the insulation layer at full scale where it meets a window, a floor and the roof, showing every fastener that passes through it.
• Calculate the annual heat loss through one unit area of each assembly and the savings of one more layer of insulation.
• Recommend an insulation material for each layer, considering fire, moisture, temperature and embodied carbon.