Thermal comfort

The eighth seminar begins with a vote. Holm sets the seminar room's thermostat to 73 °F, waits twenty minutes, and asks each student to rate how they feel on a scale from cold to hot. Wren, in a sweater, votes neutral; Joon-ho, who cycled in, votes slightly warm; Ingrid, sitting by the cold window, votes slightly cool; Callum votes neutral but says the air feels stuffy. 'Four people, one room, one temperature, four different answers,' Holm says. 'Comfort is not a temperature. It is a state of mind that depends on the air, the surfaces, the air movement, the humidity, what you are wearing, what you are doing, and what you expect. Today we look at how simulation predicts it.'

The six factors

Thermal comfort depends on four environmental factors and two personal ones. The environmental factors are air temperature, mean radiant temperature (the average temperature of the surfaces a person exchanges radiant heat with, weighted by how much of the view each occupies), air speed and humidity. The personal factors are metabolic rate, measured in met units, where 1 met is a person seated quietly, and clothing insulation, measured in clo, where 1 clo is roughly a business suit. A simulation can calculate the environmental factors; the personal factors must be assumed, and their ranges should be tested like any other uncertain input.

Mean radiant temperature is the factor architects control most directly and most often forget. A person near a large cold window loses heat by radiation to the glass even if the air is at a comfortable temperature, which is why Ingrid felt cool. Operative temperature, roughly the average of air and mean radiant temperature in still air, combines the two into one number and is what most comfort criteria use.

Fanger's heat balance model

In 1970 the Danish engineer Ole Fanger published a model that predicts the average thermal sensation of a large group of people from the six factors. It is based on the body's heat balance: a person is comfortable when the heat produced by metabolism equals the heat lost by convection, radiation, evaporation and breathing, with skin temperature and sweating at levels typical of comfort. The model gives the predicted mean vote (PMV) on a seven-point scale from −3 (cold) through 0 (neutral) to +3 (hot), and the predicted percentage dissatisfied (PPD), the share of people expected to vote outside the central three points. Even at a PMV of zero, about 5 in 100 people are dissatisfied: no condition pleases everyone.

The model is codified in ISO 7730 and in ASHRAE Standard 55, the North American comfort standard, which was updated as ASHRAE 55-2023. It is most reliable in air-conditioned buildings where conditions are steady and people's clothing and activity are known. The students implement the ISO 7730 algorithm and test three conditions in the hub's reading room.

# Two ways to judge comfort: Fanger's PMV/PPD (ISO 7730) and the adaptive model of ASHRAE 55
import math
def pmv(ta, tr, vel, rh, met, clo):
    pa = rh * 10 * math.exp(16.6536 - 4030.183 / (ta + 235))
    icl = 0.155 * clo; m = met * 58.15; w = 0.0; mw = m - w
    fcl = 1.05 + 0.645 * icl if icl > 0.078 else 1.0 + 1.29 * icl
    hcf = 12.1 * math.sqrt(vel); taa = ta + 273; tra = tr + 273
    tcla = taa + (35.5 - ta) / (3.5 * icl + 0.1)
    p1 = icl * fcl; p2 = p1 * 3.96; p3 = p1 * 100; p4 = p1 * taa
    p5 = 308.7 - 0.028 * mw + p2 * (tra / 100) ** 4
    xn = tcla / 100; xf = xn
    for _ in range(150):
        xf = (xf + xn) / 2
        hcn = 2.38 * abs(100 * xf - taa) ** 0.25
        hc = max(hcf, hcn)
        xn = (p5 + p4 * hc - p2 * xf ** 4) / (100 + p3 * hc)
        if abs(xn - xf) < 1.5e-5:
            break
    tcl = 100 * xn - 273
    hl1 = 3.05e-3 * (5733 - 6.99 * mw - pa); hl2 = 0.42 * (mw - 58.15) if mw > 58.15 else 0.0
    hl3 = 1.7e-5 * m * (5867 - pa); hl4 = 0.0014 * m * (34 - ta)
    hl5 = 3.96 * fcl * (xn ** 4 - (tra / 100) ** 4); hl6 = fcl * hc * (tcl - ta)
    ts = 0.303 * math.exp(-0.036 * m) + 0.028
    v = ts * (mw - hl1 - hl2 - hl3 - hl4 - hl5 - hl6)
    return v, 100 - 95 * math.exp(-0.03353 * v ** 4 - 0.2179 * v ** 2)
def show(t):
    return f"{t * 1.8 + 32:.1f} F"
def c(f):
    return (f - 32) / 1.8
for label, ta, tr, clo in (("winter, sweater", c(70), c(67), 1.0), ("winter, cold window nearby", c(70), c(62), 1.0),
                           ("summer, light clothing", c(78), c(78), 0.5)):
    v, ppd = pmv(ta, tr, 0.1, 40, 1.2, clo)
    print(f"{label:28s} air {show(ta)}, radiant {show(tr)}: PMV {v:+.2f}, PPD {ppd:.0f} in 100")
# adaptive model for the reading room running free in a July heat spell
prevailing = c(72)   # prevailing mean outdoor temperature, C
t_comf = 0.31 * prevailing + 17.8
print(f"adaptive neutral temperature {show(t_comf)}; 80 in 100 accept {show(t_comf - 3.5)} to {show(t_comf + 3.5)}")
ops = [24.5 + 3.8 * math.sin(2 * math.pi * (h - 9) / 24) + 0.12 * (h // 24) for h in range(7 * 24)]
occupied = [t for h, t in enumerate(ops) if 9 <= h % 24 < 21]
over = sum(1 for t in occupied if t > t_comf + 3.5)
print(f"occupied hours above the 80 band in the week: {over} of {len(occupied)}")

winter, sweater              air 70.0 F, radiant 67.0 F: PMV -0.32, PPD 7 in 100
winter, cold window nearby   air 70.0 F, radiant 62.0 F: PMV -0.59, PPD 12 in 100
summer, light clothing       air 78.0 F, radiant 78.0 F: PMV +0.18, PPD 6 in 100
adaptive neutral temperature 76.4 F; 80 in 100 accept 70.1 F to 82.7 F
occupied hours above the 80 band in the week: 25 of 84

With air at 70 °F and surfaces at 67 °F, a reader in a sweater has a PMV of −0.32, slightly cool but within the common comfort range of −0.5 to +0.5, with 7 in 100 dissatisfied. Next to a cold window, with a mean radiant temperature of 62 °F, the PMV falls to −0.59 and dissatisfaction nearly doubles, although the air temperature has not changed. In summer, light clothing at 78 °F gives a PMV of +0.18. Holm points to the second result: the hub's triple glazing, which keeps the inner pane warmer, is a comfort measure as well as an energy measure. A model that reports only air temperature would never show it.

The adaptive model

In the 1990s field studies of buildings around the world found that people in naturally ventilated buildings, who could open windows and adjust their clothing, were comfortable over a much wider range of temperatures than Fanger's model predicted, and that their preferred temperature followed the outdoor climate of recent days. Richard de Dear and Gail Brager used these data to develop the adaptive comfort model, adopted in ASHRAE 55 in 2004 and, in a similar form, in the European standard EN 16798-1. It applies to occupant-controlled, naturally conditioned spaces without mechanical cooling, where people are engaged in near-sedentary activities.

In the ASHRAE version, the neutral operative temperature depends on the prevailing mean outdoor air temperature, a running average of recent days. Bands around it define the conditions that 80 or 90 in 100 occupants find acceptable.

The second part of the students' program applies the adaptive model to the reading room during a July heat spell, with the room running free on natural ventilation. With a prevailing mean outdoor temperature of 72 °F, the neutral temperature is about 76.4 °F, and 80 in 100 people accept operative temperatures from about 70 to 82.7 °F. In the simulated week, 25 of the 84 occupied hours lie above the upper limit. Without mechanical cooling, the reading room would be too warm for about a third of the opening hours in that week. As a neighborhood cool room in a heat wave, it needs more: either the ceiling fans and night ventilation the strategy assumes, modeled properly, or mechanical cooling from the heat pumps for the worst days.

Air movement

Air movement cools people by convection and evaporation, and in warm conditions it extends the acceptable range considerably. ASHRAE 55 allows higher operative temperatures when occupants have control of elevated air speed, such as ceiling fans; in the adaptive model, an air speed of about 180 ft/min raises the upper limit by about 3.2 °F, and more at higher speeds. A ceiling fan uses a few tens of watts; the cooling it saves may be worth many times that. Modeling it requires knowing the air speed at occupants, which simple energy models do not calculate. Comfort tools such as the CBE Thermal Comfort Tool, developed at the University of California, Berkeley, apply the standard's elevated air speed method to given conditions.

In cold weather the reverse applies: unwanted air movement, a draft, causes local discomfort. Cold air falling down a tall window is a classic cause. The students recall the hub's tall reading room windows and the radiant floor along them that was meant to counter the downdraft.

Local discomfort

Even when the whole body is in balance, parts of it may be uncomfortable. ASHRAE 55 and ISO 7730 set limits on four kinds of local discomfort: radiant asymmetry, such as a cold window on one side or a hot ceiling above; drafts; vertical air temperature difference between head and ankles; and floor surface temperature that is too warm or too cold. These matter in the hub. The daycare's radiant floor must stay below about 84 °F at its surface, because children sit and lie on it; the reading room's tall windows create radiant asymmetry for readers next to them; the hall's stratification can leave ankles cold and heads warm.

Overheating criteria

Comfort criteria are often turned into overheating criteria for design: limits on the number or share of hours above a threshold. Practice varies. Some codes and programs use a fixed limit, such as no more than a set number of occupied hours above 79 °F; others use the adaptive bands; the British CIBSE TM59 method for dwellings combines adaptive criteria for living rooms with a fixed night-time limit for bedrooms. Some governments have begun to set limits for housing: several US cities and counties have introduced maximum indoor temperature requirements for rental housing, a response to deaths in recent heat waves. For vulnerable occupants, such as seniors and young children, the health threshold may be lower than the comfort threshold.

Ingrid applies one such check to Greenway Homes, the students' second-year housing project, with a 2050s heat-wave week. The top-floor south apartments exceed the adaptive upper limit for many evening hours, and their bedrooms stay above 79 °F all night. The model shows why: the windows can be opened only a little for child safety, the corridors are single-loaded on the north so there is no cross-ventilation path, and the dark roof heats the top floor. Exterior blinds, a light roof and transom openings to the corridor bring the bedrooms below the limit in all but the hottest night.

Exercise 8: comfort in a free-running room

Each student simulates one naturally ventilated room in their project for a typical summer and a future heat wave.

• Report hourly operative temperature during occupied hours.
• Plot the results against the adaptive bands.
• Count hours above the 80 upper limit and identify their causes.
• Test at least two passive measures and one with fans.

Self-critique checklist

• Have I used operative, not air, temperature?
• Is the adaptive model applicable to this space?
• Have I assumed realistic clothing and activity, and tested their ranges?
• Have I considered local discomfort?