Thermal comfort and the PMV/PPD index: calculation per ISO 7730

PMV (Predicted Mean Vote) is a thermal-comfort index on a scale from −3 (cold) to +3 (hot) that predicts the average subjective thermal sensation of a group of people in a given environment. PPD (Predicted Percentage of Dissatisfied) expresses the percentage of dissatisfied people. ISO 7730 defines the comfort zone: PMV = −0.5 to +0.5 → PPD < 10%.

Why humidity is part of thermal comfort

Air humidity affects thermal comfort in two ways:

1. Evaporation of sweat — at higher relative humidity, sweat evaporates less readily and the body’s thermoregulation becomes less effective, which we perceive as heat
2. Dry air — below φ = 30% it causes drying of the mucous membranes, eye irritation and a drop in comfort

In the PMV model, humidity enters through the partial pressure of water vapor $p_w$ [Pa] (denoted $p_a$ in ISO 7730).

The six factors of thermal comfort

PMV depends on 6 variables:

Quantity	Symbol	Typical value
Air temperature	$t_a$	18–26 °C
Mean radiant temperature	$t_r$	= $t_a$ (indoor spaces)
Air velocity	$v_a$	0.1–0.3 m/s
Relative humidity	$\varphi$	30–60%
Metabolic rate	$M$	1.0–2.0 met
Clothing thermal resistance	$I_{cl}$	0.5–1.5 clo

PMV is a group average, so it never satisfies everyone: even at the optimum, 5% remain dissatisfied. In practice the complaints come mainly at the winter and summer extremes, where the matching air treatment (humidity control in winter, dehumidification in summer) was left out of the design because of the higher capital and running costs.

Calculating PMV (simplified)

The full PMV calculation per Fanger involves an iterative solution of the body’s heat balance. As a rough guide: for $t_a = t_r$ and $v_a < 0.1$ m/s, approximately:

$$\text{PMV} \approx \left(0.303 \cdot e^{-0.036 \cdot M} + 0.028\right) \cdot L$$

where $L$ is the thermal load on the body (the difference between the metabolic heat and the heat losses).

In practice PMV is computed with dedicated software.

The PMV–PPD relationship

$$\text{PPD} = 100 - 95 \cdot e^{-\left(0.03353 \cdot \text{PMV}^4 \,+\, 0.2179 \cdot \text{PMV}^2\right)}$$

PMV	PPD [%]	Rating
0	5%	Optimum (5% always dissatisfied)
±0.5	< 10%	Comfort zone (Category I)
±1.0	26%	Category II
±2.0	77%	Category III — unacceptable

ASHRAE 55 comfort zone vs. ISO 7730

ISO 7730 (Fanger model):

• Category I: PMV = −0.2 to +0.2 → PPD < 6%
• Category II: PMV = −0.5 to +0.5 → PPD < 10%
• Category III: PMV = −0.7 to +0.7 → PPD < 15%

ASHRAE 55-2023 (operative-temperature model):

• Comfort zone on the ψ-chart (operative temperature vs. humidity ratio)
• Winter comfort: $t_{op}$ 20–24 °C
• Summer comfort: $t_{op}$ 23–26 °C
• Humidity: x ≤ 12 g/kg (upper condensation limit)

Humidity in the winter season — a typical problem

Case: an office, −12 °C outside, air handling without humidification.

Outdoor air: t = −12 °C, φ = 80% → x = 1.0 g/kg

After heating to t = 20 °C: φ = 7%

Result: PMV shifts toward discomfort (dryness), PPD rises. Staff complain about dry air, eye irritation and static electricity. Humidification is essential if comfort is to improve.

Solution: humidify to φ = 40–50% → x = 5.8–7.3 g/kg → required moisture addition $\Delta x = 7.3 - 1.0 = 6.3$ g/kg; moisture flow rate $\dot{m}_w = \dot{m} \cdot \Delta x$.

Humidity in the summer season — the risk of high humidity

Summer air: t = 30 °C, φ = 60% → x = 16.2 g/kg.

In an air-conditioned office: $t_a$ = 24 °C, φ = 60% → x = 11.3 g/kg.

Without dehumidification (if the cooling process does not drop the temperature below the dew point), φ in the room can rise above 60%, bringing a risk of mould and discomfort.

Solution: the cooling coil must dehumidify the air to x < 9.5 g/kg (corresponding to $t_d < 13$ °C), followed by reheating before supply to the room. The result is a markedly better PMV.

Air velocity and draught

Per ISO 7730, the local discomfort caused by draught (DR — Draught Rate) must not exceed 15% (Cat. I) or 20% (Cat. II). The air velocity in the occupied zone should not exceed:

• Winter: $v_a \le 0.15$ m/s
• Summer: $v_a \le 0.25$ m/s

Practical takeaways

Humidity rarely dominates the PMV on its own, but it decides comfort at the extremes. In winter, heated air without humidification falls to φ ≈ 7% and pushes the PPD up through dryness — humidify to 40–50% RH. In summer, cooling that does not reach the dew point leaves φ above 60% — the coil must dehumidify to x < 9.5 g/kg ($t_d < 13$ °C) before reheating. And keep the air velocity within 0.15 m/s in winter and 0.25 m/s in summer, or draught becomes the dominant complaint regardless of the PMV.