Determination of PMV and PPD and specification of the conditions for thermal comfort

A method for predicting the thermal sensation and the degree of discomfort (thermal dissatisfaction) of people exposed to moderate thermal environments according to ISO 7730. The PMV (Predicted Mean Vote) and PPD (Predicted Percentage of Dissatisfied) are key indices in the field of thermal comfort, particularly in HVAC (Heating, Ventilation, and Air Conditioning) design. They help to quantify human thermal comfort in indoor environments based on environmental and personal variables.

PMV (Predicted Mean Vote)

PMV is an index that predicts the average thermal sensation of a large group of people based on the following factors:

1.  Air temperature
2.  Relative humidity
3.  Air velocity
4.  Mean radiant temperature
5.  Clothing insulation level (Clo)
6.  Metabolic rate (Met)

The PMV scale ranges from -3 to +3:

• +3: Very hot
• +2: Hot
• +1: Warm
•   0: Neutral (optimal comfort)
• -1: Cool
• -2: Cold
• -3: Very cold

PMV is essentially the mean vote of thermal sensation for a group of people exposed to the same environment. It assumes that not all individuals have the same perception of comfort, so the value represents the average. The goal of most HVAC systems is to maintain a PMV close to 0 (neutral), meaning that most people will feel comfortable.

PPD (Predicted Percentage of Dissatisfied)

PPD is directly linked to PMV and estimates the percentage of people who would be dissatisfied with a particular thermal environment. Even in an ideal environment (PMV = 0), some individuals will feel too warm or too cold. The relationship between PMV and PPD is non-linear.

For example:

• When PMV = 0, about 5% of occupants will feel discomfort (PPD = 5%).
• As PMV moves away from 0 (either positive or negative), the PPD increases, meaning more people feel discomfort.

The following are typical PMV ranges and corresponding PPD values:

• PMV = 0:    PPD ≅ 5%
• PMV = ±0.5: PPD ≅ 10%
• PMV = ±1.0: PPD ≅ 25%
• PMV = ±2.0: PPD ≅ 75%

The graph below shows the relationship between PPD and PMV.

Application in Indoor Environment Design

In practice, both PMV and PPD are used to design and evaluate HVAC systems and thermal environments, aiming to achieve a comfortable indoor climate. ASHRAE (American Society of Heating, Refrigerating, and Air-Conditioning Engineers) standards, such as ASHRAE Standard 55, include PMV and PPD as central metrics in their thermal comfort models. The objective is typically to keep the PMV between -0.5 and +0.5, which corresponds to a PPD of less than 10%, thus ensuring that the majority of people feel comfortable.

Influence of Environmental and Personal Factors

The PMV-PPD model takes into account a range of environmental and personal factors that influence thermal comfort:

• Clothing insulation (Clo): Measures the insulation provided by clothing. Heavier clothing increases Clo values, while lighter clothing reduces it.
• Metabolic rate (Met): Represents the heat generated by the human body. Higher activity levels (such as exercising) lead to higher Met values, while sedentary activities (like office work) have lower Met values.

Example in Practice

In an office environment, where the goal is to maintain comfort for the majority of occupants, HVAC systems are usually designed to maintain air temperature, humidity, and other environmental conditions such that the PMV stays around 0, resulting in a PPD of 5-10%. This minimizes the number of people who would feel too hot or cold.

Achieving optimal PMV and PPD values not only improves occupant satisfaction but also enhances productivity, reduces absenteeism, and ensures energy-efficient HVAC operation by avoiding over-conditioning.

These indices have been implemented in various international standards, such as ISO 7730 and ASHRAE 55, making them indispensable tools for architects, engineers, and facility managers in creating comfortable indoor environments.

Recommended thermal comfort requirements

Recommended thermal comfort requirements for spaces for human occupancy. It is recommended as acceptable that the PPD be lower than 10%. This corresponds to the following PMV criteria:

-0.5 < PMV < +0.5

Light, mainly sedentary, activity during winter conditions (heating period)

The conditions are the following:

1. The operative temperature shall be between 20 °C and 24 °C.
2. The vertical air temperature difference between 0.1 m and 1.1 m above the floor (i.e. ankle and head level) shall be less than 3 °C.
3. The surface temperature of the floor shall normally be between 19 °C and 26 °C, but floor heating systems may be designed for 29 °C.
4. The mean air velocity shall be less than specified in the figure below.
5. The radiant temperature asymmetry from windows or other cold vertical surfaces shall be less than 10 °C (relative to a small vertical plane 0.6 m above the floor.
6. The radiant temperature asymmetry from a warm ceiling shall be less than 5 °C (relative to a small horizontal plane 0.6 m above the floor).
7. The relative humidity shall be between 30 % and 70 %.

Light, mainly sedentary, activity during summer conditions (cooling period)

The conditions are the following:

1. The operative temperature shall be between 23 °C and 26 °C.
2. The vertical air temperature difference between 0.1 m and 1.1 m above the floor (i.e. ankle and head level) shall be less than 3 °C.
3. The mean air velocity shall be less than specified in the figure below.
4. The relative humidity shall be between 30 % and 70 %.

Typical values for Met and Clo

Below are two tables summarizing typical Met (Metabolic Rate) and Clo (Clothing Insulation) values commonly used in thermal comfort assessments:

Activity	Metabolic Rate (Met)
Resting (seated quietly)	0.8
Reading or Writing	1.0
Seated, light office work	1.2
Standing, light activity	1.4
Standing, medium activity	1.8
Walking (3 km/h)	2.0
House cleaning	2.5
Walking (5 km/h)	2.8
Heavy work (lifting, etc.)	3.5
Running (8 km/h)	8.0

Clothing Type	Clothing Insulation (Clo)
Nude	0.0
Summer, light clothing	0.5
Typical indoor clothing	0.6
Long-sleeve shirt, trousers	0.7
Light business suit	0.9
Business suit with sweater	1.0
Winter clothing	1.3
Winter clothing with coat	1.5
Heavy winter coat, thermal gear	2.0

Notes:

• Met values increase with activity level. For example, sitting quietly has a Met of around 1.0, while walking or moderate physical activity is around 2.0.
• Clo values represent the insulation provided by clothing. A value of 0 corresponds to being nude, while typical indoor clothing ranges from 0.5 to 1.0 Clo. Heavier winter clothing can range up to 1.5-2.0 Clo.

PMV and PPD calculator

Input

Clothing:

[ clo ]

Metabolic rate M:

[ met ]

External work W:

[ met ]

Air temperature t_a:

[ °C ]

Mean radiant temperature t_r:

[ °C ]

Air velocity v_a:

[ m/s ]

Relative humidity RH:

[ % ]

Output

PMV:

PPD:

[ % ]

Calculate