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4.7 Fanger's comfort equation 89

4.7 Fanger's comfort equation

The comfort equation developed by Fanger (1972) was established from experimental

work with North American subjects and allows the calculation (by computer or, withdifficulty, manually using diagrams) of

thecombination

ofactivity, clothing and environmentalfactors that will produce thermal comfort (see section 4.1). It was subsequently checked byapplying it to Danish subjects and excellent correlation found. Fanger concludes his equationis appropriate within the temperate zone for adults, regardless of sex. The thermal balance

of the body for comfort is expressed in simple terms by

H-Ed-Esw - Ere -L =R + C (4.9)

where His the internal rate of bodily heat production (related to the activity), Ed is the

heat loss by vapour diffusion through the skin (insensible perspiration and not subject to

thermo regulatory control), Esw is the heat lost by the evaporation of sweat, Ere is the latent

heat loss by respiration, L is the sensible heat loss by respiration, R is the radiation loss from

a clothed person and Cis the similar convective loss. Fanger's comfort equation then

defines comfort for the case when a function of the relevant variables

equals zero, namely:

f(Z,lc1, ta, Trm, a, V) =

0 (

4.10)

where lc1 is the insulating value of the clothing, ta is the ambient dry-

bulb temperature and

a the relative humidity. Fanger finds the effect of relative humidity

is not great for persons in comfort balance and that for such people a

change in humidity from 0 per cent to 100 per cent can be compensated by

a temperature decrease of about 1.5C to 3.0C. Clothing and activity arevery significant: an increase in clothing from 0 clo to 1.5 clo corresponds to

a decrease of 8C in the dry-bulb for sedentary work (115 W) but to l9C

for more strenuous activity (345 W).

Using his comfort equation Fanger (1972) has derived an index of

thermal sensation, making it possible to predict a mean comfort response

(predicted mean vote, abbreviated as PMV), on a standard scale from-3 to +3, in a

large group of persons for any combination of the four environmental variables, activity and

clothing. Tables and diagrams are given to simplify the intrinsically complicated

mathematical approach to this. The predictedpercentage dissatisfied (abbreviated PPD) for an

indoor climate is perhaps more meaningful. The PPD is determined from the PMV for several

positions in a room. After measurement of the environmental variables the lowest possible

percentage of dissatisfied persons (abbreviated LPPD) attainable by altering the

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temperature can be established. To quote Fanger: 'The magnitude of the LPPD is an

expression for the non-uniformity of the thermal environment and is therefore suitable for

characterising the heating or air conditioning system .. .'. Table 4.4 is based on Fanger's

work and quotes some dry-bulb temperatures and associated air velocities in an

environment of 50 per cent relative humidity, with the

Table 4.4 Temperature and air velocity for zero PMV at various do-values for sedentary workers

do-value 0

Temp (0C) 29

Velocity 0.5 to

(m s-1) 0.15

0.5

28 27 26

0.5 to 0.2 to 0 to

1.0 0.3 0.1

1.0

25 24

0.5 to 0.2 to

1.0 0.3

1.25

24 22

1.0 to 0.1 to

1.5 0.15

1.5

22

0.5to

1.0