Cornell University Ergonomics Web

DEA3500: Ambient Environment: Thermal Environment


Gram calorie = quantity of heat required to raise the temperature of 1 gram of water from 14.5 to 15.5C.
Calorie = 1000 gram calories
Joule = 4.184 Calories (Calorie = old kcal)
Watt = 1 Joule/second


6 major variables determine how warm a person feels:

Physiology of thermal sensation (see McIntyre, 1980)

Thermal Comfort Indices
Over the past 50 years much research effort has been devoted to developing indices predicting thermal comfort. 3 main indices are currently used.

Fanger's comfort equation

Fanger's basic assumption--thermal comfort is defined in terms of the physical state of the body rather than that of the environment i.e. what we actually sense is skin temperature and not air temperature. For thermal comfort need:

Fanger derived his comfort equation from extensive survey of literature on experiments. on thermal comfort.

Fanger's Comfort Equation This equation contains terms which relate to:

Fanger's Equation
(hc = convective transfer coefficient w/m2 K)
H - 0.31(57.4 - 0.07H - Pa) - 0.42(H-58) - 0.0017M(58.7 - Pa) - 0.0014M(34 - Ta) =
3.9 x 10-8fcl {(Tcl + 273)4 - (Tr + 273)4} + fcl hc (Tcl - Ta)

Where the clothing surface temperature, Tcl, is given by
Tcl = 35.7 - 0.0275H + 0.155Iclo {H - 0.31(57.4 - 0.07H - Pa) - 0.42(H - 58) - 0.0017M(58.7 - Pa) - 0.0014M(34 - Ta)}.

In addition to this, discomfort may occur when the skin is wetted (sweat, water, etc.) and Fanger has produced an equation for skin wettedness which can be used as a test to exclude conditions which satisfy the comfort equation:
Predicted Mean Vote (PMV)

The problem with Fanger's equation is that when people are not satisfied, this is not a measure of how uncomfortable deviation is; therefore Fanger developed PMV = mean vote on ASHRAE scale (Hot warm slightly warm neutral slightly cool cool cold). PMV can be predicted from Fanger's equation thus:
PMV = 4 + (0.303 exp(-0.036H) + 0.0275) x {6.57 + 0.46H + 0.31Pa + 0.0017HPa + 0.0014HTa - 4.13 fcl (1 + 0.01dT) (Tcl - Tr) - hcfcl (Tcl - Ta)}

where Tcl (surface temperature of clothed body) =
35.7 - 0.0275H + 0.155 Iclofcl (4.13 (1 + 0.Old Temp) 1 + 0.155 Iclofcl (4.13 (1 + 0.Old Temp)thc

where hc = 2.4(Tcl - Ta)0.25 or 12.1 square root of v (air speed) which is greater
and dT = Tr - 22.

Predicted Percentage of Dissatisfied (PPD) Can be derived from PMV (see transparency) and this relates to the temperature range.
While PMV gives good results for standard conditions of sedentary activity and light clothing, it has yet to be validated across a range of clothing and activity. Also PMV is effectively a measure of the thermal load of the thermoregulatory system, therefore a comfortable person who increases his metabolic rate by say 20 w/m2 (0.34 met) will experience the same change in thermal load whatever his clothing insulation BUT with high clo values the resulting increasing skin and body temperature must be greater than for low clo values and therefore one intuitively should expect a greater change in thermal sensation.

In experimental tests of thermal comfort Fanger's equation has proved very successful. The experiments all show that comfort relates to the perceived skin temperature and not to environmental variables or clothing. Experiments also show that for sedentary work and light clothing Ss led to a preferred temperature close to the 25.6C predicted by Fanger's equation. Also to date no evidence has been found for systematic individual differences in preferred temperatures. There are no effects of age, sex, race, etc.; differences in preferred temperatures often due to clothing differences.

Skin wettedness equation

w= (H - 58) / (4.6hc (57.4 - 0.07H - Pa)) + 0.06
when w is too high, leading to discomfort.
However, upper limit of w depends on metabolic rate and therefore limit is estimated using
w 0.0012M + 0.15


Age effects - non-significant
Nationality - non-significant
Sex effects - non-significant
Time-of-day effects - non-significant

Practical Applications

Fanger's comfort equation is comprehensive and complex and therefore too cumbersome for manual calculation each time. So it is practical to use the 28 comfort diagrams produced by Fanger, P.O. (1973) Thermal Comfort, McGraw Hill, NY.

E.g. 1a) Staff in office engaged in sedentary work
(70 w/m2 - 1.2 met.)
Clothing light (0.5 clo)
Relative humidity (50%)
Horizontal air velocity = 0.5 m/s
ta = tr = 26.6C
(ta = air temperature, tr = mean radiant temperature)

1b) increase clothing to 1 clo: ta = tr = 23.3C

1c) increase activity to 1.5 met (90 w/m2) - e.g. shop assistants walking round air velocity 4 m/s, so the ta = 20.8C. 

2) Swimming baths with rest places
Sedentary (1 met = 60 w/m2)
nude (0 clo)
RH = 80%
relative air velocity 0.1 m/s
ta = tr = 28.0C
See transparency 2
Suppose swimming gala for spectators in light clothes
(0.5 clo)
ta = tr = 25.1C

Example 3 (4) - air temperature is not equal to radiant temperature
Winter conditions. Mean radiant temperature in long distance bus calculated to be 5K lower than air temperature. What air temperature is necessary for passenger comfort?
Activity - 1 met (60 w/m2 - resting)
Clothes - 1 clo (not overcoats)
Air velocity - .2 m/s
RH - 50%
ta = 25.5C
tr = 20.5C for comfort.

Example 4a (5a)
Air conditioned theatre. Sedentary people(60 w/m2 = 1 met)
Clothes - 1 clo
RH = 50%
Air velocity .1 m/s
ta = tr = 23C

4b) (5b) During theatre performance: body heat radiation leads to increased tr 4 K higher than ta. Assume tr now 25C. What is new ta for comfort? ta = 21.25C

Subjective temperature (SUBT)

The problem with Fanger's equation and SET is that both are complex and have to be evaluated by computer. Consequently a simpler, practical index based on physical variables which gives a good approximation for comfort has enormous value. This is McIntyre's SUBT.

TSUB(subjective temperature) = temperature of a uniform enclosure with Ta = Tr , v = 0.1 m/s and RH = 50%

Based on this it is possible to simplify Fanger's equation.

TSUB = 33.5 - 3 Iclo - (0.08 + 0.05 Iclo) H (where H is metabolic heat production).

For clothing insulation up to 1.5 clo and activities up to 150 w/m2, the error of Fanger's equation is .5K. 

When air speed is low (v 0.15 m/s) and at temperatures near enough to comfort for humidity not to have an appreciable effect on warmth, subjective temperatures is a function of ta and tr thus:

TSUB = 0.56 ta + 0.44 tr , v 0.15 m/s

At higher air speeds:

TSUB = .44tr + 0.56 (5 - (square root of 10v)(5 - ta))
.44 + .56 (square root of 10v)

Go to the next lecture