The Humid Operative Temperature

13.5 The Humid Operative Temperature

Much effort has gone into deriving a single index that will indicate en- vironmental heat stress for humans. The environmental variables that affect heat stress are radiation, temperature, vapor pressure, and

sion conductances to heat and vapor. For cold stress, where latent heat loss is treated as a fixed value relatively independent of environment, the standard operative temperature adequately combined radiation and heat transfer characteristics of the environment into a single number. An appropriate energy budget equation was then used to indicate the strain imposed by a given stress, the stress being indicated by the operative temperature. It would seem reasonable to attempt to extend the opera- tive temperature concept to include atmospheric vapor pressure. If this could be done, it would again enable the combination of all relevant en- vironmental variables into a "stress index," and with an appropriately derived energy budget equation, could indicate the resulting strain on the individual.

The derivation proceeds in a way similar to the derivation of the opera- tive temperature in Ch. 12: substitute Eq. (12.16) for

and Eq. (12.19) for into Eq. (13.7) to get an energy budget equation in terms of phys- iologic and environmental variables. The vapor mole fraction difference in Eq. (12.16) can be approximated using the Penman transformation (discussed in detail in Ch. 14) to give:

D (13.8) where A is the slope of the saturation vapor pressure versus temperature

e, - e,

+ e, -

function (Ch. 3) and D is the vapor deficit of the atmosphere. The slope

A has a fairly strong temperature dependence. If its value is taken at the average of

and then Eq. (13.8) is almost exact. Taking A at the average of and gives adequate accuracy for our purposes here. With

Humans and their Environment

these substitutions, the energy budget equation becomes:

where =

, and

Pa The humid operative temperature (Gagge, 1981) is the temperature of a

uniform enclosure, with a humidity of 100 percent. For a person in such

a humid chamber, (13.9) reduces to:

where is the temperature of the enclosure, or the humid operative temperature. The required definition of humid operative temperature is obtained by subtracting Eq. (1 3.10) from Eq. (1 3.9) to give:

These equations are more general forms of Eqs. (12.1 1) and (12.19) since, as

becomes small, * becomes large, making

+ *) go to one

and terms with y* in the denominator go to zero. Equation (13.1 1) is the heat stress index we were seeking, since it combines all of the relevant environmental variables into a single equivalent temperature. As with

the operative temperature is equal to the body temperature of an ectotherm (with M - = 0) for the environment specified by

The temperature of a copper sphere covered with black, moistened cloth and filled with water, has been used to determine wet globe temper- ature and these measurements have been related to human comfort in hot environments. The exchange properties of such a system are not identical to those for a human, so the temperature measured in this way would not

be the humid operative temperature. It is possible, though, that wet globe temperature would correlate with

When some air movement is present, the skin surface is wet, and clothing vapor and heat transfer resistances can be assumed equal, y* becomes almost equal to y. At body temperature, the term

+ y) is

0.17. The second term in Eq. (13.1 1) is therefore quite small and is usually only a few degrees different from