Operative Temperature

12.6 Operative Temperature

We returnnow to the definition of the operative temperature that was in- troduced

(12.1 1). There we explainedthat the operative temperature combines air temperature and radiation in a single equivalent tempera- ture. This is a convenient way to represent the animal environment for at least two reasons. First, temperature is intuitively useful because it is easier for us to picture how an animal would respond to a 20°C change in temperature than it is to picture how it would respond to a 400 W change in absorbed radiation. Second, a lot of the knowledge we have on thermal physiology of animals comes

experiments conducted in en- vironmental chambers. The operative temperature allows us to use results of these experiments directly in outdoor situations where the combined radiation and temperature produce an operative temperature equivalent to conditions in the environmental chamber.

The operative temperature (sometimes called the equivalent blackbody temperature) is the temperature of a blackbody cavity (with air tempera- ture equal to wall temperature) that provides the same heat load (or cold stress) as is present in the natural environment of the animal. Another way of saying that the heat load is the same in the two environments is to say that M - for the animal is the same in the two environ- ments. Therefore a mathematical definition of the operative temperature can be obtained by substituting Eq. (12.1 1) for M - in Eq. (12.10)

Operative Temperature

and solving for

The result is:

The operative temperature is the air temperature plus or minus some tem- perature increment which depends on absorbed radiation, wind speed, characteristic dimension of the animal, and temperature. In a blackbody cavity (a room or metabolic chamber) where the wall and air tempera- tures are equal, the absorbed radiation is equal to the emittance at air temperature, so

Outdoors, in the shade or under clouds, and with high wind (high conductance) the radiation increment is small. Un- der a clear night sky

at air temperature, so

smaller than the

In bright sunshine, the operative temperature can be much larger than air temperature.

Example 12.2. As an example of the calculation of we find the op- erative temperature for a person in a 1

wind, 30" C air temperature, and

sun. We assume the environmental conditions are those given in Example 11.4. If we assume the angle between the solar beam and the axis of the person, is

0.26 (Fig. 11.6). For dark cloth- ing, we assume

then

0.97, so (refer to Example 11.4 for details):

= 0.8 and &, =

An average characteristic dimension for a person (legs, arms, body, etc.) is d =

0.17 m, so the boundary layer conductance (forced convection with naturally turbulent wind) is:

mol

0.46 The radiative conductance is:

x 5.67 x

= 0.22 The operative temperature is (Eq. (12.19)):

When we want to make the point that a day is extremely hot we often say something like "it was a hundred degrees

in the shade," implying that one would feel much hotter than 100 degrees in the sun. The oper- ative temperature conveys this same sentiment quantitatively. It adds a temperature increment to the air temperature to indicate the temperature of a room which would feel the same as the heat load in the sun. In the

Animals and their Environment

example just given, the equivalent temperature would be uncomfortably hot (well above body temperature) even though the air temperature is not uncomfortably high.

If windspeed in this example were increased to 3 would de- crease to 43" C. If white clothing with a, =

0.3 were worn, would be

C at = 1