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Thursday, 27 October 2011 19:47

Case Study: Heat Indices: Formulae and Definitions

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I. Index of thermal stress (ITS)

The improved heat balance equation is:

where  is the evaporation required to maintain heat balance,  is the solar load, and metabolic heat production H is used instead of metabolic rate to account for external work. An important improvement is the recognition that not all sweat evaporates (e.g., some drips) hence required sweat rate is related to required evaporation rate by:

where nsc is the efficiency of sweating.

Used indoors, sensible heat transfer is calculated from:

For outdoor conditions with solar load,  is replaced with  and allowance made for solar load (RS ) by:

The equations used are fits to experimental data and are not strictly rational.

Maximum evaporation heat loss is:

and efficiency of sweating is given by:


nsc = 1, если


nsc = 0.29, если

The index of thermal stress (ITS) in g/h is given by:

where  is the required evaporation rate , 0.37 converts  into g/h andnsc is the efficiency of sweating (McIntyre 1980).

II. Required sweat rate

Similar to the other rational indices,  is derived from the six basic parameters (air temperature (), radiant temperature ( ), relative humidity air velocity (v), clothing insulation ( ), metabolic rate (M) and external work (W)). Effective radiation area values for posture (sitting = 0.72, standing = 0.77) are also required. From this the evaporation required is calculated from:

Equations are provided for each component (see table 8 and table 9). Mean skin temperature is calculated from a multiple linear regression equation or a value of 36°C is assumed.

From the required evaporation (Ereg) and maximum evaporation (Emax) and sweating efficiency (r), the following are calculated:

Required skin wettedness 

Required sweat rate 

III. Predicted 4-hour sweat rate (P4SR)

Steps taken to obtain the P4SR index value are summarized by McIntyre (1980) as follows:

If , increase wet bulb temperature by .

If the metabolic rate M > 63 , increase wet bulb temperature by the amount   indicated in the chart (see figure 6).

If the men are clothed, increase the wet bulb temperature by .

The modifications are additive.

The (P4SR) is determined from figure 6. The P4SR is then:

IV. Heart rate

where M is metabolic rate,  is air temperature in °C and Pa is vapour pressure in Mb.

Givoni and Goldman (1973) provide equations for predicting heart rate of persons (soldiers) in hot environments. They define an index for heart rate (IHR) from a modification of predicted equilibrium rectal temperature,

IHR is then:

where M = metabolic rate (watts), = mechanical work (watts), clo = thermal insulation of clothing,  = air temperature = total metabolic and environmental heat load (watts),  = evaporative cooling capacity for clothing and environment (watts).

The equilibrium heart rate (in beats per minute) is then given by:

for IHR 225

that is, a linear relationship (between rectal temperature and heart rate) for heart rates up to about 150 beats per minute. For IHR >225:

that is, an exponential relationship as heart rate approaches maximum, where:

= equilibrium heart rate (bpm),

65 = assumed resting heart rate in comfortable conditions (bpm), and t = time in hours.

V. Wet bulb globe temperature index (WBGT)

Wet bulb globe temperature is given by:

for conditions with solar radiation, and:

for indoor conditions with no solar radiation, where  Tnwb= temperature of a naturally ventilated wet bulb thermometer, Ta = air temperature, and  Tg = temperature of a 150 mm diameter black globe thermometer.



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