Heat stress calculator

The Heat Stress Calculator is a manually operated, mechanical computer and program for determining human thermal discomfort or heat stress, reported as an equivalent heat stress temperature (HST), for any given summer air temperature, relative humidity, wind velocity, sky condition, time-of-day, terrain, and individual physical activity level. The calculator consists of six circular and partial discs concentrically mounted for adjustment of their scales by rotation to various positions relative to each other and to stationary front and back windowed panels. The Heat Stress Temperature is the equivalent air temperature under standard moderate thermal and activity conditions that would result in the same heat stress produced by the actual conditions experienced. Under these standard conditions, the equivalent heat stress temperature represents a constant sweat rate--sweating being a principle indicator of thermal discomfort--and is read from isohids (lines of constant sweating) plotted on a grid of the body's heat load which must be dissipated by the evaporation of sweat, to the environment's cooling capacity to perform this evaporation. The body's evaporative heat load requirement is computed as the sum of heat generated by the level of physical activity plus solar heat gain, less heat loss by convection. Solar heat is computed by aligning the observed sky condition with the time-of-day, and then adjusting for terrain. Convective cooling is computed by aligning wind velocity with the observed air temperature (line) on a wind velocity-convective cooling grid. The environment's evaporative cooling capacity is computed by setting wind velocity, and then aligning relative humidity with the observed air temperature (line) on a humidity-evaporative cooling capacity grid.

SUMMARY OF THE INVENTION 
A principal objective of the present invention is to program the multiple 
formulas of physiological response to the thermal environment in a hand 
operated circular sliderule type mechanical computer which may be used for 
determining thermal discomfort or heat stress in the human body. This 
programming involves appropriate simplification and combination of 
formulas and unique design of the sliderule type mechanism to permit 
relatively quick and easy introduction of the input variables and 
computation. 
A second objective of the invention is to report heat stress in a 
meaningful and readily understandable manner. The level of heat stress, or 
thermal discomfort experienced by the human body, is thus reported as an 
equivalent temperature to which one can readily relate rather than an 
arbitrary and unfamiliar index number requiring definition. Heat Stress 
Temperature (HST) is the equivalent air temperature under moderate weather 
conditions and personal physical activity that would result in the same 
thermal discomfort produced by the actual temperature and weather 
experienced and activity performed. The standard conditions are: relative 
humidity, 35 percent; wind velocity, 2.5 mph; sun, haze; time, 1 pm; 
terrain, grass; and physical activity, walking 2.5 mph. No heat stress 
occurs under these standard conditions for an average male dressed in 
light summer clothing at an air temperature of 70.degree. F. The 
equivalent Heat Stress Temperature is further made meaningful by 
identifying environmental sensation (e.g., warm, hot, etc.) and body 
strain (e.g., moderate, severe, etc.) associated with rising HSTs. 
A third objective of the invention is to utilize the body's sweat rate as 
the best single indicator of heat stress, and to establish a functional 
relationship of sweat rate with the two principal governing factors--the 
body's evaporative heat load requirement and the environment's evaporative 
cooling capacity--both factors measurable in terms of observed thermal 
environment and physical activity conditions. This relationship is 
established by use of a psychometric chart on which isohids of constant 
sweat rate are plotted. The chart's ordinate scale of air vapor pressure 
is converted to a scale of associated environment evaporative cooling 
capacity at standard wind velocity; the abscissa scale of air temperature 
is converted to a scale of associated body evaporative heat load 
requirement at standard wind velocity, sky condition, time-of-day, 
terrain, and physical activity level. With this conversion, the isohids 
become lines of constant equivalent temperature. 
A fourth objective of the invention is to calculate and report in 
meaningful terms, the basic relationship which establishes human heat 
stress--the absolute level and relative ratio of the body's evaporative 
heat load requirement and the environment's evaporative cooling capacity. 
The absolute values calculated are reported in small windows on the front 
of the calculator. The heat transfer rates for heat load and cooling 
capacity are expressed as a percent with 100 equal to the energy expended 
in jogging at a 10 minute per mile pace. 
A fifth objective of the invention is to facilitate operator use, yet 
retain valid heat stress measurement, by limiting the input variables to 
observable and measurable key environmental factors and incorporating 
other key varables into the programmed formulas. Thus inputs are limited 
to seven: air temperature, relative humidity, wind velocity, sky 
condition, time-of-day, terrain, and individual physical activity level. 
Heat storage within the body and work performed are programed as variables 
within the computer formulas. Pulminary ventilation, rest breaks, 
clothing, and body sex, weight, and age are programmed as constant 
factors. 
A final objective of the invention is to facilitate operator use by scaling 
the input variables in units or terms which are readily understood, and 
may be measured or estimated by the user. Physical activity is therefore 
described in terms of severity (e.g., light, moderate, heavy) with 
specific common activities identified on the severity scale as benchmarks 
(e.g., walking 4 miles per hour). Sky conditions are described in terms of 
cloudiness (e.g., clear, haze), and shadow status (e.g., distinct, soft). 
This invention is a hand operated, circular sliderule type mechanical 
computer which can be used for quickly and easily determining heat stress 
in the human body (reported as an equivalent temperature) based on inputs 
of observed air temperature, relative humidity, wind velocity, sky 
condition, time-of-day, terrain, and on the individual's physical activity 
level. The calculator consists of six circular cardboard or plastic discs 
fastened at the center and mounted in a housing consisting of stationary 
front, intermediate, and back panels. All formulas used in calculating the 
equivalent Heat Stress Temperature are programmed in the scales, grids, 
and indicator arrows printed on the calculator. Rotation and alignment of 
input values on these measuring elements perform the calculations.

The "cut out" labels on all drawings indicate areas that are either cut out 
if the pieces are made of cardboard, or are clear or cut out if the pieces 
are made of plastic. 
DESCRIPTION OF THE PREFERRED EMBODIMENT 
The heat stress calculator of the present invention consists of three 
attached body parts--front panel (FIG. 1), rear panel (FIG. 2), and 
intermediate panel (FIG. 3), which serve as a stationary housing for a 
central axis for six concentric full or partial discs (FIGS. 5-10), which 
are turned to record thermal environment conditions and physical activity 
level as inputs. The process of recording the input data automatically 
computes heat stress as an equivalent temperature under standard moderate 
thermal (weather) and activity conditions. The standard conditions are: 
relative humidity, 35%; wind velocity, 2.5 mph; sky, haze; time-of-day, 1 
pm; terrain, grass; and physical activity, walking 2.5 mph. These standard 
conditions are represented by green dots on the scales involved. 
Also standardized are sex (male), age (youth to middle), body build (slight 
to medium), clothing (cotton short or long sleeved shirt, open at collar, 
cotton short or long trousers, light socks and shoes--the clothing 
ensemble having a clo-value of 0.5), and hourly rest breaks during 
physical exercise. 
The body panels and discs are made of laminated cardboard approximately 
0.016"-0.024" thick or plastic approximately 0.020" thick. The panels are 
attached at their edges, as required, by staples, glue, or other 
appropriate bond to establish a rigid body. 
The uniqueness of this invention is the computer mechanism and scale 
program which establish the relationships of the three body panels and six 
rotating concentric discs and their scales so as to compute by sliderule 
type procedures specially developed formulas involving linear, 
exponential, and grid functions to derive a final equivalent temperature 
output from seven input variables (air temperature, relative humidity, 
wind velocity, sky condition, time-of-day, terrain, and physical activity 
level), two formula programmed variables (work and body heat storage), and 
four fixed factors (pulminary ventilation cooling, rest breaks, clothing, 
and body condition). 
All scales, marks, and arrows printed on the parts of the calculator are 
positioned in such a manner that when the parts are assembled the scales, 
marks, and arrows of any two or more parts involved in a sliderule type 
computation of a given formula are calibrated in common angular units and 
are located immediately adjacent to each other for direct alignment and 
scale reading. 
Heat transfer rates are normally measured in watts per square meter of body 
skin surface (watts/m.sup.2). To improve operator understanding of the 
relative magnitude of heat involved, all scales of heat transfer on the 
calculator are expressed as a percent of 100 equal to the heat transfer 
rate during the maximum evaporative cooling of the body under ideal 
thermal conditions of low temperature and humidity, and high wind 
velocity. This transfer rate of 435 watts/m.sup.2 may be understood as 
roughly the energy required to jog at a 10 minute per mile pace. Thus, any 
heat transfer rate can be judged relative to this known energy expenditure 
rate of 100 percent. While this measure of the absolute level of heat 
transfer is meaningful to the operator, the relative values of heat 
transfer involved are critical to the programming of the calculator. 
Briefly stated, the calculator computes, as a function of air temperature 
(dry bulb), the body's evaporative heat load requirement and the 
environment's evaporative cooling capcity under standard thermal and 
activity conditions, to establish a grid for isohid lines of constant 
sweating and comfort which may be interpreted under the standard 
conditions as lines of equivalent temperature. 
The formula programmed for the body's evaporative heat load requirement is: 
heat gain from solar radiation, plus net body heat production from 
physical activity, minus heat loss from convective cooling. The scales 
involved--referred solar heat gain 20 (FIG. 7), net body heat produced 9 
(FIG. 2), convective cooling circumference 12 (FIG. 5), and body 
evaporative heat load requirement 15 (FIG. 6), are recorded in common 
linear angular units (12.degree.=43.5 watts/m.sup.2 or 10% heat transfer 
rate) for sliderule type addition. 
The heat load from solar radiation is calculated in STEP 1 by the operator 
turning the solar radiation disc (FIG. 8) to align the time-of-day 22 with 
the sky condition 8 on the body back panel (FIG. 2). The, in STEP 2 the 
operator reads the solar radiation heat gain 11, printed on the 
intermediate body (FIG. 3), in window 23 on the solar disc (FIG. 8) 
opposite the terrain condition 24, and transfers this reading to the 
referred solar heat gain scale 20 on disk E (FIG. 7), by aligning the 
solar arrow 16 on tab 17 on wheel D (FIG. 6) with the read value. (Tab 17 
on wheel D fits through the arcuate slot 21 on wheel E.) In STEP 3, net 
body heat produced 9 (FIG. 2) from physical activity is calculated by 
aligning the physical activity arrow 14 printed on wheel C (FIG. 5) with 
the physical activity level scale 10 printed on the body rear panel (FIG. 
2). 
Convective cooling is computed in STEP 4 by aligning the 1st input wind 
velocity 19 printed on disk E (FIG. 7) with air temperature from the 1st 
input air temperature line overlay 13 on the grid of wind velocity radius 
19a vs convective cooling circumference 12 printed on wheel C (FIG. 5). 
The alignment occurs at the left edge of the window directly below the 1st 
input temperature arrow 18. The computed body evaporative heat load 
requirement, equal to solar heat gain plus net body heat produced from 
physical activity minus convective cooling, is read from scale 15 on wheel 
D (FIG. 6) through the left window 1 on the body front panel (FIG. 1). 
Referring now to FIGS. 2, 3, and 7, the sky condition 8, printed at the top 
of the stationary back panel (FIG. 2), the time-of-day 22, and terrain 24 
scales printed on the rotating solar disc (FIG. 8), and the solar 
radiation heat gain scale 11 printed on the stationary intermediate body 
panel (FIG. 3), are recorded on angular logarithmic adjacent (when 
assembled) scales for sliderule type muliplication based on average 
attenuation of solar heat load in the human body by these three factors 
(sky, time, and terrain). The formula programmed is: solar heat 
load=maximum solar heat load (127 watts/m.sup.2 or 29.2% heat transfer 
rate).times.sky attenuation.times.time-of-day attenuation.times.terrain 
attenuation. The attenuation rates for sky conditions are: clear, 100%; 
slight haze, 85%; haze, 54%; overcast, 38%; cloudy overcast or open shade, 
27%; and cloudy overcast or dark shade, 18.5%. The time-of-day (daylight 
savings time) attenuation rates are: 1 pm, 100%; 2 pm or 12 noon, 95%; 3 
pm or 11 am, 87%; 4 pm or 10 am, 75%; 5 pm or 9 am, 60%; and 6 pm or 8 am, 
46%. The attenuation rates for terrain are: desert or city streets, 
104.8%; grass and scattered trees, 100%; and forests, 92%. 
The grid (FIG. 5) of wind velocity radius 19a vs convective cooling 
circumference 12 with 1st input air temperature line overlay 13 used to 
compute convective cooling, is an angular derivation of the plot 
illustrated in FIG. 11. The plot of convective cooling (C) is initially 
estimated from the formula C=5.0 V.sup..3 (skin temperature--air 
temperature) in watts/meter.sup.2, where wind velocity (V) is the 
effective wind velocity on the skin surface in miles per hour and skin 
(95.degree. F.) and air temperatures are in degrees Fahrenheit. The 
resulting wind velocity lines 32 are modified to account for known 
empirical evidence and their steepness is increased slightly as air 
temperature approaches 95.degree. F. to account for slightly rising skin 
temperature. Note that when air temperature equals skin temperature of 95 
degrees F. there is no convective cooling, and that at higher air 
temperatures heat is gained by the body from air convection. 
Strictly for layout design and not a programmed formula, the 1st input wind 
velocity scale 19 (FIG. 7) and co-aligned wind velocity radius 19a of the 
wind velocity versus convective cooling grid (FIG. 5), are scaled 
proportionate to wind velocity to the 0.3 power to provide simple physical 
spacing on both scales and the 1st input temperatue line overlay 
consistent with the functional relationship involved. 
Referring now to FIG. 2, printed on the lower left of the body back panel 
is a linear physical activity level scale 10 reading in mets (1 met=58.2 
watts/meter.sup.2) of energy expenditure (metabolism) and further 
described in terms of severity (e.g., sedentary, light, moderate). The 
scale also contains benchmark known physical activities (e.g., standing, 
21/2 mile per hour walk, 10 minute mile run). Although reading in internal 
energy expenditure (metabolism) to permit the operator to enter the 
exertion aspect of physical activity as an input, the scale is calibrated 
to measure net body heat production rate (metabolism less energy expended 
for work, energy loss through publmonary ventilation, and energy stored) 
as measured on the adjacent net body heat produced scale 9. These 
relationships are shown in FIG. 12. 
Referring to FIG. 12, work performed 33 (change in kinetic and potential 
energy of the body plus any external load movement and friction) (W) is an 
elliptically shaped exponential function of metabolism (M). Expressed as a 
percent of metabolism, work begins at a sedentary activity level, 
increases at a decreasing rate, and levels, approaching a maximum of 
approximately 24 percent of body metabolism at high activity levels. 
Storage (S) of heat in the body is also an elliptically shaped exponential 
function 34 of metabolism reaching a maximum of 15 percent of metabolism 
at high activity levels. At exhausting physical activity levels (10 mets 
or more) this 15 percent storage rate approaches 100 watts/meter.sup.2, a 
rate which will store heat to the body's capacity in one hour. Since this 
storage rate is programmed into the calculator and must be maintained, the 
physical activity level entered must include rest breaks every hour to 
dissipate body heat to renew storage capacity. 
Pulmonary ventilation (V) 35 or heat loss through respiration equals a 
relatively constant average 7.5 percent of metabolism. 
The rate of net body heat produced (M-W-S-V) 36 is derived from the curves 
of work, storage, and pulmonary ventilation, and is shown to decline 
exponentially as a percent of metabolism as physical activity increases. 
The environment's evaporative cooling capacity is a function of air 
temperature, relative humidity (relative humidity and temperture establish 
air vapor pressure), and wind velocity. It is calculated in STEP 5 by 
aligning the 2nd input wind arrow 31 on wheel A (FIG. 10) opposite the 
observed velocity on the 2nd input wind velocity scale 7 on the body front 
panel (FIG. 1). The, in STEP 6, the operator turns wheel B (FIG. 9) 
through the cut-out 6 on the left side of the calculator front panel (FIG. 
1) to align the observed 2nd input air temperature line 28 (on wheel B) 
with the observed relative humidity 29 on wheel A (FIG. 10). The alignment 
occurs at the left edge of the window directly below the 2nd input 
temperature arrow 30. The resulting computed cooling capacity is read from 
the environment's evaporative cooling capacity scale 25a printed on wheel 
B (FIG. 9) opposite the cooling capacity arrow in the right window 5 on 
the body front panel (FIG. 1). 
The grid of relative humidity radius 29a vs environment evaporative cooling 
capacity circumference 27 with 2nd input air temperature line overlay 28 
(FIG. 9) used to computer evaportive cooling capacity is an angular 
derivation of these three factors from the psychometric chart plot of 
lines of constant relative humidity 38 illustrated in FIG. 13. The 
environment's evaporative cooling capacity (E) 37 is substituted for the 
vapor pressure ordinate for a standard wind of 2.5 mph according to the 
formula: E=101.84 V.sup..6 (skin vapor pressure--air vapor pressure) in 
watts/m.sup.2 where skin vapor pressue equals 5.62 kpa (mm Hq). At 
standard conditions of 70.degree. F. air temperature and 35% relative 
humidity, the standard wind velocity of 2.5 mph results in an evaporative 
cooling capacity of 522 watts/m.sup.2 or a 120% heat transfer rate. 
Attenuation of evaporative cooling capacity by the formula for various 
selected 2nd input wind velocities relative to 2.5 mph used for wind scale 
7 (FIG. 1) are: calm (1.5 mph), 73.3 %; slight (2.5 mph), 100%; light (4 
mph), 132.5%; gentle (7.5 mph), 193.3%; and 10 MPH, 230%. This attenuation 
is based on evaporative cooling capacity as an exponational function of 
wind velocity to the 0.6 power. Cooling capacities above 100 percent are 
theoretical and used to calculate the effects on evaporative cooling of 
combinations of relatively low temperature, humidity, and high wind 
speeds, and are utilized only when the body's maximum effective sweat rate 
has not been reached. 
The 2nd input wind scale 7 (FIG. 1), and in FIG. 9 the environment's 
evaporative cooling capacity circumference scale 27 of the relative 
humdity vs cooling capacity grid with 2nd input air temperature line 
overlay, the environment evaporative cooling capacity circumference scale 
25, and the environment evaporative cooling capacity scale 25a, are 
recorded in common logrithmic angular units for sliderule type 
multiplication. The relative humidity scale 29 (FIG. 10) and co-radial 
aligned relative humidity radius 29a (FIG. 9) of the relative humidity 
versus environment evaporative cooling capacity grid are scaled in linear 
proportion. 
To determine equivalent temperature in STEP 7, the operator reads the 
computed body evaporative heat load requirement 15 printed on wheel D 
(FIG. 6) opposite the heat load arrow in the left window 1, on the front 
panel (FIG. 1). Then, opposite this heat load value on the referred heat 
load scale 2, the operator reads, directly below the equivalent 
temperature arrow 3, the equivalent Heat Stress Temperature from the 
adjacent equivalent temperture line overlay 26 seen through the center 
window 4. 
Referring to FIG. 9, the grid of body evaporative heat load requirement 
radius 2a versus environment evaporative cooling capacity circumference 25 
with equivalent temperature line overlay 26 printed on wheel B (FIG. 9) is 
an angular derivation of the isohids 39 (lines of constant sweating) plot 
on the psychometric chart illustrated schematically in FIG. 14. The 
isohids 39 represent equivalent temperature lines when the vapor pressure 
scale ordinate is converted to resulting environment evaporative cooling 
capacity 40 at standard wind velocity (2.5 mph); and the air temperature 
scale abscissa is converted to body evaporative heat load requirement 41 
at standard wind velocity (2.5 mph), sky conditions (hazy), time-of-day (1 
pm), terrain (grass), and physical activity level (walking 2.5 mph). 
Approaching and above the 100% relative humidity line 42, the isohids have 
been extended and modified slightly to establish equivalent temperature 
lines in this area. The equivalent temperature lines are labeled according 
to the temperature value where the isohid intersects the standard relative 
humidity line of 35 percent 43. 
It is important here to cite the conditions under which there is no body 
evaporative heat load. Referring to FIG. 11, note that at 70.degree. F. 
the standard conditions result in convective cooling of 37.6% heat 
transfer rate which exactly equals the body's net heat production walking 
2.5 mph (21.8%) plus the solar heat gain under a haze sky (15.8%). Thus 
the body's evaporative heat load requirement is zero (no heat strain) at 
70.degree. F. The standard conditions have been selected to establish 
70.degree. F. as an easily recognizable temperature for no heat strain. 
Critical to establishing this zero body evaporative heat load requirement 
at 70.degree. F. are the following heat transfer relative ratios involved: 
solar heat gain at 1 pm, haze sun, and grass terrain, 1.00; net body heat 
produced from walking 2.5 mph, 1.38; and convective cooling at 70.degree. 
F. and wind velocity 2.5 mph, 2.38. Other notable benchmarks where 
convective cooling equals the sum of solar heat gain (1.00) plus net body 
heat produced resulting in a zero body evaporative heat load requirement, 
occur for net body heat produced from standing, 0.85, at 71.5.degree. F. 
and 1.5 mph wind; for net body heat produced from walking 4 mph, 2.11, at 
67.degree. F. and 4 mph wind; and for net body heat produced from running 
at an 8 minute per mile pace, 4.37, at 56.degree. F. and 7.5 mph wind. In 
each instance the wind velocity is the average effective wind on the skin 
surface as a convective cooling factor resulting from the combination of 
air velocity and physical movement speed. 
Strictly for layout design and not a programmed formula, the referred 
evaporative heat load requirement scale 2 (FIG. 1) and the co-radial 
aligned heat load requirement radius 2a of the heat load requirement 
versus evaporative cooling capacity grid (FIG. 9), are established on a 
logarithmic scale to provide simple physical spacing on both the scale and 
equivalent temperature line overlay 26 consistent with the functional 
relationship involved. Similary, the wind velocity scales 19 (FIG. 7) and 
19a (FIG. 5) are proportional to V.sup..3 or the resulting convective 
cooling capacity. The relative humidity scale 29 (FIG. 10) and relative 
humidity radius 29a (FIG. 9) are linear. 
The seven STEPS of entering and processing data in the calculator are 
summarized in abbreviated written instructions on the front and back 
panels of the calculator. A table of benchmark Heat Stress Temperatures 
and related environmental sensation and heat strain is printed on the 
front panel to guide the operator in properly interpreting equivalent 
temperatures. 
It is noted that the instant invention was designed for a specific set of 
standard conditions which include the physiological response of a male of 
average weight, build, and age, dressed in light summer garments of 0.5 
clo. However, the present calculator could be easily modified for 
appropriate use in connection with other standard inputs without altering 
the basic design features. 
While particular embodiments of the present invention have been shown and 
described, it is apparent that changes and modifications may be made 
without departing from this invention in its broader aspects; and 
therefore, the aim in the appended claims is to cover all such changes and 
modifications as fall within the true spirit and scope of this invention.