CHAPTER 9
Leisure Thermal Comfort
In-The-Sun
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e have, thus far, concentrated on PMVSHADE
– and have ignored direct and reflected sun rays. Such avoidance of
direct solar influence was motivated by three considerations:
• Much of our prior focus was directed to
the summer season – which is a popular time for vacations, tours and visits –
and during this season, climate within many regions of the United States,
especially in the lower latitudes, is hot and humid. For these reasons,
conditions in the shade were emphasized.
•
PMVSHADE applies to each of the three temperature conditions,
MAXTMP, MINTMP and AVETMP.
(On the other hand,
PMVSUN applies only to the MAXTMP condition.)
• Estimating PMVSUN for any
region and season depends on the counterpart value for PMVSHADE.
Thus, the previous information base for PMVSHADE lays the groundwork
for our PMVSUN estimations.
Whereas estimating PMVSHADE
indices involves looking at a table, estimating PMVSUN indices
requires a four-function calculator. This extra effort is worthwhile because
the boundaries of midday thermal comfort can be pushed back and expanded. The
warming effect of solar rays often converts otherwise chilly regions into
midday comfort paradises. Thus, PMVSUN estimates can enable us to
identify those off-season opportunities that do not seem obvious.
Simple Formula for Calculating PMVSUN
We previously used the
term MRTSHADE to represent a fictitious enclosure whose sides
are all at the same temperature as the air. Depending on time of day, MAXTMP,
MINTMP and AVETMP were used as functional synonyms for MRTSHADE.
On the other hand, MRTSUN applies
only to the MAXTMP condition – approximately 3:00 PM local standard
time.
In this book, we
estimate values of MRTSUN by referring to one of four seasonal
charts*
(see Figures 9-2 through 9-5, pages 180-183).
The formula for calculating PMVSUN
is shown below:
PMVSUN = -7.40222 + .598822 x PMVSHADE + 0.094754 x MRTSUN (Equation 9-1) (99.96% of error in PMVSUN Index is explained
by the two independent variables, utilizing fifty-five sets of data points.)
Regression Equation for MAXTMP Conditions
Step-By-Step
Calculation of PMVSUN Indices
As explained below,
the PMVSUN index is computed in three stages. In essence, this
calculation enables us to convert an environment of shade into an
environment of sun. We do this by adding the influence of solar energy
(MRTSUN) to our outdoors thermal comfort index (PMVSHADE).
Remember, PMVSHADE implies that
mean radiant temperature is equal to ambient air temperature. PMVSUN
implies an additional heat load due to solar radiation.
First Step: Select a PMVSHADE
Index
We select a PMVSHADE
thermal com–fort index from one of the preceding tables discussed in Chapters 4
through 8, for a region and season of interest.
Example:
select the PMVSHADE value of
“-1.86” for San Francisco in October (see Table 5-2, page 69).
(This value is also included in Table 9-1, page 176.)
Notice that the
starting value of PMVSHADE for October
(“-1.86”) is uncomfortably
cold. Direct solar rays will change this for the better.
Second Step: Estimate an MRTSUN
Value
Refer to Figures 9-2
through 9-5 (pages 180-183) and
visually estimate an MRTSUN (black globe temperature) value for
specific localities. In these figures, the contour lines (MRTSUN
isotherms) appear coarsely spaced, but usually they are adequate for our
purposes. We make a best estimate of MRTSUN by estimating between
any two adjacent contour lines.
Example: for San Francisco in
October, consult Fig–ure
9-5, page 183, and
find the approximate value “90” for MRTSUN (also known as solar
black globe temperature). (For San Francisco, this value is included within
Table 9-2, page 177.)
“PMVSHADE implies that
mean radiant temperature is equal to ambient air temperature. PMVSUN implies an additional heat load due to solar
radiation.”
Third Step: Use Regression
Equation
To Compute PMVSUN
Use Fanger-based
regression equation to cal–culate estimated value for the PMVSUN in–dex.
Example:
Using previous values, in boldface below:
PMVSUN =
0.01 = -7.40222 + 0.598822 x -1.86
+
0.094754 x 90
Exposure to Sun at Midday
We can appreciate the
word “leisure” – in “leisure thermal
comfort” – when we are exposed to
direct sun during the summer.
Thus, our predicted (derived from regression
equation) PMVSUN value of “0.01” compares closely*
with the Fanger-calculated value of “-0.01” (see “San Francisco” in Table 9-3,
page 178).
Off-Scale Thermal Comfort Indices Fall Into the Heat Stress
Domain
Calculated values of
PMVSHADE and PMVSUN in excess of “+4.0” (corresponding to
unusually hot and humid July conditions within the United States) are
mathematically undefined; accordingly, these were suppressed from the
mathematical regression equation (boxed Equation 9-1, page 173).
Note: The regression equation plot of
Figure 9-6, page 184, exhibits very satisfactory linearity even while incorporating
out-of-range PMV values up to “+4.0” (and likewise the large range of values
less than “-3”).
In Tables 9-1 through 9-3, high off-scale
PMV values greater than “+4” are highlighted by light grayscale. Such off-scale
high PMV values fall into the heat stress domain.
Detailed discussion of heat stress is beyond
the scope of this book and for such discussion the reader is referred to Gulf
Weather Corporation’s document, which displays easy-to-use heat stress contour
maps for the northern and southern hemispheres. An elementary discussion of
heat stress is provided in Appendix 2. ■
