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expanding ashrae comfort zones 29 jan 2005 the ashrae 55-2004 comfort standard (based on worldwide surveys of 21,000 people) defines the winter and summer comfort zones below with equal air and wall temperatures, equal human activity levels, and a fixed 0.1 m/s air velocity: t (f) rh clo pmv ppd 67.3 86 1 -.4778556 9.769089 75.0 66 1 .4732535 9.676994 78.3 15 1 .5239881 10.74283 70.2 20 1 -.4779105 9.770202 74.5 67 .5 -.4747404 9.706658 80.2 56 .5 .5145492 10.53611 82.2 13 .5 .5003051 10.23146 76.5 16 .5 -.4883473 9.982468 the winter zone assumes heavier clothing with more thermal resistance (clo=1), and the summer zone assumes lighter clothing (clo=0.5). the zones are defined by a +/- 0.5 score on a "predicted mean vote" comfort scale that varies from -3 (very cold) to +3 (very warm.) the 4 corners of each zone are based on high and low temperatures and humidities. the "percentage of people dissatisfied" (ppd) score is based on the pmv. even with pmv = 0 ("comfortable"), about 6% of the people are dissatisfied... if people are willing to change clothing more than twice a year (early pa farmers had one set of clothes for work and another for church, and washed them twice a year, when they also took baths :-) and we vary air velocity with a ceiling fan, these zones can be expanded, which can make a solar house or one heated and cooled with the help of a whole-house fan more efficient. we can also raise the upper comfort temperature limit in air with lower humidity, and vice versa. the ashrae 55-2004 standard contains a basic program to help do this. here are some calculations based on nrel's long-term december and august weather averages for san diego: 20 clo = 1'clothing insulation (clo) 30 met=1.1'metabolic rate (met) 40 wme=0'external work (met) 50 ta=19.6'air temp (c) 60 tr=19.6'mean radiant temp (c) 70 vel=.1'air velocity 80 rh=0'relative humidity (%) 90 data 68.8,0.0062,0.05,1 100 data 83.9,0.0062,0.5,0.5 110 data 67.1,0.0121,0.05,1 120 data 82.9,0.0121,0.5,0.5 130 for case = 1 to 4 140 read tc,wa,vel,clo 145 ta=(tc-32)/1.8'air temp (c) 146 tr=ta'mean radiant temp (c) 150 pa=29.921*3377.2/(1+.62198/wa)'water vapor pressure (pa) 160 def fnps(t)=exp(16.6536-4030.183/(ta+235))'sat vapor pressure, kpa 170 if pa=0 then pa=rh*10*fnps(ta)'water vapor pressure, pa 180 icl=.155*clo'clothing resistance (m^2k/w) 190 m=met*58.15'metabolic rate (w/m^2) 200 w=wme*58.15'external work in (w/m^2) 210 mw=m-w'internal heat production 220 if icl<.078 then fcl=1+1.29*icl else fcl=1.05+.645*icl'clothing factor 230 hcf=12.1*sqr(vel)'forced convection conductance 240 taa=ta+273'air temp (k) 250 tra=tr+273'mean radiant temp (k) 260 tcla=taa+(35.5-ta)/(3.5*(6.45*icl+.1))'est clothing temp 270 p1=icl*fcl:p2=p1*3.96:p3=p1*100:p4=p1*taa'intermediate values 280 p5=308.7-.028*mw+p2*(tra/100)^4 290 xn=tcla/100 300 xf=xn 310 n=0'number of iterations 320 eps=.00015'stop iteration when met 330 xf=(xf+xn)/2'natural convection conductance 340 hcn=2.38*abs(100*xf-taa)^.25 350 if hcf>hcn then hc=hcf else hc=hcn 360 xn=(p5+p4*hc-p2*xf^4)/(100+p3*hc) 370 n=n+1 380 if n>150 goto 500 390 if abs(xn-xf)>eps goto 330 400 tcl=100*xn-273'clothing surface temp (c) 410 hl1=.00305*(5733-6.99*mw-pa)'heat loss diff through skin 420 if mw>58.15 then hl2=.42*(mw-58.15) else hl2=0'heat loss by sweating 430 hl3=.000017*m*(5867-pa)'latent respiration heat loss 440 hl4=.0014*m*(34-ta)'dry respiration heat loss 450 hl5=3.96*fcl*(xn^4-(tra/100)^4)'heat loss by radiation 460 hl6=fcl*hc*(tcl-ta)'heat loss by convection 470 ts=.303*exp(-.036*m)+.028'thermal sensation transfer coefficient 480 pmv=ts*(mw-hl1-hl2-hl3-hl4-hl5-hl6)'predicted mean vote 490 goto 510 500 pmv=99999!:ppd=100 510 print tc,wa,vel,clo,pmv 520 next case dry bulb humidity air vel. clothing predicted mean temp (f) ratio (m/s) (clo) vote (pmv) 68.8 .0062 .05 1 -.4997552 83.9 .0062 .5 .5 .4852427 67.1 .0121 .05 1 -.491671 82.9 .0121 .5 .5 .4890098 nrel says average daily highs and lows are 48.8 and 66.1 f with w = 0.0062 pounds of water per pound of dry air in december and 67.3 and 77.8 with w = 0.0121 in august. an airtight well-insulated house with thermal mass and internal heat gain and a smart whole-house fan controller would barely need heating or cooling all year. architects call this "thermal sailing." with inexpensive solar heating and whole-house fan heating and cooling, it would be more efficient to make the house air temperature closer to the upper comfort limit on an average winter day and closer to the lower comfort limit on an average summer day, in order to store lots of thermal energy in the mass of a house. a mean radiant (wall) temp that's less than the house air temp in winter and greater in summer would allow raising the upper winter air comfort temp limit and lowering the lower summer air comfort temp limit. occupants might also vary activity levels and wear clothing with more or less resistance, eg a sweater as well as a long- sleeve shirt in wintertime. nick innova airtech instruments has an excellent comfort web site: http://www.impind.de.unifi.it/impind/didattica/materiale/microclima/innova/thermal.htm |