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re: cool me down
21 aug 2004
christopher a. steele  wrote:

>sometimes it gets so hot around here it's difficult to sleep at night
>(to the point i sometimes have to get up two or three times to cool
>off in the shower just to get comfortable for a few minutes).

sir turtle might suggest a space heater to raise the room temp to 95 f,
which he describes as "too cold," vs 60 f ("too hot" :-)

>i'm curious: given 'x' ambient temperature in my bedroom at night (and
>'y' relative humidity, i suppose) and closed bedroom windows and
>doors, how do i calculate the amount of heat (heat load??) that has to
>be 'removed' from my body so that i can sleep comfortably...

an ashrae-standard 154 pound human dissipates 253 btu/h when sleeping.

>is there a formula?

sure. ashrae-standard 55-2004 ("thermal environmental conditions for human
occupancy") defines two "comfort zones," winter (with a clo = 1 clothing
thermal resistance) and summer (clo = 0.5.) its basic program estimates
the predicted mean vote (pmv: +3 hot, +2 warm, +1 slightly warm, 0 neutral,
-1 slightly cool, -2 cool, and -3 cold) and the predicted percentage
dissatisfied (ppd) based on clothing, activity, metabolic rate, external
work, air temp, mean radiant temp, air velocity, and rh...

50 clo = 1'clothing insulation (clo)
60 met=1.1'metabolic rate (met)
70 wme=0'external work (met)
80 ta=19.6'air temp (c)
90 tr=19.6'mean radiant temp (c)
100 vel=.1'air velocity (m/s)
120 rh=86'relative humidity (%) make one of rh or pa non-zero...
130 pa=0'water vapor pressure
140 def fnps(t)=exp(16.6536-4030.183/(ta+235))'sat vapor pressure, kpa
150 if pa=0 then pa=rh*10*fnps(ta)'water vapor pressure, pa
160 icl=.155*clo'clothing resistance (m^2k/w)
170 m=met*58.15'metabolic rate (w/m^2)
180 w=wme*58.15'external work in (w/m^2)
190 mw=m-w'internal heat production
200 if icl<.078 then fcl=1+1.29*icl else fcl=1.05+.645*icl'clothing factor
210 hcf=12.1*sqr(vel)'forced convection conductance
220 taa=ta+273'air temp (k)
230 tra=tr+273'mean radiant temp (k)
250 tcla=taa+(35.5-ta)/(3.5*(6.45*icl+.1))'est clothing temp
260 p1=icl*fcl:p2=p1*3.96:p3=p1*100:p4=p1*taa'intermediate values
300 p5=308.7-.028*mw+p2*(tra/100)^4
310 xn=tcla/100
320 xf=xn
330 n=0'number of iterations
340 eps=.00015'stop iteration when met
350 xf=(xf+xn)/2'natural convection conductance
360 hcn=2.38*abs(100*xf-taa)^.25
370 if hcf>hcn then hc=hcf else hc=hcn
380 xn=(p5+p4*hc-p2*xf^4)/(100+p3*hc)
390 n=n+1
400 if n>150 goto 550
410 if abs(xn-xf)>eps goto 350
420 tcl=100*xn-273'clothing surface temp (c)
440 hl1=.00305*(5733-6.99*mw-pa)'heat loss diff through skin
450 if mw>58.15 then hl2=.42*(mw-58.15) else hl2=0'heat loss by sweating
460 hl3=.000017*m*(5867-pa)'latent respiration heat loss
470 hl4=.0014*m*(34-ta)'dry respiration heat loss
480 hl5=3.96*fcl*(xn^4-(tra/100)^4)'heat loss by radiation
490 hl6=fcl*hc*(tcl-ta)'heat loss by convection
510 ts=.303*exp(-.036*m)+.028'thermal sensation transfer coefficient
520 pmv=ts*(mw-hl1-hl2-hl3-hl4-hl5-hl6)'predicted mean vote
530 ppd=100-95*exp(-.03353*pmv^4-.2179*pmv^2)'predicted % dissatisfied
540 goto 580
550 pmv=99999!:ppd=100
580 print ta,rh,clo,pmv,ppd

t (c)   rh   clo   pmv            ppd

19.6    86   1     -.4778556      9.769089
23.9    66   1      .4732535      9.676994
25.7    15   1      .5239881      10.74283
21.2    20   1     -.4779105      9.770202
23.6    67   .5    -.4747404      9.706658
26.8    56   .5     .5145492      10.53611
27.9    13   .5     .5003051      10.23146
24.7    16   .5    -.4883473      9.982468

the first 4 lines are the winter comfort zone corners.
the second 4 lines are the summer comfort zone corners.

an average person is "comfortable" when the pmv = 0.

"travis jordan"  writes:

>the ashrae calculations for heat gain assume 600 btu/h per person.
>that's 150 calories / hour.

that works for large btus.

mj  writes:

>being uncomfortable typically has more to due with humidity than 
>temperature...

the ashrae 55-2004 comfort zone disagrees, based on surveys of 21,000 people.

nick




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