
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 ashraestandard 154 pound human dissipates 253 btu/h when sleeping.
>is there a formula?
sure. ashraestandard 552004 ("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 nonzero...
130 pa=0'water vapor pressure
140 def fnps(t)=exp(16.65364030.183/(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=mw'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+(35.5ta)/(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*xftaa)^.25
370 if hcf>hcn then hc=hcf else hc=hcn
380 xn=(p5+p4*hcp2*xf^4)/(100+p3*hc)
390 n=n+1
400 if n>150 goto 550
410 if abs(xnxf)>eps goto 350
420 tcl=100*xn273'clothing surface temp (c)
440 hl1=.00305*(57336.99*mwpa)'heat loss diff through skin
450 if mw>58.15 then hl2=.42*(mw58.15) else hl2=0'heat loss by sweating
460 hl3=.000017*m*(5867pa)'latent respiration heat loss
470 hl4=.0014*m*(34ta)'dry respiration heat loss
480 hl5=3.96*fcl*(xn^4(tra/100)^4)'heat loss by radiation
490 hl6=fcl*hc*(tclta)'heat loss by convection
510 ts=.303*exp(.036*m)+.028'thermal sensation transfer coefficient
520 pmv=ts*(mwhl1hl2hl3hl4hl5hl6)'predicted mean vote
530 ppd=10095*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 552004 comfort zone disagrees, based on surveys of 21,000 people.
nick

