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re: ac short cycling
8 jun 1996
my short cycling guru friend paul milligan  wrote:
>   nick@vu-vlsi.ee.vill.edu (nick pine) wrote:
>~>>paul milligan (pjm@nando.net) writes:

>~>>>       there is no quantifiable time period that defines 'short cycling'
>~>>>in this context ( as opposed to certain other failure mode contexts we use
>~>>>the same term to describe ).

>~~>nonsense. less than 10% on-time is a short cycle. next question? :-)
 
>	how can you make such a statement without working within parameters
>of load and delta ?  ( hint - you can't )

oops :-)

>	short cycle ( again, in the context of system usage, not failure
>modes )is not a question of percent of running time vs total period, it
>is rather the pattern of on/off cycles, and their relative time structures.

hmmm.

>	example #1- hot, hot day, leaky house, poor insulation:
 
>		unit runs 5 minutes, satisfies, calls again in 5 minutes,
>runs 5 again, etc.  that _is_ short cycling, and yet run time is 50 % !
 
>	example # 2 - 80 degrees outside, dryish, evening
 
>	unit runs 5 minutes to acheive 77 inside, satisfies, shuts off. 
>does not call again for an hour.  that is _not_ short cycling, but run 
>time is <10 % !

good examples. perhaps we should say "short cycling is a condition in which
an ac cycles more than 6 times per hour." or "short cycling is a bicycle trip
of less than 3 miles."

here are some more examples:

        example # 3a - 80 degrees outside, 5k btu ac in an 8' cubical room
at 80 f inside, with 6" concrete walls with a heat capacity of 22 btu/f-ft^3,
surrounded by 2" of polystyrene foam with an r-value of 10. the walls have
a thermal mass of 8x8x6x6/12x22 = 4224 btu/f, so the unit runs for 3x4224/5k
= 2.5 hours to achieve 77 inside, satisfies, shuts off. the room with a time
constant of rc = r10/(64x6)x4224 = 110 hours takes t hours to warm to 79 f
where 79 = 80 + (77-80)exp(-t/110) ==> t = -110 ln((80-79)/(80-77)) = 154 hr, 
ie 6 days, then the ac comes on again and cools it to 77 f in 2x4224/5k =
1.7 hours, and so on. is that short cycling?

        example # 3b - 80 degrees outside, 5k btu ac in an 8' cubical room 
at 80 f inside, with 2" polystyrene r10 foam walls with a heat capacity of
0.5 btu/f-ft^3, surrounded by 6" low-thermal-resistance concrete walls. the
inside walls have a thermal mass of 8x8x6x2/12x0.5 = 32 btu/f, so the unit
runs for 3x32/5k = 0.0192 hours or 1.15 minutes to achieve 77 inside, shuts
off, the room with a time constant of rc = r10/(64x6)x32 = 0.83 hours takes
-0.83 ln(-1/3) = 1.16 hours to warm to 79 f, the ac comes on again and cools
it to 77 f in 2x32x60/5k = 0.77 minutes, and so on. is that short cycling? 
 
        example # 4a - 86 f outside 8 hours a day, 67 for 8 hours a day, and
77 for 8 hours a day, 8' cubical room with 6" concrete walls on the inside,
initially 77 f, surrounded by r10 foam. phila owner takes ac to junkyard, gets
1 cent/pound, and buys a $5 100 watt window fan at a garage sale. during the
night with the fan on, the concrete walls have a surface air film thermal
conductance of about 2 btu/hr-f, so the room has an rc time constant of about
1/2/(64*6)x4224 = 5.5 hours. during the day, buttoned up, the room temp rises
to t(8) = 86 + (77-86)exp(-8/110) = 77.6 f, and during every night the owner
turns on the fan for t hours, where 77 = 67 + (77.6-67)exp(-t/5.5), so
t = -5.5 ln((77-67)/(77.6-67)) = 2.14 hr, and so on. is that short cycling? 

        example # 4b - 86 f outside 8 hours a day, 67 for 8 hours a day, and
77 for 8 hours a day, 8' cubical room with 6" concrete walls on the inside,
initially 77 f, surrounded by r10 foam. wise phila owner removes three piece
suit, dons shorts and t-shirt, sells fan and lives in 77.6 f room during the
day, 76.4 f room at night. 

        example # 5a - 86 f outside 8 hours a day, 67 for 8 hours a day, and
77 for 8 hours a day, phila owner and loony brother build stone house with
13 million pounds of rocks, including rocks for the roof (see recent mother
earth news) and foam the outside with 4" of urethane. rc = 20,800 hours, so
if the house starts out one summer morning at 65 f, by the end of an 86 f
day, the indoor temperature rises to t(8) = 86 + (65-86)exp(-8/20,800)
= 65.00692 f. 

        example # 5b - from june through august in philadelphia, when the
average outdoor temp is 74.7 f, the indoor temperature in this house with
a 29 month time constant rises to about 74.7 + (65-74.7)exp(-3/29) = 66 f,
while the brothers open their house sometimes at night to their low-thermal-
mass sunspace with its solar-dried dessicant floor to remove some humidity,
while venting the hot sunspace to the outside on sunny days. a layer of
wood chips or vermiculite or crushed stone or a thin layer of concrete over
foam might work as a dessicant floor...

        example # 5c - september arrives, with an average daytime high
temperature of 77.6 f, and the owners get ready for winter in this house
with 3,000 ft^2 of walls with 2 million btu/f of thermal mass with an indoor
surface thermal conductance of about 2 btu/f, ie an indoor time constant of
1/2/3,000x2 million = 333 hours or 2 weeks, by opening the windows for t
hours during the later part of the month, to raise the house temperature
to 73 f, where 73 =  77.6 - (77.6-66)exp(-t/333), so t = -333 ln(0.39)
= 308 hours or 12.8 days.

        example # 5d - winter arrives, with about 6,000 heating degree days,
at a 70 f base temperature, and the house loses 24x6,000x3,000/r30 = 14
million btu, and cools from 73 to 67 f. the average daily min temps in may
and june are 53 and 62. the brothers open the house up on 10 cool nights in
early spring to allow it to cool to 65 f, and the summer begins again.

        example # 5e - loony brothers wear sweaters in winter, t-shirts
in summer, and leave the south-facing windows closed all year :-) 

nick

ps: lent 700 ft^2 of 13.9 cent/ft^2 black 80%-solar-absorbing shadecloth to
the local newspaper, the collegeville independent, "neutral on nothing--
accept and defend the truth, whatever the source!" so they could see how their
comfort and ac bills change when they hang it over their barn red south wall
with r11 insulation and 84 ft^2 of double pane windows. they are worried about
the building inspector, so they are thinking of stenciling it with big red 
letters saying "vietnam--1964-1973," to exempt it from the building code as
self-expression (their publisher's a lawyer :-) they might add "desert storm--
1990-1991," in red poster paint, so it will bleed in the rain. 




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