Monday, September 30, 2013


If 100 people live on a circle 5 miles from church and they each drive 10 miles per week to and from church, that's 1000 miles per week, ie 50 gallons of gas at 20 mpg, ie $150/week at $3/gallon.

The circle circumference is 10Pi = 31.4 miles. If 20 cars move 5 people each, efficiently, they move 20x10 = 200 miles per week in and out + 2x20/100x31.4 circular miles, in a pie-shaped wedge, ie 451 miles per week, using 451/20 = 22.6 gallons of gas worth $67.70.

The weekly difference is $150-$67.70 = $82.30, ie $4280 per year, not counting reduced wear and tear on the cars or environmental benefits or increased socialization opportunities.

The basic economics make sense, but this needs social engineering, eg considerations of fairness, flexibility, privacy, safety, personality conflicts, and so on.

Why doesn't everyone car pool? How can computers help? Who travels with whom, and in what order? How can we avoid George feeling burdened, or personality conflicts with Alice? What happens if someone decides to skip church one week or only comes once a month or isn't ready to go when the driver shows up?

Poland had a national Autostop (hitchhiking) system in the 70s. A person by the side of a road would hold up a book with a target symbol on it, and a driver would stop and give her a ride, in exchange for a coupon torn from the book. The coupons were national lottery tickets redeemable by the driver. The trips were also insured for safety by the government.

At one point, the Israeli army mostly traveled by hitchhiking...

>... In Cuba, picking up hitchhikers is mandatory by government vehicles, if passenger space is available. Hitchhiking is encouraged, as there are few cars, and designated hitchhiking spots are used. Waiting riders are picked up on a first come first go basis.

>In 2009 carpooling represented 43.5% of all trips in the United States[1] and 10% of commute trips.[2] The majority of carpool commutes (over 60%) are "fam-pools" with family members.

>Carpooling, or car sharing as it is called in British English, is promoted by a national UK charity, Carplus, whose mission is to promote responsible car use in order to alleviate financial, environmental and social costs of motoring today, and encourage new approaches to car dependency in the UK. Carplus is supported by Transport For London, the British government initiative to reduce congestion and parking pressure and contribute to relieving the burden on the environment and to the reduction of traffic related air-pollution, in London.

>Challenges for carpooling

>Flexibility - Carpooling can struggle to be flexible enough to accommodate en route stops or changes to working times/patterns. One survey identified this as the most common reason for not carpooling. To counter this some schemes offer 'sweeper services' with later running options, or a 'guaranteed ride home' arrangement with a local taxi company.

>Reliability - If a carpooling network lacks a "critical mass" of participants, it may be difficult to find a match for certain trips. In addition, the parties may not necessarily follow through on the agreed-upon ride. Several internet carpooling marketplaces are addressing this concern by implementing online paid passenger reservation, billed even if passengers do not turn up.

>Riding with strangers - Concerns over security have been an obstacle to sharing a vehicle with strangers, though in reality the risk of crime is small.[12] One remedy used by internet carpooling schemes is reputation systems that flag problematic users and allow responsible users to build up trust capital, such systems greatly increase the value of the website for the user community. 

>Real-time ridesharing (also known as instant ridesharing, dynamic ridesharing, ad-hoc ridesharing, or dynamic carpooling) is a service that arranges one-time shared rides on very short notice. This type of carpooling generally makes use of three recent technological advances:

>GPS navigation devices to determine a driver's route and arrange the shared ride
>Smartphones for a traveler to request a ride from wherever they happen to be
>Social networks to establish trust and accountability between drivers and passengers

>These elements are coordinated through a network service, which can instantaneously handle the driver payments and match rides using an optimization algorithm.

>Real-time ridesharing is promoted as a way to better utilize the empty seats in most passenger cars, thus lowering fuel usage and transport costs. It can serve areas not covered by a public transit system and act as a transit feeder service. It is also capable of serving one-time trips, not only recurrent commute trips.Furthermore, it can serve to limit the volume of car traffic, thereby reducing congestion and mitigating traffic's environmental impact.

>One potential drawback may be economic harm to the auto industry due to sharing; however, some auto companies such as Daimler are quite supportive of real-time ridesharing research. Opposition may also come from taxi companies and public transit operators.


>Early real-time ridesharing projects began in the 1990s, but they faced obstacles such as the need to develop a user network and a convenient means of communication. Gradually the means of arranging the ride shifted from telephone to internet, email, and smartphone; and user networks were developed around major employers and universities. As of 2006, the goal of taxi-like responsiveness still generally eluded the industry; "next day" responsiveness was considered the state of the art.

>Most instant ridesharing services are still in their early stages. Successful pilot projects have been completed, but no real-time ridesharing company seems to have yet reached a critical mass of users.

>Two dynamic ridesharing pilots in Norway received government funds from Transnova in 2011. One pilot in Bergen had 31 passenger in private cars during one day. Thirty-nine users acted as drivers or passengers between June 30 and September 15 with four ridesharing episodes or more. The phone apps that was used was Avego Driver and cell client, a prototype developed for the NPRA of Norway. The other pilot is run by the company Sharepool.

>In France, real-time ridesharing is provided by Geocar from Villefluide, which focuses on the commute market and utilizes a cluster model and algorithms.

>Nous sommes spécialisés depuis 2008 dans les problématiques de déplacements liés au travail. Grâce à notre expertise, nous sommes capables de penser à l’échelle d’organisations afin de proposer à chaque employé la meilleure solution personnalisée de mobilité. Plans de mobilité, déménagements d’entreprises, covoiturage domicile travail, inter-modalité, VilleFluide est un acteur majeur de la mobilité 2.0.

"Notre vision est celle d’un monde où les déplacements du futur seront plus responsables, plus partagés et plus économiques. Notre ambition est à la fois de marier le meilleur des technologies à un concept entièrement innovant de réseau local de transport pour apporter des solutions de partage aux trajets récurrents, quotidiens, en relation avec tous les autres moyens de déplacements.

Nous poursuivons notre effort de R&D afin de toucher un public le plus large possible. En particuliers ceux qui ont un besoin fondamental de faire évoluer leurs pratiques de mobilité, pour des raisons économiques le plus souvent.

En vue d’atteindre cet objectif, nous nouons des partenariats stratégiques, avec des industriels, mais aussi des collectivités locales et territoriales, qui ont compris l’énorme bénéfice qu’elles pouvaient tirer de ces nouvelles solutions de déplacements."

>Wedrive est l’application grand public de VilleFluide. Il s’agit de la première application permettant de covoiturer vraiment chaque jour pour aller travailler.

Wedrive is Villefluide's smartphone app, which uses facebook.

A church transportation system with a fixed schedule and one fixed destination and fixed origins might not need GPS or smartphones, but it seems to need a mechanism for fairness, eg the Phoenixville Area Time Bank

If a driver (eg George) gives a passenger (eg Alice, who is unable to drive a car) a ride to church, and that takes another 0.8 hours, Alice could give George 1.2 hours from her time bank account (earned by babysitting or cooking?) , and George could get a different time bank member to mow his lawn for an hour.

If Alice is not ready to go on one Sunday morning when George arrives at her house, and that makes 4 people 1/2 hour late for church, Alice could donate 0.8+4x0.5 = 2.8 hours to the time bank that week, with an appropriate distribution to the accounts of George and the other 3 passengers. If George's late start makes everyone 1/2 hour late for church, George could donate extra time to the bank...


Thursday, September 26, 2013

A combined solar closet in Pittsburgh

Young Ben would like to live inexpensively on a farm near Pittsburgh... offers a 12' by 56' 2 bedroom mobile home with a new steel roof, a front kitchen, and a large bath, in very good condition for $3,900.00. lists "Antique CLASS C - 22' MOTOR HOME for sale - pictures sent to serious inquires - inspected and ready-to-go anywhere you want. Mechanically VERY RELIABLE, needs TLC (tune-up) - everything works. Great for camping, hunting, or just fix it up for the ultimate tail-gator mobile. Comes with kitchen, refrigerator, stove, oven, microwave, furnace, holding tanks (for gray and black water), full bathroom, overhead bed, couch, chair and dinette table. It has a 350 small block engine (that is very reliable), and transmission also very reliable, no slips or bangs, very smooth. Very easy to drive and is still being driven daily. Selling for $1500, or best offer."

Here's one for $100... "1974 Holly Park mobile home for sale. Must be moved. Serious inquiries only; sold as-is. You move it. Needs repairs and attention, but would make a great hunting cabin."

Ben has also been offered the free use of a pop-up camper. None of these structures have much thermal insulation, but they could be solar-heated if enclosed in a strawbale structure inside an inexpensive plastic film greenhouse. Ben might be happy living inside a strawbale structure without a pop-up camper, with a strawbale bed and a strawbale table and a sawdust toilet.

An 8'x12'x8'-tall room with about 536 ft^2 of R55 dry 2' strawbale walls would have thermal conductance G = 536/55 = 9.7 Btu/h-F... 10 cfm of fresh air would raise the conductance to about 20. Keeping it 70 F on an average 31.5 F December day in Pittsburgh would only require (70-31.5)20 = 770 Btu/h. says 1.7 kW/m^2 of sun falls on a vertical south wall and 1.91 falls on a south wall with a 45 degree slope on an average December day with a 35.1 average daytime temp. Suppose a 6 cent/ft^2 4-year 14'x24' R1 sloped polyethylene film south wall with 90% solar transmission and 100% longwave IR transmission connects the top edge of the south room wall to the ground 10' south of the room wall and transmits 0.9x14'x24'x1.91x317 = 185K Btu and keeps the room 70 F for 24 hours and radiates heat from the ground inside the wall and the south room wall at absolute Rankine temp Ta to an outdoor temp Ts (R) and 185K = 24h(70-31.5)20 + 6hx0.1714E-8V(Ta^4-Ts^4)480ft^2, where V = 1/4 is the approximate view factor of the radiating surfaces. (A more expensive and durable polycarbonate south wall would block longwave IR.)

Duffie and Beckman's 2006 Solar Engineering of Thermal Processes book has equation (3.9.2) for sky temperature Ts = Ta[0.711+0.0056Tdp+0.000073Tdp^2+0.013cos(15t)]^(1/4), where Ts and Ta are in degrees Kelvin and Tdp is the dew point temp in degrees Celsius and t is the number of hours from midnight.

Ta = 35.1+460 = 495.1 degrees R, ie 495.1/1.8 = 275.1 degrees K. NREL says the humidity ratio w = 0.0030 pounds of water per pound of dry air on an average December day in Pittsburgh, which makes the partial pressure of water in air Pa = 29.921/(0.62198/w-1) = 0.145 "Hg, which makes the dew point Tdp = 9621/(17.863-ln(Pa)) = 486 R, ie 486-460 = 26 F, ie -3.3 C. With t = 12 hours (noon), cos(15t) = -1, so Ts = 275.1[0.711-0.0056x3.3+0.000073x3.3^2-0.013)]^(1/4) = 253.2 K, ie 1.8x253.2 = 455.7 R, ie -4.3 F, 39 F degrees less than the air temperature.

... 185K = 24h(70-31.5)20 + 6hx0.1714E-8V(Ta^4-455.7^4)480 makes 166.5K = 1.234E-6(Ta^4-455.7^4), so Ta = 649.5 R, ie 190 F. A quarter-cylindrical R1 film wall with a 10' radius and a 24' length and 377 ft^2 of surface with 190 F air inside and 35.1 F (495.1 R) air outside would lose 6h(190-35.1)377ft^2 = 350.4K Btu/day to the outdoor air, which is more than the solar input, so 190 is too hot.

If 185K = 6h(T-495.1)377 + 1.234E-6(Ta^4-455.7^4), ie T = 576.9 - 5.46E-10(Ta^4-455.7^4). Plugging in T = 540 R on the right makes T = 554.0 on the left. Repeating makes T = 549.0, 550.8, and 550.2 R, ie 90.2 F, warm enough to solar heat the room on an average day.

If the room is 70 F at dusk and 60 at dawn, 18 hours later, and 60 = 31.5+(70-31.5)e^(-18/RC), time constant RC = -18/ln((60-31.5)/(70-31.5)) = 60 hours = C/G, and C = 60hx20Btu/h-F = 1200 Btu/F of room temp thermal mass with lots of surface can store average-day heat, eg 1200/5 = 240 8"x8"x16" hollow concrete blocks, but they would take up a lot of space in the room. Putting 2 750 ml glass bottles of Pellegrino water into the holes in each block would raise its capacitance to about 9 Btu/F and lower the number of blocks to 1200/9 = 133.

But it seems more interesting to combine daily and cloudy-day heat storage in a single higher-temp glazed Solar Closet with 8'x8' of R1 vertical polycarbonate south air heater glazing over an insulated south wall. If the room is 70 F for 16 hours per day and 60 F for 8 hours and we count Ben's 300 Btu/h body heat for 8 hours and ignore the south room wall heat gain from the 90.2 sunspace air during the day, we need to store 8h((60-31.5)20-300)+16h(70-31.5)20 = 14.5K Btu of average-day heat. With lots of surface, we can store this heat in C Btu/F of daily mass cooling from T (F) to 60, with (T-60)C = 14.5K, ie T = 60+14.5K/C.

If the air heater glazing transmits a constant 0.9^2x1.7x317/6h = 73 Btu/h-ft^2 of sun with a 90.2+73xR1 = 163 F Thevenin equivalent temperature and the daily mass warms to T = 163-(60-163)e^(-6/RC) F in 6 hours of sun, and we replace T with 60+14.5K/C, 60+14.5K/C = 163-(60-163)e^(-6/RC), ie 14.5K/C = 103(1-e^(-6/RC), ie 141/C = 1-e(-6/RC), and an R = 1/64 glazing resistance makes 141/C = 1-e(-384/C), ie C = 141/(1-e^(-384 /C)). Plugging in C = 160 on the right makes C = 155.1. Repeating makes C = 153.9, then 153.7 Btu/F, eg 31 hollow sparsely-stacked concrete blocks cooling from 60+14.5K/155 = 154 to 60 F on an average night.

But wait! An 8"x8"x16" hollow concrete block with 2 4"x4"x8" holes has 384 in^2 for the solid faces + 192 in^2 for the two faces with holes + 256 in^2 for the holes, totaling 832 in^2, ie 5.78 ft^2. With a 1.5 Btu/h-F-ft^2 slow-moving airfilm conductance, one block's airfilm conductance is 8.67 Btu/h-F, and 31 blocks have a 269 Btu/h-F film conductance.

If the blocks absorb 14.5K/6h = 2417 Btu/h from hot air, the air will be 2417/269 = 9 F warmer than the blocks. And the air in the air heater has to be warmer than the air near the blocks for thermosyphoning to occur. One empirical chimney formula says cfm = 16.6Asqrt(HdT), where A is the area of the chimney opening in square feet and H is the chimney height in feet and dT (F) is the temperature difference between the chimney and outdoor air. With 6"x8' slots at the top and bottom of an 8' tall air heater, A = 4 ft^2 and H = 8'. Heatflow in Btu/h is cfmxdT, approximately, so Btu/h = 2417 = 16.6x4xsqrt(8)dT^(3/2) makes dT = 12.9^(2/3) = 5.5 F. With 2 1 ft^2 vents to the room and an 8' height difference, 770 = 16.6x1xsqrt(8)dT^(3/2) makes dT = 16.4^(2/3) = 6.4 F.
Given these effects, the daily heat store has a smaller temp swing, so it needs more capacitance... If  T = 66.4+14.5K/C = 148.5-(66.4-148.5)e^(-384/C), ie 14.5K/C = 82.1(1-e^(-384/C), ie C = 177/((1-e^(-384/C)). Plugging in C = 200 on the right makes C = 207 on the left. Repeating makes C = 210.0, then 210.9 Btu/F, eg 42 hollow concrete blocks cooling from 135.4 to 66.4 F. Or fewer blocks, since 42 would have more surface than 31, with smaller charging and discharging temp drops.

Heating the room directly for 6 hours with 90.2 F air from the sunspace instead of air from the daily store would also reduce the number of blocks required in the daily store. And a thermosyphoning air-air heat exchanger could help. If 31.5 F air falls down through the corrugations of 64 ft^2 of 8 mm Coroplast and 10 cfm of 65 F air rises up between the Coroplast faces with possible condensation and freezing, NTU = AU/Cmin = 128ft^2x0.75Btu/h-F-ft^2/10Btu/h-F =  9.6, and E = 9.6/10.6 = 0.906, and Tco =  31.5+E(65-31.5) = 61.9 F, and Tho = 65-E(65-31.5) = 34.6 F, with 46.7 and 49.8 F average air temps in the hot and cold chimneys and a 3.1 F difference between the averages. Not much, for thermosyphoning air. So maybe this heat exchanger needs 2 small DC fans that only run when the indoor RH or CO2 concentration exceed 60% or 1000 ppm, with an Arduino controller that can also shut off the cold air fan if condensation in the outgoing air passage begins to freeze, eg

Without these refinements, the room needs 5x14.5K = 72.5K Btu for 5 cloudy days in a row, with an approximate solar heating fraction of 1-2^-5 = 0.97. This could come from 72.5K/(135-70) = 1108 Btu/F of cloudy-day mass with lots of surface cooling from 135 to 70F, eg 2 vertically-stacked 450 Btu/F steel 55 gallon drums with plastic film liners surrounded by a layer of rocks inside a 3'-diameter x 6' tall cylindrical welded-wire ag fence gabion.

If the drums are well-insulated with strawbales, trickle-charging them hot won't require much daily overflow hot air from the daily air heater, which could first heat the daily store to 135 with thermosyphoning air and a passive one-way plastic film damper, then heat the cloudy store behind the daily store with more thermosyphoning air and another film damper.

Friday, September 20, 2013

A large streamwater heat exchanger

Drew asks about a 2 million Btu/h heat exchanger (big enough to heat 40 houses):

>a heat pump loop cooled by gravity flow stream thru a shell and tube htx...
>200 gpm 90 degrees on tube side  heat pump loop
>600 gpm 70 degrees gravity flow on shell side. 8 inch pipe stream water

So the heat capacity rate ratio Z = Cmin/Cmax = 1/3.

>It is now able to get the leaving loop water temp down to 75

So the heat exchanger effectiveness E = (90-75)/(90-70) = 0.75
= (1-e(-NTU(1-Z)))/(1-Ze(-NTU(1-Z))), ie
0.75-0.75x0.33e^(-NTU(1-1/3)) = 1-e^(-NTU(1-1/3)), ie
0.75-0.25e(-NTU2/3) = 1-e^(-NTU2/3), ie
0.75e^(-NTU2/3) = 0.25, ie
e^(-NTU2/3) = 1/3, ie
-NTU2/3 = -1.099, ie
NTU = 1.648 = AU/Cmin, ie
AU = 1.648x200x500 = 165K Btu/h-F.  

>1) if we parallel another identical htx my guess is flow would be 100 gpm on each tube side still 600 gpm on shell sides and the leaving loop water would drop to 72.5? what you think?

If the 600 gpm is divided into 2 300 gpm streams for the 2 heat exchangers,
Z = 1/3 and NTU = 165K/(100x500) = 3.3 and
E = (1-e(-3.3x2/3)))/(1-e(-3.3x2/3))/3)
= 0.8889/0.9630 = 0.9231, so
Tho = Thi-E(Thi-Tci)
= 90-0.9231(90-70)
= 71.54 F. Or a bit more, with less water velocity in the tubes. and say
a single moving water film has conductance
U = 100+200V Btu/h-F-ft^2, with V in fps, eg
U = 1500 at V = 7 fps.

>2) as an alternate we are thinking of laying some poly pipe directly in the stream.  my suggestion is 20 100 foot 1 inch pipes in parallel so the loop water flow in each would be 10 gpm. Stream flows at about 7 fps.  what's your guess as to the leaving loop temp?

1" 100 psi NSF HDPE pipe with a 0.07" wall thickness would have a 0.38x6.93/0.07 = 37.6 Btu/h-F-ft^2 conductance. The water velocity inside the pipe would be about 10gpm/60s/m/7.48g/ft ^3/(Pi(1.049"/24)^2) = 3.7 fps with a 100+200x3.7 = 843 Btu/h-F-ft^2 film conductance. With 7 fps water on the outside, U = 1/(1/843+1/37.6+1/1500) = 35.15 Btu/h-F-ft^2. A = 100'xPi1.12"/12 = 29.3 ft^2 makes NTU = AU/Cmin = 29.3x35.15/(10x500) = 0.206. With an infinite stream heat capacity and Z = 0, E = 1-e^-NTU = 0.186, and Tho = Thi-E(Thi-Tci) = 90-0.186(90-70) = 86.3 F.

>3) as another alternate, we are thinking of diverting some drainage water from the exterior of the parking garage to an isolated  section of the stream bed and laying the pipes in it. its advantage is it is 50 degrees. There is less flow perhaps 200 gpm.  if this were in a 2 inch by 24 inch crossection with the tubes it would flow at about 3 fps. What do you think the exiting loop temp would be?

U = 1/(1/843+1/37.6+1/700) = 34.23 Btu/h-F-ft^2. NTU = 29.3x34.23/(10x500) = 0.201. With Z = 1, E = NTU/(NTU+1) = 0.167, and Tho = 90-0.167(90-50) = 81.6 F.


Thursday, September 5, 2013

Opaque attic roof heating revisited

With radiation loss, a roof with an absolute Rankine temperature T would have 0.1714E-8(T^4-Ts^4)+(T-(35.5+460)2 = 150 Btu/h, where Ts is the effective sky temperature in Rankine degrees. Duffie and Beckman's 2006 Solar Engineering of Thermal Processes book has equation (3.9.2) for sky temperature Ts = Ta[0.711+0.0056Tdp+0.000073Tdp^2+0.013cos(15t)]^(1/4), where Ts and Ta are in degrees Kelvin and Tdp is the dew point temp in degrees Celsius and t is the number of hours from midnight.

Ta = 35.5+460 = 495.5 degrees R, ie 495.5/1.8 = 275.3 degrees K. NREL says the humidity ratio w = 0.0028 pounds of water per pound of dry air on an average December day in Allentown, which makes the partial pressure of water in air Pa = 29.921/(0.62198/w-1) = 0.135 "Hg, which makes the dew point Tdp = 9621/(17.863-ln(Pa)) = 484 R, ie 484-460 = 24 F, ie -4.2 C. With t = 12 hours (noon), cos(15t) = -1, so Ts = 275.3[0.711-0.0056x4.2+0.000073x4.2^2-0.013)]^(1/4) = 249.6 K, ie 1.8x249.6 = 449.3 R, ie -10.7 F, 46 F degrees less than the air temperature.

And 0.1714E-8(T^4-449.3^4)+(T-495.5)2 = 150 makes T = (1141-(T^4-449.3^4)0.1714E-8)/2. Plugging in T = 530 on the right makes T = 537.8 on the left. Repeating this makes T = 533.7, 535.9, 534.8, 535.3, 535.0, and 535.2 R, ie 75.2 F, which is not much greater than 70 F, so the roof can't provide much space heating in December, even at noon in direct beam sun. says 2.62 kWh/m^2 (2.62x317 = 831 Btu/ft^2) of sun falls on a south roof with an 18.4 degree slope on an average 26.6 F January day with a 34.3 high and a 0.0022 humidity ratio in Allentown. February, March, April, and May bring 3.36, 4.43, 5.32, and 5.65 kWh/m^2 with 29.3, 37.7, 0.0024, 39.4, 48.8, 0.0032, 49.7, 60.4, 0.0046, 60.3, 71.3, and 0.0074 average and high temps and humidity ratios, and so on. If 80% of the sun falls on the roof in all but 3 hours of daylight, opaque attic roof heating does not look at all promising:

10 PI=4*ATN(1)
20 S=1.714E-09'Stephan-Boltzman constant
30 LAT=40.5'north latitude (degrees)
40 DATA 26.6,34.3,2.62,.0022,-20.9
50 DATA 29.3,37.7,3.36,.0024,-13.0
60 DATA 39.4,48.8,4.43,.0032,-2.4
70 DATA 49.7,60.4,5.32,.0046,9.4
80 DATA 60.2,71.3,5.65,.0074,18.8
90 DATA 69.4,80.0,5.80,.0104,23.1
100 DATA 74.1,84.5,6.06,.0122,21.2
110 DATA 72.2,82.3,5.43,.0120,13.5
120 DATA 64.7,75.1,4.70,.0097,2.2
130 DATA 53.2,63.8,3.87,.0064,-9.6
140 DATA 43.1,51.8,2.48,.0044,-18.9
150 DATA 31.8,39.2,2.25,.0028,-23.0
160 FOR MONTH=1 TO 12
180 TDF=(TA+TM)/2'average daytime temp (F)
185 TDFP=INT(10*TDF+.5)/10'rounded tdf
190 TDR=TDF+460'daytime temp (R)
200 TD=(TDF+460)/1.8'daytime temp (K)
210 PA=29.921/(.62198/W-1)'vapor pressure ("Hg)
220 TDPF=9621/(17.863-LOG(PA))-460'dew point temp (F)
230 TDP=(TDPF-32)/1.8'dew point temp (C)
240 TSKY=TD*(.698+.0056*TDP+.000073*TDP^2)^.25'sky temp (K)
250 TSKYF=1.8*TSKY-460'sky temp (F)
260 X=-TAN(PI*LAT/180)*TAN(PI*DEC/180)'find day length
270 ICOS=-ATN(X/SQR(-X*X+1))+PI/2'inverse cosine (radians)
280 DAYL=2/15*ICOS*180/PI'day length (hours)
290 SINT=.8*317*SUN/(DAYL-3)'solar intensity (Btu/h-ft^2)
300 TR=530'initial roof temp (R)
305 FOR I=1 TO 10
310 TR=(2*TDR+SINT-S*(TR^4-TSKYR^4))/2'roof temp (R)
315 NEXT I
320 TRF=TR-460'roof temp (F)

01  30.5   -17.9104       9.462032      102.8209      31.75281
02  33.5   -14.2666       10.48372      113.86        37.80908
03  44.1   -1.409027      11.72648      128.7402      50.34619
04  55.1    13.38834      13.08379      133.7942      59.52539
05  65.8    30.77084      14.25374      127.3213      64.54016
06  74.7    45.41767      14.84857      124.1399      69.43659
07  79.3    52.98224      14.5795       132.7187      75.28638
08  77.3    50.6933       13.57763      130.1849      73.11206
09  69.9    39.54871      12.2507       128.8465      67.81403
10  58.5    21.59882      10.89256      124.3491      58.66553
11  47.4    5.783173      9.73297       93.41019      40.42139
12  35.5   -10.78049      9.165865      92.54176      31.68912

The average roof shingle temps are less than 70 F except for the months of July and August, when the outdoor temperature is warm enough that the house doesn't need heat.

This could be refined with a simulation using hourly TMY2 weather data, but so far it looks doomed... 


Tuesday, September 3, 2013

Solar attic heating

Richard asks a $20 question :-)

>I live in Kutztown, PA in a 3,000 SQ FT detached 2 story "colonial" - I've had the idea that there must be some way to recover the attic's heat in winter for assistance in living space heat...

You can recover some heat from the attic with a blower in series with a heating thermostat in the house and a cooling thermostat in the attic, eg 2 of these $20 line voltage thermostats:

Kutztown has a 40.5 degree north latitude, so the max sun elevation at noon on 12/26 is 90-40.5-23.5 = 26 degrees. A 4/12 south roof with an 18.4 degree elevation would receive about 250cos(90-18.4-26) = 150 Btu/h/ft^2 in full beam sun at noon, which could raise a dark shingle temp by 150/2 = 75 F on a calm day with a 2 Btu/h-F-ft^2 still airfilm conductance and no radiation loss.

Solar Attic, Inc of Minneapolis claims a 30% space energy savings using their system, which seems optimistic. IIRC, their system sold for $1400 until the 40% tax credit disappeared in 1984, when the price dropped about 40% to $900. These days, they mostly focus on swimming pool heating with air-to-water heat exchangers (like car radiators) in attics.

If the house is cooler than (say) 70 F and the attic is warmer than 80 F, the thermostats would allow the blower to circulate attic air through the house through supply and return air paths. One of the paths could have a one-way plastic film damper to avoid warm house air flowing up into the attic at night. The blower would draw down warm air from the highest point in the attic with the ridge vent (if any) blocked and gable vent doors closed. A vertical east-west plastic film partition could confine warm air to the space under the south roof. This can work a lot better with a steep transparent south roof, as described at:

You could also add winter heat to the house with one of Gary Reysa's simple thermosyphoning air heaters over an insulated south house wall, described at:

NREL says 800 Btu/ft^2 of sun falls on a south wall on an average 31.8 F December day with a 39.2 high and an average 35.5 F daytime temp in Allentown, PA, so an average 0.9x8ft^2x800/6h = 960 Btu/h of heat would enter a 1 ft wide x 8' tall strip of R1 polycarbonate air heater south glazing with 90% solar transmission.

One empirical chimney formula says C = 16.6Asqrt(HdT) cubic feet per minute of air will naturally flow up through a warm vertical H' tall duct with A ft^2 of cross-sectional area and a dT (F) temp diff between the top and the bottom, with CdT Btu/h of heatflow. If the solar heat that flows into the 8' strip equals the heat that flows into the room plus the heat that flows from the warm glazing to the outdoors, with a 3% vent area and A = 0.03x8 = 0.24 ft^2, 16.6x0.24sqrt(8)dT^1.5+(70+dT/2-35.5)8ft^2/R1 = 960 Btu/h makes dT = (60-0.355dT)^(2/3). Plugging in dT = 20 on the right makes dT = 14.1 on the left. Repeating makes dT = 14.4, then 14.4, with a T = 84.4 F air heater outlet temp and C = 43 cfm and a 43x14.4 = 616 Btu/h useful heat output for the 8' strip and a 100x616/800 = 77% solar collection efficiency and a 616x6h/8ft^2 = 462 Btu/ft^2 air heater gain on an average December day. A 4'x8' air heater would collect the heat equivalent of 4.6 therms of natural gas during the month of December.

Thanks for asking a question. Please let me know if you'd like further clarification.