🚀 go-pugleaf

Nick Pine wrote:
> 
> William R Stewart  <wstewart@patriot.net> wrote:
> >Nick Pine wrote:
>
> >>Here's another litmus test for an energy expert: what will the average water
> >>temperature be inside a 4' cube full of water surrounded by 5 R20 foam walls,
> >>sitting outside in December, when the air has an average 24 hour temperature
> >>of 36 F and the sun puts 1,000 Btu/ft^2/day of heat into the R1 glazed side
> >>of the box? And how will that change over time if we shade the sunny wall?
> >>Anyone care to answer that question? I'll offer a $10 reward to the first
> >>person who answers it correctly.

> >You don't give enough data in order to answer your question, and your question
> >is not clearly stated.\
> >The water in the cube would rise to a steady state temperature of
> >36 +80 = 116 oF if the energy input were continuous.
> 
> Perhaps, but recall the problem:
> 
> >>the sun puts 1,000 Btu/ft^2/day of heat into the R1 glazed side of the box. 
> >>And how will that change over time if we shade the sunny wall?
> >When shaded, the water in the cube would fall over time to 36oF.

I showed how it would change over time.  You owe me ten bucks, Nick :-)

> >A complete answer with specific times would require calculus, if specific
> >times was what you were looking for.

Otherwise, simple arithmetic would give the wrong answer, as this is obviously
not a linear relationship.

> Yes, that was what I was looking for. More than the obvious... Finding the
> form of the answer requires calculus, but Newton did that once, a long long
> time ago. Finding the answer just requires plugging some numbers into a
> simple formula, if you know the formula.

Present the formula and we will see if it produces the correct answer, or even
 a very close answer.
 
> >4000 lbs of water would require 2.5 hours of 1600 btu/hr energy input, again
> >without considering the loss through the cube walls.

So here is an answer with a specific time; what's your beef?
 
> True, but why are you talking about heating rather than cooling?

Because you asked for it!!!

> Sorry. No $10. Would you like to try again?

Welcher!

>                     *     *     *
> 
> At this point, Mr Stewart changes the subject:
> 
> >Now, if you;
> >  -moved the water inside to the interior sunspace of a 68oF house,
> >  -made the glazing 7'x10 (4 in the entire house on the south side)
> 
>     ie 280 ft^2 of south glazing?
> 
> >  -used a flatter 4"x4'x10' water wall (4 in the entire house), 4" away
> >   from the glazing inside the house,
> 
>     ie about 400 pounds of water? 4" away from the glazing? Transparent
>     water? Hmmm :-) I guess you won't be able to see very clearly out of
>     those windows, but they will let in some light...
> 
> >  -used an R4 glazing when the sun was shining,
> 
> With how much solar transmittance, at what cost, and what happens when the
> argon leaks out?Some of these $40/ft^2 high-R windows have low solar
> transmittance, on the order of 50%. Hmmm, 280 ft^2 x $40/ft^2 = $11,200.

You must be thinking of R8 windows; Where do you get your figures?
I'm not going with low-E due to insolation losses.

> >   and an extra R8 window cover when the sun wasn't shining,
> 
> How would you do that? Movable insulation, at $10/ft^2, installed? 

Again, where do you get your prices?

>Will you move it twice a day religiously? 

Just like you close your windows when it gets to cool at night.

>Will it leak any air around the edges?

Probably, but certainly much less than an outdoor thin film sunspace.
 
> >then you would have a direct, passive solar design that retained the sun's
> >heat energy in the building interior and released it slowly into the
> >interior at night
> 
> Right. Another "direct loss" house :-)

Er, do you have a house that does not lose heat when it is cold outside?

> >Care to try the math?
> 
> Sure. I like this arithmetic. Let me get a cup of coffee... Now I'm back,
> 200 Btu later. I've had this espresso machine for about 3 months now. I
> guess if some people like me find it fun to wiggle the valves on an espresso
> machine with all the steam and noise and watch the milk temp rise with a
> thermometer twice a day, others might find it fun to move window insulation
> all over a house twice a day, for three months... Or, maybe you only move
> the window insulation on a cloudy winter day--but no, you want to do it at
> night too... or you might leave some windows covered all winter, like Pat
> Hennin or Malcolm Wells, in semi-hibernation, huddled in cold dark rooms.
> 
> >assume another 60 ft^2 of window at R4 during the day, adding
> >   another R8 at the other 14 hours.
> 
> OK. That's a long winter day...

You forgot to add R8, you only added R4
 
> >Assume R24 walls and R38 ceiling.
> 
> OK. Let's assume that includes the 2x6's, etc, that act as thermal shunts,
> ie the equivalent thermal resistance of the entire wall is R24. This is not
> just a wall with layers of insulation with R-values that add up to R24
> (which might have a much lower R-value), and the insulation is installed
> properly with no gaps, etc. Are you sure about all that?

Another inch of polyisocyanurate, and various other siding and finishing
materials.
 
> >Assume a two story, 24'x 48' floorspace house with 8' ceilings.
> 
> OK. I guess you mean the footprint on the ground is 24 x 48?

Right.

> So the house volume is 24 x 48 x 16 = 18432 ft^3. 
> >Assume an outside temperature of 36 oF
> 
> OK. (The average will be warmer during daylight, which is good.)
> 
> >Assume 0.25 air changes per hour (optional).
> 
> OK. That's 0.25 x 18432 ft^3/hr = 4608 ft^3/hr or 77 cfm :-) I'll assume
> (I almost said "guess") this is leakage thru walls, etc, without an air-air
> heat exchanger... Will the finished house have a blower door testing spec?

Yes, and the top limit will be 0.25 air changes; I expect alot less.
 
> May we also assume you use a frugal 500 kWh/month of electricity, ie an
> average of about 700 Watts? 

Why does this matter?  I will be using a 2kW photovoltaic system.

> (Steve Baer only uses 80 kWh/mo :-) 

How much do you use, coffee and all?

> This is
> equivalent to 700 x 3.41 = 2387 Btu/hr. Let's add the heat from two
> 300 Btu/hr people inside the house for 16 hours a day, and one 150 Btu/hr
> dog and a 50 Btu/hour cat, full-time. Total internal energy generation:
> 2387(24)+600(16)+200(24) = 72K/day.
> 
> >Assume 100 Btu/hr/ft^2 insolation over 10 hours every day.
> 
> OK.
> 
> >Make an assumption about the thermal storage of the rest of the interior
> >items/material.
> 
> How about 1 lb of water/ft^2 of walls and ceiling? (1/2" drywall has the
> equivalent of 1/2 lb of water/ft^2, so you may need some concrete furniture..)
> I'll make some other assumptions, too.

OK

> I guess we'd want to know the thermal resistance of this house for starters.
> So let's add up the thermal conductances U = Sum(Ai/Ri) and find
> the reciprocal 1/U...
> 
> We have 340 ft^2 of windows, 

4 sets of 10' x 7' windows = 2800 ft^2

>R4 during a 10 hour day (Uday = 340/4 = 85)
> and R8 during a 14 hour night 

R12 at night; R4 + R8

(Unight = 340/8 = 43), with an average daily
> Uwindow = (10xUday+14xUnight)/24 = 60.
> 
> Uwalls = (2(24+48)x16-340)/R24 = 82, and Uceiling = 24x48/R38 = 30.
> 
> And Uinf = 77 Btu/hr-F.
> 
> So U = 60+30+77 = 167 Btu/hr-F and R = 0.006, over 24 hours.

These numbers have to be revisited.

> At night the U value would be lower, after you devotedly travel around
> the house and painstakingly put up your night insulation on every window,
> making sure the edges are ever so carefully sealed, akin to some little
> twice-daily religious experience... Unight = 43+30+77 = 150 Btu/hr-F.
> 
> What will the steady state energy flow be for this house after a long
> string of average December days, with an average amount of sun?
> 
> The energy Ein that flows into this house in a day might be
> 
>   280 ft^2 windows

That should be 2800 ft^2

 x 50% transmission

Try 75%

 x 1000 Btu/ft^2/day = 140K
>                             +  internal energy generation =  72K
>                                                 total Ein = 212K. 
> And the energy Eout that flows out of the house might be
> 
>   24 hours x (68-36) x 167 = 128 K Btu/day.

Of course, these numbers must be revisited as well.
 
> Now, thermal mass: the house has about 3500 ft^2 of walls and ceilings with
> a thermal mass equivalent to 3,500 pounds of water and another 400 pounds
> of actual water.

10' x 4' x 4" is ~13 ft^3.  Water is 62.4 lbs/ft^3.  There are
four water walls.

The water will weigh close to 3250 lbs.

> Let's call this 4,000 Btu/hr-F. 

You need to revisit this number as well.

> So if you make the temp of
> the house, say, 80 F at dusk, at the end of an average day, with some sun,
> after a long string of December days, each with 1000 Btu/ft^2/day of sun,
> during the night the house will lose approximately 14 hours (80-36) 150 =
> 100K Btu, which might come from the 4,000 Btu/F of thermal mass cooling plus
> 14/24 hours x 72K = 42K of internal energy generation, ie the temperature of
> the house might drop to 80 - (100K-42K)/4K = 65 F at dawn.

You have so many corrections to make before you hit this paragraph that I am
reluctant to mention the ones within.

You have not yet tried to establish the temperature of the water in the
water walls.  Your assumption seems to be 1 oF, though there is no evidence
of how you tried to calculate this.

> How much backup heat will you need in an average year? 

My wife wants a fireplace, so I will likely go with a masonry firestove,
often referred to as a Finnish or Russian fireplace, with outside combustion
air.


> Were you planning to have hot water in this house? How were you planning
> to do that? 

Solar hot water, most likely active.


> A better way to compare heating systems
> might be their yearly heating bills, including the electrical power to run
> the heating system. 

The model I am planning on building (2250 ft^2) required $168 worth of heat for an entire
winter.  Reference "Solar Today", Sept/Oct 1995, article on manufactured house.

> >Some people prefer the passive method, and it is not your perogative
> >to tell them that they are wrong in preferring that.
> 
> Oh sure it is, and it seems kind to tell people, if their passive houses are
> such miserable and expensive performers.

Try the numbers again, then we'll talk.

Cheers,

Will Stewart