Monday, December 08, 2008

Toilet-Water Heating: Last Crackpot Post For A While

Last night was the first really good cold one here in the Smallish City. The temp outside when I got up this morning was 13F/-11C, with a windchill of 0F/-18C. Brisk!

However, this will be the last post for a while on the topic of home-heating/cold-adaptation/practical thermodynamics. Not because I've lost interest in the subject (or turned on my heat). But just because I'm getting tired of hearing my name and the word "crackpot" in the same sentence. So I'm going to try to give it a rest for a couple weeks. Rest assured, however, that I will not be firing up the furnace just yet.

Before we move on to some lesser topic, though, I do have one more question for my cold-region-dwelling readers to ponder. And that question is: how much energy does your toilet-tank-water heater use?

Yes, you heard me-- how much? Oh, you don't have a dedicated toilet-tank water heater? Then you are using your home furnace to heat your toilet tank water. No, for real, you are.

Every time you flush, the room-temperature water in the tank goes bye-bye, and the tank refills with cold water. Which, over the next couple hours, pulls heat out of the bathroom until it, too, is room-temp... and ready to be flushed away again.

How much energy are you wasting this way? Well, I got to thinking about that. And came up with a nice formula. First you need to know these simple things:

1) Volume (in gallons or liters) of your toilets' tanks (this is in the range of 4-5 gallons for traditional North American toilets. Less for Europeans, of course.) Call this "V".
2) Number of flushes per day in your house. Call this "n".
3) Difference between your room temperature and your incoming cold water temperature. (Use ˚F if you used gallons for V; ˚C if you used liters). Call this number "Td". (My cold water, incidentally, comes in at 48F/9C)

Calculate this product: V x N x Td. Call that "P"

Now you can find the how much warmth your flush down the toilet in winter . One way to think of it is to imagine what equivalent wattage of light bulb you could have on, 24/7, all winter, to use the same energy. That is P/10 (if you used gallons/Fahrenheit in your calculations) or P/20 (if you used liters/centigrade). Imagine that little light bulb right in the sewer pipe leading away from your house, warming it away 'round the clock. Certainly seems useful, no?

If you're actually heating with electricity, you could estimate how much coal your powerplant burns daily to warm your toilet water. That number is P x .0021 lbs of coal (if you used Imperial units) or P x .001 kg (if you used metric units). (This assumes an average North American power plant, which is about 30% efficient.)

Or, if you heat with oil, you could figure how much oil you burn, over the course of a winter, to warm your toilet water. For those using Imperial units, that number (in gallons) is N/100. For those working in metric, it is (in liters) N/50. (Assuming your furnace, like mine, is 83% efficient, and heating season is six months long.)

So, under present Turbopalace conditions (Room temp = 55F, Water temp =48F, no housemate, toilet using 5 gallons per flush, estimating four flushes a day), I'm burning a 14W lightbulb equivalent, which represents 1/4lb of coal a day, or wasting 1.4 gallons of oil a winter. If I got a housemate (doubling the flushes) and turned the heat up to 69F, the result changes to a 84W bulb, 1.75lbs of coal a day, or 8.4 gallons of oil. Which starts to be significant, no?

If you have a family of five, and everyone flushes three times a day, and you keep your bathrooms at 70F... well, now you're talking about 16.5 gallons of oil. That's enough fuel to drive a diesel Jetta from Philadelphia to Atlanta!

What can you do about this horrendous waste of energy? I have several suggestions, which I present in order of least to most likely to make you look discernibly like a crackpot:

1) Insulate the toilet tank to minimize heat transfer into the tank water. You could affix some closed-cell foam to the inside walls of the tank... or tape a some bubble wrap to the back. Or even just casually pile a bunch of magazines on the back of the toilet! Yes, insulating your toilet is totally crackpot-- but because the modifications are unlikely to be detected by friends and family, you will likely get away with it.

2) Reduce the volume of water in the toilet tank. Ideally, you could install new low-flow toilets-- but that's very pricey. Instead you could use the old brick-in-a-bag-in-the-tank method, or one of the many gadgets from the hardware store to reduce tank volume. Friends and family may notice a change in flushing power, which could cause them to wonder if you've done something strange. But you could probably just blame this on the water company or something.

3) Try to cluster toilet use in time, and/or minimize how many toilets in the house get used. As it take a couple hours for a tankful of cold water to get warmed to room temp, using the same toilet several times in within a couple hours is much more efficient than flushing three separate toilets and letting all of them warm up again. However, unless done with extreme subtlety, family and friends are likely to notice your efforts at this sort of behavioral modification. You might get away with sabotaging one of the household's toilets and not getting around to "fixing" it until spring.

4) Maintain the rule of "If it's brown, flush it down; if it's yellow, let it mellow." Okay, for sure this will get you labeled as a nutjob. But it would be hugely more efficient. First, you are heating far fewer tanks of water per day. Second, you get to reclaim some, um, biological heat from the, er, unflushed warm liquid in the toilet bowl. Depending on personal daily urine output, and how warm you keep the house, this free, otherwise-flushed body heat amounts to between 6 and 25 grams of coal per person per day-- that is minimum of a kilo of coal per winter per person.

5) Ditch the toilet and build an outhouse. This is by far the best idea, but one which will be noticeable not only to family and houseguests, but also to the neighbors and city health inspectors. So it's a bit out of reach here. But if you live in the country, consider it.

22 Comments:

Anonymous Anonymous said...

As a fellow inhabitant of smallish-city, I've been enjoying your comments on heating. You're putting some thought into a subject that for many of us is ignored. Keep on going!

I am struck by your post on the water in the toilet tank. It feels like something's wrong there. Maybe it's just because I've never thought about that particular heat sponge before.

12/8/08, 1:55 PM  
Blogger Johanna said...

Hey, I know who started the crackpot labeling, I do believe you took fairly careful aim at yourself there. Besides, who does not like a non-threatening crackpot in the neighbourhood? (aside from, presumably, the people who would have to share your cold house and smelly bathrooms)

It does, however, amaze me that you have - several times now - dismissed certain technologies as "too expensive" (higher efficiency dryers, low flow toilets, increasing insulation of home, newer furnace) - given your obvious prowess at the calculations, you could include how long it would take to recoup the investment. Include incentives (if you have them - for instance, I was exempted from provincial sales tax based on the energy star rating of my washing machine) and various scenarios (how is your water metered? do you have smart meters for electricity?)

Might distract you from the Salvation Army bell ringing...

12/8/08, 2:09 PM  
Blogger Turboglacier said...

P.S. For skeptics, and to check that my math is right, I present the following work-through example, in metric:

A toilet with a 16-liter tank, flushed three times a day, in a 20C room, with cold water coming in at 9C.

One kcal of heat warms one liter of water 1˚C. So to warm one tank of water to room temp, you need to supply (16L)*(20˚-9˚) = 176 kcal.

To warm three tanks a day, you need 176 * 3 = 528 kcal.

1 kcal = 0.001163 kilowatt hrs. So 528 kcal = 528 * 0.001163 = 0.614 kWH.

1 kWH = burning 1,000 watts for one hour = burning 42 watts for 24 hours.

So 0.614 kWH = 42W * 0.614 = burning a 26W light bulb for 24hrs.

Producing 0.614 kWH of electricity in a powerplant with 30% efficiency requires 0.614/0.3 = 2.05 kWH of heat per day from burning coal.

Coal contains about 8.14 kWH per kg. So you need 2.05/8.14 = 0.25kg of coal per day.

Alternatively, if you're heating with an oil furnace for 180 days per year, and the furnace has 83% efficiency, you will need (0.614 kWH/day)*(180 days)*(1/0.83) = 133 kWH worth of oil for the season.

Fuel oil contains about 11.6 kWH per liter. So to get 133 kWH, you would go through 133/11.6 = 11.5 liters of oil per winter.

These numbers come out pretty close to the approximations in the post...

12/8/08, 2:29 PM  
Blogger Turboglacier said...

Okay, fair point about improved technology Johanna. So, I priced new low-flow toilets. They are in the range of $500-$800 each. So replacing both toilets in the Palace would be, roughly, $1,200. Assuming I didn't hire someone to do the work. Plus about $25 to dispose of the old toilets at the dump.

These toilets use about 1.6 gallons per flush, instead of my current 5 gallons. So, a 2/3 savings on the annual toilet-energy bill. Under the housemate/warm house scenario, that's a savings of $12.03/year.

The water and sewer savings are actually much more valuable. At our (roughly) 2¢/gallon charge, the usage reduction saves $192.72/year on water. So, the total is $204.75/year.

Which means the new toilets would pay for themselves in $1,225 / $204.75 = 5.98 years.

Of course, if I put the $1,225 in a 4% CD for six years instead of buying toilets, it would be worth $1,550... so make that more like 7 years to get a full return on investment.

12/8/08, 2:49 PM  
Blogger C Neal said...

I love the crackpot posts. And I submitted this one to Treehugger.com - brilliant. I'd never thought about toilet water as a heat sink before.

Another idea: use and flush the toilet right before a hot shower. The cold tank can absorb some of the heat from the steamy shower and retain it, instead of letting it escape elsewhere.

12/8/08, 2:49 PM  
Blogger brushfiremedia said...

Pretty much every toilet on the market now uses 1.6-1.8 gpf don't they? A quick search online turns up low-flow toilets for as low as 177 each.

No need to pay for disposal. Leave them on the sidewalk and they will be gone by morning. Yes, a bit gross, but also true.

12/8/08, 3:04 PM  
Blogger Johanna said...

You do not earn your crackpot label after all. A true crackpot would decommission the downstairs toilet, thus taking advantage of the same amount of savings and recouping investment of only one new toilet in under three years. Not to mention increased savings of a dual-flush toilet, since am assuming that current data were collected without the mellowing rule and thus the majority of flushes would be in the 0.9 to 1.1 gallon range. I see lots of said toilets advertised for around $300. Also not accounted for in your calculations are rising water/sewer costs over time. I see these are projected as a *minimum* of 3% increase per annum for your location.

12/8/08, 3:10 PM  
Blogger Turboglacier said...

Rebuttal:

Okay, the toilets I priced were more on the industrial-strength end, stored pressure to blow the water down the chute. Some of these gravity-based low-flow units I've encounter have been rather underpowered, so to speak. I want a reliable flush.

Yes, I forgot altogether to mention sensibility of dual-flush toilets. Because I've yet to see one in this country. Apparently, they are a European idea which leads to Socialism, so we're avoiding that.

12/8/08, 3:17 PM  
Blogger Turboglacier said...

And P.S., J.-

Decommissioning the downstairs toilet would not be the best approach, since it is the colder of the two bathrooms. I am, rather, trying not to use the upstairs toilet...

12/8/08, 3:20 PM  
Blogger brushfiremedia said...

Yes, the dual-flush units don't seem readily available here. I tried to source one locally in the smallish-city during my recent bathroom renovation. No luck.

12/8/08, 4:02 PM  
Blogger brushfiremedia said...

Oh, and I just want to say that crackpot or not, I too appreciate the continued crackpotish posts. They're definitely great food-for-thought.

12/8/08, 4:03 PM  
Anonymous winst said...

Of course the better way of dealing with the energy waste from draining heat-bearing water is to use a drainpipe heat exchanger.

12/9/08, 9:26 AM  
Blogger Turboglacier said...

Winst-

I don't think that would work very easily with this "application". Given the speed with which a large volume needs to be delivered from the tank to the bowl to do the important work, I can't see how one could effectively fit a heat exchanger in that part of the system. And given large-diameter nature of flotsam and jetsam leaving the toilet bowl, it seems to me that putting a heat exchanger the sewer-line end would also be problematic. Unless you first ran it through a macerator pump. But now things are starting to get nasty.

12/9/08, 9:38 AM  
Anonymous Valerie said...

Hey, can you come over to school and teach the kids how to do math? This is exactly the thing to show them how math relates to their everyday lives! Or something.

12/9/08, 3:39 PM  
Blogger Heather said...

I love the crackpot posts. Keep 'em coming. It's a blog. That's what blogs are for!

12/9/08, 9:30 PM  
Anonymous Anonymous said...

sir, you are not a crackpot but a hero. i keep the thermostat at 50 at a location further south and am embarrassed to say i turned my heat on way back in november. i am weak.

12/10/08, 12:06 PM  
Anonymous brewman said...

Simple Solution - Just In Time Fill (tm)

Wait to fill the tank until using the toilet.

12/10/08, 8:23 PM  
Blogger Turboglacier said...

Brewman:

That is total genius. Yes, that IS the solution (though it also IS crackpot.)

Ideally, every toilet should have three buttons: Big flush, small flush, and FILL. You don't push FILL until you're about to make use. Fantastic.

12/10/08, 8:42 PM  
Blogger Heather said...

Anyone have contact at Kohler? We gotta get you a patent on this, TG.

12/10/08, 8:50 PM  
Blogger David Andersen said...

One question, which you can verify experimentally: Are you sure that the water actually reaches room temperature by the time of your next flush? It's tough to compute this theoretically (depends on the surface area and the airflow), but it's easy to just measure the water temp, er, just *before* making use of the facilities. I bet you'll find that it doesn't actually warm all the way up - particularly when there's a larger difference between the temperatures or a shorter cycle time between uses.

Okay, I'll remove my geek hat now.

12/13/08, 11:29 AM  
Blogger Turboglacier said...

David-

I wish I could report empirically on this, but have not been able to do gather the data-- because these days my bathroom is colder than my toilet tank water. And I'm not going to warm my bathroom up to 70 F just to perform the experiment.

Maybe a reader with a warm house could try it, though, and report results? Here's my prediction: I'd say if you have a bare ceramic toilet tank, holding about 4 gallons, and the difference between room temp and incoming-cold-water-temp is 20F, that within two hours of a flush the tank water will be within 5F of room temp.

(Note: much of the water refilling the toilet tank will have been previously sitting in your pipes elsewhere in the house, and so may already have done some of its warming. To get the best data, you need first to run a cold water tap long enough to see what at what temp the water enters the house-- use that for the comparison with room temp.)

12/13/08, 11:51 AM  
Anonymous Pop said...

Here is a double saving: We used to keep a bucket in the shower to collect water during showers. Then we poured it right into the toilet (not into the tank) to flush it. It generally works. Water is very expensive here, so two savings. Plus having a few pails of water in the bathroom must have increased the relative humidity a bit which is good in the winter.

12/15/08, 1:11 PM  

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