Scaling Problem: House Size and Heating Bills

December 25th, 2014 by Potato

There was an article in the Globe & Mail a while ago claiming that it’s best to go with a smaller house because the bigger the house, the bigger the associated bills. Ok, that makes perfect sense.

But then it went on to claim that “it would seem reasonable to assume that it would cost twice as much to heat (or air condition) a 3,200 square foot home than it would one that is 1,600 square feet. But, as reasonable as this seems, it’s incorrect; it actually costs more than twice as much. […] Circumstances vary, but it can cost up to three times as much or more to heat and cool a home that is only twice as big.”

Now that just doesn’t make physical sense to me. We all know how scaling laws work: assume you have a spherical house, then the surface area will scale by r^2, while the volume will scale by r^3.

Ok, we don’t live in spherical houses, but still, this guy’s math must be way off. So I thought about it, and scaling with houses is actually a problem without any clear answer. Let’s set aside the complications like your own body heat or the waste heat of your home server farm (everyone has that, right?) and just talk about heat loss through the outside walls: even narrowed down with all that ceteris paribus it’s still a tricky question because houses are not spherical.

The simplest case I can think of is to take a cubical house. It has 6 unit surfaces: the roof, floor, and 4 walls. Now if you make that house twice as big by adding a second storey, the roof and ground floor are the same, and you’ve doubled the size of your walls (8 unit-walls). So doubling your floor space was less than doubling in your heat transfer area: only 1.67 times as much.

There are other ways to double the size of a house. You could go longer: expanding your floor plan from a unit square to a 2×1 rectangle. You only save on one shared wall between the unit squares in that case, so you do nearly double the outside area: 6 unit walls facing the outside, 2 floors, 2 roofs… but that’s again a 1.67 times increase (though more roof and floor with fewer walls added). Oh yeah, that’s just the first case turned sideways.

If you want to go crazy with shapes you could try find a way to get really inefficient. If you built a really long house (or made a C-shaped house to fit it on the lot — same difference for walls) that was 5 times as big as our unit square house, then it would be 3.67 times as costly to heat… wait that’s still going in the way I thought it would, with bigger houses being more costly, but scaling less than the increase in space.

In fact, the only way the author’s math works out is if you do non-apples-to-apples comparisons, like one house at 1,600 sq.ft. with 8’ ceilings and one at 3,200 sq.ft. with 16’ ceilings to drive the volume up but not the livable space measured in square feet. Or maybe it comes down to one of the complications I ignored, like floors and walls being roughly equivalent in terms of heat loss… but I doubt it.

He does mention more windows and doors just after the part I quoted, but again that doesn’t make sense to me. Yes, I lose more heat through my door than through a solid wall, but my house has two doors. A slightly bigger house would still have two doors. My parents’ house, which is maybe 2.5-3 times the size of our house, does have four doors, and my friend’s parents’ house, which is in-between, has three. But again, the number of doors are not scaling up faster than the increase in the size of the house. And the portion of the walls that are windows is not really any different with the bigger house.

So I will conclude for now that yes, a larger house will cost more to heat and cool, but it’s likely to scale less than the difference in size, because math. Fortunately, the massive building boom of recent times means that somewhere out there are a few developments with good test houses, ones built with the same insulation and materials and styles, but to different sizes. If anyone has some experimental data to back up (or refute) the spherical house reasoning, I’d love to hear it.

Ridiculous Article on EVs

January 12th, 2012 by Potato

Netbug sends along this opinion piece on electric cars after discussing it with his family, saying “I’m sure the math is sound, but I think he’s missing the point… Can you refute the article articulately or am I way off base?”

I’ve only read it twice, but I’m sure he’s missing the point. Moreover, I’m not sure the math is sound. He uses a particularly bizarre way of figuring the cost/savings of EVs, and even then gets his figures wrong.

Let’s start with his assumptions about fuel economy for gas cars. Note that he does not spell them out. To maintain consistency, through most of this I’ll be using US units, figures, and data sources.

A CAFE compliant new car will offer an average fuel economy of 33.3 mpg while a CAFE compliant new light truck will offer an average fuel economy of 25.4 mpg.

Well, right off the bat, that’s untrue. CAFE is not a measure of any particular car, it’s a fleet average, and it includes the contribution of electric vehicles and hybrids (plus some voodoo about ethanol credits). Moreover, it uses a modified scale/test procedure: 33 MPG for CAFE terms is more like 25 MPG on the current EPA test, and even lower real-world. Look up the EPA ratings. I picked a Ford Focus (compact car): it’s at 28 MPG combined. Even compact cars aren’t at the numbers he’s using. According to Natural Resources Canada, the average fuel consumption of the current light vehicle fleet is just under 11 L/100km, or 21.8 MPG.

Now, there is room to quibble there: that’s for a range of cars from new to 10+ years old, whereas new cars will be slightly better. Still, your comparison car is not going to be getting 30 MPG, and especially not when you consider that you should be comparing to the city mileage since EVs are for urban settings.

At 30 mpg, the owner of a new light duty vehicle will consume about 420 gallons of gas per year

He didn’t go through his math, but let’s go backwards: 420 gallons * 30 MPG = 12600 miles/year. That’s probably a reasonable figure to use (I’ve seen 15k mi as more common, but that may just be a case of rounding to a prettier number; not sure what the figure is for those with daily driving commutes). At 22 MPG, that’s more like 572 gallons.

Then he goes to another paper, and somehow gets that electrification doubles the cost of the car (from $19k to $39k). That again is a pretty suspect analysis. For instance, a general rule-of-thumb is that the engine & transmission are 20-40% of the value of a car, yet that paper somehow found that the engine & transmission were just 13% of the cost of a gas car. Moreover, we can buy EVs on the market today that do not cost that much — the Nissan Leaf is “only” $35k (USD), the Prius plug-in has a gas engine and a plug-in battery, is larger and nicer than a $19k comparable car, and is only $32k (USD). Indeed, from looking at US manufacturer’s websites, a compact car with automatic transmission is more like $21k than $19k, and that’s still not adjusting for non-driving features.

The ultimate obscenity is that a conversion from gasoline drive to electric drive will not reduce the total amount of energy used in transportation.

This statement is unsupported by the author, and with good reason: it is patently false. Half the reason to go to electrification or hybridization is the efficiency gain: electric motors are just simply more efficient at turning chemical potential energy into kinetic energy than internal combustion engines. Plus, you can shift the source of that energy from oil to natural gas, hydro, or other renewables.

So, if we re-do his analysis with more realistic numbers (all US figures), we have that the incremental cost for an EV ($21k to $35k) is $14k. That’s saving 572 gallons of gas/year, or 14.1 bbl/yr, or 212 bbl/car lifetime. That works out to a cost of $66/bbl. Which is less than the current cost of oil. Now, this is not the method I would have chosen to make a comparison, but even using his analysis the point he’s reaching for isn’t made.

He also forgot a lot of factors that make EVs a better choice.

Direct financial ones like: Less mainenance cost (no oil changes, spark plugs, timing belts, water pumps, brake pads, etc., etc., etc.), lower fueling costs (oil is an expensive and volatile commodity).

Plus, environmental factors like: Less total pollution (even on a 100% coal power source, an EV is arguably cleaner than a conventional car, and most places are only a fraction coal-powered); pollution shifting (no more smog in city centres!); self-reliance (you can make your own electricity if you’re a doomer, whereas refining your own gas is hard; plus, the cars are quiet and good for sneaking up on zombies). And that efficiency gain.

So right now, going with an EV is close to break-even (though maybe just one the far side). You get all the nice stuff on top of that, but it’s also new, unfamiliar technology. That’s why the subsidies come in: to help make it not only better, but cheaper, to get the ball rolling.

I’m sure the author was cautious in his conclusion, pointing out that his back-of-the-envelope paper, pencil, and calculator analysis could have some holes, that it’s a bit of a strange approach to take (cost per barrel of oil offset?) and that EVs might in fact make some sense…

Electric drive proponents are selling a house of cards based on fundamentally flawed assumptions and glittering generalities that have nothing to do with real world economics. Their elegant theories and justifications cannot withstand paper, pencil and a four function calculator. Shiny new electric vehicles from General Motors (GM), Ford (F), Nissan (NSANF.PK), Toyota (TM), Tesla Motors (TSLA) and a host of privately held wannabe’s like Fisker Motors and Koda are doomed to catastrophic failure. Their component suppliers will fare no better.

Oh wow, he really got the whole foot in there, didn’t he.

Now, as usual, I’m not saying that EVs are going to suddenly take the market by storm: there’s a lot of range anxiety to conquer. They’re not suitable for everyone. But no car is. There are about 1.5M families in the GTA alone; of those, about half have 2 or more cars. I’d estimate that something like 15% of those have (or could easily have) one car that is largely used just for commuting within the GTA — in other words, there’s potentially a market for about 100k EVs in the GTA alone. It’s a niche, but a respectably large one; one that’s worth developing. The economic argument may not be a slam-dunk on its own, but it’s a far cry from a house of cards doomed to catastrophic failure.

Why MicroFIT?

December 13th, 2011 by Potato

I recently was pointed to Canadian Doomer’s site, where I saw this comment:

“Ontario Hydro is paying $0.80/kwh to those who sell them electricity on the MicroFIT program. But consumers are paying $0.05 to $0.10/kwh. This makes absolutely no sense, unless Ontario Hydro knows that they will soon be charging consumers MORE than $0.80/kwh. Look at your hydro bill and imagine it multiplied by 8.”

Well, no, it’s the price they have to pay to get solar off the ground. Very few people wanted to pay ~8x the price of grid power to buy their own solar panels, so the companies weren’t making panels, so the panels were expensive, etc… By offering enough money that PV would be profitable, it bootstrapped the industry, and broke the vicious cycle. The industry has already brought the price down by huge amounts (panels now cost half or a third of the price in just 3 years), and the government is going to cut microFIT any day now (they’ve already started dragging their feet with applications).

That lead CD to ask the follow-up question:

“Why does Ontario Hydro care so much about getting solar off the ground when they’re not making money on it?”

The short answer is that it’s because it’s the right thing to do.

The longer answer is to first up realize that Ontario Hydro is not an independent company: this isn’t Capital Power or Emera or Fortis offering money to install panels, it’s the government. And sometimes the government subsidizes things for social rather than strictly economic reasons.

Consider other breaks offered recently for green technologies:

The federal government was offering up to $2000 to buy a hybrid car, until just a year or two later, they changed their minds and took that incentive away. Many provincial governments (including Ontario) also offered rebates of several thousand dollars ($2k in Ontario) for hybrid cars (and similarly, no PST on bicycles). Those rebates by our government as well as others around the world — notably the US, which had various tax credits as well as other incentives to buy hybrids like free parking and HOV lane passes — were very helpful in getting this fuel-efficient technology off the ground. Hybrids are now reasonably mainstream, something like 4% of the overall passenger car market, and still growing quickly. However back 10 years ago, a hybrid was a very difficult sell: they were more expensive than a traditional car, there was a lot of uncertainty over how reliable they would end up being (a sentiment that still persists, even with over a decade of experience), how much they would cost to maintain… and all that was on the back of gas prices that were still measured in cents per litre. So those subsidies helped level the playing field until the cost of the cars and the price of gas brought us to where we are today, where $1.20/L looks cheap, and it seems stupid to buy anything other than a Prius. And while I tend to focus on how awesomely quiet my car is and the gas savings, the fact is that the gas savings is in part a side-effect of the hybrid’s original goal, which was to reduce pollution — an important social goal in an urban country.

So back to the solar subsidy: by guaranteeing a certain return on the panels, people became interested in purchasing them. The government could stand up and say that, for at least the next few years, there would be a certain level of demand for panels, which allowed panel manufacturers to go to their investors and raise money to build factories and invest in R&D to make more efficient and cheaper panel technologies, and basically got the whole ball rolling. Ontario and Germany really lead that area*, and factories really started churning out panels to meet the new demand, and to build capacity in the hopes that a certain superpower with a lot of desert would also decide to start subsidizing solar energy in the future (let’s call it “Nerizonda”). In just a few years we’ve gone from a world where you had to be an eco-nerd and know someone at NASA just to get a panel, to one where salesmen call up on a weekly basis to let you know how much the panels are on sale this week. Indeed, the build-up has been so rapid that now we’re facing a glut (exacerbated by Germany and other nations scaling back their subsidies for new projects now that they can declare victory), and panels can in some cases be had for below cost.

Now, the solar subsidy could have come in many forms: the government could have directly purchased the panels themselves, and installed them in parks or on government buildings, or even installed government-owned panels on private homes. They could have subsidized the purchase price directly. Instead, they chose this strange scheme that involved all the overhead of metering the panels, and making regular payments (or deducting from the power bill) for 20 years running. And that decision comes down to politics: the budget looks cleaner with a long-standing trickle of money for a program than it does with a big buy over just a few years, even if the total cost is the same. Furthermore, to give Dalton a little bit of credit for being political operators, there was going to be a big delay between starting the MicroFIT program and when the bulk of the payments would start rolling out the door, and in-between was another election. So for the 2011 election, hardly any microFIT payments would have shown up on the budget, and by the ~2016 elections, the program will have ended; off the radar either way.

It’s also important to note that there were several levels to the FIT program: for large commercial solar farms, the rate was less than half what an individual could get under the MicroFIT program. So from a “this is how much OPG expects power to cost in the future” point of view, that might be the upper-end figure to use. Why pay more for smaller systems? Several good reasons:

  • In part as an experiment. People have been talking about distributed generation for years, and the government wanted some data on what that would actually look like. Which meant that you had to find some way to get people to put some kind of generator in their homes, and test out how well the load-balancing and monitoring systems worked. So getting solar out there in particular was a bit of a bonus on that front.
  • In part to raise awareness. You can give money to a big corporation like Samsung to build a giant solar farm in the middle of nowhere, and accomplish your goal of bootstrapping the industry. But if you can get it on people’s homes they’ll see it every day, they’ll talk about it with their neighbours, and it’s also nice to pay your own citizens rather than a faceless corporation. From a political point of view, that also helps make it an issue you can focus on in an election if you want to.
  • In part for long-term efficiency synergies. A giant centralized solar farm is a great way to quickly get solar power on the grid if that’s your only goal. But one of the beautiful things about solar is that its nicely correlated with peak air conditioner demand: just as the sun is beating on your house is also when your panels are at their maximum output. That benefit could potentially go away if Toronto is getting sun while the solar farm on Lake Huron is experiencing clouds. Though you need more inverters and monitors, you don’t need any transmission capacity to be built or maintained, since the generation is right at the site of demand. And on top of all that, you get the synergies that come with rooftop solar: the panel itself helps to shade a house and keeps it cooler than a typical asphalt shingle, further reducing peak power demand.
  • In part for short-term inefficiencies. The fastest, most efficient way to get X number of panels installed and tied into the power grid is to go with a giant centralized solar farm: make braces and connect panels in assembly-line fashion in a consistent, controlled environment. You can even bulldoze any hills if you can’t find a naturally flat spot. But when you’re introducing a program in the middle of a recession, maybe you don’t necessarily want to be as efficient as possible, maybe you also want a little bit of economic stimulus for good measure: help create jobs for guys to crawl around roofs and take measurements and figure out where the bolts should go.

As for that central question of why? Well, because it’s a green, emission-free, renewable energy source. It has some side-benefits (correlated with air conditioner demand, cooling synergies), but also some negatives (inconsistent, extremely difficult to plan power loads with, expensive even after the cost reductions from recent investments). It has a good image, and getting to some single-digit percent of our power mix being wind and solar is something we can do a little chest-thumping over (never underestimate the importance of chest-thumping, it’s a trillion-dollar industry). Plus, innovations that are created for stationary solar may translate to other applications (space systems, remote self-sustainability).

* – I’m going from memory here folks, apologies if I forgot any other pioneers.

Tater’s Takes – Whale Poop and Fireflies

July 15th, 2011 by Potato

A new frozen yogurt place opened up called Kiwi Kraze, and they have the guess the weight of your sundae and get it for free deal. So I did, and I did :) That may have been related to the fact that despite officially moving the goalposts back from the “don’t gain” to “lose weight” objective now that vacation is over, I gained weight this week. Grrr. It may be because I had a number of real Cokes enter my inventory (free > calories).

Then there were a tonne of fireflies out tonight on my walk home. It’s truly magical once you realize you’re not having a stroke.

I’m starting to turn negative on my BB. I like the keyboard, and between email, calendar syncing, and the omnipresence of the hivemind, I’m finding a smartphone to be just ever so handy these days, but I think my next one might be a droid. I like BBM, and I want to be patriotic, but I really don’t know anyone who said “hey, I really miss the days of trying to carefully manage system memory in DOS. I wish there was a phone that let me relive that experience.” I’ve got 4 GB free for photos and music, I don’t know why my cache of 160-char SMSes and apps has to stay in the shallow end… Recently, my ringer just stopped working. The little message light would still flash, and most of the time the vibration would still go off to alert me to a call or message, but no audio. From searching online, this is a frightfully common problem with the BB, and there are a host of zany solutions, including turning it off and on, pulling the battery out (which is a different off and on), and yes, trying to clear out the pathetic amount of “application memory” available. Some combination of that and doing this to the part near the speaker ended up fixing it.

Random hilarious conversation snippets:

“What are wild Popples called? Armadillos?” I’m eternally amazed at how the mind works sometimes. Like when trying to think of an animal that balls itself up at a sign of danger, one goes first to Popples, and from there to their wild equivalent, armadillos (though I would have also thought Popples had a strong hedgehog influence). Actually, I’m amazed anyone remembers Popples at all.

Links:

A surprisingly good read on whale poop. (HT: Barry Ritholtz)

John Hempton describes the problem auditors of Chinese RTO frauds faced, that may let them off the hook: in some cases, the banks were in on it. If the banks have lost credibility, what are the implications of that?!

An excellent real-world application of Mathematica. Stupid brownie nuts. “I hate nuts in Brownies.” “Who does that?” “I don’t know, old people?”

The Globe has another article lamenting the limitations of electric cars, this time moaning that the cars can’t handle the all-day all-out testing of an automotive press junket. The author seems to be a bit misinformed, or got his tenses wrong: “pure electric vehicles will be glorified golf carts, useful for short distances, in good weather conditions.” Depending on what you mean by short distances, that’s true: they’re good for commuting within the city, but I wouldn’t count on one for trips to the cottage. But most families in urban areas have two cars (and pretty much all the ones with cottages do), so there is a market for an electric commuter as a 2nd vehicle. But I’m not saying anything new for you guys. Most outrageous was the closer: “The infrastructure necessary for the next generation of volume-produced passenger vehicles will determine their success. […] My money is on fuel cells and hydrogen stations.” I’ll take that bet.

Yet another bank housing analyst turns bearish on Canadian real estate.

And Canadian Business has a bearish article out as well.

A 3D printer using… chocolate. It makes so much sense: it’s a self-binding polymer-type product, so it can form complex 3D shapes (like bunnies), and is well-suited to being put down in layers. Plus, it’s chocolate!

Tater’s Takes

May 30th, 2011 by Potato

What a crazy couple of weeks. This last week in particular featured back-to-back all-nighters as I tried to finish my thesis revisions. The crazy thing is the revisions weren’t even that bad, I just have enough trouble writing the fluffy bits that go around the sciency bits the first time around, and re-writing them seems to completely drain me. Since this week was largely fuelled by my discovery of delicious home-made onion rings, I’m afraid to even step on a scale to see where I’m at now. Anyway, it’s over, the latest revised version is out of my hands, and I just slept 24 of the last 30 hours; feeling much better now. I’ve got the penultimate exam to study for now, and hopefully a week of working out to make up for the weeks featuring dozens of hours in a chair per day…

On with the links!

The Neurologica blog has a few neat posts, including a follow-up to the CBC Marketplace report on homeopathy. A homeopathy advocate complained to the CBC, but their review found that the report was fair. “The achievement of balance does not mean mathematical equivalence; rather, the important principle is that different views are, in the words of the CBC policy, “reflected respectfully.” Also, a post about human echolocation.

A pair of articles in the Financial Post on condo speculators and using the housing bubble to sell out and fulfill your dreams. I know a few people my parents’ age who realized in the last few years that they could sell their house and retire off the proceeds if they moved even just a little ways outside the GTA. I’m surprised it hasn’t been more.

Google’s using its search data to discover interesting trends, such as uncovering the spread of flu-like symptoms. There are a lot of other possibilities for the correlation of search terms with real-life events, like getting a leading indicator of unemployment.

The CDC has created a clever page to use the threat of a zombie plague to inspire disaster readiness for more mundane emergencies.

Via BoingBoing, an interesting case in Texas on radiation in the drinking water, and the implications of margin-of-error. On the one hand, I can see the rationale for using the most liberal interpretation of the stats: who wants to tell a bunch of Texans that there’s slightly elevated levels of radioactivity in their drinking water (less than the margin-of-error above the limit), especially if the regulatory thresholds are set conservatively anyway. But, it’s not proper to consistently subtract the margin of error like they did. That’s the most optimistic interpretation of the data, but not actually the correct one. If it was a one-off reading, you could perhaps make that argument, but when it consistently happens then no, you know that the “true” value you’re measuring is indeed above the threshold.

Germany has decided to shut down nuclear power by 2022. I find that surprising: that’s a big shift to make in a deceptively short time period. According to the article, 23% of Germany’s power came from nuclear prior to the Japanese tsunami. In the wake of the fear that followed, Germany promptly shut down its 7 oldest reactors, and I’m surprised to see that sentiment following on for so long to have this much impact even on their newer reactors. 23% is a lot of power to have to find elsewhere. For comparison, roughly 8 years ago Ontario vowed to shut down our coal plants within 5 years, and it was a challenging goal to meet — indeed, the goalpost was moved to 10 years down the road pretty quickly (2014). We’re pretty close here in 2011: 8 of 19 units have been shut down, and the remainder are seeing less utilization. And coal was just about 20% of our energy mix before the phase-out. So the Germans have some pain ahead of them, and some hard choices: what on earth are they going to use to replace that much baseload power? Or will they have to pick one fifth of their things to turn off when the brownouts and rolling blackouts threaten?