Super insulate your hot water tank

Perhaps you’ve seen them… those insulating jackets for wrapping around a hot water tank to reduce heat loss. Do they work? Yup. Are they worth it? Maybe. But can you do better? Definitely. In this article I want to demonstrate that it usually makes sense to add MUCH more insulation around a hot water tank than you might otherwise think.

Is there such a thing as too much insulation? If so, how much is too much?

Yes, there is, and it can be defined as follows: If adding more insulation costs you more than it saves you over a tolerable payback period then it’s too much insulation. You can think of “cost” in terms of dollars or in terms of environmental footprint depending what your concerns are. Assuming you’re primarily interested in saving money, it’s fairly easy to estimate what you can save by adding more insulation to a hot water tank. A typical electric hot water tank may consume around 250W of continuous power on average. Over one year that amounts to 2190 kWh of energy. Where I live electricity costs about $0.07 per kWh so a typical electric water heater with no additional insulation might cost about $150 per year to operate. Depending on use, perhaps $50 of this is actually used to raise the temperature of the incoming cold water. The remaining $100 is wasted in the form of heat dissipation to the surroundings.  A typical electric hot water tank may have about 5cm thickness of fiberglass insulation built-in. Assuming you will be insulating the outside of the tank with a similar material, the power consumption to maintain a given tank temperature will be inversely proportional to the total insulation thickness. So if you add another 5cm of insulation, doubling the total thickness, you will half the cost per year to maintain the tank at temperature. With a little math, it’s not difficult to figure out how much insulation can be added to achieve payback within a certain number of years.

Algebra is your friend

Let’s define some variables:

T = original insulation thickness (cm)
A = original cost of dissipated heat ($ per year)
C = cost of adding T cm of new insulation ($)
Y = payback period (years)
F = thickness of additional insulation (cm)

What we want to know is the maximum insulation thickness F that will payback within Y years? This is the thickness at which the cost of the insulation exactly equals the savings in the the first Y years (ignoring the cost of your own labor).

Cost of insulation = CF/T
Annual cost to operate (before) = A
Annual cost to operate (after) = AT/(F+T)
Savings after Y years = YA(1-T/(F+T))

Setting the cost equal to the savings yields

CF/T = YA(1-T/(F+T))

Solving for the thickness F (trust me on the algebra) yields

F = TYA/C - T

Now let’s pick some reasonable values

T = 5 cm
A = $100 (Assuming $150 total per year, $100 of which is waste heat)
C = $20

Substitution into the formula yeilds

F = 5*Y*100/20 - 5 = 25*Y - 5

So if you want payback within 1 year, you can splurge on up to 25*1-5 = 20 cm of insulation (about 8″ thick). Add any more than that and your costs would exceed your savings in the first year. If you can tolerate payback within 2 years, add up to 25*2-5 = 45 cm of insulation (about 18″ thick). Does this seem like a lot? It certainly is when you consider most water heater blankets sold for the purpose are only around 4 or 5 cm thick (2″) at best. But it makes sense. Essentially what it means is that adding insulation is cheap compared to the cost of wasted heat. Given that a 4 or 5 year payback isn’t unreasonable this analysis seems to indicate that for all intents and purposes there basically is no such thing as too much insulation for a hot water tank. It makes economic sense to fill ALL the available space around a hot water tank with insulation.

Some caveats

  1. If your hot water tank is located in a heated area of your home, then during your heating season, the heat dissipated from your tank is not wasted. It heats your home. You will pay for the same amount of heat whether it is produced by your hot water tank or your heating system. Therefore, when you calculate A above, you should only consider the period of the year that you are not heating your home. My hot water tank is located in an unheated garage, so any heat it dissipates is wasted regardless of whether I’m currently heating my home.
  2. If you have a gas hot water tank with a continuous pilot flame and an open flue, your savings from insulating will be much less than predicted above. This is because the main source of heat loss in such a tank is not through the outside walls of the tank but up the chimney. I converted my gas hot water tank to electric both because I wanted to reduce heat loss up the chimney and because I wanted to run the tank on a timer. A side benefit of the modification was that I could benefit more from super insulating the tank.
  3. To simplify the calculations, I ignored interest. Including interest would decrease the calculated thickness for any given payback period. The longer the period, the greater the discrepancy. However, even with a 4 year payback period, the error is probably only around 10%.

It might not be pretty but it works

I purchased a batt of Roxul insulation for about $35. This is about the same price as some insulating blankets designed specifically for hot water tanks, but it is enough for about 12″ of insulation around my tank which is more than 5 times what you would get with an insulating blanket. The images below sho before during and after insulating my hot water tank.

Warning! It’s best practice to use only non-flammable materials for insulating any heating appliance. Fiberglass or rock wool batts like those used for insulating walls are a good choice. Sleeping bags, quilts, newspaper, etc are not.

Although these images show what appears to be a gas hot water tank, I must emphasize that it is not. A gas hot water tank cannot be insulated on all sides like this since it would interfere with draft and could result in poor combustion and possibly carbon monoxide poisoning. I converted this tank to electric precisely so I could insulated it well and put it on a timer. For more information on the conversion process read Convert your gas hot water tank to electric. Running the tank on a timer had already reduced its energy consumption considerably. With the additional insulation I was able to reduce “on-time” of the heating element from 6 hours per night to 3 hours per night. It’s currently winter and the garage is cold. Last summer, I operated the tank only 3 hours per night without any additional insulation. I imagine this summer I will be able to reduce the on-time to around 2 hours per night. The heating element is about 520W. The reduction from 6 to 3 hours of operation per night corresponds to a reduction in average power consumption from 130W to 65W, or a savings of 65W. The savings will be less in the summer, since less power is required then anyway, but over an entire year, savings will likely be in the ballpark of 350 kWh or about $24 at $0.07/kWh. I know what you’re thinking. That’s not much, but within the first two years it is enough to pay for the cost of the insulation which validates the above calculations. The savings would be greater if not for the fact that I already modified the tank for high efficiency operation on a timer.

Despite appearances, I’m growing fond of my “frankentank”.

Update (Nov 18, 2009) What about optimum insulation for a house?

A couple people have inquired about how the same type of formula might be applied to determine the optimum insulation for a house. A house has the added complexity of different insulation thicknesses for attic, walls, basements, crawlspaces, doors and windows, and three modes of heat loss: air leaks, conduction to the air, and conduction into the ground. It also has another mode of heat gain: solar. The lifetime of a house is also much longer so it makes sense to consider interest rates and potentially increasing heating costs. Let’s make some gross assumption to simplify the problem. First, let’s assume solar gain and losses into the ground cancel each other out exactly so we can ignore them. Second, lets assume interest (which is an incentive to keep your money in the bank) and rising heating costs (which is an incentive to spend your money on insulation) also cancel each other out exactly. Finally, to avoid the issue of different insulation thicknesses, rather than calculating an additional thickness F, let’s calculate a thickness ratio R of the new thickness to the original thickness and assume we change the insulation thickness by the same ratio everywhere (including doors and windows which may not be practical but makes the math a lot easier). Doing a little algebra we find:

R = (F+T)/T = F/T + 1 = YA/C

C represents the cost of the original insulation. Let’s take my home as an example. My walls are 2×4 studs with R13 insulation. My attic is 2×6 joists with R19 insulation (soon to be increased to R47). I estimate the cost of insulation in the walls (including lumber, doors and windows since those costs will all increase to increase the effective insulation thickness) is about $6/m2. I estimate the cost of insulation in my ceiling is about $3.50/m2. My house has a wall area of about 350 m2. The ceiling area is about 200 m2.  So my total original cost of insulation is C = 350*$6 + 200*$3 = $2700.

A is the original cost of heat loss through the insulation per year. I spend about $1100 per year on heating. Of that I expect about $350 is due to air infiltration. Adding more insulation won’t help with that, so my original cost of heat loss through the insulation is A = $1100 – $350 = $750.

Y is the acceptable payback period. Let’s assume we want payback within 25 years, so Y = 25. Substituting those numbers into the formula yields

R = 25*750/2700 = 6.9

So based on this formula if I were building my house from scratch and I could wait 25 years for payback, I would do well to make the walls about 7 times thicker than they are and add 7 times more attic insulation than I currently have. That would put the walls at around R90 and the attic at around  R133. So it looks like my house insulation has MUCH less than a 25 year payback period at today’s heating costs. Perhaps it is closer to a 4 year payback. I suspect that based on fuel prices when the house was built it may have had a 10 year payback.

Where I live, the minimum recommended insulation for new construction is for R20 walls and R40 ceilings. Based on my estimates above that might offer around a 10 year payback. The suggested insulation for an energy efficient home is for R40 walls and R60 ceilings. Based on my estimates above that might offer about a 15-20 year payback. From a moral standpoint, the insulation will last the lifetime of the home, so it makes sense to use a payback period equal to the lifetime of the home, even if you don’t expect to live there that long. In that case even the suggested insulation for an energy efficient home seems insufficient since most homes last longer than 20 years.

Anyway, I am sure that not all my assumptions are valid. In particular, depending where you live and how well your home is designed for passive solar heating, it’s likely that solar gain may be significant compared to losses into the ground. But I hope I got my main point across: the optimum amount of insulation depends on what payback period you can tolerate.

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29 comments on “Super insulate your hot water tank

  1. Interesting results. It would be neat to see a similar calculation for the optimum amount of insulation to use when building a house. I bet if you target a 10-15 year payback, it probably makes economic sense to put 1 to 2 ft of insulation in the walls and 2-3 feet of insulation in the attic. Of course the cost calculation would also need to factor in the additional lumber and the reduced square footage of living space due to thicker walls. Great post.

  2. Hi Pondered. Thanks for the comment. That is an interesting idea. Depending on the size of the home, the climate, weather-tightness, I think you might find that the optimum insulation thickness is reached more quickly in the case of a home than in the case of a hot water tank. This is because in the case of a home there are some free heat sources: solar gain, occupant body heat, lighting and other electrical appliances. At a certain insulation thickness, the cost of heating will drop to zero. I haven’t done the math to figure out what that thickness might be for a typical home, but I do recall reading an article about a person in eastern Canada who built a passively heated solar home with 11″ of insulation in the walls and he found he paid $200-$300 in heating bills per year. He built his walls as a 2×6 framed inner wall and another 2×6 framed outer wall, with the studs out of phase. He also used a continuous, unbroken vapor barrier between the two walls, with all electrical and plumbing routed on the inside of the vapor barrier, resulting in an extremely well sealed building envelope.

  3. very interesting info here, i am always in favor of messing with basic and mass products to maximize gain and efficiencies. The transformation of the gas heater sounds quite rigged tho, i am not sure if i would be comfortable with a bent up old element as my heating element which may short out on the inside of the tank. Also if you super insulate a gas hot water tank, care must be taken to not impede the air intake and outlet where heat and flame may pose a fire hazard. i in the past superinsulated a very small electrical tank and it used next to NO power at all. I used a vapor barrier and cardboard to hold the insulation reasonably consistently around the tank. Cardboard makes a wonderfully fitting cover for the insulation batts but again, watch the flame/fire hazard.
    Nice work, impressive and highly useful for those of us able to rig things, kinda dangerous for some who THINK they are Mr. Fix-it’s tho, lousy craftsmen, keep clear and don’t burn down your families!! Admit if you are NOT that guy and keep safe. Thanks for pursuing this info at a time critical for our planet to reduce energy consumption, wake up North America, it’s time to do this type of stuff!!

  4. Hi Markus,
    The bent element is surprisingly robust. I think if you experienced the bending process and held the final result in your hands you would have more confidence in it. The likelihood of a short seems no greater than in it’s original application as a stove element. Steel pots are used on these elements all the time, with a danger of electrocution to any person touching the pot if the element ever shorted out so I think these elements are designed to be quite safe in that regard.

    I don’t recommend super-insulating a gas hot water tank (with open flue) unless you first convert it to electric and cap the flue as I did. The dangers are much greater (explosion, fire and carbon monoxide poisoning) with a gas tank, and the gains from adding insulation are much less since several hundred watts are dissipated into the tube at the center of the tank and up the chimney regardless of how much you insulate the outside of the tank. This loss cannot be eliminated without capping the tank (which cannot be done safely while it is operating on gas).

    Thanks for your comments.

  5. Do you know of any similar tests for wall insulation? I want to build a new house with 10″ think walls and as much insulation as I can get. My assumption is that a well insulated wall and ceiling will pay for itself in low heating / cooling costs and inert insulation requires no maintenance during the life of the house. My builder ( and several friends) say that insulation will only go so far. Once you have insulated to around R 40 in the ceiling and R20 in the walls, you loose any advantage.

    That does not make sense to me. But does anyone actually know the optimum amount of insulation to install?



  6. Hi Dan,
    You’re right to question your friends and builder. 10″ walls will definitely reduce energy consumption. It’s just a question of how long it will take for the additional cost of insulating to be payed back in reduced energy costs.

    Because insulation lasts for the lifetime of the home, the “moral” choice is to design for a payback period equal to the lifetime of the home. I don’t know for certain, but based on my calculations it seems that recommended R-Values (R20 walls and R40 ceilings) are based on about a 20 year payback. If you expect your home to last 40 years or more, you could double the recommended R-values and still achieve payback over the lifetime of your home.

    I added some more information to the original article since a couple people have asked about home insulation. Thanks for your comment.

  7. There are a few other factors to consider.If you are in a climate where you use the heat more than the air- I refer to actual balance of heat- not time. you are not saving as much. Also, depending on if your heat system is an exchange system or pure electric. In a house with heat strip heating and electric heater(and heater is running), you save almost nothing as long as airflow is good and the WH is not up against an outside wall. I live in FL so, insulation helps in 2 ways- lower water heater cost and lower cost on A/C since it does not have to cool the extra air the WH is heating. I have a heat exchanger that gets the water hotter than the electric as long as the air is on . The WH is unplugged 8 months of the year and the water is super hot all summer. The water(even at 120)is able to remove much more heat than the 95 degree air outside, which in turn lowers the A/C portion of the bill!

  8. To be considered when building a new home or upgrading an old home:
    Super-insulate the home enough such that the capital cost of the heating/cooling equipment is drastically reduced.

    If you don’t need a heater/cooler, you can save thousands on capital cost and instead ‘pipe’ it into insulation costs. The best news is that there is no running cost for insulation.

  9. I’m in the market for a new hot water tank, and would like to switch from propane to electric so that I can not only super-insulate, but also preheat with solar. I have tons of sun shine almost year round, and my chief goal would be to be able to keep that water hot enough throughout the night as to be able to shower in the morning, and replenish the tank with hot water from the roof during daylight hours (still in the planning stages, though). Thanks for documenting all of this.

  10. I inherited an 80 gallon electric hot water tank when I bought my house (in your general area, specifically, Seattle).
    Sounds like you’ve seen the inside of a hot water tank, so I’d like your opinion regarding what would be involved in converting this tank to a 50 gallon capacity, which is all my wife and I probably need. My guess is I’d simply have to disable the top heating element (leaving the bottom one enabled), and install a new water-level sensing switch to cause filling to stop at the desired height. What do you think?

  11. Hi Tim,
    There is no water level sensing switch in a hot water tank. The tank is always completely full of water, so modifying it as you described is not possible.

  12. A compairson would be awesome.
    taken over 2 years.
    First year you put on a KWh mesurement thingie on the powerplug, and a KWh mesurement on the wateroutput aswell. Then from januar 1’st to januar1’st you can see the input/output and the loss of the tank.
    year 2 you do all the same all over bu with you’r superinsulation :D
    Would be nice to actuarly see numbers.
    Keep up the good work

  13. I think you need to check your numbers. If your attic is 200 m2, which is reasonable, then your walls must be approximately 14m on a side or a total of 56 linear m. If you have 1200m2 of wall area, your house is 21m high or 7 stories.

  14. But remember insulating your hot water tank alot will make the wires inside the tank get HOT and could cause a fire!!!

  15. @ Noirceuil, Thanks for being on the ball and checking my numbers. You are absolutely right. I’ve updated the post with a wall area of 350m^2 (60m perimeter by a little under 6m high). The new results suggest much more insulation is worthwhile. Thanks again.

  16. Hi Rob,

    As far as I know there are some considerations when insulating pipes.

    Basically as the diameter of the insulation increases the outer surface also increases which means there may be some point at whith the insulation is counter efective :).

    That also means that for very small diameter pipes no insulation is the best solution.

    When I have first heard that it sounded very unintuitive, but then I have found some information about that on the internet.

  17. hi Rob,
    Thanks for the interesting article. I will have to think about it more.

    Frequently when reading references to adding insulation to a water heater, the first step is “put your hand on it and see if it is warm”. If it is, further insulation is of no value. I usually stop at that point, but now I’m wondering if that is bad information. (my water heater is an 80 gallon one, in a somewhat heated basement. It actually feels cool to the touch, so seems unlikely it is losing much heat thru the walls. Oh, I have the water temp set to the lowest, about 120 degrees, and the heater was a more efficient one 12 years ago when I purchased it. Due to be replaced within a few years.) One nuisance with being scientific with a water heater is that it isn’t easy to see how many watts it is using; can’t plug it into my Kill-a-watt.

    Oh, I can provide some info on superinsulating a house. I can’t provide any calculations, but suspect your figures of R80 walls and R133 ceilings are excessive. (perhaps look at passivehouses, I think they use less insulation and still require no heating input) I would guess more like R60 and R80 would be cost effective. Also, I just scanned your calculations, suspect you didn’t add in costs for materials to contain/support the insulation. Guess it depends on what material you use, cellulose would require a wall, maybe foam wouldn’t.

    I speak from some experience here, I built a double wall superinsulated house in 1984, and have been living there since then. But mistakes were made, I’m still trying to improve things. I used two 2×4 walls, set about six inches apart. Fiberglass insulation batts, let’s see, it must be about R45 (R13 + R19+R13). There is a continuous vapor barrier just outside the inner wall. At least it was continuous when installed, seems like I have been punching holes thru it for 25 years. Ceiling is about R60, fiberglas attic batts topped with several inches of cellulose.

    Wall thickness is a good/bad item. Our windows are set at the outside, so we have big windowsills (about ten inches). Nice to put plants on, etc. But if you are off to the side of a window, your view is reduced due to their thickness.

    I can’t report good numbers on my house. I had actually hoped it would be passive, not needing any heat. But it was built over time, so for the first 15 years we didn’t have the inner wall insulated (nor drywall). We started with a woodstove heater, but grew tired of coming home to a cold house. Eventually installed a geothermal waterfurnace. The house has consistently used more energy to heat than calculations predicted. (In Michigan, we thought it would be ~$200 per winter) Again, this is hard to calculate, since all the electrical use is lumped together, maybe it is using $900 per winter, with today’s electric rates.

    Our biggest current problem is raccoons. They have busted thru my cedar siding in several spots, and nest in the cavity between the two walls. Packing down much of the fiberglas batts. Trying to decide what to blow in there (InsulCrete or Retrofoam or ?) to fix that problem.

    Back to your R80/R133 insulation levels: you might find cooling would be a problem at that level. We never used to be AC people, but since the waterfurnace included that, we have become somewhat hooked. (also, seems like summers have become hotter, and there is this aging thing, seems like the heat affects you more…) On one hand, more insulation means your AC can run less for the same cooling. On the other hand, TV’s, fridges, etc put out a fair amount of heat. Solar gain thru the windows in the morning/evenings mean you have to adjust shades so the house doesn’t warm up as fast.

    To conclude these ramblings: a friend build a superinsulated house in 2000. He used ICFs (insulating concrete forms). I would heartily recommend that over my system. I think the thickest ones are 12″, whatever R factor that gives is probably a fair tradeoff for Michigan.

  18. Sorry, long post, and of course I don’t see the typo until I submit….

    I meant: “if the water heater surface ISN’T warm, there is no value to adding insulation”. (and again, I’m not stating this as a fact, just something I frequently read and seems to have some validity…)

  19. Hi John,
    You are probably right about the house insulation calculations. As indicated in the post, I made some big assumptions to simplify the math.

    While the statement “if the water heater surface isn’t warm, there’s no value in adding insulation” makes sense in principle, here’s why I don’t think it’s true in practice:

    Consider the heat path, and temperatures along it. Tw is the interior water temperature. Ts is the surface temperature. Tair is the ambient air temperature. The thermal resistance between Tw and Ts (the existing tank insulation) is very high compared to the thermal resistance between Ts and Tair (just a thin boundary layer of air). The result will be that Ts is much nearer to Tair than it is to Tw, even though a significant amount of heat may be flowing through the wall. In plain English, any heat that comes through the wall is immediately dissipated to the air, so the surface temperature will not be much warmer than the ambient air temperature.

    There is also the issue that a metal surface usually feels cool to the touch because metal conducts heat so well. If you use an infrared thermometer you will find that a metal surface that feels cool to the touch may actually be many degrees above ambient temperature.

    Theory aside, I can say from experience that my tank felt cool to the touch before I added extra insulation, but when I slide my hand in between the tank and the exterior insulation now it feels VERY warm to the touch. All of the heat that is now so easily detectable was simply escaping to the air before.

  20. Rob, thanks for the response. I’m going to check into this further. Someone else mentioned that site, I was looking that over, too. They also suggested putting a thermometer on the tank, then covering it with insulation to evaluate.

    I’ll also check it with an infrared thermometer. I did notice that my pressure valve was very warm at the top, so at least I can add some insulation there.

    Since my water heater is on borrowed time, I probably won’t do much with the current one.

    (PS I was reading about that model passive house in Illinois. It has about R60 on all six sides and an electric bill of $30 in the worst winter month. They don’t provide just the heating cost, so still leaves some questions. ~1200 sq ft house in 5600 heating degree days)

  21. Hi Rob,
    I am going to convert oil to gas and my contractor recommend indirect gas water heater. I decided to stay put with my electric water heater since it still good. I was thinking about to insulated the tank and adding the timer. Seeing your post and pictures which is the great idea. But, is it ok to wrap the whole tank like that? I’m sured it’s ok since you did it. Also, I have some attic insulation that I pick up from freecycle, is it ok to use them? I know it’s a stupid question but I’m only single mom who know nothing about anything but try to save money. Thank for your help.

  22. Hi Tk,
    It’s perfectly fine to wrap an electric tank completely like that. Attic insulation should be fine. It’s a good precaution not to wrap anything flammable around electric appliances. If it’s fiberglass or rock wool it should be fine. Whatever it is you can try burning a small piece with a match or lighter to confirm. Good luck.

  23. Amazing. I’ve searched high and low for something like this, and on a fluke web search (“insulate water heater with batts”) I finally found this article.

    I’ve already planned out almost the same exact thing. I’m going to be using Roxul as well. I’ve built a wood platform so I can stick several inches of insulation under the water heater, and I’m going to use Roxul to insulate the water pipes too. Since the Roxul is so thick, it can even completely envelop the TPR valve while providing an empty space for the lever to safely operate.

    It’s just baffling to me why people obsess over building energy efficiency, but when it comes to water heaters, they just shrug and say “it doesn’t feel warm, so there’s no point in adding more insulation.” Simple math can easily show this to not be true. No one does a “warm to the touch” test in an attic or on a wall, because it is unscientific and ineffective. Since water heating is the #2 energy use in most homes, doing the math matters.

    The savings is more modest than insulating your attic, but it’s also much cheaper and easier to do. I think modern water heaters usually have 1-2 inches of polyurethane insulation, giving an R-value of 6-15 or so (calculating R-value on a cylinder is complicated). This would be considered pathetic in an attic, and mediocre in a wall.

    By my back-of-the-envelope math, adding about 8 inches of Roxul around the water heater would save me about $15/yr with an electric water heater (COP=~.95), but I have a heat pump water heater (COP=~2.5) so the savings will be much less. It’ll take 10+, maybe 20+ years to recoup, but since most people have plain electric water heaters, they could recoup the costs in 5 years or less. I don’t see why this isn’t more widespread. It’s cheap, easy, and is a foolproof investment.

    Regarding pipe insulation, the typical stuff is R-2. If you look around, you can find R-4. If you REALLY look hard, you can track down some that’s about R-8 (Thermacel 1″ wall on Grainger, item numbers: 2CKN1 2CKN2 2CKN3 2CKN5 2CKL9). But why stop at R-8? You can add more R-value for cheaper by slicing Roxul up into long rectangles that you fit around the pipes. Obviously this won’t work in some cramped areas, but in many houses, the majority of pipe has several inches of open space around it, except where it crosses joists.

  24. I think your first formula is wrong. The cost of insulation is just CF, not CF/T. This makes sense because the cost of the insulation you buy should not depend on the thickness of the original insulation. If I go to Home Depot and buy some fiberglass batting, the cashier doesn’t ask me how much insulation I have at home.

    This is also apparent by looking at units. The cost of insulation should have units of currency (dollars in this case). F is the thickness of insulation and has units of length (cm in this case). C is the cost of insulation PER thickness, and has units of currency per length (dollars/cm in this case).

    Your error propagates down in your calculation, so you should have F = YA/C – T, not F = YAT/C – T.

    YA/C has units of [time]*[currency/time]/[currency/length] = length. Both F and T have units of [length]. Your formula has [time]*[currency/time]*[length]/[currency/length] = 1 (dimensionless), which you set equal to [length].

    If you still don’t believe me, check a few values. Suppose you’ve already super-insulated, and have T = 100 cm. What would the payback time be for adding another 5 cm? You wouldn’t expect to make your money up very quickly since you’re barely changing things.

    To get the payback time for a given insulation upgrade, solve for Y = (F+T)C/A in my case, or Y = (F+T)C/(AT) in yours. For F = 5 cm, T = 100 cm, C = $20/cm, and A = $100/year. In my case, Y = 21 years. In your case, Y = 0.21 years.

    Additionally, the water heater is cylindrical, meaning that the circumference grows with insulation amount, but you get the basic idea.

  25. Hi Craig,
    I think you misunderstood my definition of C.

    C is the “cost of adding T cm of insulation”. Yes, T is the original insulation thickness, but in this case I am saying C is what it would cost to add T more cm of insulation. It is an arbitrary choice for convenience. I could have said C is the cost of adding 1cm of insulation in which case C would be $/cm as you assumed. But as I have defined C, it is NOT the cost PER thickness. It is the absolute cost of a specified thickness (T). C has units of $ (as indicated in brackets in my definition), not $/cm. To get $/cm you need to divide by the thickness (T) that C is the cost of. Thus C/T is the cost per thickness in $/cm and C/T * F is the cost of adding thickness F. C/T * F has units of $, just like we want.

    In your example (adding 5cm of insulation to 100cm), if C is $20 (which is probably lower than you’d actually pay to add over 3ft of insulation), then the cost per unit thickness C/T is only $0.20/cm. Adding 5cm costs only $1 but will in theory reduce operating costs by about 5% (the percentage increase in insulation thickness) saving about $5 per year on the current $100/yr operating cost. Spending $1 to save $5 per year has a payback of about 0.2 years. So the formula makes sense as long a you recognize that C is in $, not $/cm.

    You are correct that the water heater is cylindrical and to keep things simple I have not accounted for the increasing circumference as the insulation thickness grows. I’ve assumed that most people will not be adding so much insulation that this has a significant effect on the results. For typical changes in thickness (say just doubling or tripling the original thickness), the formula given should be a good approximation.

  26. I just ran across this web site, Very interesting.
    Last year the company I work for replaced the roof, removing a lot of polystyrene insulation. I grabbed all I could!
    I build a 16 x 16 shop building using 8″ x 4’x10′ sip’s. I got these on the cheap. 50$ each. I split these in half, then built up the wall to 7′ stick framing. Then filled in the cavity’s with the polystyrene. The floor is 9″ I joists, the roof is 6″ all cavity’s filled with the poly. I built the roof cathedral for windows up top and to give a feeling of more space.
    The wife and granddaughter came out to shop the other week, within 15 min it started getting hot with the three of us in there! I’m sold on SIP’s my next house will be built using these. My little shop was a test bed and I love it!
    We’re doing a huge remodel on the house we have now. I’m using the poly sheets to insulate the walls and ceilings, maybe the roof if I have enough.

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