tim laqua dot com Thoughts and Code from Tim Laqua

13Jan/134

The Garage Heater

Being a life long Minnesota resident, running propane heaters in the winter to keep the garage warm is incredibly common... and incredibly smelly. Eventually your eyes start burning from all the stuff in the air. Add in some degreaser and it gets really enjoyable in there. This age-old problem led me to try and figure out how to keep it warm in there without the trusty propane heater (or kerosene - that's equally terrible). The only two viable options are Electric and Natural Gas. I don't really care which - I just want to pick the most cost effective one. If you ask anyone, the answer is always natural gas. But why? How much more efficient is natural gas? I care because natural gas requires a gas line, while electric would just require another (big) circuit (the natural gas heaters require a circuit as well, just way more logically sized). Ever wonder how those electric heaters rated in watts translate to the BTU rated natural gas heaters? I did. I also wondered how much all this propane is costing... and why I have to run the heater so frequently.

First things first, I looked at my gas bill and it's billed in therms. That's kind of the standard unit i'll use, a therm is 100,000 btu (and wherever I say BTU, i really mean BTU per hour). How's that translate to electricity? Well, 1 watt = 3.414 btu so one therm 29,291 watts. Then I went and looked at my electric bill and it's billed in Kilowatt hours so now I can just multiply by my per kWh cost ($0.10).

Electric costs roughly $2.92 per therm
Natural Gas cost roughly $0.67 per therm

That's a difference of $2.25 per therm consumed. Let's say I think I need a 75K BTU heater. That's 75% of a therm, so for every hour I run it, it would cost $1.69 more for electric. Now let's assume the Natural Gas setup cost $1,000 more to install - it would take 591 hours to eat up the cost difference.

Ok, got that sorted out, now what about this propane stuff, what's that cost? First we have to sort out how much is in the tank (just using 20lb tanks) and divide by the fill cost. Turns out one gallon of propane has 91,600 BTU. But I buy propane in pounds, so one gallon is 4.24 lbs - meaning there's 4.6 pounds required per therm. On the high side, i'm paying about a buck a pound (if they actually filled the tanks up to 20lbs).

Propane costs roughly $4.60 per therm

That's a whole bunch - definitely need to stop using propane. Now let's try to figure out how much heat I actually need rather than just using the 'ol "bigger is better" logic. It takes 0.018 btu per cubic feet to raise the air 1 degree fahrenheit and my garage is 34' x 22' x 9' = 6,732 cubic feet. If I did the math right, it would take 121.176 BTU per degree we want to heat it.

Now for the heat loss part...

We'll assume we don't have any doors cause the math gets stupid.

2 22' x 9' 2x4 uninsulated walls (396 sq ft)
2 34' x 9' 2x4 uninsulated walls (612 sq ft)
1 34' x 22' r13 insulated ceiling (748 sq ft)

So 1008 sq ft of uninsulated walls and 748 sq ft of r13.

Now we google around for an R value for those walls. 1/2 plywood. Looks like 0.63 (awesome).

For now let's assume we want to keep the garage 40 degrees warmer than the outside. The heat load formula looks something like u factor * sq ft * temp differential = btu per hour. Now what's u factor? It's just 1/R value (that's what the internet tells me anyway) - it's how conductive the material is with regard to heat.

u factor of walls is 1/0.68 = 1.47
u factor of ceiling is 1/13 = 0.07

1.47 * 1008 * 40 = 59,270 btu/hour
0.07 * 748 * 40 = 2,094 btu/hour

Which means to maintain a 40 degree temperature differential in my garage (assuming it's perfectly sealed, no air loss) it would require 61,364 btu. Which means a 75,000 BTU heater will be able to maintain a 40 degree temp diff. Let's back that out to how many btu's i need per degree.

61,364 / 40 = 1534.1 btu

So a 75,000 BTU heater could maintain a 48.9 degree temperature differential. I wonder how many degrees it could maintain if I insulated the walls...

That would make the wall u factor roughly the same as the ceiling (0.07). And let's just do the math for 1 degree.

0.07 * 1008 = 70.56 btu
0.07 * 748 = 52.36 btu

So 122.92 BTU per degree now. That's an incredible difference, I am fairly sure that insulating the walls is a MUST and that plywood sheathing is absolutely pouring heat out of the garage. To test this theory, I figured I'd just go buy a bunch of insulation - $7.88 for kraft faced r13 roll that covers 40sq ft. The two short walls are completely uninsulated - the long walls are partially finished on one side and have some garage doors on the other side. I measured the uninsulated parts of the garage and I needed 596 sq feet, so 15 rolls plus an extra comes to $126.08. Acceptable for a weekend project.

And yes, earlier calculations were made assuming I had no doors and it was a completely uninsulated square. I have real numbers now.

Current:
R13 Ceiling: 0.07 * 748 = 52.36
R6? Garage Doors: 0.16 * (112+63) = 28
R15 Exterior Door: 0.07 * 21 = 1.47
Uninsulated Walls: 1.47 * 600 = 882
Finished Wall space: Ignore this - it's always warmer on the other side of this particular space

Which comes to a total heat loss of 963.83 btu per degree of difference.

If I insulated the walls, that space would drop from 882 btu down to 42 btu (0.07 * 600 = 42) for a total of 123.83 btu per degree of difference for the whole garage.

What's a difference of 840 btu per degree cost me? I looked at the forecast and it looks like an average of around 10 degrees on Saturday. I want to keep it 66 degrees in there for 8 hours (same temp as my house, so i don't have to deal with the finished wall math). At a 56 degree differential, that extra heat loss is around 47,040 btu per hour for 8 hours... 376,320 btu.

Given our above calculations all went back to therms, this is 3.76 therms.

Natural Gas: $0.67 * 3.76 = $2.51
Electric: $2.92 * 3.76 = $10.98
Propane: $4.60 * 3.76 = $17.29

Now how many similar days would it take to offset the cost of the insulation?
Natural Gas: $126.08 / $2.51 = 50 days
Electric: $126.08 / $10.98 = 12 days
Propane: $126.08 / $17.29 = 8 days

Now that we've done all that, someone brought up the floor. The floor?!?! Hot air goes up, who cares about the floor! Honestly, I have no idea how to bring the floor in to the equation. I did find that the slab has an R value of around 1 so if it's 748 sq ft, it would lose 748 btu per degree per hour - which is a bunch. But again, hot air rises... sort of. I think heat just kinda goes where it can. For now, I'm ignoring the cold floor, I'll try to sort that out later. And in the spirit of ignoring the floor, I made a spreadsheet to do all this math cause it's getting pretty tedious.

Uninsulated, how hot could a 75,000 btu heater keep my garage? It could maintain a temperature differential of 77.8 degrees if it ran constantly:

Uninsulated Max Temp

What could that same 75,000 btu heater maintain if I insulated the walls? Clearly somethings amiss here, but according to my math, like over 500 degrees of differential, so the whole garage would burst in to flames before heat loss was equal to the output of the heater. But I'm ignoring tons of factors in these examples, like air exchange loss, the garage floor, etc. Take it with a grain of salt.

Insulated Max Temp

Since we're changing the heat loss by insulating, what happens is we not only need less energy to change the temp but we will also lose the heat that we have much slower - here's an example of the heat loss if we heated it up to 85 degrees and just let the temp drop back to outside temp:

Uninsulated, we lose over 9 degrees a minute up at 85 degrees - it's a curve, heat loss is always relative to the temperature differential so as that shrinks, so does the loss:
Uninsulated Temp Drop

Insulated, we're only losing around a degree a minute:
Insulated Temp Drop

Now let's say we want to maintain a temperature differential of 60 degrees constantly. The only way to really do that would be to buy a heater that matches your heat loss at that temp differrential and run it constantly. Uninsulated, a 60,000 BTU heater could maintain a 62 degree temp differential. Insulated... I would need less than 9000 BTU (again, ignoring things like the floor). Nobody wants to run them constantly though, so we'll just buy the 75,000 btu one and see the difference there. If we're going to let it kick on and off, you have to pick an acceptable temp range for it to do its thing - if you only have a few degrees of range, it'll be kicking on and off constantly. We'll go with keeping it between 75 and 60 degrees.

Uninsulated, the heater will have to kick on for 6 minutes, turn off for 2 minutes (up at 75 degrees, it would lose over 8 degrees a minute):
Uninsulated Temp Maintain

Insulated, the heater will need to kick on for 2 minutes and turn off for 20 minutes (insulated, it's losing around a degree a minute).
Insulated Temp Maintain

I'm positive most of this is wildly inaccurate - so I ordered a temperature sensor so I can graph out what actually happens to see how far off this sort of calculation is. More on that in a future post.

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Comments (4) Trackbacks (1)
  1. the depth of your temporary insantity boggles my mind sometimes 🙂

  2. Um, this. is. it. I dig this. I expect a cube and arduino sensors to further flesh this out. =)

  3. Excellent work here. I hope you don’t mind if I plunder some of your calculations. Heat is socialist in nature and just wants to make everything the same temperature, so consider adding the floor into your calculations. Although remember that the ground will not be as cold as the outside air so reduce the degree difference. Another thing to consider is the efficiency of each heating system. BTU output / BTU input, for electrical this is 100%, but for natural gas it can vary depending on the system from 95% to 75%.

    Up here in Canada we have a computer program that does all the calculations for us, but it is nice to see it all pieced out. Thank you.


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