Igloo mythbusting...

[hikingfish]

Hi All,
Since I didn't get to do my igloo last weekend (weather and my back weren't cooperating), so I decided to crunch a couple of numbers and check to see if some stuff I had read online was actually possible or not (not really mythbusting...but I love that show, so...).

I read that it is possible to build an igloo by only using the snow contained within the circle that defines the base of the igloo. Possible or no?

It seems to be possible! Even if you calculate that you will be able to use approx. 70% of the snow in the igloo's base (because eventually, as you near the edges of the circle, you rectangular blocks won't fit, only a portion of the blocks would fit) and if you approximate the shape of the igloo as a half-sphere (which is isn't quite, but again, this is going for worst case), it still works. The key is the shape of the blocks. For my calculations, I used blocks that were 2 ft. wide, 2 ft. high and 6 in. thick. With every block you make, you will remove 1 sq. ft. of snow in the igloo's floor surface (2 ft. wide * 6 in. thick = 1 sq. ft.) but that block will allow you to cover the surface area of 4 sq. ft (2 ft. wide * 2 ft. high = 4 sq. ft.).

Calculations here:
http://spreadsheets.google.com/pub?key=pCihbgy7dJ8rPFOCOuVXjLQ

Let me know if you spot any mistakes! I'd be glad to edit the spreadsheet. And let me know of any comments... I'd be happy to discuss them all afternoon (writing code documention papers today,...boooring! )

 

[Hikes4fun]

GeezLouise.... You have way too much free time The only thing worse is that I had the time to check out the spreadsheet

 

[hikingfish]

Unfortunately, my bad back keeps me from doing long hikes like I used to

So, I have to keep day dreaming about the stuff I love!

Fish

 

[Hikes4fun]

Well I hope your back gets better!! There's nothing worse than being laid up
PS--Great pics!! I especially like the 3 beers in the pan!

 

[teejay]

Your calculations seem okay but for just one thing. They assume you have suitable snow that's already compressed and consolidated 2 feet deep.

Waiting for Doug Paul.

teejay

 

[nartreb]

You *could*, if your igloo sits on a few feet of well-compacted snow, but why would you want to? Better to cut blocks somewhere else, so your igloo's floor is at least as high as the surrounding area.

circle area = pi * r * r.
So for snow depth d, available snow volume = pi * r * r * d.

semi-sphere surface area = 1/2 * 4 * pi * r * r.
So for wall thickness t, wall volume = 2 * pi * r * r * t.

We're interested in the boundary condition where available snow equals wall volume, in other words

pi * r * r *d = 2 * pi * r * r * t

Cancelling, we get:

d = 2t.

In other words, as long as the snow depth is at least twice the wall thickness, you can do it.

Roughly speaking, anyway. This calculation neglects two important problems.
1. wall thickness. I calculated wall volume as surface area * thickness, which is approximately correct for a thin enough curved wall, but for curved walls it matters whether you're measuring inside radius or outside radius. If you measure the inside radius, the volume in the wall is larger than what the formula states. If you measure the outside radius, the volume is lower. For a real-world igloo problem, you don't want to undermine the walls, so the available snow has to be measured using the inside radius. That means that d=2t should be more like d=2.1t or something.

2. Fractional blocks. My formula assumes you can make blocks from all the snow inside the radius, but as you know, in the real world you can't divide a circle into rectangles exactly. Even if you don't mind making half-blocks and quarter-blocks, you have to square off the curves. The greater the wall thickness (relative to the radius), the worse this problem is. I know my differential calculus class provided an exact formula for fixing this, but I'm not *that* bored at work. (Though I'm intrigued it was as bad as 70%. Are you not even allowing half-blocks?) So call it d=3t and spend the time performing a snow dance (it's frickin' 15 degrees centigrade down here today!).

 

[Stash]

What if you used pks4000's Ice Box from Grand Shelters? http://www.vftt.org/forums/showthread.php?t=27479&page=4
You don't have to cut blocks then and can use all the snow. Of course you'd have to calculate the change in density being dependant on how hard you pack it and/or the temp at the time of build.

 

[hikingfish]

Well I hope your back gets better!! There's nothing worse than being laid up
PS--Great pics!! I especially like the 3 beers in the pan!

Yes, tell me about it. At least it gives me a chance to spend time studying other outdoor related topics! There has to be at least one good point about a broken back

Thanks for the pics. In that same album, did you see the pic where we were trying to throw frozen granola bars through a block of snow with 3 holes in it? Not sure what it's called in English, but in french it's called "jeux de poches" (games of holes?).

Your calculations seem okay but for just one thing. They assume you have suitable snow that's already compressed and consolidated 2 feet deep.

Waiting for Doug Paul.

teejay

Yes, absolutely. Either wind-packed (ideal) or self-packed (good enough).

What if you used pks4000's Ice Box from Grand Shelters? http://www.vftt.org/forums/showthread.php?t=27479&page=4
You don't have to cut blocks then and can use all the snow. Of course you'd have to calculate the change in density being dependant on how hard you pack it and/or the temp at the time of build.

I made a homemade icebox type device...and after spending 7 hrs making an igloo, I figured there had to be a faster way of doing them Plus, after watching a couple of inuit videos on youtube, I wanted to give a try at building an igloo with only a knife.

 

[hikingfish]

You *could*, if your igloo sits on a few feet of well-compacted snow, but why would you want to? Better to cut blocks somewhere else, so your igloo's floor is at least as high as the surrounding area.

There's a perfectly good reason for doing this: Imagine being in -45C temps with howling winds on the flattest piece of land you've ever seen. What would be the first thing you'd want to do? That's right, get out of the wind, and fast! That's the reason inuits take their blocks from inside the igloo...as soon as you have 1 row of blocks up, you're already 4 ft deep in your igloo (2 ft deep hole created by the extracted blocks) and a partial wall 2 ft high formed by the actual block. Also, you want to be done as soon as possible. So the least distance you have to cover while moving the blocks between the quarry and their destination, the better.

When I tried making an igloo with only my knife (a 9ft diameter igloo), there was a fair wind that day and let me tell you, already after I laid that first row of blocks, I was out of the wind. I was shocked at how well just a couple of feet high wall could deflect all the wind.

circle area = pi * r * r.
So for snow depth d, available snow volume = pi * r * r * d.

semi-sphere surface area = 1/2 * 4 * pi * r * r.
So for wall thickness t, wall volume = 2 * pi * r * r * t.

We're interested in the boundary condition where available snow equals wall volume, in other words

pi * r * r *d = 2 * pi * r * r * t

Cancelling, we get:

d = 2t.

In other words, as long as the snow depth is at least twice the wall thickness, you can do it.

I'll re-read this tomorrow!

Roughly speaking, anyway. This calculation neglects two important problems.
1. wall thickness. I calculated wall volume as surface area * thickness, which is approximately correct for a thin enough curved wall, but for curved walls it matters whether you're measuring inside radius or outside radius. If you measure the inside radius, the volume in the wall is larger than what the formula states. If you measure the outside radius, the volume is lower. For a real-world igloo problem, you don't want to undermine the walls, so the available snow has to be measured using the inside radius. That means that d=2t should be more like d=2.1t or something.

The outwardmost side of your blocks would be on the circle's line. I'll re-read this again tomorrow though, I have to fly!

2. Fractional blocks. My formula assumes you can make blocks from all the snow inside the radius, but as you know, in the real world you can't divide a circle into rectangles exactly. Even if you don't mind making half-blocks and quarter-blocks, you have to square off the curves. The greater the wall thickness (relative to the radius), the worse this problem is. I know my differential calculus class provided an exact formula for fixing this, but I'm not *that* bored at work. (Though I'm intrigued it was as bad as 70%. Are you not even allowing half-blocks?) So call it d=3t and spend the time performing a snow dance (it's frickin' 15 degrees centigrade down here today!).

I didn't allow any fractional blocks, nor did I account that one might make the blocks slightly thinner as you go up. In any case, I tried to make all my calculations use the worst-case of everything. No fractional blocks, only 70% usable snow area of the base circle, half-sphere dome, etc. As for the 70%, I drew some circles and rectangles the size of the non-fractional blocks and fitted as many as I could in the circle. That gave me a worst case scenario of 71% I believe. I included 2 images that show how I laid the blocks in the igloo. They're not optimal. One might be able to squeeze an extra couple of blocks, but again. If it works for the numbers I calculated, it would work with a couple of extra blocks too, right?

Ouch, big post! Great stuff! I'm only going to partially reply...I'll post more tomorrow.

 

[DougPaul]

Nartreb's analysis looks good to me.

From what I have read the Inuit prefer to use windslab which (from the same source) is relatively common in their areas. (Or perhaps, the are smart enough to only build an igloo when they can find adequate windslab.)

Doug

 

[sardog1]

I was shocked at how well just a couple of feet high wall could deflect all the wind.

From what I have read the Inuit prefer to use windslab which (from the same source) is relatively common in their areas. (Or perhaps, the are smart enough to only build a igloo when they can find adequate windslab.)

All right. I have held my tongue in check for lo these many days, but the truth will out:

1. Mountaineers have used the benefits of snow walls for many years to reduce cooling and wind forces. I suspect that they borrowed the idea from polar explorers who were in turn familiar with Inuit and other Native/First Nations shelters.

2. Igloos are only practical for shelter during travel when you have windslab at hand. Otherwise, they are an enormous waste of energy and time, and a real threat to your well-being from getting soaked by perspiration during the construction.

3. Much of my youth was spent building igloos. It was feasible and fun in Minnesota, where the wind arrives from Saskatchewan and Manitoba via the Dakotas. It is "generally" neither of these in New England.

(And a snow knife is what you want for the task.)

 

[Hobbitling]

One thing you should consider is that the strongest shape for an igloo (or any arch) is not a hemisphere (half circle cross section) but a catenary curve, taller than it is wide, almost cone shaped. It is the shape that a string or rope makes when the ends are held and the middle is allowed to drape (except upside down of course), and it isn't the same thing as a parabola.

I believe the ice box igloo making gadget accomplishes this shape by lengthening the pole length with each row of blocks. This also prolongs the structure's life, since the roof of an igloo will sag at a predictable rate, while the diameter will generally stay relatively constant.

 

[hikingfish]

One thing you should consider is that the strongest shape for an igloo (or any arch) is not a hemisphere (half circle cross section) but a catenary curve, taller than it is wide, almost cone shaped. It is the shape that a string or rope makes when the ends are held and the middle is allowed to drape (except upside down of course), and it isn't the same thing as a parabola.

Absolutely correct. And if you can give the formula for a "alysséide" dome (the dome like 3d structure you get from spinning a catenary around a vertical axis, see, I did do some research lol), I'll gladly switch the formula in the spreadsheet Jokes asides, I'm using a half-sphere which is a worst case scenario: If it worst for a half-sphere, it'll work with an alysséide dome, since it's surface is a bit smaller.

 

[RoySwkr]

This article from The Hippo suggests that in poor snow conditions you build a wall and put a tarp over the top:
http://www.hippopress.com/090122/mQA.html

 

[hikingfish]

You *could*, if your igloo sits on a few feet of well-compacted snow, but why would you want to? Better to cut blocks somewhere else, so your igloo's floor is at least as high as the surrounding area.

circle area = pi * r * r.
So for snow depth d, available snow volume = pi * r * r * d.

semi-sphere surface area = 1/2 * 4 * pi * r * r.
So for wall thickness t, wall volume = 2 * pi * r * r * t.

We're interested in the boundary condition where available snow (volume) equals wall volume, in other words

pi * r * r *d = 2 * pi * r * r * t

Cancelling, we get:

d = 2t.

In other words, as long as the snow depth is at least twice the wall thickness, you can do it.

Hmm, from playing in my backyard, I knew something was fishy about that last sentence. You're mixing area and volume. I don't get the same results:

Volume of sphere: 4/3*pi*r^3
Volume half-sphere: 2/3*pi*r^3

r = radius of inner sphere (liveable area in igloo)
t = thickness of wall (assuming it's constant across the igloo)
Volume inner sphere = 2/3*pi*r^3
Volume outer sphere = 2/3*pi*(r+t)^3
See attached pic

Total volume of snow required to build wall = V outer - V inner
V total = V outer - V inner
V total = 2/3*pi*(r+t)^3 - 2/3*pi*r^3
For igloo of 9 ft diameter (4.5 ft radius) and 0.5 ft wall thickness
V total = 262 - 191
V total = 71 cu. ft. of snow

Total volume of snow available in cylinder under the igloo:
where d = depth of blocks = 2 ft
V avail = pi * r * r * d
V avail = pi * 4.5^2 * 2
V avail = 127 cu. ft. of snow

This is assuming you use 100% of the available snow...but even at 70% usability, you'd be fine (127 * 0.7 = 88 cu. ft.)

Since V avail >= V total needed, you could build a 9 ft. diameter igloo with the snow contained within it's circular base.

Even using volume instead of surface area, it seems this "myth" seems to hold up.

Fish

 

[hikingfish]

Nartreb's analysis looks good to me.

From what I have read the Inuit prefer to use windslab which (from the same source) is relatively common in their areas. (Or perhaps, the are smart enough to only build an igloo when they can find adequate windslab.)

Doug

Right, they will only build igloos with the right snow (windslab). They have a poker device they use to poke in the snow and check to make sure the snow that makes up their blocks will be consistant. The best snow is apparently when all the snow making your blocks was deposited from the same storm.

Fish

 

[hikingfish]

All right. I have held my tongue in check for lo these many days, but the truth will out:

1. Mountaineers have used the benefits of snow walls for many years to reduce cooling and wind forces. I suspect that they borrowed the idea from polar explorers who were in turn familiar with Inuit and other Native/First Nations shelters.

2. Igloos are only practical for shelter during travel when you have windslab at hand. Otherwise, they are an enormous waste of energy and time, and a real threat to your well-being from getting soaked by perspiration during the construction.

3. Much of my youth was spent building igloos. It was feasible and fun in Minnesota, where the wind arrives from Saskatchewan and Manitoba via the Dakotas. It is "generally" neither of these in New England.

(And a snow knife is what you want for the task.)

I'm not sure exactly what you mean in your second point. Of course it's more work, that's for sure, to stomp an area with your snowshoes/skis for 20 minutes and then wait for that area to sinter. But you can (and should!) take your time while stomping and afterwards building the igloo so you don't sweat. Exactly as one should do for any snow shelter. If you're building a snow shelter in wet snow, then that's another story. But then again, you probably should of brought a tent if conditions are so close to freezing point. Wouldn't you agree?

As for point #3, I can agree with you on that one! Even here in Quebec, windslabs are very rare. Windslabs are usually just the right snow texture too...and I've always wondered if stomped-on snow could be used as well to build and igloo, since the blocks are heavier, they might not hold as well when tilted inwards towards the end of the construction.

Fish

 

[Tim Seaver]

The Sweat Thing Goes for Caves Too!

2. Igloos are only practical for shelter during travel when you have windslab at hand. Otherwise, they are an enormous waste of energy and time, and a real threat to your well-being from getting soaked by perspiration during the construction.

Have to agree on the perspiration thing! After learning this the hard way on a very stormy night at Edmands Col building a snow cave (taking turns digging), the next time I returned with a few friends with a different strategy - let one person do the digging, knowing full well that they will be a semi-miserable heap of sweat-soaked flesh from the effort. Then, once inside, that person gets the royal treatment - fresh clothes, and into a dry sleeping bag where they are then served food and drink from his/her thankful companions.

Snow Cave at Dingmaul Rock

Keith in the Cave


Gene Prater's first edition of "Snowshoeing" had en excellent chapter on snow shelter building - here is the new version of his book, which I have not read.

 

[spencer]

This article from The Hippo suggests that in poor snow conditions you build a wall and put a tarp over the top:
http://www.hippopress.com/090122/mQA.html

Yankielun just hosted a how-to workshop here at U. Maine last week. Apparently he and a bunch of students built several structures on the mall. Unfortunately, I don't get across campus too often so I haven't seen them yet. I fear that the heavy rain today has done serious damage. I guess I should get over there and check them out.

Here is an article about the event.

 

[nartreb]

In other words, as long as the snow depth is at least twice the wall thickness, you can do it.

Hmm, from playing in my backyard, I knew something was fishy about that last sentence. You're mixing area and volume. I don't get the same results:

I was approximating volume as surface area (of, say, the outside) * thickness, which works for a straight wall or a thin enough shell.

Using your more precise formula for wall volume (what you called "total volume"; a math teacher would call it "shell volume"):

wall volume = 2/3*pi*(r+t)^3 - 2/3*pi*r^3
where r is the inner radius and t is the wall thickness
= 2/3 * Pi * ( r^3 + 3*r^2*t + 3*r*t^2 + t^3) - 2/3 * pi * r^3
= 2*pi*r^2t + 2*pi*r*t^2 + 2/3(pi * t^3)

Now compare that to the volume available in the cylinder under the inner radius r, if the snow depth is d:
available snow = pi * r^2 * d

As before, set available snow equal to wall volume. Also, out of laziness, write "p" for pi:

2p(r^2)t + 2prt^2 + (2/3)pt^3 = p(r^2)d

Cancelling is not as easy (I shouldn't have multiplied out, above), but we can get to:

2(r^2)t + 2rt^2 + (2/3)t^3 = (r^2)d

or
d = 2t + (2rt^2)/(r^2) + (2t^3)/(3r^2)

which, as I said, means d should be a bit more than 2t. How much more?

In any real-world igloo, we know that r is going to be, conservatively, at least ten times as big as t. (Example, nine-foot igloo, half-foot-thick walls, r is 18 times t. Edit: that's wrong. In this example the diameter is 18 times t, but r is only 9 times t. Calculations that follow are close to this real-world example, but not good for the intended purpose of setting a conservative bound.) Let's see what happens if we replace "r" with "10*t".

d = 2t + 2(10t)(t^2)/((10t)^2) + (2t^3)/(3(10t)^2)
= 2t + (20t^3)/(100t^2) + (2t^3)/300t^2
= 2t + (1/50)t + (1/150)t.

d = 2.026667 * t

In other words, the extra terms are pretty negligible; 2t was darn close. The bigger r is compared to t, the more negligible the extra terms are.

edit: the above still ignores the fractional-blocks problem. If we assume 70% usability, we get
usable snow = 0.7 * p *r^2 * d.
Repeating the above calculations leads to:
0.7 d = 2.026667 t
d = 2.895 * t.
Like I said, call it d = 3t and it's close enough for field work.