The sagging of the igloo itself is mainly due to the density of the snow used in building the igloo. Cold fluffy snow will compress much more than snow that is old and has turned to ice crystals. If the igloo is to be used for just a few days, the sagging is generally not a problem at all.
The most common problem arises when the first layer of the igloo is built using the fresh powdery snow laying around and then the older underlying snow is used to complete the igloo. The older snow is much denser than the powder snow and it will not compress as much as the powder snow. The older snow is also heavier than the powder snow and the extra weight results in the powder layer compressing more than it would if the entire igloo is built of powder.
When the entire igloo is built of the same density and weight of snow, it will retain its catenary shape as the snow compresses and the igloo sags over time. The catenary shape causes the pressures within the wall to be directed directly into the wall and the wall will not sag in or get pushed out.
When the first layer compresses more than the top layers, the lower layer ends up tipping in as it compresses and if the upper part of the igloo doesn't compress as much, the catenary shape is lost and the first layer will sag down to the floor in a week or two's time.
The other case where the less denser snows will cause problems is when the sun is very warm and the sunny side of the igloo warms up allowing the sunny side of the igloo to compress more than the rest of the igloo. This results in the part of the igloo that gets the most sun sagging in and it will make the entire igloo sag down to the floor in a couple weeks time. It can also sag fast enough that you will lose your head room on the sunny side of the igloo in one days time.
The foundation or platform for the igloo also plays a critical roll in how an igloo sags.
The surface of the snow is all that is packed if the platform is packed using snowshoes or skis, therefore it is better to pack with just boots and break down as deep as possible and then pack your way up and out of the snow. If only the surface of the snow is packed, the outside edge of the platform will sag down as the underlying snow compresses from the weight of the igloo on the platform. This ends up looking like the floor is erupting up into the igloo. In this case, the edge of the platform tips down causing the first layer of the igloo to tip out which distorts the catenary shape in such a way that the first layer continues to tip out and the upper layers of the igloo sag in.
If the door is cut up into the wall, the upper part of the igloo looses enough support that it makes the wall bow out in the door area. Little walls coming away from the igloo and beside the door will help to prevent the igloo wall from bowing out.
The door should also be built on the shady side of the igloo to lessen the sagging in the door area.
Using the igloo and warming up the inside helps prevent sagging of the igloo because of the ice layer that forms on the inside of the igloo after you leave and it gets cold inside again.
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