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I want to blow insulation into my attic. The door into my attic is on the floor and made up of a large board which doesn't have hinges. I have to push the door up and slide it over in order to gain access to the attic. That means when I blow in insulation, I can't blow any in on the door or in the area that I will slide the door over to.

Will this gap in insulation cause major hot or cold air loss? Are there alternatives to this?

You don't put blow in above the door. Use batts or cut several layers poly board insulation to mimic slightly less than your attic cover. 4-5 layers will give you good coverage.

This will not provide a perfect barrier but is the recommended way of handling attic openings.bb

Before you add insulation, consider air sealing your attic, meaning use a closed cell foam to seal penetrations in ceiling such as top plates, holes for electrical, lighting and plumbing. This will prevent air communication between the attic and the conditioned space something that just adding blown in insulation cannot do. If you are experiencing comfort issues in your home, are looking for energy saving or health benefits reach out to home performance professionals and have a blower door test preformed to determine the amount of air leakage your home has and get the best solution. If you're interested in this take a look at Corbett Lunsford and his youtube channel Home Performance.

But to answer your question build a wall around your attic access to prevent the blown in insulation from falling through, put a seal on the attic access frame (kinda like a door seal) and adhere bats of insulation to the door itself.

Here is a link for some air sealing tips. https://www.energyvanguard.com/blog/56102/The-3-Rules-of-Air-Sealing

And here is one for why it's important http://energysmartohio.com/how_it_works/air-sealing/