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Bigelow Aerospace develops expandable (inflatable/foldable) space stations. Their flagship is their cylindrical BA330 which has the dimensions 13.7 by 6.7 meter when expanded. Current ISS modules seem to have a diameter of less than 5 meter. But this is not far from the dimensions of fairings of Atlas V, Delta IV Heavy, Proton and Ariane 5. They have 5.0-5.4 meter fairing diameter. The mass of the BA330 (20-23 tons) is on the limit of what those rockets can launch to LEO. SLS might get fairings with up to 10 meter diameter.

So why go through the extra trouble of making their space station expandable? Is the extra 1.3-1.7 meter diameter so important? Wouldn't a static structure, maybe made by the same materials, be much simpler and cheaper to develop and manufacture, lighter and less risky to deploy in space?

If the BA330 is primarily a technology demonstration, what would be the use of space station modules which have larger diameter than the payload fairings of today's and near-future launchers?

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That 5.0 meters is the outer diameter of the payload fairing. Payloads obviously cannot be that large. In fact, they are constrained to be a bit smaller. The figures below depicts the Delta IV Heavy and Atlas V static volume (volume that a payload can occupy).

http://www-eng.lbl.gov/~lafever/SNAP/OldFiles/DELTA%20PAYLOAD%20OVERVIEW_files/d4hfairings.gif
Image source: http://www-eng.lbl.gov/~lafever/SNAP/OldFiles/DELTA%20PAYLOAD%20OVERVIEW.htm


Image source: http://www.ulalaunch.com/products_atlasv.aspx

Note that the Delta IV Heavy and Atlas V both constrain payloads to 4.57 meters in diameter. One would think that the Ariane 5 with its 5.4 meter fairing would accommodate a wider payload. This is not the case. The Ariane 5 accommodates the same size payload as does a Delta IV Heavy or Atlas V. A Proton M is in the same class.

That 4.57 meters includes space for the un-deployed solar arrays and for vibrations. One would be hard pressed to launch a standalone rigid structure much bigger than the 4.2 meter diameter ISS Destiny module on an existing launch vehicle. Yes, we can wait (and wait and wait) for the Senate Launch System to come on line, but it's going to be a long wait.

That increase from 4.2 meters to 6.7 meters in diameter alone is quite significant. That's a 60% increase in diameter, or a 154% increase in cross section area. The volume increases even more with inflatables thanks to length. The BA330 will have over three times the pressurized volume of the Destiny module.

References:

Section 6, "Payload Fairings," of the Delta IV Users Guide describes the constraints on payload size on a Delta IV.

Section 6, "Payload Fairings," of the Atlas V Launch Services User's Guide describes the constraints on payload size on an Atlas V.

Annex 5, "Usable volume under fairing and SYLDA 5," of the Ariane 5 User's Manual describes the constraints on payload size on an Ariane 5.

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Usable volume rises quickly with radius (r2) so a cylinder with a diameter of 6.7 m has almost twice the usable volume of a cylinder of 5 m diameter.

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