He has spent about $180 million of his own money so far and has said he is willing to spend up to $320 million more. An expansion of the factory will double the amount of floor space as the company begins the transition from research and development to production.

Mr. Bigelow only occasionally gives interviews, and except for Michael N. Gold, the director of Bigelow’s Washington office, the employees almost never speak publicly. A company document titled “Some Important Bigelow Aerospace Cultural Values” implores employees, “Keep your work and the work of your co-workers very private from people outside the company.” (Mr. Gold said that the confidentiality stems from federal regulations designed to protect technological information and that the engineers are busy working.)

The Las Vegas site is hemmed by barbed wire and patrolled by armed guards.

The soundness of the business case is unknown to outsiders. Mr. Bigelow declines to say if he has firm commitments from any countries or companies to rent space on his space stations. In recent years, he has played down the notion that he is building a space hotel for rich tourists, although he says space tourism could provide a part of his business.

Over the past year, Mr. Gold visited countries like Japan, South Korea, Singapore, the Netherlands, England and Sweden to gauge interest. A stay on a Bigelow station, including transportation, is currently priced at just under $25 million a person for 30 days. That is less than half the more than $50 million a seat that NASA is paying for rides alone on Soyuz spacecraft to the International Space Station. Doubling the stay to 60 days adds just $3.75 million more.

For a country or company willing to sign up for a four-year commitment, the lease for an entire six-person module would cost just under $395 million a year, and that would include transportation for a dozen people each year. “You see why this is attractive for the sovereign client market,” Mr. Gold said.

Image INFLATABLE NASA’s Echo satellite was basically a Mylar balloon. Bigelow’s design uses aluminized and foam skins. Credit... NASA

The Bigelow prices are good through 2018, and Mr. Bigelow said the prices would drop by then if, as he expects, rocket prices drop.