Since SpaceShipOne spun through 29 rolls flying out of the atmosphere in 2004, the ship’s designer, Burt Rutan, has been promising a new and improved design for his follow-on ship–one that won’t shake, rattle, and roll paying passengers quite so much.

SpaceShipTwo, to be owned and operated Richard Branson’s Virgin Galactic, has been coming together behind closed doors, with its exact configuration a closely guarded secret.

That’ll change next Wednesday when Rutan and Branson appear in a rare joint press conference at the Museum of Natural History in New York to show off some scale models.

Virgin’s also debuting a new look for its branding and “livery,” as they’re calling it. Still based on Branson’s eye, the logo, for one, will undergo a makeover.

Besides the new ship configuration, the big question on everyone’s mind is how things are going for the project since last summer’s fatal test stand accident that has forced a halt to development on the spaceship while an investigation grinds on.

Virgin remains upbeat, planning for test flights to begin this summer, with the first spaceflights next year, and revenue flights to begin in 2010, according to a MarketingWeek article (via RLV and Space Transport News).

It’ll be interesting to see what Rutan says about that, since he has thus far steadfastly refused to hold himself and his company to any sort of schedule.

Check in here for links to my reporting on the unveiling after it takes place.