I'm writing a Colonization story, and I'm trying to determine which propulsion system would be the best option. The destination is Kapteyn b, 12.76Ly from Earth, and our 40K colonists will be in Cryonic Suspension for the journey. I need an option that gives me at least 10% Light Speed for what will obviously be a huge vessel. Assume this takes place 50-100 years from now, so no Warp Drive or Antimatter systems. I don't mind getting a little creative, but I'd like to keep it as realistic as possible. Thanks in advance.
I would recommend a Bussard Ramjet, in particular a Ram Augmented Interstellar Rocket (RAIR). This was basically a Bussard ramjet which carried its own fuel, and only used the hydrogen it scoops up in the interstellar medium as propellant. This avoids drag issues which are believed to make the Bussard Ramjet impossible.
However, be aware that the demands of this are extrordinary. If you accelerate to 20% light speed, and then decelerate back to 0, you achieve your goal of 10% light speed. However, achieving 20% light speed calls for 1.8PJ/kg in the ideal setting. Practically speaking, the demands will be greater than that, because no engine is 100% efficient. That's on par with the energy consumption of all of Greenland in 2008 (I really do love Wikipedia's Orders of Magnitude: Energy page). Now generation ships are big. They're more than a kilogram. If we assume the generation ship is 417,289 kg, which is the mass of the ISS (which supports the lives of a handful of people, not a colony), you're talking about numbers on par with the yearly energy consumption of the entire world. For a more realistic sized generation ship, you're talking energy on par with the total energy reserves on Earth.
So it is worth noting that, to make this practical, your tech is going to have to advance at least to the point where we can start tapping the massive energy of the sun. We can't rely on just what's on earth. That should help set a lower bound on the tech level.
Have you looked at Atomic Rockets?
You need either an insane fuel-to-payload ratio or energetic fuels like antimatter -- which is (unlike warp) solid physics, with only the engineering missing.
If you don't want that:
- Laser-boosted lightsail.
- A little engine and payload section on a big iceball, and a much longer flight time.
Rockets are not a good idea at all for this application. Essentially rockets operate by throwing mass (the propellant) out of the exhaust at speed ve pushing the rocket away with an acceleration that is equal to -ve / mship * dmpropellant/dt. Usually rockets have to bring their own propellant, unless it is a ramjet design as stated in another answer.
The problem is the time frame involved and the sheer size of the numbers. First, there is the mass of the ship (without fuel and propellant). We can estimate that at 500 kg per colonist (optimistically)) times 40k = 20e6 kg.
You do not want to squash your colonists so your acceleration is set to a steady 1g ~ 10 m/s. To reach 0.1c you would need 300e6 / 10 = 3e7 seconds or slightly less than a year at 347 days.
At that point you coast at a leisurely 0.1c to your destination 12.76 lightyears away taking approximately 127 years. Near the destination you decelerate at 1g again for another year, bringing your total journey time to 129 years.
So, how much propellant would you have to bring? For that, we turn to the inverse of the Tsiolkovksy equation for your trajectory (acceleration + deceleration):
mdry * e 2 dv / v = mwet,
or with a typical exhaust velocity of 1000 km/s (nuclear pulse propulsion):
20e6 * e 2 * 300 = 7.54e267 kg which is 'slightly' more than the mass of the universe by several orders of magnitude.
20e6 * e 2 = 148e6 kg
Still, when you start your journey you will burn 5kg (148e6/30e6) of propellant/fuel (uranium, thorium in the case of a 100% efficient fission fragment rocket) per second. That is a lot ...