There are two limitations you did not take into account. The first is the rocket equation, https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation . You need a thrust with a very high exhaust velocity - much higher than what an ion drive can produce - to get to relativistic speeds. Otherwise something like 99.999999999999% of the ship's mass will need to be propellant. I worked it out a few weeks ago at https://news.ycombinator.com/item?id=12281830#12282399 . The ratio of payload to propellant for ~0.8c using engines 10x better than an ion engine was 1 to 74 quadrillion.
The second is to have enough thrust to get to relativistic speeds for the human passengers in their lifetime. A engine with an ISP of 8000 s (about 10x better than the current best ion engine) would get there eventually, but long after any crew died of old age.
To get 4.25 lightyears in a year requires a continuous acceleration of a good sized fraction of a gravity. We simply don't know how to do that, outside of theoretical proposals like Dyson's "Super" Orion. Quoting https://en.wikipedia.org/wiki/Project_Orion_(nuclear_propuls... :
> At 0.1c, Orion thermonuclear starships would require a flight time of at least 44 years to reach Alpha Centauri, not counting time needed to reach that speed (about 36 days at constant acceleration of 1g or 9.8 m/s2). At 0.1c, an Orion starship would require 100 years to travel 10 light years.
There are two limitations you did not take into account. The first is the rocket equation, https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation . You need a thrust with a very high exhaust velocity - much higher than what an ion drive can produce - to get to relativistic speeds. Otherwise something like 99.999999999999% of the ship's mass will need to be propellant. I worked it out a few weeks ago at https://news.ycombinator.com/item?id=12281830#12282399 . The ratio of payload to propellant for ~0.8c using engines 10x better than an ion engine was 1 to 74 quadrillion.
The second is to have enough thrust to get to relativistic speeds for the human passengers in their lifetime. A engine with an ISP of 8000 s (about 10x better than the current best ion engine) would get there eventually, but long after any crew died of old age.
To get 4.25 lightyears in a year requires a continuous acceleration of a good sized fraction of a gravity. We simply don't know how to do that, outside of theoretical proposals like Dyson's "Super" Orion. Quoting https://en.wikipedia.org/wiki/Project_Orion_(nuclear_propuls... :
> At 0.1c, Orion thermonuclear starships would require a flight time of at least 44 years to reach Alpha Centauri, not counting time needed to reach that speed (about 36 days at constant acceleration of 1g or 9.8 m/s2). At 0.1c, an Orion starship would require 100 years to travel 10 light years.