Devin-M said:
Not bad, a trip to Alpha Centauri in a human lifespan with 1/10th the takeoff mass of a Falcon 9…
There's a LOT of simplifications and unrealistic assumptions made in this thread. A significant number of the more impossible assumptions were made by me. I took a little time to make some graphs to (hopefully) make the topic a little clearer.
These graphs shows the
maximum possible change in velocity for a self-propelled spacecraft at revalistic velocities. Reserving fuel to slow down requires calculating in terms of
rapidity, which I felt would make the answer too technical for this context. The take away is that these graphs are valid
if and only if the acceleration is unidirectional, using the following formula:
$$ \Delta v = c ~tanh~\frac {Velocity_{exhaust}}{c} ~ln ~\frac {mass_{wet}}{mass_{dry}}$$
Recall that c = 299,792,458 m/s, and ##mass_{dry}## is
everything that is not the fuel. Engines, life support, shielding, fuel storage infrastructure, etc. Therefore, ##mass_{wet} = mass_{dry} + mass_{fuel}##.
This first graph shows what I think is the most "realistic" data. Rocket exhaust between 0 and 0.5 C, with a mass fraction between 0 and 100. Notice the asymptotic behavior of the graph in two dimensions:
##\Delta##v depends on the natural logarithm of the mass fraction (##ln \frac{mass_{wet}}{mass_{dry}}##) so high velocity space travel requires a mass fraction of no less than ##e##, or your craft can never accelerate up to the exhaust velocity.
##\Delta##v
also is a function of hyperbolic tangent, which conveniently handles the pesky can't-travel-faster-than-light issues. As your mass fraction approaches infinity and your exhaust approaches c, your maximum ##\Delta##v approaches c as well. This helps to underline why the graph is only valid for unidirectional acceleration: it's assumptions make it impossible to carry over c ##\Delta##v.
Alright, but what if you
really wanna go fast. Increasing the mass fraction, as show in the figure above, allows for much higher velocity travel with lower exhaust velocity. The downside is
very little usable payload:
$$ \frac {mass_{wet}}{mass_{dry}} = \frac {mass_{dry} + mass_{fuel}}{mass_{dry}}$$
At a mass fraction of 1000, every 1kg of ship needs 999kg of fuel, and again: that 1kg must include the mass of whatever stores the 999kg of fuel, as well as every other component of the ship.
Given the impracticality of an ever-increasing mass fraction, what about increasing the exhaust velocity? The figure above shows the relation if the engines' exhaust velocity can be scaled up to .999c. Increasing impulse is substantially more effective than increasing the mass fraction. This implies that efforts made towards interstellar travel should focus more on increases in engine impulse than increases in fuel capacity.
This post has strayed a little far from the original question asked, so to bring it back to the relevant context, the purely fusion powered engine discussed has an impulse of ~ 0.14c
If it is 100% efficient at turning protium into iron. Hopefully the cacophony of other posters balking at that demonstrates the folly of assuming that such an engine could be constructed.
If you care less about how possible it is to build, the figure below shows the maximum unidirectional ##\Delta##v of a spacecraft powered by 100% efficient H
1 to Fe
56 fusion engines.
Again, these are theoretical values, and make no claims on the practicality or possibility of building such a spacecraft.
If you would like to learn about the various elements that go into designing a spacecraft, I strongly recommend
The New SMAD. The book is a little pricey, but it's an amazing resource used throughout the industry. The section on spacecraft and payload design is about 430 pages long and walks you through the various elements and considerations.
If you'd like to learn about more realistic orbital maneuvers, the way current spacecraft move in space, I've found both
Orbital Mechanics for Engineering Students and
Interplanetary Astrodynamics to be great books. These are textbooks used to teach the material to undergraduate students and do a fantastic job covering the basics in an entertaining and (relatively) easy to follow manner. Getting where you're trying to go in space is substantially more complicated than pointing where you want to go and hitting the gas. That said, they assume a strong background in physics and calculus, as well as at least a moderate ability in programming.