Trajectory to Mars with one month trip time?

[gutza1]

I was wondering what kind of trajectory should a Mars mission use to reach the Red Planet in one month, and how much delta-v would it require? Is there a way to achieve that trajectory with the VASIMR engine?

[Mr Shifty]

You'd have to use some very high impulse (30 km/s) or constant acceleration maneuver. There's a table at atomic rockets with details.

Wikipedia has your VASIMR answer. Seems you'd need a nuclear reactor and some future-tech energy conversion technology.

[Kryten]

I get 40km/s, assuming a Brachistochrone trajectory (i.e. accelerate half way, turn ship around, decelerate half way), using the calculations provided here. There's a good chance I've converted something incorrectly or missed something because I'm pretty tired right now, but it sounds about right to me. It's theoretically possible for a ship with VASIMIR to provide that kind of delta-V, but it'd require hige amounts of power, with all the caveats that brings in space (radiators et.c.).

[magnemoe]

I get 40km/s, assuming a Brachistochrone trajectory (i.e. accelerate half way, turn ship around, decelerate half way), using the calculations provided here. There's a good chance I've converted something incorrectly or missed something because I'm pretty tired right now, but it sounds about right to me. It's theoretically possible for a ship with VASIMIR to provide that kind of delta-V, but it'd require hige amounts of power, with all the caveats that brings in space (radiators et.c.).

Accelerating to midpoint and then brake only makes sense if you have free power but limited trust, solar sail is a good example.

For all other settings you would want to increase trust even if it hit other performances, if you are able to do the burn in less than a week then brake for similar at the target.

The burn close to turnover has low impact on your travel time.

[Streetwind]

Well, you could run the numbers about what kind of payload you could carry with today's technology...

A SAFE-400 reactor weighs roughly half a ton, while producing 100 kW of power and 300 kW of heat that needs to be removed. Maybe that heat could be used in secondary conversion cycles, but for the moment, let's stick to the core specification. The Ad Astra VF-200 consumes 200 kW of power, so we need two reactors, some power management hardware, the engine itself, and ~700 kW worth of radiator area (the engine also produces significant waste heat). I have no idea how much that would weigh, but let's assume a final drive section weight of 1.5 tons. It would have an Isp of 4500s and output 5 N of thrust.

Now you have to add propellant, and then payload. The rocket equation says that a vessel massing 9 tons - carrying the drive section mentioned above, plus 5 tons of argon propellant, half a ton of tankage and structure and systems, and finally 2 tons worth of payload would yield 35,800 m/s of dV. Not shabby at all! Maybe you can't make 30 days with that kind of dV, but perhaps 40 or 45 might be realistic, and that's already a big improvement over the kind of travel time we can expect from chemical engines today.

The question of how the acceleration profile would look like for a 9 ton vessel with 5 N of thrust, I leave to those who are better with math than I am

To put things into perspective, a 2-ton payload would IIRC be enough to carry Curiosity and its descent system, for example. Not that that one had a particular reason to hurry, but hey, it's a SUV-sized rover! And considering a Falcon Heavy can lift over 50 tons to LEO, you could quintuple this hypothetical craft and get a 45-ton variant with five VASIMR engines delivering 25 N of thrust, carrying 10 tons of payload with the same 35.8 km/s dV. That's definitely enough to go manned.

Of course, it might be a problem to find dozens of tons of argon propellant on Mars to refuel the vehicle for the return trip...

Edited November 18, 2014 by Streetwind

[Mr Shifty]

The question of how the acceleration profile would look like for a 9 ton vessel with 5 N of thrust, I leave to those who are better with math than I am

A month of constant acceleration with 5N of thrust would get you about 1500 m/s, which is not enough to reach escape velocity from LEO even using impulse engines. (Constant acceleration trajectories are generally less efficient than impulse trajectories.) 5N is a little over a pound of force; it ain't gonna shift 9 metric tons with any speed.

[Streetwind]

Alright, so it has the dV, but not the thrust.

I suppose you could start removing propellant to bring the mass down until the acceleration profile and the flight time line up. But that's not an adequate answer to the question of what must be done to perform a 30-day Mars transit.

That's maybe the kind of thing that NTRs would be better suited at than nuclear electric propulsion. They would have the thrust... although I wonder if a solid-core would have the Isp, even a modern one. I'd estimate it possible to hit somewhere between 1000s and 1500s. Unfortunately, no such engine exists (in contrast to the VF-200), and neither do the more powerful, theorized liquid-core or gas-core variants.