For orbital transfers to Mars, a Hohmann transfer is often proposed since it minimizes the fuel consumed. Here is what that looks like.

This was generated by the Spacecraft Control Toolbox function DVHoh.m. 255.2 days is a long time for a crew to be exposed to cosmic radiation. NASA has proposed using a nuclear thermal engine to speed things up. The best combustion engines, like the RL10B-2, use hydrogen and oxygen and have a specific impulse of 465 seconds. This is obtained by running them hydrogen-rich. Nuclear thermal, which is only heating hydrogen, can reach 900 seconds. The higher your specific impulse, the less fuel you use for a given velocity change.

A mission to Mars consists of an Earth escape segment, a heliocentric segment, and Mars entry. You can do them all with the same rocket or use separate stages or methods. For example, you could depart from low-Earth orbit (LEO), do the transfer, and enter low-Mars orbit (LMO) with one stage. As an alternative, the launch vehicle could take the Mars transfer vehicle into a heliocentric orbit. Instead of using the transfer stage to do a powered entry into Mars orbit, you could use aerobraking. Aerobraking could be used, in theory, for both Mars entry and to replace the burn into Mars heliocentric orbit (that is, to match the heliocentric velocity of Mars).

We wrote a MATLAB script in the Spacecraft Control Toolbox to explore some of these concepts. Here are the results:

```
Specific impulse nuclear thermal 900.00
Specific impulse H2/O2 465.00
Tank Fraction 0.10
Time Hohmann 255.23 days
Time Fast Transfer 150.23 days
Mass fraction Nuclear Thermal Hohmann 0.30
Mass fraction Nuclear Thermal Fast 0.12
Mass fraction H2/O2 Hohmann 0.05
Mass fraction H2/O2 Lambert Only 0.03
Total Delta-V Hohmann 9.03 km/s
Delta-V Hohmann 4.41 km/s
Total Delta-V Fast Transfer 14.35 km/s
Delta-V Fast Transfer Lambert 9.73 km/s
Departure 4.43 km/s
Arrival 5.30 km/s
Delta-V Earth Escape 3.19 km/s
Delta-V Mars Entry 1.43 km/s
```

The Tank Fraction is the fraction of the spacecraft’s dry mass that is proportional to the fuel mass. This is composed mostly of fuel tanks. The mass fraction is how much mass is left when the spacecraft reaches Mars, not including the fuel tanks. The total Delta-V assumes one stage is used to go from LEO to LMO. Lambert’s law is used for the fast transfer. We break up the Lambert maneuver into departure and arrival velocity changes. In principle, you could aerobrake 5.3 km/s + 1.43 km/s.

The fast transfer is shown below. Contrast it with the Hohmann transfer.

This was generated using the Spacecraft Control Toolbox function, PlanetTransferLambert.m.

I need to play with this toolbox! I have been following the options and the NERVA rocket seemed to be a good interim step to get to mars. (The nuclear salt water rocket, thought totally theoretical, seemed even better… an idea to follow)

I was playing in a google spreadsheet with a rather ridiculous “what if” we could do constant acceleration, how long to get from earth to mars. It made me realize I was ignoring thrust to weight ratio of the drive itself. I have come to think that we need to begin separating fuel from reaction mass. In a Chemical rocket, they are one in the same. But independently of how you put the energy in, it is the reaction mass that generates the acceleration to change the Velocity.

Picking a mass out of the air like 12000kg (crew dragon) and assuming an infinity long fuel line and straight line distances, I was calculating just the reaction mass for .1g to 1g. So just the .1g would be fantastic for trip time of 70 to 90 hours to flip and burn. The extremely low thrust of the DFD means the number of engines needed would be unreasonable.

So could a possible design for high a thrust fusion rocket be, from left to right, a frc plasma injected into an area where it is heated to fusion conditions and then the plasma is ejected out the back outside the magnetic containment as a new frc replaces it in the heating chamber. This region is a nozzle that is cooled internally and with a film of hydrogen(just h2 reaction mass). I was thinking that injectors outside the dfd section could grow the fusion region and the isolation instead of magnetic could be a balance of amount and direction of H2 with injected fuel. Can a fusion region exist like this or would the non ionized H2 just dilute the plasma and snuff out the reaction?

Thanks Jeff! Check out this blog post

https://www.psatellite.com/doing-the-mars-run-with-fusion-propulsion-at-1-g/

It will allow you to do the calculations you need.

Thanks! I did start at 1G just to get a laugh. I knew the numbers would be astronomical (groan). Is there a compromise that reduces fuel by 2 orders of magnitude but reduces each way to a few weeks, a lot of the Human issues are reduced and less supplies needed for the trip itself.

I tried to come up with realistic alternatives. One thought would be human centric. I wonder what it would take in fuel and time to start the journey at 1G from earth and taper off the acceleration such that at the flip point which has now moved, we would be about .65G and they would arrive in orbit with gravity being .376G.

Another idea comes from another persons blog post. from a fuel point getting rid of mass reduces fuel needed to slow down so if a “tug” was able to disconnect from the capsule and a short(er) duration high G like 5G’s for 30 min and continue on an ellipsoidal path would it re-cross the mars orbit at the time needed to go home. A short burst from the launcher High G chemical 🙁 , would allow the return capsule to catch up for the ride home.

One more question has been bothering me, if I may? I see the thrust equation for a rocket is linear relation for exit velocity and mass flow rate. And exit velocity is often used almost interchangeably for specific impulse. So 1000kg/sec and exit velocity of 200m/sec vs 20kg/sec @ 10000m/sec are both 200KN of thrush, what is the mass flow rate of the 10MW dfd at full thrust agumentation. I saw those in talks Stephanie gave and will review but even to come up with .1G the number of engines seemed unreasonable. If they cannot scale in diameter and only perhaps in length, can the dfd ever be used for high-thrust applications?

DFD is not suitable for high-thrust applications, at least based on the MHD models we are using. If you try to get too high a thrust, the thrust goes to zero.