Fueling the Rockets
Tsiolkovsky’s rocket equation can be used to determine the delta-v or change in velocity attainable for a given mass fraction, (m sub initial)/(m sub final), and the figure at the bottom of this page displays the required delta-v for points in the Earth-Moon and Mars-Phobos-Deimos systems. Given the performance specifications for the Shuttle’s engines, the most efficient main rocket engines currently in production, the total required delta-v for a one-way trip from Earth’s surface to Mars is about 18.7 kilometers per second (kps); for reference, the delta-v to get into low-Earth orbit (LEO) is around 11 kps. Plugging this number into our rocket equation, we get a truly prohibitive mass fraction: 67.2! To turn that number on its head, that’s the same as saying that only 1.5% of the total mass is the space vehicle, the remainder being fuel. From an engineering standpoint, that’s totally unrealistic, even assuming dramatic materials science breakthroughs. Mass fraction is the reason why most rockets have stages; staging enables a space vehicle to shed dead weight and improve its performance.
In this particular case, the solution was to launch pieces into LEO individually and assemble them there; that way, the largest portion of the work was already done and the fuel load of the Mars-bound vessel was reduced. Our mass fraction using this method is far lower, around 11.1 (~90% fuel). Of course, the fuel still needs to be expended to get the vehicle into orbit (and the total fuel required to get the parts to orbit is higher, since the total empty mass of all the launch vehicles is also higher), but the delta-v when launching the mission from that point is much more reasonable. Total fuel expenditure could be dramatically reduced by relying on an aerocapture maneuver on arrival at Mars rather than using a braking maneuver (total delta-v would be 3.8 kps, and mass fraction would be 2.4). For much the same reasons as aerocapture on return to Earth, making the atmosphere do the work is a much more fuel-efficient strategy. For the aerocapture profile, the return trip to Earth would require 6.9 kps delta-v for a round-trip total of 10.72 kps and mass fraction of 11.45, numbers definitely achievable through the use of staging. One way to decrease the overall delta-v required even further would be to establish a foothold on the Moon and assemble/launch the vehicle from there, since the delta-v to achieve escape velocity from the Moon is 2.2 kps compared to 13.22 from the Earth’s surface. Considering that the delta-v required to achieve escape velocity from Eath’s gravitational well is greater than that required for the mission from that point on, such a change would mean very significant savings in terms of fuel required. Gravitational assists can also reduce the required velocity, usually at a cost in terms of transit time and trajectory complexity.