Week 9: Just keep swimming, just keep coding, just keep CADing…
Kira A -
Hey everyone! Welcome back to my journey to implement the orbit-raising maneuver into a cislunar cargo mission of my design. Last week, I gave you guys a little insight into the process of designing components for my spacecraft in FreeCAD. This week I wanted to give you guys a little sneak peek at the physical 3D-printed motor from the rough design I included in my previous blog.
Computer-Aided Design and 3D Printing
While this model is not the final design, I prefer to print each iteration of the components I am modeling to ensure that the 3D printers I use can replicate the models with enough precision to fit each part together when assembling the full spacecraft. FreeCAD, as I stated in my last blog, allows you to set certain parameters for the dimensions of your models, however, it is almost always easier to see if each part fits the other with the physical models.
If you recall my last blog, you might notice that this print is missing the valves at the top. This is because I modeled it as one part, not multiple, which made the print job more difficult for my printer as it was unable to properly support the tiny valves. This is another reason why I prefer to print out multiple iterations of each component I model.
This week, I plan to complete printing each component of my spacecraft and assemble it so that those of you who attend my presentation can get hands-on experience with my project and better visualize each major component of the spacecraft.
Coding in MATLAB
Beyond this past week’s CAD journey, I have been working in MATLAB to implement the different methods of orbit-raising as well as translunar injection to compare the fuel expended for each. I am still working on the orbit-raising analysis, but I plan to complete it by the end of this week. As for the translunar injection analysis, I have been able to dive a little deeper into what theoretical options there are, and what I have been able to calculate in MATLAB.
As I mentioned in a previous blog, I will be inserting my spacecraft into a near-rectilinear halo orbit (NRHO) to take advantage of its unique stationkeeping and communication properties and dock with the proposed NASA Gateway station orbit for cargo transfer. To do so, my spacecraft must not only perform an injection burn, but a plane change maneuver, as the NRHO lies almost perpendicular to the Earth-Moon plane. For this reason, the delta-v required for this maneuver is very high in comparison to other selenocentric (around the Moon) orbit insertions. The following are three translunar injection orbits being considered by agencies such as NASA for upcoming missions that address the issue of high delta-v requirements: Ballistic Lunar Transfers, Weak Stability Boundary Transfer (WSB), and Perilune Rendezvous Method (PRM). For the scope of my mission, however, I will not be implementing any of them because they require that I consider the Sun’s gravitational influence on my spacecraft, which would complicate my calculations beyond my current capabilities. In the future, using what I learn from this project and my further schooling, I would love to investigate these transfer orbits in more depth and possibly implement them into this project.
Ballistic Lunar Transfers (BLTs):
BLTs (unfortunately, not the sandwich) exist not only for translunar injection orbits, but for a variety of injection orbits for other bodies in space. BLTs take advantage of the Sun’s gravity to raise perigee (around the Earth, so for the transfer orbit) and inclination by going out to an apogee of approximately 1-2 million kilometers! For reference, the distance from the Earth to the Moon is about 384,400 kilometers. BLTs have been used in previous lunar missions such as the Hiten (Celestial Maiden) Mission carried out by the Institute of Space and Astronautical Science (ISAS) of Japan and the Gravity Recovery and Interior Laboratory (GRAIL) carried out by NASA.
Weak Stability Boundary Transfer (WSB):
The weak stability boundary transfer (WSB), similar to the BLT, uses the gravitational influence of the Sun, Earth, and Moon to make a low energy transfer to NRHO. WSB requires very little delta-v (<100 m/s), but because it is so low energy, it takes almost 100 days to complete, outrageous for any manned missions, yet still suitable for cargo missions.
Perilune Rendezvous Method (PRM):
Lastly, the perilune rendezvous method (PRM) is a proposed translunar injection to NRHO method. Again, it is very similar to both the BLT and WSB because it takes into account more than just the gravitational influence of the Earth and the Moon on the spacecraft, however, it has the shortest transfer period out of the three (18 days), making it desirable for quick cargo transfer. The PRM does require about 545 m/s delta-v, which is more than the WSB, so it depends on the time and fuel constraints of the mission objective whether or not a space agency might consider using it.
Unfortunately, with the knowledge I have now, I am unable to implement any of the methods for translunar injection discussed above without derailing the focus of the project to translunar injection and not orbit-raising and mission design. However, that did not stop me from finding a solution with what knowledge I have. In MATLAB, I calculated the delta-v needed and fuel expelled for four types of translunar injections to a NRHO. Below, the table displays the values of delta-v and delta-m (change in mass due to fuel expelled) for two-burn methods and three-burn methods for insertion at both the perilune and apolune. The two-burn method, which I found to be more efficient, employs one burn at the perigee of the transfer orbit and another at the apogee to both change the velocity in order to establish a new orbit around the Moon and to change the inclination. On the other hand, the three-burn method uses one burn at the perigee of the transfer orbit, one burn at the apogee to establish the new orbit, and one again at the perigee at the second approach to change the inclination of the new orbit around the Moon. The following values of the orbits used in my calculations are based on the values provided by ISRO and NASA for the Chandrayaan 3 mission (initial orbit) and the Gateway station (objective orbit).
Initial Orbit (around Earth): 170km x 170km
Objective Orbit (around Moon): 1700km x 70,000km
As you can see, the most efficient of the four methods is the two-burn apolune insertion, narrowly beating the three-burn apolune insertion. For this reason, the two-burn apolune insertion is what I will use when I tie in the orbit-raising maneuver to complete the mission. You can also see that the delta-v requirements for each method are measured in km/s, not m/s, which signifies that they are wildly inefficient compared to the methods I described earlier, but I work with what I can!
Next week and Acknowledgements
Continuing into this week, I plan to finish coding the different orbit-raising maneuvers into MATLAB and complete the mission! Furthermore, I will assemble my spacecraft and continue to add to my final presentation.
Thank you so much to Dr. Goodwin, Dr. Farooq, and Mr. Joseph for allowing me to experience the ups and downs of this process while still supporting me and guiding me to the goal. Lastly, thank you to all of you who tuned in. Hope to see you next time!
Ad Lunam!
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