3.4. Model Analysis#
3.4.2 Model Analysis
Our work on the preliminary analysis helped identify the major components that would have to be traded between, but there were still a large number of viable configurations for the three launch vehicles. There were 39,168 possibilities for launch vehicles, accounting for two and three-stage launch vehicles with a choice of four propellants and three materials for each stage! Designing over 39,000 vehicles in order to make an absolute decision on cost was impossible. Instead, we chose to use a simplified model analysis technique. This technique required multiple stages with a system of codes that the team refined between iterations.
Our scope for this system of codes was quite large. We designed codes to vary a number of parameters for each possible configuration. After specifying a specific combination of propellants and materials for the vehicle and a required total V, the code would vary the V allotted per stage and also each stage’s inert mass fraction, creating a host of possible configurations.
A propulsion code would size each of these test vehicles and determine the required propellant mass in each stage. Many of these designs did not budget enough inert mass, so a structural code was written to weed out those cases. These two codes left only test vehicle cases that delivered the required energy and were realistic to construct. All of these cases were possible solutions for the material, propellant, and V combination selected. In order to find the optimum the case the lowest gross liftoff mass (GLOM) and cost were recorded for each case and compared. The team repeated this process for all possible configurations with a few possible V values (9000, 12000, 15000 and 18000 m/s) that encompassed our feasible range of V.
At this point in the analysis, the propulsion, structure, and cost codes were based on historical data. Important values for material thickness, number of structural members, engine mass, propellant performance characteristics, and required hours for manufacture and launch support were all derived from studies of previously successful designs.
Cost was the most important factor when considering possible configurations, so in order to rank the designs, the team created a simple cost model. This first model included costs for the materials used in the vehicle, the cost of propellant, handling modifiers for toxic or cryogenic propellants, and also modifiers for a balloon or aircraft launch that incorporated rental fees associated with these launches. We believed that other costs would be similar across all models so they were not incorporated at this time.
This iteration of this design process involved a great deal of effort by the team. There was minimal automation and due to the sheer number of configurations and limits to computational time, an exhaustive analysis was not possible. Also, because our models were still based on historical data, it would have been hasty to trust these results completely. We examined a subset of the total number of cases with a test matrix that included design variations that touched on each of the variables. That helped highlight some of the high level decisions to be made.
Our test matrix involved only a couple of thousand cases at our selected V values, but revealed some valuable trends. Configurations with a solid propellant in the upper stage were most attractive across the board in terms of cost and GLOM. Also, two-stage vehicles were routinely out-performed by their three-stage counterparts. It was clear that we wanted to make the top stage the lightest possible. Seeing the difference in GLOMs between a titanium and steel top stage showed how important it was to limit the mass placed in that stage. These trends helped trim the design matrix for subsequent model analysis.
This analysis however did not help with determining our launch method. The costing models were still missing a lot of key costs that would affect the different launch types. Also we had yet to determine the difference in V from a ground launch and an air launch. This first analysis helped us to see what areas we needed to investigate further to make our model analysis more accurate and complete.
With our testing iteration done and the process understood, we prepared for a more extensive study on the launch vehicles. Before we could finalize our design, we needed to make sure that we examined the possible configurations with a much more detailed model. Each group on our team worked to make their codes include important physics and provide a holistic view of the launch vehicle.
Our design in other areas of the project has also matured and some changes were made to the overall design. Most important was our decision to move the majority of the avionics into the second stage. Analysis showed that having high-mass items like the battery and self-destruct mechanism in the final stage quickly overshadowed the mass of the payload and washed out any difference between the three satellites. Also, we found that placing these items in the second stage lowered GLOM and total cost. We had also decided on using purely pressure-fed systems in order to avoid the high cost of turbo-pump machinery.
The propulsion codes were revised to no longer rely solely on historical data. Instead, optimum expansion ratios and mixture rations were selected by using NASA’s thermochemistry code and engine performance parameters were recalculated for each stage for each possible case. In other words, the important characteristics for the propulsion system were specified and made-to-order on a case-by-case basis. Calculations for pressurant were also included.
Another update included changes in the structures codes to dynamically designed each stage’s inert components as well. Based on the g-loading predicted by the trajectory requirements, the number and size of each structural member was modified. Tanks for the pressurant, thrust vector control propellant, and main propellant were each designed with fidelity indicative of our final design. Intertank regions and payload fairing were also sized for each vehicle as well.
In order to manage all of the 39,000 cases we developed a naming scheme incorporating the payload, launch type, propellants, and tanks. Each case was assigned an 8 character (3 stages) or 6 character (2 stages) code. The first 2 characters represented the payload and launch type. S for the small, 200g payload, M for the medium, 1 kg payload and L for the large 5kg. The launch type was represented by either G for ground, B for balloon, and A for aircraft. The following characters were for each stage, 2 characters per stage. The first character represented the propellant type, C for Cryogenic, S for Storable, D for Solid and H for Hybrid. The second character is for the tank material, S for Steel, A for Aluminum, C for Composite and T for Titanium. One example is MG-CA-SC-DT this is a 1kg ground launch case with a cryogenic and aluminum first stage, storable and composite second stage, and a solid with titanium third stage.
One limitation that plagued our analysis was the limited computational resources available and the requirement for manual input for each configuration. Each possible configuration took upwards of 5 minutes, so for thousands of cases, this translated into days on a typical workstation. For the second analysis, a more capable automation routine was written and streamlined so that it could be run remotely on the department’s servers. We still required almost three days to run all possible configurations, but it was possible to evaluate each and every option to totally exhaust the design space. With the more refined propulsion and structures codes, we felt ready to limit the number of models under consideration to only a mere handful. The following tables list the 5 winning cases for each payload.
Table 3.4.2.1 Winning Cases – 200gModel Name / Cost / GLOM (kg)
SB-CA-DA-DS / 4134770.44 / 6348
SB-CA-DA-DA / 4135005.02 / 6348
SB-CA-DA-DT / 4174441.05 / 6348
SG-CT-DT-DA
SA-CT-DT-DA / 4294144.03
4294144.03 / 6528
6528
Table 3.4.2.2Winning Cases – 1kg
Model Name / Cost / GLOM (kg)
MB-SA-DS-DA / 4085248.85 / 11497
MB-SA-DA-DA / 4086343.04 / 11497
MG-SA-DA-DA / 4104172.25 / 9292
MA-SA-DA-DA / 4104172.25 / 9292
MB-SA-DA-DT / 4125954.08 / 11497
Table 3.4.2.3Winning Cases – 5 kg
Model Name / Cost / GLOW
LG-SA-DS-DA / 4103413.74 / 11572
LA-SA-DA-DA / 4104510.54 / 11572
LG-SA-DA-DS / 4110887.84 / 13573
LB-SA-DA-DA / 4224938.33 / 12678
LB-CA-DA-DA / 4247196.12 / 10177
We used this data to set up trends and find errors in our analysis. We also came to the conclusion that we couldn’t always pick the model with the lowest cost. If the cost between two designs were close and we went with the smaller GLOM. Since there are a lot of uncertainties in our cost models we knew it would be a safer to relate the GLOM because it was associated with physics, rather than cost and we had more confidence on the physics calculation that than the calculation of cost. Engine costs for example are based off historical data and then the inflation rate of the years since the data. This is probably not the most accurate prediction of cost because technology is constantly changing and making production of complex systems more efficient and thus more affordable. Another reason the physics is more reliable is due to the fact that our costs are based on estimates from companies providing space rated components which may or may not meet our exact specifications, our requirements are a lot more relaxed than more space missions so the costs for different components could vary greatly.
From this surface analysis we were able to gain a better insight into what ranges of inert mass fractions and ∆V breakups would be feasible. This data relationship was hard to make any correlations about a ground verses an air launch because we were using a ∆V of 12,000 m/s, given from trajectory, for all of the cases.A comparison between a ground and air launch can not be reasonable without having different ∆V requirements for the launch type.
The next step was to fix the analysis for hybrid and storable propulsion. We gained more information about the costs associated with having variable and directional thrusts which depended on the propulsion system. LITVC and gimbaling varies the thrust, but the system depends on the propellant and thus costs are not equal across all possible models. We also developed a more in-depth launch type cost modifier before the next model run was completed.
This coding system was slightly limited due to the fact that the GLOM values are not optimized between the structures and propulsion codes. From the ideal rocket equation, the propulsion’s code calculated an inert mass required and then it passed that mass into structure’s code to see if the case was feasible. Yet, the minimal mass that structures calculated was not recorded.
We did not have the computational power that would be needed to run thousands of cases each to an optimized configuration. Thus we used the model analysis to optimize and pick the best cases from the trends and data given here. Trends like having titanium saves mass in the GLOM but it is only cost effective to have titanium in an upper stage because it is smaller and not as much material is required.
The model analysis eventually morphed into an optimization task with trajectory. In this phase additional codes which just added more details in cost and mass like hoops in the tanks and cost quotes from a few additional companies. This analysis resultedin limiting the cases to the models we selected.
Author: Alan Schwing and Danielle Yaple