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. Accounting for two and three-stage launch vehicles with a choice of four propellants and three materials for each stage, there remained slightly over 5,600 possibilities for each vehicle! To design all of the 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 DV, the code would vary the DV allotted per stage and also each stage’s the 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 also could be realistically constructed. All of these cases were possible solutions for the material, propellant, and DV combination selected, but in order to find the optimum the case with the lowest gross liftoff weight (GLOW) and the case with the lowest cost were recorded. The team repeated this process for all possible configurations with a few possible DV values that encompassed our feasible range of DV.
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 man-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.
The first 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 helped highlight some of the high level decisions to be made.
Our first look involved only a couple of thousand cases at our selected DV 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 GLOW. Also, two-stage vehicles were routinely out-performed by their three-stage counterparts. It was clear that we wanted to make the top stage lightest possible. Seeing the difference in GLOWs 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 DV from a ground launch and an air launch. This first analysis helped us to see what areas we needed to further investigate to make our model analysis more accurate and complete.
With our first iteration done and the process understood and tested, 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 lowed GLOW and total cost. We also had 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 of 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.
We also updated the structural codes in order to dynamically design each stage’s inert components as well. Based on the g-loading predicted by the trajectory requirements, the number and size of each structural members 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.
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 and 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.
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 3.4.2.2 Winning 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 3.4.2.3 Winning 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
Listed above are the top 5 winning cases for each payload. 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, straight up. If the cost were close and we went with the smaller GLOM. Since there are a lot of uncertainties in our cost models it would be a safer to relate the GLOM which we have more confidence on the physics calculating 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 number because technology is constantly changing and making production of complex systems more efficient and thus more affordable.
From this first 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 for all of the cases and you can’t really compare a ground and air launch without having different ∆V requirements.
The next step was to fix the analysis for hybrid and storable propulsion. We gain more information about costs of having variable and directional thrusts which depended on the propulsion system. We also developed a more indepth launch type cost modifier before the next model run.
This coding system is slightly limited due to the fact that the GLOM values are not optimized between the structures and propulsion codes. Propulsion’s code calculate an inert mass required from the ideal rocket equation and then it is passed into structure’s code to see if the case is feasible.
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 which is physically correct and optimized 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 stage additional codes where added and brought us to the models we selected.
Author: Alan Schwing and Danielle Yaple