3.4.2 Model Analysis ( Schwing and Yaple)

3.4.2 Model Analysis (Schwing and Yaple)

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 V, the code would vary the V 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 V 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 V values 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 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 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 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 V 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.

Listed above are the top 5 winning cases for each payload. From this list we selected our winning case for each payload. As you can see we didn’t always pick the model with the lowest cost. If the cost were close and we went with the smaller GLOW. Since there are a lot of uncertainties in our cost models it would be a safer to relate the GLOW 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.

Discussion about different launches!

Over all the model analysis provided us enough information to limit all of our final models down to a top 3 choices for each payload size and finally we were able to limit it down to one case for each payload. These cases are shown below.

STILL NEED TO ADD STUFF WHEN NEW CASES COME OUT!!!