### Introduction

In this series, we have been developing a model for an electro-magnetic railgun (Figure 1). To this point, it has primarily been a descriptive model, capturing concept of operation, requirements, architecture and mechanical and electrical design. However, a key benefit of Model-Based Systems Engineering (MBSE) is that it can couple the descriptive models with quantitative analytical models that allow us to estimate cost and performance, evaluate alternatives, and test requirements from the earliest stages of system development.

*Figure 1 Simplified physics of electromagnetic railgun*

### Railgun Analysis

A constant problem in integrating architecture, design and analysis is the need to keep models from the three domains consistent. This is complicated by the on-going changes in the system as it goes through development. There are two basic approaches to the problem:

### Intrinsic

One can embed the analysis and simulation models in the architecture model. SysML, for example, has parametric model elements that can connect value properties and constraints and there are tools that can execute these models, i.e. solve for and return the results to the SysML model.

This approach has the advantage that architecture and analysis are closely coupled in the same tool. It makes the analysis easily available to the system engineer, which is convenient when it must be executed repeatedly, as with trade studies. However, architecture modeling tools are typically not optimal for analysis and simulation and the analyst specialists resist giving up their familiar specialized tools.

### Extrinsic

The alternate approach is model transformation, i.e. to take a part of the architecture model and use it to create a congruent model in a simulation tool. The analyst takes this starting model and adds the equations and other infrastructure needed for an executable simulation. Because the architecture and analysis models can change and diverge, this approach requires a mechanism for comparing and updating the models as the project goes forward.

*Figure 2 Tiered Railgun Analysis schema*

We will look at examples of both approaches in this TechNote. Figure 2 represents an Intrinsic analysis using relatively low-fidelity approximations captured as a SysML parametric model. It is organized as a tiered analysis, where the brown blocks in Figure 2 represent system components or subsystems and the green blocks hold the constraining equations for the analysis. The system component blocks hold values such as mass or resistance that are static characteristic of the components. In this model, the rail length derives from the CAD model in Part 3, Figure 3, via the parametric connection and unit conversion shown in the same figure. The analysis blocks hold the constraints as well as the final or intermediate values of the analysis, such as projectile energy or muzzle velocity, and reference the component blocks for the static values.

*Figure 3 SysML parametric diagram, Projectile Performance block*

The analysis is divided into three tiers, which can facilitate development, testing and re-use.

**ProjectilePerformance**holds the physics of the electromagnetic rail gun. Inside the block is the parametric model represented in Figure 3. Starting from values such as rail current and resistance and projectile mass, results such as exitVelocity and projectileEnergy can be calculated. The equations at this stage are rough approximations, adequate when detailed rail geometry and support structures have not been developed. Bear in mind that SysML parametric relationships are acausal. Which values are inputs and which are outputs is not defined until later at instantiation.

*Figure 4 SysML parametric diagram, ElectricalPerformance block***ElectricalPerformance**describes the electrical characteristics of the power system generating the high DC currents. This is captured in the parametric diagram shown in Figure 4. The shotEnergy value calculated by ElectricalEnergy constraint block is larger than the projectileEnergy because of electrical losses due to rail system resistance and inductance. One key parameter is rechargeTime, the time between firings while the capacitor recharges, which is an important factor in weapon utility.**ReqtsVerification**takes the values of projectile energy, exit velocity and recharge time calculated above, with the quantitative requirement tests shown in Part 2, Figure 2, and returns binary Pass/Fail verification results for these three requirements.

### Next Steps

In the final part of this blog series, we will use the Intercax parametric solver to execute the model we have built, including trade studies of beam length and electrical power. We will also examine the extrinsic approach described above, using the connectivity structure of the SysML model as a foundation for a congruent Simulink model for more detailed and higher fidelity simulations.

**Related posts:**

- MBSE for Railgun Design | Part 1
- MBSE for Railgun Design | Part 2
- MBSE for Railgun Design | Part 3
- MBSE for Railgun Design | Part 4 (this post)
- MBSE for Railgun Design | Part 5 (coming soon)