RocketDynamicsLab

Sensitivity Analysis and Uncertainty Propagation

Reference: FM04.pdf Sec. 3.4 “Dispersion Analysis”, Table 2, Figs. 10-21. Code: src/simulator/dispersion.py.

Why dispersion matters (the paper’s framing)

An unguided rocket has no feedback loop correcting its flight path — its impact point is entirely determined by initial conditions and physical parameters that are never known perfectly. The paper’s introduction identifies three phases contributing to total dispersion:

  1. Production inaccuracy — propellant mass/composition, total mass, moments of inertia, resultant center of gravity.
  2. Boosting-phase disturbances — launcher deflection, tip-off, thrust/fin misalignment, atmospheric gusts during the few seconds of powered flight.
  3. Free-flight disturbances — wind-profile fluctuations, atmospheric density variation, and static rocket-property uncertainty acting over the whole remaining flight.

The method: one-parameter-at-a-time sensitivity sweeps

Table 2 lists twelve uncertain parameters, each given a plausible uncertainty range (e.g. launch pitch angle ±2°, rocket mass ±2%, air density ±4%). For each parameter, the paper:

  1. Holds every other parameter at its nominal value.
  2. Sweeps the one parameter of interest across its stated range.
  3. Re-runs the full 6-DOF trajectory simulation for each sample.
  4. Records the resulting range error, drift error, and radial error relative to the nominal impact point.
  5. Plots error vs. parameter value (Figs. 10-21) to see which parameters the impact point is most sensitive to.

This is local, one-at-a-time (OAT) sensitivity analysis — simple, interpretable, and cheap (one 1-D sweep per parameter, no combinatorial explosion), but it does not capture interaction effects between parameters (e.g. does a mass error matter more or less when air density is also off?). Global/variance-based methods (Sobol indices, full factorial or Latin-hypercube Monte Carlo) capture those interactions at higher computational cost — a natural extension exercise.

This lab’s implementation

dispersion.monte_carlo_dispersion(param, n_samples, ...) reproduces this workflow for any of the ten parameters in DEFAULT_UNCERTAINTIES (a Table 2-derived list), returning value/range-error/drift-error/radial- error arrays exactly analogous to Figs. 10-21. The Sensitivity Analysis GUI page lets you pick a parameter, choose a sample count, and see the scatter plot live, then compare it side-by-side across parameters to reproduce the paper’s qualitative conclusion:

“the rocket motor parameters (burning time, propellant mass and mean thrust value) have a great effect on the rocket range and its impact point error.” (Sec. 4, Conclusion)

What “uncertainty range” means here

Table 2’s ranges (e.g. [-2%, +2%] for total mass) represent a manufacturing/measurement tolerance band, not a probability distribution per se. This lab treats the sweep as either a uniform grid across the range (default, matching the paper’s plotting style) or, for students who want to go further, a Monte-Carlo draw from a normal distribution scaled to the range (distribution="normal") — an explicit invitation to discuss which distributional assumption is appropriate for a manufacturing tolerance (uniform? normal? triangular?) and how that choice changes the resulting impact probability ellipse, which real artillery dispersion analysis ultimately cares about (Circular Error Probable, CEP).

Professor Notes

A strong assignment extension: instead of one-at-a-time sweeps, draw all ten parameters simultaneously from their distributions (a full Monte Carlo run of, say, 500 trajectories) and plot the resulting impact-point scatter as a 2-D (range, drift) cloud — this is the actual dispersion ellipse a fire-control or accuracy-requirements engineer would compute, and it is not simply the sum of the individual OAT sensitivities unless the underlying model is linear (Exercise 8).

Student Exercises

See assignments.md Exercise 8.

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