Possible Extensions

The model here is a starting point. Several additions could meaningfully improve it:

• Drag coefficient \(C_d\) — assumed constant throughout. In reality, \(C_d\) depends on the Mach number and Reynolds number, both of which change during flight. A \(C_d(V, h)\) table derived from wind tunnel data would improve accuracy at high speeds.
• Cross-sectional area \(A\) — assumed fixed. For a tumbling or spinning projectile, the effective presented area changes over time.
• Dynamic viscosity — included in the NASA dataset but unused here. It becomes relevant in low-speed, low-altitude regimes where viscous effects are non-negligible.
• Wind — a horizontal wind profile \(u(h)\) could be incorporated by adjusting the effective horizontal velocity at each altitude.
• Extended altitude range — above 50 km, the exponential plus spline approach breaks down. A layered ISA or NRLMSISE-00 model would be required.
• 3D motion — the current model is two-dimensional. Real trajectories include lateral drift from the Coriolis effect and crosswinds.

Author’s Note

Computational modeling has become a standard tool across science and engineering — not as a replacement for theory or experiment, but as a bridge between the two. A few reasons it has become so widely adopted:

• Analytical limits — many realistic physical systems have no closed-form solution. Numerical methods can solve them to any required precision.
• Experimental cost — physical experiments are often slow and expensive. A validated computational model can explore a large parameter space at a fraction of the cost.
• Theory-experiment gaps — simulations can quantify the discrepancy between theoretical predictions and observed measurements, pointing to where additional physics is needed.
• Engineering design — simulations allow iterative refinement before anything is physically built.

This project demonstrates the same pattern at a small scale: take an idealized model, identify where it diverges from reality, source the relevant data, build a correction, and re-simulate.

This project established a working pattern I expect to apply in other domains. The same approach — take a standard model, identify a real-world correction, source observational data, fit a function, and re-simulate — applies broadly to: fluid dynamics, biochemical kinetics, ecological modeling, socioeconomic modeling, financial modeling and more. Most of the data needed for this kind of work is publicly available through government agencies and research institutions or could be sourced via contextual means.

This project is asked not to be regarded as a scientific-research work and this report is not to be judged as a scientific paper. The project was undertaken as a practice exercise in the field of “computational science”, more specifically “physics”. I hoped to use conventional tools and techniques used in data science workflows– in a physics model, driven by the curiousity established from my undergrad in the subject or even deeper roots! And I really enjoyed doing it. Newer original ideas are currently under development!