Re-entry Stagnation-Heating Uncertainty Study
A ballistic Earth-entry study of trajectory, stagnation-point convective heating, heat load, dynamic pressure, and uncertainty across vehicle and atmospheric conditions.
Project definition
Problem statement
A spacecraft entering an atmosphere experiences a short, severe heat pulse while its speed, density environment, and dynamic pressure change rapidly.
The engineering problem is to quantify how entry speed, flight-path angle, ballistic coefficient, nose radius, atmospheric density, and heating-correlation uncertainty affect the peak heat flux and total heat load.
Project objectives
- Implement a spherical-Earth ballistic entry model with altitude-dependent density and gravity.
- Calculate stagnation-point convective heat flux, accumulated heat load, dynamic pressure, and radiation-equilibrium screening temperature.
- Compare 111 controlled deterministic cases across speed, angle, ballistic coefficient, nose radius, and correlation coefficient.
- Run 600 reproducible uncertainty trajectories and quantify output distributions.
- Rank input influence using monotonic sensitivity measures and explain coupled effects.
- Verify the atmosphere interpolation and heating equation with independent analytical checks.
Project structure
Project components
Atmosphere model
Interpolates tabulated 1976 U.S. Standard Atmosphere density from sea level to 120 km.
Entry dynamics
Integrates altitude, speed, and downward flight-path angle with spherical-Earth gravity and drag.
Heating model
Calculates cold-wall stagnation convective heating, accumulated heat load, and equilibrium temperature screening.
Deterministic study
Runs the prepared vehicle and entry-condition matrix and records terminal-altitude and atmospheric-skip outcomes.
Uncertainty study
Uses a fixed-seed Latin hypercube experiment for six uncertain inputs and calculates distributions and rank sensitivities.
Evidence builder
Exports full-precision CSV and JSON results and produces 14 labelled figures.
Methodology
Project workflow
- 01Define the entry case
Select the entry speed, flight-path angle, ballistic coefficient, nose radius, density scale, and heating coefficient.
- 02Integrate the trajectory
Advance the equations until 25 km altitude or an atmospheric-skip event while retaining the complete state history.
- 03Calculate thermal quantities
Evaluate heat flux, heat load, dynamic pressure, and equilibrium temperature throughout the trajectory.
- 04Run the studies
Complete the deterministic matrix, heating surface, and fixed-seed uncertainty experiment.
- 05Verify and compare
Check the governing relationships, review event outcomes, and compare distributions, sensitivities, and extreme cases.
Demonstration scenario
The student runs the baseline 7.8 km/s, 6 degree entry and obtains a 190.12 W/cm2 peak heat flux near 47.29 km with an 85.99 MJ/m2 heat load. The uncertainty study then shows why ballistic coefficient and flight-path angle matter strongly, while atmospheric-density scaling has a small isolated rank correlation because it changes both deceleration and local heating.
Engineering
Tools and method
- Tools
- The project uses Python, NumPy, SciPy, pandas, Matplotlib, Jupyter for subject analysis, simulation, and results.
- Trajectory model
- A nonrotating, zero-lift, spherical-Earth point-mass model with variable gravity and a tabulated atmosphere.
- Thermal model
- A Sutton-Graves-type cold-wall stagnation correlation with explicit coefficient comparisons and radiation-only equilibrium screening.
- Experiment
- A 111-case deterministic study, a 3,315-row heating surface, and 600 fixed-seed uncertainty trajectories.
- Evidence
- Full-precision CSV and JSON records, 14 generated figures, analytical checks, and retained baseline history.
- Verification
- Thirty automated tests with full core statement and branch coverage, repository validation, static checks, and a dependency audit.
Testing
Evaluation
Evaluation measures
- Peak stagnation-point heat flux and its altitude and speed
- Integrated convective heat load
- Peak dynamic pressure and equilibrium-temperature screening value
- Terminal-altitude and atmospheric-skip outcomes
- Uncertainty percentiles and rank sensitivity for six inputs
- Heating-law elasticity and atmosphere-table agreement
Project boundaries
- This is a preliminary ballistic entry and stagnation-heating study, not a flight-certified thermal-protection-system design.
- The point-mass model excludes lift, Earth rotation, winds, ablation, material response, shape change, guidance, and full nonequilibrium radiation.
- The alternative heating coefficients are engineering comparisons and are not presented as complete independent correlation models.
- The highest-speed cases require higher-fidelity gas chemistry, radiation, material-response, and experimental evidence before design use.
Included
- 01Python trajectory, atmosphere, heating, and uncertainty source code
- 02111 deterministic trajectories and 600 uncertainty trajectories
- 033,315 heating-surface cases with CSV and JSON results
- 0414 generated result figures and three sourced NASA literature images
- 0530 automated tests with 100 percent core coverage
- 06Complete project files and analysis material in a private GitHub repository
- 0770-page project documentation in PDF and editable Word formats
- 088-page setup and usage guide in PDF and editable Word formats
- 0950 annotated references
Project record
No information is collected on this page.
- Permanent project ID
- GP-AE-1QO5JID
- Catalogued
- 21 Aug 2026
- Completed
- 26 Aug 2026
- Verified
- 26 Aug 2026
- Demonstration
- Included in repository
Handover
After purchase
- 01Payment is confirmed
The project is marked unavailable and cannot be purchased again.
- 02Repository access is granted
The buyer's submitted GitHub account receives access to the private repository.
- 03The purchase record is delivered
The certification sheet is prepared from the reviewed buyer details and sent privately by email.