Flight Inputs
Formula Used
The simulator uses a simplified two-dimensional point-mass model. Thrust acts along the instantaneous flight direction. Gravity acts downward. Aerodynamic drag opposes motion relative to the wind.
| Quantity | Relationship | Meaning |
|---|---|---|
| Drag | D = ½ρCdAv² | Aerodynamic resistance |
| Acceleration | a = F / m | Net force divided by mass |
| Mach | M = v / asound | Speed relative to sound |
| Dynamic pressure | q = ½ρv² | Aerodynamic loading indicator |
How to Use This Calculator
Enter the rocket geometry, environmental assumptions, and stage values. Choose a constant thrust or a simple thrust curve. Select the number of stages, then set dry mass, propellant mass, thrust, burn time, and specific impulse for each stage. Choose atmosphere and gravity models suitable for classroom exploration. Press Calculate Trajectory to generate the flight path and result summary. Review maximum altitude, speed, acceleration, Mach number, dynamic pressure, burnout conditions, flight duration, and ground distance. Use the charts to compare altitude, velocity, and aerodynamic pressure throughout the simulated flight. Export trajectory rows as CSV for further study. Use the PDF button to create a compact report containing project details and key results.
Understanding Rocket Trajectory Simulation
What the model represents
A rocket trajectory changes because thrust, gravity, drag, and mass interact. This calculator uses a two-dimensional point-mass model for educational exploration. It begins with launch conditions and advances the motion using small time steps. At every step, the program estimates atmospheric density, aerodynamic drag, gravitational acceleration, remaining mass, and active thrust. These values produce acceleration, which updates velocity and position.
Why staging matters
Staging changes the vehicle mass during flight. A spent stage can be removed after burnout, reducing inert mass carried by later stages. The tool supports up to three simplified stages. Each stage can use its own dry mass, propellant mass, average thrust, burn time, specific impulse, and separation delay. The first stage may also use a user-entered thrust curve.
Reading the results
Maximum altitude shows the highest simulated point above the launch level. Time to apogee shows when that peak occurs. Dynamic pressure combines air density and relative speed, so it can rise and later fall as the atmosphere thins. Mach number compares rocket speed with an approximate local sound speed. Burnout values show the state near final powered flight completion.
Important limitations
This page is not a certified flight dynamics package. It ignores rotational motion, detailed stability, changing drag coefficients, lift, guidance, structural flexibility, weather layers, terrain, and full six-degree-of-freedom behavior. The curved-Earth setting is only a visualization adjustment within a local frame. Results should therefore be treated as approximate educational estimates. For real launches, follow applicable laws, range rules, manufacturer guidance, and qualified safety procedures. The safest simulations are those used for learning.
Using exported data
CSV output makes the simulation easier to inspect elsewhere. Students can graph altitude, speed, pressure, mass, or thrust independently. Comparing several safe classroom scenarios can show sensitivity to assumptions. PDF reports provide a compact summary for project notes. Always document the selected model settings beside conclusions.
Example Reference Table
| Parameter | Example value | Typical educational purpose |
|---|---|---|
| Launch angle | 85° | Nearly vertical ascent study |
| Diameter | 0.12 m | Reference area calculation |
| Drag coefficient | 0.45 | Simplified aerodynamic estimate |
| Time step | 0.10 s | Numerical integration interval |
| Atmosphere | Exponential | Density decrease with altitude |
Frequently Asked Questions
Is this suitable for real launch certification?
No. It is a simplified educational simulator and should not replace certified flight software or range safety analysis.
What does the thrust curve do?
It lets stage one use time-thrust points instead of a single constant thrust value. The calculator interpolates between points.
Why can dynamic pressure peak before apogee?
Dynamic pressure depends on both speed and air density. Speed may rise while atmospheric density falls, producing an earlier peak.
How many stages are supported?
The page supports one, two, or three simplified stages for classroom comparisons and hobby simulations.
What can I download?
CSV exports contain the trajectory time series. PDF exports contain the project title, model assumptions, and key calculated results.