Rocket Trajectory Calculator

Enter Rocket Parameters

Initial Speed (m/s)

Starting launch speed before thrust integration begins.

Launch Angle (degrees)

Initial velocity direction above horizontal.

Thrust Angle (degrees)

Fixed thrust pointing angle during powered flight.

Initial Height (m)

Launch platform or tower elevation above ground.

Average Thrust (N)

Average axial thrust during the burn interval.

Burn Time (s)

Powered flight duration used for mass loss.

Initial Mass (kg)

Total launch mass including propellant.

Propellant Mass (kg)

Mass consumed linearly during the burn.

Drag Coefficient

Aerodynamic resistance coefficient for the body.

Reference Area (m²)

Projected frontal area for drag calculations.

Air Density (kg/m³)

Constant atmospheric density for the model.

Gravity (m/s²)

Local gravitational acceleration value.

Time Step (s)

Smaller steps improve numerical resolution.

Maximum Simulation Time (s)

Safety stop if the trajectory does not end.

Example Data Table

Scenario	Launch Angle (°)	Thrust (N)	Burn Time (s)	Initial Mass (kg)	Propellant (kg)	Apogee (m)	Range (m)
High Arc Test	80	8,500	12	120	55	5,910	3,460
Shallower Flight	62	8,500	12	120	55	4,280	5,980
Heavy Vehicle	75	9,600	10	160	60	4,760	3,920
Thin Atmosphere Case	78	8,500	12	120	55	6,480	3,860

These rows are illustrative engineering examples for comparison and setup guidance.

Formula Used

1) Mass Change During Burn
m(t) = m₀ − ṁt, for 0 ≤ t ≤ burn time
ṁ = propellant mass ÷ burn time

2) Aerodynamic Drag
D = 0.5 × ρ × C_d × A × v²

3) Horizontal and Vertical Accelerations
a_x = (T cos θ_T / m) − (D / m)(v_x / v)
a_y = (T sin θ_T / m) − (D / m)(v_y / v) − g

4) Time Marching Update
v_x,new = v_x + a_xΔt
v_y,new = v_y + a_yΔt
x_new = x + v_xΔt + 0.5a_xΔt²
y_new = y + v_yΔt + 0.5a_yΔt²

This calculator applies a simplified two-dimensional point-mass model with constant gravity, constant air density, constant drag coefficient, fixed thrust direction, and linear propellant depletion during burn.

How to Use This Calculator

Enter the launch speed, launch angle, and thrust angle.
Provide thrust, burn time, initial mass, and propellant mass.
Set drag coefficient, reference area, air density, gravity, and time step.
Choose a maximum simulation time long enough for landing.
Press Calculate Trajectory to show results above the form.
Review apogee, burnout, impact, peak speed, and dynamic pressure.
Use the CSV export for full trajectory points and the PDF export for a report snapshot.

Frequently Asked Questions

1) What kind of rocket motion does this calculator model?

It models two-dimensional powered and unpowered flight with gravity, drag, and changing mass during propellant burn. It is suitable for conceptual trajectory studies.

2) Does the vehicle mass change during flight?

Yes. Mass decreases linearly while propellant burns, then remains constant at dry mass for coast and descent calculations.

3) Why does the time step matter?

The solver advances motion in small increments. Smaller time steps usually improve accuracy, especially during high-acceleration burn and near ground impact.

4) Is air density changing with altitude here?

No. This version uses a constant density value entered by the user. That keeps the model simple and transparent for engineering comparisons.

5) Can I use this for orbital launch analysis?

Not reliably. Orbital work needs guidance laws, staging, rotating Earth effects, variable atmosphere, and curved-flight dynamics beyond this simplified calculator.

6) What units should I enter?

Use SI units throughout: meters, seconds, kilograms, newtons, square meters, kilograms per cubic meter, and meters per second squared.

7) What does peak dynamic pressure indicate?

Peak dynamic pressure reflects the highest aerodynamic loading environment. Engineers often watch it because structural and control demands rise near that condition.

8) What do the CSV and PDF files contain?

The CSV stores full time-history points. The PDF gives a summary report plus a trajectory preview table for quick sharing and documentation.