Enter rocket and flight data
Sample input set
| Parameter | Example Value | Unit | Purpose |
|---|---|---|---|
| Initial mass | 50,000 | kg | Total liftoff mass. |
| Propellant mass | 32,000 | kg | Consumable mass during the powered burn. |
| Burn time | 120 | s | Total engine burn duration. |
| Mass flow rate | 266.67 | kg/s | Propellant consumed each second. |
| Exhaust velocity | 3,200 | m/s | Momentum term for thrust generation. |
| Drag coefficient | 0.45 | — | Shape-related drag strength. |
| Reference area | 10 | m² | Frontal area used for drag estimates. |
| Flight angle | 90 | deg | Vertical ascent case. |
Core equations behind the calculator
F = ṁ × Ve + (Pe − Pa) × Ae
This combines momentum thrust and pressure thrust.
Fnet = Fthrust − m × g × sin(θ) − Fdrag
Gravity is projected along the chosen ascent angle.
Fdrag = 0.5 × ρ × Cd × A × v²
Drag rises quickly with speed, especially during dense-atmosphere ascent.
a = Fnet / m
As mass drops during burn, acceleration usually increases.
Δv = Veff × ln(m0 / mf)
This is an ideal estimate, so real burnout speed can differ.
Steps for practical use
- Enter initial mass, propellant mass, and burn time.
- Select direct thrust or engine-derived thrust mode.
- Provide mass flow rate, or let the page infer it.
- Enter flight angle and gravity for your scenario.
- Enable drag if atmospheric losses matter.
- Add air density, drag coefficient, and reference area.
- Submit the form to view performance cards and the Plotly graph.
- Use CSV or PDF export to save the calculation output.
Rocket acceleration questions
1) What is the difference between direct and derived thrust?
Direct mode uses a known thrust value. Derived mode calculates thrust from mass flow, exhaust velocity, nozzle exit pressure, ambient pressure, and nozzle exit area.
2) Why does acceleration usually increase during the burn?
The rocket becomes lighter as propellant is consumed. If thrust stays roughly constant, the same or similar force acts on less mass, so acceleration rises.
3) Why can burnout speed differ from ideal delta-v?
Ideal delta-v ignores gravity loss, drag, steering loss, and model simplifications. The simulated burnout speed reflects net force during the powered segment only.
4) What does the flight angle represent here?
It is the path angle measured from the horizontal. At 90 degrees, gravity fully opposes thrust along the path. Smaller angles reduce that opposing component.
5) What happens when thrust-to-weight ratio is below one?
A vertical rocket with TWR below one cannot lift off because thrust does not exceed weight. The calculator will show low or negative initial acceleration.
6) When should I include drag?
Include drag for atmospheric ascent, launch vehicle studies, and early trajectory estimates. Disable it for simplified vacuum cases or quick first-pass comparisons.
7) How small should the time step be?
Smaller time steps improve resolution but increase computation. For steady burns, 0.1 to 1 second usually works well. Faster transients need smaller values.
8) Can this calculator replace full trajectory software?
No. It is an engineering estimator for powered-burn acceleration and related metrics. Detailed mission design still needs multi-stage, guidance, atmosphere, and orbital modeling.