Formula Used
Frontal area: A = π × (diameter ÷ 2)².
Burning mass: m(t) = liftoff mass − propellant mass × (time ÷ burn time).
Total impulse: I = average thrust × burn time.
Drag force: Fd = 0.5 × air density × Cd × area × relative speed².
Horizontal acceleration: ax = (thrust × cos(angle) + drag x force) ÷ mass.
Vertical acceleration: ay = (thrust × sin(angle) + drag y force) ÷ mass − gravity.
Position is updated with small time steps. Recovery drag starts after apogee and deployment delay.
How to Use This Calculator
Enter the loaded rocket mass and propellant mass. Add the motor average thrust and burn time from the motor data sheet.
Enter the body diameter and a reasonable drag coefficient. Use lower drag for cleaner rockets and higher drag for rougher shapes.
Set the launch angle, rail length, launch height, wind speed, air density, recovery size, and recovery drag coefficient.
Press the calculate button. Review altitude, range, rail exit speed, burnout speed, and landing speed.
Use the CSV option for spreadsheets. Use the PDF option for a simple launch report.
Planning a Model Rocket Flight
A model rocket flight looks simple, yet many forces act at once. The motor pushes the rocket upward. Gravity pulls it down. Drag slows it through the air. Wind moves the air mass sideways. This calculator brings those parts into one practical estimate, so a launch team can review height, range, speed, and landing conditions before flying.
Why Trajectory Estimates Matter
Small changes can move the landing point far away. A few degrees of launch angle can add long downrange travel. A wider body creates more drag. A stronger wind can push the rocket during coast and recovery. Launch field size, tree lines, roads, and spectators should always guide the final decision. The calculator does not replace a safety code. It supports better planning.
Inputs That Shape the Result
Liftoff mass is important because thrust must accelerate all rocket parts. Propellant mass lowers the rocket mass during burn. Average thrust and burn time control powered acceleration. Diameter and drag coefficient estimate air resistance. Recovery diameter and recovery drag estimate parachute or streamer descent. Wind speed is treated as air moving along the downrange axis. Time step controls the simulation detail.
Understanding the Flight Phases
The powered phase begins at ignition. Thrust acts along the launch angle. The rocket gains speed and usually leaves the guide rail quickly. The coast phase starts after burnout. No thrust remains, so gravity and drag shape the path. Apogee occurs when vertical speed changes from positive to negative. After the deployment delay, recovery drag is applied. This slows descent and increases drift time.
Reading the Output
Maximum altitude shows the highest point above the launch pad. Range estimates horizontal landing distance from the pad. Burnout speed shows energy at motor cutoff. Rail exit speed helps judge whether the rocket may leave the guide with stable motion. Flight time helps recovery teams prepare. Landing speed is useful for checking recovery performance.
Using Results Wisely
Use conservative values when uncertain. Test with stronger wind, heavier mass, and higher drag. Compare several motor choices. Keep launches within local rules and field limits. Real rockets can weathercock, rotate, or suffer deployment issues. Treat every result as an estimate, then leave a strong safety margin.
FAQs
Is this calculator suitable for real launch approval?
No. It provides estimates for planning. Always follow local rules, field limits, club guidance, and model rocket safety codes before launch.
What does launch angle mean?
It is measured from the ground. A 90 degree angle is vertical. Lower values send the rocket farther downrange.
Why is wind speed downrange positive?
The calculator uses one horizontal axis. Positive wind moves air in the landing direction. Negative wind moves it toward the opposite direction.
What drag coefficient should I use?
Many simple model rockets use estimates near 0.5 to 0.9. Rough surfaces, large fins, and external details can increase drag.
Why include propellant mass?
Rocket mass drops during motor burn. Including propellant mass gives a better powered flight estimate than using one fixed mass.
What is rail exit speed?
It is the estimated speed when travel distance reaches the guide rail length. Higher rail exit speed usually helps early stability.
Does recovery diameter affect landing range?
Yes. A larger recovery device slows descent. It can also increase wind drift because the rocket spends more time descending.
Why do actual flights differ from results?
Real flights can weathercock, spin, flex, deploy late, or face changing winds. Use the output as an estimate, not a guarantee.