How the model rocket altitude predictor works

This predictor integrates the rocket's equation of motion in small time steps, starting at liftoff and continuing until the rocket decelerates to zero vertical velocity (apogee). At each step the net force on the rocket equals motor thrust minus drag minus gravity. Thrust follows the motor's published thrust curve so acceleration is highest near motor burnout when the rocket is lightest but still producing thrust. After burnout only drag and gravity act, and the rocket coasts up to apogee. Drag at each step is calculated from the standard equation ½ρv²C_dA, where ρ is air density (reduced at altitude with a simple atmosphere model), v is instantaneous velocity, C_d is the drag coefficient and A is the rocket's cross-section area.

Choosing the right drag coefficient

C_d is the single biggest source of error in any altitude prediction. Typical values: a well-finished low-power rocket with sanded fins and a smooth nose cone sits around 0.55 to 0.65. Minimum-diameter competition rockets can reach 0.35 to 0.45 with careful filleting and polishing. High-power rockets with thicker airfoil fins and larger launch lug or rail button hardware run 0.6 to 0.9. Rough finish, paint over-spray, exposed launch lugs and blunt fin leading edges all push C_d up. When in doubt, 0.6 is a reasonable default for most sport rockets.

What affects predicted apogee most

In order of approximate impact for a typical flight: (1) total impulse of the motor, doubling impulse roughly doubles altitude for the same rocket. (2) Liftoff mass, weight the rocket accurately including recovery gear, altimeter, motor and adapter. (3) Drag coefficient, big swings in apogee come from a bad C_d estimate. (4) Body diameter, frontal area scales as radius squared. (5) Launch site altitude and air temperature, thinner air means less drag and higher apogee, so the same motor goes further at Black Rock (1400m) than it does at sea level.

Low, mid and high-power rockets

The tool works across the full range of amateur rocketry: low power (motor classes A through D, apogees from 30m to about 300m), mid power (E, F, G, apogees typically 100m to 700m), and high-power (H onwards, apogees from a few hundred metres to tens of kilometres for advanced projects). Multi-stage rockets with separate booster motors need a separate prediction for each stage using the post-burnout velocity of the previous stage as the new starting condition; this tool handles single-stage flights directly.

How accurate is the prediction?

Typical real-flight altitudes land within 5 to 15% of the predicted value when inputs are accurate. Underprediction usually means the real C_d is lower than estimated (smoother finish, smaller launch hardware); overprediction usually means the real C_d is higher (rougher surface, exposed launch lugs) or that the rocket flew off-vertical losing altitude to lateral velocity. For dedicated competition flights or when hitting exact altitude targets matters, full-featured simulators like OpenRocket or RockSim include aerodynamic stability modelling that this quick predictor does not.

Frequently asked questions

How accurate is it? Typically within 5-15% of actual flight altitude with accurate inputs.

What C_d should I use? 0.55-0.65 for sport rockets; 0.35-0.45 for minimum-diameter competition rockets; 0.6-0.9 for high-power with larger hardware.

Does it account for wind? No; this predictor calculates vertical apogee only. Use the drift calculator for lateral distance.

What inputs do I need? Motor thrust curve, liftoff mass, drag coefficient, body tube diameter. Launch altitude and temperature refine the result.

Are apogee and maximum altitude the same? Yes, apogee is the peak of the flight where vertical velocity reaches zero.