# Model Rocket Altitude & Motor Calculator Estimate peak rocket altitude, maximum velocity, and exact motor burn time using your rocket specifications and motor data. --- - **Canonical URL:** https://dothecalculation.com/calculators/model-rocket-altitude-calculator - **Category:** Hobbies & Leisure Utilities - **Publisher:** Do The Calculation (https://dothecalculation.com) - **Cost:** Free, no account or sign-up required - **Privacy:** Runs entirely in the browser; inputs are never sent to a server - **Methodology:** https://dothecalculation.com/methodology --- ## Estimate model rocket apogee and peak velocity Compute rocket flight parameters, apogee altitude, burnout speed, and coast duration based on rocket weight, diameter, and motor impulse. - Boost and coast phase height solver - Aerodynamic drag (Cd) simulation - Rocket motor class comparisons ## The Aerodynamics of Model Rocket Flight Estimating the altitude of a model rocket requires solving the classical differential equations of motion under gravity and aerodynamic drag. A model rocket flight is divided into two major phases: the boost phase (where the motor is burning, providing thrust) and the coast phase (from motor burnout up to the highest point, the apogee). During the boost phase, the forces acting on the rocket are thrust, gravity, and drag. Drag increases with the square of velocity: \(D = \frac{1}{2} \rho A C_d v^2\) (where \(\rho\) is air density, A is cross-sectional area, \(C_d\) is the drag coefficient, and v is velocity). The net acceleration during boost is: \(a = \frac{F_{\text{thrust}} - D}{m} - g\). Because drag changes with speed, calculating velocity at burnout and boost height requires integrating this equation over the burn time of the motor. A well-designed rocket with a smooth nose cone and fins has a low drag coefficient (typically 0.45 to 0.75), whereas rough construction or mismatched body tubes can raise this significantly, drastically reducing peak altitude. ## Calculating Boost Height, Burnout Velocity, and Apogee To model the boost phase, we use the average thrust (F) and burn time (t) of the rocket motor. We define a drag term \(k = \frac{1}{2} \rho A C_d\). The maximum velocity at burnout (v1) can be modeled as: \(v_1 = q \times \tanh(p \times t)\) (where \(q = \sqrt{\frac{F - mg}{k}}\) and \(p = \frac{\sqrt{(F - mg)k}}{m}\)). The boost phase height (y1) reached when the motor burns out is: \(y_1 = \frac{m}{2k} \ln\left(\frac{thrust - mg}{thrust - mg - k v_1^2}\right)\). After burnout, the motor stops thrusting, and the rocket coasts. The deceleration during coast is \(a = -g - \frac{k}{m} v^2\), which yields a coast height (y2) of: \(y_2 = \frac{m}{2k} \ln\left(\frac{mg + k v_1^2}{mg}\right)\). The total apogee is \(y_1 + y_2\). ## Understanding Rocket Motor Classes and Impulses Model rocket motors are classified by alphabetical letters (A, B, C, D, etc.), where each letter represents double the total impulse (power) of the previous class. An A motor has a total impulse of 1.26 to 2.50 Newton-seconds (N·s), a B motor has 2.51 to 5.00 N·s, and a C motor has 5.01 to 10.00 N·s. Selecting the right motor requires balancing rocket mass and wind conditions. If the rocket is too heavy, the thrust will not overcome gravity, resulting in a failed launch. Our rocket calculator models these physics to help you select a safe motor delay time. Hobbyists can also utilize our [Scale Converter](/calculators/scale-converter) when converting blueprints or building scale replicas of real-world space vehicles. ## How to Use This Calculator Enter your rocket's empty weight in grams, body tube diameter in millimeters, and drag coefficient (0.45 for a smooth ogive nose cone up to 0.85 for a flat one). Add the motor's average thrust in Newtons and burn time in seconds, both printed on the motor label or found in Estes/Aerotech data sheets. The calculator returns apogee, burnout velocity, boost height, and coast height. ## Worked Example: A Typical B6-4 Motor Flight With the calculator's defaults — an 80-gram rocket, 24mm diameter, Cd of 0.75, 10 N average thrust, and a 1.2-second burn — the rocket reaches an apogee of about 383 meters (1,258 feet), with a burnout velocity of roughly 121 m/s (271 mph). Of that total height, the boost phase (while the motor is firing) contributes about 78 meters, and the coast phase (after burnout, coasting up on momentum) contributes the remaining 306 meters — a reminder that most of a model rocket's altitude is actually gained after the motor stops burning, not during the boost itself. ## Related Calculators For a more detailed drag simulation that also models fin area and nose cone shape, see the [Model Rocket Aerodynamic Drag & Apogee Calculator](/calculators/model-rocket-drag-apogee-calculator). ## Frequently asked questions ### What is apogee? Apogee is the highest point reached by a rocket during flight, where upward velocity is zero. ### How does rocket mass affect altitude? A lighter rocket travels faster and higher on the same motor, but if it is too light, wind resistance will limit its height. There is an optimal mass for every motor. ### What is a typical drag coefficient (Cd) for a model rocket? Typical Cd ranges from 0.45 for highly polished, streamlined rockets to 0.8 or higher for boxy, unpolished designs. ### What do the numbers in motor codes mean (e.g., C6-5)? The letter (C) is the impulse class; the first number (6) is average thrust in Newtons; the second number (5) is the delay time in seconds before the ejection charge fires. ### Why does a rocket delay time matter? If the ejection charge fires before apogee, the rocket is moving fast, risking parachute tear. If it fires after, the rocket has nose-dived, risking impact damage. ### How does rocket diameter affect altitude? A larger diameter increases frontal area and aerodynamic drag, significantly reducing peak altitude. ### Does weather affect model rocket altitude? Yes. Wind increases drag and causes the rocket to tilt (weathercock) into the wind, reducing vertical height. ### What is total impulse? Total impulse is the total force delivered by the motor over its burn duration, measured in Newton-seconds. ### Can I launch a model rocket in high winds? It is unsafe to launch in winds exceeding 20 mph. The rocket will cock into the wind and fly horizontally. ### What is the parachute ejection charge? A small gunpowder charge at the top of the motor that pressurizes the body tube, pushing out the nose cone and parachute. ### How is air density modeled? This calculator assumes standard sea-level air density of 1.225 kg/m³ at 59°F (15°C). ### Is a larger motor always better? No. Rockets have maximum structural speed limits. Over-powering a small rocket can cause it to shred or fly out of visual range. ## Related concepts - **Aerodynamic Drag (Cd)** — The force opposing motion through a fluid. - **Total Impulse** — The mathematical integral of motor thrust over time. - **Weathercocking** — The tendency of a rocket to turn into the wind during flight. ## Related guides - [Understanding Calculator Formulas: How DTC Turns Inputs into Results](https://dothecalculation.com/blog/site-guides/understanding-calculator-formulas) — Understand how Do The Calculation formulas are presented, what the explanation blocks mean, and how to verify calculator logic before using a result in a real decision. ## Related calculators - [Model Rocket Aerodynamic Drag & Apogee Calculator](https://dothecalculation.com/calculators/model-rocket-drag-apogee-calculator) — Simulate rocket flight to calculate peak altitude, apogee, drag coefficient, and maximum velocity using numerical integration. - [Metal Detector Target Depth Estimator](https://dothecalculation.com/calculators/metal-detector-depth-calculator) — Estimate the maximum target detection depth for your metal detector based on coil size, frequency, and soil mineral type. - [RC Flight Time & Battery Power Calculator](https://dothecalculation.com/calculators/rc-flight-time-calculator) — Estimate RC multirotor or airplane flight duration, battery power draw, and thrust-to-weight ratio for your specific setup. - [Recipe Scale & Multiplier Calculator](https://dothecalculation.com/calculators/recipe-scaler-calculator) — Scale recipe ingredient quantities up or down by any multiplier or exact serving size to cook the perfect portion every time. - [Wood Shrinkage & Seasonal Movement Calculator](https://dothecalculation.com/calculators/wood-shrinkage-radial-calculator) — Model exact wood shrinkage and seasonal dimensional changes based on relative humidity, temperature, and wood species type. - [Yarn Yardage & Project Estimator](https://dothecalculation.com/calculators/yarn-yardage-estimator) — Estimate the exact total yarn yardage and number of skeins needed for knitting or crocheting blankets, sweaters, and hats. --- _This calculator is for educational and planning purposes. Always verify measurements, conversions, and material requirements before making purchases or physical builds._ --- _Source: [Do The Calculation](https://dothecalculation.com/calculators/model-rocket-altitude-calculator). Quote freely with attribution and a link to this page._