 # Launching a Rocket

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The launch of a spacecraft is fundamental to all space activity. As a rocket flies it loses mass, because most of its mass is fuel (pure hydrogen and oxygen) that provides the propulsive force.

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This Demonstration shows the dynamics of an ideal rocket from launch time to measured burn-out time, based on Newton's laws and Tsiolkovsky's rocket equation. Specify the rocket parameters and launch with the trigger.

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Contributed by: Frederick Wu (October 2008)
Open content licensed under CC BY-NC-SA

## Snapshots   ## Details

Graphic, top right: Tsiolkovsky's rocket equation, which defines the relationship between exhaust velocity and mass ratio

Graphic, bottom right: rocket dynamic parameters of acceleration, velocity, altitude and burn-out time

Graphic, left: 3D rocket dynamic launch model with altitude function control

Snapshot 1: ideal rocket specification that surpasses first escape velocity

Snapshot 2: ideal rocket specification that surpasses second escape velocity

Snapshot 3: 3D Earth scale model, with the launch site (yellow) and rocket altitude (red)

simplified assumptions:

1. gravity and aerodynamic drag effects are neglected

2. single stage rocket, initial velocity is zero

3. vertical launch or pitch angle is 90°

4. a constant exhaust velocity

5. a constant mass flow rate

governing equations:

1. Tsiolkovsky's rocket equation or rocket velocity: 2. mass flow rate: 3. maximum flight time or fuel burn‐out time: 4. rocket altitude: 5. rocket acceleration: , from and above governing equations 1 and 2

symbols: is the rocket velocity. is the efficient exhaust velocity, constrained within a range 2500-4500 , using today's liquid‐fueled rocket chemical technology. is the initial rocket mass. is the current or final rocket mass; decreases during flight until all the liquid fuel is burned out. is the final rocket mass, usually regarded as payload. is the mass ratio, , which is usually in the range from 3 to 8; 14 is difficult to achieve. is the mass flow rate, which depends on rocket engine design and specification; it indicates the rate at which the mass of the rocket is decreasing. Also called "specific impulse". is the rocket flight time, , which is the fuel burn-out time or the maximum flight time. is the rocket acceleration. It is difficult for the human body to withstand high acceleration; 15-20 G is the maximum tolerance limit. (1 G is the acceleration due to gravity.)

References:

J. Peraire, "Variable Mass Systems: The Rocket Equation," MIT OpenCourseWare, 2004.

M. J. L. Turner, "Newton's Third Law and the Rocket Equation," Rocket and Spacecraft Propulsion, 2nd ed., New York: Springer, 2005 pp. 14–17.

M. J. L. Turner, "Launch Vehicle Dynamics," Rocket and Spacecraft Propulsion, 2nd ed., New York: Springer, 2005 pp. 115–144.

M. Voshell, "High Acceleration and the Human Body," 2004.

## Permanent Citation

Frederick Wu

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