Rocket Flight Simulation
It is important to simulate the flight of your rocket before flying for several reasons:
This site provides data files for use with the various flight simulators. On this page is a description of simulation in general. See the simulators page for a list of existing simulator programs. There is also a simple rocket flight simulator available on this site in the motor guide.
See also John's flight physics article for more details of these forces and the calculations employed.
There are three main forces that affect the altitude to which a rocket will fly:
Another force that affect a rocket's flight is wind. However, this is usually left out of simulations and rockets are only flown in low-wind conditions.
In the graph above, you can see a rough illustration of how the forces apply to a rocket in flight. Thrust simply follow's the motor's thrust curve. Gravity is a (relatively) constant force. Drag increases sharply with increasing speed (proportional the square of the velocity). Drag is highest near the end of the motor's burn (when all the thrust has been applied and maximum speed achieved).
A rocket flight is broken down into several phases:
During powered flight, the motor is providing thrust and the rocket is accelerating upward. Because of this, the velocity and drag are increasing. The thrust applied by the motor varies from moment to moment according to its characteristic burn pattern (graphed by its thrust curve). Near the end of powered fight, hobby rockets reach max Q, which is usually where "shreds" occur.
While coasting, the momentum of the rocket is still carrying it upward, but since the motor is no longer providing thrust the speed is decreasing due to gravity and drag.
The apogee point is critical in all simulations since it provides the maximum altitude reached by the rocket. The time from burnout to apogee is also important for choosing a delay time when using motor ejection since the recovery system should be triggered when the rocket is moving slowly.
Because most flight simulation is concerned with altitude achieved, the descent (or recovery) phase is usually of less interest. The simulations perfomed by the motor guide stop at apogee.
The graphs below are from a simulation done with a simple rocket flying on an AeroTech M1939 (one of the author's favorite motors). Click on the links below the graph to see how the different forces and measurements change during the flight.
Thrust is the force provided by the motor. Graphing it over time produces the motor's "thrust curve." This does not include any other factors and comes from an actual static test of the motor. These files, which are specific to each motor, are the purpose of this site.
Acceleration is the sum of all forces acting on the rocket. Thrust is pushing the rocket up during the burn, gravity is pulling it down through the entire flight, and drag is slowing its speed. Note that in these graphs, negative values are chopped off at zero. This makes it appear that the acceleration reaches zero and stays there. In reality, the acceleration becomes negative when the rocket starts slowing down.
Drag is calculated from the speed of the rocket, since it is proprtional to the square of the velocity. Note how similar the drag and velocity curves are, except that the drag curve is steeper because of the square function.
Velocity is the speed the rocket is traveling. This is determined at any given point by taking the velocity at the previous point and applying the acceleration at the current point. (For rockets that stay in the lower atmosphere, max Q occurs at maximum velocity.)
Altitude is the height above ground reached by the rocket. This is determined at any given point by taking the altitude at the previous point and applying the velocity at the current point. Apogee is reached when velocity is zero, which defines the highest point reached by the rocket. Note that we stop simulating at apogee; otherwise, the altitude would drop again to zero during the descent phase.
For the mathematically minded, the acceleration is the sum of static and dynamic forces, the velocity is an integration of the acceleration, and the altitude is an integration of the velocity.