Fundamentals of Rocket Stability This pamphlet was developed using information for the Glenn Learning Technologies Project. For more information, visit their web site at: http:/www.grc.nasa.gov/WWW/K-12/aboutltp/EducationalTechnologyApplications.html Flying model rockets is a relatively safe and inexpensive way for students to learn the basics of aerodynamic forces and the response of vehicles to external forces. Like an airplane, a model rocket is subjected to the forces of weight, thrust, and aerodynamics during its flight. On this slide we show the parts of a single stage model rocket. We have laid the rocket on its side and cut a hole in the body tube so that we can see what is inside. Beginning at the far right, the body of the rocket is a green cardboard tube with black fins attached at the rear. The fins can be made of either plastic or balsa wood and are used to provide stability during flight. Model rockets use small, pre-packaged, solid fuel engines The engine is used only once, and then is replaced with a new engine for the next flight. Engines come in a variety of sizes and can be purchased at hobby stores and at some toy stores. The thrust of the engine is transmitted to the body of the rocket through the engine mount. This part is fixed to the rocket and can be made of heavy cardboard or wood. There is a hole through the engine mount to allow the ejec- tion charge of the engine to pressurize the body tube at the end of the coasting phase and eject the nose cone and the recovery system. Recovery wadding is inserted between the engine mount and the recovery system to prevent the hot gas of the ejection charge from damaging the recovery system. The recovery wadding is sold with the engine. The recovery system consists of a parachute (or a streamer) and some lines to connect the parachute to the nose cone. Para- chutes and streamers are made of thin sheets of plastic. The nose cone can be made of balsa wood, or plastic, and may be either solid or hollow. The nose cone is inserted into the body tube before flight. An elastic shock cord is connected to both the body tube and the nose cone and is used to keep all the parts of the rocket together during recovery. The launch lugs are small tubes (straws) which are attached to the body tube. The launch rail is inserted through these tubes to provide stability to the rocket during launch. During the flight flight of a model rocket small gusts of wind, or thrust instabilities can cause the rocket to wobble, or change its attitude in flight. Like any object in flight, a model rocket rotates about its center of gravity (cg), shown as a yellow dot in the figure. The rotation causes the axis of the rocket to be inclined at some angle a to the flight path. Whenever the rocket is inclined to the flight path, a lift force is generated by the rocket body and fins, while the aerody- namic drag remains fairly constant for small inclinations. Lift and drag both act through the center of pressure (cp) of the rocket, which is shown as the black and yellow dot in the figure. On this slide we show three cases for which the flight direction is exactly vertical. In the center of the figure, the rocket is undisturbed and the axis is aligned with the flight direction. The drag of the rocket is along the axis and there is no lift generated. On the left of the figure, a powered rocket has had the nose of the rocket perturbed to the right. On the right of the figure, a coasting rocket has had the nose of the rocket perturbed to the left. We denote the angle in both cases by the symbol a. Considering the powered rocket case, we see that a lift force is generated and directed towards the right or downwind side of the rocket. On the coasting rocket case, the lift is directed towards the left, also the downwind side of the rocket. For the powered case, both the lift and the drag produce counter-clockwise torques (or twists) about the center of gravity; the tail of the rocket will swing to the right under the action of both forces and the nose will move to left. For the coasting case, both lift and drag produce clock- wise torques about the center of gravity; the tail of the rocket will swing to the left under the action of both forces and the nose will move to the right. In both cases, the lift and the drag (Continued on page 4) forces move the nose back towards the flight direction. Engineers call this a restoring force because the forces restore the vehicle to its initial condition. A restoring force exists for this model rocket because the center of pressure is below the center of gravity. If the center of pressure is above the center of gravity, the lift and drag forces main- tain their directions but the direction of the torque generated by these forces is reversed. This is called a de-stabilizing force. Any small displacement of the nose will generate forces that cause the displacement to increase. For a stable model rocket, the center of pressure must be locat