The forces on a model rocket change dramatically in both magnitude and direction throughout a typical flight. This figure shows the forces on a rocket during the downward coasting portion of the flight. At the end of the powered portion of the flight, the model rocket uses up all its fuel, the engine goes out, and the thrust goes to zero. The rocket then coasts upward until the velocity goes to zero and the maximum altitude is reached. Because weight is still acting on the rocket, it immediately begins to fall back to earth. As the rocket falls, only two forces act on the rocket: the weight and the aerodynamic drag. If the flight path is vertical, the weight and drag are aligned towards the center of the earth. If the flight path is at some angle to the vertical, the drag is multiplied by the cosine of the angle as shown on the powered rocket slide. Since the drag is opposed to the flight direction, the drag and the weight are opposing forces, as shown on the slide.
The acceleration of the rocket can be determined by solving Newton's Second Law of Motion, as shown at the right on the slide. The acceleration is defined relative to the ground with up being positive. The drag depends on the square of the velocity, as shown on the slide. Initially, the velocity is low and the drag is smaller than the weight. The acceleration is then negative, and the rocket falls toward the earth, gaining speed as it falls. Since the speed increases, the drag increases. And a point is soon reached where the drag is equal and opposite to the weight. The acceleration then becomes zero and the rocket falls at a constant terminal velocity. We can determine the magnitude of the terminal velocity by equating the drag and the weight and solving for the velocity, as shown at the lower left of the figure. The terminal velocity depends on the weight, the drag coefficient, the air density, and the reference area. The typical value of the drag coefficient for a model rocket is about 0.75, about one-half of the drag for a similar sized flat plate. A low drag coefficient produces a high terminal velocity. Likewise, the small cross-sectional area of most model rockets also produces a high terminal velocity. To slow the descent (and save the rocket for later flights), a small explosive charge is used to deploy a parachute for recovery of the rocket.
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byTom
Benson
Please send suggestions/corrections to: benson@grc.nasa.gov