# Flight Profiles of Estes Alpha Model Rocket

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This Demonstration simulates the flight of an Estes Alpha model rocket. The effect of air resistance is taken into account. The altitude and velocity at any time during the flight can be shown using a slider. The time window can be adjusted to focus, for example, on the early moments of the flight. The effect of air resistance is clearly seen in the velocity and altitude graphs. Three different rocket engines can be selected to illustrate the effect of changes in average thrust and thrust duration. The drag coefficient may be adjusted so that its effect may be seen. The time to parachute ejection is calculated and velocity and altitude at this time are plotted.

Contributed by: Richard L. Kahler (November 2014)
Open content licensed under CC BY-NC-SA

## Details

The flight profile is calculated using NDSolve to compute the velocity as a function of time. Newton's second law gives a differential equation for the velocity, . The equation is complicated by several factors: the thrust and the mass change as the propellant is burned, and the air resistance is a function of the velocity. The thrust is approximated using a constant average thrust during the boost phase. Values for the total impulse and thrust duration are obtained from NAR certified engine data, August, 1996. The average thrust is the impulse divided by the thrust duration. The mass is approximated using a constant average mass computed using the mass of the rocket, .039 kg for a typical Alpha model, plus one half the mass of the propellant, again from the Estes data. The drag is calculated using the equation , where is the drag coefficient, approximated as 0.6 for the Alpha model rocket; is the density of air, 1.2 kg/ at 20 °C and 101kPa; is the cross section area of the Alpha rocket calculated as a circle of radius 0.012 m; and is the velocity of the rocket. With these simplifications, NDSolve easily computes a numerical solution for . The height is obtained by numerically integrating the velocity solution. The velocity and height are plotted as a function of time from liftoff.

Reference

[1] Estes Rockets. "001225-Alpha®." (Nov 18, 2014) www.estesrockets.com/rockets/kits/skill-1/001225-alphar.

## Permanent Citation

Richard L. Kahler

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