Modeling the Boost Phase of the RS68A Rocket Engine

by August Weber

Submitted : Fall 2013

This is a demonstration of what can be done using the variables associated with the Delta IV Medium expendable launch system. The system consists of two engines, a first stage rocket, propellant, a cryogenic second stage, and composite payload fairing. Using their masses, shapes dimensions, and the data associated with this configuration, it is possible to calculate the burnout altitude, velocity, and time based on these known values. In regard to a RS68A rocket engine pushing one Common Booster Core (CBC), the known values are the total boost mass, the acceleration of gravity, the cross sectional area of the rocket, the drag coefficient based on the shape effect of a bullet, the air density at a certain temperature, the motor thrust and the motor impulse. This information is mostly collected from the Delta IV Users Guide and converted as needed to fit the constraints of the metric equations being used.

Formulating equations that consider wind resistance consists of summing up the forces on the rocket, breaking up equivalent terms in to Leibniz notation, and integrating them to go from force to altitude, force to velocity, and force to time. By having the proof of these formulas, we are able to go back to them and adjust variables as needed. For example, the air density value will change according to the temperature which will affect air resistance, and in turn the velocity and displacement will change. By my calculations the rocket altitude was within 16% of actual value, my burnout time was correct at 245 seconds and my velocity was within 87.6% actual. This can be explained due to things like trajectory curvature differences and certain values that are unavailable to the public regarding specific engine characteristics.

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