How does Weight Affect a Rocket’s Flight Trajectory

Missions or flight regimes that are carried out with rockets are optimized to have certain parameters like Delta V, range, time to target, altitude and etc.

The thrust profile is important to consider when talking about rocket weight. Thrust profiles in some rockets are not constant and this directly affects the flight profile and can give information on what type of mission that the rocket is designed for.

Here is an equation to highlight that is directly impacted by the changing mass of a rocket.

The Rocket Equation

Where m_0 is the initial mass, m_f is the final mass, Delta V ideal is the ideal velocity increment, g_0 is gravity at sea level, and I_sp is the specific impulse of the propellant.

The ideal velocity is how much velocity is imparted to the system. The specific impulse is a parameter that explains how efficient a propellant is and is in the units of seconds. It is composed of Force divided by the mass flow rate times gravity.

Specific Impulse

A specific impulse of 120 seconds will provide an impulse of 120-pound seconds per pound of propellant. The area underneath the thrust vs. time is a way to calculate impulse.

The internal propellant mass of the rocket will be decreased on ignition.

If the rocket uses a solid propellant, then its internal burn area will increase based to the rocket’s grain geometry. The specific impulse can vary from the changing burn area.

This is figure 11-16 from George Sutton’s “Rocket Propulsion Elements.”

Neutral grain geometries have thrust profiles that are constant after ignition. Progressive and regressive grain geometries have thrust profiles that either increase after ignition or decrease after ignition, respectively.

If the rocket uses liquid propellant, then the mass of the propellant and oxidizer tanks will decrease and are filled with a pressurant gas.

The maximum thrust to weight ratio is achieved right after burnout with rockets with a constant thrust profile.

The exhaust fumes at the rocket’s nozzle may also affect the coefficient of drag of the rocket with changing altitude which can add the drag force at those altitudes.

Another point to mention is that to reach greater specific impulses, the rocket will have to be split up into multiple stages. The mass required for a traditional single-stage orbit rocket is undefined.

an image generated from a Matlab script I wrote

All of these factors should be taken into account when iterating through the parameters to determine the rocket’s trajectory. Depending on how the rocket was designed, these and many other parameters may affect the location of where the center of gravity is placed within the rocket. Besides thrust, any forces of significant magnitude acting on the rocket can tilt the rocket at the rocket’s center of mass and can cause instability if unaccounted for when determining a rocket’s flight trajectory.

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