Calculating Loads on the Rocket

To calculate the loads on the rocket, we use a Matlab script and data from the OpenRocket simulation. We gather the rocket’s time, vertical and lateral acceleration, mass, thrust, drag, and angle with respect to the ground from the OpenRocket simulation and export this data as a .csv file. With this data, we can use Matlab to calculate the forces on the rocket in the following steps:

1. Pull data from the csv file
2. Convert mass to gravitational force on the rocket, in rocket coordinates. To convert forces from Earth coordinates to rocket coordinates, you need to transform the forces to the new coordinate system. You can read more about transformation matrices for stresses here. We use the 2D transformation matrix for stresses because stresses are just scaled forces (force/area), and because we’re looking at a slice of the rocket with the axial and transverse loads. We’re ignoring hoop stresses because they are not as significant, and this will simplify the analysis.
3. Use the accelerations and mass to find the total force on the rocket. Subtract the weight, thrust, and drag from this total force to get the aero forces on the rocket.
4. Sum forces to calculate the compressive force and convert to pounds so we can test it on imperial machines 😊
5. Include a 1.5 safety factor per this NASA design document. Aerospace standard for unmanned spacecraft is 1.25, but we’re using 1.5 because we expect variation in our wet layups.
6. Use this data to graph the forces on the rocket.
7. You can calculate the stresses on the rocket by dividing the force per unit area.

You can read through our code here:stress_graphs.m

Calculating the compressive stresses within the rocket. 

If we perform a free body analysis of a cut rocket (modelling the rocket as a single large beam), we can compute the expected compressive stress at each axial location on the rocket using:

$//<![CDATA[ \begin{array}{l}T(x) = -m(x) (a+g) - D'(x)\end{array} //]]>$

where m(x ) is the mass above position x, a is the instantaneous acceleration of the rocket, g is the acceleration due to gravity, and D'(x ) is the drag component acting on the rocket above position x. x is the axial location you are interested in, measured from the tip.

The derivation and a detailed explanation of how to use this formula is available here:

Compressive_Loads_Analysis.pdf