Overview
The case needs to not break.
Define Operating Parameters
The a priori requirements for the design of a case usually come from vehicle level design choices, such as outer diameter and length. These are usually supplemented by system level requirements, such as operating pressure, safety margins, and integration constraints. A typical set of requirements could look like the table below:
| Requirement | Parameter |
|---|---|
| Outer Diameter | 6.00 in |
| Length | 87.00 in |
| MAWP | 900 psi |
| Burst Pressure | 1800 psi |
| Working Temperature | 400° F |
Material Selection
The selection of materials for a rocket motor case is an interesting endeavour. Typical constraints are availability, cost, lead time, availability of appropriate casting tubes and liners, compatibility with commercial standards, etc. Find the main article here.
Stress in a Pressure Vessel
Hoop stress in a thin-walled cylinder can be written:
| \sigma_H = \frac{Pd}{2t} |
Where the stress is equal to the Pressure times the diameter divided by two times the thickness of the cylinder.
Since the diameter and pressure are usually known, this leaves you with two knobs to turn, the thickness of the case, and the material properties which dictate the maximum stress. Another way to work through these equations would be to select a diameter, a thickness, and a maximum stress and then calculate the maximum pressure you could run a case at. This route is more likely if you're re-rating a commercial case or trying to decide if an existing case is appropriate for a given test.
The longitudinal stress in a thin walled cylinder can be written:
| \sigma_H = \frac{Pd}{4t} |