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The piston must be able to supply enough force at its operating pressure to break the shear pins with a 2x safety factor, which is the safety-critical guideline for parachute components presented by NASA. [5] According to standards established by the Aerospace Corporation, there must also be a minimum 1.5 design burst factor. [4]
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Given Aluminum 6061-T6 as the material, which typically has a tensile yield strength of approximately 276 MPA (this analysis neglects the internal temperature of the piston due to the combustion of black powder, because we assume the temperature effects will be transient).
Another requirement of the piston is that it cannot break the shear pins prematurely due to an internal build-up of pressure caused by the altitude difference. Between 4,245 ft (the altitude of Truth or Consequences, NM) and 152,945 ft ASL (a simulated upper bound on performance as of January 4, 2018), the pressure difference is approximately (given by the 1976 Standard Atmospheric Calculator using no temperature offset) -86600 Pa. Thus, the following graph of maximum piston area based on the amount of shear pins used can be estimated:
Resources:
The following resources are useful materials for learning about pressure vessel and piston theory:
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