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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 (Section 3.3.1.5). As of January 4, 2018, we are designing for 180lbs of shear pins, and thus the piston must supply 360lbs. The same source (Section 3.3.1.6) dictates a design burst pressure factor of 2x the maximum design pressure, which aligns with DTEG requirement 4.2.2. [5] ThenThus, we expect the piston to determine when the cylinder will burstburst when it supplies 720 lbs. Here, we make use of thin-walled pressure vessel theory [2], paraphrased below:
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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 gas produced by the combustion of black powder. A transient thermal spike could degrade material properties when the piston is pressurizing, but we assume that the magnitude of energy released is negligible compared to the thermal mass of the aluminum). The tensile yield strength can be used to calculate the design burst pressure. For this preliminary analysis, the wall thickness is chosen as to be a 0.25x reduction in that of the previously-qualified piston bore (part 6491K254 on McMaster):
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Applying P = F*A where F is 720 lbs at burst and A is the area of bore, we find:
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Then, assuming a circular bore, area takes the form A = πr2
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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:
Terminology
Resources:
The following resources are useful materials for learning about pressure vessel and piston theory:
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