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At this stage of the analysis, radius can be constrained further: 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 ≈ 12.56 psi.
Applying a 2x safety factor to premature separation (again in accordance with safety-critical recovery components as dictated by NASA), we calculate the maximum allowable radius of the piston [5]:
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| body | F_{sep} = P_{diff}*A_{bore} |
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| body | F_{sep} = P_{diff}*\pi*r_{bore}^2 |
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| body | \sqrt\frac{F_{sep}}{P_{diff}*\pi} = r_{bore} |
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| body | \sqrt\frac{0.5 * 180lb}{} |
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Terminology
Resources:
The following resources are useful materials for learning about pressure vessel and piston theory:
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