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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 and we can solve for the radius of the cylinder.
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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.
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Terminology
Resources:
The following resources are useful materials for learning about pressure vessel and piston theory:
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