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Given Aluminum 6061-T6 as the material, which typically has a tensile yield strength of approximately 276 MPA 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 to be a 0.25x reduction in that of the previously-qualified piston bore (part 6491K254 on McMaster):

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The relevant dimensions and properties of 6453K153 are enumerated in the table below:

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As you can see, both steel and aluminum rods have large factors of safety on buckling due to piston force.

Burst Factor of Safety

Here we calculate the precise burst factor of safety on our piston. Some details:

• • Aluminum 6061-T6 has a tensile yield strength of approximately 276 MPa = 40.03 ksi
  • The inner radius of the piston bore is 0.5625in
  • The outer diameter of the piston bore is 1.18125

The necessary pressure for a separation of 360 pounds is calculated as follows:

P_sep = 362.17 lb/in²

This gives a ~5.8x factor of safety on burst.

Premature Separation Factor of Safety

Next we check the factor of safety on premature separation, knowing that as previously calculated the pressure difference for flight will be approximately 12.56 psi (it will actually be much less due to a much lower expected altitude as of 2/2/2018):

Given that we plan to use 180lb of shear pins, this provides a minimum of 14.4 factor of safety on premature separation due to internal pressure buildup.

Resources:

The following resources are useful materials for learning about pressure vessel and piston theory:

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