Analysis included:

Projectile Exit Velocity Analysis

• Compute exit velocity as projectile leaves the barrel. This is used to calculate projectile distance analysis. (Spreadsheet was formulated to iterate and compute results with varying input parameters)

Projectile Distance Analysis

• How far the projectile will travel taking account for air friction and dynamic rope forces.  Rope gains in mass as it leaves the launcher so differential equations were formulated to compute values (Matlab® program was created to simulate distance at different angles, rope lengths, projectile mass, air densities, temperature, etc)

Optimum Mass Analysis

• If the mass is too heavy the projectile will not go far enough.  If projectile is too light is will not carry the rope far enough. (1.7lb)

Recoil Analysis

• Using conservation of linear momentum, formulas were created to compute the recoil velocity and force knowing the mass of the launcher and projectile, time for projectile to leave launcher and speed of exiting projectile. (Recoil speed: 5.2 ft/s with 68.2 lb of force)

Pressure Vessel Analysis

• Max pressure cylinder can hold using hoop stress calculation (370 PSI with Safety Factor of 4 - ASME Pressure Vessel Standards)
• Infinite-life safety factor with cycling from 0 to 150 psi using Von Mises effective stress calculations (Safety Factor of 4.35)

Bolt and Gasket Analysis

• Bolt pattern (12 bolts)
• Required preload on bolts (2338.8lb)
• Gasket sizing and material (Unconfined rubber gasket)
• Fatigue, static yielding, joint separation and leakage safety factors at 3000 cycles (2.62, 1.03, 54.53, 1.04 respectively)