Black Powder Calculations
This ground test used 0.2 grams of black powder, which was calculated in the following manner:
Step 1: Determine volume in the piston prior to rod extension
For this test, we assumed that the Piston Cup would be seated perfectly on the coupler. Given known integration challenges, this is not a perfect assumption. We also assumed that, in order to do this, we would not have to extend the rod of the piston to have an initial displacement. This is not a correct assumption, as the rod certainly requires an initial displacement. We will be working to qualify the impact of this initial displacement and will update this page as necessary.
Flight Piston Dimensions: An estimate for piston volume prior to rod extension is 0.5599π [1.08 in for depth and (1.44/2)2π = 0.5184π in2 for area]
Step 2: Determine necessary force to break shear pins
This test used 3x 6-32 shear pins, which take approximately 60 pounds each to break according to a rocketmaterials.org experiment. This totals to 180 lb necessary to separate the rocket. A 2x factor of safety was applied for a desired 360 lb.
Step 3: Determine PSI inside the piston necessary to achieve required force
360 lb-f = x * 0.5184π in2
x = 221 psi
Step 4: Determine PSI inside the piston necessary to achieve required force
Step : Evaluate Assumptions
Additional assumptions (besides those already mentioned are):
- Admittedly this math is sensitive to the volume, which we only estimated.
- The BP calculator assumes an ideal gas, which isn't true.