This page will detail the procedure we have gone through to calculate the number of shear pins you need for your rocket. A script has been written and attached to the end of this wiki. Important things to note are that these calculations are based off of ideal gas equations (PV=nRT). The results have been compared to online Black Powder calculators and output the same values. Some calculators even use empirical data which supports our script.
¶ What the script outputs:
- Number of shear pins required (safety factor already accounted for) for both your Main parachute section and your Drogue parachute section.
- Amount of black powder you will need for your compartment size in grams
¶ What the script needs (inputs):
- Shock load from drogue deployment (yet to be implemented: only the portion of load on the main chute section)
- Dimensions of the two pressurised sections
- Desired pressure in the two sections
¶ Rationale
- Shock load from drogue should not deploy main -> this is achieved by an appropriate number of shear pins
- Black powder in main section should overcome shear pins required in 1
¶ Hence the script
- Calculates shear pins required at drogue section to withstand force during ascent
- Calculates BP required for drogue deployment (to achieve 15psi)
- Accounts for shear pins on drogue section (to correct psi and hence BP required)
- Ensures blast is withstood by main section by putting appropriate number of shear pins
- Calculates BP required for main deployment (to overcome shear pins)
| Crash course on the Ideal Gas law |
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¶ How it worksThe ideal gas laws are, as the name states, ideal and not a perfect representation on what is actually happening on the molecule scale, however they are more than accurate enough for our applications. The important things to understand when considering a black powder charge inside a closed compartment is:
Considering ¶ PV = nRTP = Desired pressure inside the compartment, in psi. (typically between 8 and 15 if you don't know where to start) V = Volume of your compartment, in inches cubed (Length * Diameter^2 * 1/4 * pi). n = mass of black powder, in lb (mass) , note: this is not mass of gaseous products because our R constant already accounts for this. R = Empirical gas constant for black powder. 266 (lbf/(lbm*degrees ranken) T = Final temperature after detonation (obtained from empirical results, always the same). 3307 (degrees ranken).
1 lbm = 454 grams
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¶ Single deployment rocket
For a single deployment rocket, assume the drogue parachute is the main parachute in the Matlab script. You can skip steps 4 and 5 in the script.
¶ Questions to be answered:
- Other (inertial) loads from eg booster flameout?
From OpenRocket, at booster burnout acceleration decreses from 100 ms^-2 to 15 ms^-2, load generated (by loss of booster thrust force) is approximately (100-15)*mass of rocket times a 0.5 factor to account for net force on rocket, is approximately 1kN.
- Two models for parachaute deceleration?
a) parachute is ideal and travels at slower speed, "tugs" the rocket to travel at same speed, KE reduced, and process repeats b) parachute produced speed proportional drag which decelerates rocket and parachute
Calculator link: https://github.com/icl-rocketry/Shearpin-BP-calculator.git
References: