I use 2.5mm shear screws, so i'm providing full working here for you to be able to adjust it to your requirements.
Nylon 6/6 Resin has nominal shear strength of 69,00KPa at 23 degrees Celsius.
I use the major diameter of the screw rather htan the thread area for calculating shear, as it gives me a margin of error for allowing manufacturer tolerances.
The major diameter of the 2.5mm screw is 2.48mm.
The cross-sectional area of a round shear pin, as these screws are being treated is simple to compute.
area = pi * radius2
The major shear area is 4.830mm2
69,000KPa means the shear force required is 69,000,000Newtons per square meter, or 69Newtons per square mm.
The therefore will require 333.27Newtons to shear each pin.
The ejection charge must be capable of over pressurising the parachute bays to the point that the three shear pins, and friction of the coupler is overcome and the airframe separates. As the airframe is a constant diameter, and the number of shear pins and expected coupler friction is constant the only variable determining the quantity of black powder is the length of the bay.
Using a simplified equation of black powder combustion, we know that approx. 0.0155 moles of gas products is generated per gram of black powder.
With three shear pins requiring 333.27 Newtons of force to break and an estimated 23 newtons of friction to overcome (assuming your nose is loose), an estimated 1022.81 newtons of force is required to separate the airframe.
In an airframe with an inner diameter of 99.1mm, giving 7713.246mm2 of area to act upon, 132.6KPa is required to cause separation. An oversizing of 20% to allow for incomplete combustion or other factors yields a required 159.12KPa pressure requirement.
The ideal gas law states that
PV = nRT
Where:
P is the pressure in atmospheres
V is the volume in litres
n is the moles of gas products
R is the gas constant of 0.082058L atm/mol K
and T is the temperature in Kelvin.
1 atmosphere is equal to 0.101325MPa, meaning we require 1.57 atmospheres of pressure from the black powder combustion.
To solve for moles of gas products required:
n=PV/RT
For your rocket with a volume of 793.571cm3 require
n=(1.57*0.793571)/(0.082058*3273)
n=0.00463893735mol
divide by the number of moles of gas per gram of bp and you require 0.299g of black powder.
These calculations do give you an over-sized charge, but not to the point of most online calculators that use rule of thumb formulas do. Never had a calculated ejection charge fail on me
You may need to adjust nose cone friction if you have anything other than a easy fit (although I've had my primary ejection charge blow off ones that basically needed to be hammered in).
