Overview
; There will be 3 4 sets of bolts connecting the bulkhead to the nose cone and/or the AV bay.
The first are 1) radial bolts along the base of the nose cone that connect to the bulkhead. The largest force these will have to withstand is from the deployment of the piston.
2) radial bolts along the mission package tube that connect to the bulkhead. These These will have to withstand forces from two sources: the piston and the acceleration of the rocket. So, we need to find the approximate maximum forces due to both (with a safety factor of 2), and use the greater force to determine which arrangement and size of bolts we'll need.
3) 8 bolts in the bulkhead that connect to the piston
4) a set of three bolts that connect the AV tower to the bulkhead
Radial Nose Cone Bolts
First, we need to calculate the maximum force from the piston. According to recent sims, the maximum force it'll exert on the whole system will be 2250lbs during the main deployment. However, the nose cone only feels its inertia, so
F_nc_section = F * M_nc_section/M_whole_rocket.
Currently, the mass budget of the rocket has a dry mass of 79 lbs. Assuming that the
M_nc_section = M_nc + M_nc_tip + M_nc_extension = 5.6 lbs,
then
F_nc_section = (2250lbs)*(5.6lbs)/(79lbs) =160 lbs.
Applying the safety factor of two and adding a a couple of pounds to the nose cone in case it goes over its mass budget,
F_nc_section = (2250lbs)*(10lbs)/(79lbs)*2 = 570lbs.
To calculate the arrangement, number, and size of bolts, we'll analyze the shear strength of the bolts.
Stress = Force/Area
Shear Area = (Number_bolts)*(Diameter_bolt)*(Thickness)
The thickness depends on the bulkhead design, but if we assume the NC is thinner, then thickness = 0.9 in. If we look at the shear strength of steel bolts to determine the amount of force they can withstand, we find a maximum allowable stress of 15 ksi (http://www.ssina.com/download_a_file/fasteners.pdf; table at the bottom of page 9). We can plug these in along with the maximum force to find
(Number_bolts)*(Diameter_bolt) = (570lbf)/(15000 lbf/(in^2) * .09 in) = .4222 in
Assuming we have eight bolts
Diameter_bolt = .4222/8 = .0528 in
All this means is that the bolt will be able to withstand the shear stresses on it, and it won't snap under those forces as long as it has a minimum .0528 in diameter. So, essentially any standard bolt in an 8 hole radial pattern will suffice.
However, we also need to analyze the shear strength of the G12 fiberglass so that we know it won't deform under the force. Unfortunately, the shear strength of G12 isn't known (we called the manufacturers), so we want to run tests to ensure it won't break/deform under that force. The general plan is to use an Instron to apply 570 lbs of shear force to a sample of G12 tubing with the same thickness as the nose cone that's attached to some aluminum tubing that's the same thickness of the bulkhead with the a variety of bolt sizes to make sure it will withstand the force during flight. If it fails, we'll try some other bolt sizes and perhaps patterns.
Radial Mission Package Tube Bolts
Next, the force due to acceleration. Recent sims (Hermes II Simulations log) predict a maximum acceleration of about 800 ft/(s^2), which is approximately 25G. After applying the safety factor of two, we can expect an acceleration of 50G. The bolts on the bulkhead have to be able to withstand the force of everything attached to the bulkhead (AV tower, piston, recovery, NC assembly) accelerating with the rocket. Assuming they weigh about 50lbs and accelerate at 50G, then the
F = (50lbs)(50G) = (22.68kg)*(490 m/(s^2)) = 11113.2 N = 2498.35 lbs.
So it's clear that this will be the maximum amount of force that the bolts will have to withstand.
To calculate the arrangement, number, and size of bolts, we'll analyze the shear strength of the bolts.
Stress = Force/Area
Shear Area = (Number_bolts)*(Diameter_bolt)*(Thickness)
The thickness depends on the bulkhead design, but if we assume the NC is thinner, then thickness = 0.9 in. If we look at the shear strength of steel bolts to determine the amount of force they can withstand, we find a maximum allowable stress of 15 ksi 15 ksi (http://www.ssina.com/download_a_file/fasteners.pdf; table at the bottom of page 9). We can plug these in along with the maximum force to find
(Number_bolts)*(Diameter_bolt) = (2498.35lbf)/(15000 lbf/(in^2) * .09 in) = 1.851 in
Ideally, we want the Number_bolts to be 6 so that even if half of them were loaded at any time (and there have to be at least 3 bolts fully loaded at any time because 3 points define a plane), they would be able to withstand the force since the safety factor was 2. Therefore, we have Assuming we have eight bolts
Diameter_bolt = 1.851/
...
8 = .
...
All this means is that the bolt will be able to withstand the shear stresses on it, and it won't snap under those forces. Now, we need to calculate the yield strength of the bolts given that they're loaded in tension.
231 in
We However, we also need to analyze the shear strength of the G12 fiberglass tubing in this case, so that we know we're planning on running a similar test in this case to ensure it won't break/deform under the force.