Analysis

The Analysis consists of kinematics and dynamics to calculate the forces acting in the system. With these forces, mechanics of materials can be used to find the stresses acting on different parts can be calculated to find the required design parameters for different parts of the device.

Requierments:

The central rods must be capable of withstanding 300lbs of force without buckling
The Nose cone must be attached to the rocket with at least 3 shear pins
The two central rods must always overlap by at least 3in
The two central rods can telescope out 10in
The lower central rod must withstand 300lbs of force without separating from the nosecone
The shear pins cannot shear under 1000lbs of force
The nosecone can withstand shear under 500lbs of force
The nosecone can withstand 100lbs impact force without permanent deformation.
The capsule only experiences 50% of the impact
The Head Plate can withstand 100lbs of impact force without permanent deformation.
The collar of the central rods cannot deflect by more than 0.01in under 100lbs of force at one end.

Main axial forces

Analysis 5 and 9 are the two largest forces that act on the structure of the payload. analysis 5 is the force needed to shear through the shear pins and thus the force of ejection acting along the central rod. the force calculated is 5675N needed to shear the pins and with a safety factor of 1.5, the new force is 8513N.

Analysis 9 is the impact force from landing. using a 10lb payload, impacting at 30mph, and using an impact distance of 5in from the spring, the calculated max force of impact is 6424N

while the calculations show that the ejection force is higher than the impact force, that isn't entirely true. The CO2 ejector will cause a lot of pressure build up in the payload bay, which is how it would normally shear through the pins. This means that a large portion of the force needed to shear the pins wont actually travel through the payload at all.

Rod Material

This analysis is for determining the better material for the central rod of the payload. using the calculations for the main axial forces, the diameter needed for a steel or aluminum rod is calculated. It was found that you could use a thinner steel rod for the same strength as the aluminum, but the steel rod will still be several times heavier, so we went with the aluminum rod.

Central Rod size

This analysis is for calculating the necessary size for the central rod of the payload. The rod will be ~40in long and made from aluminum 6061-O. the calculations were done under the assumption that the rod was in a fixed- free configuration. This rod will need to withstand the 6424N force from impact without buckling. the calculations found that the rod needed to be 1.75in in diameter with a thickness of 1/8in. alternatively a 1.5in diameter with a 1/4in thickness would also work.

Central Rod deflection

This analysis is for determining the deflection of the rod as a cantilever beam, a worst case scenario, under 1000lbf at the end. The calculations showed that under these conditions, the rod deflects by 0.0092in which is within acceptable tolerances and shows that the rod is not likely to be damaged from bending in this fashion.

Head Plate thickness

This analysis is for determining the thickness of the top plate. this plate will need to be strong enough to withstand the forces traveling axially through the rod, or else the rod will brake the plate and into the head of the payload. The calculations show that a thickness of 0.1in could theoretically withstand the forces, its just barely, thus a thickness of 0.5in was chosen instead.

Small Rod

This analysis is for determining whether the small telescoping rod could be thinner and slide inside the larger rod, or if it would need to be outside for strength. using a diameter of 0.75in and a thickness of 0.125in, it was found that a inner telescoping rod would be able to withstand the calculated forces.