Overview

The HADES Cup transfers load from the piston and diaphragm to the booster section, breaking the shear pins and initiating the Recovery deployment sequence.

v1.0: Pathfinder

The first edition of the cup is a simple aluminum cylinder that accepts the Diaphragm at one end via grub screws. It is a simple aluminum cylinder with measured dimensions:

Thickness (t)	0.1"
Inner Radius (r_i)	5.725"
Length (l)	14"
Useable Packing Volume (in³)	341

Ground testing has shown that the cup does not buckle under normal piston operating loads, even those as high as 3500 lbs (an order of magnitude greater than normal operating loads) as we predict we saw in November 10, 2017 Hermes Ground Test.

v2.0: Hermes Dimensions

Development

In addition to a change in outer diameter to accommodate the switch from a 6" ID to 6" OD rocket body, v2.0 of the Hermes cup involves making mass saving cuts.

To quickly determine structural integrity, we can perform a buckling calculation, assuming long vertical cuts are made:

Given some amount of aluminum from the cup on both ends of the column, this scenario is best approximated as a double-wall-mount buckling problem. Only first order buckling is possible, because the mission package tube constrains the cup in one direction. Thus the critical buckling load is:

$\begin{array}{l}P_{cr} = \frac{4 \pi ^2 E I}{L^2}\end{array}$

From Matweb, the Young's Modulus of aluminum is 68.9 GPa = 1.00e+7 psi. The area moment of inertia for a rectangle under buckling is $\begin{array}{l}\frac{bh^3}{12}\end{array}$ . Given a 0.1" cup thickness, h, we can solve for the minimum width of each column, b. We apply a 2x factor of safety on the piston load (360 lbs) and generalize the number of columns as n_c. Assuming evenly spaced columns, each column will endure an equal amount of load. An additional factor of safety is applied when we set L = 14", the total height of the cup:

$\begin{array}{l}\frac{720 lb}{n_{c}} = \frac{4*\pi ^2 *10^7 psi * b *(0.1 in)^3}{12*(14in)^2}\end{array}$

$\begin{array}{l}b = \frac{4.3 in}{n_{c}}\end{array}$

So if, for example, 8 evenly-spaced columns are used, the minimum necessary width of each column is 0.54 inches.

Dimensions

The dimensions for the Hermes cup were chosen in part due to an investigation on Hermes Packing Procedures and Volumes. Here, we found that pathfinder packing volume is roughly appropriate. Thickness of the cup increased, but we used this new thickness when simulating for mass saving cuts. Because the airframe is 5.85" ID, we want some tolerance between the OD of the cup and the ID of the airframe. On the Pathfinder vehicle, this was measured as ~0.25" in tolerance by using paper to measure the circumferences. In reality however, the Pathfinder tubes are quite out-of-round and visual measurements show a maximum tolerance around 0.15" (between diameters). Because we would like to limit frictional forces that will detract from the useful work done by the piston, we will go with the former tolerance, bringing the required outer radius of the cup to be 2.8" and correspondingly the inner radius to be 2.675". Due to the need to maintain roughly the same packing volume as Pathfinder, the overall length of the cup must be adjusted to ~15"

Thickness (t)	0.125"
Inner Radius (r_i)	2.675"
Outer Radius (r_o)	2.8"
Length	15"
Useable Packing Volume	~340 in³

Mass Saving Cut Options

We ultimately chose to pursue the column design due largely to the simplicity of fabrication and decreased likelihood of line entrapment.

Optimized Cup Cuts for Column Design

Here are the spreadsheet calculations for the optimized cup cuts given the column design: Calculations for CADs (Cup and Diaphragm).xlsx

Ultimately, to increase the safety factor, we chose to increase reduce the cut width by a factor of 2. Simulation results are below.

Flight 1

Due to manufacturing constraints, only 4 of the mass saving cuts were implemented. This design did not fair well in shipping, future teams are suggested to place the diaphragm and a similar feature in the cup for travel.