The Hermes Recovery deployment sequence is "lines first," which has several advantages, noted by Wolf in his Parachute Seminar.
Lines First Deployment Example from Knacke (sourced from Wolf)
We will conduct research into the deployment sequence to mitigate possible failures, ensure a stable descent, and help inform our camera choices.
To inform our choice of camera, we need to gather information on chute deployment and inflation rates.
The rate of drogue parachute inflation will depend on the airstream conditions and the parachute dimensions and its materials. To begin analysis, we examined the NASA TM X-1786 "Wind-Tunnel Investigation of Inflation of Disk-Gap-Band and Modified Ringsail Parachutes at Dynamic Pressures Between 0.24 and 7.07 Pounds Per Square Foot."
Most notably, this paper provides a mean empirical curve relationship for parachutes given their geometric porosity. This formula does not take into account atmospheric conditions or parachute type (i.e. disk-gap-band, ringsail). This makes it appropriate only for preliminary analysis:
\frac{t_{f}}{D_{o}} = \frac{0.65\lambda_{g}}{V} |
In this formula, tf is the filling time in seconds, and Do is the nominal canopy diameter. is the canopy geometric porosity. To develop a range of possible fill times, we use the following estimates:
Using these estimates, we generate the following plot of fill time as a function of velocity. To select a representative range of velocities, we examined the range of possible main-deployment conditions (using the chart featured in the Hermes Disk Gap Band Design page as a basis for our analysis). This analysis also made use of 1976 COESA Standard Atmospheric model, as calculated using the MATLAB function atmoscoesa.
For a first-pass analysis, we assume that inflation will occur within 10 seconds of apogee. Neglecting drag due to the high altitude: . For a range of post-apogee deployment times, we can generate the following velocities for our analysis:
times = linspace(0,10); velocities = times*9.81; figure(); gpor = 10; % sample geometric porosity, as a percent D0 = 4; % 4 ft inflation_times = 4*0.65*gpor./velocities plot(velocities, inflation_times); |
Then, we can generate the following graph of inflation times based on velocity:
We currently do not know how to qualify exactly how long after apogee the drogue parachute will begin inflation. This may depend (to varying degrees) on the following things:
The time after apogee that inflation occurs depends for two reasons. First, it will impact the inflation time, as seen the graph above. It is important to note that in this graph, the airstream velocity will be increasing during inflation (as the drag force may not yet be sufficient to fully counteract gravity), so you cannot simply calculate the inflation time by determining the airspeed at the moment inflation begins. It will be faster.
The second reason why timing matters is "the v2 law" which was found by skydiving research conducted by Potvin and Peek. This states that "the maximum deceleration sustained... is proportional to the square of the jumper's speed prior to slider descent." In simple terms, the faster Hermes is going prior to parachute inflation, the worse the deployment forces will be.
Our main parachute will be released at an altitude of approximately 2,000 ft. We will use two Tender Descenders for redundancy. There are two configuration options, series and parallel:
There are many advantages to a parallel configuration. Notably:
One disadvantage is that you have to be sure that the Kevlar line (or another type of line if you so choose) will not abrade.
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geometric porosity: the percent of the nominal canopy surface area that is removed due to vents and gaps
Potvin and Peek, Parachute Opening Shock Basics
https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19690014164.pdf