The 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.

Chute Inflation

To inform our choice of camera, we need to gather information on chute deployment and inflation rates.

Drogue Parachute Inflation

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."

• Notably, the chute used in the study (~15 feet diameter) is much larger than our expected drogue parachute (~4 feet diameter)
• Study chute had geometric porosity ~12.5%
• Fabric: 2.0 oz/yd² dacron
• Shroud lines: 550-lb coreless braided dacron, 15 ft long
• 5.52 lb mass

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, t_f is the filling time in seconds, and D_o is the nominal canopy diameter.  is the canopy geometric porosity. To develop a range of possible fill times, we use the following estimates:

• Geometric porosity of 10% (for the purpose of selecting a camera, this value was chosen as a conservative estimate, as it will minimize inflation time and require a higher frame rate)
• An anticipated diameter of 4 feet

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, the following ranges of altitudes and Mach numbers were selected:

• Altitude: 90,000ft to 150,000ft
• Mach: 0.5 to 2

The following lines of MATLAB can be used to calculate a range of possible velocities:

altitudes = linspace(90000,150000); %range of altitudes in meters
machs = linspace(0.5,2); %range of Mach numbers
altitudes = convlength(altitudes, 'ft', 'm'); %convert altitudes to meters
[T, a, P, rho] = atmoscoesa(altitudes); %use Standard Atmospheric Model
velocities = machs.*a; %calculates all possible deployment velocities

Then, we can generate the following graph of inflation times based on velocity:

Terminology

geometric porosity: the percent of the nominal canopy surface area that is removed due to vents and gaps

Resources

https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19690014164.pdf