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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.

• 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 anticipated fill time ranges from

We are in the process of conducting a more thorough analysis, as described below:

For the purpose of a simplified analysis, we examined a 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 dynamic pressures 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.

First, we examined the range of possible dynamic pressures, which depends on both the deployment speed and air density (which depends on altitude). 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

 TO BE CONTINUED...

Terminology

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

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