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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:we assume that inflation will occur within 10 seconds of apogee. Neglecting drag due to the high altitude:

altitudestimes = linspace(900000,15000010); %range of altitudes in meters
machs
velocities = 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 velocitiestimes*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:

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Terminology

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

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