¶ Size calculations
Using the equation below, the area required for a parachute can be obtained:
S = (2 x g x m)/(rho x Cd x V^2)
where S is the area of the parachute, g is the gravitational acceleration, m is the total mass of the rocket (estimated to be 47 kg), rho is the density of air (1.225 kg/m^3), Cd is the drag coefficient of the parachute and V is the descent velocity, estimated to be about 5 m/s for the main chute and 35 m/s for the drogue chute. Using this area, the diameter of the parachute can be found using:
D = sqrt(4*S/pi)
For Sporadic Impulse, and the associated conditions:
g = 9.81 m/s^2
m = 47 kg
rho = 1.225 kg/ m^3
For the drogue chute, the descent velocity, V, was estimated to be approximately 35 m/s while for the main chute, this was taken to be 5 m/s . Hence, while sourcing and comparing parachutes, the available sizes were compared to the size required with their associated coefficients of drag, as an appropriate size is required to be able to achieve the desired descent velocity but also to not exceed the desired drag and have the rocket drift too far. These comparisons are further detailed in the table below.
¶ Main parachute comaprisons
| The Rocketman | Name | Size (diameter) | 15ft/s mass | 25ft/s mass | Cost | Weight | Packing Volume | Cd | Size required |
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Standard Low-Porosity 1.1 Ripstop Parachute | 20 ft | 70 lbs | 185 lbs | $375 | N/A | N/A | 0.97 | 19.751 |
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Ultra-Light Parabolic Parachute | 20 ft | 70 lbs | 185 lbs | $750 | 0.620 kg | 4.0D" x 10.21L"= 128.30”^3 | 0.97 | 19.751 |
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Ultra Light Annular Parachutes | 16ft | 53.5 lbs | 147.8 lbs | $480 | 0.593 kg | 4.0D" x 9.77L"= 122.89"^3 |
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High Performance CD 2.2 Parachute | 16ft | 118.6 lbs | 328.7 lbs | $620 | 1.848 kg | 6.0D” x 11.52L”= 325.85"^3 | 2.2 | 13.115 |
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Ultra Light High Performance CD 2.2 Parachute | 16ft | 118.6 llbs | 328.7 lbs | $1,257.48 | 0.502 kg | 1.375D" x 3.08L" = 58.94”^3 | 2.2 | 13.115 |
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Star PolyConical Parachutes | 14 ft | 52.2 lbs | 144.9 lbs | $315 | 1.542 kg | 4.0D" x 26.45L"= 319.93"^3 |
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? |
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Rotating Star Parachute | 14 ft | 68 lbs | 188.7 lbs | $490 | 1.542 kg | 4.0D" x 26.45L" = 319.93"^3 | 1.67 | 15.052 |
| Fruity Chutes |
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Descent Rate |
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Iris Ultra | 10ft | 79lbs @ 20ft/s |
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(currently sold out) | 1.021 kg | 199.9"^3 | 2.2 | 13.115 |
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Iris Ultra Compact | 20 ft | 179lbs @ 15ft/s | 318lbs @ 20ft/s | (currently sold out) | 3.150 kg | 472.2"^3 | 2.2 | 13.115 |
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Iris Ultra Light | 14ft | 88lbs @ 15ft/s |
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$1060 | 0.732 kg | 143.4"^3 | 2.2 |
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¶ Drogue parachute comparisons
| The Rocketman | Name | Size (diameter) | 15ft/s mass | 25ft/s mass | Cost | Weight | Packing Volume | Cd | Size required |
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Standard Low-Porosity 1.1 Ripstop Parachute | 3ft | 1.7 lbs | 4.4 lbs | $40.50 | 0.0680 kg | 2.6D" x 2.25L”= 11.94”^3 | 0.97 | 2.822 |
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Ultra-Light Parabolic Parachute | 3ft | 1.7 lbs | 4.4 lbs | $81 | 0.0315 kg | 2.0D" x 2.08L”= 6.52”^3 | 0.97 | 2.822 |
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Ultra Light Annular Parachutes | 3ft | 2 lbs | 5.2 lbs | $70 | 0.099 kg | 3.0D" x 2.91L"= 20.58"^3 |
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High Performance CD 2.2 Parachute | 3ft | 4.2 lbs | 7.4 lbs | $100.50 | 0.136 kg | 2.6D” x 4.52L”= 24"^3 | 2.2 | 1.874 |
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Ultra Light High Performance CD 2.2 Parachute | 3ft | 4.2 lbs | 7.4 lbs | $111.18 | 0.0425 kg | 1.375D" x 3.08L" = 4.57”^3 | 2.2 | 1.874 |
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Star PolyConical Parachutes | 3ft | 2.4 lbs | 6.7 lbs | $75 | 0.0629 kg | 2.0D" x 4.15L"= 13.05"^3 |
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Elliptical Parachute | 3 ft | 4.8 @ 20ft/s |
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$70 | 0.125 kg | 2.6D” x 4.52L” = 24.00"^3 | 1.6 |
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Checkered Ringsail Parachute | 3 ft | 1.62 lbs | 4.5 lbs | $95 | 0.0629 kg | 2.0D" x 4.15L" = 13.05"^3 |
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| Fruity Chutes |
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Descent Rate |
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Iris Ultra | 3ft | 7lbs @ 20ft/s |
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$107.83 | 0.142 kg | 27.6"^3 | 2.2 | 1.874 |
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Iris Ultra Compact | 3ft | 4lbs @ 15ft/s |
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$142.97 | 0.0595 kg | 11.9"^3 | 2.2 | 1.874 |
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Iris Ultra Light | 3ft | 4lbs @ 15ft/s |
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$170.93 | 0.0471 kg | 9.2"^3 | 2.2 | 1.874 |
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Compact Elliptical Parachute | 3 ft | 4.8 lbs @ 20 ft/s | $76.50 | 0.092 kg | 18.0"^3 | 1.5 | 2.269 | |
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Elliptical Parachute | 3 ft | 4.8 lbs @ 20 ft/s | $76.53 | 0.128 kg | 21.2"^3 | 1.5 | 2.269 | |
Links to the information about inflation time:
1) https://www.sto.nato.int/publications/AGARD/AGARD-AG-319/AGARD-AG-319.pdf
2) https://arc.aiaa.org/doi/abs/10.2514/1.26286?journalCode=ja