Webbing lengths must be selected carefully to satisfy several constraints such that parachutes enter the airstream (and do not remain confined within the vehicle). For Project Hermes, the webbing constraints and resulting calculations are summarized below:
For the Hermes Pathfinder vehicle, the relevant dimensions are:
| Variable | Length (in inches) | Description |
|---|---|---|
| hmp | 51.3 | Total height of mission package |
| lmp | 17.8 | Distance from diaphragm to end of mission package |
| lfc | 4.75 | Depth of booster coupling section |
| hfc | 40.5 | Total height of booster including coupling section |
| RB | 27 | Height of deployment bag, includes the flap length |
| DM | 114 (9.5 ft) | Diameter of the main parachute |
| RM | 80.6 | Height of the main parachute (found using 0.707 aspect ratio): RM = DM*0.707 |
| SM | 126 | Length of shroud lines on the main parachute |
| DD | 34.4 (2.87 ft) | Diameter of the drogue parachute |
| RD | 24.3 | Height of the drogue parachute (found using 0.707 aspect ratio): RD = DD*0.707 |
| SD | 48 | Length of shroud lines on the drogue parachute |
Using these variables, a set of constraints was generated to ensure successful Recovery system deployment. The constraints are summarized in the table below:
| Constraint | Description |
|---|---|
| WA,H > WA,E,F,G + RD + SD + lfc | When lines between the mission package and fin can are fully extended, the drogue parachute must be within the airstream. |
| WA,E,F = lmp | Placing the junction between the tender descender (TD) and the main chute load paths at the edge of the mission package reduces the likelihood that the main parachute will enter the airstream prior to the designated release altitude of 2,000 ft. |
| WC,D > RB | The line connecting the top of the main chute canopy to the inside of the deployment bag must be long enough such that the main parachute is not stuck inside the deployment bag upon full line extension. |
| WA,B > lmp + 6hmp | "[T]he parachute should be ejected to a distance equivalent to more than four times–and preferably six times–the forebody diameter" (Knacke, 5.2.2) Although either the fin can or the mission package could be interpreted as the forebody due to potentially similar drag forces, we select the mission package for the Pathfinder vehicle due to its greater height. |
| WA,E,F,G - lmp > 9hmp - \sqrt{S_{D}^2 - \frac{D_{D}}{2}^2} | This constraint reduces the impact of forebody wake on the drogue parachute during drogue descent. The same definition of forebody is chosen as in the previous constraint for the same reason. We subtract the vertical height of the shroud lines to reach a total canopy distance of ~9 forebody diameters. Unknown User (jcoray@mit.edu) add source? |
| WA,H > lmp + hmp + lfc | Assuming full line extension, the mission package and booster section should not hit one another during descent. This neglects the effect of drag on these sections and their respective masses. |
| WA,E,F < WA,B + SM + RM + WC,D,F | Prior to firing the tender descender, the load should go through the shorter (TD) path. |
Webbing lengths were calculated using the constraints with the addition of reasonable factors of safety.
| Webbing Length Variable | Length (in) | Factor of Safety | Reasoning |
|---|---|---|---|
| WA,H | 295.4 | 4 | The absolute minimum factor of safety required for the constraints is a little above 3.6 so that was rounded up to 4. |
| WA,E,F,G | 189.8 | 1 | The 5DD in the constraint equation was determined arbitrarily so the factor of safety is redundant. |
| WA,B | 473.8 | 1 | The 4DM in the constraint equation was determined arbitrarily so the factor of safety is redundant. |
| WA,E,F | 17.8 | 1 | A factor of safety is not desirable here because the exact length is desired. |
| WC,D | 270 | 10 | In subsonic flow, upstream disturbances could disrupt the airflow using minimal length on this webbing. |
| WD,F | 12 | 1 | There's no clear constraint on this length, so an arbitrary small length was chosen. |
Resources
T.W. Knacke, Parachute Recovery Systems: Design Manual