For the Hermes Pathfinder vehicle, the relevant dimensions are:
| Variable | Length (in inches) | Description |
|---|---|---|
| hmp | 57.4 | Height of the mission package from nose cone tip to the end of the airframe |
| lmp | 14.5 | Depth into the cup |
| lfc | 7.6 | Depth of booster coupling section |
| hfc | 86.23 | Total height of booster including coupling section. |
| RB | 7.5 | Height of the main deployment bag, not including flaps (should make sure there is enough margin on relevant constraint(s)). |
| 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 (may change when we update the main) |
| RD | 31 | Height of the drogue parachute (measured 2/15/2018) |
| SD | 100 | Vertical length (accounts for confluence angle) of the drogue shroud lines. Taken from the DGB parameters spreadsheet. |
| FD | Forebody diameter used for drogue parachute shock cord calculation. Please see the extended note on calculation below. | |
| DD | 38 | Disk diameter of the drogue parachute. Taken from the DGB Parameters spreadsheet. |
Constraints and Calculations v2.0
These calculations and constraints are only a preliminary estimation, with the following assumptions:
- Neglect drogue deployment bag as of right now, we will take this into account on calculations further down the line.
- Vehicle dimensions are subject to change
- Main parachute shroud line length are subject to change–I also don't think this value accounts for the confluence angle, so it will actually be a little lower than advertised.
| Constraint | Description |
|---|---|
| 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,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,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,G - lmp > 8.5*FD- SD | This constraint reduces the impact of forebody wake on the drogue parachute during drogue descent. Please see the extended note below on the calculation of forebody diameter. We subtract the vertical height of the shroud lines to reach a total canopy distance of ~9 forebody diameters.1 |
Note on Drogue Forebody Diameter
As noted in Hermes Descent Dynamics, it is difficult to predict the falling orientation of the mission package and booster during drogue descent. For this reason, we evaluate the worst case possibility (supersonic descent is already somewhat of a worst case scenario, so we have multiple methods of redundancy): the booster falls horizontally below the drogue parachute. In this scenario, the actual forebody area (FA) is calculated by multiplying the drogue diameter by the booster diameter, yielding approximately 227 in3. The effective forebody diameter is calculated below via the equivalent circle technique presented in Knacke section 5-23 [2]:
F_{D} = \sqrt{\frac{4F_{A}}{\pi}}
where FA = 227 in3
FD = 17 in
Resources
[1] Clark & Tanner, "A Historical Summary of the Design, Development, and Analysis of the Disk-Gap-Band Parachute"
[2] T.W. Knacke, Parachute Recovery Systems: Design Manual