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Assuming that the mission package is falling nose down (it is planned to be stabilized that way via Hermes Payload System), it will have a coefficient of drag of approximately 0.2, given a fineness ratio of approximately 9 [2].Then, taking the same reference area as the axial configuration for the booster, we find a CdS of 0.00364 m2.

Descent Rates

Drogue

Given the previously mentioned CdS of 0.662 m2 at Mach 0.137 (which corresponds to approximately 150 ft/s at sea level), an air density of 1.225 kg/m3 at sea level, and a dry rocket mass of 89.83 lbs = 40.75kg (taken from the Hermes Mass Budget on 1/31/2018–this includes the drogue parachute itself, but we'll ignore this for now), we can calculate the approximate descent of the rocket under drogue when it reaches main deployment altitude (roughly sea level–I'm neglecting the 2000ft AGL and the altitude of Spaceport):

Mathinline
bodyF_{D, dro} = \frac{1}{2} \rho C_{D} S V^2 = m_{dry}*g

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Because the CdS of the drogue is 2 orders of magnitude greater than that on the mission package, we expect there to be a good deal of tension in the line connecting the drogue and the main. At sea level, we can calculate approximately how many pounds of force will be available to extract the deployment bag from the cup (assuming it hasn't fallen out prematurely) and then the main from the deployment bag. Velocity is chosen as the lower bound for steady state velocity

Mathinline
bodyF_{extraction} = F_{D,dro} - F_{D, mp} = \frac{1}{2}*1.225 \frac{kg}{m^3}*(18.46 \frac{m}{s})^2*[CdS_{dro}-CdS_{main}]

Mathinline
bodyF_{extr.} = 208.72\frac{kg}{ms^2}*[0.662 m^2-0.00364 m^2]

Fextr. ≈ 137.4 N = 31 lbs

Given the deployment bag from cup extraction force of roughly 4.52 lbs found during the December 2, 2017 Ground Test (this number may change due to a new deployment bag and different packing procedures) as well as the 2-3 pound parachute from deployment bag extraction force found during the Hermes Parachute Packing investigation, we expect that we will have more than sufficient extraction force.

Drogue to Booster

As previously mentioned, the variability in falling orientation makes it difficult to predict the relative ratio of CdS between the drogue and the booster. Given our current estimations, the drogue could see anywhere between 1.25x and 45x the amount of drag on the booster (if they are going the same velocity).

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