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Descent Characteristics

Reynolds Number Regime

Relative Descent Dynamics

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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.

Descent

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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:

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

Mathinline
bodyF_{D, dro} = \frac{1}{2}*1.225 \frac{kg}{m^3}*0.662 m^2 *V^2 = 40.75 kg * 9.81 \frac{m}{s^2}

V ≈ 31.4 m/s = 103 ft/s

This velocity is well within an acceptable range per Requirement 3.1.1 of the DTEG.

One important caveat to this analysis is that this assumes the drogue will be pulling the entire rocket. As we see above, the CdS of the drogue and that of the booster section may be comparable, depending on the falling configuration. If this occurs, there will not be tension on the booster webbing, and the drogue therefore will not be "carrying its weight." Hermes' descent under drogue will occur faster. 1 To take this into account, we can bound the velocity neglecting the weight of the booster section. According to the mass budget, the propulsion system plus fin can weigh 

 

1 Admittedly, there is some super weird coupling in this system. If the drogue and mission package start to travel faster downwards than the booster section, eventually the webbing will be fully extended between the mission package and the booster and it will start to pull it down. Then maybe you'd enter some sort of periodic pattern of the webbing jerking the booster down and it falling behind again? I am not sure but I'm going to neglect this from my analysis.

Main

Relative Descent Rates

Drogue to Mission Package

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, there will

Resources

[1] DRAG OF CIRCULAR CYLINDERS FOR A WIDE RANGE OF REYNOLDS NUMBERS AND MACH NUMBERS

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