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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.

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Mathinline
bodyF_{D, dro} = \frac{1}{2}*1.225 \frac{kg}{m^3}*0.662 m^2 *V^2 = 14.09 kg * 9.81 \frac{m}{s^2}

V 18.46 m/s = 61 ft/s

This is a little lower than the suggested range, but not unreasonably so. Plus, as I mention in the footnote below, this is a pretty complex system and difficult to perfectly predict at all times. 

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 (Adapted from PDR Fall 2017)

We will be using the Therion main parachute. Using test flight data from Project Raziel under this parachute, we determined the effective coefficient of drag of the rocket (which accounts for the drag on the body of the rocket, too.) 2. In the flight test we saw an approximate landing speed of 6.5 m/s, corresponding to a CD,eff,main of:3

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

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

2 Because Raziel separated in two locations rather than just one, this number may vary from what will be seen on Hermes, which has a single separation point and a different height. We're using it here as an approximation for right now. One idea is to use a pitot tube to test for wind speed and rig the parachute up on a windy day with a fish scale or load cell. If a convenient opportunity during spring semester presents itself for this, we can do that. Or we can just use new flight test data from when we fly it (assuming it works...)

3 Within these calculations, reference area was chosen as the largest cross section of the parachute, which is approximated as having a 9.5 ft diameter (1.4478 m radius). We reduced this area by 4% to account for the approximate area lost to the spill hole. Mass was calculated using the after-burnout mass taken from the OpenRocket flight test model.

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

Drogue to Mission Package

dd

Resources

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

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