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81 lines
2.2 KiB
Markdown
81 lines
2.2 KiB
Markdown
# SIM_parachute
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### Background
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On October 14, 2012, 43-year-old Austrian daredevel Felix Baumgartner broke the
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world record for the highest-ever skydive after jumping from a balloon at an
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altitude of 127,852 feet. He reached a top speed of 843.6 mph, spent approximately
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4 minutes 19 seconds in free-fall, and landed safely approximately 11 minutes
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after jumping.
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### Simulation
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The simulation only considers the forces of gravity and drag, and only motion in
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the vertical. The acceleration of the skydiver is determined by summing the
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forces of gravity and drag acting on him and then dividing by his mass. His
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velocity is determined by integrating his acceleration over time, and his
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altitude by integrating his velocity over time.
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Desired outputs are:
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* Plot of altitude vs. time.
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* Plot of velocity vs. time.
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* Time of touchdown.
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##### Gravity
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Where:
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* m = mass of the skydiver.
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* g = acceleration of gravity.
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##### Drag
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Where:
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* C<sub>d</sub> = Coefficient of drag
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* ρ = air density
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* v = instantaneous velocity
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* A = cross-sectional area of the jumper
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#### Air Density and Gravity Data
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The table at:
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<http://www.engineeringtoolbox.com/standard-atmosphere-d_604.html>
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provides both gravity (g) and air density (ρ) at various altitudes.
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From these data we interpolate, to approximate the air density and gravity at
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specific altitudes.
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#### Parachute Deployment
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Parachute deployment is modeled, using a Trick event (in input.py) that simply
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increases the skydiver's
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1. cross-sectional area (A) and
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2. coefficient of drag (C<sub>d</sub>).
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at the specified time.
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### Felix Baumgartner Jump Scenario
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* dyn.groundAltitude = 1000
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* dyn.parachutist.altitude = 38969.6 meters
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* dyn.parachutist.velocity = 0.0
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* dyn.parachutist.area = 0.75
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* dyn.parachutist.Cd = 0.75
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* dyn.parachutist.mass = 82.0
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At 4 minutes and 19 seconds, pop the chute:
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* dyn.parachutist.Cd = 1.3
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* dyn.parachutist.area = 30.0
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#### Results
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##### Altitude vs Time
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##### Velocity vs Time
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