mirror of
https://github.com/nasa/trick.git
synced 2025-02-19 08:46:32 +00:00
77 lines
2.2 KiB
Markdown
77 lines
2.2 KiB
Markdown
### Background
|
|
On October 14, 2012, 43-year-old Austrian daredevel Felix Baumgartner broke the
|
|
world record for the highest-ever skydive after jumping from a balloon at an
|
|
altitude of 127,852 feet. He reached a top speed of 843.6 mph, spent approximately
|
|
4 minutes 19 seconds in free-fall, and landed safely approximately 11 minutes
|
|
after jumping.
|
|
|
|
### Simulation
|
|
The simulation only considers the forces of gravity and drag, and only motion in
|
|
the vertical. The acceleration of the skydiver is determined by summing the
|
|
forces of gravity and drag acting on him and then dividing by his mass. His
|
|
velocity is determined by integrating his acceleration over time, and his
|
|
altitude by integrating his velocity over time.
|
|
|
|
Desired outputs are:
|
|
* Plot of altitude vs. time.
|
|
* Plot of velocity vs. time.
|
|
* Time of touchdown.
|
|
|
|
##### Gravity
|
|
|
|
|
|
Where:
|
|
|
|
* m = mass of the skydiver.
|
|
* g = acceleration of gravity.
|
|
|
|
##### Drag
|
|
|
|
|
|
Where:
|
|
|
|
* C<sub>d</sub> = Coefficient of drag
|
|
* ρ = air density
|
|
* v = instantaneous velocity
|
|
* A = cross-sectional area of the jumper
|
|
|
|
#### Air Density and Gravity Data
|
|
The table at:
|
|
<http://www.engineeringtoolbox.com/standard-atmosphere-d_604.html>
|
|
provides both gravity (g) and air density (ρ) at various altitudes.
|
|
From these data we interpolate, to approximate the air density and gravity at
|
|
specific altitudes.
|
|
|
|
#### Parachute Deployment
|
|
Parachute deployment is modeled, using a Trick event (in input.py) that simply
|
|
increases the skydiver's
|
|
|
|
1. cross-sectional area (A) and
|
|
2. coefficient of drag (C<sub>d</sub>).
|
|
|
|
at the specified time.
|
|
|
|
### Felix Baumgartner Jump Scenario
|
|
|
|
* dyn.groundAltitude = 1000
|
|
* dyn.parachutist.altitude = 38969.6 meters
|
|
* dyn.parachutist.velocity = 0.0
|
|
* dyn.parachutist.area = 0.75
|
|
* dyn.parachutist.Cd = 0.75
|
|
* dyn.parachutist.mass = 82.0
|
|
|
|
At 4 minutes and 19 seconds, pop the chute:
|
|
|
|
* dyn.parachutist.Cd = 1.3
|
|
* dyn.parachutist.area = 30.0
|
|
|
|
|
|
#### Results
|
|
|
|
##### Altitude vs Time
|
|
|
|
|
|
##### Velocity vs Time
|
|
|
|
|