trick/trick_sims/SIM_parachute
jmpenn ee2f824550
Disable unneeded SimObjects from default_trick_sys.sm in Trick exampl… (#1719)
* Disable unneeded SimObjects from default_trick_sys.sm in Trick example sims.

* Take out unit test disable. Add some S_defines I forgot.
2024-05-23 10:12:27 -05:00
..
DP_Product Wrote a README file that clearly describes the simulation. Also updated the simulation code to be clear and consistent with the documentation. Fixes #36 2015-03-27 15:56:15 -05:00
images Add picture to SIM_parachutist README 2015-08-04 17:13:49 -05:00
models/parachute move parachute models to SIM_parachute and fix up S_overrides.mk 2016-02-22 12:41:20 -06:00
Modified_data Wrote a README file that clearly describes the simulation. Also updated the simulation code to be clear and consistent with the documentation. Fixes #36 2015-03-27 15:56:15 -05:00
RUN_Baumgartner_jump Python3 exec open (#907) 2019-11-14 13:35:57 -06:00
README.md Fix heading in SIM_parachute README.md 2017-05-11 17:27:35 -05:00
S_define Disable unneeded SimObjects from default_trick_sys.sm in Trick exampl… (#1719) 2024-05-23 10:12:27 -05:00
S_overrides.mk move parachute models to SIM_parachute and fix up S_overrides.mk 2016-02-22 12:41:20 -06:00

SIM_parachute

Picture of Parachutist

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

Fgrav=m*g

Where:

  • m = mass of the skydiver.
  • g = acceleration of gravity.
Drag

Fdrag=0.5Cdragrhov^2A

Where:

  • Cd = 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 (Cd).

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

Plot of Altitude vs Time

Velocity vs Time

Plot of Velocity vs Time