Python Programming Project: Skydiver Descent Trajectory Analysis

This project simulates the descent trajectory of a recreational skydiver using Python code within the Spyder environment. The assignment investigates how various parameters affect the skydiver's trajectory, addressing specific research questions. The methodology involves creating and implementing Python code based on established simulation techniques and mathematical models like the Langevin equation. The project includes free body diagrams illustrating the forces acting on the skydiver, analysis of projectile motion, and the generation of trajectory simulations. The results, presented through screenshots, demonstrate the skydiver's path over time and provide insights into the impact of factors like gravity and drag. The discussion section analyzes the results and compares them to existing research. The project aims to provide a comprehensive understanding of skydiver trajectory simulation using Python.

Python Programming
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Table of Contents
1. Introduction.................................................................................................................................2
2. Methods........................................................................................................................................2
3. Results..........................................................................................................................................2
4. Discussion.....................................................................................................................................6
5. Conclusion...................................................................................................................................6
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1. Introduction
The study is undertaken to simulate the descent trajectory of a recreational skydiver. Python
code needs to be created for the simulation of skydiver’s jump, based on some given conditions.
The investigation will be made on how the trajectory is affected by various parameters. The
research question are provided with solution and screenshots generated. The purpose of the research
is to show how much the trajectry of a skydriver is getting affected when numerous elements are
provided.
2. Methods
The code is done in Spyder. The generated outcome in the code of python (Hetland, 2010). the
study is done and technical specifications include Spyder. the standard methods for the simulation
of the descent trajectory of a recreational skydiver is used (Lutz, n.d.). The taks are done
accordingly. all the techniques for the simulation of the trajectory is used in python code. the
needed modifications are made in the standard techniques. 5 related samples were taken and used
for the simulation (Hammond & Robinson, 2000).
Simulation
Many areas of the simulation domain are different if just a single slice of the simulation domain
approximately a small particle trajectory. The different regions also behave different with respect to
the trajectory calculation it is used to calculate the trajectory at once and it copy to the other
different regions. This type of method will be interpreting as calculating one Dimensional
simulation and distribution them over a greater Dimensional simulation domain as possible
("Skydiving", 2017).
Trajectory-Simulation Model
The overall velocity of skydiver in a horizontal and vertical plane was basically divided into
height dependent, horizontally homogeneous defines the horizontal velocity and also fluctuating
with turbulent velocities ("skydiving | sport", 2017). Considering the skydiver position and the
velocity association called as Makov process, the following equation are the langevin model for a
skydiver and velocity. Equation (1) as follows.
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The probability Density of skydiver is p(x, z, U, w, t) that the fluid element “occupies” a
given location in a phase space. It go forward to deterministically, and for the specific model (1)
selected here is governed through the Fokker Planck calculation:
Equation (2)
The following are the solution of the equation 2.
Equation (3)
Equation (4)
The following equation is the sample solution of the equation 3 which should met the condition of
the equation 4.
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3. Results
The simulation for the descent trajectory of a skydiver is generated using Spyder. The
Python code is attached in the implementation part. The simulation for the skydiver's jump is based
on the provided conditions. The code generated in python.
Task 3
 The free body diagrams showing the forces acting on the skydiver during the jump (McNeil,
2010). It consist of a simplified form of the body
I. The forces and moments are showed by the free body diagram.
II. The forces shown as direct arrows pointing in the way and they reflects on the body
III. The moments shown as curved arrows pointing in the way and they reflects on the
body.
IV. This diagram consists of a coordinate system
The more number of moments and forces seen in a free body diagram and it contains on the
particular problem and assumptions of convention made. The assumptions are friction and avoiding
air resistance and rigid bodies are assumed.
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Where:
g - Acceleration due to gravity, which is 9.8 m/s2
m - Mass
D - Drag force which acts upwards
W – Gravity that forces downwards
v - Speed
vt = constant value
Task 4
a) During free-fall.
The force of gravity which pulls the skydiver down is:
At the free-fall, a diver executes diverse varieties of acrobatic maneuvers such as
 Spinning
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 Moving forward
 Moving backward
The diver does this just by altering the form of his/her body to move along with the
direction of the wind. So that the skydiver can effectively changes the way of the drag force
acting on his body, much the same way airplane wings can be oriented to produce a desired
motion for the plane.
b) With the parachute deployed.
Task 5
Python function that computes the trajectory of the skydiver after leaving the aircraft until landing
on the ground.
Start time, s
t_0 = 0
End time, s
t_end = 10
Number of time steps
N = 1000
Implementation
Result screenshots
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The below screenshots provides results for the tasks provided. The graph explains the
trajectory of the sky driver (Hammond & Robinson, 2000). The trajectory or flight path is shown
below in the screenshot. It is the actual path which moves object and is followed through space as a
function with respect to time. The skydiver performs a projectile motion. The path is shown clearly
with the different view colors.
The trajectory can also be explained in a mathematical way. The trajectory range starts from 0 and
ends up to 80.the position of the skydiver differs according to time. The height differs from each
trajectory motion of the skydiver. The geometrical path trajectory of the skydiver is created using
python code which runs in Spyder.
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The below screenshot shows how the psition of the skydiver gets changes based on time
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The below screenshot shows the trajectory motion of the skydiverfrom 0 to the other points like
20,40,60 and 80.
The results generated and the answers are found to the research question (Alchin, 2010).
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4. Discussion
the results imply that the trajectory is generated by coding in python and the platform used is
spyder. The generated outcomes perfectly fits the requiremnts given (Hammond & Robinson,
2000).
other reserachers have found that the trajectory and the state of motion is computed but the
skydriver doesnot stops at the right time before landing. The proposed method is justified that it
generates the trajectory range (Alchin, 2010). The perspectives for the future research is to create
the trajectory which stops before landing.
5. Conclusion
The forces on the skydiver varies throughout the motion of the trajectory. Additional
information for computing the forces are required at any instant in time. All the results are
integrated and explained in clear way. The validity of the results are justified. The investigation is
made on how the trajectory is affected by various parameters. The research question is provided
with solution and screenshots generated. Description for the questions is provided where ever
neccesary.
References
Alchin, M. (2010). Pro Python. [New York]: Apress.
Hammond, M., & Robinson, A. (2000). Python programming on Win32. Beijing: O'Reilly.
Hetland, M. (2010). Python Algorithms. [New York, N.Y.]: Apress.
Lutz, M. Python pocket reference.
Skydiving. (2017). Physicsclassroom.com. Retrieved 6 September 2017, from
http://www.physicsclassroom.com/mmedia/newtlaws/sd.cfm
skydiving | sport. (2017). Encyclopedia Britannica. Retrieved 6 September 2017, from
https://www.britannica.com/topic/skydiving
McNeil, J. (2010). Python text processing beginner's guide. Birmingham, U.K.: Packt Pub.
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