cfmdarts

cfmdarts is a Python library that simulates the projectile motion of darts.

Table of Contents

1. Introduction
2. Installation
3. Tutorials
4. How To Guides
5. Explanation
6. License

Introduction

This project has an extremely trivial goal. Simply input 3 values relating to the throw of a dart

• tilt angle
• swivel angle (both in degrees)
• initial velocity (in metres per second).

Then output the score of which is obtained. This project involves many areas of mathematics to solve. Primarily Mechanics and Geometry.

Installation

Use the package manager pip to install cfmdarts.

pip install cfmdarts

NOTE: It is recommended to have a Python version which is greater that 3.6 to be installed.

Tutorial

In order to use cfmdarts is really simple. To use in your project, you type

import cfmdarts

How To Guides

These next guides are simple pieces of code to get you started using cfmdarts.

Creating a new Projectile object.

import cfmdarts

#Creating a new Projectile object called Object1
#with tilt_angle=2, swivel_angle=1.5 and initial_velocity=21

Object1 = Projectile(2,1.5,21)

Outputting a new Projectile objects range, height and shift values.

import cfmdarts

#Creating a new Projectile object called Object1
#with tilt_angle=2, swivel_angle=1.5 and initial_velocity=21

Object1 = Projectile(2,1.5,21)

##This outputs the follow
print(Object1.range())
print(Object1.height())
print(Object1.shift())

Output:

2.370812418203357
0.02019783552359672
0.06206063411897303

Creating a coordinates object to calculate and output the cartesian and polar coordinates

import cfmdarts

#Creating a coordinates object called coord1
#with tilt_angle=2, swivel_angle=1.5 and initial_velocity=21

Coord1 = coordinates(2,1.5,21)

## These two statements below print out the
## cartesian and polar coordinates.
print(Coord1.cartesian_coordinates())
print(Coord1.polar_coordinates())

Output:

[0.06206063411897303, 0.02019783552359672]
[0.06526465250874554, 18.027647207949578]

Creating a data simulation using the dart_simulation that returns a final score.

import cfmdarts

#Creating a variable called 'simulation1'.
simulation1 = dart_simulation(2, 1.5, 21)

##Outputs the final score from simulation1
print(simulation1)

Output:

13

Example of a dart simulation that has an incorrect input case with tilt_angle being an invalid input

import cfmdarts

#Creating a variable called 'simulation1'.
simulation1 = dart_simulation(-91, 2, 29)

##Outputs the final score from simulation1
print(simulation1)

Output:

null shot, please ensure the tilt and swivel angles are both between -90 and 90, and that the velocity is positive

Explanation

Phase I - Projectile In 3D

We must first consider the 2-dimensional plane $(x,y)$ in which our dart travels through. Doing, we can model the trajectory of the dart using projectile motion in order to obtain the range, height, and shift of the dart relative to the bullseye. We can say that air resistance of the dart is negligible.

Phase II - Geometry Of Dartboard

Determining the score is precisely the same as determining the position at which the dart landed on the dartboard. We will obtain (via the specified throw) 2 distances relative to the distance from the bullseye. Using these 2 values as Cartesian coordinates, we can translate the position into polar form $r, \theta $ via similar methods to determining the modulus and argument of a complex number. See the ``coordinates" class in how this was achieved.

License

MIT