{
 "cells": [
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# **Coefficient of a Moving Baseball**\n",
    "\n",
    "[Twitter](https://x.com/dec1costello) | [GitHub](https://github.com/dec1costello) | [Kaggle](https://www.kaggle.com/dec1costello) | [LinkedIn](https://www.linkedin.com/in/declan-costello-7423aa137/)"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Overview**\n",
    "\n",
    "In this analysis, I used Python to recreate [\"Simplified Models for the Drag\n",
    "Coefficient of a Pitched Baseball\" by David Kagan & Alan M. Nathan](http://baseball.physics.illinois.edu/DragTPTMay2014.pdf) measuring the drag coefficient. I hope to provide value to the baseball community by combining my interests of weather and baseball."
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Variables**\n",
    "Descriptions taken from the Kagan and Nathan's Paper. The following is a list of the important variable to understand for this notebook.\n",
    "\n",
    "*   **Altitude** - Altitude is a distance measurement, usually in the vertical or \"up\" direction, between a reference datum and sea level. \n",
    "\n",
    "*   **Average Humidity** - Average Humidity is a measure of the amount of water vapor in the air throughout a day. Relative humidity is the ratio of the actual vapor pressure of water vapor to the saturation vapor pressure of water. In other words, it's how much water is in the air divided by the most water that could possibly be there. For example, if it's 97% relative humidity outside, that means the air only needs 3% more water vapor to achieve complete saturation of 100%. \n",
    "\n",
    "*   **Air Pressure** - Air pressure is the force exerted by air on any surface it touches. It's also known as atmospheric pressure or barometric pressure. Air pressure is caused by the weight of air molecules pressing down on the Earth. The pressure changes as you move upward from sea level into the atmosphere. The highest pressure is at sea level where the density of the air molecules is the greatest. \n",
    "\n",
    "*   **Air Density** - Air density is the mass of air per unit volume, or how much a certain volume of air weighs. It's denoted by the Greek letter rho, ρ. Air density depends on the temperature, pressure, and humidity of the air. Air density decreases with increasing altitude because there's less air pushing down from above and gravity is weaker farther from Earth's center.\n",
    "\n",
    "*   **Drag Length** - Drag is a force exerted by a fluid stream on an object moving through it or on any obstacle in its path. Drag can also be called fluid resistance. \n",
    "\n",
    "*   **Drag Coefficient** - The drag coefficient, or CD, is a dimensionless quantity that quantifies the drag or resistance of an object in a fluid environment, such as air or water. It's a value that demonstrates how streamlined an object is and how much it is affected by drag. The lower the value, the lower the effects of drag will be on that object. \n"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# **Installation**\n",
    "\n",
    "The following installs the necessary packages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import seaborn as sns"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# **Drag Length Equation (6)**\n",
    "\n",
    "Given Weight of a Baseball, Circumference of a Baseball, and Air Density\n",
    "\n",
    "\n",
    "\n",
    "\n",
    "$$\\delta = \\frac{8\\  \\pi\\ W}\n",
    "{P_{e}\\ c^2} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Drag_Length_Equation(Weight_lbs, Circumference, Air_Density_lbsft3):\n",
    "    return (8*np.pi*Weight_lbs)/(Air_Density_lbsft3*np.square(Circumference))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(186.39834483802875)"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Weight_lbs         = 0.32   # Baseball Weight in lbs\n",
    "Circumference      = 0.76   # Baseball Circumference in feet\n",
    "Air_Density_lbsft3 = 0.0747 # lb/ft^3 Air Density\n",
    "\n",
    "s = Drag_Length_Equation(Weight_lbs, Circumference, Air_Density_lbsft3)\n",
    "s # Drag_Length"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# **Drag Coefficient Equation (3)**\n",
    "\n",
    "Given Drag Length, ay, and v0y\n",
    "\n",
    "$$ C_{d} =  \\delta \\frac{a_{y}}\n",
    "{v0_{y}^2} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Drag_CoeF(s, v0y, ay):\n",
    "    return (s * (ay/np.square(v0y)))"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Initial Position**\n",
    "\n",
    "$$ r_{0} =  (-1.566ft)\\hat{x} + (50.000ft)\\hat{y} + (5.780ft)\\hat{z} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "r0x =  -1.566\n",
    "r0y =  50.000\n",
    "r0z =   5.780"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Initial velocity**\n",
    "\n",
    "$$ v_{0} =  (2.631 \\frac{ft}{s})\\hat{x} + (-122.644\\frac{ft}{s})\\hat{y} + (-3.435\\frac{ft}{s})\\hat{z} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "v0x =    2.631\n",
    "v0y = -122.644\n",
    "v0z =   -3.435"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Acceleration Vector**\n",
    "\n",
    "$$ a =  (-6.387 \\frac{ft}{s^2})\\hat{x} + (25.067\\frac{ft}{s^2})\\hat{y} + (-21.810\\frac{ft}{s^2})\\hat{z} $$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "ax =  -6.387\n",
    "ay =  25.067\n",
    "az = -21.810"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "np.float64(0.3106360103464578)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Weight_lbs         = 0.32   # Baseball Weight in lbs\n",
    "Circumference      = 0.76   # Baseball Circumference in feet\n",
    "Air_Density_lbsft3 = 0.0747 # Air Density in lb/ft^3 \n",
    "\n",
    "s = Drag_Length_Equation(Weight_lbs, Circumference, Air_Density_lbsft3)\n",
    "\n",
    "cd = Drag_CoeF(s, v0y, ay)\n",
    "cd # Drag Coefficient"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Analysis**\n",
    "\n",
    "What happen to cd as Circumference of a baseball, Weight of a baseball and Air_Density_lbsft3 fluctuate?"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Fluctuating Circumference**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Circumference', ylabel='cd'>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Weight_lbs             = 0.32                                          # Baseball Weight in lbs\n",
    "list_of_circumferences = [round(x * 0.01, 2) for x in range(50,100)]   # Baseball Circumference in feet\n",
    "Air_Density_lbsft3     = 0.0747                                        # Air Density in lb/ft^3 \n",
    "\n",
    "new_s_list = []\n",
    "\n",
    "for i in list_of_circumferences:\n",
    "    new_s_list.append(Drag_Length_Equation(Weight_lbs, i, Air_Density_lbsft3))\n",
    "\n",
    "new_cd_list = []\n",
    "\n",
    "for s in new_s_list:\n",
    "    new_cd_list.append(Drag_CoeF(s, v0y, ay))\n",
    "\n",
    "fluct_circumferences = pd.DataFrame(np.column_stack([list_of_circumferences, new_s_list, new_cd_list]),\n",
    "                                    columns = ['Circumference', 'Drag_Length', 'cd'])\n",
    "fluct_circumferences['Weight_lbs'] = 0.32\n",
    "fluct_circumferences['Air_Density_lbsft3'] = 0.0747\n",
    "\n",
    "sns.lineplot(data = fluct_circumferences, x='Circumference', y='cd')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Fluctuating Weight**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Weight', ylabel='cd'>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Weight_lbs_list        = [round(x * 0.001, 3) for x in range(310,330)] # Baseball Weight in lbs\n",
    "Circumference          = 0.76                                      # Baseball Circumference in feet\n",
    "Air_Density_lbsft3     = 0.0747                                    # Air Density in lb/ft^3 \n",
    "\n",
    "new_s_list = []\n",
    "\n",
    "for i in Weight_lbs_list:\n",
    "    new_s_list.append(Drag_Length_Equation(i, Circumference, Air_Density_lbsft3))\n",
    "\n",
    "new_cd_list = []\n",
    "\n",
    "for s in new_s_list:\n",
    "    new_cd_list.append(Drag_CoeF(s, v0y, ay))\n",
    "\n",
    "fluct_circumferences = pd.DataFrame(np.column_stack([Weight_lbs_list, new_s_list, new_cd_list]),\n",
    "                                    columns = ['Weight', 'Drag_Length', 'cd'])\n",
    "fluct_circumferences['Circumference'] = 0.76\n",
    "fluct_circumferences['Air_Density_lbsft3'] = 0.0747\n",
    "\n",
    "sns.lineplot(data = fluct_circumferences, x='Weight', y='cd')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Fluctuating Air Density**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: xlabel='Air Density', ylabel='cd'>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "Weight_lbs              = 0.32                                        # Baseball Weight in lbs\n",
    "Circumference           = 0.76                                        # Baseball Circumference in feet\n",
    "Air_Density_lbsft3_list = [round(x * 0.0001, 4) for x in range(700,800)] # Air Density in lb/ft^3 \n",
    "\n",
    "new_s_list = []\n",
    "\n",
    "for i in Air_Density_lbsft3_list:\n",
    "    new_s_list.append(Drag_Length_Equation(Weight_lbs, Circumference, i))\n",
    "\n",
    "new_cd_list = []\n",
    "\n",
    "for s in new_s_list:\n",
    "    new_cd_list.append(Drag_CoeF(s, v0y, ay))\n",
    "\n",
    "fluct_circumferences = pd.DataFrame(np.column_stack([Air_Density_lbsft3_list, new_s_list, new_cd_list]),\n",
    "                                    columns = ['Air Density', 'Drag_Length', 'cd'])\n",
    "fluct_circumferences['Weight_lbs'] = 0.32\n",
    "fluct_circumferences['Circumference'] = 0.76\n",
    "\n",
    "sns.lineplot(data = fluct_circumferences, x='Air Density', y='cd')"
   ]
  },
  {
   "attachments": {},
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## **Future Analysis**\n",
    "\n",
    "In the future, I plan to use temperature, average humidity, and altitude to [calucalte a more accurate air density](https://www.engineersedge.com/calculators/air-density.htm) using [live weather data](https://barometricpressure.app/denver). Will be on the lookout to see if [seam height data](http://baseball.physics.illinois.edu/HRReport2019.pdf) is ever available as well."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "env",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.2"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}