{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"slideshow": {
"slide_type": "slide"
}
},
"source": [
"# Terminal Velocity\n",
"by [Paulo Marques](http://pmarques.eu), 2013/09/23\n",
"\n",
"---\n",
"\n",
"This notebook discusses the drag forces exerted on a body when traveling through air. \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"![](http://upload.wikimedia.org/wikipedia/en/8/89/Parachuters_in_hybrid_formation.jpg) "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"A falling body is subject to two forces: a downward force, $\\vec{F_g}$, due to gravity, and an upward force $\\vec{F_a}$, due to air resistance. Let's consider a body with mass $m$. Assuming an upward oriented YY axis, the following applies:\n",
"\n",
"$$ F_g = - g \\cdot m $$\n",
"\n",
"$$ F_a = - sgn(v) \\cdot {1 \\over 2} \\rho C_D A v^2 $$\n",
"\n",
"In these formulas, $m$ is the mass of the body, $\\rho$ is the density of air ($\\approx 1.2 Kg/m^3$), $g$ is the accelaration of gravity ($\\approx 9.8 m/s^2$), $v$ is the velocity of the body, $C_D$ is the drag coeficient of the body and $A$ is its cross-section area. $sgn(x)$ is the sign function that given a number returns +1 for positives and -1 for negatives. In the formula it makes the force always contrary to the movement of the body.\n",
"\n",
"Thus, the resulting force $\\vec{F}$ experienced by the body is:\n",
"\n",
"$$ F = - g \\cdot m - sgn(v) \\cdot {1 \\over 2} \\rho C_D A v^2 $$\n",
"\n",
"Given that force is directly related to accelaration, and accelaration to velocity:\n",
"\n",
"$$ v = \\frac{dy}{dt} $$\n",
"\n",
"$$ F = m \\cdot \\frac{dv}{dt} $$\n",
"\n",
"substituting, we get this differencial equation:\n",
"\n",
"$$ m \\cdot \\frac{dv}{dt} = - g \\cdot m - sgn(v) \\cdot {1 \\over 2} \\rho C_D A v^2 $$\n",
"\n",
"In fact, this can be expressed as a system of differential equations in the form ${\\bf f}' = {\\bf g}({\\bf f}, t)$:\n",
"\n",
"$$ \\begin{cases} \\frac{dy}{dt} = v \\\\\\\\ \\frac{dv}{dt} = -g - sgn(v) \\cdot {1 \\over 2} {\\rho \\over m} C_D A v^2 \\end{cases} $$\n",
"\n",
"---\n",
"\n",
"So, let's simulate this with Python!\n",
"\n",
"Let's start by importing some basic libraries:"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Populating the interactive namespace from numpy and matplotlib\n"
]
}
],
"source": [
"%pylab inline\n",
"from scipy.integrate import odeint\n",
"from math import sqrt, atan"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We now define the initial conditions and constants of the problem."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"# Constants \n",
"g = 9.8 # Accelaration of gravity\n",
"p = 1.2 # Density of air\n",
"\n",
"# Caracteristics of the problem\n",
"m = 0.100 # A 100 g ball\n",
"r = 0.10 # 10 cm radius\n",
"Cd = 0.5 # Drag coeficient for a small spherical object\n",
"y0 = 1000.0 # Initial height of the body (1000 m)\n",
"v0 = 10.0 # Initial velocity of the body (10 m/s^2, going up)\n",
"A = math.pi*r**2 # Cross-section area of the body"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As said, let's define a system of ordinary differential equations in its normal form ${\\bf f}' = {\\bf g}({\\bf f}, t)$. (In the code bellow we substitute $g()$ for $gm()$ so that it doesn't clash with the acceleration of gravity constant - $g$)."
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"sgn = lambda x: math.copysign(1, x) # Auxiliary function to calculate the sign of a number\n",
"\n",
"def gm(f, t):\n",
" (y, v) = f # Extract y and v (i.e., dy/dt) from the f mapping\n",
" \n",
" dy_dt = v # The differential equations\n",
" dv_dt = -1.0*g - sgn(v)*(1./2.)*(p/m)*Cd*A*v**2\n",
" \n",
" return [dy_dt, dv_dt] # Return the derivatives"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Let's define the conditions to numerically solve the problem, including a time vector:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"# Initial conditions (position and velocity)\n",
"start = [y0, v0]\n",
"\n",
"# Time vector (from 0 to 5 secs)\n",
"tf = 5.0 \n",
"t = linspace(0, tf, int(tf*100))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Now let's solve the equations numericaly and extract the corresponding $y(t)$ and $v(t)$:"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"f = odeint(gm, start, t)\n",
"\n",
"y = f[:, 0]\n",
"v = f[:, 1]"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Finally, we can plot the solution."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[]"
]
},
"execution_count": 6,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
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