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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Initial Value Problems - Project\n",
"\n",
"![Initial condition of firework with FBD and sum of momentum](../images/firework.png)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We are going to end this module with a __bang__ by looking at the flight path of a firework. Shown above is the initial condition of a firework, the _Freedom Flyer_ in (a), its final height where it detonates in (b), the applied forces in the __Free Body Diagram (FBD)__ in (c), and the __momentum__ of the firework $m\\mathbf{v}$ and the propellent $dm \\mathbf{u}$ in (d). \n",
"\n",
"The resulting equation of motion is that the acceleration is proportional to the speed of the propellent and the mass rate change $\\frac{dm}{dt}$ as such\n",
"\n",
"$$\\begin{equation}\n",
"m\\frac{dv}{dt} = u\\frac{dm}{dt} -mg - cv^2.~~~~~~~~(1)\n",
"\\end{equation}$$\n",
"\n",
"If we assume that the acceleration and the propellent momentum are much greater than the forces of gravity and drag, then the equation is simplified to the conservation of momentum. A further simplification is that the speed of the propellant is constant, $u=constant$, then the equation can be integrated to obtain an analytical rocket equation solution of [Tsiolkovsky](https://www.math24.net/rocket-motion/) [1,2], \n",
"\n",
"$$\\begin{equation}\n",
"m\\frac{dv}{dt} = u\\frac{dm}{dt}~~~~~(2.a)\n",
"\\end{equation}$$\n",
"\n",
"$$\\begin{equation}\n",
"\\frac{m_{f}}{m_{0}}=e^{-\\Delta v / u},~~~~~(2.b) \n",
"\\end{equation}$$\n",
"\n",
"where $m_f$ and $m_0$ are the mass at beginning and end of flight, $u$ is the speed of the propellent, and $\\Delta v=v_{final}-v_{initial}$ is the change in speed of the rocket from beginning to end of flight. Equation 2.b only relates the final velocity to the change in mass and propellent speed. When you integrate Eqn 2.a, you will have to compare the velocity as a function of mass loss. \n",
"\n",
"Your first objective is to integrate a numerical model that converges to equation (2.b), the Tsiolkovsky equation. Next, you will add drag and gravity and compare the results _between equations (1) and (2)_. Finally, you will vary the mass change rate to achieve the desired detonation height. \n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"1. Create a `simplerocket` function that returns the velocity, $v$, the acceleration, $a$, and the mass rate change $\\frac{dm}{dt}$, as a function of the $state = [position,~velocity,~mass] = [y,~v,~m]$ using eqn (2.a). Where the mass rate change $\\frac{dm}{dt}$ and the propellent speed $u$ are constants. The average velocity of gun powder propellent used in firework rockets is $u=250$ m/s [3,4]. \n",
"\n",
"$\\frac{d~state}{dt} = f(state)$\n",
"\n",
"$\\left[\\begin{array}{c} v\\\\a\\\\ \\frac{dm}{dt} \\end{array}\\right] = \\left[\\begin{array}{c} v\\\\ \\frac{u}{m}\\frac{dm}{dt} \\\\ \\frac{dm}{dt} \\end{array}\\right]$\n",
"\n",
"Use [two integration methods](../notebooks/03_Get_Oscillations.ipynb) to integrate the `simplerocket` function, one explicit method and one implicit method. Demonstrate that the solutions converge to equation (2.b) the Tsiolkovsky equation. Use an initial state of y=0 m, v=0 m/s, and m=0.25 kg. \n",
"\n",
"Integrate the function until mass, $m_{f}=0.05~kg$, using a mass rate change of $\\frac{dm}{dt}=0.05$ kg/s. \n",
"\n",
"_Hint: your integrated solution will have a current mass that you can use to create $\\frac{m_{f}}{m_{0}}$ by dividing state[2]/(initial mass), then your plot of velocity(t) vs mass(t)/mass(0) should match Tsiolkovsky's_"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"%matplotlib inline\n",
"plt.rcParams.update({'font.size': 22})\n",
"plt.rcParams['lines.linewidth'] = 3"
]
},
{
"cell_type": "code",
"execution_count": 320,
"metadata": {},
"outputs": [],
"source": [
"def simplerocket(state,dmdt=0.05, u=250):\n",
" '''Computes the right-hand side of the differential equation\n",
" for the acceleration of a rocket, without drag or gravity, in SI units. \n",
" Arguments\n",
" state : array of three dependent variables [y v m]^T\n",
" dmdt : mass rate change of rocket in kilograms/s default set to 0.05 kg/s\n",
" u : speed of propellent expelled (default is 250 m/s) \n",
" Returns\n",
" dstate: array of three derivatives [v dvdt dmdt]^T\n",
" '''\n",
" dstate = np.zeros(np.shape(state))\n",
" dstate[0] = state[1]\n",
" dstate[1] = u*dmdt/state[2]\n",
" dstate[2] = -dmdt\n",
" return dstate\n",
"\n",
"def euler_step(state, rhs, dt):\n",
" '''Update a state to the next time increment using Euler's method.\n",
" Arguments\n",
" state : array of dependent variables\n",
" rhs : function that computes the RHS of the DiffEq\n",
" dt : float, time increment\n",
" Returns\n",
" next_state : array, updated after one time increment'''\n",
" next_state = state + rhs(state) * dt\n",
" return next_state\n",
"\n",
"\n",
"def heun_step(state,rhs,dt,etol=0.000001,maxiters = 100):\n",
" '''Update a state to the next time increment using the implicit Heun's method.\n",
" Arguments\n",
" state : array of dependent variables\n",
" rhs : function that computes the RHS of the DiffEq\n",
" dt : float, time increment\n",
" etol : tolerance in error for each time step corrector\n",
" maxiters: maximum number of iterations each time step can take\n",
" Returns\n",
" next_state : array, updated after one time increment'''\n",
" e=1\n",
" eps=np.finfo('float64').eps\n",
" next_state = state + rhs(state)*dt\n",
" for n in range(0,maxiters):\n",
" next_state_old = next_state\n",
" next_state = state + (rhs(state)+rhs(next_state))/2*dt\n",
" e=np.sum(np.abs(next_state-next_state_old)/np.abs(next_state+eps))\n",
" if e<etol:\n",
" break\n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 294,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Max Height (Euler, N=10000): 402.219521 m\n",
"Max Height (Heun, N=10000): 402.259501 m\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N=50\n",
"tmax = 4\n",
"t = np.linspace(0, tmax, N)\n",
"dt = tmax/N\n",
"y0 = 0 # initial position\n",
"v0 = 0 # initial velocity\n",
"m0 = .25 # initial mass\n",
"\n",
"#Euler approximation solution set calculation\n",
"euler_sol = np.zeros([N,3])\n",
"euler_sol[0,0] = y0\n",
"euler_sol[0,1] = v0\n",
"euler_sol[0,2] = m0\n",
"for i in range(N-1):\n",
" euler_sol[i+1] = euler_step(euler_sol[i], simplerocket, dt)\n",
"\n",
"#Heun approximation solution set calculation\n",
"heun_sol = np.zeros([N,3])\n",
"heun_sol[0,0] = y0\n",
"heun_sol[0,1] = v0\n",
"heun_sol[0,2] = m0\n",
"for i in range(N-1):\n",
" heun_sol[i+1] = heun_step(heun_sol[i], simplerocket, dt)\n",
"\n",
"#Next we will decrease the step size\n",
"N2=10000\n",
"tmax2 = 4\n",
"t2 = np.linspace(0, tmax2, N2)\n",
"dt2 = tmax2/N2\n",
"y02 = 0 # initial position\n",
"v02 = 0 # initial velocity\n",
"m02 = .25 # initial mass\n",
"\n",
"#Euler approximation solution set calculation\n",
"euler_sol2 = np.zeros([N2,3])\n",
"euler_sol2[0,0] = y02\n",
"euler_sol2[0,1] = v02\n",
"euler_sol2[0,2] = m02\n",
"for i in range(N2-1):\n",
" euler_sol2[i+1] = euler_step(euler_sol2[i], simplerocket, dt2)\n",
"\n",
"#Heun approximation solution set calculation\n",
"heun_sol2 = np.zeros([N2,3])\n",
"heun_sol2[0,0] = y02\n",
"heun_sol2[0,1] = v02\n",
"heun_sol2[0,2] = m02\n",
"for i in range(N2-1):\n",
" heun_sol2[i+1] = heun_step(heun_sol2[i], simplerocket, dt2) \n",
"\n",
"#max altitude calculations\n",
"y_max_euler = max(euler_sol2[:,1])\n",
"y_max_heun = max(heun_sol2[:,1])\n",
"print('Max Height (Euler, N=10000):',round(y_max_euler,6),'m')\n",
"print('Max Height (Heun, N=10000):',round(y_max_heun,6),'m')\n",
"\n",
"#Plot 1 Formatting\n",
"plt.plot(t,euler_sol[:,1],label='Euler Explicit');\n",
"plt.plot(t,heun_sol[:,1],label='Heun Implicit');\n",
"plt.title('Rocket Height vs Time (N=50)\\n');\n",
"plt.xlabel('Time (seconds)');\n",
"plt.ylabel('Rocket Height (m)');\n",
"plt.legend(bbox_to_anchor=(1, 0.8));\n",
"\n",
"plt.show()\n",
"#Plot 2 Formatting\n",
"plt.plot(t2,euler_sol2[:,1],label='Euler Explicit');\n",
"plt.plot(t2,heun_sol2[:,1],label='Heun Implicit');\n",
"plt.title('Rocket Height vs Time (N=10000)\\n');\n",
"plt.xlabel('Time (seconds)');\n",
"plt.ylabel('Rocket Height (m)');\n",
"plt.legend(bbox_to_anchor=(1, 0.8));\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__Discussion:__ We can see in the above plots that the explicit Euler approximation of the solution and the implicit Heun approximation of the solution converge as the timestep within the solution is decreased. The Euler approximation results in a maximum rocket altitude of 402.22 meters. The Heun approximation results in a maximum height of 402.26 meters. Increasing the value for N, the number of timesteps, would cause these values to become closer. Next we will compare both solutions to the analytical solution, the Tsiolkovsky equation, by comparing the mass ratio to the rocket velocity."
]
},
{
"cell_type": "code",
"execution_count": 295,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N=50\n",
"m0=.25 #define intial mass\n",
"u=250 #define thrust velocity\n",
"dmdt=.05 #define constant mass change rate\n",
"t_max=4 #define max time\n",
"t = np.linspace(0, t_max, N)\n",
"\n",
"#Euler approximation mf/m0 vs velocity\n",
"mfm0_euler = np.zeros(N)\n",
"for i in range(N):\n",
" mfm0_euler[i] = euler_sol[i,2]/m0\n",
"plt.plot(mfm0_euler,euler_sol[:,1],label='Euler')\n",
"#Heun approximation mf/m0 vs velocity\n",
"mfm0_heun = np.zeros(N)\n",
"for i in range(N):\n",
" mfm0_heun[i] = heun_sol[i,2]/m0\n",
"plt.plot(mfm0_heun,heun_sol[:,1],label='Heun')\n",
"#Analytical calculation of mf/m0 vs velocity\n",
"v_analytical =np.zeros(N)\n",
"mfm0_analytical =np.zeros(N)\n",
"m_analytical =np.zeros(N)\n",
"for j in range(N):\n",
" m_analytical[j] = m0-dmdt*t_max*j/N\n",
" mfm0_analytical[j] = m_analytical[j]/m0\n",
" v_analytical[j] = -u*np.log(mfm0_analytical[j])\n",
"plt.plot(mfm0_analytical,v_analytical,label='Analytical')\n",
"\n",
"\n",
"plt.title('Mass Ratio vs Velocity (N=50)\\n');\n",
"plt.xlabel('Mass Ratio $m_{current} / m_0$');\n",
"plt.ylabel('Velocity (m/s)');\n",
"plt.legend();\n",
"\n",
"plt.show()\n",
"\n",
"#Next we decrease the step size\n",
"N2=10000\n",
"m02=.25 #define intial mass\n",
"u2=250 #define thrust velocity\n",
"dmdt2=.05 #define constant mass change rate\n",
"t_max2=4 #define max time\n",
"t2 = np.linspace(0, t_max2, N2)\n",
"#Euler approximation mf/m0 vs velocity\n",
"mfm0_euler2 = np.zeros(N2)\n",
"for i in range(N2):\n",
" mfm0_euler2[i] = euler_sol2[i,2]/m02\n",
"plt.plot(mfm0_euler2,euler_sol2[:,1],label='Euler')\n",
"#Heun approximation mf/m0 vs velocity\n",
"mfm0_heun2 = np.zeros(N2)\n",
"for i in range(N2):\n",
" mfm0_heun2[i] = heun_sol2[i,2]/m02\n",
"plt.plot(mfm0_heun2,heun_sol2[:,1],label='Heun')\n",
"#Analytical calculation of mf/m0 vs velocity\n",
"v_analytical2 =np.zeros(N2)\n",
"mfm0_analytical2 =np.zeros(N2)\n",
"m_analytical2 =np.zeros(N2)\n",
"for j in range(N2):\n",
" m_analytical2[j] = m02-dmdt2*t_max2*j/N2\n",
" mfm0_analytical2[j] = m_analytical2[j]/m02\n",
" v_analytical2[j] = -u2*np.log(mfm0_analytical2[j])\n",
"plt.plot(mfm0_analytical2,v_analytical2,label='Analytical')\n",
"\n",
"\n",
"plt.title('Mass Ratio vs Velocity (N=10000)\\n');\n",
"plt.xlabel('Mass Ratio $m_{current} / m_0$');\n",
"plt.ylabel('Velocity (m/s)');\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__Discussion:__ We can see from the two above plots the approximations of the solution do converge to the analytical solution as the number of timesteps is increased."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"2. You should have a converged solution for integrating `simplerocket`. Now, create a more relastic function, `rocket` that incorporates gravity and drag and returns the velocity, $v$, the acceleration, $a$, and the mass rate change $\\frac{dm}{dt}$, as a function of the $state = [position,~velocity,~mass] = [y,~v,~m]$ using eqn (1). Where the mass rate change $\\frac{dm}{dt}$ and the propellent speed $u$ are constants. The average velocity of gun powder propellent used in firework rockets is $u=250$ m/s [3,4]. \n",
"\n",
"$\\frac{d~state}{dt} = f(state)$\n",
"\n",
"$\\left[\\begin{array}{c} v\\\\a\\\\ \\frac{dm}{dt} \\end{array}\\right] = \n",
"\\left[\\begin{array}{c} v\\\\ \\frac{u}{m}\\frac{dm}{dt}-g-\\frac{c}{m}v^2 \\\\ \\frac{dm}{dt} \\end{array}\\right]$\n",
"\n",
"Use [two integration methods](../notebooks/03_Get_Oscillations.ipynb) to integrate the `rocket` function, one explicit method and one implicit method. Demonstrate that the solutions converge to equation (2.b) the Tsiolkovsky equation. Use an initial state of y=0 m, v=0 m/s, and m=0.25 kg. \n",
"\n",
"Integrate the function until mass, $m_{f}=0.05~kg$, using a mass rate change of $\\frac{dm}{dt}=0.05$ kg/s, . \n",
"\n",
"Compare solutions between the `simplerocket` and `rocket` integration, what is the height reached when the mass reaches $m_{f} = 0.05~kg?$\n"
]
},
{
"cell_type": "code",
"execution_count": 36,
"metadata": {},
"outputs": [],
"source": [
"def rocket(state,dmdt=0.05, u=250,c=0.18e-3):\n",
" '''Computes the right-hand side of the differential equation\n",
" for the acceleration of a rocket, with drag, in SI units.\n",
" Arguments \n",
" state : array of three dependent variables [y v m]^T\n",
" dmdt : mass rate change of rocket in kilograms/s default set to 0.05 kg/s\n",
" u : speed of propellent expelled (default is 250 m/s)\n",
" c : drag constant for a rocket set to 0.18e-3 kg/m\n",
" Returns\n",
" derivs: array of three derivatives [v (u/m*dmdt-g-c/mv^2) -dmdt]^T\n",
" '''\n",
" dstate = np.zeros(np.shape(state))\n",
" dstate[0] = state[1]\n",
" dstate[1] = (u*dmdt/state[2])-9.81-c/state[2]*(state[1]**2)\n",
" dstate[2] = -dmdt\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 326,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Max Height (Euler, N=10000): 425.297572 m\n",
"Max Height (Heun, N=10000): 425.352256 m\n"
]
},
{
"data": {
"image/png": 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9meDovdtduwp36CzRc0rpWldx6uyCS+KCde0RUj6V624tBQqy8Jktr5GRE+4rUhj9O2w7fnk93Gn4yfaTAv/MYP88E6gn7rX5gCdi3qcSEnPCfY3rbD8/wXOIe62rJLGnNNKyTTaFTZZhZ0Bdq06kCbon7t9ucPlq3FkOw3DD6S/HHcNehhs6/1TgMHWtN4m28QSuxegOXOfAtbhTxef4Oi8lOlJzqnHHtux8GKdl515gV1yrxnjcYbRiXII0BXdo7hi2H3UVVV2AGzDxWdyXXtjp1hVKVUtU9Rrc63UPLtFbg3tuhbiB7u4FDsaNTp1u/Y/gkplXcK/3ZtzgciNw13iaFSie6dABiWJ4ExiCG/BuOamfwhtW51y27Uf2g6qGdVb9A+7H7EXc+2Ul7pDoalwLzrVAd1Udn2lsVZWqblLVs3GDeT6CG39pPW4/rcRdM+523Pvp2gw29XHg/tgUykTG2Embuv5X++Gezyzc+9+YnJIyvp+NMWXgO/JGOi73UtWpYeWNMcZkxlp0jKlYQ/ztr6Q+SrIxxpgyskTHmCwSkR1ClvUA/uhnX1V3hpQxxphyZIeujMkiEfkA18n2eVx/n/W4kYGPBq7BdVDfBOypqmHXxDLGGJMFlugYk0UiMpboMPvxbAL+oKqvh5QxxhiTJZboGJNFIrIfcALuFP52uAEhN+HGi/kA+I+qzs9dhMYYU7NYomOMMcaYass6IxtjjDGm2rJExxhjjDHVliU6xhhjjKm2anyiIyIaZ9oqIitFZLa/2N4tIjIo17GaxPyFOSOv36As1NdGRK4QkbdFZK6IrBeRTSKyVES+EpH7ROSwDC+UWSmIyLDIvst1LKnyF8BUEdnugqAiMijm8xx6+YSY8oPKLejtt5vnL/B7vog8KiLf+++etF8LEWnoL6D6nYisEZG1/v41ItIgxTq6iMg9IvKziGwUkeUi8pGInJZGHPuLyAsiskBENvvbF3wn/VTrOM1vd7mPY6aPq3PIOi39Z3S9iLRNdVumhsj1xbZyPZHaBfUi0zTgmFzHbFPc17FL4HUalEE9ecA/gA0pvifmACfl+vlnuO+GRZ5PguWR5zos17H6eGrjri6vwOFxlg+KeY1WA01D6guWL/N7pwzPIzbObaY06umEu05WorqmAx2T1HEYiS/Eq8AbQH6SOq4h8QVti4Grk6yfD7wZEsMa3LUBE61/my/3cK7fozZVrqnGt+gEPAM0DkztgD2As4DXcFdu7gaMFpFbchWkKT8iUh93sdX/A+oDC/z9fYGOQAugB+6Clc/jLr7YBXdhVVNxzsVdZfxrVX0vhfLNgD+Xb0gZm417T01OZyURyQdGA7vhLqB5BS7x6eTvb/bLRvuy8erYFXgZaIJ7z58AtMG91x/xxY4F/hsSx0nAP3FHCT4D9gda+9vP/OP/EpHfhzyd/xK9RMojfvttfDwLfHwv+XjjuRN3aZWz/Sjkxji5zrRyPRH9tzAqSbm9cF9GkfLn5Tp2m7Z5fboEXptBZaxjVKCOx4C6ScrvgvuR+TzXz7+c922ladHB/WDO8/GcnKDMoEDMs4i2BuyQQvkyvXfK+FzaAUcE4wq+B1Os48JA7KfGWX5qYPnwBHW84JdvALrGWf4I0VaZnnGW1wXm+zI/xH5u/PIpfvm8eJ8roCfR1qBH4izvSrSV9fmQ/fGoL/N0rt+rNlWeyVp0UqSq3wGHAmv9Q7eJSOMchmSySEQGA2f62TGqeo6qbg5bR1Vn4f7p/rO84zOljsS1VqzHHU5J5l+4lrcmwF/KMa60qeoiVX1XVVdlUM3F/vYHVX0mzjaewSUfABfFLheR1sDv/Oyjqjozzjauxe3DWsAFcZYPwbV4Alwf+7nx89f52U64y6HEutDXv9VvL/Z5zMQlMQAnikirOHWAa5kHOCHsunOmZrFEJw3+h+12P9scd1hrG4FOjcN8Z8OLROQL37lZReSyQNkWInK676z3s4hs8B1e54vISyJyWCpxicjxIvKhiKz2nfF+EJFrRaR+TEfLLuk+ZxGp7eu4S0TG+21s8c/nc99ht2HI+jf4bc/1811E5EHfwXez79z7sojslUIs+4nI6zGdFO8QkRbpPq84rvS3JcAlqa6kzjtxYt1mv4tIcxH5p4hMEZF1/vE9A+V3EZHLROQ9EVkoIkX+tZwmIiNEZPd42xeR231dhSJSLyxWETkjEFPXwONxOyOLyNiYx0bK9h33B4lIRxEp9vPxfgiDddYNfBbuDiubwPn+9lVV3ZhC+VnAk/7+pSLSsgzbrJREZCdcSwjAiyFFI8t6+3WCjib6OxC3DlVdCnziZ4+NUyRyuGkjMCZBDGP88mR1fOK3F08kvlrET5bwcS4A6gFnJChjappcNynleiLFQ1eB8m0C64wOqe8C4OPAfGS6LFD2uzjLY6cHk8Rzf8i6k4DfBua7lGH//CmFGKcBnROsf4MvMxd3DajCBHVsAgYniaMkwbrzgYMC84PSfI6Ncf8kFXgvS++rQYF4DiHatB+c9vRlm6awj4uA0+Nsp3egzIlJYnrPl/sm5vFhkTpiHh+bQlyDfNl3/PzXSWI4MbBu7zT3aUO/H5QEh63i7PtBuMOakfVuT1Y+G69/Bu+bUfFeiwRlfxeIO+yzMzhQbmjMsvv841sJOVSL66AfqWOHmGWRw1Khh3CBz32572Mebxmo+x8h69cLfE7vCSn3mC/zRS5fS5sqz2QtOmlS929jtp8dGFL078BvcB3k9sB1ZN0b9+MRsQh4APdvpg+u814nXELwGO6HfXiif8kicjHR5uivcD+orYBdcc2/3YG70nl+cWwG3gLOAfbB/Wi08vH+BViI66T9fJJ6mgKv4I7RD8Vd0XtH3OGiQtxx/Mclzuna/rDSfwABZgDH4xLOLsBluM6mj5X5GbrXMc/f/zyDehJ5AvcjfSmwM+51PgRYHCjzA3ATcDCwO+7LvysuUf0Qd0bKoyLSO1ixqv4AfO9nE54GLCI7+m0CPJ1i3EfiksCI4WzbYb8xrqMpRPf/gEStT16kFXS8jz0dA3H7AWBcqiup6lxgpJ+9WETapLNR36rZKMNJ0tlmiroF7s9OWMqdGRjRPUEdizT8UG3cOkSkFu59miyGYB27xeyPlJ6Hqm4i+pmJfR5B3/rbAnEnGJiaLteZVq4n0mzR8eu8E1gvP0F9ClyYYWyRjoZz8dclCyyrjzttVnFf+vXirH9STDxdymH/tQvEcVCc5TcEtv8d0DBOmaGBMkfEWf6DX7YAaBVn+SC2be0ZlOZzOD+w7u+ztF8GBercjG+9yaC+531dT8RZ9heirT4tEqx/mS+zJXYfkoXTy4E6wDJf7rYEZdoS/Uee9mcDlwgqsDKNfT/IP9YR12qowL+TlU+0fzKYUvrskV6Lzr8D9TcKKdc4UO6umGWRVuXxSbY1JFDHkMDjwdbIO5PUcVegbOPA48cFHg8dvgOY4MtNCCmzZ6C+7b6TbKp5k7XolE1h4H6iDm8/qeqDGW7nCX/bmei/pohjcS0ZAH9T929nG6r6Aq6lp9yo6iLgfT97aJLiV6nqr3Eefx2XLAH0Cy4QkQKgl5/9h6oujxPDWFxrUVk1D9xfk6iQiNQJ+ceel2g94HFVnZRBfBDtZxJvHz+LS/TycYeG4om09rwXbx9mSlWLgKci20qwP87AtZxtAp4rw2YipwwnazmIF98vRDuzDpfqMahcsG/cdp//gGBfpkYJ6ghbP6yOVGPIdh2xzyNoVuB+z4SlTI1hiU7ZBJtdNUGZt1OqSKSbiNwd6OgbHBk1mBR0i1l1X3+7HtcXKJFUzkxJFmMDEbnYd5RdJK7DtAbijPy4xsYYtDlRnKpaAvzsZ3eMWbx/4P7rIfW/GrIsmVQPK1wHrEswHRCy3lspBSFysIg84TsgrxORksA+jtTRVmLO9vPJ5kd+drvDVyLSDejrZ1M9bFUWkcNX7XAD0MUa5m9fU9XCOMuTiZxpszq0VGL/wv2Q1sMNbpcSVR2lqpLhNLeMMYfJxuGwSB2JvseSbSuV78KKqCNageo6XMsluEPApoazRKdsmgbuJ/rSTfqvU0QuxB2WuRz3Q9SMaF+RsG2C658CMNMnColMSxZHkhi74job3of78WqL60+TSoxBy1V1S8jyDf42drj6Lv62UFWXhKz/U8iyZIKn94Y9h7IKfS+IOztvJK4vzhm4hLERib/U48UYSWD2jXNmTST5WUcWEt9EVPVH4Gs/u80ZiSIykGi/isfLuIlIolOm07F9QviQnz1PRDqGla8C1gfuh51xF+ynsj5m2fo4ZeIJ1r8+wf2KrCP2ecSKfC8nOg3d1CCW6JTNbv52ZciP94YEjwMgIvvgzpjKx3UmPRd3bLkNbsyPxv42IraTbqS5N96hoKBkXwhhMebhWkp28tv5J66jdCfcIbtIh9TIYYiw6z4Vp7rZmPlIE3Wy51Hm54nrAxWRsFVKVa8N/kvHnemVitD3Aq6PzTB/fzRuJNjuuH+jkX0cPJ023n5+xW9HcIPEBZ0SKaOpnZKdiUirzrEiEjwkOMzfzifa+pQLt+D2U13cqNdJVeLOyCsC91uHlAsuW5mgjrD1w+pYh+sblk4dm9n285rq8wguj30exiRkiU6a/NkrO/vZLzOo6iLcj9IcYKCqPqaqk1V1maquU9X1hCcOkQQn4Rg2Xtix7GQOJNo/5nf+h/5TVf1FVVer6nofZ7IYMhH5Qkz2PDJ5nl8RTcT2DytYTiKDvr2gqseq6quqOl1VVwb2caJWNAB8mUhrTWmiIyL7En2/ludhq4jnca9ZXXyC5c98OckvH5WkBTJMpG9RmQeCU3fW5AN+9mwJuVBkwGkkPmSZ6pTKdtI1PXB/54Sl3B+ViNgW3kgd7UQk7D0WrKN0u/61jAwyGBZDsI4Zqho8RJXS8/DxRfpWJWupjiTZWe+PZqoeS3TSd3bg/vsJSyUXGSzuDVVN9I+/d4LHwZ2mDbCrP8UzkbB+M8lEYlytqu+GlAuLM1Nz/W2zJKcFh53SHMof0//Qzw5O8ccvK8SN3ho5hBLWQTeVfRzpDNxdRCJ9ciJJz0LC+3JlhU+4IgO7DfO3Q4menTMqg+ozTnS823DJWD5uGIiqakLg/oCQcvsE7n+XoI48oCCFOuapamxrSqSOvSXx9bTyccNrAEwMLlPVFbiWPgh/Hv2IHtqfmKiQ78MWicMSHWOJTjp834e/+tlVRMfmKIvIv6ews3VOD1n2hb9tjDs9NpHj0ogpVtIYRWQ/tv23l23BcW2ODyk3NMPt3OFvawH3ZlhXOoL/ouPuZ5/InhJvWYz/AZFRZU/zPy6Riyg+l0FLytaw+OKIHL4qEJGeRPvrjFXVOQnWScVUf7tzJoeC/A/rfX72TNw1y8LKV8rOyH5fRvZJorPtgst+iLP/38KdsZewDnGXifiNn30zTpHR/rY+iUcsPoZo/5uwOg7024snEl8J4R38g6/n1ISlTI1hiU6KRGQPXAtOpCPoX/2/17KKdFA9PF6TsYgcTJxLTASMJnoq9C0J6vgd0bOzMomxiYhs1x9FRJoQPQxQLlR1PNEvq2slzjVuRGQQrl9LJtv5gOgp3ENE5HFJckmFLFlG9PBcoqT0OlJomVPVYqIDN54MHEX0rJOn4q6Umsg/+HapFFbVL4l2Dr+eaF+msnZCjogMTtic7YdbSNcduOvW1QauzrCuXLrf3/YRkT/ELvSP7eFnt/usquoy3JXLwXXQjpf03YxrISkh2pk7aDTwi79/k4jUiYmhDnCjn51P/CRlBNEhEm6O8zx2wfVjBHgpyRAJkVahIuCbkHKmpqiIwXoq80R0YKmncf08ItOOuDEYzsB9EWwNlA0bpjzp4Gq+3LBA2feB/XA/St1wP2wbcD/wCevDjbQbWf457gelBe4499W4MSdmBcp0SXPfNCV6yYYlfl908vvmd8CPuL4t03yZsXHquMEvm5tkW2NJMHAjbuyYyHOYjhstuJWP5Y+4H6zgleUHlfG90MC/FpF6FuBGmN4XaO/3RzvcqeS34w4HRcr+JqauQanud7a9avp/cf2iWuCa6iPLpqZSH+7wQ6TcHH/7fZLtl74XEyx/yy//GTc6cSNcglCbmIEsAxrU7uoAACAASURBVOtcEYhDcUl5/Qw/q8FLQJwWUi647xO+F4gOQKiplC+PCdgLd1goMr0ViGWfmKlJnPXzgcm+/CbcwJAd/HQZ0UESJxEzuGmgjl39Z0hxh8SPx3X67Y5LQCLxPBDyPIKDk37iPzMt/e0ngWUJB+TEJWKRciP89lvjPu+RS6isAXZNsk/tEhA2bTPlPIBcT3G+6MKmacBRKdY3LEm5Wrgm3ETb+gWX9IQlOhLzRRQ7fe+/tCLzHcqwf05m2yQvOBXjkq1RlGOi45eHXevqFzK41lXMdmrjxlvZkOJ7Yg5wSpx6BgXKdEmyzTZsm6jFTp/gLseQan0/xaz/1yTlh0XKJlh+eEhscfc1LhEtCpR7KEuf1zd8fU+FlBmULD5frhnRUb1zlejMTfF9FravO+H+ACRabzrQKUkch+GSiER1vEGCRClQxzW474RE3xVXJ1k/n/DvxDXAYUnqEKJJ0eUV+VraVHknO3QVXzGuJWMerpPqrbihxLurakoDASajrr/E8bgxdCbh/nmtx7WS3IK7ZMD0xDW4XyVVHY5rXRmL+yLY4Ou4EfcvcGtglXVliPN53NlXY3A/CkW4lo4Xca0YFdKfRVX/i+sn8CbudNTNuNaq/+A6Oc7J0na2quo1uFaxK4F3cV+cG3DPfRmuOfw+XAKwi6o+m+E2l+Jab/6Nex5bcH3AvsIlkgez7aiyyQQPU5XgRk7OJL73gCNwlz5ZxrbvqUTrLCfa7wIyP2wVETl0cryIZHS2n7pBC8tyBfVKRVXn4z4D/4f7Lomc6TXJP7a3LxNWx/9w16+7D/e52oQ7ZPkxcIaqHqfh42Chqv/CfVe8hLuOX5G/fQk4UFVvSbL+FlU9FtdyPNZvf5OP5z6gj48zzIG4zv2biY4sb2o4UdVcx2DKkYhcjvsyXwc0VXvBTQURkadxZ339qKpZGYrfd8yejTtd+9RMk0xTvYjII7i+PM+qaux4UqaGshad6m+Iv51oSY6pKCLSlOhZctlqzYm0hN7qZy/NVr2m6hORlrhD7cW4VnFjAEt0qjw/DkuiZb8nesbLi4nKGVMOzsN17i6PQwiP4vrL7SMiR2S5blN1XYnrKD9SVafkOhhTedihqypORJYCz+A6C07D9Z/YCTfuyqW4zrWzgD008cCExmRMRGoDdXDJ9bO4S5iMUNULy2Fbx+Le81+r6sBs12+qFt+aMwfXGbmrqi7OcUimErFEp4oTkU2EXx5gAXCEqtrAWaZc+ausBy0Deqsbq8UYY3LCDl1Vfafh+kBMwQ13Hjxj52qghyU5poItx10M9gBLcowxuWYtOsYYY4yptqxFxxhjjDHVliU6xhhjjKm2LNExxhhjTLVliY4xxhhjqi1LdIwxxhhTbVmiY4wxxphqyxIdY4wxxlRblugYY4wxptqyRMcYY4wx1ZYlOsYYY4yptizRMcYYY0y1ZYmOMcYYY6otS3SMMcYYU21ZomOMMcaYassSHWOMMcZUW5boGGOMMabaskTHGGOMMdWWJTrGGGOMqbYs0THGGGNMtWWJjjHGGGOqLUt0jDHGGFNtWaJjjDHGmGrLEh1jjDHGVFuW6BhjjDGm2rJExxhjjDHVliU6xhhjjKm2LNExxhhjTLVliY4xxhhjqq3auQ6gqmvZsqV26dIl12EYY0yVMmHChBWq2irXcZjqzxKdDHXp0oXx48fnOgxjjKlSRGRermMwNYMdujLGGGNMtWWJjjHGGGOqLUt0jDHGGFNtWaJjjDHGmGrLEh1jjDHGVFuW6BhjjDGm2rJExxhjTFq2FG1i/L2nsXj21FyHYkxSlugYY4xJy3ej/kLBytE0efJgvhvzUK7DMSaUJTrGGGNS9uNnr9N/0VMANGQTG1YvyXFExoQr08jIIpIHtAKaAauBFapanM3AjDHGVC6FyxfR+sM/lc5/X7eAgadcm8OIjEku5URHRA4EjgMOBnoBElisIvID8DHwhqp+ktUojTHG5JSWlDB/5DD2oBCAlTSl7bCR1MrLy3FkxoQLTXREpBZwLvBHYHe2TW42AWuBJkA9oI+f/iQiPwL3AI+pakk5xG2MMaYCjX/xVvpt+KZ0fv5v7mKvtp1yGJExqUnYR0dEDge+B0YAXYE3gUuBAqCBqjZQ1R1VtQHQEOiHS4jGALv59b4XkcPK9ykYY4wpT3OnfE2fn+4qnf+y9cnsdfCJOYzImNSFdUZ+B2gO/Blop6rHq+r9qjpRVTcFC6rqRlWdoKr3qepxQHvgSmAHX0/aRORfIqJ++ktIuVNE5DMRWSMi60VkvIhc7Fujwuov03rGGFOTbFy/hrxXz6aObAVgZt4u7H3Wv3MclTGpC/tRvwrYRVX/o6or06lUVVeo6t3Azr6etIhIP+CvgCYpdz/wDK6V6TPgfVxr0n3Ay77TdNbWM8aYmubHR8+jY8lCAH7VutQ5aST16jfIcVTGpC5hoqOqd8S23KRLVTep6p3prCMidYFRwFLgjZByJwAXAUuAPVT1GFU9HneY7SfgeOCSbK1njDE1zcQ376dv4Xul81P2up7Ou/XJYUTGpK8yHqa5CegBDAfWhJS72t9epaozIw+q6lLgQj/7tziHosq6njHG1BgLZk6i+4QbS+e/aXoE/Y+7KIcRGVM2lerHXEQGAFcAz6rq6JByHYC+QBHwUuxyf3r7QmBHYJ9M1zPGmJpk88b1bHn+TBrIZgDmSQd6nvswIpJkTWMqn7QHDPTJyEFAO9xp5fGoql6QZr31gCeAVcCfkhTfy99OVdWNCcqMw3WK3gv4MsP1jDGmxvj+sUvoVzwXgM2aT9HQx2jUuGlugzKmjNIZMLAh8AJwZOShkOIKpJXoAP8EugEnq+qKJGV38rfzQsrMjymbyXrGGFMjTHp3JP1WvFY6P7HHXxm4hzVwm6ornRadW4CjgELgWWAmsD4bQYjIvsBlwOuq+kIKqzTyt7+GlInE1jgL621DRM4Hzgfo1MkGzDLGVA+L5/7ELl9fXTo/vuGB7HNiwtE9jKkS0kl0fodLcvZU1fnJCqdKROoDI3GjLKfa0y3SmhR6+nkW19uGqj4MPAxQUFCQUV3GGFMZbCnaxPqnz6At7qj+QmlD13NHIrUqVVdOY9KWzju4GfBpNpMc71+4MWz+rKqLU1xnnb9tFFImsmxd4LGyrmeMMdXadyMvp+vWGQBs0TzWHv0QTZu3yHFUxmQunRadWZTPWVrHAyXAmSJyZsyy7v72QhE5BvhZVc8F5vrHO4fU29Hfzg08Vtb1jDGm2vrh4xfpv/jZ0vlvd/0T+xUclMOIjMmedBKdkcANItJaVZdlOY5awIEhy3f2UzM//52/7Ski9ROcQdUvpmwm6xljTLW0YuFsOn7y59L5SfUGMPCUv+cwImOyK50Wmv8AHwIfiUhYUpIWVe2iqhJvwp1uDnClf2xPv84vwESgDrDdleV8fB1wox9/FdhWmdYzxpjqaGvRZlaMOpVm/kj9Unag49mjqJVn/XJM9ZHyu1lVS4CzcIeZPhKRDSLys4jMiDNNL7eIo27xt7eJyK6RB0WkNfCAn73Vx52N9YwxplqZOPJyum/5EYBiFZYfej8tWrfLcVTGZFc64+h0Bj7B9WER3GCBOycoXu5nIqnqyyLyIO6yDT+IyAfAFuAQoAnwOu4inVlZzxhjqpPvP3ia/oufKZ3/eqeL2W+/o3IYkTHlI50+OrcDnYAvcIexfiZL4+iUlapeJCKfAxfj+vjkAdOAx4EHE7XKlHU9Y4ypDhbN+Ykun19ZOv9dvX0YePpNOYzImPIjqqk1vojIclxi011VN5drVFVIQUGBjh8/PtdhGGNMSjZv+pUFdxzALsWzAFhMK+pd8gXNW7ap0DhEZIKqFlToRk2NlE6Ps7rAt5bkGGNM1fXDIxeWJjlFmkfhMY9UeJJjTEVKJ9GZDLQqr0CMMcaUr4mjR1Cw8o3S+fHdr2R3Gy/HVHPpJDp3Ar/xVy83xhhThcyfNoHu468rnR/X6CAGnnRVDiMypmKk0xl5HHAX8L6I3AW8ByzAnW6+HVVdlHl4xhhjMrVx/Rp48QwaiOt5MF/a0+28x+06VqZGSCfR+cXfCnCdnxLRNOs2xhhTDrSkhJ8ePou9SxYAsFHrsOV3o2jSdIccR2ZMxUgnGVlMBYyPY4wxJnsmvHIXBWs/LJ3/fs/rGdCrfw4jMqZipZzoqGqH8gzEGGNMds2a9Cl7TLnVtcMDXzc7hgG/vTi3QRlTwewArTHGVEOFyxfR6I2zqCNbAfg5b2f6nPcQIpLjyIypWJboGGNMNVO8dQsLH/0DbXQFAGu1IXVOfpL6DRvlODJjKl7CREdEumZjAyKyWzbqMcYYk5oJj19Gz82TSud/PuBuOnXtncOIjMmdsBadH0XkYRHpVJaKRaSTiDwCTClbaMYYY9I16d2R9F/0dOn8Fx3OY+/BJ+cwImNyKyzRGQWcDcwSkXdE5GQRaR1WmYi0FpFTROQ9YBZwFjAya9EaY4xJaP70iez2VXQQwO/q7cM+Z92Ww4iMyb2EZ12p6nki8iBuROTDgcMARGQO8BOwElgLNAFaAD2ALn51AT4ErlTVSRhjjClX69esQl44rXRQwAWyIzuf/zR5eXk5jsyY3Ao9vVxVJwIHi0hv4BJgCLCzn+JZCLwBPKCqP2YzUGOMMfFpSTGzHj6NPiULAdigddk49Ak67GCXJzQmpXF0VPUH4ALgAhHpDuwJtAaaAoXAMmCiqs4sr0CNMcbEN+6pv9P/1y9K56f0vZn+e+yTw4iMqTzSvkyDqk4DppVDLMYYY9I09dPXKJj9QOmggF+2+j37HntBboMyphKxcXSMMaaKWjJvOu0/uoRa4q7OMzW/FwXn3pfjqIypXCzRMcaYKmjTr2v59cmTacZ6AJaxA63Pfo46devmODJjKhdLdIwxporRkhJ+GnEGuxTPBqBI81hx5CO0alumYc+MqdYs0THGmCpm3FPXste6j0vnJ/S8hh4DBucwImMqL0t0jDGmCvnho+dc52PvqxbHs8+JV+QwImMqN0t0jDGmivhl+nfs9Onlgc7Hvel7vl2R3JgwlugYY0wVsLZwOfL8H2jERgAW04o2575gnY+NSSLlcXREpB3wq6quSVKuKdBQVRdlGpwxxhgo3rqF+SNOopcuBtzIx+uHPkXXNu1zHFnFmTBhQpe8vLzza9WqdaSqNs91PCb3RGR1SUnJO8XFxQ/37dt3bqJy6QwY+AvuQp/nJCl3J+5inmkPRmiMMWZ74x/7EwM2TSidn9r/Fvr1GZjDiCrWhAkTuuTn57/apk2bZs2aNVtXp06dFXa4rmZTVYqKivILCwtPXrp06RETJkwYmijZSefQlVA69mZKZY0xxmRowpsPMmDxM6XzX7Q7i35HJ/u/Wb3k5eWd36ZNm2Zt2rRZVbdu3S2W5BgRoW7dulvatGmzqk2bNs3y8vLOT1S2PProNAU2l0O9xhhTo8ya9Cm9Jvy9dP67+gPZ55y7chhRbtSqVevIZs2arct1HKZyatas2bpatWodmWh56OEl3y8nqEGcx4J17Q4cBsxNJ0hjjDHbWrF4Lk1eP5O6sgWAubU6ssvwZ8nLy8ttYDmgqs3r1KmzItdxmMqpTp06W1S1ZaLlyfrRLAA0MH+in8IIrp+OMcaYMti0YR2Fj53ArqwCYA0NkVOep0nTHXIcWe7Y4SqTSLL3RrJEZxHRRKcdsBFYnaBsEbAQeA34b+ohGmOMidCSYn564BT22vozAFu1FnMPvp8+u/bKcWTGVE2hiY6qdojcF5ES4EVVPbvcozLGmBrq28evYMD6T0vnx+1+NQMPPD6HERlTtaVzCvh5wIzyCsQYY2q6CW8+yIAFI0vnv2x5IgNPujKHERlT9aWc6KjqY+UZiDHG1GTTv/0fvSdcWzo4x6R6/el/wYPWN8WkpH379r0XLVpUJ1m50aNHzzjmmGMyOoNNRPoCqOqEZGUrgzIN6ifuk9ccqJeojI2MbIwxqVk89ydav30OdWQrAHNqdWan4S9QOz8/x5GZqmb//fdf27p16y2Jlrdv3z7hsuoqrURHRAqAG4EDgfohRTXduo0xpiZaV7iSoidPpC1rAVhFE/JPf5GmzWruGVam7K666qolmbbYVDfpXOtqIPARELmC3FrAdqYxxpRR8dYtzB3xe3qX/ALAZs1nyVGP02On7jmOzJjqI52RkW/CJTkjgfaq2kxVOyaayidcY4ypPiY8PJzem8aXzk/a+x/0GHBoDiMyNcWYMWMai0jf/v37d4u3fPr06XVEpG/79u17p1Pv5s2b5fbbb2/Vt2/fbk2aNNmzbt26e3fu3LnXueee22HRokXbNa7cc889LUSk7wknnNBlyZIlecOGDevYvn373vn5+XsPHjx4l7I+v6B0Di/1B6apas26yIoxxpSDcc//k/7LXi6d/6L92ex33PAcRmRMZlatWlXr0EMP7Tpx4sRGjRo1Ku7Vq9eGJk2aFE+ZMqXBY4891ubtt99u/vHHH0/v1q1bUZx1axcUFPRYv359XkFBwbo99thDmzdvvjUbcaWT6NQCJmdjo8YYU5NNfv9p+v50R+kZVuMbHsjAs21AeVO1nXHGGV0mTpzY6Igjjlj95JNPzmvVqlUxwNatW7n00kvbjxgxYsfTTz99p2+//XZ67Lpjx45tut9++60dPXr0rObNm5dkM650Ep0pQJtsbtwYY2qamRM/ptvnl1FL3KDz02p3p8dFz1CrBl7DKlu6/O2tvrmOoazm3np0Vk/RHjJkyG6JljVq1Kh43bp1k7K5vYgJEybUe+utt5q3a9eu6KWXXprTqFGj0stH1a5dm/vuu2/hRx991HTcuHGNvv322/r9+/ffGFy/du3a+thjj83LdpID6SU69wBPisgeqvp9tgMxxpjqbtHsH2nx5hnU8xfqXCA70vK8V2nQsHGOIzPVRdjp5fXr1896EhHx5ptvNgU45JBD1gSTnIi8vDz69++/fsaMGfU//fTThrGJTo8ePTbEO6SVDekMGPiciPQCPhCR/wPesrFyjDEmNWtXLKHkqRPYwZ9GvprGlJzyEi3btM9xZKY6ydXp5bNnz64L8NRTT7V66qmnWoWVXb58+Xa5R4cOHcolyYGQREdEEm00Dxjhy5Sw7dXNI1RV68Z53BhjapzNm35l0UPH093/N9yk+Sw+ahQ9uu6R48iqh2wf/jFQXFxcpvI9e/bc0K1bt41hZXv16rUp9rF69eqVW2tTWItOKq09dlDZGGNClBQX8+P9p7DXlh/dvApTBtxJwYDBOY7M1GR169YtAdiwYUPcYWZmzZqVVmNFx44diwD222+/dQ899NCCzCPMnrBxdPIznIwxpsYb/+il7LVubOn8110vp+CoYTmLxxiAzp07bwGYP39+3c2bN293QbUxY8Y0Tae+IUOGrAV49913m23ZUrmuMpEw0VHV4kyminwSxhhTGY178Tb6L36mdP6rlr9j4Cl/z2FExji77bZbUceOHTevW7cu74YbbtjmjOqnnnqq2ciRI1unU9/++++/YfDgwYXz58+ve/TRR+8ya9as7Ro85s2bl3/TTTe1ruhEyK5HZYwx5WDy+0+z99RbSsfK+a7+vvS7YARSK50B6Y1Jz2233bbjyJEjWyRafuqpp64aOnToWoAbbrhh4bnnnrvzrbfe2v7NN99s3qlTp81z5sypN2PGjPqXXHLJ4nvvvbdtOtt+4YUX5hxxxBFd33///WY9e/Zs2q1btw0dOnQoWrduXd7ixYvrzJ49u15JSQl/+ctflufn58fr31suLNExxpgsm/7Nu3T//DLy/Fg502vvRrdL7Grkpvx9/vnnTcKW9+nTZ0Mk0Tn77LNX161b9+c77rij7fTp0+vPmzevXo8ePTa89NJLM3v16rUp3URnhx12KPnyyy+nP/TQQzs899xzLaZOndpg6tSpDZo0aVLcunXrLaeccsry448/vrBBgwYVluQAiGpq2ws5CytWEbACGA+MUtUxZYytSigoKNDx48cnL2iMqRHm/fgtzV/8LU34FYBfpC31hr9PqzZ2CcAgEZmgqgWplJ08efLcPn36rCjvmEzVNXny5JZ9+vTpEm9ZOm2otVOcGgCdgKHAGyLyaJkjN8aYKmTp/Bk0ePGk0iRnBc2Q0161JMeYHEon0ckH7gR+Be4GCoBWQAugL3AXsN4v2wk4B9eyc5aInJzFmI0xptJZs2Ixm0f9llasAmC91mf18c/RYZceOY7MmJotnT46pwGXAweq6pcxy1YD34nIa8BYYKqqjhSR6cDnwFnA81mI1xhjKp2N69eydMSx7FayEIAirc2cwY/Qu8++OY7MGJNOi84lwGdxkpxSftnnwMWB+UnAXpkEaYwxldXWos38fP9Qdts6A3ADAk4ecCe9DxiS48iMMZBeorM7sDiFcouB7oH5WUBaAw8ZY0xVoCXFTL7/NHpvHFf62Ne7X02/o87KYVTGmKB0Ep0ioE8K5fr4shH5uL47xhhTrYx75FL6rvlf6fwX7c9h35OvymFExphY6SQ6nwO7i8g1iQqIyNVAD+CzwMM7kVpLkDHGVBnfPnntNqMef918CPuec2cOIzLGxJNOZ+QbgEOBm0XkD8ALwDzc1cs7AycBPYHNviwi0hHoDTyYtYiNMSbHxr10O/1n31s6P6HB/hRcNNJGPTamEko50VHViSJyLPAULqG5MaaIAMuBM1T1O//YZuBIYGoWYjXGmJybOHoE/ab+s3R+Sp0+9LjkRRv12JhKKq1LQKjq+yKyC/B74ECgvV+0CPgUeEFV1wfKLwPey1KsxhiTU99/8DR7jL+69PpV02p3o/PFr1O/QcPcBmaMSSjta12p6q/ASD8ZY0yN8OPnb9D9sz9RW0oAmF2rM22Gj6Zx0x1yHJkxJowdUDbGmCRmjP+QLu+fRx3ZCrjrVzU+bwzNW7bJcWTGmGQs0THGmBBzp3zDjmNOp4FsBmApLah1xhu0atspx5EZY1KR8NCViMzAnVF1uKrO9fOpUlXtlnF0xhiTQwtmfk/jl08svUjnKpqw8eRX6LKTfb0ZU1WEtejs6qc6MfOpTsYYU2UtmTed2s8cTwvWALBWG7Dit8/Rpbtd0cZUPu3bt+8tIn3HjBnTOKxc//79u4lI33vuuadFRcWWa2Gdkbv627kx88YYU60t++VndNQxtGUFABu0Lr8cOYqee+6f48iMMelKmOio6qyweWOMqY5WLJzDlsePpr0uA2Cz5jPjoBHsuc/hOY7MGFMW1hnZGGO8lYvns/Gxo2mvSwAo0jx+/M397DloaI4jM8aUVdqJjjiHi8gNInK/iJwZWNZCRHYWEUugjDFVyuplC1n/yFF0LFkIwBbN44f97mWvQ07KcWTGVIyPPvqo4THHHLNzmzZt9sjPz9+7efPmfQ4++OBd33vvvUaxZadPn15HRPq2b9++d6L6RKSviPQNe/yRRx5pvueee3Zv0KDBXg0bNtxr4MCBu8XbXibSSkhEpA/wI/A2cB0wHDdCcsRQYCZwVLYCNMaY8rZmxWIKHzqKziW/ALBVazF5wN30PezUHEdmTMW4/vrr2wwePLj722+/3bxVq1ZbBg8eXNi5c+fNn3zySdOjjjqq21133dUy29u87LLL2g0fPnzn/Px8Peigg9a0adOm6Ouvv248ZMiQ3T744IOsDTeecqLjL9D5IdAN+B9wDaUDoZd6GdgK/DZbARpjTHlau2oZKx48ip2K5wJQrMJ3/e6g4KhhOY3LmIry8ssvN7nppps6tGzZcssHH3wwbcqUKT+98847sydNmjTtnXfemdagQYPiv/3tb52+//77utnc7qhRo1qPHTv2p3Hjxk1/6623Zs+cOXPqySefvGLLli1y3XXXtcvWdtK5BMT/ATsAf1LVewFE5F/BAqq6WkR+AvplK0BjjCkv6wpXsOyBI9m1eDYAJSqM3+tfDDjm3BxHZtJyQ9PtDo9UGTesmZDN6oYMGbJbuuvcdNNN7QDuu+++uQcffPCvwWWHHXbYr5dffvnim2++ucO9997b6pFHHlmQrVj/+te/LjzggAM2RObz8vK48847Fz7//PMtJ0yY0Hjz5s1St25dzXQ76SQ6RwDTIklOiF+AAWUPyRhjyt/awhUsue9Idtv6c+lj3/a5iX1+e1EOozImM/vvv//a1q1bb0m0/JNPPmm6cuXK0t/+xYsX154yZUrDRo0aFQ8dOnRtvHUOOeSQdTfffDPjx4/Pat+ZE044YU3sY+3bt9/apEmT4rVr1+YtXbo0r1OnTlsz3U46iU5b4PUUym0AmpQtHGOMKX9rVy1j2QPbJjlf9biOgUP/mMOojMncVVddteSYY45Zl2h5//79u61cubI0YZkxY0YdVWX9+vV5+fn5oS1jq1atSvtC4GF23XXXoniPN2rUqHjt2rV5GzduzMqJTekEvQ5I5Qp2OwEryxaOMcaUrzUrFrPywSPZtXhO6WNfdf8/Bv7+ihxGZTKS5cM/NcnWrVsFXHJx2GGHFYaVbdGiRcqtK8XFxUnL5OXlpVpdRtJJdL4D9hGRNqq6NF4BEekK7Am8lY3gjDEmm1YvW0jhQ0exs+94XKLCt72uY+CJf85tYMbkyM4771wEULt2bX3llVfmprpepO/Mhg0b4ra6zJw5s068x3MhnWahkUBD4GkRaR67UEQaAQ8DecDj2QnPGGOyY+XS+awdcXjp2VUlKnzb52b2sSTH1GA77bTTlq5du24sLCysnew6WUFt27bdmp+fr4WFhbUXLVq0XaPJa6+91jS7kZZdyomOqj4LvAkcAswWkVf9ogEi8gwwBzemziuqOjqdIEQkX0QOEZG7RORrEVksIkUislBEXhaRQUnWP0VEPhORNSKyXkTGi8jFyQYuLOt6xpiqZcXiufz60BGl4+QUqzBu71vZZ+iluQ3MmErguuuuDoD1WwAAIABJREFUWwRwzjnn7PTqq69u18d206ZN8swzzzQNjm1Tt25dLSgoWA9w5ZVXtispKSkt/9577zW67bbb2ldA6ClJ9wf9d8DdQD2iY+XsDvwBaArcB5RlhK0DgQ+APwOdgQnAa8Aq4ATgYxG5Kd6KInI/8AxQAHwGvA/s5mN5WUTiHgQs63rGmKpl+cLZbHz4SDr5EY+3ai0m9ruTAccNz3FkxlQOp512WuH111+/YOXKlfknnHBC1y5duvQ6+OCDdz3iiCN23mOPPbq3atWqz2mnnbbrxIkTGwTXu/HGGxfm5+frs88+26pr1649jzzyyJ179+69+1FHHdXtzDPPXJar5xMrrURHVbeq6l+AjsDJuEED/w4MAzqr6h9VNeFpbSFKgFeA36hqW1U9RlVPUtXefjvFwN9F5KDgSiJyAnARsATYw693PO5K6z8BxwOXxG6srOsZY6qWpfNnUPTokXTURYC7rMOkAf+mn42TY8w2brjhhqWfffbZj7///e9XlJSU8OWXXzb57LPPmq5du7Z2//791911113zzjzzzFXBdQ499NBfR48ePWPgwIHrlixZUmfs2LFNAe677745//3vfxfl5plsT1QzHoun3InIo8A5wOOqek7g8fFAX+BMVX0yZp0DgbG4ZKa9qpZkul48BQUFOn78+LI/OWNMuVgwczL5zxxPG38SaJHm8cO+99D38NNyHJkBEJEJqlqQStnJkyfP7dOnz4ryjslUXZMnT27Zp0+fLvGWVZW+KN/52w6RB0SkAy5ZKQJeil1BVT8BFgI7Avtkup4xpuqYM+UrGjxzTCDJqc2U/e+3JMeYGijh6eUiktF1JlQ1m81WXf3t4sBje/nbqaq6McF644D2vuyXGa5njKkCZoz7gB3fOp0muJHlf9W6/HzII+z9m+NyHJkxJhfCxtH5JYN6NUndKRORHXF9gMD144nYyd/OC1l9fkzZTNYzxlRyUz97nZ0+OJ8GshmAtdqQBUc/SZ/+g3McmTEmV8KSkdgrk6cjk3WjlYjUBp7GndH1Ycxp65EhrH/dbsWo9f42ODZAWdcLxnU+cD5Ap06dQqoxxlSUyf97it2/uIw64gZvXUlTVp/wAj32GJjjyIwxuRTWRyc/wRQZ7fCJkDL5WYpvBG7cnl+A2IPrkWQq3d7UZV2vlKo+rKoFqlrQqlWrslZjjMmSiW8+QM8v/lia5CyhJetPGc2uluQYU+MlbNFR1YQXqhARXyRxmUyJyH9xZ1otAQ5R1SUxRSIXLQu7mmpkWfACZ2VdzxhTCY178Tb6/fiv0r8wv0g78oa9QefOu+U0LmNM5ZDVK5Fmi4jcBfwRWI5LcmbGKTbX33YOqapjTNlM1jPGVCJaUsK3I//CgF8eK31sVq0uNDlvNK3a2iFlY4xT6RIdEbkdN0LySuBQVf0xQdHIKec9RaR+gjOo+sWUzWQ9Y0wlUbx1CxMfOIsBq6Ld9qbV7s6OF46mWYvWOYzMlBdVjRxNMGYbycYDrFTj6IjIrcCVwGpckjM5UVlV/QWYiOszdGKcug7EjbuzBPgq0/WMMZXDpg3r+OHuY+kXSHIm1+tHhz/9z5KcakpEVhcVFWWr76epZoqKivJFZHWi5ZUm0RGRm4GrgEJckpNKa8ot/vY2Edk1UFdr4AE/e2uc0Y3Lup4xJofWrlrG3H8fxp4bosNbfdPkcHa//C0aNa40F0s2WVZSUvJOYWFhylfWNjVLYWFh45KSkncSLa8Uh65E5FjgWj/7M3BpgibKaap6a2RGVV8WkQeBC4EfROQDYAvuTK0mwOu4i3Ruo6zrGWNyZ9mCWWx8/Di6l0SH+Ppix9MZeN491MqrNP/ZTDkoLi5+eOnSpUcAOzRr1mxdnTp1tthhrJpNVSkqKsovLCxsvHTp0sLi4uKHE5WtFIkOsEPgfoGf4vkEuDX4gKpeJCKfAxfjroKeB0wDHgceTNQqU9b1jDEVb/608dR7/kQ6E72m4Jddr2S/U68NWctUF3379p07YcKEoYsXLz5/6dKlR6pqy1zHZHJPRFaXlJQ8X1xc/HDfvn3nJiyXqBOPiBSF1J+HG4cmUTKgqlo31WCrMruopzHla9o379LunbNp4sf4LNI8JhXcSv8h5+c4MpOJdC7qaUwmwlp0krX2CJWoj48xpvqZOOYheo27pnQgwPVan1mHPER/u26VMSZFYclM15BlxhhTbrSkhG+fvJoBc0eUDgS4gmas+u3T9NnrgNwGZ4ypUsJGRp5VkYEYYwzAlqJNTH7gTAYUvlv62NxaHck//RV226lbDiMzxlRFlaUzsjHGsLZwOb88eAIFm6NDaH1fZy86D3+ZpjtY/1NjTPos0THGVAqL505jy5Mn0LNkQelj3zQ7ir0uHEWdujXi3AZjTDmwzsTGmJybOfFj6ow6jE6BJOfLzhfR/4/PWJJjjMmItegYY3Jq4piH6TnuGurKFgCKtDaTC/7FvkMuyHFkxpjqwBIdY0xOlBQXM+7xyxmw8InSM6tW05hFRzxKv4FH5DY4Y0y1YYmOMabC/bp2FT+POIUBG6LXzZ0nHeCU5+nZtXcOIzPGVDeW6BhjKtSiOT9R9NTv6VMyv/SxSfX6s9MFz9O0eYscRmaMqY5S7owsIvuKyC4plNtZRPbNLCxjTHX005djaPDEYLoEkpwv25xKryvetiTHGFMu0jnr6nPgmhTKXQ18VrZwjDHV1biX7mDX986gGesB1+n4mz7/ZN8LH6B2fn6OozPGVFfpHrqSconCGFNtbd70K98/fD79Vo3Z5nIOy49+nAH9D8ltcMaYaq88+ui0AjaWQ73GmCpm6S8zWfvEH+i3dWbpYzPzdqXRsBfZvWPSI+HGGJOx0EQnTl+b1iH9b2oDuwOHA9OyEJsxpgqb+vkbtP/gYrqyrvSxcY0PoefwUTRo2CSHkRljapJkLTqfAxqYP9JPYQR4OJOgjDFVl5aU8O3T11Ew6z7yxH19bNE8xnW7goEnX43UsgHZjTEVJ1mi8yXRRGc/YDkwM0HZImAh8Jqqvpad8IwxVcn6/2/v3uOsrur9j7/eM1xmEARBUbmKiIggioyAmLfQrNTMlNSTdjt2U0+mpabVKfWc0k55tNLUTmVmlmm/NDXL+zVRUUTkjspVQECG+3CZ+fz++H4HZzZ7D7NhmL1n5v18PL6P5ay1vns++7uB/XF913et1e8z57bPMnrdc/Xm4yz96G2M9SKAZlYADSY6EfGh2v+WVAP8PSK+uMujMrMWZ96M19Cfz+WwmkVb66a1H8qen/8jQ3v3L2BkZtaW5TMZ+UTg3V0ViJm1XK8+cDNDXruaTtq4te7FvcYz8vybvSmnmRVUoxOdiHhiVwZiZi3PhrWrmfp/X6ai8pGtt6o2RAemHH4tR5721cIGZ2ZGfgsGAiDpKEl/lDRX0jpJt9dpO1HSNZL2btowzazYzJ8xkfduGJskOal56sO74x9ilJMcMysSea2jI+l7wPepnyDVfY0a4DvAEuCWnY7OzIpPBBPv/wVDX7+Gcm3aWv3y7idx8Jdup3OXbgUMzsysvnz2uvo4cDWwGDgH6J2l21PA+8ApTRKdmRWV9WsrmXjjWVRM/u7WJGdDdOCl4ddyxCX3OMkxs6KTz4jON4CNwEkRMQ1Aqr8jRETUSJoFDGqyCM2sKLz1xvO0v//LVNR5qmpuSV+qz/gto4ceUcDIzMxyyyfRqQBeqk1yGrAQGL7jIZlZMampruaVP17DiNk/p4Oqt9a/1PVjDDv/Nnbr0rWA0ZmZNSyfRKcT8F4j+nXGm3+atQrvLXybZb//AqM3vr71b/W66Mibh/0noz554TajumZmxSafRGcxcGAj+g0B5u1YOGZWLCb94w72n3AVQ1m3tW5muwMpP+s3jB50SAEjMzNrvHweL38KOETSuFwdJJ0J7Ac8vpNxmVmBrFu9kok3ncOICRfTNU1yqkP8q/cXGXDZ8/RzkmNmLUg+Izo/AT4D/EXSpcD/q22Q1BE4A/gFsAG4qSmDNLPmMePlx+jyyEVUxJKtdYvZi/c/+gvvVWVmLVKjR3TSSchfBMqBXwHLSTb8/AywDvg9yfyc8yPi7aYP1cx2lar1a3np1q9x4MPj6V0nyXm5ywl0uvglhjrJMbMWKq8FAyPiD5KmAt8j2fuqM9Ce5LHzJ4GrI+LlJo/SzHaZ2a8+RYeHL2J0zcKtE47XRDkzRv6AI079iiccm1mLlleiAxARrwNnSCoBegKlwHsRsbmpgzOzXWdj1Xpev/PbVCy6k1LF1vo3Oo6k57m3c0TfAwoYnZlZ02h0oiOpQ0RsXe89ImpItnrI1nd/374yK15zXn+Odn+7gNE18+s8Nl7GlGGXM/qMS1BJ3tvgmZkVpXxGdP4AjN9eJ0n9gCeAATsalJntGlUb1jH5rqsYufBO2qlma/2bHQ5lj3N+xZgBgwsYnZlZ08sn0TlD0g0RcWmuDpL2IUly+u10ZGbWpKa/+Hc6P/pNRse7W0dx1kdHJg+5lNHjL6OktLSwAZqZ7QL5JDrPAhdLmh8RN2Y2StqLZELyQOCnTRSfme2kVSuXMevOb3DEyofq1U9rP4wuZ9/OkQOHFigyM7NdL59E5zTgX8BP0mSn7jo6ewCPAQcBt0TEZU0bppnlK2pqeP2fd9Dvpas5gsqt9WuinKlDv8moMy71KI6ZtXqNTnQiYpWkjwMvAndJGhcRL0rqAvyTZCPPOyLiol0Uq5k10nsL32Lx3RcwYv2EevWvdjqaPp/5OWN6ewqdmbUN+a6jM0/SySS3sR6Q9FGSVZArgHuAf2/6EM2ssTZvquK1e37IIXNu5VBt3Fr/Ht1ZMOYaDj/pXK+LY2Ztyo6sozNJ0qeBB4CXSNbReRA4LyKiwZPNbJeZ+vwDdHnyqnoL/wFM6PFJhpx3AyO79ShccGZmBZJ3ogMQEY9I+hrJVhCPAmdGxJYmjczMGmXZoneY/6dLGLnmqXr175T0Z/2JP2aMt28wszYsZ6IjaVYjzt8MDAGmZgyHR0R4QQ6zXWjzpo289ucfMWz2Lxmpqq31a6OcKQdeSMX4y2nfoWMBIzQzK7yGRnQau/573yx1voVltgtNefo+ujz7A0bXLKh3m+qVLifQ/+wbOLJ3/8IFZ2ZWRBpKdAY1WxRm1ijzZrzKqvuvYHjVK/Xq3ynpx7px13HEUScXKDIzs+KUM9GJiLeaMxAzy61y2WJm3XMVhy+7n/51tm5YF2VMPuACKj79bTp09G0qM7NMOzQZ2cyax6aNVUy69zqGzLmNUazfepuqOsTE7qew/6d/yNh9veOKmVku+exePgQ4Hfh7RLyeo88I4GPAfRHRmMnMZpZF1FQz6Z+/Y++Xr2d0LKnXNqXDYZSdcj2jh48pUHRmZi1HPiM6FwJfAX7fQJ8VwDVAT+AbOxGXWdsUwZvP3U/ZM9dyeHX9u8cL1ItlY7/LiHHnoJKSAgVoZtay5JPoHA+8ERELcnWIiPmSJgPjdjoyszZm9qtPsenR7zNs4+R69avZjamDvsbIMy+jb8eyAkVnZtYy5ZPo9CFZHHB73sGJjlmjzZsxifcf/C4j1j1fr35DdGBSr7MZOv57HNm9Z4GiMzNr2fJJdBq7zXEAfvzDbDsWzpnCkgevZUTlo/TXB0tPbYkSJvY4lQFnXM1Yb75pZrZT8kl05gOjJSnXnlaSSoDRwMKmCM6sNVo4ezJLHrqWEZWP00dRb8G/iZ2Pp+dp1zBm0PDCBWhm1orkk+g8CvwHcBnw4xx9vklyi+vmnYzLrNVZMOt13nvovzhs1bYJzhsdR1L+saupOOzowgVoZtYK5ZPo3AB8AfiRpKHAr4EZadtg4HzgXGAt8NOmDNKsJZs/cxLLHv4vRqx6gr5ZEpz2465k+KgTCxegmVkr1uhEJ32i6mzgHuA8kqSmLgHrgHMiYm6TRWjWQs2c+Dgbnvwph63/F/2gfoJTVkH7D1/J8FEnFCo8M7M2Ia+VkSPiEUnDgW8BJwG1S7LOB/4J/DQi3mnaEM1ajqipZspT99L+pZ8zZNOb27RPLqug47irGH6EH0w0M2sOeW8BkY7WXNT0oZi1XJs3bWTyI//HnpNvZXjN/G3aJ5WPoWzc5Rxa4QTHzKw5ea8rs52wasUSpj98MwPe/gMVrKjXtjlKmdTtRPY86VuMOPiIAkVoZta27VCiI2kf4Gigd1q1CHguImNTHrNW6p2pL7PsiZ8xfMU/GKPN9drWRRlv7P1J9jv1ckb1HVigCM3MDPJMdCR1BX4GnMO2CwhWS7obuDgiVjVRfGZFo3rLFqY89Sfav3I7QzdNZgDUm2C8gq7M7P8ZDv7EJRzZwysZm5kVg3x2Ly8DHgcOT6teBd4i+ad+AFBB8jTWUElHR0RVE8dqVhArls5n9j9vp/8793BYvLdN++zSgbx/yBc59KQvMLZ8twJEaGZmueQzonMxMBKYAHwlIqbUbZQ0DLgNGAN8ndyLCpoVvZrqaqa98Dc2v/wbhq15gTGqrte+JUp4vcsxlH/oAg4edaJ3EzczK1L5JDpnAZXAxyOiMrMxIt6UdArJKM/ZONGxFmj54nnMefQ2+s+9l2G1ozd1bk+tpAvTe32KAR/9Dyr6DSpMkGZm1mj5JDqDgEezJTm1ImKlpKdI1tgxaxE2Vq1n2tP3ojf+xLB1Exijmm36TGs/lLVDz+WQEz/L2N06FyBKMzPbEfkkOgK2/QbYVtYNP82KSdTUMHPik6x66fcctOIxRrAuaagzelNJZ6b3PJl9j/8KBw8ZWZhAzcxsp+ST6LwFHCepc0SszdZBUhfg2LSvWdF5953pzH/qt/Rd8AAH5VgNYWr7Q1g//FwOOeE8jvTkYjOzFi2fROc+4Grgfklfjoi36zZKGkAyGbk7cFPThWi2cxbPm8m8Z/9A93mPcOCWWfTK0udd9WRe70/Q+9jPMXTQ8GaP0czMdo18dy8/C/gwMEPSC8A7JLeq9geOSl9vKvC/TRynWV4Wz5vJvOf+SPe5D3Pgllnsm6XPmihnevdx7DbqXIaM+gi9SjOXhjIzs5Yun93L10k6nmTU5jSSW1TH1u0C3E/y6Pm6Jo3SbDuipob5syax+OX76T7/HzmTm01RyrROFWwZdhbDjj+LUZ08sdjMrDXLd/fyZcCn0ttUx5BsASFgIfCsdy635rR500ZmvfIYayb/jb7LnqF/LKF/tn5RyrTyw9k4+DQGH3sWh3X3qsVmZm3FDu11lSY0Tmqs2a1c9i5vTXgQzf4ng1ZPYCjZBw+3JjcHfoLBx57FoT32buZIzcysGDT57uWSSoDPRcRvm/q1re3ZWLWOORMfZ820x9lz6QscUP0WFTn6rosyZnYexZYDTmLwMeOd3JiZWdMlOmmCcx7wXZLJyU50LG/VW7Ywd9orLJvyGJ0WPMugDZMZqk05+y9hT+bueQzlw05h8OiPcXh5p2aM1szMit12Ex1JvYCPAHsDS0lWR343o8+/AT8ABpLM2Vna5JFaq7R5UxVvv/E8K6c9Q/niCQzY8CYDWc/A2g6q339LlDCrwxAq9z2anhWfZOCw0ezjfabMzCyHBhMdSRcD1wEd6lRvlvT1iLhd0v7AH4BRJF9Ja4CfkDyKbraNymWLmf/m86x/+yU6v/cKA6umMbiBERuABerFoh5j6DD4BA4Y9TEO7tq9maI1M7OWLmeiI+kYPlgPZw0wC+gKDABukfQOcCfJSM9m4BbgvyNi+S6N2FqMqvVrmfvmBCrnvEj7xa+xz9qp9I6ldKvbSduet5xuzOt8GFv2O5a+FSfTd7/B9G2uoM3MrFVpaETnwrS8BfhWRFQBSBoK/AV4ACgDpgCfjoiZuzLQXSW97fY1YDhQCswgmV/0y4hozN5eBqxYupDFMyeydv7rlC6bSo+1s+i7ZQEHqXq7576rvVm4+wjoP5Z9h4+jz/4Hs6dvR5mZWRNoKNEZA8wHLo6Ird9WETFV0iXAw8AG4CMR0SLn5Ei6GbgAqAKeIBmZGgf8AhgnaXzd925QuXwJS96ewupF06lZOoPdKmewb9Vb7EklPTI7Zxmt2RTteKf9QFbucQjt+o2iz2En0KvvwKzbMpiZme2shhKdnsA/cnzRv5iWz7bgJOcMkiRnCXBMRMxO6/cGngJOBy6iDe7btbpyBcsXzmHVu7PZuGQmJe/Pocu6ueyzeSF7sLr+raftmF/Sm6VdhlG97+HsceCR7Dd0FIM7lu+y2M3MzOpqKNHpCKzM1hARlZIgSRJaqivT8oraJAcgIpZK+hrwNPBtST9vTbewqjasY+V7C1m9bAHrV7zLxhXzoHI+HdcuYveNi9mreim7s47d83zd9dGRBe33o7LLgcTew9i9/6H0HjKKft160G+XvBMzM7Pt29l1dKJJomhmkvoAI4FNwL2Z7RHxjKRFJFtcjAH+1bwRNs6WzZtYU7mCtauWs75yGRvXvM+mtSuoXr+SmvUrUVUl7TYsp7xqGZ23vM8eNe+zO+vYF7LuA9UYG6ID77brw8pO/dncdSAdeg9jrwMOp/eAoQxu1+TrT5qZme2U7X0z7ZM+fZV3e0Q8u+Nh7XIj0nJqRGzI0ecVkkRnBE2c6KyuXMH0uy6DqEZRDTVJWe9I69rVVNGueiPto4qONVV0iI2UsZGyqKKDqtkD2KMpgwOqoj1LS/dmVYd9WN+5P/QYRKdeB7HXfkPZu89ABnqXbzMzayG2l+iclB7ZRAPt0YjXLqQBaTmvgT7zM/o2mU1V6xm9/C879yJZJvo2xuYoZaW6sqq0O+s67MnGTvtQ07UfHXr0p/Pe+9OjzyB69OxNfz/1ZGZmrUBDych8WuitqUbonJbZd4RMrE3LLpkNkr4MfBmgX7/8Z6CUljZNDlgdYq06sVadWV+yO1XturCxQ1eqO3SlpmM3KO9Gaee9KOvei92696bb3n3Yo8c+9Cwtxft3m5lZW5DzGzci9mvGOJpb7XjIDiVyEXE7cDtARUVF3q9R3nl3Jgy+HJW0g5LSrWVJae3P7SkpLQGV0q5sN9p33I12ZbvRsVNnOpR3pqy8M2W7daFDhzK6lpTQdUfehJmZWRtQzLeXdqU1adm5gT61bWsa6LNDysp3Y8w532nqlzUzM7MMbXUixty07N9An9pdB+Y20MfMzMyKWFtNdCal5VBJuVavOyKjr5mZmbUwbTLRiYgFwGsku7KPz2yXdCzQh2RBxBcz283MzKxlaJOJTupHaXm9pANqKyX1JNnIFOC61rQqspmZWVvTVicjExH3Sfolyc7lUyQ9zgebeu4O3E+yuaeZmZm1UG020QGIiAskPQ9cCBwLlAIzgN8Av/RojpmZWcvWphMdgIi4G7i70HGYmZlZ01NEa138uHlIWkbDW0k0ZE9geROG0xb4muXH1ys/vl752Znr1T8i9mrKYMyycaJTQJImRkRFoeNoSXzN8uPrlR9fr/z4ellL0JafujIzM7NWzomOmZmZtVpOdArr9kIH0AL5muXH1ys/vl758fWyouc5OmZmZtZqeUTHzMzMWi0nOmZmZtZqOdEpAEn/Juk5SaskrZU0UdKFkvx51CFpsKSLJd0laYakGkkh6cxCx1ZsJLWXNE7STyVNkLRY0iZJiyTdJ+m4QsdYbCT9h6Q/S5ouaYWkzZKWSXpc0rmSVOgYi52kH6Z/J0PStwodj1k2nqPTzCTdDFwAVAFP8MH+Wl2AvwLjI6K6cBEWD0k3AhdnaRofEfc1dzzFTNIJwGPpj0uAV4F1wMHAsLT+2oj4zwKEV5QkLQR6Am8Ci0iuV39gNCDgAeBT3gomO0lHAC+S/A+zgMsi4ieFjcpsWx5BaEaSziBJcpYAwyPilIg4HRgETAdOBy4qYIjF5k3gf4CzgAOAZwobTlGrAf4CHBMR+6Z/ts6KiEOAs4Fq4HuSji9olMXlbGCPiDg8Ik6NiLMj4kjgEGApcBrwuYJGWKQkdQTuILlODxQ2GrOGOdFpXlem5RURMbu2MiKWkuyiDvBt38JKRMT/RcTlEfHniHir0PEUs4h4MiLOjIjnsrTdQ/KlBHBuswZWxCLi+YhYl6V+KnBz+uOJzRtVi3ENyWjhV4FVBY7FrEH+Qm0mkvoAI4FNwL2Z7RHxDMnw+T7AmOaNztqASWnZp6BRtBxb0rKqoFEUIUmjgW8Cd0fEg4WOx2x7nOg0nxFpOTUiNuTo80pGX7OmMigtFxc0ihZA0gCSkQoAf5HXIakM+B3wPtnnz5kVnXaFDqANGZCWDe10Pj+jr9lOk7QP8Pn0x78UMJSiJOkLwLFAe5IRr7Ek/xP4o4j4ayFjK0L/DQwGzo4I7/JuLYITnebTOS23mRNQx9q07LKLY7E2QlI74C6gK/CEbzVkdRT1Jx1vAb4H3FCYcIqTpLHAN4D703lfZi2Cb101n9o1Ofw8vzWnW0mWL1iAJyJnFRHnR4SATsBQ4EbgB8AESb0KGVuxkFQO/BZYTfLkqFmL4USn+axJy84N9KltW9NAH7NGkXQT8O8kyxmMi4glBQ6pqEXEhoiYFhGXkTwheSjwiwKHVSx+CBwIXBoRnudlLYpvXTWfuWnZv4E+fTP6mu0QST8Fvg4sI0lyZm/nFKvvt8BPgFMltY+IzYUOqMBOJ1mr6XOSMtcWOigtvybpFGBORJzfrNGZNcCJTvOpfbx3qKTyHE9eHZHR1yxvkn4MXAqsAE6MiGkFDqklqiSZq9MO6E6yMF5bV0IyaTuX/dOjW/OEY9Y4vnXVTCJiAfAa0AEYn9ku6ViSJz6WkCyrbpY3SdcBlwErSZKcyQUOqaU6hiTJqQTa/NNFEbFfRCjbQfK4OSRbQCgiDitkrGaZnOg0rx+l5fWSDqitlNQTuCX98TrvrWM7QtK1wBUkX84nRoRHBnOQdLSkz6RbGWS2HQX8Ov3x1957zqxl86aezUzSLSTbPVQBj/PBpp67A/cDZ/of1oSkw/kBcnLEAAAJpElEQVQgAYRkyfkuwGySBcsAiIg2v5K0pE/wwZ5DE4GpObrOiIjrmieq4iXp8yTzcCpJRlqXkPzZGkjy5wzgYZINZHMt8GmApDtIHs/3pp5WlDxHp5lFxAWSngcuJLnfXQrMAH4D/NKjOfXsTrKTdKZBWerauu51/rsiPbJ5BmjziQ7JdbgWOJrkaaKxJEtALCFZVPGuiLi/cOGZWVPxiI6ZmZm1Wp6jY2ZmZq2WEx0zMzNrtZzomJmZWavlRMfMzMxaLSc6ZmZm1mo50TEzM7NWy4mOmZmZtVpOdKxoSIodOO5Izz0u/fnpwr6LnSfpivS9fLTQsbQkkvZLr9vcnXydn0mqlnRoE4VmZgXklZGtmPwuS90+wEnAOuC+LO3P79KImpmkfYHvAM9GxD8KHU8b9d/AF4EbgeMLHIuZ7SQnOlY0IuLzmXWSjiNJdJZna6/jZWAIsH5XxNaMribZc+nqQgfSVkXEUkm3AZdKOiUiHip0TGa243zrylqFiFgfETMiYn6hY9lRknoA5wFvA08VOJy27jdpeXFBozCzneZEx1qFXHN06s7bkFQi6VJJUyVtkLRQ0g2SOqV995B0Y9p3o6TZki5t4HdK0tmSHpW0PD1nvqRfSdpvB97GF4Ey4M7IsgmdpG6SfpjGv77Oe3ha0pU5Yuwr6SZJM9P+qyW9IOnzktTA+/q0pEckvSdpk6RFkp6QdFGW/u0lXSTppfT1N0iaLuk6Sd2z9K/7mUjSBZJeT9/TSkkPSBqW6yJJOlrSY+nvWpO+n9MburCSRkm6N30fmyWtkjRH0t2SPpzZPyKmAq8C4yQd2NBrm1mRiwgfPor2AI4DApjbyH5PZ9TvV3s+8CdgLfAQ8ACwMm17hGT371nAYuBe4Algc9p+VZbf155kl+sguV32bHre9LTufaAiz/f6QnruUVnaOgFT0/alwN+APwJPA+8BVVnOOR6oTM+ZDfwVeAxYk9bdmeWcDum1CWALyRyou9PrsTT5J6Ne/zKS0acgmUf1EPDn9DrWXvf9G/hMfgdUAY+m129u2rYq87z03LOB6rTPa2lsL6U/35DtzwpwIrApbZuUxvdX4JW0/tYcn8d16TnfKvTfAx8+fOz4UfAAfPho6KDpEp0AZgC96rT1BZanbVPSL9qyOu0np22rgU4Zr1v7JfgM0Cej7aK0bQ7QrpHvs1P6pbupbgx12j+bvuZDma8JlAIfzqjblyTZ2gJ8DlDG+56Uvt7nM867Ka2fCRyU5fd8IqPux2n/6UDvOvXlfJAIvtjAZ/I2MLBOW0fg4bTtVxnn9eKDJO2rGW1n1UmA5ma0PZnWn5PluvYARub4TE5Lz/t7of8e+PDhY8ePggfgw0dDRxMnOh/Jct6NdZKZPbO0T07bj6lT151kFGcN0DNHPA+l553ayPd5RG2CkaP9srT9G418vevT/tfnaK9I21+tU9czTbSqgaGN+B3ldRKPE7O070kyglZvlCrjMzkly3mjapOgjPrvZfuM67TXJlZzM+prR8K65flnb1B63uJC/z3w4cPHjh+eo2NtxWaS/7PPNCctJ0bE8izts9OyV52640m+5J+JiPdy/L5n0vLIRsbXMy1X5Gh/OS2vkHSupG7beb2Pp+W9OdpfJUlCDpNUltZ9mOSW3IuRzFHZnpFAZ+DdiHgsszG9ng+mPx6X5fwtQLZH6GekZa+M+mPT8q4c8fw+R33ttbtb0lGSSnP0y/R+Wu6Vaz6TmRU/JzrWViyJiC1Z6tem5cIc59W2l9Wp2z8tT861kCHJLR2AvRoZX9e0XJ2tMSKeSV+zJ8kX+vuSpkm6XdJJWU6pjfGVHPHVkCQpJSS3bwD6p+UMGqd3Wr7TQJ+3MvrWtTjbZxIRtdegY0ZTn+38vrk56q8EXgc+RjLnaJWkZyR9X9L+Oc6BDz6LUpJH/s2sBfI6OtZW1Oxke121IwIzgQnb6ftSI1+zMi13z9UhIq6QdCvJ3JEPAUcBXwK+JOlR4OQ6iUNtjPeQTPZtyMZGxpipdpRjmyfEsvTJJp9rvsMiYomkkSSjSieSXLfRwDHAdyV9JSJ+k+XU2s+imuQWnZm1QE50zPK3IC2nRMOLGOaj9hZYj4Y6RcQ7JPOKbgSQ9CGSp68+QvJ4+u11YjwAuLaRt6EA5qXl4Eb2rx0FG9BAn9q2RY18zYYsIoltvxztueqJiBqSW5dPAkjajWTS+HXAzZLuqzOSVKv2s1gWEQ0lc2ZWxHzryix/j5PM+TmhEXNlGmsqycjKAEnljT0pIp4H7kh/rLs30yNpOT6PGJ4keV9jJQ1pRP/aeT69JY3LbFSyAOKp6Y9P5xFHLrXznj6Toz1X/TYiYl1EXE+SrJWRPbk7OC1fa3SEZlZ0nOiY5SkilgI3A92Av0k6KLNPuvjg+ZL2buRrbiC5zdWeZJJv5uudLukYSSUZ9eXACemP8+o0/Q/JHJOrJF0oaZvRW0ljJG1NhNKJ1beS/Lvwl8yF8iSVSjq1Tv8NaX+Am5Ts01Xbtwz4Jck8oAkR8cL2rkEj/JpkrZ7jJX0pI7YzgU9lO0nStyT1zVJfQfIYfg3Z52jVTiR/ameCNrPC8q0rsx1zOclTQZ8G3pT0Oskk2TKSdWqGkCy+N4Rkob3GuJ9k3sgJbLtZ6bEk2xEskzQJWEYygXksyePuM4DbajtHxAJJnyTZCPUXwHckTSV5qqsXMDAt76H+k1mXpW0fB6ZKepEkCegJHJKWdefdfI/kUfXjgNmSngQ2AEeTJBHzyWOkpSERsUjSV0kWGbw9/e+ZJLfHxgD/C1yS5dTvAv8jaTrJej8bST6jsSRJ3XURsTjLeSeQzD/6W1PEb2aF4REdsx0QEZsj4iySicEPkSQNp5F8ebYjWbH3dD546qgx7iBJEj6b5XHmO0jWxpkFDCO5JTWK5PH4S4BREbEqI8angKHAD0nmAI0BPgn0I3ls/kqSndLrnrOR5HbTeSSrPQ8DzgQOAt4ALszoX0UyP+jrwDSSR+9PIxlN+jFweES8ncc1aFBE3AWMI1mp+UA+uDU2HvhZjtMuJEmOatL4Tid5CuxB4KSI2Gb7DElDgcOBJyJiVlPFb2bNT55jZ1Y80qeqvgKMi4hs6/5YM5B0A0kCeWp493KzFs2JjlkRkbQPyajNpIg4dnv9reml86reAl6JiOMLHY+Z7RzfujIrIhGxBPgv4BhJHy10PG3UVSQrX3+j0IGY2c7ziI6ZmZm1Wh7RMTMzs1bLiY6ZmZm1Wk50zMzMrNVyomNmZmatlhMdMzMza7Wc6JiZmVmr9f8BH5cNcSm+4McAAAAASUVORK5CYII=\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N3=10000\n",
"tmax = 4\n",
"t = np.linspace(0, tmax, N3)\n",
"dt3 = tmax/N3\n",
"y0 = 0 # initial position\n",
"v0 = 0 # initial velocity\n",
"m0 = .25 # initial mass\n",
"\n",
"#Euler approximation for rocket function\n",
"euler_sol_2 = np.zeros([N3,3])\n",
"euler_sol_2[0,0] = y0\n",
"euler_sol_2[0,1] = v0\n",
"euler_sol_2[0,2] = m0\n",
"for i in range(N3-1):\n",
" euler_sol_2[i+1] = euler_step(euler_sol_2[i], rocket, dt3)\n",
"\n",
"#Heun approximation for rocket function\n",
"heun_sol_2 = np.zeros([N3,3])\n",
"heun_sol_2[0,0] = y0\n",
"heun_sol_2[0,1] = v0\n",
"heun_sol_2[0,2] = m0\n",
"for i in range(N3-1):\n",
" heun_sol_2[i+1] = heun_step(heun_sol_2[i], rocket, dt3)\n",
"\n",
"#max altitude calculations with rocket function\n",
"y_max_euler2 = max(euler_sol_2[:,0])\n",
"y_max_heun2 = max(heun_sol_2[:,0])\n",
"print('Max Height (Euler, N=10000):',round(y_max_euler2,6),'m')\n",
"print('Max Height (Heun, N=10000):',round(y_max_heun2,6),'m')\n",
"\n",
"#Plot creation/formatting\n",
"plt.plot(t,euler_sol_2[:,0],label='Euler');\n",
"plt.plot(t,heun_sol_2[:,0],label='Heun');\n",
"plt.title('Rocket Height vs Time with\\n Drag and Gravity (N=10000)\\n');\n",
"plt.xlabel('Time (seconds)');\n",
"plt.ylabel('Rocket Height (m)');\n",
"plt.legend(bbox_to_anchor=(1, 0.8));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__Discussion:__ In the above plot we can see the converged approximations of the solution with both the Euler explicit method and the Heun implicit method."
]
},
{
"cell_type": "code",
"execution_count": 311,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"N4=5000\n",
"m03=.25 #define intial mass\n",
"u3=250 #define thrust velocity\n",
"dmdt3=.05 #define constant mass change rate\n",
"t_max3=4 #define max time\n",
"t4 = np.linspace(0, t_max3, N4)\n",
"\n",
"#Euler approximation mf/m0 vs velocity\n",
"mfm0_euler3 = np.zeros(N4)\n",
"for i in range(N4):\n",
" mfm0_euler3[i] = euler_sol_2[i,2]/m03\n",
"plt.plot(mfm0_euler3,euler_sol_2[:,1],label='Euler')\n",
"\n",
"#Heun approximation mf/m0 vs velocity\n",
"mfm0_heun3 = np.zeros(N4)\n",
"for i in range(N4):\n",
" mfm0_heun3[i] = heun_sol_2[i,2]/m03\n",
"plt.plot(mfm0_heun3,heun_sol_2[:,1],label='Heun')\n",
"\n",
"#Analytical calculation from previous problem plotted again\n",
"plt.plot(mfm0_analytical2,v_analytical2,label='Analytical')\n",
"\n",
"#Plot Formatting\n",
"plt.title('Mass Ratio vs Velocity with\\n Drag and Gravity (N=5000)\\n');\n",
"plt.xlabel('Mass Ratio $m_{current} / m_0$');\n",
"plt.ylabel('Velocity (m/s)');\n",
"plt.legend();"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__Discussion:__ In the above plot we compare the mass ratio over time to the calculated velocity for a Euler explicit approximation of the solution, an implicit Heun approximation of the solution, and the analytical solution based on the Tsiolkovsky equation. We can observe that despite a large number of timesteps, the solutions do not converge because the Tsiolkovsky equation does not consider the effects of drag and gravity on the rocket. However, the solutions do converge when the mass ratio is equal to one becuase drag and gravity are negligible at that point."
]
},
{
"cell_type": "code",
"execution_count": 329,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#Comparison of rocket and simple_rocket solutions\n",
"plt.plot(t2,euler_sol2[:,1],label='Euler Explicit Simple Rocket');\n",
"plt.plot(t,euler_sol_2[:,0],label='Euler Explicit Rocket');\n",
"plt.title('Rocket Height vs Time with and \\nwithout Drag and Gravity (N=10000)\\n');\n",
"plt.xlabel('Time (seconds)');\n",
"plt.ylabel('Rocket Height (m)');\n",
"plt.legend(bbox_to_anchor=(1, 0.8));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__Discussion:__ We can see that modifying the defining function to account for air resistance and gravity does change the approximation of the solution as seen above. The simple rocket function solution does not incorperate drag or gravity, while the rocket function solution does. Interestingly, the data suggests that drag and gravity would cause the rocket to intially accelerate slower, but reach a higher maximum altitude before reaching a final mass of 0.05 kg at 4 seconds after launch."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"3. Solve for the mass change rate that results in detonation at a height of 300 meters. Create a function `f_dm` that returns the final height of the firework when it reaches $m_{f}=0.05~kg$. The inputs should be \n",
"\n",
"$f_{m}= f_{m}(\\frac{dm}{dt},~parameters)$\n",
"\n",
"where $\\frac{dm}{dt}$ is the variable we are using to find a root and $parameters$ are the known values, `m0=0.25, c=0.18e-3, u=250`. When $f_{m}(\\frac{dm}{dt}) = 0$, we have found the correct root. \n",
"\n",
"Plot the height as a function of time and use a star to denote detonation at the correct height with a `'*'`-marker\n",
"\n",
"Approach the solution in two steps, use the incremental search [`incsearch`](../notebooks/04_Getting_to_the_root.ipynb) with 5-10 sub-intervals _we want to limit the number of times we call the function_. Then, use the modified secant method to find the true root of the function.\n",
"\n",
"a. Use the incremental search to find the two closest mass change rates within the interval $\\frac{dm}{dt}=0.05-0.4~kg/s.$\n",
"\n",
"b. Use the modified secant method to find the root of the function $f_{m}$.\n",
"\n",
"c. Plot your solution for the height as a function of time and indicate the detonation with a `*`-marker."
]
},
{
"cell_type": "code",
"execution_count": 144,
"metadata": {},
"outputs": [],
"source": [
"def f_dm(dmdt,m0=0.25, c=0.18e-3, u=250):\n",
" ''' define a function f_m(dmdt) that returns \n",
" height_desired-height_predicted[-1]\n",
" here, the time span is based upon the value of dmdt\n",
" arguments:\n",
" dmdt: the unknown mass change rate\n",
" m0: the known initial mass\n",
" c: the known drag in kg/m\n",
" u: the known speed of the propellent\n",
" returns:\n",
" error: the difference between height_desired and height_predicted[-1]\n",
" when f_m(dmdt)= 0, the correct mass change rate was chosen\n",
" '''\n",
" t_max = (m0-.05)/dmdt\n",
" N = 5000\n",
" t = np.linspace(0,t_max,N)\n",
" dt = t_max/N\n",
" temp_sol = np.zeros([N,3])\n",
" temp_sol[0,0] = 0\n",
" temp_sol[0,1] = 0\n",
" temp_sol[0,2] = m0\n",
" for i in range(N-1):\n",
" temp_sol[i+1] = heun_step(temp_sol[i], lambda state:rocket(state,dmdt=dmdt), dt)\n",
" return temp_sol[-1,0]-300"
]
},
{
"cell_type": "code",
"execution_count": 145,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of brackets: 1\n",
"\n",
"The correct dmdt is in the interval 0.05 and 0.088889\n"
]
}
],
"source": [
"def incsearch(func,xmin,xmax,ns=50):\n",
" '''incsearch: incremental search root locator\n",
" xb = incsearch(func,xmin,xmax,ns):\n",
" finds brackets of x that contain sign changes\n",
" of a function on an interval\n",
" arguments:\n",
" func = name of function\n",
" xmin, xmax = endpoints of interval\n",
" ns = number of subintervals (default = 50)\n",
" returns:\n",
" xb(k,1) is the lower bound of the kth sign change\n",
" xb(k,2) is the upper bound of the kth sign change\n",
" If no brackets found, xb = [].'''\n",
" x = np.linspace(xmin,xmax,ns)\n",
" f = np.zeros(ns)\n",
" for i in range(ns):\n",
" f[i] = func(x[i])\n",
" sign_f = np.sign(f)\n",
" delta_sign_f = sign_f[1:]-sign_f[0:-1]\n",
" i_zeros = np.nonzero(delta_sign_f!=0)\n",
" nb = len(i_zeros[0])\n",
" xb = np.block([[ x[i_zeros[0]+1]],[x[i_zeros[0]] ]] ) \n",
" if nb==0:\n",
" print('no brackets found\\n')\n",
" print('check interval or increase ns\\n')\n",
" else:\n",
" print('number of brackets: {}\\n'.format(nb))\n",
" return xb\n",
"\n",
"\n",
"#Incremental search\n",
"dmdt_incr = incsearch(f_dm,.05,.4,ns=10)\n",
"print('The correct dmdt is in the interval',round(float(dmdt_incr[1,:]),6),'and',round(float(dmdt_incr[0,:]),6))\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__Discussion:__ So from the above code which executes an incremental search of the function $f_{dm}$. We can conclude that there is one zero for the function which is between values of 0.05 and 0.09 kg/s for $dm/dt$"
]
},
{
"cell_type": "code",
"execution_count": 147,
"metadata": {},
"outputs": [],
"source": [
"#Part B\n",
"def mod_secant(func,dx,x0,es=0.0001,maxit=50):\n",
" '''mod_secant: Modified secant root location zeroes\n",
" root,[fx,ea,iter]=mod_secant(func,dfunc,xr,es,maxit,p1,p2,...):\n",
" uses modified secant method to find the root of func\n",
" arguments:\n",
" func = name of function\n",
" dx = perturbation fraction\n",
" xr = initial guess\n",
" es = desired relative error (default = 0.0001 )\n",
" maxit = maximum allowable iterations (default = 50)\n",
" p1,p2,... = additional parameters used by function\n",
" returns:\n",
" root = real root\n",
" fx = func evaluated at root\n",
" ea = approximate relative error ( )\n",
" iter = number of iterations'''\n",
" iter = 0;\n",
" xr=x0\n",
" for iter in range(0,maxit):\n",
" xrold = xr;\n",
" dfunc=(func(xr+dx)-func(xr))/dx;\n",
" xr = xr - func(xr)/dfunc;\n",
" if xr != 0:\n",
" ea = abs((xr - xrold)/xr) * 100;\n",
" else:\n",
" ea = abs((xr - xrold)/1) * 100;\n",
" if ea <= es:\n",
" break\n",
" return xr,[func(xr),ea,iter]"
]
},
{
"cell_type": "code",
"execution_count": 148,
"metadata": {
"scrolled": true
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0.07908149645437243 kg/s is the correct value for dmdt to explode at a 300 meter height\n",
"the solve took 5 iterations with the mod_secant function\n"
]
}
],
"source": [
"dmdt_sec,out = mod_secant(f_dm,0.000001,.06,es=0.00000000001)\n",
"print(dmdt_sec, 'kg/s is the correct value for dmdt to explode at a 300 meter height')\n",
"print('the solve took ',out[2],' iterations with the mod_secant function')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__Discussion:__ From the use of the modified secant method, we can conclude that using a mass change rate of approximately 0.079081 kg/s would result in a mass of 0.05 kg and therefore detonation at a height of 300 meters."
]
},
{
"cell_type": "code",
"execution_count": 233,
"metadata": {},
"outputs": [],
"source": [
"#Import Runga Kutta explicit integral approximation\n",
"def rk2_step(state, rhs, dt):\n",
" '''Update a state to the next time increment using modified Euler's method.\n",
" Arguments\n",
" ---------\n",
" state : array of dependent variables\n",
" rhs : function that computes the RHS of the DiffEq\n",
" dt : float, time increment\n",
" Returns\n",
" -------\n",
" next_state : array, updated after one time increment'''\n",
" mid_state = state + rhs(state) * dt*0.5 \n",
" next_state = state + rhs(mid_state)*dt\n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 319,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Time of Detonation = 2.529 seconds\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 648x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#Part C\n",
"#Redefine solutions with updated mass change rate from modified secant function\n",
"N = 10000\n",
"y0 = 0 # initial position\n",
"v0 = 0 # initial velocity\n",
"m0 = .25 # initial mass\n",
"t_max = .2/dmdt_sec #defines max time (300m at about 2.5 s)\n",
"t = np.linspace(0, t_max, N)\n",
"dt = t_max/N\n",
"\n",
"#Runga Kutta Explicit\n",
"sol_3_RK = np.zeros([N,3])\n",
"sol_3_RK[0,0] = y0\n",
"sol_3_RK[0,1] = v0\n",
"sol_3_RK[0,2] = m0\n",
"for i in range(N-1):\n",
" sol_3_RK[i+1] = rk2_step(sol_3_RK[i], lambda state:rocket(state,dmdt=dmdt_sec), dt)\n",
"\n",
"#Heun Implicit\n",
"sol_3_heun = np.zeros([N,3])\n",
"sol_3_heun[0,0] = y0\n",
"sol_3_heun[0,1] = v0\n",
"sol_3_heun[0,2] = m0\n",
"for i in range(N-1):\n",
" sol_3_heun[i+1] = heun_step(sol_3_heun[i], lambda state:rocket(state,dmdt=dmdt_sec), dt)\n",
"\n",
"#Formatting plots and output\n",
"fig= plt.figure(figsize=(9,6))\n",
"plt.plot(t,sol_3_RK[:,0],linestyle='-',linewidth=2.5,label='Runga Kutta Explicit');\n",
"plt.scatter(t_max,sol_3_RK[-1,0],marker=(8,2,0),s=300,c='r',label='Detonation');\n",
"plt.plot(t,sol_3_heun[:,0],linestyle=':',linewidth=2.5,label='Heun Implicit');\n",
"plt.scatter(t_max,sol_3_heun[-1,0],marker=(8,2,0),s=300,c='r');\n",
"plt.xlim(0,3);\n",
"plt.grid(True)\n",
"plt.xlabel('Time Since Launch (s)');\n",
"plt.ylabel('Rocket Height (m) \\n');\n",
"plt.title('Firework Height vs Time (N=10000)\\n');\n",
"plt.legend(bbox_to_anchor=(1, 0.8));\n",
"print('Time of Detonation = ',round(t_max,4),'seconds')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"__Discussion:__ The above plot shows the height of the rocket over time until its explosion at 300 meters and a time of approximately 2.53 seconds from launch. This is based on a mass change rate of approximately 0.079081 kg/s as previously calculated. We can also see in the plot that the Runga Kutta explicit and the Heun implicit solutions have converged at this number of timesteps (N=10000)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## References\n",
"\n",
"1. Math 24 _Rocket Motion_. <https://www.math24.net/rocket-motion/\\>\n",
"\n",
"2. Kasdin and Paley. _Engineering Dynamics_. [ch 6-Linear Momentum of a Multiparticle System pp234-235](https://www.jstor.org/stable/j.ctvcm4ggj.9) Princeton University Press \n",
"\n",
"3. <https://en.wikipedia.org/wiki/Specific_impulse>\n",
"\n",
"4. <https://www.apogeerockets.com/Rocket_Motors/Estes_Motors/13mm_Motors/Estes_13mm_1_4A3-3T>"
]
}
],
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"display_name": "Python 3",
"language": "python",
"name": "python3"
},
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"codemirror_mode": {
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