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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": 103,
"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": 104,
"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",
" \n",
" Arguments\n",
" ---------- \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",
" \n",
" Returns\n",
" -------\n",
" derivs: array of three derivatives [v (u/m*dmdt-g-c/mv^2) -dmdt]^T\n",
" '''\n",
" dstate = np.array([state[1], (u/(state[2])*dmdt), -dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 105,
"metadata": {},
"outputs": [],
"source": [
"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",
" \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",
" etol : tolerance in error for each time step corrector\n",
" maxiters: maximum number of iterations each time step can take\n",
" \n",
" Returns\n",
" -------\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",
" \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",
" \n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 106,
"metadata": {},
"outputs": [],
"source": [
"def rk2_step(state, rhs, dt):\n",
" '''Update a state to the next time increment using modified Euler's method.\n",
" \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",
" \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",
" \n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 107,
"metadata": {},
"outputs": [],
"source": [
"#Setting I.C.\n",
"v0 = 0\n",
"y0 = 0\n",
"m0 = 0.25\n",
"dm = 0.05\n",
"dmdt = 0.05\n",
"N=25\n",
"\n",
"t=np.linspace(0, 4, N)\n",
"dt = t[1]-t[0]\n",
"u = 250\n",
"mf = 0.05\n",
"m = np.linspace(mf, m0, N)\n",
"\n",
"num_heun = np.zeros([N,3])\n",
"num_rk2 = np.zeros([N,3])\n",
"\n",
"num_heun[0,0] = y0\n",
"num_heun[0,1] = v0\n",
"num_heun[0,2] = m0\n",
"\n",
"num_rk2[0,0] = y0\n",
"num_rk2[0,1] = v0\n",
"num_rk2[0,2] = m0\n",
"\n",
"d_m = m/m0\n",
"v_f = -np.log(m/m0)*250\n",
"\n",
"for i in range(N-1):\n",
" num_heun[i+1] = heun_step(num_heun[i], simplerocket, dt)\n",
" num_rk2[i+1] = rk2_step(num_rk2[i], simplerocket, dt)"
]
},
{
"cell_type": "code",
"execution_count": 108,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8,8))\n",
"plt.plot(num_heun[:,2]/0.25, num_heun[:,1], label='Heuns Method (Implicit)', color='red')\n",
"plt.plot(num_rk2[:,2]/0.25, num_rk2[:,1], 'o', label='RK2 Method (Explicit)', color='black')\n",
"plt.plot(d_m, v_f, '--', label='Tsiolkovskys Equation', color='green') \n",
"plt.xlabel(\"Mass Ratio\")\n",
"plt.ylabel(\"Velocity (m/s)\")\n",
"plt.legend(loc=\"best\")\n",
"plt.grid()"
]
},
{
"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": 109,
"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",
" \n",
" Arguments\n",
" ---------- \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",
" -------\n",
" derivs: array of three derivatives [v (u/m*dmdt-g-c/mv^2) -dmdt]^T\n",
" '''\n",
" dstate = np.array([state[1], u/state[2]*dmdt-9.81-c/state[2]*state[1]**2, -dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 110,
"metadata": {},
"outputs": [],
"source": [
"num_heun_rocket = np.zeros([N,3])\n",
"num_rk2_rocket = np.zeros([N,3])\n",
"\n",
"num_heun_rocket[0,0] = y0\n",
"num_heun_rocket[0,1] = v0\n",
"num_heun_rocket[0,2] = m0\n",
"\n",
"num_rk2_rocket[0,0] = y0\n",
"num_rk2_rocket[0,1] = v0\n",
"num_rk2_rocket[0,2] = m0\n",
"\n",
"for i in range(N-1):\n",
" num_heun_rocket[i+1] = heun_step(num_heun_rocket[i], rocket, dt)\n",
" num_rk2_rocket[i+1] = rk2_step(num_rk2_rocket[i], rocket, dt)"
]
},
{
"cell_type": "code",
"execution_count": 111,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize=(8,8))\n",
"plt.plot(num_heun_rocket[:,2]/0.25, num_heun_rocket[:,1], label='Heuns Method (Implicit)', color='red')\n",
"plt.plot(num_rk2_rocket[:,2]/0.25, num_rk2_rocket[:,1], 'o', label='RK2 Method (Explicit)', color='black')\n",
"plt.plot(d_m, v_f, '--', label = 'Tsiolkovskys Equation', color='green')\n",
"plt.xlabel('Mass Ratio')\n",
"plt.ylabel('Velocity (m/s)')\n",
"plt.legend(loc=\"best\")\n",
"plt.grid()"
]
},
{
"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": 4,
"metadata": {},
"outputs": [],
"source": [
"def f_m(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",
" \n",
" arguments:\n",
" ---------\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",
" \n",
" returns:\n",
" --------\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",
" \n",
" return error"
]
},
{
"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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