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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": 297,
"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": 298,
"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",
" #does not consider drag (c) or gravity (g)\n",
" dstate = np.zeros(np.shape(state))\n",
" dstate = np.array([state[1], (u/state[2])*(dmdt), -dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 299,
"metadata": {},
"outputs": [],
"source": [
"#taken from module 3 notebook 3 'get oscilations'\n",
"def implicit_heun(state, rhs, dt, etol=0.000001, maxiters=100):\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": 300,
"metadata": {},
"outputs": [],
"source": [
"#taken from module 3 notebook 3 'get oscilations'\n",
"def explicit_rk2(state, rhs, dt):\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": 301,
"metadata": {},
"outputs": [],
"source": [
"def tsiolkovsky(state, v, u=250):\n",
"\n",
" '''Computes the Analytical Tsiolkovsky Equation for the given parameters.\n",
" \n",
" Arguments\n",
" ---------- \n",
" state : array of three dependent variables [y v m]^T\n",
" v : final velocity (m/s)\n",
" u : speed of propellent (m/s) (default is 250)\n",
" \n",
" Returns\n",
" -------\n",
" final mass of the rocket\n",
" '''\n",
" return np.exp(-(v-state[1])/u)"
]
},
{
"cell_type": "code",
"execution_count": 302,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The different methods all converge to the same value.\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 648x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#set initial conditions\n",
"y0 = 0 #initial height (m)\n",
"v0 = 0 #inital velocity (m/s)\n",
"m0 = 0.25 #inital mass (kg)\n",
"dmdt = 0.05 #mass rate change (kg/s)\n",
"m = np.linspace(mf,m0,20)\n",
"initial_state = np.array([y0, v0, m0])\n",
"\n",
"#set final conditions\n",
"mf = 0.05 #final mass (kg)\n",
"tf = abs((m0-mf)/dmdt) #final time (s)\n",
"N = 1000 #number of steps\n",
"times = np.linspace(0, tf, N) #time (s)\n",
"\n",
"#set up initial arrays\n",
"heun_array = np.zeros([N,3])\n",
"heun_array[0,0], heun_array[0,1], heun_array[0,2] = v0, v0, m0\n",
"\n",
"rk2_array = np.zeros([N,3])\n",
"rk2_array[0,0], rk2_array[0,1], rk2_array[0,2] = v0, v0, m0\n",
"\n",
"tsiolkovsky_array_implicit = np.zeros(N)\n",
"tsiolkovsky_array_implicit[0] = m0\n",
"\n",
"tsiolkovsky_array_explicit = np.zeros(N)\n",
"tsiolkovsky_array_explicit[0] = m0\n",
"\n",
"#integrate\n",
"for i in range (N-1):\n",
" heun_array[i+1] = implicit_heun(heun_array[i], simplerocket, times[i+1]-times[i])\n",
" rk2_array[i+1] = explicit_rk2(rk2_array[i], simplerocket, times[i+1]-times[i])\n",
" tsiolkovsky_array_implicit[i+1] = tsiolkovsky(initial_state, heun_array[i+1][1])\n",
" tsiolkovsky_array_explicit[i+1] = tsiolkovsky(initial_state, rk2_array[i+1][1])\n",
"\n",
"#plot data\n",
"plt.rcParams['figure.figsize'] = [9, 6]\n",
"plt.plot(heun_array[:,0], heun_array[:,2]/m0, linewidth = 16, label = 'Implicit Heun');\n",
"plt.plot(rk2_array[:,0], rk2_array[:,2]/m0, linewidth = 12, label = 'Explicit rk2');\n",
"plt.plot(heun_array[1:,0], tsiolkovsky_array_implicit[1:], linewidth = 8, label = 'Implicit Tsiolkovsky');\n",
"plt.plot(rk2_array[1:,0], tsiolkovsky_array_explicit[1:], linewidth = 4, label = 'Explicit Tsiolkovsky');\n",
"plt.xlabel('Velocity (m/s)');\n",
"plt.ylabel('m/m0');\n",
"plt.legend();\n",
"print (\"The different methods all converge to the same value.\")"
]
},
{
"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": 303,
"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",
" dstate: array of three derivatives [v (u/m*dmdt-g-c/mv^2) -dmdt]^T\n",
" '''\n",
" dstate = np.zeros(np.shape(state))\n",
" g = 9.81 #acceleration of gravity (m/s^2)\n",
" dstate = np.array([state[1], (u/state[2])*(dmdt)-g-(c/state[2])*state[1]**2, -dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 304,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The final height reached by the simple rocket is 597.6398815719729 m.\n",
"The final height reached by the rocket is 425.4432417503019 m.\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1008x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"### The Tsiolkovsky graphs have not been included because we are testing\n",
"### the numerical solutions, and we already know they are equal in value.\n",
"\n",
"#plot simplerocket data\n",
"plt.rcParams['figure.figsize'] = [14, 6]\n",
"plt.plot(times, heun_array[:,0], linewidth = 8, label = 'Implicit Heun (simplerocket)');\n",
"plt.plot(times, rk2_array[:,0], linewidth = 3, label = 'Explicit rk2 (simplerocket)');\n",
"\n",
"#find final height for simplerocket (using explicit solution because it is typically more accurate)\n",
"print (\"The final height reached by the simple rocket is {} m.\".format(rk2_array[:,0][-1]))\n",
"\n",
"#integrate for rocket function\n",
"for i in range (N-1):\n",
" heun_array[i+1] = implicit_heun(heun_array[i], rocket, times[i+1]-times[i])\n",
" rk2_array[i+1] = explicit_rk2(rk2_array[i], rocket, times[i+1]-times[i])\n",
"\n",
"#plot rocket data\n",
"plt.rcParams['figure.figsize'] = [14, 6]\n",
"plt.plot(times, heun_array[:,0], linewidth = 8, label = 'Implicit Heun (rocket)');\n",
"plt.plot(times, rk2_array[:,0], linewidth = 3, label = 'Explicit rk2 (rocket)');\n",
"plt.xlabel('Time (s)');\n",
"plt.ylabel('Height (m)');\n",
"plt.legend();\n",
"\n",
"#find final height for rocket (using explicit solution because it is typically more accurate)\n",
"print (\"The final height reached by the rocket is {} m.\".format(rk2_array[:,0][-1]))"
]
},
{
"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": 305,
"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",
" height_desired = 300 # desired detonation height (m)\n",
" mf = 0.05 #final mass (kg)\n",
" tf = (m0-mf)/dmdt #final time (s)\n",
" t = np.linspace(0,tf,1000)\n",
" dt = t[1] - t[0] #time step (s)\n",
" N = int(tf/dt) #number of steps\n",
"\n",
" #initialize solution array\n",
" solution = np.zeros([N,3])\n",
" solution [0,0] = 0\n",
" solution [0,1] = 0\n",
" solution [0,2] = m0\n",
" \n",
" for i in range(N-1):\n",
" solution[i+1] = implicit_heun(solution[i], lambda state: rocket(state, dmdt = dmdt, u = u), dt)\n",
" \n",
" error = height_desired-solution[-1,0]\n",
" \n",
" return error"
]
},
{
"cell_type": "code",
"execution_count": 306,
"metadata": {},
"outputs": [],
"source": [
"#taken from module 3 notebook 4 'getting to the root'\n",
"def incsearch(func,xmin,xmax,ns=10):\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",
" ---------\n",
" func = name of function\n",
" xmin, xmax = endpoints of interval\n",
" ns = number of subintervals (default = 10)\n",
" returns:\n",
" ---------\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",
"\n",
" \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"
]
},
{
"cell_type": "code",
"execution_count": 307,
"metadata": {},
"outputs": [],
"source": [
"#taken from module 3 notebook 4 'getting to the root'\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",
" ----------\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",
" --------\n",
" root = real root\n",
" fx = func evaluated at root\n",
" ea = approximate relative error ( )\n",
" iter = number of iterations'''\n",
"\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]\n"
]
},
{
"cell_type": "code",
"execution_count": 308,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"A.\n",
"\n",
"number of brackets: 1\n",
"\n",
"0.08888888888888889\n",
"0.05\n"
]
}
],
"source": [
"print ('A.\\n')\n",
"mn = 0.05\n",
"mx = 0.4\n",
"\n",
"xb = incsearch(f_m,mn,mx)\n",
"print(xb[0,:][0])\n",
"print(xb[1,:][0])"
]
},
{
"cell_type": "code",
"execution_count": 309,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"B.\n",
"\n",
"0.07890352919218331\n"
]
}
],
"source": [
"print ('B.\\n')\n",
"dmdt,out = mod_secant(f_m,0.0001,0.08,es=0.0001)\n",
"print(dmdt)"
]
},
{
"cell_type": "code",
"execution_count": 310,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"C.\n",
"\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 648x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"print ('C.\\n')\n",
"height_desired = 300 # desired detonation height (m)\n",
"dmdt = 0.07890352919218331\n",
"m0 = 0.25 #initial mass (kg)\n",
"mf = 0.05 #final mass (kg)\n",
"tf = (m0-mf)/dmdt #final time (s)\n",
"t = np.linspace(0,tf,1000)\n",
"dt = t[1] - t[0] #time step (s)\n",
"N = int(tf/dt) #number of steps\n",
"\n",
"#initialize solution array\n",
"solution = np.zeros([N,3])\n",
"solution [0,0] = 0\n",
"solution [0,1] = 0\n",
"solution [0,2] = m0\n",
"\n",
"#Calculate solution\n",
"for i in range(N-1):\n",
" solution[i+1] = implicit_heun(solution[i], lambda state: rocket(state, dmdt = dmdt, u = 250), dt)\n",
" \n",
"#Plot results\n",
"plt.rcParams['figure.figsize'] = [9, 6]\n",
"plt.plot(t[:N], solution[:,0], label = 'Rocket height')\n",
"plt.plot(t[-1], 300, '*', markersize = 16, label = 'Detonation height')\n",
"plt.xlabel('Time (s)')\n",
"plt.ylabel('Height (m)')\n",
"plt.legend();"
]
},
{
"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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