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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": 68,
"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": 69,
"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",
" \n",
" derivs = np.array([state[1], (u/state[2])*dmdt, -dmdt])\n",
" return derivs\n",
"\n",
"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",
" \n",
" mid_state = state + rhs(state) * dt*0.5 \n",
" next_state = state + rhs(mid_state)*dt\n",
" \n",
" return next_state\n",
"\n",
"def heun_step(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": 70,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f242233b7f0>"
]
},
"execution_count": 70,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"m_0 = .25\n",
"m_f = .05\n",
"dmdt = .05\n",
"t_total = (m_0 - m_f)/dmdt\n",
"u = 250\n",
"\n",
"# Tsiolkovsky\n",
"m = np.linspace(m_0, m_f)\n",
"v = -u*np.log(m/m_0)\n",
"\n",
"# Runge-Cutta Explicit\n",
"N_rk2 = 50\n",
"dt_rk2 = t_total/N_rk2\n",
"\n",
"num_sol_rk2 = np.zeros([N_rk2, 3])\n",
"\n",
"num_sol_rk2[0,0] = 0\n",
"num_sol_rk2[0,1] = 0\n",
"num_sol_rk2[0,2] = m_0\n",
"\n",
"for i in range(N_rk2 - 1):\n",
" num_sol_rk2[i+1] = rk2_step(num_sol_rk2[i], simplerocket, dt_rk2)\n",
" \n",
"# Heun Method Implicit\n",
"N_heun = 50\n",
"dt_heun = t_total/N_heun\n",
"\n",
"num_sol_heun = np.zeros([N_heun, 3])\n",
"\n",
"num_sol_heun[0,0] = 0\n",
"num_sol_heun[0,1] = 0\n",
"num_sol_heun[0,2] = m_0\n",
"\n",
"for i in range(N_heun - 1):\n",
" num_sol_heun[i+1] = heun_step(num_sol_heun[i], simplerocket, dt_heun)\n",
" \n",
"fig = plt.figure(figsize=(10,6))\n",
"plt.plot(m/m_0, v, label = 'Tsiolkovsky Equation')\n",
"plt.plot(num_sol_rk2[:,2]/m_0, num_sol_rk2[:,1], '--', label = 'Explicit Runge-Kutta Method')\n",
"plt.plot(num_sol_heun[:,2]/m_0, num_sol_heun[:,1], ':', label = 'Implicit Heun Method')\n",
"plt.title('Numerical Solution Convergence Test')\n",
"plt.legend(loc='best')"
]
},
{
"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": 71,
"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",
" derivs = np.array([state[1], (u/state[2])*dmdt - 9.81 - (c/state[2])*state[1]**2, -dmdt])\n",
" return derivs"
]
},
{
"cell_type": "code",
"execution_count": 72,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f24222b2390>"
]
},
"execution_count": 72,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# Runge-Cutta Explicit\n",
"N_rk2_2 = 50\n",
"dt_rk2_2 = t_total/N_rk2_2\n",
"\n",
"num_sol_rk2_2 = np.zeros([N_rk2_2, 3])\n",
"\n",
"num_sol_rk2_2[0,0] = 0\n",
"num_sol_rk2_2[0,1] = 0\n",
"num_sol_rk2_2[0,2] = m_0\n",
"\n",
"for i in range(N_rk2_2 - 1):\n",
" num_sol_rk2_2[i+1] = rk2_step(num_sol_rk2_2[i], rocket, dt_rk2_2)\n",
" \n",
"# Heun Method Implicit\n",
"N_heun_2 = 50\n",
"dt_heun_2 = t_total/N_heun_2\n",
"\n",
"num_sol_heun_2 = np.zeros([N_heun_2, 3])\n",
"\n",
"num_sol_heun_2[0,0] = 0\n",
"num_sol_heun_2[0,1] = 0\n",
"num_sol_heun_2[0,2] = m_0\n",
"\n",
"for i in range(N_heun_2 - 1):\n",
" num_sol_heun_2[i+1] = heun_step(num_sol_heun_2[i], rocket, dt_heun)\n",
" \n",
"fig = plt.figure(figsize=(10,6))\n",
"plt.plot(m/m_0, v, label = 'Tsiolkovsky Equation')\n",
"plt.plot(num_sol_rk2_2[:,2]/m_0, num_sol_rk2_2[:,1], '--', label = 'Explicit Runge-Kutta Method')\n",
"plt.plot(num_sol_heun_2[:,2]/m_0, num_sol_heun_2[:,1], ':', label = 'Implicit Heun Method')\n",
"plt.title('Numerical Soluions Accounting for Drag')\n",
"plt.legend(loc='best')"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"The solution of the more complex rocket function shows a much more linear relationship between the change in velocity and the percentage of the mass burned. This is likely due to the negative effects of gravity and drag and on the increase in velocity."
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The final height for the simple rocket case is: 566.4039857467229 m\n",
"The final height for the complex rocket case is: 407.41495010571833 m\n"
]
}
],
"source": [
"h_1 = num_sol_heun[-1, 0]\n",
"h_2 = num_sol_heun_2[-1, 0]\n",
"\n",
"print('The final height for the simple rocket case is:', h_1, 'm')\n",
"print('The final height for the complex rocket case is:', h_2, 'm')"
]
},
{
"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": 74,
"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",
" y_0 = 0\n",
" y_desired = 300\n",
" m_f = .05\n",
" t_total = (m_0 - m_f)/dmdt\n",
" N = 50\n",
" dt = t_total/N\n",
" t = np.linspace(0, t_total, N)\n",
" \n",
" num_sol = np.zeros([N, 3])\n",
" \n",
" num_sol[0, 0] = y_0\n",
" num_sol[0, 1] = 0\n",
" num_sol[0, 2] = m_0\n",
" \n",
" for i in range(N - 1):\n",
" num_sol[i+1] = rk2_step(num_sol[i], rocket, dt)\n",
" y_f = num_sol[N-1, 0]\n",
" error = y_f - y_desired\n",
" \n",
" return error\n",
"\n",
"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",
" ---------\n",
" func = name of function\n",
" xmin, xmax = endpoints of interval\n",
" ns = number of subintervals (default = 50)\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\n",
"\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]"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of brackets: 1\n",
"\n",
"Two best guesses for mass change rate are: [0.06428571] and [0.05714286] kg/s\n"
]
}
],
"source": [
"increment = incsearch(f_m, .05, .4)\n",
"print('Two best guesses for mass change rate are:', increment[0], 'and', increment[1], 'kg/s')"
]
},
{
"cell_type": "code",
"execution_count": 76,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The mass change rate needed to reach 300m in height at detonation is: 0.05758823414343776 kg/s\n"
]
}
],
"source": [
"dmdt_sol, other = mod_secant(f_m, .01, .05, es=0.000001)\n",
"print('The mass change rate needed to reach 300m in height at detonation is:', dmdt_sol, 'kg/s')"
]
},
{
"cell_type": "code",
"execution_count": 77,
"metadata": {},
"outputs": [],
"source": [
"def rocket300(state, dmdt = 0.0576, 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",
" derivs = np.array([state[1], (u/state[2])*dmdt - 9.81 - (c/state[2])*state[1]**2, -dmdt])\n",
" return derivs"
]
},
{
"cell_type": "code",
"execution_count": 78,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"Text(0, 0.5, 'Height (m)')"
]
},
"execution_count": 78,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 720x432 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"t_total_sol = (m_0 - m_f)/dmdt_sol\n",
"N_sol = 50\n",
"dt_sol = t_total_sol/N_sol\n",
"t = np.linspace(0, t_total_sol, N_sol)\n",
"\n",
"num_sol = np.zeros([N_sol, 3])\n",
"\n",
"num_sol[0,0] = 0\n",
"num_sol[0,1] = 0\n",
"num_sol[0,2] = m_0\n",
"\n",
"for i in range(N_sol - 1):\n",
" num_sol[i+1] = rk2_step(num_sol[i], rocket300, dt_sol)\n",
"\n",
"fig = plt.figure(figsize=(10,6))\n",
"plt.plot(t, num_sol[:,0])\n",
"plt.plot(t[-1], num_sol[-1, 0], marker = '*', markersize = 20)\n",
"plt.title('300m Detonation Rocket')\n",
"plt.xlabel('Time (s)')\n",
"plt.ylabel('Height (m)')"
]
},
{
"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>"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.7.3"
}
},
"nbformat": 4,
"nbformat_minor": 4
}