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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": 470,
"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": 471,
"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",
" #m=0.25 #kg \n",
" dstate = np.array([state[1], u/state[2]*dmdt,-dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 472,
"metadata": {},
"outputs": [],
"source": [
"def eulerstep(state, rhs, dt):\n",
" '''Update a state to the next time increment using 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",
" 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",
" \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",
" ################### New iterative correction #########################\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",
" ############### end of iterative correction #########################\n",
" return next_state"
]
},
{
"cell_type": "code",
"execution_count": 473,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 1152x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#initialize numerical analysis, set time step and create empty solution matrices\n",
"m0=0.25 #initial mass (kg)\n",
"mf=0.05 #final mass (kg)\n",
"dmdt= 0.05 #rate of change of mass with respect to time(kg/s)\n",
"calc_time = (m0-mf)/dmdt\n",
"\n",
"time_span_eul = np.linspace(0,calc_time, 1000)\n",
"time_span_heun = np.linspace(0,calc_time, 1000)\n",
"\n",
"dt_eul = time_span_eul[1]-time_span_eul[0] #0.01\n",
"dt_heun = time_span_heun[1]-time_span_heun[0] #0.05\n",
"N_eul = int((m0-mf)/dmdt/dt_eul)\n",
"N_heun = int((m0-mf)/dmdt/dt_heun)\n",
"\n",
"num_eul=np.zeros([N_eul,3])\n",
"num_heun=np.zeros([N_heun,3])\n",
"\n",
"\n",
"#initial conditions x(0)=0 , v(0)=0 m/s, m(0)= 0.25 kg\n",
"u=250 #average velocity of gun power propellant (m/s)\n",
"num_eul[0,0] = 0; num_eul[0,1] = 0; num_eul[0,2] = m0\n",
"num_heun[0,0] = 0; num_heun[0,1] = 0; num_heun[0,2] = m0\n",
"\n",
"\n",
"#solve numerical solutions\n",
"#i=0; \n",
"#while num_eul[i,2] >= 0.05:\n",
"for i in range (N_eul-1):\n",
" num_eul[i+1] = eulerstep(num_eul[i], simplerocket, dt_eul)\n",
" #i=i+1\n",
"\n",
"#j=0;\n",
"#while num_heun [j,2]>= 0.05:\n",
"for j in range (N_heun-1):\n",
" num_heun[j+1] = heun_step(num_heun[j], simplerocket, dt_heun)\n",
" #j=j+1\n",
"\n",
"#set range for Tsiolkocsky equation solution\n",
"mass_range=np.linspace(0.25,0.05)\n",
"\n",
"\n",
"# used to find in solution sets where mass reaches 0 kg, so plotting can be cut off there\n",
"#endpts_eul=np.where(num_eul[:,2]==0)\n",
"#endpt_eul=endpts_eul[0][0]-1\n",
"\n",
"#endpts_heun=np.where(num_heun[:,2]==0)\n",
"#endpt_heun=endpts_heun[0][0]-1\n",
"\n",
"\n",
"#plotting\n",
"fig = plt.figure(figsize=(16,8))\n",
"plt.plot(num_eul[:,2]/m0, num_eul[:,1], 'bs',label=\"Explicit Euler's method\")\n",
"plt.plot(num_heun[:,2]/m0, num_heun[:,1], 'r.',label=\"implicit Heun's method\")\n",
"plt.plot(mass_range/m0,-np.log(mass_range/0.25)*u,'k--',label=\"Tsiolkovsky equation\")\n",
"plt.legend(loc='best')\n",
"plt.xlabel('mass(t)/mass(0) [unitless]')\n",
"plt.ylabel('velocity(t) [m/s]')\n",
"plt.title(\"Convergence of Numerical Solutions (without gravity and drag) to the Tsiolkovsky equation\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As shown from the plot above, the two numerical solutions (with gravity and drag neglected)converge to the Tsiolkovsky equation. "
]
},
{
"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": 474,
"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",
" g=9.81 #gravitational constant, m/s^2\n",
" dstate = np.array([state[1], u/state[2]*dmdt-g-c*state[1]**2/state[2],-dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 475,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 1152x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#initialize numerical analysis, set time step and create empty solution matrices\n",
"time_span_eul_new = np.linspace(0,calc_time, 1000)\n",
"time_span_heun_new = np.linspace(0,calc_time, 1000)\n",
"\n",
"dt_eul_new = time_span_eul_new[1]-time_span_eul_new[0] \n",
"dt_heun_new = time_span_heun[1]-time_span_heun[0] \n",
"N_eul_new = int((m0-mf)/dmdt/dt_eul_new)\n",
"N_heun_new = int((m0-mf)/dmdt/dt_heun_new)\n",
"\n",
"num_eul_new=np.zeros([N_eul_new,3])\n",
"num_heun_new=np.zeros([N_heun_new,3])\n",
"\n",
"\n",
"#initial conditions x(0)=0 , v(0)=0 m/s, m(0)= 0.25 kg\n",
"u=250 #average velocity of gun power propellant (m/s)\n",
"num_eul_new[0,0] = 0; num_eul_new[0,1] = 0; num_eul_new[0,2] = m0\n",
"num_heun_new[0,0] = 0; num_heun_new[0,1] = 0; num_heun_new[0,2] = m0\n",
"\n",
"\n",
"#solve numerical solutions until mass reaches 0.05 kg \n",
" \n",
"for k in range (N_eul_new -1):\n",
" num_eul_new[k+1] = eulerstep(num_eul_new[k], rocket, dt_eul_new)\n",
"\n",
"for l in range (N_heun_new -1):\n",
" num_heun_new[l+1] = heun_step(num_heun_new[l], rocket, dt_heun_new)\n",
"\n",
"\n",
"# plotting\n",
"fig = plt.figure(figsize=(16,8))\n",
"plt.plot(num_eul_new[:,2]/m0, num_eul_new[:,1], 'bo',label=\"Euler's method\")\n",
"plt.plot(num_heun_new[:,2]/m0, num_heun_new[:,1], 'r.',label=\"implicit Heun's method\")\n",
"plt.plot(mass_range/m0,-np.log(mass_range/m0)*u,'k-',label=\"Tsiolkovsky equation\")\n",
"plt.legend(loc='best')\n",
"plt.xlabel('mass(t)/mass(0) [unitless]')\n",
"plt.ylabel('velocity(t) [m/s]')\n",
"plt.title(\"Comparison of Numerical Solutions (with gravity and drag) to the Tsiolkovsky equation\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can see from the plot above that the numerical solutions with gravity and drag accounted for do not converge to the Tsiolkovsky equation. The numerical solutions and equation are approximately equivalent only when the mass ratio equals 0.9 - 1.0 (very early time, when mass(t) ~= initial mass). However, as time continues, the mass decreases (causing mass(t)/mass(0) to decrease as well), and the numerical solutions approach far lower velocities than the Tsiolkovsky method's velocities. This is due to the fact that since gravity and drag are now accounted for, the rocket will be will not accelerate as quickly due to these opposing forces; the Tsiolkovsky equations neglects the effects of gravity and drag, so its acceleration is not opposed by these forces. Thus, the resulting velocities will be lower, and the height reached when mass(t)=0.05 kg will be lower as well in the new numerical explicit and implicit solutions."
]
},
{
"cell_type": "code",
"execution_count": 476,
"metadata": {
"scrolled": false
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Gravity and drag neflected:\n",
"The height reached when mass(t)=0.05 kg is 594.826 meters for Euler's method and 596.032 meters for Heun's method.\n",
"\n",
"Gravity and drag accounted for:\n",
"The height reached when mass(t)=0.05 kg is 423.986 meters for Euler's method and 424.533 meters for Heun's method.\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 1152x576 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"print(\"Gravity and drag neflected:\")\n",
"print(\"The height reached when mass(t)=0.05 kg is {:3.3f} meters for Euler's method and {:3.3f} meters for Heun's method.\".format(num_eul[-1,0],num_heun[-1,0]))\n",
"print()\n",
"print(\"Gravity and drag accounted for:\")\n",
"print(\"The height reached when mass(t)=0.05 kg is {:3.3f} meters for Euler's method and {:3.3f} meters for Heun's method.\".format(num_eul_new[-1,0],num_heun_new[-1,0]))\n",
"\n",
"fig = plt.figure(figsize=(16,8));\n",
"plt.plot(time_span_eul[:-1], num_eul[:,0],'y.',label=\"Explicit Euler, no drag/gravity\")\n",
"plt.plot(time_span_heun[:-1], num_heun[:,0],'k--',label=\"Implicit Heun, no drag/gravity\")\n",
"plt.plot(time_span_eul_new[:-1], num_eul_new[:,0],'r.',label=\"Explicit Euler, with drag/gravity\")\n",
"plt.plot(time_span_heun_new[:-1], num_heun_new[:,0],'b--',label=\"Implicit Heun, with drag/gravity\")\n",
"plt.legend(loc='best');\n",
"plt.xlabel('time [s]');\n",
"plt.ylabel('height [m]');\n",
"plt.title(\"Height reached by numerical Solutions \\nwith and without Drag and Gravity accounted for\");"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As shown above, the height reached when mass(t) equals 0.5 kg is about 595 m when gravity and drag are neglected and about 424 m when gravity and drag are accounted for."
]
},
{
"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": 477,
"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",
" height_desired=300 #meters\n",
" #calc_time = (m0-mf)/dmdt\n",
" time_span_f_m = np.linspace(0,(m0-0.05)/dmdt, 1000)\n",
" dt_f_m = time_span_f_m[1]-time_span_f_m[0] \n",
" N_f_m = int((m0-mf)/dmdt/dt_f_m)\n",
" num_f_m=np.zeros([N_f_m,3])\n",
"\n",
" #initial conditions x(0)=0 , v(0)=0 m/s, m(0)= 0.25 kg\n",
" num_f_m[0,0] = 0; num_f_m[0,1] = 0; num_f_m[0,2] = m0\n",
"\n",
" #solve numerical solutions until mass reaches 0.05 kg \n",
" for m in range (N_f_m -1):\n",
" num_f_m[m+1] = heun_step(num_f_m[m], lambda state: rocket(state, dmdt=dmdt, u=250,c=0.18e-3), dt_f_m)\n",
" #num_f_m[m+1] = heun_step(num_f_m[m], rocket, dt_f_m)\n",
" \n",
" height_predicted=num_f_m[-1,0]\n",
" error=height_desired-height_predicted\n",
" \n",
" return error"
]
},
{
"cell_type": "code",
"execution_count": 478,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Part a:\n",
"This function behaves as expected since the height reached when dmdt=0.05 kg/s is about 424 m, and f_m(0.05) is -124.533 m\n",
"(300 m - 424 m).\n",
"\n",
"We find that the error is closest to zero around 0.079 kg/s, since f_m(0.079) yields 0.29 m.\n",
"We will further refine this root using the incsearch and mod_secant functions.\n"
]
}
],
"source": [
"# We can plug in various dmdt values into f_m to see where the f_m function is closest to zero.\n",
"\n",
"print(\"Part a:\")\n",
"print(\"This function behaves as expected since the height reached when dmdt=0.05 kg/s is about 424 m, and f_m(0.05) is {:3.3f} m\\n(300 m - 424 m).\".format(f_m(0.05)))\n",
"print()\n",
"print(\"We find that the error is closest to zero around 0.079 kg/s, since f_m(0.079) yields {:2.2f} m.\\nWe will further refine this root using the incsearch and mod_secant functions.\".format(f_m(0.079)))"
]
},
{
"cell_type": "code",
"execution_count": 479,
"metadata": {},
"outputs": [],
"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",
" ---------\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"
]
},
{
"cell_type": "code",
"execution_count": 480,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Part a: (continued)\n",
"\n",
"number of brackets: 1\n",
"\n",
"Using the incsearch function, we find that the desired dmdt value to achieve the desired 300 m height is between 0.05000 kg/s and 0.08889 kg/s.\n",
"This confirms our prior conclusion from above using the f_m function.\n"
]
}
],
"source": [
"print(\"Part a: (continued)\")\n",
"print()\n",
"xb = incsearch(f_m, 0.05, 0.4, ns = 10);\n",
"print(\"Using the incsearch function, we find that the desired dmdt value to achieve the desired 300 m height is between {:1.5f} kg/s and {:1.5f} kg/s.\".format(xb[1][0],xb[0][0]))\n",
"print(\"This confirms our prior conclusion from above using the f_m function.\")"
]
},
{
"cell_type": "code",
"execution_count": 481,
"metadata": {},
"outputs": [],
"source": [
"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": 531,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Part b:\n",
"The correct initial dmdt is 0.07890355427858026 kg/s needed to match the desired 300 m detonation height.\n",
"The solve took 5 iterations.\n"
]
}
],
"source": [
"root, out = mod_secant(f_m,0.0001,0.05,es=0.0001) \n",
"\n",
"print(\"Part b:\")\n",
"print(\"The correct initial dmdt is {} kg/s needed to match the desired 300 m detonation height.\".format(root))\n",
"print('The solve took ',out[2],' iterations.')"
]
},
{
"cell_type": "code",
"execution_count": 533,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Part c:\n"
]
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 864x720 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"# part c\n",
"m0=0.25 #initial mass (kg)\n",
"mf=0.05 #final mass (kg)\n",
"dmdt_newest= 0.07890355427858026 #updated rate of change of mass with respect to time(kg/s)\n",
"calc_time_newest = (m0-mf)/dmdt_newest\n",
"\n",
"time_span_eul_newest = np.linspace(0,calc_time_newest, 10000)\n",
"time_span_heun_newest = np.linspace(0,calc_time_newest, 10000)\n",
"\n",
"dt_eul_newest = time_span_eul_newest[1]-time_span_eul_newest[0] \n",
"dt_heun_newest = time_span_heun_newest[1]-time_span_heun_newest[0]\n",
"\n",
"time_dif=(m0-mf)/dmdt_newest\n",
"\n",
"N_eul_newest = int(time_dif/dt_eul_newest)\n",
"N_heun_newest = int(time_dif/dt_heun_newest)\n",
"\n",
"num_eul_newest=np.zeros([N_eul_newest,3])\n",
"num_heun_newest=np.zeros([N_heun_newest,3])\n",
"\n",
"num_eul_newest[0,0]=0\n",
"num_eul_newest[0,1]=0\n",
"num_eul_newest[0,2]=0.25\n",
"num_heun_newest[0,0]=0\n",
"num_heun_newest[0,1]=0\n",
"num_heun_newest[0,2]=0.25\n",
"\n",
"for i in range(N_eul_newest-1):\n",
" num_eul_newest[i+1]=eulerstep(num_eul_newest[i], lambda state: rocket(state,dmdt=0.07890355427858026,u=250,c=0.18e-3),dt_eul_newest)\n",
"\n",
"for j in range(N_heun_newest-1):\n",
" num_heun_newest[j+1]=heun_step(num_heun_newest[j], lambda state: rocket(state,dmdt=0.07890355427858026,u=250,c=0.18e-3),dt_heun_newest)\n",
"\n",
"plt.figure(figsize=(12,10));\n",
"plt.plot(time_span_eul_newest[:-1],num_eul_newest[:,0],'r-',label='Explicit Euler');\n",
"plt.plot(time_span_heun_newest[:-1],num_heun_newest[:,0],'b-.',label='Implicit Heun');\n",
"plt.plot(time_span_heun_newest[-2],num_heun_newest[-1,0],'k*',markersize=20,label='Detonation')\n",
"plt.title('Height reached by Numerical Solutions with updated dm/dt of 0.0789 kg/s');\n",
"plt.xlabel('Time [s]');\n",
"plt.ylabel('Height [m]');\n",
"plt.legend(loc='best');\n",
"\n",
"print(\"Part c:\")"
]
},
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"cell_type": "markdown",
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"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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