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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": 113,
"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": 114,
"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",
" 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": 115,
"metadata": {},
"outputs": [],
"source": [
"#Explicit Method\n",
"def rk2_step(state, rhs, dt):\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",
"#Implicit Method\n",
"def heun_step(state,rhs,dt,etol=0.000001,maxiters = 100):\n",
"\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",
" last_state = next_state\n",
" next_state = state + (rhs(state)+rhs(next_state))/2*dt\n",
" e = np.sum(np.abs(next_state-last_state)/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": 116,
"metadata": {},
"outputs": [],
"source": [
"#Initial Rocket Conditions\n",
"y0 = 0 #Initial Height [m]\n",
"v0 = 0 #Initial Velocity [m/s]\n",
"m0 = 0.25 #Initial Mass [kg]\n",
"mf = 0.05 #Final Mass [kg]\n",
"dmdt = 0.05 #Mass Rate of Change [kg/s]\n",
"u = 250 #Propellant Velocity [m/s]"
]
},
{
"cell_type": "code",
"execution_count": 117,
"metadata": {},
"outputs": [],
"source": [
"t1 = (m0-mf)/dmdt #time in launch\n",
"N = 50 \n",
"t = np.linspace(0,t1,N) \n",
"dt = t[1] - t[0]\n",
"m = np.linspace(m0,mf)\n",
"v = -u*np.log(m/m0)\n",
"\n",
"#Implicit/Explicit Numerical solution arrays\n",
"num_sol_heun = np.zeros([N,3])\n",
"num_sol_rk2 = np.zeros([N,3])\n",
"\n",
"#Imp/Exp Soltion Initial Conditions\n",
"num_sol_heun[0,0] = y0\n",
"num_sol_rk2[0,0] = y0\n",
"\n",
"num_sol_heun[0,1] = v0\n",
"num_sol_rk2[0,1] = v0\n",
"\n",
"num_sol_heun[0,2] = m0\n",
"num_sol_rk2[0,2] = m0\n",
"\n",
"#Predicted Mass\n",
"heun_m = num_sol_heun[:,2]\n",
"rk2_m =num_sol_rk2[:,2]\n",
"\n",
"#Predicted Velocity\n",
"heun_v = num_sol_heun[:,1]\n",
"rk2_v = num_sol_rk2[:,1]\n",
"\n",
"#Numerical solutions for Simple Rocket in Motion\n",
"for i in range (N-1):\n",
" num_sol_heun[i+1] = heun_step(num_sol_heun[i], simplerocket, dt)\n",
" num_sol_rk2[i+1] = rk2_step(num_sol_rk2[i], simplerocket, dt)\n"
]
},
{
"cell_type": "code",
"execution_count": 121,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f171a104748>"
]
},
"execution_count": 121,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 936x504 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#Plot of Speed of Simple Rocket while Mass(fuel) is used\n",
"plt.figure(figsize = (13,7))\n",
"plt.plot(m/m0, v, label='Tsiolkovsky Method')\n",
"plt.plot(heun_m/m0, heun_v, '--', label='Heun Implicit Method')\n",
"plt.plot(rk2_m/m0, rk2_v, 'o', label='rk2 Explicit Method')\n",
"plt.xlabel('Mass %')\n",
"plt.ylabel('Velocity (m/s)')\n",
"plt.title('Simple Rocket Velocity vs. % Used Mass')\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": 119,
"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.zeros(np.shape(state))\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": 120,
"metadata": {},
"outputs": [],
"source": [
"#Initial Rocket Conditions\n",
"y0 = 0 #Initial Height [m]\n",
"v0 = 0 #Initial Velocity [m/s]\n",
"m0 = 0.25 #Initial Mass [kg]\n",
"mf = 0.05 #Final Mass [kg]\n",
"dmdt = 0.05 #Mass Rate of Change [kg/s]\n",
"u = 250 #Propellant Velocity [m/s]\n",
"g = 9.81 #Gravity constant [m/s^2]"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {},
"outputs": [],
"source": [
"t1 = (m0-mf)/dmdt \n",
"N = 50\n",
"t = np.linspace(0,t1,N) \n",
"dt = t[1] - t[0]\n",
"m = np.linspace(m0,mf)\n",
"v = -u*np.log(m/m0)\n",
"\n",
"#Implicit/Explicit Numerical solution arrays\n",
"num_sol_heun_2 = np.zeros([N,3])\n",
"num_sol_rk2_2 = np.zeros([N,3])\n",
"\n",
"#Imp/Exp Soltion Initial Conditions\n",
"num_sol_heun_2[0,0] = y0\n",
"num_sol_rk2_2[0,0] = y0\n",
"\n",
"num_sol_heun_2[0,1] = v0\n",
"num_sol_rk2_2[0,1] = v0\n",
"\n",
"num_sol_heun_2[0,2] = m0\n",
"num_sol_rk2_2[0,2] = m0\n",
"\n",
"heun_v2 = num_sol_heun_2[:,1]\n",
"rk2_v2 = num_sol_rk2_2[:,1]\n",
"\n",
"heun_m2 = num_sol_heun_2[:,2]\n",
"rk2_m2 =num_sol_rk2_2[:,2]\n",
"\n",
"for i in range (N-1):\n",
" num_sol_heun_2[i+1] = heun_step(num_sol_heun_2[i], rocket, dt)\n",
" num_sol_rk2_2[i+1] = rk2_step(num_sol_rk2_2[i], rocket, dt)"
]
},
{
"cell_type": "code",
"execution_count": 122,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f171a0f5dd8>"
]
},
"execution_count": 122,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": [
"<Figure size 936x504 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"#Plot of Speed of Realistic Rocket while Mass(fuel) is used\n",
"plt.figure(figsize = (13,7))\n",
"plt.plot(m/m0, v, label='Tsiolkovsky Method')\n",
"plt.plot(heun_m2/m0, heun_v2, label='Real Rocket Heun Implicit Method', color='red')\n",
"plt.plot(rk2_m2/m0, rk2_v2, 'o', label='Real Rocket rk2 Explicit Method', color='black')\n",
"plt.xlabel('Mass %')\n",
"plt.ylabel('Velocity (m/s)')\n",
"plt.title('Real Rocket Velocity vs. % Used Mass')\n",
"plt.legend(loc='best')"
]
},
{
"cell_type": "code",
"execution_count": 130,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f171a00a748>"
]
},
"execution_count": 130,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 936x504 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize = (13,7))\n",
"plt.plot(heun_m/m0, heun_v, '--', label='Simple Rocket Heun Implicit Method')\n",
"plt.plot(rk2_m/m0, rk2_v, 'o', label='Simple Rocket rk2 Explicit Method')\n",
"plt.plot(heun_m2/m0, heun_v2, label='Real Rocket Heun Implicit Method', color='black')\n",
"plt.plot(rk2_m2/m0, rk2_v2, 'o', label='Real Rocket rk2 Explicit Method', color='red')\n",
"plt.xlabel('Mass %')\n",
"plt.ylabel('Velocity (m/s)')\n",
"plt.title('Rocket Velocity vs. Used Mass')\n",
"plt.legend(loc='best')"
]
},
{
"cell_type": "code",
"execution_count": 102,
"metadata": {},
"outputs": [],
"source": [
"#Predicted Max Heights using Implicit and Explicit Numerical methods\n",
"imp_max_height1 = num_sol_heun[-1,0] \n",
"imp_max_height2 = num_sol_heun_2[-1,0] \n",
"exp_max_height1 = num_sol_rk2[-1,0] \n",
"exp_max_height2 = num_sol_rk2_2[-1,0]"
]
},
{
"cell_type": "code",
"execution_count": 103,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Using Implicit Integration Methods, at m_f = 0.05 the Real Rocket will reach\n",
" 425.4407782302097 meters and the Simple Rocket will reach 597.8405306687749 \n",
"meters\n"
]
}
],
"source": [
"print('Using Implicit Integration Methods, at m_f = 0.05 the Real Rocket will reach\\n',imp_max_height2, 'meters and the Simple Rocket will reach',imp_max_height1, '\\nmeters')"
]
},
{
"cell_type": "code",
"execution_count": 104,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Using Explicit Integration Methods, at m_f = 0.05 the Real Rocket will reach\n",
" 425.4342716122235 meters and the Simple Rocket will reach 597.3820385703382 \n",
"meters\n"
]
}
],
"source": [
"print('Using Explicit Integration Methods, at m_f = 0.05 the Real Rocket will reach\\n',exp_max_height2, 'meters and the Simple Rocket will reach',exp_max_height1, '\\nmeters')"
]
},
{
"cell_type": "code",
"execution_count": 123,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"'The difference in height is because the Simple rocket does not account for the effects of gravity and drag along the rockets flight. This means the Simple rocket will show faster velocities and higher heights being reached, which is calculated and shown above. '"
]
},
"execution_count": 123,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"'''The difference in height is because the Simple rocket does not account for the effects of gravity and drag along the rockets flight. This means the Simple rocket will show faster velocities and higher heights being reached, which is calculated and shown above. '''"
]
},
{
"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": 105,
"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",
" h = 300\n",
" m0 = 0.25\n",
" mf = 0.05\n",
" N = 100\n",
" time = (m0-mf)/dmdt\n",
" t = np.linspace(0, time, N)\n",
" dt = t[1] - t[0]\n",
" \n",
" num_h = np.zeros([N,3])\n",
" num_h[0,0] = y0\n",
" num_h[0,1] = v0\n",
" num_h[0,2] = m0\n",
" \n",
" for i in range(N-1):\n",
" num_h[i+1] = heun_step(num_h[i], lambda state: rocket(state, dmdt=dmdt),dt)\n",
" calc_h = num_h[:,0]\n",
" \n",
" error = h - calc_h[-1]\n",
"\n",
" return error"
]
},
{
"cell_type": "code",
"execution_count": 106,
"metadata": {},
"outputs": [],
"source": [
"def incsearch(func,xmin,xmax,ns=50):\n",
"\n",
" x = np.linspace(xmin,xmax,ns)\n",
" f = np.empty(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",
" 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",
"\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": 107,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of brackets: 1\n",
"\n",
"The closest mass change rates in the interval from dmdt=0.05 and dmdt=0.4 are [0.08571429] kg/s and [0.07857143] kg/s\n"
]
}
],
"source": [
"massrate = incsearch(f_m, 0.05, 0.4)\n",
"print('The closest mass change rates in the interval from dmdt=0.05 and dmdt=0.4 are', massrate[0],'kg/s and', massrate[1], 'kg/s')"
]
},
{
"cell_type": "code",
"execution_count": 108,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"The root of the function \"f_m\" is 0.07912698052690133\n"
]
}
],
"source": [
"root_fm = mod_secant(f_m,dx=0.0001,x0=0.0857)\n",
"print('The root of the function \"f_m\" is', root_fm[0])"
]
},
{
"cell_type": "code",
"execution_count": 126,
"metadata": {},
"outputs": [],
"source": [
"yf = 300\n",
"y0 = 0\n",
"v0 = 0\n",
"m0 = 0.25\n",
"mf = 0.05\n",
"N = 100"
]
},
{
"cell_type": "code",
"execution_count": 127,
"metadata": {},
"outputs": [],
"source": [
"dmdt = root_fm[0]\n",
"t2 = (m0-mf)/dmdt\n",
"t = np.linspace(0, t2, N)\n",
"dt = t[1] - t[0]\n",
"N2 = int(t2/dt)\n",
"\n",
"num_sol_h = np.zeros([N2,3])\n",
"\n",
"num_sol_h[0,0] = y0\n",
"num_sol_h[0,1] = v0\n",
"num_sol_h[0,2] = m0\n",
"\n",
"for i in range(N2-1):\n",
" num_sol_h[i+1] = heun_step(num_sol_h[i], lambda state: rocket(state,dmdt=dmdt),dt)\n",
"heun_h = num_sol_h[:,0]"
]
},
{
"cell_type": "code",
"execution_count": 129,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x7f171a0b8e10>"
]
},
"execution_count": 129,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 936x504 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"plt.figure(figsize = (13,7))\n",
"plt.plot(t[:N2],heun_h, ':', label='In Flight')\n",
"plt.plot(t[-1], yf, '*', label='Detonation')\n",
"plt.xlabel('time(s)')\n",
"plt.ylabel('height (m)')\n",
"plt.title('Firework in Flight')\n",
"plt.legend(loc='best')"
]
},
{
"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
}