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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": 1,
"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": 2,
"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) -dmdt]^T\n",
" '''\n",
" \n",
" dstate = np.array([state[1], (u*dmdt)/state[2], -dmdt])\n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 3,
"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",
" \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": 4,
"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",
" ################### 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": 57,
"metadata": {},
"outputs": [],
"source": [
"#initial conditions\n",
"y0 = 0 \n",
"v0 = 0 \n",
"m0 = 0.25 \n",
"dm_dt = 0.05\n",
"time_1 = (0.25-0.05)/dm_dt\n",
"t= np.linspace(0,time_1,10000)\n",
"dt=t[1]-t[0]\n",
"N=int(time_1/dt)\n",
"m_f = np.linspace(0.25, 0.05, N)"
]
},
{
"cell_type": "code",
"execution_count": 58,
"metadata": {},
"outputs": [],
"source": [
"#solution array\n",
"num_heun = np.zeros([N,3])\n",
"num_rk2 = np.zeros([N,3])\n",
"\n",
"#intial conditions\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_f/m0\n",
"v_f = -250*np.log(d_m)\n",
"for i in range(N-1):\n",
" num_heun[i+1] = heun_step(num_heun[i], simplerocket, dt)\n",
"for i in range(N-1):\n",
" num_rk2[i+1] = rk2_step(num_rk2[i], simplerocket, dt)"
]
},
{
"cell_type": "code",
"execution_count": 74,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(8,5))\n",
"plt.plot(num_heun[:,2]/m0, num_heun[:,1],color ='darkgreen',linewidth = 5, label = 'Heun Method')\n",
"plt.plot(num_rk2[:,2]/m0, num_rk2[:,1],'-.', color='tomato', linewidth=5, label = 'Runge Kutta')\n",
"plt.plot(d_m,v_f,'--',color='skyblue', linewidth =5, label = 'Tsiolkovsky')\n",
"plt.vlines(0.2,-100,400, linewidth=1, label = 'm_f = 0.05')\n",
"plt.xlim(1,0)\n",
"plt.ylim(0,450)\n",
"plt.ylabel('Velocity [m/s]')\n",
"plt.xlabel('Mass ratio')\n",
"plt.legend(bbox_to_anchor=(1,1));"
]
},
{
"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": 8,
"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",
" \n",
" return dstate"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"#solution array\n",
"num_heun_drag = np.zeros([N,3])\n",
"num_rk2_drag = np.zeros([N,3])\n",
"\n",
"\n",
"#intial conditions\n",
"num_heun_drag[0,0] = y0\n",
"num_heun_drag[0,1] = v0\n",
"num_heun_drag[0,2] = m0\n",
"\n",
"num_rk2_drag[0,0] = y0\n",
"num_rk2_drag[0,1] = v0\n",
"num_rk2_drag[0,2] = m0\n",
"\n",
"d_m = m_f/m0\n",
"vf = -250*np.log(d_m)\n",
"for i in range(N-1):\n",
" num_heun_drag[i+1] = heun_step(num_heun_drag[i], rocket, dt)\n",
"for i in range(N-1):\n",
" num_rk2_drag[i+1] = rk2_step(num_rk2_drag[i], rocket, dt)"
]
},
{
"cell_type": "code",
"execution_count": 43,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Height for the Huen Method SIMPLEROCKET = 597.479579 meters\n",
"Height for the Runge Kutta Method SIMPLEROCKET = 597.4795756 meters\n",
"\n",
"Height for the Huen Method ROCKET = 425.3522472 meters\n",
"Height for the Runge Kutta ROCKET = 425.3522474 meters\n"
]
}
],
"source": [
"height_heun = num_heun[:,0]\n",
"height_rk2 = num_rk2[:,0]\n",
"height_heun_drag = num_heun_drag[:,0]\n",
"height_rk2_drag = num_rk2_drag[:,0]\n",
"print('Height for the Huen Method SIMPLEROCKET =',round(height_heun[-1],7),'meters')\n",
"print('Height for the Runge Kutta Method SIMPLEROCKET =',round(height_rk2[-1],7),'meters')\n",
"print()\n",
"print('Height for the Huen Method ROCKET =',round(height_heun_drag[-1],7),'meters')\n",
"print('Height for the Runge Kutta ROCKET =',round(height_rk2_drag[-1],7),'meters')"
]
},
{
"cell_type": "code",
"execution_count": 75,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(8,5))\n",
"\n",
"plt.plot(num_heun_drag[:,2]/0.25, num_heun_drag[:,1],color = 'lightgreen',linewidth = 4, label = 'Heun Method')\n",
"plt.plot(num_rk2_drag[:,2]/0.25, num_rk2_drag[:,1],'--',color = 'mediumpurple', linewidth=4, label = 'Runge Kutta')\n",
"plt.plot(d_m,v_f, linewidth =2,color = 'tomato', label = 'Analytical')\n",
"plt.xlim(1,0)\n",
"plt.vlines(0.2,-100,225,linewidth=1,label='m_f=0.05')\n",
"plt.ylabel('Velocity [m/s]')\n",
"plt.xlabel('Mass ratio')\n",
"plt.legend(bbox_to_anchor=(1,1));"
]
},
{
"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": 12,
"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",
" y0 = 0 # initial position\n",
" v0 = 0 # initial velocity \n",
" time_2 = (0.25-0.05)/dmdt\n",
" t2= np.linspace(0,time_2,10000)\n",
" dt=t2[1]-t2[0]\n",
" \n",
" N=int(time_2/dt)\n",
" height_desired = 300\n",
"\n",
" #initialize solution array\n",
" height2 = np.zeros([N,3])\n",
"\n",
" #Set intial conditions\n",
" height2[0,0] = y0\n",
" height2[0,1] = v0\n",
" height2[0,2] = m0\n",
"\n",
" for i in range(N-1):\n",
" height2[i+1] = rk2_step(height2[i],lambda state: rocket(state,dmdt=dmdt, u=250),dt)\n",
" height_predicted = height2[:,0]\n",
" error = height_desired - height_predicted[-1]\n",
" \n",
" return error"
]
},
{
"cell_type": "code",
"execution_count": 13,
"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",
" 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": 14,
"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": 72,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"number of brackets: 1\n",
"\n",
"3A) Lower Bound: 0.0786 kg/s\n",
" Upper Bound: 0.0857 kg/s\n",
"\n",
"3B) The actual root: 0.0791 kg/s\n"
]
}
],
"source": [
"#3A\n",
"change_rate = incsearch(f_m,0.05,0.4);\n",
"print('3A) Lower Bound:', round(change_rate[1,0],4),'kg/s')\n",
"print(' Upper Bound:', round(change_rate[0,0],4),'kg/s')\n",
"\n",
"print() #3B\n",
"root_fm = mod_secant(f_m,0.0001,0.08571429,es=0.000001);\n",
"print('3B) The actual root:', round(root_fm[0],4),'kg/s')"
]
},
{
"cell_type": "code",
"execution_count": 24,
"metadata": {},
"outputs": [],
"source": [
"y0 = 0 # initial position\n",
"v0 = 0 # initial velocity \n",
"dmdt3 = 0.0791\n",
"time_3 = (0.25-0.05)/dmdt3\n",
"t3= np.linspace(0,time_3,10000)\n",
"dt3=t3[1]-t3[0]\n",
" \n",
"N=int(time_3/dt3)\n",
"height_needed = 300\n",
"t_plot = np.linspace(0,time_3,N)\n",
"\n",
"#initialize solution array\n",
"height3 = np.zeros([N,3])\n",
"\n",
"#Set intial conditions\n",
"height3[0,0] = y0\n",
"height3[0,1] = v0\n",
"height3[0,2] = m0\n",
"\n",
"for i in range(N-1):\n",
" height3[i+1] = rk2_step(height3[i],lambda state: rocket(state,dmdt=dmdt3, u=250),dt3)\n",
" height_predicted = height3[:,0]"
]
},
{
"cell_type": "code",
"execution_count": 73,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 576x360 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fig = plt.figure(figsize=(8,5))\n",
"\n",
"plt.plot(t_plot, height_predicted,'-.', color ='darkgreen', label='Predicted Path')\n",
"plt.plot(t_plot[-1],height_needed, '*', markersize = 15 ,color ='magenta',label='Detonation Height')\n",
"plt.xlabel('Time [s]\\n')\n",
"plt.ylabel('Height [m]\\n')\n",
"plt.legend(bbox_to_anchor=(1,1));\n",
"plt.title('Height vs Time\\n');"
]
},
{
"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>"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"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
}