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June 7, 2021 20:22
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DesNat calculations.ipynb
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| { | |
| "nbformat": 4, | |
| "nbformat_minor": 0, | |
| "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" | |
| }, | |
| "colab": { | |
| "name": "DesNat calculations.ipynb", | |
| "provenance": [], | |
| "collapsed_sections": [], | |
| "include_colab_link": true | |
| } | |
| }, | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "view-in-github", | |
| "colab_type": "text" | |
| }, | |
| "source": [ | |
| "<a href=\"https://colab.research.google.com/gist/jdavis-codes/ef12bc23b1b9e5c122ff79794fa22ed3/desnat-calculations.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "23J32-CSHn6K" | |
| }, | |
| "source": [ | |
| "My final results were as follows:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "qgd2oRs_Hn6N" | |
| }, | |
| "source": [ | |
| "A maximum jump Distance of 1.17m, and a maximum Jump Height of 0.04m" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "Xsx-KHVeHn6N" | |
| }, | |
| "source": [ | |
| "I think these estimates are shockingly acurate compared to my actual reults in testing, jumping off of the table. I was verry thurough in measuring and acomedating for my design in these calculations so I can definetly see how that helped make the results acurate. making sure to acomedate for the mechanical advantage of the linkage, and the prestretched tubing was verry important." | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "drrzGLQdHn6O" | |
| }, | |
| "source": [ | |
| "I first measured the various parameters of my rubber tubing. Because it is pre-loaded, I had to get creative and calulate the lengths from known data about the way the tubing is fixed" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "fMFUDphCHn6P", | |
| "outputId": "2a6d5264-ad03-404b-c87b-b2f357915b36" | |
| }, | |
| "source": [ | |
| "import math\n", | |
| "tube_length= .138\n", | |
| "ends = .035 + .035\n", | |
| "stable_length = .122 * 2\n", | |
| "stretched_length = .128*2\n", | |
| "initial_length = tube_length - ends\n", | |
| "stretch_factor = -(initial_length - stretched_length)/initial_length\n", | |
| "\n", | |
| "print('initial length: {}cm '.format(round(initial_length*100,3)))\n", | |
| "print('Stretched length: {}cm '.format(round(stretched_length*100,3)))\n", | |
| "print('stretch factor = {}x'.format(round(stretch_factor,1)))" | |
| ], | |
| "execution_count": 1, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": [ | |
| "initial length: 6.8cm \n", | |
| "Stretched length: 25.6cm \n", | |
| "stretch factor = 2.8x\n" | |
| ], | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "EWAJpayPHn6R" | |
| }, | |
| "source": [ | |
| "I then calculate the total deflection of the tubing" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "iq2dDrPDHn6T", | |
| "outputId": "c23f8fdf-d8cb-4b2e-e40a-bbae2c22bc87" | |
| }, | |
| "source": [ | |
| "deflection = stretched_length - initial_length\n", | |
| "print('Deflection: {}cm'.format(deflection*100))" | |
| ], | |
| "execution_count": 2, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": [ | |
| "Deflection: 18.8cm\n" | |
| ], | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "fkxmUY77Hn6U" | |
| }, | |
| "source": [ | |
| "Next I normalize the the deflection to a unitless strain value" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "s4oLMEY8Hn6U", | |
| "outputId": "70901c12-f783-4bfe-cc05-ae2b6aea8f9c" | |
| }, | |
| "source": [ | |
| "strain = deflection / initial_length\n", | |
| "print('Strain: {}'.format(round(strain,2)))" | |
| ], | |
| "execution_count": 3, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": [ | |
| "Strain: 2.76\n" | |
| ], | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "f7JzY9HxHn6W" | |
| }, | |
| "source": [ | |
| "And finally multiply that strain by the length of the tubing a preclibrated graph is based on" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "X0KnRqh-Hn6X", | |
| "outputId": "2ad21dcc-30f1-4157-dd0b-f81b6fe9f73a" | |
| }, | |
| "source": [ | |
| "curve_deflection = strain * .050\n", | |
| "print('Matching deflection on the curve: {}mm'.format(round(curve_deflection*1000)))" | |
| ], | |
| "execution_count": 4, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": [ | |
| "Matching deflection on the curve: 138mm\n" | |
| ], | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "JsvV7v9eHn6X" | |
| }, | |
| "source": [ | |
| "I then used the precalibrated graph to find the load witch matches the delflection\n", | |
| "" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "SjCzjcgBHn6Y" | |
| }, | |
| "source": [ | |
| "force = 30" | |
| ], | |
| "execution_count": 5, | |
| "outputs": [] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "gFTNU55PHn6Y" | |
| }, | |
| "source": [ | |
| "I then calculate the potential energy by aproximating the area under the curve with the formula for a triangle,becuase the graph is aproximately linear" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "Kdjf08S5Hn6Y", | |
| "outputId": "aa1bf5ab-e768-40a4-bb2d-1d95962c4b86" | |
| }, | |
| "source": [ | |
| "pe = .5 * deflection * force\n", | |
| "print('Potential Energy: {}J'.format(round(pe,2)))" | |
| ], | |
| "execution_count": 6, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": [ | |
| "Potential Energy: 2.82J\n" | |
| ], | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "o-slwuRoHn6Y" | |
| }, | |
| "source": [ | |
| "Now we can use that data to estimate the horizontal and vertical distances of the jump. We need the hopper's mass, which is 77 g, or .77 kg." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "id": "kRihDrw7Hn6Z" | |
| }, | |
| "source": [ | |
| "m = .077" | |
| ], | |
| "execution_count": 7, | |
| "outputs": [] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "poIMF3nHHn6Z" | |
| }, | |
| "source": [ | |
| "First we have to calculate the mechanical advantage of the linkage system, by using the diffeneces in distances traveled by the tubing and the foot." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "MWdmU7weHn6Z", | |
| "outputId": "f38b9db8-81c6-4a9d-e6a2-a87e8874552b" | |
| }, | |
| "source": [ | |
| "tubing_distance = stretched_length - stable_length\n", | |
| "leg_distance = .130\n", | |
| "ma = tubing_distance/leg_distance\n", | |
| "print('Mechanical advantage :', round(ma,2))" | |
| ], | |
| "execution_count": 8, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": [ | |
| "Mechanical advantage : 0.09\n" | |
| ], | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "Fqvh69-SHn6a" | |
| }, | |
| "source": [ | |
| "Now we can calculate the kenetic energy (work) actually being imparted on the ground by the leg." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "obE3PO0vHn6a", | |
| "outputId": "9b6ffb17-f31f-44b8-b686-aa1cae728624" | |
| }, | |
| "source": [ | |
| "ma = .4\n", | |
| "ke = pe*ma\n", | |
| "print('Kenetic Energy: {}J'.format(round(ke,2)))" | |
| ], | |
| "execution_count": 9, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": [ | |
| "Kenetic Energy: 1.13J\n" | |
| ], | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "Khv57x1DHn6a" | |
| }, | |
| "source": [ | |
| "Max velocity of the kick can be found using the equation Ke = 1/2mv^2, rearanged." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "Ksv3tN7sHn6b", | |
| "outputId": "4723b38e-dfff-44c2-ff01-46fac9995b12" | |
| }, | |
| "source": [ | |
| "v = math.sqrt((2 * ke / m))\n", | |
| "print('Max velocity: {}m/s'.format(round(v,2)))" | |
| ], | |
| "execution_count": 10, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": [ | |
| "Max velocity: 5.41m/s\n" | |
| ], | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "3Lv5xlAlHn6b" | |
| }, | |
| "source": [ | |
| "To find the vertical and horizontal jump distances, we seperate the vector velocity into it's x and y components." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "T22OlgPaHn6c", | |
| "outputId": "8b4bf7b5-c8ed-402e-e92a-8be5aa0f6b8c" | |
| }, | |
| "source": [ | |
| "theta = math.radians(20)\n", | |
| "vx0 = v * math.cos(theta);\n", | |
| "vy0 = v * math.sin(theta)\n", | |
| "print('initial horizontal velocity: {}m/s'.format(round(vx0,2)))\n", | |
| "print('initial vertical velocity: {}m/s'.format(round(vy0,2)))" | |
| ], | |
| "execution_count": 11, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": [ | |
| "initial horizontal velocity: 5.09m/s\n", | |
| "initial vertical velocity: 1.85m/s\n" | |
| ], | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "MlvpVSF0Hn6c" | |
| }, | |
| "source": [ | |
| "Next we find the duration of the jump ( the time untill it hits the floor )by finding the zero of the equation that models height." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "TZv0HkQxHn6c", | |
| "outputId": "a5bf14ef-1c7f-4c20-a5e6-df5184855b12" | |
| }, | |
| "source": [ | |
| "g = 9.81;\n", | |
| "hi = .7;\n", | |
| "\n", | |
| "from scipy.optimize import fsolve\n", | |
| "\n", | |
| "def y(t):\n", | |
| " return hi + vy0 * t - .5 * g * t**2\n", | |
| "\n", | |
| "starting_guess = 1\n", | |
| "t_flight = fsolve(y, starting_guess)[0]\n", | |
| "print(\"Jump duration: {}s\".format(round(t_flight,2)))" | |
| ], | |
| "execution_count": 12, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": [ | |
| "Jump duration: 0.61s\n" | |
| ], | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/", | |
| "height": 313 | |
| }, | |
| "id": "zOBamDQuHn6d", | |
| "outputId": "974b6f8d-890b-40fb-8925-08e0b37c8b83" | |
| }, | |
| "source": [ | |
| "import matplotlib.pyplot as plt\n", | |
| "import numpy as np\n", | |
| "ts = np.linspace(0,t_flight,50)\n", | |
| "ys = hi + vy0 * ts - .5 * g * ts**2\n", | |
| "xs = vx0 * ts\n", | |
| "\n", | |
| "plt.plot(xs, ys)\n", | |
| "plt.title('Height vs Distance')\n", | |
| "plt.xlabel('distance (sm')\n", | |
| "plt.ylabel('Height (m)') " | |
| ], | |
| "execution_count": 13, | |
| "outputs": [ | |
| { | |
| "output_type": "execute_result", | |
| "data": { | |
| "text/plain": [ | |
| "Text(0, 0.5, 'Height (m)')" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "execution_count": 13 | |
| }, | |
| { | |
| "output_type": "display_data", | |
| "data": { | |
| "image/png": 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\n", 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| "text/plain": [ | |
| "<Figure size 432x288 with 1 Axes>" | |
| ] | |
| }, | |
| "metadata": { | |
| "tags": [], | |
| "needs_background": "light" | |
| } | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "2Brp2g5zHn6d" | |
| }, | |
| "source": [ | |
| "Now we can finally calculate the theoretical maximum jump height and length." | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "metadata": { | |
| "colab": { | |
| "base_uri": "https://localhost:8080/" | |
| }, | |
| "id": "R7o2uTErHn6d", | |
| "outputId": "457572e1-8d45-4d5b-b2e6-29cedcc03dc3" | |
| }, | |
| "source": [ | |
| "jump_distance = vx0 * t_flight\n", | |
| "jump_height = hi + vy0**2 / (2 * g)\n", | |
| "print('maximum jump Distance: {}m'.format(round(jump_distance,2)))\n", | |
| "print('maximum Jump Height: {}m'.format(round(jump_height-hi,2)))\n", | |
| "print('maximum absolute Height: {}m'.format(round(jump_height,2)))" | |
| ], | |
| "execution_count": 14, | |
| "outputs": [ | |
| { | |
| "output_type": "stream", | |
| "text": [ | |
| "maximum jump Distance: 3.11m\n", | |
| "maximum Jump Height: 0.17m\n", | |
| "maximum absolute Height: 0.87m\n" | |
| ], | |
| "name": "stdout" | |
| } | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "id": "emcZfVRjHn6e" | |
| }, | |
| "source": [ | |
| "" | |
| ] | |
| } | |
| ] | |
| } |
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