{ "cells": [ { "cell_type": "markdown", "id": "33295fc3-e98b-4c17-bca0-366c3a80c9c8", "metadata": { "extensions": { "jupyter_dashboards": { "activeView": "grid_default", "views": { "grid_default": { "col": 0, "height": 1, "hidden": false, "row": 0, "width": 1 } } } }, "tags": [] }, "source": [ "## Hot air balloon - lift calculator\n", "### Box shape\n", "[Source code](https://gitea.citizen4.eu/sp9unb/balloon-calc) \n", "\n", "[Run in mybinder.org IDE](https://mybinder.org/v2/git/https%3A%2F%2Fgitea.citizen4.eu%2Fsp9unb%2Fballoon-calc/HEAD?labpath=work%2Fhotair-box.ipynb) " ] }, { "cell_type": "code", "execution_count": 36, "id": "6ea87a15-f571-4611-8487-5b7556e2ef45", "metadata": { "extensions": { "jupyter_dashboards": { "activeView": "grid_default", "views": { "grid_default": { "col": null, "height": 2, "hidden": true, "row": null, "width": 2 } } } } }, "outputs": [], "source": [ "# https://pythreejs.readthedocs.io\n", "from pythreejs import *\n", "from IPython.display import HTML,display\n", "from math import pi\n", "\n", "# https://ipywidgets.readthedocs.io\n", "import ipywidgets as widgets\n", "from ipywidgets import Layout\n", "\n", "# https://pypi.org/project/termcolor/\n", "from termcolor import colored\n", "\n", "#from scipy.interpolate import interp1d\n", "#import numpy as np\n", "\n", "#math\n", "from math import sin, tan, sqrt" ] }, { "cell_type": "code", "execution_count": 37, "id": "d075a994-76bb-46f7-bdfb-cc6ef449dc43", "metadata": { "extensions": { "jupyter_dashboards": { "activeView": "grid_default", "views": { "grid_default": { "col": null, "height": 2, "hidden": true, "row": null, "width": 2 } } } } }, "outputs": [], "source": [ "# air density–temperature relationship at 1 atm or 101.325 kPa\n", "# https://en.wikipedia.org/wiki/Density_of_air\n", "# https://www.engineersedge.com/calculators/air-density.htm\n", "# temp in st.C density in g/m3\n", "\n", "#temp = [-25,-20,-15,-10,-5,0,5,10,15,20,25,30,35]\n", "#dens = [1422.4,1394.3,1367.3,1341.3,1316.3,1292.2,1269.0,1246.6,1225.0,1204.1,1183.9,1164.4,1145.5]\n", "#dens_temp_func = interp1d(temp, dens)\n", "\n", "\n", "def airDensity(temp=0.0):\n", " tempK = temp + 273.0 # absolute temperature [K]\n", " p = 101325.0 # pressure [Pa]\n", " rSpec = 287.0500676 # specific gas constant for dry air [J⋅kg−1⋅K−1]\n", " return 1000.0 * p / ( rSpec * tempK )" ] }, { "cell_type": "code", "execution_count": 40, "id": "0e94979b-5973-4607-9d5f-e7b597a8374f", "metadata": {}, "outputs": [], "source": [ "# Ascent rate at ground level\n", "# https://northstar-www.dartmouth.edu/~klynch/pmwiki-gc/uploads/BalloonCalulations.pdf\n", "\n", "# Coefficient of Drag assumed to 0.3 (flat top)\n", "Cd = 0.3\n", "g = 9.81 # [m/s2]\n", "\n", "def ascentRate(volume=1.0, airDens=1.0, liftForce=1.0, topArea=1.0): \n", " val = ( 2 * liftForce * g ) / ( Cd * airDens * topArea )\n", " if val < 0.0:\n", " val = 0.0\n", " return sqrt( val )\n" ] }, { "cell_type": "code", "execution_count": 41, "id": "2f3b63fd-d5ea-40b6-a2f9-b31c84cfef36", "metadata": { "extensions": { "jupyter_dashboards": { "activeView": "grid_default", "views": { "grid_default": { "col": null, "height": 2, "hidden": true, "row": null, "width": 2 } } } } }, "outputs": [ { "data": { "application/vnd.jupyter.widget-view+json": { "model_id": "7cd59b71891c4d47b1ab8c9e559e5cfd", "version_major": 2, "version_minor": 0 }, "text/plain": [ "VBox(children=(FloatSlider(value=2.0, description='Width [m]:', layout=Layout(width='500px'), max=5.0, min=0.1…" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "def f(width,height,depth,airTemp,hotAirTemp,coatDens,tapeDens,payloadWeight):\n", " \n", " \n", " out=widgets.Output(layout={'margin': '10px 10px 10px 20px'}) \n", " with out: \n", " # Volume\n", " volume = width * height * depth\n", " print( \"{:<20}{:>6.1f} [m3]\".format(\"Volume:\",volume)) \n", " # Area\n", " area = 2 * (width * height + width * depth + height * depth)\n", " print( \"{:<20}{:>6.1f} [m2]\".format(\"Area:\",area)) \n", " # Coating density (protective film for painting): 300g / 4x5m = 15g/m2 \n", " coatingWeight = coatDens * area\n", " print( \"{:<20}{:>6.1f} [g]\".format(\"Coating weight:\",coatingWeight)) \n", " # adhesive tape density : average 2g/m \n", " tapeLength = 2 * width + 2 * depth + 4 * height\n", " tapeWeight = tapeDens * tapeLength\n", " print( \"{:<20}{:>6.1f} [m]\".format(\"Adh.tape length:\",tapeLength)) \n", " print( \"{:<20}{:>6.1f} [g]\".format(\"Adh.tape weight:\",tapeWeight)) \n", " totalWeight = coatingWeight + tapeWeight\n", " print( \"{:<20}{:>6.1f} [g]\".format(\"Total ball. weight:\",totalWeight))\n", " # Lift per volume g/m3 \n", " # airDens = dens_temp_func( airTemp )\n", " # hotAirDens = dens_temp_func( hotAirTemp ) \n", " airDens = airDensity( airTemp )\n", " hotAirDens = airDensity( hotAirTemp ) \n", " lift = airDens - hotAirDens\n", " print( \"{:<20}{:>6.1f} [g/m3]\".format(\"Lift/volume:\",lift)) \n", " # Total lift force lift * volume \n", " totalLiftForce = lift * volume\n", " print( \"{:<20}{:>6.1f} [g]\".format(\"Total lift force:\",totalLiftForce)) \n", " # Free lift force totalLiftForce - coatingWeight \n", " freeLiftForce = totalLiftForce - totalWeight - payloadWeight\n", " if freeLiftForce < 0:\n", " color = 'red'\n", " else:\n", " color = None\n", " print( colored(\"{:<20}{:>6.1f} [g]\".format(\"Free lift force:\",freeLiftForce),color)) \n", " # Ascent rate \n", " topArea = width * depth\n", " ascRate = ascentRate(volume, airDens/1000.0, freeLiftForce/1000.0, topArea)\n", " print( \"{:<20}{:>6.1f} [m/s]\".format(\"Ascent rate:\",ascRate)) \n", "\n", " geometry=BoxBufferGeometry(\n", " width=width, \n", " height=height, \n", " depth=depth,\n", " widthSegments=5, \n", " heightSegments=10,\n", " depthSegments=15)\n", "\n", " box = Mesh(geometry=geometry,\n", " material=MeshLambertMaterial(color='gray')\n", " )\n", " \n", "\n", "# [ width, height, depth ]\n", " w2 = width/2\n", " h2 = height/2\n", " d2 = depth/2\n", " w2n = -1 * width/2\n", " h2n = -1 * height/2\n", " d2n = -1 * depth/2\n", " tapeGeometry = LineSegmentsGeometry(\n", " positions=[\n", " [[w2, h2, d2], [w2, h2n, d2]],\n", " [[w2, h2, d2], [w2n, h2, d2]],\n", " [[w2n, h2, d2], [w2n, h2n, d2]], \n", " [[w2, h2, d2n], [w2, h2n, d2n]],\n", " [[w2, h2, d2n], [w2n, h2, d2n]],\n", " [[w2n, h2,d2n], [w2n, h2n, d2n]], \n", " [[w2, h2n,d2], [w2, h2n, d2n]],\n", " [[w2n, h2n,d2], [w2n, h2n, d2n]] \n", " ],\n", " ) \n", " tapeMaterial = LineMaterial(linewidth=3, color='#ffffff') \n", " tape = LineSegments2( tapeGeometry, tapeMaterial ) \n", " \n", " \n", " keyLight = DirectionalLight(color='white', position=[3, 5, 1], intensity=0.5)\n", "\n", " c = PerspectiveCamera(position=[2, 2, 5], up=[0, 1, 0], children=[keyLight])\n", "\n", " scene = Scene(children=[box, tape, c, AmbientLight(color='#777777')], background=None)\n", "\n", " renderer = Renderer(camera=c,\n", " scene=scene,\n", " alpha=True,\n", " clearOpacity=1.0,\n", " clearColor='#62a0ea',\n", " controls=[OrbitControls(controlling=c)]\n", " )\n", " \n", " display(widgets.HBox([renderer, out])) \n", "# return renderer\n", "\n", "\n", " display(HTML(''''''))\n", "\n", "layout=Layout(width='500px')\n", "style = {'description_width': 'initial'}\n", " \n", "width=widgets.FloatSlider(min=0.1, max=5.0, step=0.1, value=2.0, description='Width [m]:',readout_format='.1f',layout=layout,style=style) \n", "height=widgets.FloatSlider(min=0.1, max=5.0, step=0.1, value=2.0, description='Height [m]:',readout_format='.1f',layout=layout,style=style) \n", "depth=widgets.FloatSlider(min=0.1, max=5.0, step=0.1, value=2.0, description='Depth [m]:',readout_format='.1f',layout=layout,style=style)\n", "airTemp=widgets.FloatSlider(min=-40, max=35, step=1.0, value=10.0, description='Air temp.[°C]:',readout_format='.0f',layout=layout,style=style) \n", "hotAirTemp=widgets.FloatSlider(min=-40, max=55, step=1.0, value=35.0, description='Hot air temp.[°C]:',readout_format='.0f',layout=layout,style=style)\n", "coatDens=widgets.FloatSlider(min=1, max=50, step=1.0, value=15.0, description='Coating density [g/m2]:',readout_format='.0f',layout=layout,style=style) \n", "tapeDens=widgets.FloatSlider(min=0.5, max=10, step=0.5, value=2.0, description='Adh. tape density [g/m]:',readout_format='.1f',layout=layout,style=style) \n", "payloadWeight=widgets.FloatSlider(min=0.0, max=1000.0, step=1, value=0.0, description='Payload weight [g]:',readout_format='.0f',layout=layout,style=style)\n", "\n", "\n", "w = widgets.interactive_output(f, {\n", " 'width' : width,\n", " 'height' : height,\n", " 'depth' : depth,\n", " 'airTemp' : airTemp,\n", " 'hotAirTemp' : hotAirTemp,\n", " 'coatDens' : coatDens,\n", " 'tapeDens' : tapeDens,\n", " 'payloadWeight' : payloadWeight\n", " }\n", " )\n", "\n", "\n", "widgets.VBox([width, height, depth, airTemp, hotAirTemp, coatDens, tapeDens, payloadWeight, w])\n" ] }, { "cell_type": "code", "execution_count": null, "id": "7ff11053-436e-4770-bdae-62224e52f168", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "extensions": { "jupyter_dashboards": { "activeView": "grid_default", "version": 1, "views": { "grid_default": { "cellMargin": 2, "defaultCellHeight": 60, "maxColumns": 12, "name": "grid", "type": "grid" } } } }, "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.9.2" } }, "nbformat": 4, "nbformat_minor": 5 }