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"## Hot air balloon - lift calculator\n",
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"### Inverted pyramid shape\n",
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"[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-pyramid.ipynb) "
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"# 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",
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"#import numpy as np\n",
"\n",
"#math\n",
"from math import sin, tan, sqrt"
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]
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"cell_type": "code",
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"execution_count": 20,
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"# 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− −
" return 1000.0 * p / ( rSpec * tempK )"
]
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"execution_count": 21,
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"# Ascent rate at ground level\n",
"# https://northstar-www.dartmouth.edu/~klynch/pmwiki-gc/uploads/BalloonCalulations.pdf\n",
"\n",
"# Coefficient of Drag assumed to 0.285 (spherical top) \n",
"Cd = 0.285\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"
]
},
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"# math: https://pl.wikipedia.org/wiki/Wielok%C4%85t_foremny\n",
"\n",
"# radius of the circle described on the polygon\n",
"def outradius(a=1.0,n=3):\n",
" return a / ( 2 * sin( pi / n ))\n",
"\n",
"# radius of the circle inscribed in the polygon\n",
"def inradius(a=1.0,n=3):\n",
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" return a / ( 2 * tan( pi / n )) \n",
"\n",
"# edge length\n",
"def edge_len(r=1.0,h=1.0):\n",
" return sqrt(pow(r,2) + pow(h,2))\n",
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"\n",
"#pyramid area/volume\n",
"def base_area(a=1.0,n=3):\n",
" return 0.5 * n * pow(outradius(a,n),2) * sin( 2 * pi / n)\n",
"\n",
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"def volume(a=1.0,h1=1.0,h2=1.0,n=3):\n",
" return base_area(a,n) * ( h1 + h2 ) / 3\n",
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" \n",
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"def surface_area(a=1.0,h1=1.0,h2=1.0,n=3):\n",
" return 0.5 * a * n * ( sqrt( pow(h1,2) + pow(inradius(a,n),2)) + sqrt( pow(h2,2) + pow(inradius(a,n),2)) )\n",
" \n"
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"VBox(children=(IntSlider(value=3, description='Segment num:', layout=Layout(width='500px'), max=12, min=3, sty…"
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"def f(num,width,heightT,heightB,airTemp,hotAirTemp,coatDens,tapeDens,payloadWeight):\n",
"\n",
" out=widgets.Output(layout={'margin': '10px 10px 10px 20px'}) \n",
" with out: \n",
" # Volume\n",
" vol = volume(width,heightB,heightT,num)\n",
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" print( \"{:<20}{:>6.1f} [m3]\".format(\"Volume:\",vol)) \n",
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" # Area\n",
" area = surface_area(width,heightB,heightT,num)\n",
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" print( \"{:<20}{:>6.1f} [m2]\".format(\"Area:\",area)) \n",
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" # Coating density (from: protective film for painting): 300g / 4x5m = 15g/m2 \n",
" coatingWeight = coatDens * area\n",
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" print( \"{:<20}{:>6.1f} [g]\".format(\"Coating weight:\",coatingWeight)) \n",
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" # adhesive tape density : average 2g/m \n",
" tapeLength = num * ( edge_len(outradius(width,num),heightT) + edge_len(outradius(width,num),heightB) )\n",
" tapeWeight = tapeDens * tapeLength\n",
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" 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",
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" # 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",
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" print( \"{:<20}{:>6.1f} [g/m3]\".format(\"Lift/volume:\",lift)) \n",
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" # Total lift force lift * volume \n",
" totalLiftForce = lift * vol\n",
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" print( \"{:<20}{:>6.1f} [g]\".format(\"Total lift force:\",totalLiftForce)) \n",
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" # Free lift force totalLiftForce - coatingWeight \n",
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" freeLiftForce = totalLiftForce - totalWeight - payloadWeight\n",
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" if freeLiftForce < 0:\n",
" color = 'red'\n",
" else:\n",
" color = None\n",
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" print( colored(\"{:<20}{:>6.1f} [g]\".format(\"Free lift force:\",freeLiftForce),color)) \n",
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" # Ascent rate \n",
" topArea = base_area(width,num)\n",
" ascRate = ascentRate(volume, airDens/1000.0, freeLiftForce/1000.0, topArea)\n",
" print( \"{:<20}{:>6.1f} [m/s]\".format(\"Ascent rate:\",ascRate)) \n",
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" \n",
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"# coating geometry \n",
" bottomGeometry = CylinderBufferGeometry(\n",
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" radiusTop=outradius(width,num), \n",
" radiusBottom=0.0, \n",
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" height=heightB, \n",
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" radialSegments=num, \n",
" heightSegments=1, \n",
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" openEnded=True, \n",
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" thetaStart=0, \n",
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" thetaLength=2.0*pi)\n",
" \n",
" bottomCylinder = Mesh(bottomGeometry,\n",
" material=MeshLambertMaterial(color='#c0c0c0'),\n",
" position=[0,0,0] \n",
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" )\n",
" \n",
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" zTop = ( heightB + heightT ) / 2.0\n",
" topGeometry = CylinderBufferGeometry(\n",
" radiusTop=0.0, \n",
" radiusBottom=outradius(width,num), \n",
" height=heightT, \n",
" radialSegments=num, \n",
" heightSegments=1, \n",
" openEnded=True, \n",
" thetaStart=0, \n",
" thetaLength=2.0*pi)\n",
" \n",
" topCylinder = Mesh(topGeometry,\n",
" material=MeshLambertMaterial(color='#c0c0c0'),\n",
" position=[0,zTop,0] \n",
" ) \n",
" \n",
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" keyLight = DirectionalLight(color='white', position=[3, 5, 1], intensity=0.5)\n",
"\n",
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" c = PerspectiveCamera(position=[2, 2, 6], up=[0, 1, 0], children=[keyLight])\n",
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"\n",
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" scene = Scene(children=[bottomCylinder,topCylinder, c, AmbientLight(color='#777777')], background=None)\n",
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"\n",
" renderer = Renderer(camera=c,\n",
" scene=scene,\n",
" alpha=True,\n",
" clearOpacity=1.0,\n",
" clearColor='#62a0ea',\n",
" controls=[OrbitControls(controlling=c)])\n",
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" display(widgets.HBox([renderer, out])) \n",
"\n",
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"\n",
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"\n",
"display(HTML('''<style>\n",
" .widget-hbox { margin-top: 20px; }\n",
" </style>'''))\n",
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"\n",
"layout=Layout(width='500px')\n",
"style = {'description_width': 'initial'}\n",
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" \n",
"num=widgets.IntSlider(min=3, max=12, step=1, value=3, description='Segment num:',layout=layout,style=style) \n",
"width=widgets.FloatSlider(min=0.1, max=5.0, step=0.1, value=3.0, description='Segment width [m]:',readout_format='.1f',layout=layout,style=style) \n",
"heightT=widgets.FloatSlider(min=0.1, max=5.0, step=0.1, value=1.0, description='Height top [m]:',readout_format='.1f',layout=layout,style=style) \n",
"heightB=widgets.FloatSlider(min=0.1, max=5.0, step=0.1, value=2.0, description='Height bottom [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",
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" \n",
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"w = widgets.interactive_output(f, { 'num' : num,\n",
" 'width' : width,\n",
" 'heightT' : heightT,\n",
" 'heightB' : heightB,\n",
" 'airTemp' : airTemp,\n",
" 'hotAirTemp' : hotAirTemp,\n",
" 'coatDens' : coatDens,\n",
" 'tapeDens' : tapeDens,\n",
" 'payloadWeight' : payloadWeight\n",
" }\n",
" )\n",
"\n",
"widgets.VBox([num, width, heightT, heightB, airTemp, hotAirTemp, coatDens,tapeDens,payloadWeight, w])\n"
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