Watching our balloon filling – I started worry.
It looks pretty promising on a picture, however balloon is currently about 2/3 full (perhaps more), but it is not yet floating! Is my trivial calculation going to be enough? Wikipedia the Density of Air article states that “At 1013.25 hPa and 15°C, air has a density of approximately 1.225 kg/m³ “. Mr. Google helped with the same on Hydrogen coming with “density of hydrogen is equal to 0.082 kg/m³ at 0°C”. Volume of our balloon and weight of its shell is quite unknown here. (I know I should have weight it!!!) I assume that volume will be around 0.4m3 and weight 400g.
With assumption that Archimedes principle works same way for ships as well as for airships, we can use that 0.4m3 to get our lifting power. 1.225kg x 0.4 – 0.088kg x 0.4 lift -> 548g (5480N) of lifting force. Now minus those 400g above … and we should be still somw 1480N surplus.
So let’s use Excel to give us some ideas on where are our boundaries.
| 760 | 664.12 | 614.12 | 564.12 | 514.12 | 464.12 | 414.12 | 364.12 | 314.12 | 264.12 | 214.12 | 164.12 |
| 740 | 641.38 | 591.38 | 541.38 | 491.38 | 441.38 | 391.38 | 341.38 | 291.38 | 241.38 | 191.38 | 141.38 |
| 720 | 618.64 | 568.64 | 518.64 | 468.64 | 418.64 | 368.64 | 318.64 | 268.64 | 218.64 | 168.64 | 118.64 |
| 700 | 595.9 | 545.9 | 495.9 | 445.9 | 395.9 | 345.9 | 295.9 | 245.9 | 195.9 | 145.9 | 95.9000000000001 |
| 680 | 573.16 | 523.16 | 473.16 | 423.16 | 373.16 | 323.16 | 273.16 | 223.16 | 173.16 | 123.16 | 73.1600000000001 |
| 660 | 550.42 | 500.42 | 450.42 | 400.42 | 350.42 | 300.42 | 250.42 | 200.42 | 150.42 | 100.42 | 50.4200000000001 |
| 640 | 527.68 | 477.68 | 427.68 | 377.68 | 327.68 | 277.68 | 227.68 | 177.68 | 127.68 | 77.6800000000001 | 27.6800000000001 |
| 620 | 504.94 | 454.94 | 404.94 | 354.94 | 304.94 | 254.94 | 204.94 | 154.94 | 104.94 | 54.9400000000001 | 4.94000000000005 |
| 600 | 482.2 | 432.2 | 382.2 | 332.2 | 282.2 | 232.2 | 182.2 | 132.2 | 82.2 | 32.2 | -17.8 |
| 580 | 459.46 | 409.46 | 359.46 | 309.46 | 259.46 | 209.46 | 159.46 | 109.46 | 59.46 | 9.46000000000004 | -40.54 |
| 560 | 436.72 | 386.72 | 336.72 | 286.72 | 236.72 | 186.72 | 136.72 | 86.72 | 36.72 | -13.28 | -63.28 |
| 540 | 413.98 | 363.98 | 313.98 | 263.98 | 213.98 | 163.98 | 113.98 | 63.98 | 13.98 | -36.02 | -86.02 |
| 520 | 391.24 | 341.24 | 291.24 | 241.24 | 191.24 | 141.24 | 91.24 | 41.24 | -8.75999999999999 | -58.76 | -108.76 |
| 500 | 368.5 | 318.5 | 268.5 | 218.5 | 168.5 | 118.5 | 68.5 | 18.5 | -31.5 | -81.5 | -131.5 |
| 480 | 345.76 | 295.76 | 245.76 | 195.76 | 145.76 | 95.76 | 45.76 | -4.24000000000001 | -54.24 | -104.24 | -154.24 |
| 460 | 323.02 | 273.02 | 223.02 | 173.02 | 123.02 | 73.02 | 23.02 | -26.98 | -76.98 | -126.98 | -176.98 |
| 440 | 300.28 | 250.28 | 200.28 | 150.28 | 100.28 | 50.28 | 0.279999999999973 | -49.72 | -99.72 | -149.72 | -199.72 |
| 420 | 277.54 | 227.54 | 177.54 | 127.54 | 77.54 | 27.54 | -22.46 | -72.46 | -122.46 | -172.46 | -222.46 |
| 400 | 254.8 | 204.8 | 154.8 | 104.8 | 54.8000000000001 | 4.80000000000007 | -45.1999999999999 | -95.1999999999999 | -145.2 | -195.2 | -245.2 |
| 380 | 232.06 | 182.06 | 132.06 | 82.0600000000001 | 32.0600000000001 | -17.9399999999999 | -67.9399999999999 | -117.94 | -167.94 | -217.94 | -267.94 |
| 360 | 209.32 | 159.32 | 109.32 | 59.3200000000001 | 9.32000000000005 | -40.68 | -90.6799999999999 | -140.68 | -190.68 | -240.68 | -290.68 |
| 340 | 186.58 | 136.58 | 86.5800000000001 | 36.58 | -13.42 | -63.42 | -113.42 | -163.42 | -213.42 | -263.42 | -313.42 |
| 320 | 163.84 | 113.84 | 63.84 | 13.84 | -36.16 | -86.16 | -136.16 | -186.16 | -236.16 | -286.16 | -336.16 |
| 300 | 141.1 | 91.1 | 41.1 | -8.89999999999998 | -58.9 | -108.9 | -158.9 | -208.9 | -258.9 | -308.9 | -358.9 |
| 280 | 118.36 | 68.36 | 18.36 | -31.64 | -81.64 | -131.64 | -181.64 | -231.64 | -281.64 | -331.64 | -381.64 |
| 260 | 95.62 | 45.62 | -4.38 | -54.38 | -104.38 | -154.38 | -204.38 | -254.38 | -304.38 | -354.38 | -404.38 |
| 240 | 72.88 | 22.88 | -27.12 | -77.12 | -127.12 | -177.12 | -227.12 | -277.12 | -327.12 | -377.12 | -427.12 |
| 220 | 50.14 | 0.139999999999986 | -49.86 | -99.86 | -149.86 | -199.86 | -249.86 | -299.86 | -349.86 | -399.86 | -449.86 |
| 200 | 27.4 | -22.6 | -72.6 | -122.6 | -172.6 | -222.6 | -272.6 | -322.6 | -372.6 | -422.6 | -472.6 |
| cm2 / g | 200 | 250 | 300 | 350 | 400 | 450 | 500 | 550 | 600 | 650 | 700 |
All places where you see negative values (or red ones below) – we don’t want to be there!
Another aspect here is the air density constant 1.225 kg/m³ … which is not a constant at all. This value changes under number of circumstances. Local temperature, pressure, moisture in the air … and almost always it plays against our need! I went through several graphs and formulas and it is pure magic. (Did you know that air’s density is actually lowering with an amount of moisture?)
I’ve been writing this article in preparation of my defence in case everything would go wrong, but meanwhile …
.. it floats! 😀 I’m going to make myself a Peppermint tea to celebrate! 😀
