Balloon Lift with Lighter than Air Gases
It has long been known that if immersed in a gas or liquid, an object will displace a volume of that gas or liquid equivalent to its own volume. By comparing the weight of the object vs the weight of this displaced volume of gas or liquid, you can determine if the object will float or sink like the proverbial stone. Some dude allegedly thought this up while lounging in his bath.
When a balloon is filled with something other than air and then released in air, it will float or sink based on the same principle. If the weight of the volume of air displaced by the balloon is less than the weight of the balloon and the gas inside, the balloon will drop to the ground.
If the weight of the air displaced by the balloon is greater than the weight of the balloon and the gas inside, the balloon will float upwards. This force, or buoyancy, either positive or negative, is exactly the difference in the weight of the balloon and its contents, versus the weight of the volume of air displaced.
As volumes get large on any balloon, the problem of distributing the load stress becomes great. Large plastic lifting balloons have extremely strong strips incorporated into the multiple seams that join the gores together running from top to bottom. Designs from the 1800's used nets to contain the balloon and distribute the stress of the suspended load.
One of the most famous of the Civil War balloons was made by the Confederacy of donated undergarments of the ladies of the South, all silk and the only source of silk the South had at the time. It was hoped that it would counter the shocking success of Union balloons which were providing airborne intelligence of opposing troop movements that was proving devastating. The southern patchwork balloon only flew once before it was captured by the Union, a disappointment and an afront for which General Longstreet claimed he never found it in his heart to forgive the Union.
These early balloons used hydrogen. While atomic hydrogen is only one fourth the weight of atomic helium, hydrogen forms a diatomic molecule as a gas, and thus has a molecular weight of half of helium, reducing the lift advantage. Since hydrogen is explosive in mixtures with air of more than 4 percent, it is a great fire hazard and serious explosion hazard in large quantities. Helium being an inert gas does not form a diatomic molecule as a gas. Thus hydrogen is only half the weight of helium, not one fourth as you might suspect by looking it up on a periodic table. H2 = 2 * Atomic Weight 1; vs He = 1 * Atomic Weight 4.
Hydrogen is easily manufactured by several chemical reactions such as the action of hydrochloric acid on mossy zinc metal and the action of sodium hydroxide on aluminum metal pellets or punchings. This ability to make the gas on the spot has always been attractive. During the civil war special wagons with large wooden tanks full of acid were used to generate the inflation hydrogen required on the spot.
Helium is mined, or more exactly drilled for. In the Oklahoma and Texas panhandles are natural gas wells that contain up to 4% or more Helium. This natural resource is very rare. The gas field must be encased in radioactive rock or no helium is produced. The alpha particle decay in the surrounding radioactive rock over millions and millions of years creates the helium. An alpha particle is just a helium nucleus. When it slows down and regains its two electrons, it becomes a helium molecule. Thus the radioactive rock makes helium, one molecule at a time, to accumulate in the same pocket as the natural gas.
In the 1930's Germany asked the USA many times for helium for its Zepplins. The US was concerned that helium had other military uses and horded it as a strategic material. For this reason, the Hindenburg was still lofted with hydrogen on its last disastrous flight, instead of being converted to helium as Germany had been trying to do for years.
Helium is a natural byproduct of the liquefaction of the natural gas for pipeline shipment from these special gas fields. Helium liquefies at a much lower temperature than natural gas, close to absolute zero (4 degrees Kelvin). The volume left over after liquefaction is mostly helium ready to be stripped off and sold to the US Government Bureau of Mines. Few people seem concerned that this is a non-renewable and expendable natural resource, tied to very few gas wells in the world.
Natural gas or Methane is also lighter than air, not because it contains helium, which most of it does not, but because it is just less dense than air. It can be used to fill balloons, but it suffers from the same flammability and explosion hazard as hydrogen. Methane gas is roughly half the weight of air and provides anemic, but useful lift. Propane and Butane are too heavy, besides being flammable and explosive in the right mixtures with air.
Artificial gas as is used in many city gas mains will not work. It is loaded with Ethane and other gases in addition to methane and thus turns out to be heavier than, or about the same density as air. Only natural methane gas will work effectively. Some artificial gas supplies may be supplemented with hydrogen, so the exact weight of these mixtures of "gas" is hard to guess.
One should also mention hot air. The density of air goes down as it expands with temperature. Thus hot air surrounded by cold air will rise. It simply displaces a volume of colder air that is heavier than its hotter self, thus positive lift. If hot air is trapped in a balloon envelope, it will generate lift because the air inside is actually lighter, or less dense than the cooler air outside.
People have made and flown model hot air balloons. Hot air will give about .3 ounce per cubic foot of lift, or approximately 1/5th to 1/4th ounce per cubic foot depending on relative temperature of the air inside the balloon and outside. It is possible to imagine a small hot air balloon that might lift an antenna wire. But I have not heard of anyone trying this. Some of the model hot air balloons are quite elegant with radio controlled burner valves.
Here are some simple computations of lift of balloons. To get the real value, you would have to first weigh the uninflated balloon, any cord or other material used for closing and sealing the balloon, any nets or other lift distributing contraptions and subtract those weights.
Also a latex balloon generates some backpressure which increases the density of the gas inside and again lowers the lift. You should also take off about half a percent, to one percent of total lift for the backpressure of the inflated balloon and the resulting compression of the internal gas. This backpressure is low, maybe on the order of 5 mm of mercury, but still enough to affect lift.
Really large lifting balloons are designed of plastic sheet, very thin, and designed to be inflated limp so they have no backpressure. Some are designed to have a specific backpressure at a specific float altitude. These superpressure balloons, as they are called, can establish a stable altitude and ride wind currents around the world!
During World War II, the Japanese bombed the US Mainland with gas balloons of a very clever design which floated up into the jet stream and crossed the Pacific in only a few days. They had a simple but effective control based on sandbag releases and gas releases to maintain a reasonable float altitude, even during night/day temperature transitions. It is nearly unbelievable that these simple contraptions worked, but they did! One might base a trick question on this like "During WWII, did the Japanese successfully bomb Montana?"
Few balloons are exactly spherical, even the so called super rounds, so using a sphere to approximate volume vs diameter is a simplification. Latex balloons are available from distributors for such companies as Qualatex. They commonly have latex balloons designed to be inflated to 30 to 36 inches. These are not weather balloons, but heavy gauge latex balloons and rather rugged. The Canadian Company Tilco has heavy duty balloons in the 40 inch range, a bit larger than the Qualatex versions. TufTex also makes a very good quality 36 inch range balloon. Usually the Jewel or Crystal colors of these balloons inflate better, since the dyes used modify the latex less than some of the other colors. Some of these are available in clear as well. Which color would be best? that is hard to answer, but of course something like black would heat up faster.
They are fluted balloons and a tiny bit boxy, but generally quite round, and not the pear shaped like the smaller party type balloons. There is a product called "High Float" that can be added to the inside of the balloons before inflation. It coats the inside with a liquid plastic that seals the balloon more effectively against helium loss. Of course it adds a small amount of weight as well, but it greatly increases "float time." People have even been known to wash the outside of balloons with diluted High Float to coat the outside and reduce oxidation and sunlight damage. Sunlight is extremely BAD for latex balloons, especially inflated ones.
Weather balloons are a very special and fragile item, but places like Edmund Scientific can sell them in small quantities. They can be quite large, on the order of 16 feet, but their light gauge does not lend them well to the rigors of teathered flight. Chloroprene is a type of dipped latex product that is treated with a substance somewhat like household bleach after dipping to modify the latex and make it more environmentally resistive. These balloons are more expensive but should last longer inflated outside.
In between the heavy gauge display balloons like the Tilco, Qualatex and TufTex types, and the super thin weather balloons, are Pilot Balloons, about one meter balloons designed to be released and tracked for wind speed and direction measurement. They are more rugged than weather balloons, can inflate to quit a bit more than 1 meter in diameter and not terribly expensive. They are excellent candidates for antenna lifting. Certain weather instrument supply companies sell them. They are often available in chloroprene.
However, keep in mind that you need to fill these balloons with helium gas. The large commercial high pressure helium cylinders, the big ones weighing in at well over 100 pounds and requiring a regulator to dispense, contain about 230 cubic feet of helium each. The actual amount depends on pressure and can range from 190 cubic feet to 242 cubic feet in a typical range of tank pressures.
Such cylinders are about nine inches around and 51 inches tall. One cubic foot of gas is about 28 1/3 liters or just under 7.5 gallons. Such a cylinder should inflate a balloon about 7.5 feet in diameter and lift about 15 pounds or so. There is also a 9.25 by 55 inch cylinder which typically holds about 285 cubic feet. It is higher pressure and quite heavy.
Handling such cylinders requires experience. They can be quite dangerous and tricky to maneuver, as well as hazardous to feet and toes. Once a cylinder has a regulator attached to it, it is quite dangerous and needs to be secured if in an upright position. If it falls over with its protective cap removed and a regulator attached, the valve stem could break off the cylinder, with devastating results. The cylinder would take off like a rocket of considerable power.
A number of smaller cylinders are available, including light weight, low pressure aluminum "party" cylinders. These are much safer to transport and use, but hold much less helium. These are sometimes even filled with a mixed gas called "balloon gas" that has some air in it, reducing lift vs pure helium.
There is a great, new cylinder, also aluminum that holds about 150 cubic feet of helium. It only weighs about 50 pounds and uses standard regulators. Helium in such a tank costs about 30 cents per cubic foot, but the cylinders often require a very stiff deposit as much as $150, but which is refundable when the cylinder is returned in good condition.
For the seriously deranged, there are even 100 liter dewars of liquid helium which can convert to about 2,668 cubic feet of gas. This is enough to inflate a 17.5 foot balloon and lift nearly 170 pounds. Enough to lift a person, but you really do not want to go there, even if you could afford a delivery of 100 liters of liquid helium, it is tricky stuff to handle and rather hazardous unless you know exactly what you are doing. Real nut cases can even check out 250 liter dewars of liquid helium, but fortunately the incredible price of such an item restricts it to serious professional users with adequate training and BIG accounts.
After the gas is decided, it is still not easy to discover the density of the air displaced. Density of air vs altitude is very tricky! Humidity and temperature change with altitude along with pressure, making density of air vs altitude something that basically has to be measured. There is a thing called the "standard atmosphere" where a good estimate of temperature, humidity and pressure vs altitude can be made. Meteorology books often have a table of the "standard atmosphere" and you will be surprised at how non-linear air density vs height really is.
The balloon will respond to lowered pressure by expanding as it rises. There are a lot of variables to consider. Burst altitude is very tricky to estimate as a result.
Balloon pressure vs inflation in a latex balloon first decreases as diameter goes up and then increases as maximum inflation is approached and all the stretch in the latex surface is used up. Larger balloons will have a lower internal pressure than a smaller or less inflated one of the same thickness and type of latex. This has to do with the surface area changing at a different rate than the volume.
In spite of all of the above, the following tables serve as a fairly good estimate of best case lift at sea level.
Standard Temperature and Pressure = 20 degrees C and 760 mm Mercury
STP = 760 mm pressure and 20 C
Weight of air per liter at STP = 1.20 gr/l
Weight of helium per liter at STP = 0.18 gr/l
Net lift per liter of helium at STP = 1.03 gr/l
A typical balloon should provide from 4 to 5 mm of overpressure and
reduce lift to .9935 of these figures.
For small spherical helium balloon sizes:
Dia. inches Vol. Liters Lift/gr Lift/lbs
6 1.85 1.90 0.0042
8 4.39 4.51 0.0099
10 8.58 8.81 0.0194
12 14.83 15.22 0.0335
14 23.55 24.17 0.0533
16 35.15 36.07 0.0795
18 50.04 51.36 0.1132
20 68.65 70.45 0.1553
22 91.37 93.77 0.2067
Dia. inches Vol. Liters Lift/gr Lift/lbs
Any gas with a molecular weight less than air will generate lift. If you remember your high school chemistry you can easily figure the molecular weight of a gas based on its formula and check it against the approximately 28 grams per mole for air.
For instance, it is easy to make acetylene gas by the reaction of water on Calcium Carbide. It is C2H2 as a formula. It is (2*12) + (2 * 1) = 26 grams. True that is a bit lighter than air, but not a practical amount.
Propane is C3H8, (3*12) + (8*1) = 44 grams, as heavy as CO2, and a balloon filled with either would drop like a basketball. Butane is even worse C4H10 or 58 grams, more than twice as heavy as air. Ethane is C2H6 or 30 grams, several grams too heavy. Oxygen is 32 grams and four grams per mole too heavy. Nitrogen is 28 grams, not surprising since most of the density of air is due to nitrogen. A balloon filled with Neon would float, if you could afford the high price of inflating one with this rare inert gas. As mentioned before Carbon Dioxide is 44 grams and much too heavy.
The practical possibilities rapidly narrow down gas selection to Hydrogen, Helium and [marginally] Methane. Plus, of course, Hot Air, something not yet explored for lofting antennas as near as I can determine, but practical in theory. Helium would the the number one choice given its combination of lift and safety.
Here are a few typical wire facts to give some idea of the lift required for a given antenna wire, remember you also have to lift the balloon itself and any insulators or mooring strings, etc.:
16 gauge bare copper wire is 7.8 pounds per 1000 feet and 4.02 ohms 18 gauge bare copper wire is 4.9 pounds per 1000 feet and 6.39 ohms 20 gauge bare copper wire is 3.1 pounds per 1000 feet and 8.05 ohms 22 gauge bare copper wire is 1.9 pounds per 1000 feet and 16.1 ohms Double film insulated magnet wire: 16 gauge 125 feet/lb 18 gauge 200 feet/lb 20 gauge 316 feet/lb 22 gauge 502 feet/lb Single film insulated magnet wire: 14 gauge 79 feet/lb 16 gauge 127 feet/lb 18 gauge 203 feet/lb 20 gauge 319 feet/lb 22 gauge 507 feet/lb
Approximate lift of spherical volumes in liters of Helium, Hydrogen and Methane (Natural Gas) in diameters of feet and lift in pounds. Assuming standard temperatures and pressures and no significant overpressure. Remember that hydrogen and methane are serious explosion and fire hazards.
Dia. Ft. Vol. l Lift gr. Lift Lbs. 1 14.83 15.2 0.03 2 118.62 121.7 0.27 3 400.34 410.9 0.91 4 948.96 973.9 2.15 5 1853.45 1902.2 4.19 6 3202.76 3287.0 7.25 7 5085.86 5219.7 11.51 8 7591.72 7791.5 17.18 9 10809.30 11093.7 24.46 10 14827.58 15217.7 33.55 11 19735.50 20254.8 44.65 12 25622.05 26296.2 57.97 13 32576.18 33433.3 73.71 14 40686.87 41757.4 92.06 15 50043.07 51359.8 113.23 16 60733.75 62331.8 137.42 17 72847.88 74764.7 164.83 18 86474.42 88749.8 195.66 19 101702.34 104378 230.12 20 118620.61 121741 268.40 21 137318.18 140931 310.70 22 157884.03 162038 357.24 23 180407.11 185154 408.20 24 204976.41 210369 463.79 Dia. Ft. Vol. l Lift gr. Lift Lbs.
Dia. Ft. Vol. l Lift gr. Lift Lbs. 1 14.83 16.5 0.04 2 118.62 132.3 0.29 3 400.34 446.4 0.98 4 948.96 1058.1 2.33 5 1853.45 2066.6 4.56 6 3202.76 3571.1 7.87 7 5085.86 5670.8 12.50 8 7591.72 8464.8 18.66 9 10809.30 12052.5 26.57 10 14827.58 16532.9 36.45 11 19735.50 22005.3 48.51 12 25622.05 28568.8 62.98 13 32576.18 36322.7 80.08 14 40686.87 45366.2 100.02 15 50043.07 55798.5 123.02 16 60733.75 67718.7 149.29 17 72847.88 81226.0 179.07 18 86474.42 96419.8 212.57 19 101702.3 113399.0 250.00 20 118620.6 132263.0 291.59 21 137318.2 153111.0 337.55 22 157884.0 176042.1 388.11 23 180407.1 201155.5 443.47 24 204976.4 228550.5 503.87 Dia. Ft. Vol. l Lift gr. Lift Lbs.
Note: Natural gas in many places is close to pure methane. In others it contains significant amounts of hydrogen or heavier gases such as ethane, CO2 and water vapor. Also this chart does not apply to artificial gas, liquefied petroleum gas, propane, or butane all of which will be heavier than methane.
Dia. Ft. Vol. l Lift gr. Lift Lbs. 1 14.83 7.3 0.02 2 118.62 58.0 0.13 3 400.34 195.9 0.43 4 948.96 464.3 1.02 5 1853.45 906.9 2.00 6 3202.76 1567.1 3.45 7 5085.86 2488.5 5.49 8 7591.72 3714.7 8.19 9 10809.30 5289.0 11.66 10 14827.58 7255.2 16.00 11 19735.50 9656.7 21.29 12 25622.05 12537.0 27.64 13 32576.18 15939.6 35.14 14 40686.87 19908.2 43.89 15 50043.07 24486.3 53.98 16 60733.75 29717.2 65.52 17 72847.88 35644.7 78.58 18 86474.42 42312.2 93.28 19 101702.3 49763.3 109.71 20 118620.6 58041.5 127.96 21 137318.2 67190.3 148.13 22 157884.0 77253.2 170.32 23 180407.1 88273.8 194.61 24 204976.4 100295.7 221.12 Dia. Ft. Vol. l Lift gr. Lift Lbs.
If your project gets too ambitious, you need to watch out for the Federal Aviation Administration. They have rules about kites and balloons, both free balloons and moored balloons. Here are some sample regulations. For the latest information you should check the FAA's own web site. Note that at the time these regulations were current, balloons less than six feet in diameter and flown less than 150 feet above the ground were generally exempted:
05/2002