Carrying the Dreams of the Montgolfier Brothers to Other Worlds

Balloons – Early Thermodynamics Machines

A team of JPL engineers tests whether a large balloon can measure earthquakes from the air. The team proposes to measure “Venus-quakes” from the upper atmosphere of Venus, using an armada of balloons. The author is on the left holding a fan to inflate the solar balloon. Image Credit: NASA/JPL-Caltech

For this post I invited fellow thermodynamics enthusiast Mike Pauken, principal engineer at NASA’s Jet Propulsion Laboratory and author of Thermodynamics for Dummies, to share with us his involvement with the design of balloons for Venus. He kindly accepted my offer. Please extend a warm welcome to Mike! – Bob Hanlon

Before getting to his post, allow me to give you some more background on Mike

Mike Pauken is a principal engineer at NASA’s Jet Propulsion Laboratory operated by the California Institute of Technology. He was first introduced to the world of ballooning while teaching at Washington University in St. Louis, Missouri. Steve Fossett, a Wash U. alum, was attempting to be the first person to fly around the world solo in a balloon. The university was serving as his mission control center for his flight attempts. Fossett ditched his balloon in Russia in 1997 because his cabin was freezing, and Mark Wrighton, the university chancellor, promised Fossett that he’d have his mechanical engineering faculty look at improving his cabin heater. Mike was one of the faculty tapped to fix this problem. A few years later, while working at JPL, they were looking to add experienced balloon engineers on a Mars balloon technology development project. Knowing Mike had helped Steve Fossett, they thought Mike was an expert balloon technologist. Mike protested that he knew nothing about balloons, but that didn’t matter. Mike was signed on to the Mars balloon team anyway. Now, twenty years later, Mike’s primary research area is developing planetary aerial vehicles. He is currently working on balloon concepts for flying in the upper Venus atmosphere. In addition to developing Venus balloons, Mike is also working with a team to develop an instrument that would fly on a Venus balloon to detect infrasound waves generated by Venus seismic activity. We currently do not know how seismically active Venus is compared to Earth and Mars, but understanding seismic activity levels of rocky planets is a key element to figuring out how terrestrial bodies form. More information about this research is available here.

Mike’s work in planetary balloon technology development and expertise in thermodynamics has resulted in the development of this mini-series of posts on balloons and their development in the context of thermodynamics with a vision for the future of balloons to explore other planets in our solar system. This 3-part series starts with an historical context of balloons with the rise of thermodynamic advancement, then explores the fundamental physics behind the concepts of buoyancy and hydrostatic pressure to explain why balloons work, and concludes with a general discussion of balloon flight on other planets.

Series Title: Carrying the Dreams of the Montgolfier Brothers to Other Worlds

Part 1: Balloons – Early Thermodynamic Machines

Part 2: Why do balloons float?

Part 3: Like a Bird on Venus

Part 1: Balloons – Early Thermodynamic Machines

« Jacques est-ce que tu te souviens quand nous étions enfants et que nous rêvions de voler comme des oiseaux et de voir le monde d’en haut? » Demanda Étienne « et bien j’ai une idée … »

“Do you notice that smoke from a fire rises up? How do clouds float so high? Imagine if we could capture the clouds or smoke from a fire and put it into a bag, may the bag not fly upwards?” Étienne (Stephen) and Jacques (John) Montgolfier may have had such a conversation in the summer of 1782 in Annonay, France.

By November 1782, Étienne fabricated a rectangular bag, about 40 cubic feet in volume, from fine silk. He burned paper under the open bottom of the bag to create “rarefied air” and soon the bag ascended rapidly to the ceiling. A short while later, after this initial success, the brothers repeated the experiment outdoors and the silk bag rose to about 70 feet before returning back to the ground as the gas cooled. Delighted with the success of these experiments, the Montgolfier brothers resolved to build a larger machine. This second prototype had a volume of about 650 cubic feet and after the fires underneath warmed the air inside the balloon, it broke loose from its mooring and ascended 600 feet in the air before returning to the ground.

Gaining confidence in their new invention, the brothers built a third machine, this time with a diameter of about 35 feet. They did not have a name for this new machine yet. On April 25, 1783, they lit the fires under this large envelope and again the ropes holding it down gave way and it rose more than 1000 feet before returning back to Earth about three quarters of a mile away. Having privately achieved these successes, Étienne and Jacques were ready for a public display of their new invention.

On Thursday June 5, 1783, a crowd assembled to witness the new aerostatic experiment. The enormous linen bag could hold over 23,000 cubic feet of gas when filled. By now the brothers were able to calculate that the experiment could lift about 490 pounds. Burning straw and wood under the platform holding the experiment above the fire, it soon filled out to a spherical shape. Eight men held it down. When the ropes were set free, the machine rose to about 6000 feet in 10 minutes and then it landed about a mile and a half away to the astonishment of the viewers. Thus, began the race for ascending into the air and seeing the world as birds view it.

Soon after the news of the Montgolfier brother’s achievement reached Paris, the scientific community there began thinking of ways to do the experiment themselves. The information from Annonay reported the Montgolfier machine was filled with a gas that was half as heavy as common air.

Short break for some quick calculations

Let’s pause a moment here and do some quick calculations on the Montgolfier balloon using a volume of 23,000 cubic feet, 490 pounds of lift, and density half of common air. It’s always good to do a bit of fact checking, especially these days; we can’t just take anyone’s word for it. The lift force of a balloon is determined from the this relatively simple equation:

F = V·g·(ra – rb)

Where F is the lift force, V is the balloon gas volume, g is the gravitational acceleration, ra is the density of the atmospheric gas, and rb is the density of the balloon gas. In this system the balloon gas density is the hardest to measure, so let’s assume this is the greatest unknown and solve for it. I prefer working in SI units (metric system) and we have a lift of 2180 Newtons, a volume of 650 cubic meters, air density of 1.2 kilograms per cubic meter, and gravitational acceleration of 9.8 meters per second squared. The gas density inside the balloon is estimated by solving the following equation for rb:

2180N = 650m3·9.8m/s2·(1.2 – rb)kg/m3

Where we find that rb is approximately: 0.85 kg/m3, which is about 70% as dense as air, not half as dense. The reader may then calculate the bulk average gas temperature inside the balloon would have been about 136°C (278°F) as an exercise using the Gay-Lussac gas law. If the lift capacity were unknown and the density inside the balloon was taken as true, we would discover the lift capacity would be on the order of 860 pounds, much higher than the Montgolfier brothers estimate, and the average gas temperature would be about 313°C (595°F). Silk burns at about 206°C, so we know the balloon gas temperature wasn’t this hot and the density could not have been nearly half that as ordinary air.

Continuing – The First Hydrogen Balloon

Getting back on track in 1783: The scientists in Paris imagined that a new gas was discovered that was previously unknown because it was heavier than inflammable air (hydrogen) yet lighter than common air. The scientists concluded that inflammable air would be a better gas for the experiment than that used by the Montgolfier brothers. A subscription to fund the Paris experiment was quickly raised and Jacques Charles (of subsequent Charles Law fame) was appointed to oversee the work. But how to build a large bag to hold inflammable gas? It leaked through paper and silk; there was no such thing as plastic or latex. It was decided to build the bag from lutestring silk, a material with a very fine thread and a plain weave, and then varnish it with a dissolved elastic gum to make it as impermeable as they could.

At this point the inflated bag resembled a giant ball and it was thus called a Balloon. The new balloon was about 13 feet in diameter and weighed only about 25 pounds including a valve at the bottom to seal in the inflammable gas. The second problem to overcome was generating the required volume of inflammable gas. Such a large quantity had never previously been produced. The first attempt to produce the inflammable gas consisted of using a chest of lead-lined drawers filled with iron filings and dilute vitriolic (sulfuric) acid. The chest of drawers had a pipe connecting it to the balloon. It turned out that this arrangement wasted more gas than went into the balloon.

A second apparatus was set up using a cask filled with dilute acid, and iron filings were poured into it through a bung hole. The gas was connected to the balloon using a varnished leather tube. A dilute solution of sulfuric acid produces only hydrogen and iron sulfate, but as the reaction generates a significant amount of heat, much water is evaporated and thus the Charles balloon was filled with a mixture of hydrogen and water vapor. The balloon and pipe were prone to overheating and water was pumped against them to keep them cool. The water vapor thus condensed and the water inside the balloon was intermittently drained.

The process to fill the 13-foot diameter hydrogen balloon took 3 days compared to the tens of minutes it took to fill the 35-foot diameter hot air balloon of the Montgolfier brothers. The gas-filled Charles balloon was ready for a public demonstration only 83 days after the first public viewing of the Montgolfier balloon; truly an astonishing accomplishment! During the night of August 27, 1783, the inflated balloon was moved 2 miles on a cart from the Place of Victories to the Camp of Mars in Paris. The balloon was topped off with hydrogen in front of a crowd of onlookers, giving them an idea of how the balloon was filled.

At 5 pm, the balloon was launched in a rain storm and rose over 3000 feet in two minutes. The balloon was lost in dark clouds for about 45 minutes when it finally came down in a field about 15 miles away. The balloon had ruptured at high altitude which caused it to come down after such a short flight. The expansion of the gas contained in the balloon as it rose up in the air was not accounted for prior to the flight, but Jacques Charles realized this caused the bursting of the balloon upon examination afterwards and learned not to overfill the balloon on the ground. You can read about how well the balloon was received by a group of farmers that found it soon after it landed if you do a little bit of investigating on your own.

The reader might be interested in seeing how the Montgolfier brothers and Jacques Charles inflated and launched their balloons. The sketch below is in Tiberius Cavallo’s book describing the method of launching hot air and hydrogen balloons in the 1780s. A description of the figure is available in the Public Domain from Digital Science History.

Image credit: Cavallo, Tiberius. “Plate II: Illustrating the Chemical Apparatus and Balloons Used for Hydrogen Generation.” In The History and Practice of Aerostation. London, England: Printed for the author and sold by C. Dilly, P. Elmsly, and J. Stockdale, 1785. https://digital.sciencehistory.org/works/n296x033r.

Lift Gases

For the first 140 years of balloon flight, hot air and hydrogen were the dominate lift gases in use. Hydrogen was known as inflammable air in the early days of ballooning. A mere 17 years prior to Charles making his first hydrogen balloon, Henry Cavendish determined the density of inflammable air and found it was between 7 and 11 times lighter than air in 1766. (You can imagine how hard it would be to measure hydrogen’s density accurately in the day. I would suspect his samples may have also contained some water vapor as Jacques Charles found when he inflated his balloon. It is actually about 15 times lighter than air.) The idea of making a vessel to contain hydrogen such that it would float in air was made soon after this discovery. Dr. Joseph Black, who had been working for years with hydrogen showing how it burns and explodes, realized it could be used to create a vessel that could float in the air. Dr. Black thought that making such a vessel would be an amusing experiment for his students in 1767. But what would you use to make a thin vessel to contain the hydrogen? Dr. Black decided to make the vessel from the allantois of a calf, basically the fetal sac of a cow. He never did find time to make such an experiment even though he went to the trouble of actually getting an allantois for it. The hydrogen container proved to be a hard problem to solve, but Jacques Charles was the first to succeed in a big way in 1783.

Helium, the most common balloon gas today, was not discovered until 85 years after the first hydrogen balloon was flown. It was first observed in spectral lines on the Sun during an eclipse in 1868, and Norman Lockyer named the newly discovered element “Helium” after the Greek Titan of the Sun, Helios, by adding the “ium” ending, thinking it was similar to the alkali metal series which all have the same ending, e.g. sodium, potassium, etc. It wasn’t found on the Earth until 1895 outgassing from uranium ore. Helium generation from uranium ore is not sufficiently productive to be a useful source for filling balloons. Large deposits of helium were discovered in 1903 in natural gas reservoirs, which is where we obtain helium for today’s uses. The first use of helium in an airship was for the U.S.S. Shenandoah, a 2-million-cubic-foot rigid airship commissioned in 1923. It consumed practically all the U.S. government supply of helium to fill it at the time.

Balloons in the Thermodynamic Timeline: Relative to the Gas Laws

If we place ourselves in the year 1783, we do not have the same perspectives on thermodynamics related to balloon flight as we do today or even 50 or 100 years ago. A floating balloon touches on buoyancy, density, pressure, temperature, the ideal gas law, and the kinetic theory of gases. Furthermore, a balloon also performs work! And in some cases, converts heat directly to work. The development of the balloon occurred in the heyday of the advancements in understanding the workings of machines through thermodynamics. Let’s take a brief look at the state of thermodynamics in the context of the invention of the balloon.

Tiberius Cavallo wrote “The History and Practice of AEROSTATION” in 1785 and provided a contemporary account of the early days of balloon development including a review of relevant knowledge from a thermodynamic point of view. Every detail I described above about the Montgolfier balloon and the Charles balloon came from this valuable resource. I recommend the reader download this volume for their own benefit. It was known that the density and volume of air could be changed by “means of fire” or removing pressure as demonstrated by the invention of the air pump in the mid-1600s. Quantification of the relationship between pressure and volume were first determined from experiments performed by Robert Boyle and published in 1662. Cavallo writes: Doubling pressure decreases the volume of air by half. Heat expands the air while cold contracts the air. One degree of heat, according to the scale of Fahrenheit’s thermometer, seems to expand the air about one five hundredth part. Not too bad actually since today we know it is one part in 460.

Working with the hydrogen balloon, Jacques Charles observed the change in volume with temperature when it was cooled with water. This led him, four years later (1787), to experiment with gas volumes and temperature changes. Details of these experiments by Charles are hard to find since he did not publish them. Charles wasn’t the first to make this observation, nor the last. Joseph Louis Gay-Lussac (also an avid balloonist) discussed the experiments with Charles for measuring the volume of 5 different gases at constant pressure over a temperature range from 0 to 80°C. A bit critical of Charles’ apparatus, Gay-Lussac made improvements upon the experimental method, and he gave Jacques Charles credit for his work in his publication of the results. The details of the volume-temperature relation experiments are all thoroughly described (in French) in: “Sur le dilatation des gaz et des vapeurs,” Annal. Chim. 43 (1), 137–175, 1802. You can find a sketch of Gay-Lussac’s experimental apparatus here.

Having touched upon Boyle’s Law and Gay-Lussac’s Law I should mention that in July 1811 Amedeo Avogadro published his hypothesis that samples of different gases with the same volume, pressure, and temperature have the same number of molecules. This hypothesis is the last element needed to formulate the ideal gas law. Although we have all the pieces for assembling the ideal gas law by 1811, it wasn’t formally put together until 1834 by Benoît Clapeyron. The fact that so much time elapsed from the initial formulation of the various relationships between pressure, volume, temperature, and the number of molecules in a gas (from 1662 to 1811) to formalizing them into the ideal gas law is due to the difficulty in seeing the big picture on how these separate laws are related to each other. Furthermore, getting new ideas accepted in the science community is not an easy task. Usually it takes several influential investigators conveying the message to make the case stick. Using the kinetic theory of gases, the ideal gas law was independently derived by August Krönig in 1856 and Rudolf Clausius in 1857. Thus, it still took nearly 25 years using multiple proofs to formally define and accept the ideal gas law that we use today without question.

The connection between the kinetic theory of gases, first described by Daniel Bernoulli in 1738, and balloons is not intuitively apparent. But consider that a balloon is a volume containing a gas at a specific pressure, temperature and density; we want to understand why a balloon has buoyancy from a molecular or microscopic point of view. The kinetic theory of gases is the roadmap connecting the micro-scale phenomena to the macro-scale effects. We will look at why there is such a thing as hydrostatic pressure and buoyancy starting with the kinetic theory of gases in more detail in a second blog. Please come back next month to hear the rest of the story on understanding the cause of buoyancy and hydrostatic pressure from kinetic theory.

If you’re not up for doing a French to English translation, the first sentence of this blog reads:

“John, do you remember when we were kids and we dreamed of flying like birds and seeing the world from above?” Asked Stephen, “well I have an idea …”

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