Notes

All air particles in the atmosphere are drawn by the downward force of gravity. But the pressure in the air creates an upward force working opposite gravity's pull. Air density builds to whatever level balances the force of gravity, because at this point gravity isn't strong enough to pull down a greater number of particles.

This pressure level is highest right at the surface of the Earth because the air at this level is supporting the weight of all the air above it -- more weight above means a greater downward gravitational force. As you move up through levels of the atmosphere, the air has less air mass above it, and so the balancing pressure decreases. This is why pressure drops as you rise in altitude.

This difference in air pressure causes an upward buoyant force in the air all around us. Essentially, the air pressure is greater below things than it is above things, so air pushes up more than it pushes down. But this buoyant force is weak compared to the force of gravity -- it is only as strong as the weight of the air displaced by an object. Obviously, most any solid object is going to be heavier than the air it displaces, so buoyant force doesn't move it at all. The buoyant force can only move things that are lighter than the air around them.

For buoyancy to push something up in the air, the thing has to be lighter than an equal volume of the air around it. The most obvious thing that is lighter than air is nothing at all. A vacuum can have volume but does not have mass, and so, it would seem, a balloon with a vacuum inside should be lifted by the buoyancy of the air around it. This doesn't work, however, because of the force of surrounding air pressure. Air pressure doesn't crush an inflated balloon, because the air inside the balloon pushes out with the same force as the outside air pushing in. A vacuum, on the other hand, doesn't have any outward pressure, since it has no particles bouncing against anything. Without equal pressure balancing it out, the outside air pressure will easily crush the balloon. And any container strong enough to hold up to the air pressure at the earth's surface will be much too heavy to be lifted by the buoyant force.

Another option would be to fill the balloon with air that is less dense than the surrounding air. Because the air in the balloon has less mass per unit of volume than the air in the atmosphere, it would be lighter than the air it was displacing, so the buoyant force would lift the balloon up. But again, fewer air particles per volume means lower air pressure, so the surrounding air pressure would squeeze the balloon until the air density inside was equal to the air density outside.

The hot air balloon had a HUGE impact on the history of civilization, in that it was the first type of aircraft that existed. It is not clear that the airplane would have been developed if the Montgolfier brothers had not first proved that people could rise into the air and survive. The natural philosophers of the time (people like Franklin & Voltaire) took great interest. Balloons were critical in the development of a study that is now called Meteorology, as well as aerial navigation techniques. In 1793, the French government formed an air arm to the Army, and balloons were used for reconnaissance during the French Revolution. During this period, the hydrogen balloon became more popular than the hot ­air balloon. Pierre Blanchard and Dr. John Jeffries made the first balloon flight from one nation to another.

They flew across the English Channel from England to France. The flight covered about 20 miles and required almost two hours to complete. Blanchard also piloted the first balloon in the United States. The flight took place in Philadelphia, Pennsylvania, on January 9, 1793, and among the many witnesses was President George Washington. Hot air balloons played a big part in the American Civil War. It gave an advantage to see above the trees and see an enemy before they could surprise attack! It came very useful for civil war(s).Hot air balloons have made significant impact in history as early as the Shang dynasty in around 1500 BC when kites with small paper balloons lit with lamps gave
signals/messages at night during invasions by Xiung nu.

Hot air lamps with silk fiber material around 3000 BC in China is found in history. Hot air balloons were used for strategic aerial attacks on enemies by countries like China/Japan that had for bombing England & London in modified Zeppelin. Hot air balloons have developed the hot air balloon. It was used for observations in the American civil war & by Germans in WWI & scientific investigations.The French Committee of Public Safety created a Corp d’Aerostiers in 1794.
The balloons first went into action during the battles of Charleroi and Fleurus later that year. The Corps remained in service until it was disbanded during the Egyptian campaign. The Hot air balloons were being used for when they have spotted the enemy. With an ability to soar a thousand feet above the landscape, balloons gave military leaders a platform that allowed them to see for miles around and decide their advantage. Both sides used hot air balloons as their backup if needed.The largest balloons (Union and Intrepid) had a capacity of 32,000 cubic feet of lifting gas and could carry 5 people aloft.

Constitution and United States had 25,000 cubic foot envelopes and could carry up to three people. Washington had a 20,000 cubic foot bag and could carry two people aloft. With a capacity of 15,000 cubic feet each, Eagle and Excelsior were one man craft. Smaller balloons could be inflated and sent skywards in a shorter amount of time. Larger balloons carried more observers and could include telegraphers and their gear. Balloons were normally inflated with city gas when it was available, as in Washington and Richmond. In the field, Thaddeus Lowe designed and the Navy Yard constructed special inflation wagons.The Intrepid was the largest balloon used during the Civil War and could carry 5 men aloft. All attempts to hit a hot air balloon always failed because it can quickly change course and it is thousands of miles in the air.
A hot air balloon needs to be slightly negatively buoyant. If a particular design can lift 1000lbs, an ideal flight weight might be 900 lbs so that, in the event of a burner failure, the balloon will slowly descend. If the payload for a given flight is only 600 lbs (fuel, pilot, passengers) then 300 lbs of ballast (sandbags) will be needed to keep the buoyancy in the correct range. Other ballast is used mostly for helium balloons, not hot air balloons. The rate of descent of a hot air balloon is controlled by the time the burners are burning.

If it is going down too fast, you burn longer. You may have two burners but if you lose one, the other one can keep the balloon aloft. they are always much larger than needed. The design weight is based upon the volume of the balloon and a particular temperature of the air in the balloon which must be below the melting point of the fabric. Typically you don't need ballast to adjust payload in a hot air balloon. IN a helium balloon, the only way you can go back up after starting a descent (by dumping helium) is the drop some weight. So ballast would be helpful with helium balloons.

A hot air balloon is called a hot air balloon because, the inside is heated up inside the balloon.
Hot air balloons in their early days were used by the U.S. military for dropping bombs. Now days balloons are used for three reasons: sport(competition), recreational(just for fun), and commercial(paid balloon flights). Hot air ballooning is very fun and interesting. You never know will the winds will take you, you never know what kinds of surprises will be thrown at you and the ride is gently and sort of peaceful. The only reason I say sort of peaceful is because the burners are loud. Commercial balloons are usually larger however some pilots give private flights without any other passenger which will be a smaller balloon usually about 90,000 cubic foot envelope. Sport ballooning usually involves small balloons that are round 56,000 cubic foot envelopes. The largest commercial balloon built to date is 600,000 cubic feet. A hot air balloon works by the burner burns the propane warming the air.

This air is then captured in the ballon. Since this air is warmer, and therefore less dense, than the surrounding air, this air has a tendancy to rise, similar to how air is lighter than water, so air bubbles in the water tend to rise. This rising air, captured in the ballon creates lift, raising the balloon. Since the basket and burner are attached to the balloon, they follow underneath and the burner continually warms air to keep the balloon rising. To set the balloon down, they simply turn down or off the burner and the air in the balloon cools, thereby lowering the amount of lift.

There are fewer air particles per unit of volume inside the balloon, but because those particles are moving faster, the inside and outside air pressure are the same.
All of this is assuming that the air in the balloon and the air outside the balloon exist under exactly the same conditions. If we change the conditions of the air inside the balloon, we can decrease density, while keeping air pressure the same. As we saw in the last section, the force of air pressure on an object depends on how often air particles collide with that object, as well as the force of each collision.

So, to lower air density in a balloon without losing air pressure, you simply need to increase the speed of the air particles. You can do this very easily by heating the air. The air particles absorb the heat energy and become more excited. This makes them move faster, which means they collide with a surface more often, and with greater force.

For this reason, hot air exerts greater air pressure per particle than cold air, so you don't need as many air particles to build to the same pressure level. So a hot air balloon rises because it is filled with hot, less dense air and is surrounded by colder, more dense air.