57 Airships, Blimps, & Aerostats

Introduction

Airships, balloons, and blimps generate buoyancy lift or aerostatic lift using an envelope filled with a less dense gas than air, such as helium, enabling them to fly freely and “float” without needing forward airspeed. Such aircraft have been collectively called “airships” or “aerostats.” Today, they are more usually referred to as “Lighter-Than-Air” or LTA airplane, a selection of such vehicles being shown in the figure below. Furthermore, because an LTA aircraft does not require much of a runway, albeit still needing a relatively large terrestrial footprint for takeoff and landing, they can also be classified as a form of vertical/short take-off and landing (V/STOL) aircraft. Technically, any unpowered and free-floating type of LTA aircraft is considered a balloon, and one that is powered and steerable is called an airship.

There are diverse types of Lighter-Than-Air (LTA) in the aviation spectrum. Unpowered LTA aircraft are considered balloons, and powered, steerable LTA aircraft are called airships.

Historically, airships have suffered from the public perception as lumbering giants of the sky with an accompanying poor safety record. However, airships and aerostats have been used successfully for over a century in many applications, including military surveillance, anti-submarine warfare, border patrol, passenger and cargo transport, and advertising. The most famous are the giant Zeppelin airships and the Goodyear blimps. During the 1920s and 1930s, several Zeppelin airships were used to transport passengers across the oceans and worldwide in luxury compared to airplanes of that era. However, airships obtained a poor reputation for safety after the Hindenburg erupted in a massive fireball^[1] and was destroyed in 1937, in full view of the world’s media, after a successful flight carrying passengers across the Atlantic.

While airships have seen minimal practical use since the 1940s, technological advancements, growing concerns about environmental pollution from conventional airplanes, and a global focus on sustainable transportation, have sparked renewed interest in airships. Much of the engineering knowledge about airships dates back over a century, and most technical data reports from the NPL/RAE research labs in Britain and NACA in the U.S. date to the 1920s and 1930s, including extensive wind tunnel tests. However, aerospace engineers still need to be aware of the history of airships in terms of their successes and failures, how they work, and their general performance characteristics. Furthermore, engineers must be able to objectively and confidently assess the potential future of airships as part of the aviation spectrum.

Modern types of airships, which by any standard are giant aircraft, dwarfing the A380 and Boeing 747 (even the Hindenburg was three times longer and twice as tall as a 747), can potentially carry substantial payloads up to 100,000 kg (220,000 lb) over distances of thousands of miles, albeit at relatively low airspeeds, while producing low carbon emissions. Several companies, including Lockheed Martin, Hybrid Air Vehicles, Aeroscraft, and LTH, have been actively involved in airship research and development.

In particular, hybrid airships have gained considerable attention in recent years, an example being shown in the photograph below. This variation has a cambered tri-hull shape, with disk-shaped cushions on the underside to serve as undercarriage. Hybrids create both aerostatic (buoyancy) lift as well as aerodynamic (motion) lift, offering several advantages over legacy airships.^[2] regarding performance, payload, and cruise speed. Modern airships have also taken advantage of advanced aviation safety features, including multiple redundant fly-by-wire flight control systems, active health monitoring, and advanced avionics and navigation systems.

The Lockheed Martin P-791 is an experimental hybrid airship that generates both aerostatic and aerodynamic lift.

Modern airships could also incorporate advanced propulsion systems, such as hybrid electric, hydrogen fuel cell, or solar energy technologies. This type of propulsion gives excellent efficiency, lower energy costs, and a smaller carbon footprint.^[3] As climate change and sustainability concerns continue to increase, airships may soon find a new niche in aviation, perhaps with them servicing an Amazon or Walmart distribution center near you! While airships fly relatively slowly compared to airplanes, their cruise speeds are still much faster than sea ships and as fast as any terrestrial vehicle or truck. They also have the advantage of flying directly from one place to another over land or sea.

However, any future implementation and widespread adoption of new generations of airships will still depend on many interrelated factors, including further technological advancements, regulatory considerations, public perception, economic viability, wider availability of hangarage and maintenance facilities, and the ability to tolerate all-weather operations. Indeed, while the future of airships shows much technical promise, it remains to be seen how (or if) such aircraft can mature to become an important and viably economic part of the future commercial aviation spectrum.

Learning Objectives

Know about the history of balloons, airships, and other aerostats.
Understand the principles of buoyancy and aerostatic lift.
Appreciate the aerodynamic performance characteristics of airships.
Understand how an airship is controlled during flight using buoyancy and propulsion.
Be aware of the stability, handling qualities, and unique flight characteristics of airships.

History

The first LTA aircraft was a hot-air balloon, which was also the first human-carrying flight vehicle capable of sustained flight. It was designed in France by the Montgolfier brothers in 1783. Their balloon was made of paper and silk and rose to an altitude of about 2,000 m (6,560 ft) without a pilot. A few weeks later, a larger balloon, the Aerostat Reveillon, was launched carrying pilot Jean-François Pilâtre De Rozier, who ascended to the end of its 90 m (295 ft) rope tether. A month later, De Rozier and the Marquis d’Arlandes made aviation history by conducting the first free flight in a balloon, which ascended to around 150 m (492 ft) and drifted approximately 8 km (5.5 miles) before safely landing.

An artist’s sketch of the first free flight of a Montgolfier hot air balloon circa 1783.

Benjamin Franklin, who from 1776 to 1778 was on a diplomatic commission to France, witnessed some of these early balloon flights. He was so impressed that he predicted that balloons would soon have considerable military value for “conveying intelligence into, or out of, a besieged town, giving signals to distant places, or the like.” Indeed, tethered balloons were to be used during the American Civil War for battlefield surveillance. They could reach altitudes of up to 300 m (984 ft), giving a great vantage point for soldiers, who used signal flags to send information down to their commanders.

For the next 150 years, hot-air balloons saw limited interest and were surpassed by the use of airships and many other forms of aircraft. However, in the 1960s, hot-air ballooning became a popular recreational activity and sporting event. In 1987, Richard Branson and Per Lindstrand became the first to cross the Atlantic in a hot air balloon, flying 2,900 miles (4,670 km) in 33 hours. Branson and Lindstrand paired up again in 1991 and were the first to cross the Pacific in a hot air balloon. They traveled 6,700 miles (10,800 km) in 47 hours from Japan to Canada, breaking the world distance record by traveling in the high-altitude jet stream. Four years later, Steve Fossett became the first to complete the Transpacific balloon route as a solo pilot, riding the winds and the jetstream for four days while traveling from South Korea to Canada.

The need for balloons that could be combined with propulsion led to the development of airships with rigid internal structures known as dirigibles. The first dirigible was built and flown in 1852 by Henri Giffard, who used a steam engine driving a propeller. Today, an airship is usually defined as any powered, steerable aircraft inflated with a lighter-than-air gas. Early airships were filled with hydrogen gas, which is highly reactive if not spontaneously explosive. Several airships had caught fire even before the infamous Hindenburg disaster in 1937. Using inert helium rather than explosive hydrogen as the buoyant gas would have prevented the Hindenburg from catching fire.^[4]

The LZ127 Graf Zeppelin, as shown in the photograph below, was a German airship filled with hydrogen as the buoyant gas that made the first successful transatlantic passenger flight in 1928. It flew from Friedrichshafen, Germany, to Lakehurst, New Jersey, in the U.S., covering approximately 3,000 miles (4,800 km) in 112 hours. This impressive achievement was a milestone in the history of airship travel. It demonstrated the feasibility of long-distance passenger-carrying airship flights in relative comfort compared to airplanes of that era. In 1928, travelers could still travel faster by trains than by airplanes, such as the Ford Trimotor, which was was so noisy that passengers had to stuff cotton wool in their ears.

The “Graf Zeppelin” photographed landing in Berlin, Germany, circa 1931.

The British, as did the U.S., soon developed airships derived from German designs. The R100 and its sister ship, R101, were built in 1922 as part of a British government initiative to establish airships to transport passengers and mail from Britain to the most distant parts of the British Empire, including India, Australia, and Canada. The R100 first flew in December 1929 and made a well-publicized return crossing of the Atlantic to Canada in the summer of 1930. But following the demise of the R101, it was scrapped. While other British airships were built through to the end of 1930, they were largely unsuccessful. The U.S.S. Macon, as shown in the photograph below, and the U.S.S. Akron were among the largest airships ever built. Although the hydrogen-filled, Zeppelin-built LZ 129 Hindenburg and the LZ 130 Graf Zeppelin II were longer, these two U.S. Navy airships were the most voluminous helium-filled dirigibles. Unfortunately, both U.S. airships were destroyed in the mid-1930s, further diminishing the operational and safety reputation of airships.

The U.S. Navy airship, U.S.S. Macon photographed flying over New York City in 1944. Airships made in the United States used helium as the buoyant gas.

A blimp, essentially a “pressure airship,” has its shape maintained by the gas pressure inside the envelope. Unlike a dirigible, with its structural skeleton, a blimp loses its shape when the internal pressure is reduced. The B-class blimps, as shown in the photograph below, were patrol airships operated by the U.S. Navy during and shortly after WWI and used with much success for convoy and antisubmarine patrol duty. The design of the B-class blimps allowed them to operate effectively over coastal waters, providing a vital service in detecting and deterring submarine threats during a critical period in naval warfare.

The B-1 airship was operated by the U.S. Navy during WWI. The B-1 is easily identified by the dual lower fins, later B-types having only a single fin.

In 1925, Goodyear Tire & Rubber Company began building blimps. These aircraft were first used for advertising but then proved valuable for numerous military purposes during various campaigns throughout WWII. Goodyear’s blimps proved a valuable asset to the Navy because they could stay airborne for long periods without using much fuel. Newer versions of blimps have a minimal internal structure made of lightweight composite materials such as carbon fiber, classifying them as semi-rigid airships.

Tethered aerostats have offered a unique and valuable solution for specific applications that require a stable, long-duration aerial platform. The tethered design provides advantages in terms of stability, cost-effectiveness, and prolonged observation capabilities. Their wartime use dates back two centuries to gather intelligence, observe enemy activities, and direct artillery fire. A form of aerostat called a barrage balloon proved an effective defensive measure by the British during WWI and WWII; see the photograph below. They disrupted enemy flights, forced aircraft to fly at higher altitudes, and provided early warning by visually alerting ground forces of incoming aircraft. Aerostats in the form of blimps are still used today by the Tethered Aerostat Radar System (TARS) to watch over the southern U.S. border; each aerostat is moored to the ground with a cable, and its altitude can be raised and lowered with a winch.

Barrage balloons at Omaha Beach in France during the early days of the Allied invasion of Europe in June 1944.

Anatomy of LTA Aircraft

LTA aircraft comprise various types of balloons, airships, and other aerostats. As aeronautical technology evolved, the name “balloon” has become reserved for hot air balloons, which are recreational aircraft. While the name “aerostat” still encompasses most types of LTA aircraft, an aerostat is usually considered an unpiloted LTA aircraft tethered to the ground with a cable. The name “airship” is reserved for a piloted LTA with a propulsion system, allowing the aircraft to fly from one place to another while carrying a payload or doing something worthwhile.

Balloons (Thermal Aerostats)

A balloon or thermal aerostat is the simplest form of unpowered aerostat. Because balloons have limited control capability and drift freely in the winds, they are generally flown in light winds and good weather. Notable uses of balloons in modern aviation include weather balloons for meteorology (usually filled with helium) and sporting “hot-air” balloons for recreation, the latter being shown in the figure below.

Balloon types of aerostats have become synonymous with the numerous colorful hot-air balloons used for recreation.

Hot air balloons have a propane burner to heat the air inside the envelope. As the air heats up, it becomes less dense than the surrounding cooler air, so the balloon envelope will inflate, causing a buoyancy force. There is little difference in the density of hot and cold air, so the envelope must be voluminous to lift even a couple of people. Hot air balloons carry ballast, usually sandbags, which can be dropped or emptied to reduce weight. The pilot can open a parachute valve by pulling down on a cord to let some hot air escape and control the balloon’s altitude, i.e., to achieve neutral buoyancy. Those who have flown in hot air balloons generally say it was a serene and picturesque experience, the uncertainty of the landing point being part of the excitement of this type of aerial adventure.

Stratospheric Balloons

There are also balloons designed for flight in the upper stratosphere and at the edge of space, an example being shown in the figure below. They typically fall into two main types: zero-pressure and super-pressure balloons. Both of these types utilize helium gas for buoyancy. They are the only type of flight vehicle that can be operated in this region of the atmosphere, which ranges from 50,000 ft to 150,000 ft (about 15 km to 45 km) in altitude, which is too low for satellites and too high for airplanes. The payload gondolas can carry experiments on science, astronomy, atmospheric chemistry, as well as weather sensors. At the end of the mission, the payload is severed from the balloon and recovered by parachute.

Stratosphere balloons utilize helium gas for aerostatic lift.

Zero-pressure stratospheric balloons have release valves that allow the pressure inside the balloon to remain the same as the outside. These balloons will continue to rise until they find a buoyancy altitude or burst; potentially, they can stay aloft for weeks or months. Super-pressure balloons are entirely sealed and maintain a higher pressure inside the balloon, allowing it to maintain its operational altitude despite temperature changes that occur day and night. Super-pressure balloons are launched partially filled with helium, and as the balloon ascends and ambient air pressure decreases, the helium expands to fill the envelope, and it reaches its desired float altitude.

Dirigibles

Airships (dirigibles and blimps) are traditionally piloted and use engines driving propellers or fans for forward propulsion. Depending on their structural design, airships are divided into three types: rigid, semi-rigid, or blimp (pressure airship). Semi-rigid airships usually fall into the blimp class. The classic rigid airship, a dirigible, has an internal space-frame structure surrounding its gas containers (gasbags), as shown in the figure below.

A dirigible is a classic rigid airship with an internal space-frame structure surrounding its gas containers.

The Zeppelins of the 1920s through the 1940s are well-known examples of dirigibles, which used hydrogen as the buoyant gas; the airships in the U.S. used helium. The main structure is usually aluminum, but more modern dirigibles are more likely to use composites. The internal structure provides the shape and rigidity of the airship, but the outer covering or envelope is unpressurized. The covering must be a strong and durable fabric, but it does not have to be gas-tight like a blimp because the buoyant gas inside a dirigible is contained in a series of separate gas bags.

The gondola or car is the compartment suspended below the envelope, where the passengers, crew, and other equipment are housed. The integral internal structure connects the gondola, empennage, engines, and gas cells, carrying and distributing the loads across the entire structure. The engines may be located on the gondola, but because of the expansive rigid internal structure of a dirigible, there are multiple hard points, and the engines can be placed almost anywhere. The vertical stabilizer, or fin, helps maintain the aircraft’s directional stability, and the horizontal stabilizer gives pitch stability. Airships utilize various control surfaces to help maneuver, including rudders and elevators, which are used for yaw and pitch control, respectively.

Blimps

A non-rigid airship, also known as a blimp, maintains its shape from the pressure of the buoyant gas within it. Blimps may have some external bracing or reinforcement to support the weight of the gondola and engines. However, in the classic blimp, the gondola is suspended from the top of the envelope by a catenary curtain (like a hanging chain) with attached cables, as shown in the figure below; these cables are internal to the gas envelope. Buoyancy is controlled using air-filled ballonets that allow the center of buoyancy to be modified for control and trim. The iconic Goodyear GZ20A blimps were used until 2017. The new semi-rigid Goodyear Zeppelin NT blimps, which have an internal structure, are extensively used in the U.S., especially at major sporting events such as the Super Bowl and the Daytona 500.

Anatomy of an airship in the form of a classic blimp.

Semi-Rigid Airships

The modern version of the Goodyear blimp, as shown in the figure below, is a semi-rigid blimp (Zeppelin NT), which can be noted by the absence of internal suspension cables holding the gondola. This airship uses helium as the buoyant gas, a modern successor of the classic Zeppelin dirigibles of the 1930s. Semi-rigid airships have an internal structure supporting the gas envelope and other components such as the gondola, engines, and tail surfaces. However, the envelope maintains its shape using the internal pressure of the helium, so semi-rigid airships still fall into the blimp class. The engines drive propellers or ducted fans to provide the thrust necessary to propel the airship forward or backward, and vectoring the thrust can significantly help maneuverability. Modern airships use water ballast rather than lead shot, but otherwise, the features of the semi-rigid airships (Goodyear still calls them blimps) are similar to dirigibles.

Anatomy of an airship in the form of a semi-rigid blimp. The photograph is of a Zeppelin NT, a new class of helium-filled airships.

Tethered Aerostats

A tethered aerostat is anchored to the ground on a cable; in the photo below, it is tethered to its mooring. Letting out the cable allows the aerostat to rise and be tethered at various altitudes. A ballonet is used to control the buoyancy. Such aerostats have been employed for persistent aerial surveillance over a designated area. Equipped with multiple sensors, cameras, and radar systems, aerostats can monitor the movement of troops, detect threats, and provide real-time intelligence. Tethered aerostats are also utilized for telecommunications purposes. Lifting communication equipment, such as antennas and repeaters, to high altitudes can enhance wireless communication networks over a wide area. This technology can be particularly useful in remote areas where traditional communication infrastructure may be limited or damaged. A typical system consists of a tethered aerostat capable of radar surveillance and high-resolution imagery over a large area from only a few thousand feet high.

Anatomy of a tethered aerostat. While relatively simple, they can carry a variety of sophisticated radars, cameras, and sensors.

Hybrid Airships

Hybrid airships are intended to combine some of the features of airplanes and airships. As shown in the figure below, these innovative vehicles carry a fraction of their weight from buoyancy and the remainder from aerodynamic lift generated by their airframe shape. Their aerodynamic lift production may be as high as 30% of their weight.

Hybrid airships are intended to fill the gap between the low operating cost and low airspeeds of traditional airships and the higher speed but higher fuel consumption of airplanes. By combining dynamic and buoyant lift, hybrids can cruise at higher airspeeds with a greater payload compared to a pure airship. Because of their large size, they have a significant payload capacity compared to other aircraft types. This makes them suitable for various applications, including cargo transportation, disaster relief efforts, and remote access operations. However, they do need ample hangar space for maintenance and storage, which is also a consideration of where and when they can operate.

Led Zeppelin – Going Down Like a Lead Balloon!

Led Zeppelin is one of the most famous rock bands of all time. They recorded nine albums between 1968 and 1979 and sold over 300 million copies. The name “Led Zeppelin” stemmed from a humorous conversation in 1967 among several musicians about the new band’s chances of going down like a lead balloon. Their lead guitarist, Jimmy Page, then came up with the name “Led Zeppelin,” and everything else is now history.

Buoyant (Lifting) Gases

A buoyant gas or lifting gas is any gas that produces buoyancy or aerostatic lift, so this gas must be less dense than the surrounding air. Well-known buoyant gases include hydrogen and helium, as well as hot air. The choice of buoyant gas depends on availability, cost, and safety. Helium is the most suitable for airship and aerostat operations because it is non-flammable and non-toxic. However, helium is relatively expensive,^[5] and supplies can be intermittent. Hot air, as a buoyant gas, is limited to recreational balloons.

Hydrogen

Hydrogen (H₂) is the lightest and most buoyant lifting gas, with a molecular weight of 2.016. It is low density and provides maximum aerostatic lift per unit volume, often called lifting capacity. It is readily available and relatively inexpensive. However, hydrogen is highly reactive and potentially explosive, posing safety risks. Many hydrogen-filled airships were lost in the 1920s because of fire and explosion, and the use of hydrogen decreased significantly after the Hindenburg disaster in 1937. Aviation regulators currently ban the use of hydrogen for airships, but this position may change if hydrogen is ultimately approved for use as a fuel on airplanes.

Helium

Helium (He) is the second lightest gas, with a molecular weight of 4.003. Helium is non-flammable and safer than hydrogen. Helium is not reactive and does not support combustion. It is commonly used in modern airships and some types of balloons. Helium is extracted from underground gas pockets as a by-product of natural gas refinement. It is a relatively rare gas and expensive, especially at the volumes needed for an airship. Helium is a commodity, and its price varies daily. But filling a Goodyear blimp with helium would cost about $100,000 versus $15,000 for hydrogen.

Ammonia

Ammonia (NH₃) is lighter than air, but with an atomic weight of 17.02, it is considerably heavier than hydrogen or helium. It has a good lifting capacity but is a pungent, choking gas that is toxic and corrosive. However, ammonia is less flammable than hydrogen. It was used in some early airships before the availability of hydrogen and helium in the quantities needed. Because ammonia is highly toxic, its release into the atmosphere poses numerous environmental hazards, and its use for LTA aircraft has been permanently discontinued.

Hot Air

Hot air is produced by heating ambient air using propane burners. Air has a molecular weight of about 29. Hot air is less dense than the surrounding air, creating buoyancy. It does not pose the safety concerns associated with hydrogen. Hot air has a much lower lifting capacity than gases like hydrogen or helium, so a greater volume is required to produce buoyancy. Balloons using hot air require almost constant heating to maintain buoyancy because of rapid heat transfer through the thin gas envelope.

Summary of Buoyant Gases

The table below summarizes the essential properties of buoyant gases, with air as the reference. The density values are given in grams per liter (g/L) at standard temperature and pressure (STP), which has the same numerical value in units of kg/m³. While hot air is easy and inexpensive to produce, it does not have much lifting capacity, so the gas envelope needs to be very large and voluminous.

Property	Hydrogen	Helium	Ammonia	Hot Air	Air (reference)
Chemical Formula	H₂	He	NH₃	N₂+ O₂ + mixture of other gases	N₂+ O₂ + mixture of other gases
Density	0.08988 g/L (STP)	0.1786 g/L (STP)	0.769 g/L (STP)	1.14 g/L (30^oC) Varies based on temperature	1.225 g/L (STP) Varies based on temperature
Color	Colorless	Colorless	Colorless	Colorless	Colorless
Odor	Odorless	Odorless	Pungent	Odorless	Odorless
Flammability	High	None	None	None	None

Property

Hydrogen

Helium

Ammonia

Hot Air

Air (reference)

Chemical Formula

H₂

NH₃

N₂+ O₂ + mixture of other gases

Density

0.08988 g/L (STP)

0.1786 g/L (STP)

0.769 g/L (STP)

1.14 g/L (30^oC) Varies based on temperature

1.225 g/L (STP) Varies based on temperature

Color

Colorless

Odor

Odorless

Pungent

Odorless

Flammability

High

None

Where does helium come from?

Helium is a naturally occurring element in the Earth’s atmosphere, but its concentration is too low for economical extraction. Helium is also found in underground gas deposits, which migrates upward to the top of the gas pocket because of its low density. The helium that accumulates can then be separated and collected. The U.S. is the world’s largest helium producer; the sole source of helium in the U.S. comes from a plant operated by the Bureau of Mines in Texas. However, helium is a finite resource, and its annual and long-term availability is unpredictable. Consequently, recent efforts have been made to promote the conservation and responsible use of helium. Ironically, modern airships may revert to using hydrogen if helium sources are limited or it becomes cost-prohibitive.

Principle of Buoyancy

Archimedes’ principle is used to analyze the aerostatic forces on LTA aircraft. This principle states that the upward or buoyancy force exerted on a body immersed in a fluid equals the weight of the fluid that the body displaces. This behavior is true whether the body is wholly or partially submerged in the fluid and is independent of the body’s shape. As shown in the figure below, the resulting force acts upward at the displaced fluid’s center of buoyancy (also the center of mass). This principle is commonly used in problems involving the hydrostatic or aerostatic analysis of all “floating bodies,” such as boats, ships, balloons, and airships.

Archimedes’ principle states that the upthrust or buoyancy force on a body immersed in a fluid equals the weight of the displaced fluid.

To better illustrate the concept of buoyancy, consider the scenarios shown in the figure below. The object’s volume is the same in each case, but its weight differs, ranging from $W_1$ (the heaviest) to $W_3$ (the lightest). If the object is entirely immersed in the fluid, then the upthrust of buoyancy force, $F_b$ , will be

(1) $\begin{equation*} F_b = \varrho_{\tiny \rm fl} \, {\cal{V}} \, g \end{equation*}$

where ${\cal{V}}$ is the volume of the object and hence the volume of the displaced fluid, and $\varrho_{\rm \scriptsize fluid}$ is the density of the displaced fluid. The buoyancy force only depends on the weight of the fluid displaced by the object, not the weight of the object. However, the net force on the object is a balance between the buoyancy and the weight, i.e.,

(2) $\begin{equation*} F_{\rm net} = F_b - W = \varrho_{\tiny \rm fl} \, {\cal{V}} \, g - \varrho_{\tiny \rm obj} \, {\cal{V}} \, g = \left( \varrho_{\tiny \rm fl} - \varrho_{\tiny \rm obj} \right) \, {\cal{V}} \, g = W_{\tiny \rm fl} - W_{\tiny \rm obj} \end{equation*}$

where $\varrho_{\tiny \rm obj}$ is the density of the object.

The buoyancy force on an immersed object depends on the weight of the fluid displaced by the object, not the object’s weight.

If the object is heavier than the buoyancy force, i.e., $W_{\tiny \rm fl} < W_{\tiny \rm obj}$ , it will sink. If the object has a weight equal to the buoyancy force, i.e., $W_{\tiny \rm fl} = W_{\tiny \rm obj}$ , it will have neutral buoyancy and reach an immersed depth where it will neither sink nor rise in the fluid. The body will rise in the fluid if the buoyancy force exceeds the weight, i.e., $W_{\tiny \rm fl} > W_{\tiny \rm obj}$ . Eventually, if the body is made light enough, it will float on the surface of the fluid interface. In this case, only partial immersion may be needed to displace the fluid required to create the buoyancy force to balance the weight, i.e., like a boat or a ship.

Now consider a hot-air balloon floating in the atmosphere, as shown in the figure below. The balloon’s envelope contains hot (i.e., warmer) air so that it will have a lower density than the surrounding cooler air. Using Archimedes’ principle, the balloon’s buoyancy force will equal the weight of the displaced colder air. The balloon’s net weight will include the weight of its envelope and structure (including anything in the basket hanging below) plus the weight of hot air. Therefore, the net force acting on the balloon will equal the difference between the balloon’s net weight and the weight of the displaced air.

In aerostatic equilibrium, the upthrust on a balloon will equal its weight. Its center of gravity lies well below the center of buoyancy, giving it high pendular stability to external disturbances

For neutral buoyancy, the weight of hot air inside the balloon, $W_{\rm hot}$ , plus the weight of the balloon itself, $W_b$ , equals the buoyancy lift, $L$ , or upthrust $F_b$ , i.e.,

(3) $\begin{equation*} F_b - \left( W_b + W_{\rm hot} \right) = 0 \end{equation*}$

The buoyancy lift is given by

(4) $\begin{equation*} F_b = L = \varrho_{\rm hot} \, g \, {\cal{V}} \end{equation*}$

where ${\cal{V}}$ is the volume of the balloon’s envelope. The weight of the hot air will be

(5) $\begin{equation*} W_{\rm hot} = \varrho_{\rm hot} \, g \, {\cal{V}} \end{equation*}$

Therefore, for neutral buoyancy, then

(6) $\begin{equation*} W_b = \left( \varrho_{\rm air} - \varrho_{\rm hot} \right) \, g \, {\cal{V}} \end{equation*}$

Check Your Understanding #1 – Buoyancy of a hot-air balloon

A hot air balloon becomes neutrally buoyant at an altitude of 1,100 m where the outside air temperature is 10.5 $^{\circ}$ C. With all its cargo, the balloon has a mass of 500 kg (excluding the air in the balloon), displacing a volume of 7,000 m³. Assume that the pressure inside the balloon is the same as that outside. Determine the air temperature inside the balloon to give it neutral buoyancy. At 1,100 m, the air density can be considered 1.102 kg/m³.

Show solution/hide solution.

For neutral buoyancy, the weight of hot air inside the balloon $W_{\rm hot}$ + the weight of the balloon itself $W_b$ = the lift or upthrust $F_b$ (according to Archimedes’ Principle) caused by the weight of displaced cool air, i.e., there is no net vertical force on the balloon so that

$F_b - \left( W_b + W_{\rm hot} \right) = 0$

The air volume displaced by the balloon is $\cal{V}$ = 7,000 m ${^3}$ . Therefore, the weight of cool air displaced by the balloon is then.

$W_{\rm cool} = {\cal{V}} \, \varrho_{1100} \, g = 7,000 \times 1.102 \times 9.81 = 75,674.3~\mbox{N}$

which is equal to the upward buoyancy force $L$ according to Archimedes’ Principle. The mass of the balloon is 500 kg, so its weight, $W_b$ , is 500 $g$ = 500 $\times$ 9.81 = 4905.0 N. Notice that $\varrho_{1100}$ is the density of the displaced air at a height of 1,100 m, which is given as 1.102 kg m ${^{-3}}$ .

Therefore, for neutral buoyancy (i.e., $F_b = L = W_b + W_{\rm hot}$ if the net vertical force is zero), the weight of the hot air in the balloon must be

$W_{\rm hot} = F_b - W_b = 75,674.3 - 4905.0= 70,769.3~\mbox{N}$

This means that the corresponding density of the hot air inside the balloon must be

$\varrho_{\rm hot} = \frac{W_{\rm hot} }{g \cal{V}} = \frac{70,769.3}{9.81 \times 7,000} = 1.031~\mbox{kg m${^{-3}}$}$

which is less than the density of the surrounding cool air, as expected.

We are asked to determine the corresponding temperature of the hot air, for which we can use the equation of state, i.e.,

$p = \varrho \, R \, T$

We are told to assume that the pressure inside the balloon is the same as that outside the balloon so

$p = \varrho_{\rm cool} \, R \, T_{\rm cool} = \varrho_{\rm hot} \, R \, T_{\rm hot}$

Rearranging gives the ratio of the temperatures as

$\frac{T_{\rm hot}}{T_{\rm cool}} = \frac{\varrho_{\rm cool}}{\varrho_{\rm hot}} = \frac{1.102}{1.1031} = 1.069$

The outside air temperature at 1,100 m is 10.5 $^{\circ}$ C or 283.65 $^{\circ}$ K. Therefore, the temperature of the hot air needed for neutral buoyancy will be

$T_{\rm hot} = 1.069 \, T_{\rm cool} = 1.069 \times 283.65 = 303.22~\mbox{$^{\circ}$K} \approx 30.1~\mbox{$^{\circ}$C}$

so a differential balloon internal temperature of about 20 $^{\circ}$ C at this altitude and temperature conditions.

Geometric Characteristics of Aerostats

Traditionally, airships and many aerostats have streamlined hull shapes based on prolate spheroids, i.e., those that look like fat cigars; spheres closely approximate balloons. An ellipsoid, shown in the figure below, is the most general shape in this geometric class of bodies of revolution that includes, in special cases, prolate and oblate spheroids, as well as spheres.

An ellipsoid is a general class of geometric shapes that includes prolate and oblate spheroids and spheres.

Regarding aerodynamics and other characteristics of such shapes, the key geometric parameters of interest are the ellipsoid’s projected frontal area, volume, surface area, and slenderness ratio. Aerodynamic coefficients used in the analysis may be based on any or all of these parameters. Therefore, it is essential to understand how they are defined.

Projected Frontal Area

The projected frontal area, $S_{\rm ref}$ , of a general ellipsoid is

(7) $\begin{equation*} S_{\rm ref} = \pi \, a \, c \end{equation*}$

In the case of a prolate spheroid where $a = c$ , or a sphere where $a = b= c$ then

(8) $\begin{equation*} S_{\rm ref} = \pi \, a^2 = \frac{\pi \, D_{\rm max}^2}{4} \end{equation*}$

Volume

The general formula for the volume of an ellipsoid is

(9) $\begin{equation*} {\cal{V}} = \frac{4}{3} \pi \, a \, b \, c \end{equation*}$

Notice that when $a = b = c$ , then this formula is the volume of a sphere, i.e.,

(10) $\begin{equation*} {\cal{V}} = \frac{4}{3} \pi \, a \, b \, c = \frac{4}{3} \pi \, a^3 \end{equation*}$

The formula for the volume of a prolate spheroid with $b > a$ and $c = a$ is

(11) $\begin{equation*} {\cal{V}} = \frac{4}{3} \pi \, a \, b \, a = \frac{4}{3} \pi \, a ^2\, b \end{equation*}$

Surface Area

The surface area of a spheroid is a surface of rotation, which is given by

(12) $\begin{equation*} S_w = 2 \pi \, b^2 + \pi \frac{a^2}{e} \ln\left(\frac{1 + e}{1 - e}\right) \end{equation*}$

where the eccentricity, $e$ of an prolate spheroid is

(13) $\begin{equation*} e = \sqrt{ 1 - \frac{b^2}{a^2}} \end{equation*}$

For aerodynamic problems, the surface area $S_w$ is called the “wetted area.

In the case of $e \rightarrow 0$ , Eq. 12 becomes infinite. However, if the logarithm term is expanded as a Taylor series, then

(14) $\begin{equation*} S_w = 2 \pi \, b^2 + 2 \pi \frac{a^2}{e} \left(e + \frac{e^3}{3} + \frac{e^5}{5} + \frac{e^7}{7} + \ . . . \right) \end{equation*}$

giving

(15) $\begin{equation*} S_w = 2 \pi \, b^2 + 2 \pi \, a^2 \left(1 + \frac{e^2}{3} + \frac{e^4}{5} + \frac{e^6}{7} + \ . . .\right) \end{equation*}$

so for a sphere with $e = 0$ and $a = b$ , then

(16) $\begin{equation*} S_w = 4 \pi \, a^2 \end{equation*}$

In general, an approximate formula for the wetted area of a general ellipsoid is

(17) $\begin{equation*} S_w \approx 4 \pi \left( \frac{ (a \, b)^\alpha + (a \, c)^\alpha + (b \, c)^\alpha}{3} \right)^{1/\alpha} \end{equation*}$

where $\alpha$ = 8/5.

Slenderness Ratio

The aerodynamic characteristics of airships are often expressed in terms of the slenderness ratio. The slenderness ratio, $\lambda$ , for an prolate spheroid is defined as

(18) $\begin{equation*} \lambda - \frac{2b}{2a} = \frac{L}{D_{\rm max}} \end{equation*}$

where $L$ is the length and $D_{\rm max} = 2 a$ is the maximum diameter.

Definition of the slenderness ratio, $\lambda$ , for a prolate spheroid.

The slenderness ratios of a family of prolate spheroids are shown below. Most airships fall in the range 4 < $\lambda$ < 6, which, based on historical precedent, has been found to give the lowest average aerodynamic drag.

Examples of the slenderness ratios of a family of prolate spheroids. Airships tend to have values in the range of 4 to 6.

Center of Buoyancy

In understanding the flight characteristics of LTA aircraft, it is paramount to determine the aerostatic buoyancy force and the center of buoyancy, i.e., where the resulting buoyancy force can be assumed to act. The center of buoyancy or the center of the aerostatic lift is also the center of volume and gravity of the displaced air. Therefore, the center of buoyancy can be determined by finding the center of volume of the buoyant gas within the airship’s envelope.

It is useful to first illustrate the process in two dimensions, which means finding the center of area of a slice of a three-dimensional object. In reference to the figure below, the total area can be determined using

(19) $\begin{equation*} A = \int y \, dy = \int x \, dx \end{equation*}$

Method of calculating the center of area (center of buoyancy) on a two-dimensional surface.

The first moments of area are given by

(20) $\begin{equation*} M_{xx} \int_{A} y \, x \, dx \end{equation*}$

and

(21) $\begin{equation*} M_{yy} \int_{A} x \, y \, dy \end{equation*}$

The location (coordinates) of the center of area, $(\overline{x}, \overline{y})$ , are then determined using

(22) $\begin{equation*} \overline{x} = \frac{M_{yy}}{A} = \frac{1}{A} \int_{A} x \, y \, dx \end{equation*}$

and

(23) $\begin{equation*} \overline{y} = \frac{M_{xx}}{A} = \frac{1}{A} \int_{A} y \, x \, dy \end{equation*}$

Naturally, the process can be extended to three dimensions involving volumetric integrals. In practice, an approximate center of buoyancy will be determined numerically because there is unlikely to be an exact formula for an airship’s shape. In this case, the integrals in the equations above will be replaced by numerical summations based on the actual shape. Most CAD software allows an automatic calculation of the volume and center of volume of a shape.

The concept of the center of buoyancy is important for LTA aircraft.

Aerostatic Trim

In the absence of aerodynamic forces, a stationary free-flying airship or other LTA aircraft will be in static equilibrium when the center of gravity lies directly below the center of buoyancy, as shown in the figure below, i.e., the upthrust from buoyancy equals the weight, as given by

(24) $\begin{equation*} L = F_b = W \end{equation*}$

Notice that the center of gravity for an airship is generally well below the center of buoyancy, which gives the aircraft significant pendular stability about the pitch and roll axes. In aerostatic trim or the static equilibrium condition, most airships are not entirely level but can be seen to take on a slightly nose-high attitude. Airships have very little inherent stability about the yaw axis, although disturbances in yaw are heavily damped by the aerodynamic forces on the fuselage and vertical tail(s).

In aerostatic trim conditions and without any thrust vectoring, the center of gravity of an airship will lie below the center of buoyancy.

The buoyancy force, $F_b$ , or aerostatic lift, $L$ , on the airship will be equal to the net weight of the air displaced less the weight of the helium inside the envelope, i.e.,

(25) $\begin{equation*} F_b = L = \left( \varrho_{\rm air} - \varrho_{\rm He} \right) g {\cal{V}} \end{equation*}$

where ${\cal{V}}$ is the volume of the gas envelope, $\varrho_{\rm air}$ is the density of air, and $\varrho_{\rm He}$ is the density of helium gas. If the net sum of the structural, fuel, and payload weight of the airship is $W$ , then for vertical force equilibrium and neutral buoyancy, then

(26) $\begin{equation*} W = \left( \varrho_{\rm air} - \varrho_{\rm He} \right) g {\cal{V}} \end{equation*}$

Therefore, for a given set of atmospheric conditions, the needed volume of the helium gas can be determined to provide a specific buoyancy force to overcome the airship’s weight.

Check Your Understanding #2 – Buoyancy of an airship

An airship has a gas envelope with a 296,520 ft³ volumetric capacity. Helium is used as the buoyant gas. If the airship has an empty weight of 14,188 lb and a maximum fuel load of 960 lb, what would be the maximum payload the airship could carry? Assume MSL ISA standard atmospheric conditions. The density of helium can be assumed to be 0.0003192 slugs/ft³. Ignore the effects of any ballast.

Show solution/hide solution.

The upforce (lift), $L$ , on the airship will be equal to the net weight of the air displaced less the net weight of the gas inside the envelope, i.e.,

$L = \left( \varrho_{\rm air} - \varrho_{\rm He} \right) g {\cal{V}}$

where ${\cal{V}}$ is the volume of the gas envelope. The gross weight of the airship will be the sum of the empty weight, $W_E$ , plus the fuel weight, $W_F$ , plus the payload, $W_P$ , i.e.,

$W = W_E+ W_F + W_P$

For vertical force equilibrium at takeoff, then $L = W$ , so

$W_E + W_F + W_P = \left( \varrho_{\rm air} - \varrho_{\rm He} \right) g {\cal{V}}$

Rearranging for the payload weight gives

$W_P = \left( \varrho_{\rm air} - \varrho_{\rm He} \right) g {\cal{V}} - W_E - W_F$

Using the numerical values supplied gives

$W_P = \left( 0.002378 - 0.0003192 \right) \times 32.17 \times 296,520 - 14,188.0 - 960.0 = 4,429.2~\mbox{lb}$

Therefore, the maximum payload at the takeoff point would be 4,429 lb.

Ballast

Some form of ballast is used on most types of LTA aircraft. Ballast is any material placed on board a buoyant aircraft to add non-structural weight for balance and/or trim. Water ballast, carried internally in tanks, is typically used, although bags containing sand or lead shot can also be used. Besides trim and balance, ballast can be taken on or cast overboard to obtain a particular takeoff or in-flight weight and for landing and unloading the airship on the ground. For example, on a hot air balloon, ballast in the form of sandbags is used to keep it firmly on the ground as the hot air fills up the envelope. Some ballast is dropped overboard when the airship is ready to fly, and the balloon is said to weigh-off. During descent, dropping more ballast can reduce the descent rate as the balloon comes in for a landing.

Airships and blimps will also add or remove ballast as bags of lead shot or add/dump water ballast before weigh-off. The weigh-off condition means that the airship is trimmed to the condition it must operate in the initial part of the flight. To this end, ballast is added until the aircraft reaches a point where it becomes slightly heavier than the upward aerostatic buoyancy force, which is called static heaviness.

After takeoff, the pilot first gives the airship a pronounced nose-high attitude using up-elevator so the engines can provide a vertical component of thrust to overcome the static heaviness. If thrust vectoring is available, the propulsion system is swiveled to give mostly vertical thrust during the takeoff maneuver. These actions propel the airship upward and forward into a climb. As the airship gains altitude and airspeed, the airflow over the envelope generates some aerodynamic lift, and the pilot reduces the pitch attitude to reach a steady climb. Finally, the nose is lowered to almost level for the cruise.

It is important to note that “static heaviness” refers to the airship’s weight when stationary. The specific value of static heaviness of an airship can vary greatly depending on its size and configuration. Typically, the static heaviness is between 5% and 10% of the gross weight. Larger airships that carry heavy payloads must have a higher static heaviness than smaller blimps. Hybrid airships have the largest static heaviness because their hull shapes are designed to produce significant aerodynamic lift, so the takeoff and landing will involve a short runway length.

Ballonets

Ballonets (meaning little balloons in French) are the gaseous equivalent of the water ballast tanks used on submarines. They are used in airships and blimps to control buoyancy and the center of buoyancy of the lifting gas. As shown in the figure below, the ballonets consist of internal gas bags or chambers within the airship’s envelope that can be inflated or deflated with air to control the volume of the buoyant gas. Another purpose of the ballonets on blimps is to maintain the buoyant gas’s net positive differential pressure so that the envelope retains its shape.

They are used in airships and blimps to control buoyancy and the center of buoyancy.

Pressurized air is pumped into the ballonets using a system of scoops, electric pumps, ducts, valves, and pressure regulators. The air scoops are often placed where the dynamic pressure from the slipstream created by the propellers or other propulsion systems can be captured. The ballonets are operated through an automatic pressure control system to regulate the inflation and deflation processes, and any excess pressure is released by venting through a set of air valves; pilots can also control the ballonets manually.

Inflation Fraction

Recall that buoyancy or aerostatic lift is equal to the weight of the air that the buoyant gas displaces less the weight of the buoyant gas itself, i.e.,

(27) $\begin{equation*} F_b = L = \left( \varrho_{\rm air} - \varrho_{\rm bg} \right) \, g \, {\cal{V_{\rm bg}}} \end{equation*}$

where ${\cal{V_{\rm bg}}}$ is the volume of the buoyant gas contained in the envelope, $\varrho_{\rm air}$ is the density of air, and $\varrho_{\rm bg}$ is the density of the buoyant gas, e.g., helium.

The inflation fraction, $I$ , is defined as the volume fraction of the total volume of the envelope occupied by the buoyant gas, i.e., the fraction not occupied by the ballonets. If the total volume of the envelope is ${\cal{V}}$ , then the inflation fraction is

(28) $\begin{equation*} I = \frac{ {\cal{V_{\rm bg}}} }{ {\cal{V}} } \end{equation*}$

For example, an inflation fraction of 0.85 would mean that 85% of the envelope’s volume would produce buoyancy. Therefore, the buoyancy can be written in terms of the inflation faction as

(29) $\begin{equation*} F_b = L = \left( \varrho_{\rm air} - \varrho_{\rm bg} \right) \, g \, I \, {\cal{V}} \end{equation*}$

the concept being shown in the figure below. The ballonets do not produce buoyancy because they are filled with air at nominally ambient conditions, and so act like ballast in the same manner water is used for ballast on a submarine.

The concept of inflation fraction, where only a fraction of the envelope’s volume produces buoyancy.

For a rigid airship or dirigible, the volume is defined as the net volume of the buoyant gas cells; these gas cells do not fill the entire envelope, so the potential lifting capacity is less than the volume enclosed by the envelope. The individual gas cells will also have different volumes because they are distributed along the length of a shape resembling a prolate spheroid. If an individual gas cell of volume, ${\cal{V}}_n$ , with $N$ cells has an inflation fraction, $I_n$ , then the volume of buoyant gas will be

(30) $\begin{equation*} {\cal{V}}_{\rm bg} = \sum_{N=1}^{N} I_n \, {\cal{V}}_n \end{equation*}$

The process of analysis then proceeds as before.

Controlling Buoyancy

By adjusting the internal air pressure and volume in the ballonets, they will expand or contract so that the overall inflation fraction of the airship’s envelope can be modified, thereby controlling the buoyancy and center of buoyancy. Ballonets also provide a means to adjust buoyancy to compensate for changes in atmospheric conditions, i.e., pressure and temperature, solar heating of the envelope, and weight loss from fuel burn. This process allows the airship to safely ascend or descend, change its pitch attitude, and compensate for variations in the center of gravity location.

For example, as shown in the figure below, the ballonets are initially inflated with air, reducing the volume of the buoyant gas and giving the airship some static heaviness. After weigh-off and the initial climb, the external atmospheric pressure and density decrease, allowing the buoyant gas to expand. Excess air in the ballonets is vented out to maintain a constant differential pressure across the envelope, allowing the buoyant gas to expand freely, thereby keeping the airship’s net buoyancy.

As an airship gains altitude, the pressure in the ballonets is released, allowing their volume to contract.

Pressure Altitude (Gas Ceiling)

The highest achievable altitude, where the gas pressure differential reaches its design limits when the ballonets are mostly fully deflated, is called the “pressure altitude.” However, this airship term should be kept distinct from the pressure altitude used in altimetry, so the condition is best called the gas ceiling. In an emergency, an overpressure of the buoyant gas on the outside of the envelope opens the release valve and vents some buoyant gas to prevent structural issues. Typically, the pressure altitude of a blimp or other airship is about 3,000 m (roughly 10,000 ft). During descent, the ballonets are reinflated as atmospheric air density increases to maintain the envelope’s differential pressure and control the airship’s net buoyancy.

Trim Attitude

Ballonets can also trim the pitch attitude for climb and descent, as shown in the figure below. The purpose is to use the ballonets to move the center of buoyancy relative to the center of gravity. Inflating the forward ballonet will move the center of buoyancy aft, lowering the nose of the airship and reducing the pressure in the aft ballonet to maintain the buoyant gas pressure inside the envelope. Similarly, inflating the aft ballonet will move the center of buoyancy forward, raising the nose and reducing the pressure in the forward ballonet.

The ballonets can be used to trim the airship and adjust its pitch attitude.

Center of Gravity

Any aircraft’s center of gravity (c.g.) can change during flight as fuel is burned off or for other reasons. Airships are no different, and the pilot needs to monitor and maintain the center of buoyancy and ensure that the c.g. is within acceptable limits. Aircraft manufacturers provide guidelines and limits for the permissible range of c.g. at different weights, called a c.g. envelope. Operating any aircraft outside its c.g. envelope can affect its handling characteristics, stability, and maneuverability, potentially leading to unsafe flight conditions. To this end, for an airship, the ballonets can compensate for variations in the c.g. location, either before or during flight, as shown in the figure below.

Thrust Vectoring

Thrust vectoring refers to the ability of an airship to control the direction of its propulsion force. This goal is achieved by adjusting the angle of the propulsion system or its components, such as engines or propellers, to change the direction of the thrust. Thrust vectoring is not a new concept and was first used on the U.S.S. Akron and Macon airships, which used tilting propellers. The basic principle is shown in the figure below. Notice that thrust vectoring can change the magnitude and direction of the forces and moments, giving significant control of the airship independently of the aerodynamic surfaces or buoyancy. Negative thrust can also be obtained by using fully feathering propellers.

The recent Zeppelin NT uses three swiveling propellers and vectored thrust capability. This capability allows the aircraft to perform vertical take-offs and landings, stable hovering, and backward flight. The two propellers on each side of the airship generally provide forward thrust but can also swivel through 120 degrees to obtain vectored thrust. The photograph below shows that the aft engine drives a propeller that can be swiveled downward if needed and a second (non-swiveling) sideward thrusting steering propeller for precise directional (yaw) control.

The Zeppelin NT uses a swiveling rear pusher propeller and a sideward thrusting steering propeller.

Worked Example #3 – Understanding the function of the ballonets

An airship has an internal helium-filled gas bag of cylindrical shape with a length $L$ = 40 m and a radius $R$ = 10 m. There are also two ballonets containing air that can expand into the helium gas bag to reduce its volume and affect the airship’s overall buoyancy. The airship’s total mass including the full load of helium is 11,500 kg. The density of air is $\varrho_{\text{air}} = 1.225 \, \text{kg/m}^3$ , and the density of helium is $\varrho_{\text{He}} = 0.1786 \, \text{kg/m}^3$ . Determine the air volume that must be pumped into the ballonets for the airship to achieve neutral buoyancy.

Show solution/hide solution.

To achieve neutral buoyancy, the weight of the airship must equal the buoyancy force acting on it. The buoyancy force is given by the weight of the air displaced by the helium in the gas bag, which, in this case, the fully-expanded gas bag is the volume of a cylinder, i.e.,

${\cal{V}}_{\text{gas\_bag}} = \pi R^2 L = \pi (10.0)^2 \times 40 = 4,000 \pi \, \text{m}^3 \approx 12{,}566.37 \, \text{m}^3$

The weight $W$ of the airship is

$W = M g = 11{,}500 \times 9.81 = 112{,}215.0 \, \text{N}$

The buoyancy force $F_b$ is equal to the weight of the air displaced by the volume of helium, i.e.,

$F_b = {\cal{V}}_{\text{gas\_bag}} \, \varrho_{\text{air}} \, g$

where ${\cal{V}}_{\text{gas\_bag}}$ is the full expanded volume of the helium gas bag (calculated above). Therefore,

$F_b = 4{,}000 \pi \times 1.225 \times 9.81 = 4{,}000 \times 3.14159 \times 1.225 \times 9.81 = 151{,}778.4 \, \text{N}$

so it is clear that this is not a neutral buoyancy condition, and the ballonets must be filled with some air. The light helium gas is at low pressure and is easily compressed into a smaller volume by filling the ballonets.

To achieve neutral buoyancy, set the airship’s weight equal to the required buoyancy force, i.e., $W = F_b$ . The volume of air ${\cal{V}}_{\text{air}}$ needed to displace the initial value of helium when air is pumped into the ballonets can be expressed in terms of

$F_b = ( {\cal{V}}_{\text{gas\_bag}} - {\cal{V}}_{\text{air}}) \, \varrho_{\text{air}} \, g = W$

and solving for ${\cal{V}}_{\text{air}}$ gives

${\cal{V}}_{\text{air}} = {\cal{V}}_{\text{gas\_bag}} - \frac{W}{\varrho_{\text{air}} \ g} = 12{,}566.37 - \frac{112{,}215}{1.225 \times 9.81} \approx 3{,}2212 \, \text{m}^3$

Therefore, the volume of air that must be pumped into the ballonets for the airship to achieve neutral buoyancy is approximately $3{,}222 \, \text{m}^3$ .

Other Factors Affecting Performance

Other factors can affect the performance of airships besides buoyancy and its control. These include the effects of superpressure, superheat, and envelope fabrics. Along with factors such as aerodynamic shape, propulsion system, and payload, they collectively influence the airship’s efficiency, safety, and operational capabilities.

Superpressure

Blimps and other pressure airships are pressurized relative to the ambient air pressure to maintain the gas envelope’s shape and structural rigidity, which is called superpressure. Because the gondola, engines, tail surfaces, etc., are interconnected through the gas envelope, it is essential always to have some superpressure in a blimp to keep the flexible envelope tight enough to carry bending, shear, and torsional loads without crushing or buckling. Nose battens, which are lengthwise longerons, are attached to the outside of the envelope to carry mooring loads and prevent the dynamic pressure of forward motion from collapsing the gas envelope. The superpressure is typically relatively low, at about 0.5 kPa (about 10 lb/ft²). Still, it can be adjusted higher in turbulent air when some extra rigidity of the envelope might be needed.

Superheat

All LTA aircraft will be subjected to thermal effects from solar radiation. The large surface area of the envelope absorbs heat and can cause the buoyant gas inside to expand. The temperature differential of the buoyant gas over the ambient air temperature is called superheat. Excessive superheat can increase internal gas pressure and decrease density, increasing buoyancy and static lift. The ballonets automatically compensate for thermal effects in a blimp by releasing air through the valves. Excessive superheat requires some buoyant gas to be released to maintain buoyancy. It is also best to use a fabric for the gas envelope that is white or silver on the outside to reflect solar radiation and black on the inside to absorb and radiate heat outward from the inside.

Envelope Fabrics

Besides helping control superheat effects, the fabric used for the envelope of an airship plays an essential role in its construction and performance. The fabric choice affects the airship’s strength, durability, gas containment capability, and overall weight. The outer envelope of a rigid airship has to form a smooth fairing over the hull structure and gasbags. Unless it remains taut under all conditions, the airflow over the external shape will be disturbed, creating excess drag and possibly flow separation. The early airships had cotton coverings, which were tautened using cellulose dope-like fabric-covered airplanes. The envelopes of blimps are made from rubberized coated fabrics to keep them gas-tight.

The primary requirements for airship fabrics are:

Good strength-to-weight ratios, i.e., light and structurally strong.
High puncture and tear resistance, such as from accidental damage.
Resistance to environmental factors such as rain, cold, heat, and UV exposure.
Low permeability to prevent gas leakage and loss of pressure.

Modern airships use multi-layer polyester fabrics and polyurethane-coated nylon. Polyester films or woven polyester are also popular. These fabrics are lightweight, strong, and resistant to stretching, tearing, and environmental degradation. They can be coated or laminated with materials that enhance gas containment properties and increase durability. Polyurethane-coated nylon fabrics provide strength and tear resistance, while the polyurethane coating adds flexibility, gas impermeability, and protection against environmental factors. Vectran is a high-strength synthetic fiber known for its excellent resistance to heat, chemicals, and UV radiation, and it is also used for space flight applications. Tedlar is another suitable covering, a long-lasting polyvinyl fluoride film suitable for surfaces exposed to harsh environments.

Check Your Understanding #4 – Using hydrogen versus helium?

How much more payload could an airship carry if it used hydrogen as the buoyancy gas rather than helium?

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Hydrogen, being about half the density of helium, can provide more buoyancy and potentially increase an airship’s payload capacity. To estimate the potential increase in payload capacity, we need to compare the buoyant forces generated by hydrogen versus helium. A legitimate engineering comparison should also be made based on the same empty weight and fuel weight of the airship. Payload is what pays the bills, i.e., the payload is cargo. The buoyant force, $F_b$ , acting on an airship will be

$F_b = \varrho_{\rm gas} \, {\cal{V}} \, g$

where $\varrho_{\rm gas}$ is the density of the gas (hydrogen or helium), ${\cal{V}}$ and is the volume of the envelope of the buoyant gas. The lifting capacity or payload capacity, $W_P$ , of the airship is equal to the buoyancy force minus the total weight of the airship, i.e.,

$W_P = F_b - W_E - W_F$

where $W_E$ is the empty weight of the airship and $W_F$ is the fuel weight. Comparing airships using hydrogen versus helium, we can calculate their respective payload capacities, i.e., for hydrogen, then

$W_P^{\rm H_2} = \left( \varrho_{\rm air} - \varrho_{\rm H_2} \right) {\cal{V}} \, g - W_E - W_F$

and for helium, then

$W_P^{\rm He} = \left( \varrho_{\rm air} - \varrho_{\rm He} \right) {\cal{V}} \, g - W_E - W_F$

Subtracting one equation from the other gives

$W_P^{\rm H_2} - W_P^{\rm He} = \left( \varrho_{\rm air} - \varrho_{\rm H_2} \right) {\cal{V}} \, g - \left( \varrho_{\rm air} - \varrho_{\rm He} \right) {\cal{V}} \, g$

so that

$W_P^{\rm H_2} - W_P^{\rm He} = \left( \varrho_{\rm He} - \varrho_{\rm H_2} \right) {\cal{V}} \, g$

Therefore, the increase in the airship’s payload from using hydrogen will be proportional to the difference in the densities of helium (about 0.18 kg/m³) and hydrogen (about 0.09 kg/m³). The percentage increase in the payload using hydrogen versus helium will be about (0.18 – 0.09)/0.18 = 50%, which is a lot of extra payload. However, the FAA does not allow hydrogen to be used as a buoyant gas, so the question can be considered moot.

Aerodynamic Effects

The consideration of aerodynamics, as opposed to aerostatics, must consider the motion of the airship through the air. The aerodynamics of airships are important because they are flown with aerostatic heaviness, which is the amount by which a buoyant aircraft’s gross weight exceeds buoyancy. The extra lift on the airship is made up using the so-called “dynamic lift.”

Dynamic Lift

In general, the term aerodynamic lift or dynamic lift denotes the lift produced on the airship other than from its buoyancy to overcome its weight. As shown in the figure below, the dynamic lift can be produced by aerodynamic lift force from the airship when it is at an angle of attack relative to the direction of flight, by the deflection of the control surfaces, and from a component from the thrust from the propulsion system, i.e.,

$\mbox{Dynamic lift = Aerodynamic lift + Tail lift + Propulsive lift}$

Dynamic lift can be produced by aerodynamic pressures on the envelope, deflection of the control surfaces, or from a component from the thrust from the propulsion system.

A primary aerodynamic effect on an airship is its drag, which thrust and power must overcome. Nevertheless, the aerodynamic lift and moments on the hull, in particular, must also be considered. The drag on an airship will comprise both pressure drag and skin friction (boundary layer shear) drag. While the pressure drag will be affected by the projected frontal area and base pressure drag (including any flow separation), skin friction is the dominant drag source on an airship because of its large surface area; this area is called the wetted area. The lift and moment contributions come primarily from the pressure distribution on the hull.

Lift, Drag & Moment Coefficients

The drag coefficient, $C_D$ , of an airship or other aerostat is defined by

(31) $\begin{equation*} C_D = \frac{D}{\frac{1}{2} \varrho_{\infty} \, V_{\infty}^2 \, A_{\rm ref} } = \frac{2 D}{\varrho_{\infty} \, V_{\infty}^2 \, {\cal{V}}^{2/3}} \end{equation*}$

where it will be noted that the reference area is

(32) $\begin{equation*} A_{\rm ref} = {\cal{V}}^{2/3} \end{equation*}$

i.e., the envelope volume is raised to the power 2/3, which will have units of area. The reference length is defined as

(33) $\begin{equation*} L_{\rm ref} = {\cal{V}}^{1/3} \end{equation*}$

The corresponding lift coefficient, $C_L$ , is defined by

(34) $\begin{equation*} C_L = \frac{L}{\frac{1}{2} \varrho_{\infty} \, V_{\infty}^2 \, A_{\rm ref} } = \frac{2 D}{\varrho_{\infty} \, V_{\infty}^2 \, {\cal{V}}^{2/3}} \end{equation*}$

The pitching moment about some point $a$ , i.e., $C_{M_{a}}$ , is defined by

(35) $\begin{equation*} C_{M_{a}} = \frac{M_a}{\frac{1}{2} \varrho_{\infty} \, V_{\infty}^2 \, A_{\rm ref} \, L_{\rm ref} } = \frac{2 M_a}{\varrho_{\infty} \, V_{\infty}^2 \, {\cal{V}}} \end{equation*}$

For airships, the moments are usually referenced to the center of volume, i.e., the center of buoyancy.

Flow Fields

To understand the force and moment characteristics, it is first necessary to better understand the nature of the flow field on an airship at an angle of attack. The flows about airships resemble those of prolate spheroids, which have been well studied in the wind tunnel using computational fluid dynamics (CFD); an example of a CFD solution is shown in the image below. The results show that the flows around such bodies strongly depend on the angle of attack.

Nathan Scott and Earl Duque. Using detached eddy simulation and overset grids to predict ow around a 6: 1 prolate spheroid. In 43rd AIAA Aerospace Sciences Meeting and Exhibit, page 1362, 2005. — CFD simulation of the flow about a prolate spheroid with a slenderness ratio of 6.

At zero angle of attack, the boundary layer is primarily attached, although some flow separation can occur at the rear of the body, especially at lower Reynolds numbers. This is the lowest drag configuration. As the angle of attack increases, the adverse pressure gradient toward the rear upper surface of the body causes flow separation with the emergence of two primary longitudinal vortices that are laterally displaced on each side of the body. These vortices create a suction pressure and lift and cause the center of pressure to move aft, as shown in the figure below. The vortices move forward on the body with a further increase in the angle of attack and create a notable wake at the tail. The center of pressure, however, stays in front of the center of buoyancy.

Representative pressure distributions over prolate spheroids representing the shape of airships.

These complex vortical flow structures directly affect the surface pressure distribution and wall shear stresses over the body and the flow environment at the tail (where the control surfaces are placed on an airship), producing nonlinear aerodynamic forces and moments.

Lift, Drag & Moment Characteristics

The complexity of the individual flow fields about prolate spheroids, in general, and specific airship shapes, in particular, means that only general aerodynamic characteristics can be presented. Measurements of the aerodynamic characteristics of sub-scale airships are available in NACA Report 394, authored by Ira Abbott in 1931, and NACA Report 432, by Hugh Freeman in 1932. Both authors present graphs of the lift, drag, and moment characteristics of airship shapes as functions of the pitch angle and Reynolds number based on length.

Some results from NACA Report 432 are shown below, containing results for the bare hull, the hull with the tail surface and gondola, and also up and down elevator deflections. Two things become immediately apparent from these measurements. First, while the drag on an airship is relatively high compared to an airfoil or wing, the amount of dynamic lift generated is meager for the size of the body. Second, the aerodynamic characteristics are nonlinear with respect to changes in the angle of attack, which is partly a consequence of the creation of vortex flows and flow separation, as previously described. Notice also the effects of the elevator angle, which behaves analogously to a flap or aileron, increasing or decreasing the lift over and above the baseline lift.

Aerodynamic characteristics of a 1/40-scale airship as measured in the wind tunnel.

The aerodynamic pitching moment is also of interest. Moments are usually referred to as the center of volume (also the center of buoyancy), which for a prolate spheroid is at the mid-length, and for an actual airship is about 45%. Notice that the moments are nose-up (positive) for low angles, but at about 8 degrees, the moment becomes increasingly nose-down (negative).

Generalization of the Aerodynamics

Generalized aerodynamic models of airship characteristics are unavailable. However, some essential characteristics for conventional airships approximating prolate spheroids are apparent, which are summarized below in terms of the increments in lift and drag coefficients as functions of the pitch angle, also referred to as the hull angle of attack. It will be apparent that the initial slope of the lift coefficient curve at low angles of attack is at least one order of magnitude less than that of a wing, which is about 0.1 per degree. The increasing lift slope at higher angles of attack is because of the effects of vortex lift.

Representative changes in the aerodynamic lift and drag on an airship for changes in pitch angle.

A reasonable lift model without elevator deflection is

(36) $\begin{equation*} \Delta C_L = C_1 \, \alpha^2 \end{equation*}$

where $\alpha$ is in degrees and $C_1 \approx$ 0.000146 per degree angle of attack. With elevator deflection, $\delta_E$ , this latter equation can be modified to

(37) $\begin{equation*} \Delta C_L = C_1 \, \alpha + C_2 \, \delta_E \end{equation*}$

where $C_2 \approx$ 0.01 per degree angle of elevator deflection.

The corresponding drag coefficient also shows a nonlinear characteristic, a form of induced drag, i.e., “drag due to lift.” This drag contribution is relatively large compared to the baseline drag on an airship at zero angle of attack. It is possible to write this drag coefficient term as

(38) $\begin{equation*} \Delta C_D = D_1 \, \Delta C_L + D_2 \, \delta_E \end{equation*}$

paralleling the modeling of the lift-induced drag on a wing. While the value of $D_1$ will vary depending on the slenderness of the airship and other shape factors, including the effects of tail surfaces, gondola, etc., a value of $D_1 \approx$ 0.01 seems reasonable for preliminary design based on the results shown in the previous plot. Furthermore, a value of $D_2$ of about 0.02 per degree is a reasonable approximation for the effects of elevator deflection.

The aerodynamic pitching moment is also of interest, mainly because this component contributes to the stability characteristics of the airship. The results in the figure below show that at lower angles of attack, say below 8^o, depending on the trim state, the moment is positive, i.e., nose-up, indicating that the center of pressure is in front of the center of buoyancy and the center of gravity. For higher angles of attack, the moment becomes negative (nose-down), indicating that the center of pressure has now moved aft of the center of buoyancy.

Representative changes in the aerodynamic moment about the center of buoyancy on an airship for changes in pitch angle.

The change in the slope and sign of the moment curves are significant in that at low angles of attack, the aerodynamic moment is destabilizing, and a positive change in the angle of attack gives a positive (nose-up) moment. This situation changes for high angles of attack, the negative slope suggesting good pitch stability because of an aft movement of the center of pressure. Because of the dominant axisymmetry of an airship, the lateral airloads to changes in yaw angle behave similarly.

Comparisons to Drag Measurements

Measurements of the drag coefficient, $C_D$ , of ellipsoids and prolate spheroids, as well as airship models in the wind tunnel, have been compiled as a function of the slenderness ratio and the Reynolds number. The Hoerner formula is commonly used to approximate the measured drag coefficient at zero angle of attack, where

(39) $\begin{equation*} C_D = C_{D_{0}} = C_F \left( 4 \lambda^{1/3} + 6 \lambda^{-7/6} + 24 \lambda^{-8/3} \right)~\mbox{for $\lambda > 2$.} \end{equation*}$

where $\lambda$ is the slenderness ratio, i.e., $L/D_{\rm max}$ . The equivalent “flat plate” skin friction drag coefficient, $C_F$ , is a function of Reynolds number as given by

(40) $\begin{equation*} C_F = \frac{0.455}{(\log_{10} Re)^{2.58}} \approx \frac{0.045}{Re^{1/6}} \end{equation*}$

which applies only to a fully developed turbulent boundary layer. While Eq. 39 is a semi-empirical relationship, the figure below shows that it is a good approximation to the drag on prolate spheroids and airship shapes where $\lambda$ is greater than 2. However, the correlation is poor for cases approaching a sphere, especially below the critical Reynolds number.

The Horner formula for the drag of prolate spheroids agrees with measurements of airship shapes made in the wind tunnel. The measurements are presented as plotted in NACA Report 394, authored by Ira Abbott.

The measurements in this figure are presented the way they were plotted in NACA Report 394, authored by Ira Abbott, which documents the tests done on airship models of the Goodyear Zeppelins in the NACA Langley variable density wind tunnel. Tests were first performed on the general shape, and the effects of the gondola, tail surface, struts, and bracing wires were then added.

Drag Breakdown

In practice, the actual drag coefficients of airships and other aerostats can be affected by the drag and interference of the various appendages to the bare hull, such as the gondola, powerplants, rigging, stabilizers, and control surfaces, etc., leading to an increase in the drag coefficient of a baseline prolate spheroid. For example, a typical drag breakdown of an airship is given in the table below, which is helpful for initial design estimates of drag coefficients. Of course, the most reliable method of finding drag coefficients for an actual airship shape is in the wind tunnel with a Reynolds number to establish any drag coefficient sensitivity.

Component	Drag (%)
Bare hull	50
Gondola	15
Flight surfaces	10
Rigging & cables	10
Miscellaneous	5
Interference	20
Total	100

Notice that the additional drag of the gondola, fins, and rigging can be substantial. For example, Hörner gives the drag coefficient of an airship at zero angle of attack as $C_D$ = 0.023 for the hull alone and $C_D = 0.071$ for the complete airship, including nacelles, fins, etc. Recall that the drag on an airship is mostly from boundary layer shear stress or skin friction over the large surface area of the gas envelope. A larger airship with a higher Reynolds number at the same airspeed will have a lower drag coefficient. Therefore, its drag, being proportional to the wetted surface, grows with less than the square of the increase in the length scale, while the aerostatic lift is proportional to the cube of the length scale.

Power Required for Flight

To propel an airship, its aerodynamic drag must be overcome by the thrust from the propulsion system, i.e., the engines and propellers or fans. Estimates of the power required for the flight of an airship proceed along similar lines to that of the propeller-driven airplane. In the simplest terms, the maximum speed of an airship occurs when the maximum thrust generated by its engines is equal to the drag it experiences while being pushed through the air at that speed. That drag depends on the diameter and length of the airship, and more specifically, the projected frontal area and the total “wetted area” of its entire outer envelope. In general, the drag varies with the square of the airspeed, and so the power increases with the cube of the airspeed.

Analysis

The drag in level flight is given by the conventional formula, i.e.,

(41) $\begin{equation*} D = \frac{1}{2} \, \varrho_{\infty} \, V_{\infty}^2 \, S_{\rm ref} \, C_D \end{equation*}$

where in this case the reference area on which $C_D$ is based is ${\cal{V}}^{2/3}$ , so

(42) $\begin{equation*} D = \frac{1}{2} \, \varrho_{\infty} \, V_{\infty}^2 \, {\cal{V}}^{2/3} \, C_D \end{equation*}$

Using Eq. 38, the drag coefficient can be expressed as

(43) $\begin{equation*} C_D = C_{D_{0}} + \Delta C_D = C_{D_{0}} + D_1 \, C_L + D_2 \, \delta_E \end{equation*}$

where from Eq. 37 the lift coefficient is

(44) $\begin{equation*} C_L = C_1 \, \alpha + C_2 \, \delta_E \end{equation*}$

The corresponding power required for flight can be written as

(45) $\begin{equation*} P_{\rm req} = \frac{T V_{\infty}}{\eta_p} = \frac{1}{\eta_p} \left( \frac{1}{2} \, \varrho_{\infty} \, V_{\infty}^3 \, {\cal{V}}^{2/3} \, C_D \right) = \frac{1}{2 \eta_p} \varrho_{\infty} V_{\infty}^3 {\cal{V}}^{2/3} \, C_D \end{equation*}$

where $\eta_p$ can be considered as the net efficiency of the propulsive system (engine and propeller combined); notice that this value may vary with airspeed.

Check Your Understanding #5 – Estimating forward flight power for an airship

An airship with a slenderness ratio of 3.9 has a buoyant gas volume of 6,600 m³ and cruises at an airspeed of 54.5 kts (28 m/s) at MSL ISA conditions using no dynamic lift. The drag coefficient on the airship based on Eq 31 is 0.051, and the propulsive efficiency is 0.80. Estimate the power required for flight.

Show solution/hide solution.

The power required for flight can be written as

(46) $\begin{equation*} P_{\rm req} = \frac{1}{2 \eta_p} \varrho_{\infty} V_{\infty}^3 {\cal{V}}^{2/3} \, C_D \end{equation*}$

Inserting the values gives

(47) $\begin{equation*} P_{\rm req} = \frac{1}{2 \times 0.8} \times 1.225 \times 28.0^3 \times 6,600^{2/3} \times 0.051 = 111.8~\mbox{kW} \end{equation*}$

which is about 149 shp ( $\approx$ 112 kW).

Power Required Curves

The nature of the power required curves for an airship depends on many factors, partly because in regular operation, the airship may use some element of dynamic lift for flight, i.e., there is a lift-sharing effect to consider. The fraction of the total weight carried by buoyancy can be between 90% and 95% (say for a blimp) and 70% or less for a hybrid airship.

Buoyancy Only

In the case of zero dynamic lift, creatine the power-required curves is trivial because the drag coefficient can be assumed constant, i.e., $C_D = C_{D_{0}}$ , as shown in the figure below. In this case, power will increase proportionally with the cube of the airspeed according to

(48) $\begin{equation*} P_{\rm req} = \frac{T V_{\infty}}{\eta_p} = \frac{1}{\eta_p} \left( \frac{1}{2} \, \varrho_{\infty} \, V_{\infty}^3 \, {\cal{V}}^{2/3} \, C_{D_{0}} \right) = \left( \frac{1}{2 \eta_p} \, \varrho_{\infty} \, {\cal{V}}^{2/3} \, C_{D_{0}} \right) V_{\infty}^3 \end{equation*}$

Buoyancy + Aerodynamic Lift

When some dynamic lift is used for flight, the drag on the airship will be greater, so the power requirements will be greater. Assume that there is no dynamic lift from thrust, which means that the lift sharing can be written as

(49) $\begin{equation*} L = W = L_b + L_a = \epsilon W + \left( 1 - \epsilon \right) W \end{equation*}$

where $L_b$ is the buoyant lift, and $L_a$ is the aerodynamic lift. The parameter $\epsilon$ is the lift sharing fraction, so $\epsilon =$ 0.9 when 90% of the lift comes from buoyancy. The aerodynamic lift is given by

(50) $\begin{equation*} L_a = \frac{1}{2} \varrho_{\infty} \, V_{\infty}^2 \, {\cal{V}}^{2/3} \, C_L = \left( 1 - \epsilon \right) W \end{equation*}$

so the lift coefficient is

(51) $\begin{equation*} C_L = \frac{2 \, L_a}{\varrho_{\infty} \, V_{\infty}^2 \, {\cal{V}}^{2/3} } = \frac{2 ( 1 - \epsilon) W}{\varrho_{\infty} \, V_{\infty}^2 \, {\cal{V}}^{2/3} } \end{equation*}$

Notice that the lift coefficient decreases with the inverse square of airspeed, $V_{\infty}$ . The drag coefficient (assuming no elevator deflection) is then

(52) $\begin{equation*} C_D = C_{D_{0}} + D_1 \, C_L \end{equation*}$

Therefore, because the thrust required equals drag, then

(53) $\begin{equation*} T_{\rm req} = D = \frac{1}{2} \varrho_{\infty} \, V_{\infty}^2 \, {\cal{V}}^{2/3} \, C_D = \frac{1}{2} \varrho_{\infty} \, V_{\infty}^2 \, {\cal{V}}^{2/3} \left( C_{D_{0}} + D_1 \, C_L \right) \end{equation*}$

(54) $\begin{equation*} T_{\rm req} = \frac{1}{2} \varrho_{\infty} \, V_{\infty}^2 \, {\cal{V}}^{2/3} \left( C_{D_{0}} + \frac{2 D_1 ( 1 - \epsilon) W}{\varrho_{\infty} \, V_{\infty}^2 \, {\cal{V}}^{2/3} } \right) \end{equation*}$

The power required is

(55) $\begin{equation*} P_{\rm req} = \frac{T_{\rm req}\, V_{\infty}}{\eta_p} = \frac{1}{2 \eta_p} \varrho_{\infty} \, V_{\infty}^3 \, {\cal{V}}^{2/3} \left( C_{D_{0}} + \frac{2 D_1 ( 1 - \epsilon) W}{\varrho_{\infty} \, V_{\infty}^2 \, {\cal{V}}^{2/3} } \right) \end{equation*}$

so that

(56) $\begin{equation*} P_{\rm req} = \frac{1}{2 \eta_p} \varrho_{\infty} \, V_{\infty}^3 \, {\cal{V}}^{2/3} \left( C_{D_{0}} + \frac{D_1 \, V_{\infty} ( 1 - \epsilon) W}{\eta_p} \right) \end{equation*}$

(57) $\begin{equation*} P_{\rm req} = \left( \frac{1}{2 \eta_p} \varrho_{\infty} \, {\cal{V}}^{2/3} \, C_{D_{0}} \right) V_{\infty}^3 + \left( \frac{D_1 ( 1 - \epsilon) W}{\eta_p } \right) \, V_{\infty} \end{equation*}$

which for constant values of $\epsilon$ , $\eta_p$ , weight, and density altitude, is of the form

(58) $\begin{equation*} P_{\rm req} = A V_{\infty}^3 + B V_{\infty} \end{equation*}$

where

(59) $\begin{equation*} A = \frac{1}{2 \eta_p} \varrho_{\infty} \, {\cal{V}}^{2/3} \, C_{D_{0}} \end{equation*}$

and

(60) $\begin{equation*} B = \frac{D_1 ( 1 - \epsilon) W}{\eta_p } \end{equation*}$

The forgoing equations show that the power required for an airship comprises two parts: one (non-lifting) part, the parasitic power, which increases with the cube of airspeed, and another (lifting) part, which increases proportionally with airspeed, which is the induced power, as shown in the figure below. Notice that without aerodynamic lift, i.e., zero heaviness, the power required is minimal because the airship’s weight is supported by buoyancy, and there is no induced drag.

Power required for an airship as a function of airspeed.

Maximum Attainable Airspeed

The maximum achievable airspeed depends on the type of airship. Airships are large aircraft with a lot of surface area and have high skin friction drag coefficients. Therefore, the expectation is that maximum airspeeds will be relatively low compared to airplanes, which is indeed the case. Cruise speeds between 35 kts (65 kph) and 80 kts (148 kph) are possible without excessive power requirements and engine weight. However, because the power required increases with the cube of airspeed, power and fuel demands increase rapidly above this.

Therefore, the airship’s speed eventually becomes power limited, i.e., the installed power to produce the required thrust to overcome the aircraft’s drag is insufficient, limiting the airspeed that can be attained, as shown in the figure below. The Hindenburg was the fastest airship ever built, reaching about 70 kts. The current Zeppelin NT Goodyear airships cruise up to 60 kts. Notice that greater true airspeeds are possible at higher altitudes, although airships typically fly below 8,000 ft.

Power required for level flight as a function of airspeed for an airship at different density altitudes. Power increases with the cube of the airspeed.

If the airship is a blimp, then free-stream dynamic pressure may reach a point where it begins to exceed the internal gas pressure, causing the envelope to collapse. Blimps are capable of only relatively low maximum airspeeds for this reason, even with some superpressure and the addition of external longerons in the nose region or more propulsive power. Therefore, it is more than drag and power that limits the maximum airspeed of a blimp. Naturally, higher airspeeds can be achieved with rigid (or even semi-rigid) designs because the internal structure maintains the shape of the envelope.

Stability Characteristics

Airships, like all aircraft, are designed to have sufficient static and dynamic stability to be safely flown. In this regard, they tend to naturally return to their trimmed or equilibrium pitch position after a disturbance such as a gust. Both the static and dynamic stability responses of an airship are of interest and, in some ways, are similar but also different from airplanes. If all the forces and moments generated from gust disturbances tend to return the airship to its trimmed condition, then it will be statically stable. For example, for a disturbance that increases pitch angle, i.e., the airship responds nose-up. Static stability means the restoring effects will cause the nose to pitch down after removing the disturbance.

However, static stability does not necessarily mean the airship will immediately settle and reestablish its original trimmed state. It may exhibit a subsequent displacement response in time, i.e., a characteristic called dynamic response. A statically and dynamically stable aircraft is generally easier to fly. However, an aircraft may be statically stable and dynamically unstable but still flyable, especially if, like an airship, the overall dynamic response is slow enough for the pilot to control by employing regular flight control inputs.

There are several considerations regarding the stability characteristics of airships, i.e.,

The c.g. location should be close to the center of buoyancy so a restoring buoyancy moment is produced after pitch disturbance. Airships are stable in pitch roll because the c.g. lies well below the center of buoyancy, i.e., a pendular form of stability such as found on a high-wing airplane. The payload distribution, however, must always be distributed so that the c.g. position is within normal flight limits.
The area of the airship’s tail surfaces (empennage), including the size of the horizontal stabilizer and elevator, play a significant role in the directional (pitch and yaw) stability. If the surfaces are too small, they may not give enough directional stability or control authority. If the surfaces are too big, they add to the empty weight and may cause issues, e.g., a tail-heavy airship may need the addition of non-structural mass in the nose.
The mass distribution along the airship’s length affects the moment of inertia, particularly in pitch and yaw. Larger moments of inertia will increase the time constant of the dynamic stability response but inevitably make the airship more sluggish in response to control inputs. The significant apparent or added mass of airships, which is an unsteady aerodynamic effect, also contributes to their overall inertial characteristics.

Pitch Response

Moments on an airship are usually referred to as its center of volume (also the center of buoyancy), which for a prolate spheroid is at the mid-length and for an actual airship about 45% of the length from the nose. The center of gravity of an airship lies well below the center of buoyancy, as shown in the figure below. Hence, for pitch disturbances, the resulting moments about the center of gravity from buoyancy tend to stabilize.

Airships have good stability in pitch, with a restoring gravity moment about the center of buoyancy.

However, the previous aerodynamic results have shown that at lower angles of attack, say below 8^o, depending on the trim state, the aerodynamic moment is positive, i.e., nose-up, indicating that the center of pressure is in front of the center of buoyancy and the center of gravity. The change in the slope and sign of the moment curves are interesting from a stability and control perspective because the aerodynamic moment destabilizes at low angles of attack. However, this situation is hardly concerning or dangerous because of the dominant gravity moment, and an airship will have good aerodynamic pitch stability if trimmed slightly nose-up.

Critical Airspeed

Airships can experience a form of speed instability as a particular low airspeed, called the critical airspeed, is approached. This issue arises because of the location of the forward center of pressure and the low aerodynamic forces on the hull at low airspeeds and low angles of attack. With the application of an up elevator, for example, the horizontal fins need to produce a downforce to pitch the airship nose-up, as shown in the figure below. However, the net vertical force will force the airship down, not up, if the airspeed is too low, which is why it is called the critical airspeed. While referred to as an instability, strictly speaking, it is a form of control reversal. Normal control effectiveness will be restored only when the airship flies faster than its critical speed. Pilots need to be aware that this effect can occur during landing. Thrust vectoring, used on all modern airships, eliminates this adverse characteristic.

Yaw Response

Because of the dominant axisymmetry, the lateral airloads to changes in yaw angle behave similarly to those for pitch. However, in this axis, there is no gravity moment about the center of buoyancy, so directional stability is weaker than pitch stability. At low yaw angles, the center of pressure is in front of the center of gravity, producing a destabilizing moment but helping to initiate a turn. However, this effect is mild and quickly compensated for by applying the opposite rudder. The restoring moment is positive at slightly higher yaw angles, giving the airship stability.

The yaw stability of an airship is weaker than in pitch or roll.

Roll Response

Airships are very stable in roll because of the high pendular stability, as shown in the figure below. However, unlike airplanes, they perform relatively flat turns like sea ships in a flat attitude with little bank angle. At higher airspeeds and/or with a tighter radius of turn, the centripetal acceleration causes a slight natural bank angle because of the low c.g. location relative to the center of buoyancy.

Dynamic Response

The effects of an airship’s relatively high internal moments can lead to a dynamic response and long settling times, much longer than for conventional airplanes. Airships tend to have a pronounced phugoid response at lower airspeeds, as shown in the figure below. For example, even a casual observation of the Goodyear blimp will show that it has a pronounced porpoising characteristic, the phugoid response when it flies around. The response is for an extended (long) period and is easily controlled by the pilot. At higher airspeeds, the phugoid is well-damped.

Airships tend to have a pronounced phugoid response at lower airspeed. The response is for an extended period and is easily controlled by the pilot. At higher airspeeds, the phugoid is well-damped.

Like static stability, the dynamic response is affected by the position of the center of gravity relative to the center of buoyancy. Perturbations relative to the center of buoyancy also affect the frequency of the airship’s pendular motion.

Tethered Aerostats

Tethered aerostats are large, helium-filled balloons anchored to the ground with strong steel cables or another type of tether. They are designed to remain stationary at a specific location and altitude for extended periods. Tethered aerostats have seen various applications since the early 1900s, including military surveillance, telecommunications, scientific research, and advertising. Equipped with various types of sensors, cameras, and radar systems, these types of aerostats can monitor the movement of people on the ground, such as troops, detect threats or enemy activities, and provide real-time intelligence. Today, tethered aerostats are utilized for a variety of telecommunications purposes, and lifting antennas and repeaters to higher altitudes can enhance wireless communication networks over a wider area. This technology is particularly useful in military theaters or remote or disaster-stricken areas where traditional communication infrastructure may be limited or damaged.

The equations describing the behavior of a tethered aerostat involve the forces acting on the aerostat and the tether (or cable); the free-body diagram is shown below. The drag force depends on the aerostat’s shape, size, and wind speed. The cable exerts a tension force to keep the aerostat anchored to the ground. The buoyancy force must also be sufficient to overcome the weight of the cable; its weight can be calculated based on its length and linear density (mass per unit length). The cable also experiences drag force from the wind flow, which depends on its shape, diameter, and wind speed. Notice that the shape that the cable forms is called a catenary.

Free body diagram for a tethered aerostat with the tether forming the shape of a catenary.

For horizontal equilibrium, then

(61) $\begin{equation*} T_x = D + D_c = T \sin \theta_a \end{equation*}$

and for vertical equilibrium, then

(62) $\begin{equation*} T_y = F_b - W_c - W = F_b - W_c - W_E - W_P = T \cos \theta_a \end{equation*}$

The shape of the cable of reeled-out length $S$ , which then sags under its own weight $m$ per unit length, can be described by the catenary equation. Assuming the cable is anchored at the origin $(x, y) = (0, 0)$ and stretches to point $(R, H)$ at the aerostat, the general mathematical form of the catenary curve is

(63) $\begin{equation*} y = c_2 + \frac{D + D_c}{m} \cosh \left( \frac{m}{D + D_c} x + c_1 \right) \end{equation*}$

where $c_1$ and $c_2$ are constants of integration determined by these boundary conditions. Notice that the symbol cosh denotes the hyperbolic cosine function. To determine $c_1$ and $c_2$ , the boundary conditions are needed, i.e.,

At $x = 0$ , $y = 0$ , so
(64) $\begin{equation*} 0 = c_2 + \frac{D + D_c}{m} \cosh(c_1) \end{equation*}$

and

(65) $\begin{equation*} c_2 = -\frac{D + D_c}{m} \cosh(c_1) \end{equation*}$
The slope of the cable at $x = 0$ is given by
(66) $\begin{equation*} \frac{dy}{dx} = \frac{F_b - m \, S - W}{D + D_c} \end{equation*}$

Taking the derivative of the catenary equation gives

(67) $\begin{equation*} \frac{dy}{dx} = \sinh \left( \frac{m}{D + D_c} x + c_1 \right) \end{equation*}$

At $x = 0$ , then

(68) $\begin{equation*} \frac{dy}{dx} \bigg|_{x=0} = \sinh(c_1) = \frac{F_b - m \, S - W}{D + D_c} \end{equation*}$

Therefore,

(69) $\begin{equation*} c_1 = \sinh^{-1} \left( \frac{F_b - m \, S - W}{D + D_c} \right) \end{equation*}$

where sinh $^{-1}$ is the inverse hyperbolic sine function.

To find the distance $R$ downwind where the aerostat is flying, the slope of the catenary at $x = R$ is used, i.e.,

(70) $\begin{equation*} \frac{dy}{dx} \bigg|_{x = R} = \frac{F_b - W}{D + D_c} \end{equation*}$

giving

(71) $\begin{equation*} R = \frac{D + D_c}{m} \bigg( \sinh^{-1} \left( \frac{F_b - W}{D + D_c} \right) - c_1 \bigg)\end{equation*}$

Substituting for $c_1$ obtained above gives

(72) $\begin{equation*} R = \frac{D + D_c}{m} \bigg( \sinh^{-1} \left( \frac{F_b - W}{D + D_c} \right) - \sinh^{-1} \left( \frac{F_b - m \, S - W}{D + D_c} \right) \bigg) \end{equation*}$

Inserting this value for $R$ into the catenary equation can be used to find the height $H$ of the aerostat above the ground. Then the tether angle at the aerostat, $\theta_a$ , can be determined from the slope of the catenary at $x = R$ , i.e.,

(73) $\begin{equation*} \left. \frac{dy}{dx}\right|_{x = R} = \sinh \left( \frac{R \, m}{D + D_c} \right) \end{equation*}$

where sinh is the hyperbolic sine function. Therefore, the angle at which the cable intersects the aerostat is

(74) $\begin{equation*} \theta_a = \tan^{-1} \left( \sinh \left( \frac{m \, R}{D + D_c} \right) \right) \end{equation*}$

Notice that the slope of the cable at the tether point at $(0, 0)$ is zero. These foregoing equations are simplified if the drag on the cable, $D_c$ , is assumed to be small compared to the drag on the aerostat, which is reasonable for shorter cable lengths and lower wind speeds.

If the cable were assumed to be straight, the problem can be simplified significantly. The straight cable assumption is a simplification often used in preliminary design studies of tethered bodies. In this case, the (constant) angle, $\theta_a$ , with respect to the horizontal, is given by

(75) $\begin{equation*} \frac{dy}{dx} = \tan \theta_a = \frac{F_b - W}{D + D_c} \end{equation*}$

Then the height, $H$ , of the aerostat above the ground for a given cable length, $S$ , is

(76) $\begin{equation*} H = S \, \sin\theta_a \end{equation*}$

where $\theta_a$ is given by

(77) $\begin{equation*} \theta_a = \tan^{-1} \left( \frac{F_b - W}{D + D_c} \right) \end{equation*}$

Recall that this result assumes a straight cable and does not account for the canenary sag caused by the cable’s weight.

From a design perspective, it may be necessary to find the payload weight, $W_P$ , that can be carried by the aerostat at a given altitude, the operating altitude, $H$ , for a given payload, or the angle of the tether to the aerostat, $\theta_a$ , for different wind speeds, $V_{\infty}$ . The drag on the aerostat itself is given by

(78) $\begin{equation*} D = \frac{1}{2} \, \varrho_{\infty} \, V_{\infty}^2 \, {\cal{V}}^{2/3} \, C_{D_{a}} \end{equation*}$

where the drag coefficient, $C_{D_{a}}$ , for the aerostat can be estimated based on the Hoerner formula for a prolate spheroid in Eq. 39. The drag on the cable, $D_c$ , can be estimated using the Reynolds number based on the diameter and the component of the wind speed perpendicular to the cable, i.e.,

(79) $\begin{equation*} D_c = \frac{1}{2} \, \varrho_{\infty} \, V_{\infty}^2 \, A^2 \, C_{D_{c}} \cos\theta(S) \end{equation*}$

where the drag coefficient would be determined for a circular cylinder at the appropriate Reynolds number. The cable weight, which can be significant if the aerostat is at several thousand feet of altitude, can be found using the weight per unit length, $m$ , so that

(80) $\begin{equation*} W_c = m \, S \end{equation*}$

where $S$ is the length of the cable. The buoyancy force is found using

(81) $\begin{equation*} F_b = \left( \varrho_{\rm air} - \varrho_{\rm He} \right) g \, {\cal{V}} \end{equation*}$

where ${\cal{V}}$ is the volume of the gas envelope, $\varrho_{\rm air}$ is the density of the surrounding air, and $\varrho_{\rm He}$ is the density of helium.

Check Your Understanding #6 – Forces on a Tethered Aerostat

A tethered aerostat filled with helium gas is in vertical and horizontal equilibrium at the end of a 4,000 ft long cable under tension, as shown in the figure below. Assume the cable is straight and does not form a catenary. The aerostat has a volume of 200,000 ft ${^{3}}$ , and its maximum diameter is 38 ft. It has a drag coefficient of 1.2 based on the projected frontal area. The net weight of the aerostat is 4,200 lb. The cable weighs 0.25 lb per ft. The wind speed is 25 kts at all heights and has a density of 0.0022 slugs ft ${^{-3}}$ . Assume that the density of helium is $3.19\times 10^{-4}$ slug ft ${^{-3}}$ . Ignore the aerodynamic drag on the cable. Determine the equilibrium value of the angle $\theta$ .

Show solution/hide solution.

Vertical force equilibrium gives

$F_b = W_a + W_c + T \cos \theta$

$T \cos \theta = F_b - W_a - W_c$

where $F_b$ is the net buoyancy force, $W_a$ is the weight of the aerostat, and $W_c$ is the weight of the cable.

Horizontal force equilibrium gives

$T \sin \theta = D$

The net buoyancy force, $F_b$ , is given by

$F_b = \varrho_{\rm air} {\cal{V}} g - \varrho_{\rm He} {\cal{V}} g = \left( \varrho_{\rm air} - \varrho_{\rm He} \right) {\cal{V}} g$

The aerodynamic drag, $D$ , on the aerostat is given by

$D = \frac{1}{2} \varrho_{\rm air} \, V_{\infty}^2 \, A_{\rm ref} \, C_D$

Dividing the force equilibrium equations gives

$\frac{T \sin \theta}{T \cos \theta} = \frac{ D}{F_b - W_a - W_c} = \tan \theta$

so that

$\tan \theta = \frac{\displaystyle{\frac{1}{2} \varrho_{\rm air} V_{\infty}^2 A_{\rm ref} \, C_D}}{\left( \varrho_{\rm air} - \varrho_{\rm He} \right) {\cal{V}} \, g - W_a - W_c}$

Inserting the numerical values gives

$\tan \theta = \frac{\displaystyle{\frac{1}{2} \times 0.0022 \times (25.0 \times 1.688)^2 \times \left( \frac{\pi \, 38.0^2}{4} \right) \times 1.2}}{\left( 0.0022 - 0.000319 \right) \times 200,000 \times 32.17 - 4,200 - 4,000 \times 0.25}$

so that

$\tan \theta = \frac{1,493.65}{6.899.87} = 0.2165$

Therefore, the angle is given by

$\theta = \tan^{-1} \left( 0.2165 \right) = 12.3~\mbox{deg.}$

Airships of the Future?

Airships occupy a unique niche in the annals of aviation, boasting a rich history intertwined with innovation and adventure. Several companies, including Lockheed Martin, Hybrid Air Vehicles, Aeroscraft, and LTH, have been actively involved in airship development. Looking ahead, their future applications offer intriguing possibilities. Some of their potential future applications may include:

Cargo transport in remote areas lacking infrastructure or where environmental concerns limit ground transportation. Their potential to carry heavy loads over long distances with minimal infrastructure requirements makes airships appealing for specific logistical challenges.
Airship travel is a unique and leisurely mode of travel, providing passengers with breathtaking views and a sense of nostalgia. Luxury airship travel could attract travelers seeking a distinctive experience akin to luxury cruises on the oceans but in the skies.
They are stable platforms for aerial observation, surveillance, and monitoring activities such as environmental research, border patrol, and disaster response. Their slow speed and ability to hover make them well-suited for tasks requiring long-duration observation.
Airships could serve as floating communication platforms, hosting antennas for cellular networks, internet connectivity, and broadcasting services. They could be deployed to remote areas or events where establishing traditional infrastructure is impractical.
Large, eye-catching airships can fly billboards, attract attention, and promote brands or events. They offer a unique and memorable way to reach audiences, particularly in crowded urban areas or outdoor events.
Ongoing advancements in materials, propulsion, and control systems could lead to more efficient and capable airships. Research institutions and aerospace companies may continue to explore airship technologies for scientific research, experimentation, and potential breakthroughs.
Airships could deliver humanitarian aid and disaster relief to areas affected by natural disasters or conflicts. Their ability to access remote or inaccessible regions could facilitate the distribution of essential supplies and support rescue operations.
Airships have the potential to be more environmentally friendly than traditional aircraft, as they consume less fuel and produce fewer emissions per payload unit payload weight. This aspect could become increasingly important as climate change and sustainability concerns drive the demand for greener transportation solutions.

Despite these potential applications, challenges such as limited speed, susceptibility to weather conditions, high initial costs, and lack of hangarage and maintenance facilities have thus far hindered the widespread adoption of airships. However, ongoing technological advancements and evolving market demands may lead to renewed interest and investment in airship development, shaping their future role in the aviation spectrum.

Summary & Closure

Airships, also known as dirigibles, blimps, or Lighter-Than-Air (LTA) vehicles, utilize the aerostatic principle of buoyancy to stay aloft. The tenets of aerostatic lift, buoyancy, and ballast have been described along with their aerodynamic characteristics in forward flight. With advancements in technology and design, airships are being reintroduced as another mode of transportation that can combine efficiency, versatility, and environmental friendliness. New designs incorporating hybrid-electric or hydrogen propulsion systems offer more significant potential for clean and sustainable aviation. Airships consume significantly less fuel than airplanes and ships per unit cargo weight per unit distance, reducing carbon emissions. This benefit makes airships attractive for long-haul cargo transportation, much like container ships travel the oceans. The reintroduction of airships could also provide a unique and memorable way for passengers to experience recreational travel.

Recent materials, propulsion systems, and aerodynamic advancements have improved modern airships’ safety, efficiency, and maneuverability. Continued technological innovation will drive the development of more advanced airship designs, making them safer, more reliable, and economically viable. To this end, several companies and organizations have been developing and improving modern airship technology to expand their potential applications and make them a more viable transportation option. While modern airships will never replace traditional aircraft, they offer unique capabilities that suit them for specific transportation, surveillance, and perhaps tourism roles.

5-Question Self-Assessment Quickquiz

For Further Thought or Discussion

What fundamental aero-hydrostatic principle allows blimps, balloons, and airships to float in the air?
What are the main differences between blimps, balloons, and airships in terms of their structure and functionality?
How have blimps, balloons, and airships been used historically, and what are some of their modern applications?
What are the advantages of using airships for cargo transportation compared to other modes of transport?
What are the safety considerations associated with operating blimps and airships?
How have advancements in technology and materials improved the design and performance of modern airships?
What are some notable examples of airships used for scientific research or exploration?
What are the environmental benefits of using airships for transportation compared to airplanes or ships?
Can you explain the concept of hybrid airships and their potential advantages over traditional airship designs?
How do blimps and airships navigate and maneuver in the air? What controls are used?
What are some challenges or limitations that currently prevent the widespread adoption of airships in specific industries?
How could new airships contribute to tourism, and what unique experiences could they offer passengers?
Discuss any recent innovations or advancements in airship technology or design.

Other Useful Online Resources

For additional resources on balloons, airships, and blimps, follow up on some of these online resources:

Aerospaceweb: Balloons and Airships – A comprehensive resource providing information on the history, types, design, and applications of balloons and airships.
Video: “How Airships Could Overcome a Century of Failure.”
“How a Zeppelin Works.” A great video.
This old film tells the story of the Goodyear Aircraft Corporation and their manufacturing of blimps and aircraft.
“Helium, The Wonder Gas.” View the video here.
“Airships, Dirigibles & Zeppelins: Graf Zeppelin, R-100, U.S.S. Akron, Hindenburg & more!” View the video here.
“Dirigibles, Airships, & Zeppelins: Lighter-Than-Air Travel.” View the video here.
A video about the R.100’s transatlantic voyage to Canada in July 1930.
The U.S. Navy’s most successful rigid airship was the U.S.S. Los Angeles (ZR-3). View the video here.
“What It Takes To Fly The $21 Million Goodyear Blimp.” View the video here.
“The Good Years: A Blimpumentary.”
“Final Flight of Goodyear Blimp N10A Spirit of America.” View the video here.
Airships.net – A website dedicated to the history and development of airships, offering articles, photos, and detailed information about famous airships throughout history.
The Great Balloon Race – An interactive educational game that teaches the principles of buoyancy and the science behind hot air balloons.
Goodyear Blimp – The Official website of Goodyear’s famous blimps provides information about their fleet, history, and operations.
Zeppelin Museum Friedrichshafen – The official website of the Zeppelin Museum in Friedrichshafen, Germany, offers a wealth of information about the history, technology, and cultural impact of airships.
“Could Passenger Blimps Be Making a Comeback?” View the video here.
“Goodyear Airship Hangar Tour – Wingfoot Lake.” View the video here.
Airships – How a design that resembles the past could change how we fly in the future. CNN video.

The Hindenberg used hydrogen as the buoyant gas, which is extremely flammable. ↵
The hull shape would be a non-lifting prolate spheroid. ↵
Aviation emissions account for about 2.5% of global emissions but drive about 7.2% of global warming. See: Lee D., et al., "The Contribution of Global Aviation to Anthropogenic Climate Forcing for 2000 to 2018," Atmospheric Environment 244, 117834, 2020. https://doi.org/10.1016/j.atmosenv.2020.117834. ↵
The U.S., which was back then, and still is, the source of much of the world's helium, would not sell helium to Germany under the U.S. Helium Act of 1925 because it was considered a strategic asset. ↵
As of 2024 information, the price of helium gas is about $100 per cubic meter. ↵

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Introduction to Aerospace Flight Vehicles Copyright © 2022–2024 by J. Gordon Leishman is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, except where otherwise noted.