Airships, Blimps, & Aerostats

J. Gordon Leishman

67 Airships, Blimps, & Aerostats

Introduction

Airships, balloons, and blimps generate buoyant lift, also known as buoyancy or aerostatic lift, by using a large envelope filled with a gas less dense than air, such as helium. This feature lets them fly and “float” without requiring forward airspeed. These aircraft are collectively referred to as airships or aerostats. Today, they are more commonly called Lighter-Than-Air (LTA) aircraft, as shown in Figure 1. Furthermore, because an LTA aircraft does not require a large runway, although it still requires a relatively large terrestrial footprint for takeoff and landing, it can also be classified as a vertical/short take-off and landing (V/STOL) aircraft. Technically, any unpowered, free-floating LTA aircraft is considered a balloon, while a powered, steerable one is called an airship.

Lighter-than-air (LTA) aircraft come in many types. Unpowered LTA aircraft are classified as balloons, whereas powered, steerable LTA aircraft are referred to as airships.

Historically, people have seen airships as lumbering giants of the sky with a poor safety record. However, these claims are unjustified; airships and aerostats have been used successfully for over a century in various applications, including military surveillance, anti-submarine warfare, passenger and cargo transport, border patrol, and advertising. The most famous examples are the giant Zeppelin airships and the Goodyear blimps. During the 1920s and 1930s, several Zeppelin airships transported passengers across oceans and around the world in luxury, a feat that no airplanes of the era could match. However, airships acquired 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, following a successful transatlantic flight.

Modern airships are giant aircraft by any standard, dwarfing the Airbus A380 and Boeing 747. The Hindenburg itself was nearly three times as long as a Boeing 747 and more than twice as tall. Modern airship designs envision substantial payloads of up to 100,000 kg (220,000 lb) over thousands of miles, albeit at relatively low airspeeds, while producing low-carbon emissions. Several companies, including Lockheed Martin, Hybrid Air Vehicles, Aeroscraft, and LTA Research, have been involved in modern airship research and development. In particular, hybrid airships have garnered considerable attention in recent years, as exemplified by Figure 2. This variation features a cambered tri-hull shape, with disk-shaped cushions on the underside serving as the undercarriage. Hybrids generate both aerostatic (buoyancy) lift and aerodynamic (motion) lift, offering several advantages over traditional airships,^[2] regarding payload capability, field performance, and cruise speed.

The Lockheed Martin P-791 is an experimental hybrid airship that generates both aerostatic and aerodynamic lift. (Credit: *Lockheed-Martin*.)

Another example of the renewed interest in large, rigid airships is Pathfinder 1, developed by LTA Research, as shown in Figure 3. This LTA aircraft is a modern buoyant airship that relies primarily on aerostatic lift rather than significant aerodynamic lift. At approximately 124 m (407 ft) long, it shows how contemporary materials, flight-control systems, and manufacturing methods can be applied to classical buoyancy-based designs, yielding significant performance improvements and enabling new applications. Pathfinder 1 occupies a different point in the design space than hybrid airships and currently serves primarily as a technology demonstrator.

Designers are using modern materials, manufacturing methods, and control systems to revisit the concept of large buoyant airships. (Credit: *LTA Research*.)

Modern airships may also incorporate advanced propulsion systems, such as hybrid-electric, hydrogen-fuel-cell, or solar-powered technologies. These propulsion approaches offer high 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 even servicing commercial distribution centers. While airships fly relatively slowly compared to airplanes, their cruise speeds remain much faster than ships and comparable to terrestrial vehicles such as trucks and trains. They also have the operational advantage of point-to-point flight over land or sea, with sufficient speed and altitude capability to avoid most adverse weather.

However, the 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, the broader availability of hangarage and maintenance facilities, and the ability to operate in a wide range of weather conditions. While the future of airships shows considerable technical promise, it remains to be seen whether, or how, such aircraft can mature into a meaningful and economically viable part of the future commercial aviation landscape.

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 an airship’s stability, handling qualities, and unique flight characteristics.

History

The first LTA aircraft was a hot-air balloon, also significant in aviation history as the first human-carrying flight vehicle capable of sustained flight. It was designed in France by the Montgolfier brothers in 1783. As shown in Figure 4, their paper-and-silk balloon rose to about 2,000 m (6,560 ft) without a pilot. A few weeks later, they launched a larger balloon, the Aerostat Reveillon, 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 making the first free flight in a balloon, which rose to about 150 m (492 ft) and drifted about 8 km (5.5 miles) before landing safely.

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

Benjamin Franklin, then serving as a U.S. diplomat in 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 soldiers a great vantage point, and they used signal flags to relay information to their commanders.

For the next 150 years, hot-air balloons attracted little interest and were overshadowed by airships and other aircraft. However, in the 1960s, hot-air ballooning became a popular recreational activity and a competitive sport. In 1987, Richard Branson and Per Lindstrand made the first transatlantic crossing by hot-air balloon, flying about 2,900 miles (4,670 km) in 33 hours. Branson and Lindstrand paired up again in 1991 and made the first transpacific crossing by hot-air balloon, traveling about 6,700 miles (10,800 km) in 47 hours from Japan to Canada and breaking the world distance record by riding the high-altitude jet stream. Four years later, Steve Fossett became the first solo pilot to complete the Transpacific balloon route, riding the winds and the jet stream for four days from South Korea to Canada.

The need for balloons that could be propelled led to the development of airships, also known historically as dirigibles, meaning powered, steerable lighter-than-air aircraft. Henri Giffard built and flew the first dirigible in 1852, propelling it with a steam engine driving a propeller. Today, an airship is typically defined as any powered, steerable aircraft that is inflated with a lighter-than-air gas. Early airships were filled with hydrogen, a highly reactive gas that is prone to explosive combustion under certain conditions. Several airships had caught fire even before the infamous Hindenburg disaster in 1937. Using inert helium rather than hydrogen as the buoyant gas would likely have prevented the Hindenburg from catching fire.^[4]

The LZ127 Graf Zeppelin, shown in Figure 5, was a German airship filled with hydrogen as its buoyant gas and 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 achievement marked a milestone in airship travel and aviation history. It demonstrated the feasibility of long-distance passenger flights by airship and offered greater comfort than contemporary airplanes. In 1928, travelers could still travel faster by train than by airplane; for example, the Ford Trimotor was so noisy that passengers had to stuff cotton wool in their ears to save their hearing.

One of the most famous airships, the “Graf Zeppelin,” photographed landing in Berlin, Germany, circa 1931.

The British, as did the U.S., soon developed airships influenced by German rigid-airship practice. The R100 and its sister ship, R101, were developed under the British Imperial Airship Scheme of the 1920s to establish airship routes for passengers and mail between Britain and distant parts of the British Empire, including India, Australia, and Canada. Both airships first flew in 1929. The R100, which used hydrogen as the buoyant gas, made a well-publicized return crossing of the Atlantic to Canada in the summer of 1930. But following the R101’s demise, 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 Figure 6, 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 USS Macon. Airships made in the United States used helium as the buoyant gas.

A blimp, essentially a “pressure airship,” maintains its shape through the gas pressure inside the envelope. Unlike a rigid airship, which has a structural skeleton, a blimp loses its shape when internal pressure drops. The B-class blimps, as shown in Figure 7, were patrol airships operated by the U.S. Navy during and shortly after WWI, and they were used with much success for convoy and anti-submarine patrol duties. The B-class blimps operated effectively over coastal waters, providing a vital service by detecting and deterring submarine threats during a critical period in naval warfare.

The U.S. Navy operated the B-1 airship during WWI. The B-1 had dual lower fins, while later B-types had only one.

In 1925, Goodyear Tire & Rubber Company began building blimps. These aircraft were initially used for advertising but later proved valuable for numerous military applications during WWII. Goodyear’s blimps proved a valuable asset to the Navy because they could stay airborne for extended periods while consuming minimal fuel. Newer blimps have minimal internal structure, consisting of lightweight composite materials such as carbon fiber, and are classified 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 offers advantages in stability, cost-effectiveness, and extended observation capabilities. Their wartime use dates back two centuries, during which they served as platforms for gathering intelligence, observing enemy activities, and directing artillery fire. A form of aerostat, the barrage balloon, proved an effective defensive measure for the British during World Wars I and II; see Figure 8. They disrupted enemy flights, forced aircraft to fly higher, and provided early warning by visually alerting ground forces to incoming aircraft. Aerostats, in the form of blimps, are still used today by the Tethered Aerostat Radar System (TARS) to monitor the southern U.S. border; each aerostat is moored to the ground with a cable, and its altitude can be raised and lowered using a winch.

Barrage balloons at Omaha Beach in France during the early days of the Allied “D-Day” invasion of Europe in June 1944.

Anatomy of LTA Aircraft

LTA aircraft include balloons, airships, and other aerostats. As aeronautical technology evolved, the term “balloon” came to refer to hot-air balloons, which are recreational aircraft. While the term “aerostat” still encompasses most types of LTA aircraft, it usually refers to an unpiloted LTA aircraft tethered to the ground by a cable. The term “airship” is reserved for a piloted lighter-than-air (LTA) vehicle with a propulsion system that enables it to fly from one location to another while carrying a payload or performing a useful task.

Balloons (Thermal Aerostats)

A balloon, or thermal aerostat, is the simplest unpowered aerostat. Because balloons have limited control and drift with the wind, they generally fly best in light winds and good weather. Notable uses of balloons in modern aviation include weather balloons for meteorology (typically filled with helium) and recreational “hot-air” balloons, as shown in Figure 9.

Balloon-type aerostats are often associated with the colorful hot-air balloons used for recreation.

Hot-air balloons use a propane burner to heat the air inside the envelope. As the air warms, it becomes less dense than the surrounding cooler air, causing the balloon envelope to inflate and generate buoyancy. Because hot and cold air have little density difference, the envelope must be voluminous to lift even a couple of people. Hot-air balloons normally control altitude by heating the air with the burner or by venting hot air from the envelope. The pilot can open a parachute valve by pulling a cord, thereby allowing some hot air to escape and increasing the rate of descent. Ballast is more common in gas balloons, where sand or water ballast may be released to reduce weight. Those who have flown in hot air balloons generally report a serene, picturesque experience, with the uncertainty of the landing point adding to the excitement of this type of aerial adventure.

Stratospheric Balloons

Balloons are also designed to fly in the upper stratosphere and at the edge of space, as shown in Figure 10. They typically fall into two main types: zero-pressure and super-pressure balloons. Both types use helium gas for buoyancy. Stratospheric balloons are especially useful in this region of the atmosphere, which ranges from about 50,000 ft to 150,000 ft (approximately 15 km to 45 km) above sea level. This region is far below satellite orbital altitudes but above the normal operating ceiling of most aircraft, although specialized high-altitude aircraft can operate in the lower part of this range. The payload gondolas can carry experiments in science, astronomy, atmospheric chemistry, and weather. At the end of the mission, the payload is severed from the balloon and recovered by parachute.

Zero-pressure stratospheric balloons have release valves that let the pressure inside the balloon equalize with ambient pressure. These balloons will continue to rise until they reach a buoyancy altitude or burst; they are typically used for short-duration flights, although long-duration zero-pressure balloon flights are possible under favorable polar-summer conditions. Super-pressure balloons are fully sealed and maintain higher internal pressure, allowing them to remain at operational altitude for much longer despite diurnal temperature fluctuations. Super-pressure balloons are launched partially filled with helium. As the balloon ascends and ambient air pressure decreases, the helium expands to fill the envelope, allowing it to reach 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 classified as rigid, semi-rigid, or non-rigid; the latter are often called blimps or pressure airships. Semi-rigid airships form a separate class because an internal keel or framework carries concentrated loads. The classic rigid airship, a dirigible, features an internal space-frame structure that surrounds its gas containers (called gasbags), as illustrated in Figure 11.

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

Early-twentieth-century Zeppelins, including those operated during the 1920s and 1930s and into the early WWII period, are well-known examples of dirigibles that used hydrogen as the buoyant gas; the major U.S. Navy rigid airships used helium. The main structure is typically aluminum, but modern dirigibles increasingly use composites. The internal structure provides the airship’s shape and rigidity, while the outer covering, or envelope, remains unpressurized. The covering must be a strong, durable fabric, but it need not be gas-tight, as the buoyant gas inside a dirigible is contained in a series of separate gas bags.

The gondola, or car, is the compartment suspended beneath the envelope that houses passengers, crew, and other equipment. The integral internal structure connects the gondola, empennage, engines, and gas cells, carrying and distributing loads throughout the structure. The engines may be located on the gondola, but because of a dirigible’s expansive, rigid internal structure, multiple hard points allow the engines to be placed almost anywhere. The vertical stabilizer (fin) helps maintain the aircraft’s directional stability, and the horizontal stabilizer provides pitch stability. Airships use various control surfaces to maneuver, including rudders and elevators, which control yaw and pitch, respectively.

Blimps

A non-rigid airship, also known as a blimp, maintains its shape because the pressure of the buoyant gas inside it does. Blimps may have some external bracing or reinforcement to support the weight of the gondola and engines. However, in the classic blimp, a catenary curtain (like a hanging chain) suspends the gondola from the top of the envelope, with attached cables; these cables are internal to the gas envelope, as shown in Figure 12. Buoyancy is controlled using air-filled ballonet chambers, which adjust the volume of buoyant gas and can shift the effective center of aerostatic lift for control and trim; a ballonet is the gaseous equivalent of the water ballast tanks used on submarines. The iconic Goodyear GZ20A blimps were used until 2017. The current Goodyear airships retain the public name “blimp.” Still, they are Zeppelin NT semi-rigid airships with an internal structural framework, and they are widely used in the U.S., particularly at major sporting events such as the Super Bowl and the Daytona 500.

Semi-Rigid Airships

The modern version of the Goodyear blimp, shown in Figure 13, is a semi-rigid blimp (Zeppelin NT) and lacks the suspension cables supporting the gondola. This airship uses helium as its lifting gas, a modern successor to the classic Zeppelin dirigibles of the 1930s. Semi-rigid airships have a basic internal structure that supports the gas envelope and other components, such as gondolas, engines, and tail surfaces. However, unlike a true blimp, a semi-rigid airship has an internal keel or framework that carries major loads, while envelope pressure still helps maintain the aerodynamic shape. As a result, semi-rigid airships occupy a structural class between non-rigid blimps and fully rigid airships. The engines drive propellers or ducted fans to provide the thrust needed to propel the airship forward or backward, and thrust vectoring can significantly improve maneuverability. Modern airships use water ballast rather than lead shot; however, semi-rigid airships (Goodyear still calls them blimps) share features with dirigibles.

Anatomy of a semi-rigid airship. The photograph is of a Zeppelin NT, a modern helium-filled semi-rigid airship.

Tethered Aerostats

A tethered aerostat is anchored to the ground by a cable; in Figure 14, it is tethered to its mooring point. Letting out the cable allows the aerostat to rise and be tethered at various altitudes. The ballonets(s) control buoyancy. Such aerostats have been used for persistent aerial surveillance over designated areas. Equipped with multiple sensors, cameras, and radar systems, aerostats can monitor troop movements, detect threats, and provide real-time intelligence. Tethered aerostats also support telecommunications. Lifting communication equipment, such as antennas and repeaters, to higher altitudes can extend wireless network coverage over wider areas. This technology is particularly useful in remote areas where traditional communication infrastructure is limited or damaged. A typical system consists of a tethered aerostat that can provide radar surveillance and high-resolution imagery over a large area from an altitude of only a few thousand feet.

Anatomy of a tethered aerostat. While relatively simple, they can carry a variety of sophisticated radar, camera, and sensor systems.

Hybrid Airships

Hybrid airships combine features of airplanes and airships. As shown in Figure 15, these innovative vehicles rely on buoyancy to carry a fraction of their weight, with the remainder supported by aerodynamic lift generated by their airframes. Their aerodynamic lift may account for as much as 30% of their weight.

Hybrid airships are designed to bridge the gap between the low operating costs and low airspeeds of traditional airships and the higher speeds but higher fuel consumption of airplanes. By combining dynamic and buoyant lift, hybrids can cruise at higher airspeeds and carry a greater payload than a pure airship. Because of their large size, they have significantly higher payload capacity than other aircraft types. This makes them suitable for a range of applications, including cargo transportation, disaster relief, and remote access. However, they require ample hangar space for maintenance and storage, which also affects 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” came from a humorous conversation among several musicians about the new band’s chances of flopping, i.e., going down like a lead balloon. Their lead guitarist, Jimmy Page, then proposed the name “Led Zeppelin,” and the rest is history.

Buoyant (Lifting) Gases

A buoyant gas, or lifting gas, is any gas that produces buoyancy or aerostatic lift; it must be less dense than the surrounding air. Well-known buoyant gases include hydrogen, helium, and 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. As a buoyant gas, hot air is typically used only in recreational balloons.

Hydrogen

Hydrogen (H₂) is the lightest and most buoyant lifting gas, with a molar mass of 2.016 g mol^-1. It has 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 to fires and explosions, and hydrogen use declined significantly after the Hindenburg disaster in 1937.

Current FAA certification guidance (FAA AC 21.17-1A states: “Hydrogen is not an acceptable lifting gas for use in airships.”) does not accept hydrogen as a lifting gas for airships because of its flammability risk, especially for passenger-carrying operations. However, future certification practices may change if stringent safety measures are implemented, including acceptable containment, ventilation, ignition prevention, and crashworthiness measures, particularly if hydrogen is also used as an aircraft fuel.

Helium

Helium (He) is the second-lightest element, with a molar mass of 4.003 g mol^-1. 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 relatively rare and expensive, especially at the volumes required for an airship. Helium is a commodity, and its price varies daily. But as a point of reference, 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 a molar mass of 17.02 g mol^-1, it is considerably heavier than hydrogen or helium. It has a reasonable lifting capacity, but it is a pungent, choking, toxic, and corrosive gas. However, ammonia is less flammable than hydrogen. Some early airships used it before hydrogen and helium were available in sufficient quantities. Because ammonia is highly toxic, its release into the atmosphere poses numerous environmental hazards; consequently, its use for LTA aircraft has been permanently discontinued.

Hot Air

Propane burners heat ambient air to produce hot air. Air has a molar mass of approximately 29 g mol^-1. Hot air is less dense than the surrounding air, creating buoyancy. It does not pose the safety concerns associated with hydrogen. However, hot air has much lower buoyancy than gases such as hydrogen or helium, so it requires a greater volume to achieve the same buoyancy. Hot-air balloons require near-constant heating to maintain buoyancy because they lose heat rapidly 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), which is numerically equivalent to kilograms per cubic meter (kg/m³). Unless otherwise noted, the values are for standard temperature and pressure (STP).

Property

Hydrogen

Helium

Ammonia

Hot Air

Air (reference)

Chemical composition

H₂

He

NH₃

N₂ + O₂ + mixture of other gases

Density

0.08988 g/L (STP)

0.1786 g/L (STP)

0.769 g/L (STP)

1.164 g/L (30°C, 1 atm); varies with temperature

1.225 g/L (ISA MSL, 15°C); varies with temperature

Color

Colorless

Odor

Odorless

Pungent

Odorless

Flammability

High

None

Low

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 also occurs in underground gas deposits, where it migrates upward to the top of the gas pocket because it is so light. Operators can then separate and collect the accumulated helium for use. The U.S. remains one of the world’s major helium producers, extracting it from helium-bearing natural gas resources. Historically, the Federal Helium System near Amarillo, Texas, played a central role in U.S. helium storage and distribution, but it was transferred from federal to private ownership in 2024. However, helium is a finite resource, and its annual and long-term availability is unpredictable. Consequently, recent efforts have promoted helium conservation and responsible use. Ironically, modern airships may revert to hydrogen if helium becomes scarce or prohibitively expensive.

Why Not a Vacuum Airship?

Theoretically, a vacuum airship could provide the highest possible buoyancy because a perfect vacuum is lighter than any gas. However, the structural integrity required for such an airship presents a fundamental challenge. At sea level, atmospheric pressure is 101.3 kPa (14.7 psi), so any envelope containing a vacuum must withstand significant external pressure. Most lightweight materials would collapse or implode under this pressure unless they were extremely strong and rigid, which would add significant structural weight. Even advanced materials such as carbon fiber composites are currently too heavy for their strength to make such a structure viable. To achieve lift, the envelope must be both strong enough to resist collapse and light enough to weigh less than the air it displaces.

In addition, a vacuum’s lift advantage over helium is relatively small. At ISA sea-level conditions, a perfect vacuum would provide a theoretical gross lift of about 1.225 kg per cubic meter. In comparison, helium would provide a net lift of about $1.225 - 0.1786 = 1.046$ kg per cubic meter. Therefore, helium provides about 85% of the theoretical lift of a vacuum. This marginal gain does not justify the engineering challenges of building a vacuum airship. Helium- and hydrogen-filled airships, which are far easier to build and maintain, already achieve near-optimal buoyancy without the structural challenges posed by vacuum containment.

Principle of Buoyancy

Archimedes’ principle is used to analyze the aerostatic forces on LTA aircraft. This principle states that the upward buoyant force exerted on a body immersed in a fluid equals the weight of the fluid it displaces. This behavior holds whether the body is wholly or partially submerged in the fluid and is independent of its shape. As shown in Figure 16, the resulting force acts upward at the center of buoyancy of the displaced fluid (which is 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 buoyant force, on a body immersed in a fluid equals the weight of the fluid it displaces.

To better illustrate the concept of buoyancy, consider the scenarios shown in Figure 17. The object’s volume is the same in each case, but its weight varies from $W_1$ (heaviest) to $W_3$ (lightest). If the object is entirely immersed in the fluid, then the 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 object’s volume (and thus the volume of the displaced fluid), and $\varrho_{\tiny \rm fl}$ is the density of the displaced fluid. The buoyant force depends only on the weight of the fluid the object displaces, not on the object’s weight. 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 buoyant force on an immersed object depends on the weight of the fluid it displaces, not on the object’s weight; buoyant equilibrium depends on both the object’s weight and the buoyant force.

Now consider a hot-air balloon floating in the atmosphere, as shown in Figure 18. The balloon’s envelope contains hot (i.e., warmer) air, so it has a lower density than the surrounding cooler air. According to Archimedes’ principle, the balloon’s buoyant force equals the weight of the displaced colder air. The balloon’s net weight will include the weight of its envelope and structure (including any items hanging from the basket below) plus the weight of the hot air. Therefore, the net force on the balloon equals the difference between its 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) $\begin{equation*} F_b = L = \varrho_{\rm air} \, g \, {\cal{V}} \end{equation*}$

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,

(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 inside) and displaces a volume of 7,000 m³. Assume that the pressure inside the balloon equals the pressure outside. Determine the air temperature inside the balloon for neutral buoyancy. At 1,100 m, the air density is approximately 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

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

which equals the upward buoyant 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

$\frac{T_{\rm hot}}{T_{\rm cool}} = \frac{\varrho_{\rm cool}}{\varrho_{\rm hot}} = \frac{1.102}{1.031} = 1.069$

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}$C}$

Therefore, a temperature differential of approximately 20 $^{\circ}$ C is observed at these altitudes and under these conditions.

Geometric Characteristics of Aerostats

Traditionally, airships and many aerostats have streamlined hull shapes based on prolate spheroids, i.e., elongated bodies of revolution resembling fat cigars; spheres are a limiting special case of ellipsoids. An ellipsoid, shown in Figure 19, is the most general shape in this geometric class of bodies of revolution, including, in special cases, prolate and oblate spheroids and spheres.

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

For aerodynamics and other characteristics, 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 gives 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 prolate spheroid is

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

where the eccentricity, ${e}$ , of a prolate spheroid is

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

In the limit as $e \rightarrow 0$ , the prolate spheroid becomes a sphere. Using the expansion

$\sin^{-1} e = e + \frac{e^3}{6} + \frac{3e^5}{40} + \cdots$

then

$\frac{\sin^{-1} e}{e} = 1 + \frac{e^2}{6} + \frac{3e^4}{40} + \cdots$

so Eq. 12 reduces smoothly to

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

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

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

where ${\alpha}$ = 8/5.

Slenderness Ratio

The aerodynamic characteristics of airships are often expressed in terms of the slenderness ratio, as shown in Figure 20. The slenderness ratio, $\lambda$ , for a prolate spheroid is defined as

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

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 in Figure 21. 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 between 4 and 6.

Center of Buoyancy

To understand the flight characteristics of LTA aircraft, it is essential to determine the aerostatic buoyancy force and the center of buoyancy, i.e., the point through which the resulting buoyancy force is assumed to act. The center of buoyancy, or the center of the gross aerostatic lift, is the center of volume and the center of gravity of the displaced air. Therefore, the center of buoyancy is determined from the volume displaced by the external envelope shape. For a fully inflated simple envelope, this point is usually close to the center of volume of the buoyant gas. Still, the two points need not be identical when ballonets, separate gas cells, or nonuniform internal volumes are present.

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 Figure 22, the total area can be determined using

(17) $\begin{equation*} A = \int_A dA \end{equation*}$

Method of calculating the center of area, or center of buoyancy, on a two-dimensional surface.

The first moments of area about the coordinate axes are given by

(18) $\begin{equation*} M_x = \int_A y \, dA \quad \text{and} \quad M_y = \int_A x \, dA \end{equation*}$

where $M_x$ is the first moment of area about the $x$ -axis, and $M_y$ is the first moment of area about the $y$ -axis. The location of the center of area, ${(\overline{x}, \overline{y})}$ , is then determined using

(19) $\begin{equation*} \overline{x} = \frac{M_y}{A} = \frac{1}{A} \int_A x \, dA \end{equation*}$

and

(20) $\begin{equation*} \overline{y} = \frac{M_x}{A} = \frac{1}{A} \int_A y \, dA \end{equation*}$

Naturally, the process extends to three dimensions with 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 area integrals in the equations above are replaced by volume integrals or by numerical summations based on the actual shape. Most CAD software allows for the 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 Figure 24, i.e., the upthrust from buoyancy equals the weight, as given by

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

The center of gravity for an airship is generally well below the center of buoyancy, giving the aircraft significant pendular stability about the pitch and roll axes. In aerostatic trim, or in static equilibrium, most airships are not perfectly level but tend to assume a slightly nose-high attitude. Airships have very little inherent stability about the yaw axis, although aerodynamic forces on the fuselage and vertical tail(s) heavily damp yaw disturbances.

In aerostatic trim, without thrust vectoring, the center of gravity of an airship lies below the center of buoyancy.

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

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

where ${\cal{V}}$ is the volume of helium in the gas envelope, $\varrho_{\rm air}$ is the density of air, and $\varrho_{\rm He}$ is the density of helium gas. If $W$ is the sum of the structural, fuel, payload, and other non-helium weights of the airship, then vertical force equilibrium and neutral buoyancy require

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

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

Check Your Understanding #2 – Buoyancy of an airship

An airship has a gas envelope with a volumetric capacity of 296,520 ft³. It uses helium as the buoyant gas. If the airship has an empty weight of 14,188 lb (excluding the helium in the gas envelope) and a maximum fuel load of 960 lb, what is the maximum payload the airship can carry? Assume MSL ISA standard atmospheric conditions. Assume the density of helium is 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, $L = W$ , 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

$W_P = \left( 0.002378 - 0.0003192 \right) \times 32.17 \times 296,520 - 14,188.0 - 960.0 = 4,491.0~\mbox{lb}$

Therefore, the maximum takeoff payload is 4,491 lb.

Ballast

Most LTA aircraft use some form of ballast. Ballast is any material placed on board a buoyant aircraft to add non-structural weight for balance and/or trim. Water ballast, carried in internal tanks, is typically used, although bags of sand or lead shot can also be used. Beyond trim and balance, crews can take on or cast off ballast to reach a specific takeoff weight. For example, a hot-air balloon uses ballast in the form of sandbags to keep it firmly on the ground as the envelope fills with hot air. When the airship is ready to fly, some ballast is dropped overboard, and the balloon is said to weigh off. During descent, releasing additional ballast can reduce the descent rate as the balloon approaches the ground.

Airships and blimps will also add or remove ballast, such as bags of lead shot, or add or dump water ballast before weigh-off. The weigh-off condition refers to the state in which the airship is trimmed for optimal operation during the initial part of the flight. To this end, ballast is added until the aircraft is slightly heavier than the upward aerostatic buoyancy force, a condition known as static heaviness.

After takeoff, the pilot first gives the airship a pronounced nose-high attitude by applying up-elevator so the engines can provide a vertical thrust component to overcome static heaviness. If thrust vectoring is available, the propulsion system is swiveled to provide mostly vertical thrust during takeoff. These actions propel the airship upward and forward into a climb. As the airship ascends and increases airspeed, the airflow over the envelope produces aerodynamic lift, and the pilot reduces the pitch angle to maintain a steady climb. Finally, the nose is lowered to almost level for the cruise.

Static heaviness refers to the airship’s weight when it is stationary. An airship’s static heaviness can vary greatly depending on its size and configuration. Typically, the static load accounts for 5%-10% of the gross weight. Larger airships carrying heavy payloads generally have higher static heaviness than smaller blimps. Hybrid airships have the highest static heaviness because their hull shapes are designed to produce significant aerodynamic lift, so they require a short runway for takeoff and landing.

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 Figure 25, 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 a net positive differential pressure in the buoyant gas so the envelope retains its shape.

A system of scoops, electric pumps, ducts, valves, and pressure regulators pumps pressurized air into the ballonets. The air scoops are often placed where the dynamic pressure of the slipstream from the propellers or other propulsion systems can be captured. An automatic pressure control system operates the ballonets, regulating inflation and deflation, and releases excess pressure through a set of air valves; pilots can also control the ballonets manually.

Inflation Fraction

Recall that the net aerostatic lift from the buoyant gas is equal to the weight of the outside air displaced by the volume occupied by the buoyant gas, less the weight of the buoyant gas itself, i.e.,

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

where ${\cal V}_{\rm bg}$ is the volume occupied by the buoyant gas, $\varrho_{\rm air}$ is the density of the outside air, and $\varrho_{\rm bg}$ is the density of the buoyant gas, e.g., helium.

The inflation fraction, $I$ , is the volume fraction of the envelope’s total volume 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

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

For example, an inflation fraction of 0.85 means 85% of the envelope’s volume provides buoyancy. Therefore, the buoyancy can be written in terms of the inflation fraction as

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

The concept is shown in Figure 26. The ballonets do not produce buoyancy because they are filled with air at nominally ambient conditions and thus act like ballast, as water is used for ballast on a submarine.

The inflation fraction is the fraction of the envelope’s volume that produces buoyancy.

For a rigid airship or dirigible, the volume is the net volume of the buoyant gas cells; these cells do not fill the entire envelope, so the potential lifting capacity is less than the envelope’s enclosed volume. The individual gas cells will also have different volumes because they are distributed along the length of a prolate-spheroid-shaped structure. 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

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

The analysis process then proceeds as before.

Controlling Buoyancy

By adjusting the internal air pressure and volume in the ballonets, the ballonets expand or contract, changing the airship’s overall inflation fraction and controlling net buoyancy and trim. Ballonets also allow buoyancy adjustments to compensate for changes in atmospheric conditions, such as pressure and temperature, solar heating of the envelope, and weight loss from fuel burn. This process lets the airship ascend or descend safely, adjust its pitch attitude, and compensate for changes in its center of gravity.

For example, as shown in Figure 27, the ballonets are inflated with air, reducing the buoyant gas volume and setting the airship’s desired static heaviness. After the 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 to maintain a constant differential pressure across the envelope, allowing the buoyant gas to expand freely and thereby maintaining the airship’s net buoyancy.

As an airship ascends, pressure in the ballonets decreases, allowing their volume to contract.

Pressure Altitude (Gas Ceiling)

The highest achievable altitude at which the gas pressure differential reaches its design limits, with the ballonets mostly deflated, is called the “pressure altitude.” However, this airship-specific term should be kept distinct from the pressure altitude used in altimetry; therefore, the condition is best referred to as the gas ceiling. In an emergency, if the buoyant gas overpressures the ambient pressure, the release valve opens and vents some of the buoyant gas to prevent excessive stress on the envelope. 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 to maintain the envelope’s internal pressure differential and to regulate the airship’s net buoyancy as atmospheric air density increases.

Trim Attitude

Ballonets can also trim the pitch attitude for climb and descent, as shown in Figure 28. The purpose is to use the ballonets to shift the distribution of buoyant gas and the resulting line of action of the net aerostatic lift relative to the center of gravity. Inflating the forward ballonet reduces the buoyant-gas volume forward and shifts the net aerostatic lift aft, lowering the nose of the airship and reducing pressure in the aft ballonet to maintain the buoyant-gas pressure inside the envelope. Similarly, inflating the aft ballonet reduces the buoyant-gas volume aft and shifts the net aerostatic lift forward, raising the nose and reducing pressure in the forward ballonet.

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

Center of Gravity

The center of gravity (c.g.) of any aircraft can change during flight as fuel is burned off or for other reasons. Airships are no different; the pilot must ensure that the c.g. remains within acceptable limits relative to the line of action of the net aerostatic lift. 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, an airship’s ballonets can compensate for variations in c.g. location, either before or during flight, as shown in Figure 29.

The ballonets adjust the longitudinal position of the center of buoyancy relative to the c.g., helping with trim while preserving the required c.g. limits for stability and control.

Thrust Vectoring

Thrust vectoring refers to an airship’s ability 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 thrust. Thrust vectoring is not new; the Goodyear-manufactured U.S.S. Akron and Macon airships both used swiveling propellers. The basic principle is shown in Figure 30. 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 achieved by fully feathering the propeller blades, which allows the blade pitch to be set to negative values.

The recent Zeppelin NT uses three swiveling propellers and vectored thrust capability. This capability allows the aircraft to take off and land vertically, hover stably, and fly backward. The two propellers on each side of the airship generally provide forward thrust but can also swivel through 120 degrees to obtain vectored thrust. Figure 31 shows that the aft engine drives a swiveling propeller that can be lowered as 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 cylindrical helium-filled gas bag with length $L$ = 40 m and radius $R$ = 10 m. Two ballonets containing air can expand into the helium gas bag, reducing the helium volume and affecting the airship’s overall buoyancy. The airship’s total mass, including the full helium load, is 11,500 kg. The density of air is ${\varrho_{\text{air}}}$ = 1.225 kg/m ${^3}$ , and the density of helium is $\varrho_{\text{He}}$ = 0.1786 kg/m ${^3}$ . Determine the volume of air that must be pumped into the ballonets for the airship to achieve neutral buoyancy.

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To achieve neutral buoyancy, the airship’s weight must equal the buoyancy force acting on it. The fully expanded volume of the cylindrical gas bag is

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

The initial mass of the airship, including the full load of helium, is

$M_0 = 11{,}500~\text{kg}$

If no air is in the ballonets, then the mass of air displaced by the gas bag is

$M_{\text{disp}} = \varrho_{\text{air}} {\cal{V}}_{\text{gas\_bag}} = 1.225 \times 12{,}566.37 = 15{,}393.8~\text{kg}$

which exceeds the airship’s initial mass. Therefore, the airship has positive buoyancy under these conditions, and air must be pumped into the ballonets to reduce the net buoyancy.

Let ${\cal{V}}_{\text{air}}$ be the volume of air pumped into the ballonets. The helium remains inside the gas bag and is compressed as the ballonets expand, so its mass does not change. The only increase in airship mass is the mass of air pumped into the ballonets, i.e.,

$\Delta M = \varrho_{\text{air}}{\cal{V}}_{\text{air}}$

For neutral buoyancy, the displaced mass of air must equal the final mass of the airship, i.e.,

$\varrho_{\text{air}} {\cal{V}}_{\text{gas\_bag}} = M_0 + \varrho_{\text{air}}{\cal{V}}_{\text{air}}$

Solving for ${{\cal{V}}_{\text{air}}}$ gives

${\cal{V}}_{\text{air}} = \frac{\varrho_{\text{air}} {\cal{V}}_{\text{gas\_bag}} - M_0} {\varrho_{\text{air}}}$

Substituting the numerical values gives

${\cal{V}}_{\text{air}} = \frac{1.225 \times 12{,}566.37 - 11{,}500} {1.225} = 3{,}179~\text{m}^3$

Therefore, the volume of air that must be pumped into the ballonets for the airship to achieve neutral buoyancy is approximately 3,179 m $^{3}$ .

Other Factors Affecting Performance

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

Superpressure

Blimps and other pressure airships are pressurized above ambient air pressure to maintain the gas envelope’s shape and structural rigidity, a phenomenon known as superpressure. Because the gondola, engines, tail surfaces, and other components are interconnected through the gas envelope, a blimp must maintain slight superpressure at all times to keep the flexible envelope tight enough to withstand bending, shear, and torsional loads without crushing or buckling. Nose battens, which are longerons running lengthwise, are attached to the outside of the envelope to carry mooring loads and to prevent the dynamic pressure of forward motion through the air from collapsing the gas envelope. The superpressure is typically relatively low, at about 0.5 kPa (about 10 lb/ft²). Still, it can be increased in turbulent air when additional envelope rigidity is required.

Superheat

All LTA aircraft experience thermal effects from solar radiation. The envelope’s large surface area absorbs heat, warming and expanding the buoyant gas inside. The temperature difference between the buoyant gas and the ambient air is called superheat. For a fully inflated airship whose external envelope volume is essentially fixed, heating the buoyant gas does not directly increase the gross buoyant force because the volume of displaced air remains nearly constant. The mass of buoyant gas also remains constant unless gas is vented. Instead, superheat causes the buoyant gas to expand and occupy a greater fraction of the envelope volume, with the ballonets accommodating this expansion while maintaining the required internal pressure.

In a pressure airship, heating or expansion of the buoyant gas increases its volume, compressing the ballonets and forcing air through the air valves. Conversely, as the buoyant gas cools or contracts, its volume decreases, and air is supplied to the ballonets to occupy the resulting volume and maintain the required envelope pressure and shape. The ballonets accommodate changes in the lifting gas volume while preserving the envelope’s overall volume and pressure. If the ballonets fully deflate and the buoyant gas continues to heat or expand, internal pressure may reach its allowable limit. Buoyant gas may then have to be vented to protect the envelope, although this should be avoided unless necessary.

Envelope Fabrics

The envelope exterior is commonly made white, silver, or otherwise reflective to reduce solar heating. Envelope materials should also be designed to limit heat absorption and excessive heating of the buoyant gas. Beyond helping control superheat effects, the fabric used for an airship’s envelope plays a crucial 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 stays taut under all conditions, airflow over the external shape will be disrupted, increasing drag and potentially causing flow separation. Early airships used cotton coverings tautened with cellulose dope. Modern blimp envelopes are typically made from multi-layer laminated synthetic fabrics that combine a structural fabric with coatings or films for helium retention and environmental protection.

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 pressure loss.

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. Additional coatings or films can improve gas retention and environmental durability. Polyurethane-coated nylon fabrics provide strength and tear resistance, while the polyurethane coating provides flexibility and low gas permeability. Vectran is a high-strength synthetic fiber with excellent tensile strength, dimensional stability, and resistance to heat and chemicals, and is also used in aerospace applications. In airship envelopes, Vectran may serve as the structural load-carrying layer and be protected by outer films or coatings against environmental exposure. Tedlar is a long-lasting polyvinyl fluoride film suitable for external 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 buoyant gas rather than helium?

Show solution/hide solution.

Hydrogen, with a density about half that of helium, can provide somewhat greater buoyancy and potentially increase an airship’s payload capacity. However, the buoyant lift depends on the difference between the density of air and the density of the buoyant gas, not on the density of the buoyant gas alone. To estimate the potential increase in payload capacity, we compare the buoyant forces generated by hydrogen and helium, assuming the same empty and fuel weights. Payload refers to the mass of cargo, passengers, and equipment carried in addition to the empty structure and fuel.

The buoyancy force acting on an airship is given by

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

where $\varrho_{\rm air}$ is the air density, $\varrho_{\rm gas}$ is the gas density (either hydrogen or helium), and ${\cal{V}}$ is the gas volume. The payload capacity is

$W_P = F_b - W_E - W_F$

where $W_E$ is the empty weight and $W_F$ is the fuel weight. Therefore, for hydrogen and helium, respectively,

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

and

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

Subtracting the two equations gives

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

The increase in payload fraction will be

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

or

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

Using representative STP densities, the ratio of the gross buoyant lift with hydrogen to that with helium is

$\frac{F_b^{\rm H_2}}{F_b^{\rm He}} = \frac{\varrho_{\rm air} - \varrho_{\rm H_2}}{\varrho_{\rm air} - \varrho_{\rm He}} = \frac{1.225 - 0.08988}{1.225 - 0.1786} = 1.085$

Therefore, replacing helium with hydrogen increases the gross aerostatic lift by only about 8.5%. However, the percentage increase in payload capacity can exceed 8.5% because the additional lift is applied after accounting for the empty and fuel weights.

Aerodynamic Effects

Aerodynamics, unlike aerostatics, must account for the airship’s motion through the surrounding air. Although an airship is supported primarily by buoyant lift, aerodynamic forces become important during forward flight, maneuvering, and altitude changes. In particular, the hull and control surfaces can generate aerodynamic lift, often called “dynamic lift,” which supplements the buoyant lift.

Dynamic Lift

In general, aerodynamic lift, or dynamic lift, denotes the lift produced by the airship other than from buoyancy to overcome its weight. As shown in Figure 32, 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 by a component of the thrust from the propulsion system, i.e.,

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

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

A primary aerodynamic effect on an airship is its drag, which thrust and power must overcome. Nevertheless, the aerodynamic lift and moments acting on the hull must also be considered. The drag on an airship will comprise both pressure drag and skin friction (boundary layer shear) drag. While pressure drag depends on 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 wetted surface 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

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

where it should be noted that the reference area is

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

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

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

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

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

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

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

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 around an airship at an angle of attack. The flow patterns of airships resemble those of prolate spheroids, which have been extensively studied in wind tunnels and through computational fluid dynamics (CFD) analysis. An example of a CFD solution is shown in Figure 33. Results from such simulations show that the flows around these bodies depend strongly on the angle of attack relative to the freestream velocity vector.

Nathan Scott and Earl Duque. Using detached eddy simulation and overset grids to predict flow 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 on the rear upper surface induces flow separation, resulting in two primary longitudinal vortices laterally displaced on either side of the body. These vortices generate suction and lift, causing the center of pressure to move aft, as shown in Figure 34. As the angle of attack increases, the vortices move forward along the body, creating a notable wake at the tail. However, the center of pressure remains ahead 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 in the flow environment at the tail (where the control surfaces are located on an airship), producing substantially more nonlinear aerodynamic forces and moments than those of a wing.

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 pitch angle and Reynolds number, normalized by length.

Figure 35 presents some results from NACA Report 432, including data for the bare hull, the hull with the tail surface and gondola, and 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 dynamic lift it generates is relatively small for its size. Second, the aerodynamic characteristics are nonlinear with respect to the angle of attack, partly because of vortex formation and flow separation, as previously described. Notice also the effects of the elevator angle, which behaves analogously to a flap, increasing or decreasing lift above the baseline.

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 the center of volume (also the center of buoyancy), which for a prolate spheroid is at mid-length and for an actual airship is about 45%. Notice that the moments are nose-up (positive) at low angles, but at about 8 degrees they become increasingly nose-down (negative).

Generalization of Aerodynamics

Generalized aerodynamic models of airship characteristics are unavailable. However, some essential characteristics of conventional airships, which approximate prolate spheroids, are apparent, as summarized in Figure 36, which shows increments in lift and drag coefficients as functions of the pitch angle, also referred to as the hull angle of attack. At low angles of attack, the initial slope of the lift coefficient curve is at least one order of magnitude lower than that of a wing, 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

(33) $\begin{equation*} \Delta C_L = C_1 \, \alpha \left| \alpha \right| \end{equation*}$

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

(34) $\begin{equation*} \Delta C_L = C_1 \, \alpha \left| \alpha \right| + C_2 \, \delta_E \end{equation*}$

where $C_2 \approx$ 0.01 per degree 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

(35) $\begin{equation*} \Delta C_D = D_1 \left| \Delta C_L \right| + D_2 \left| \delta_E \right| \end{equation*}$

paralleling the modeling of the lift-induced drag on a wing. While $D_1$ varies with the airship’s slenderness and other shape factors, including the effects of tail surfaces, the gondola, etc., $D_1 \approx 0.01$ 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, as it significantly affects the airship’s stability. Figure 37 shows that, at lower angles of attack (i.e., below 8°), the moment is positive, indicating that the center of pressure lies ahead of the centers of buoyancy and gravity, depending on the trim state. 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 its pitch angle.

The slope and sign of the moment curves change significantly. At low angles of attack, the aerodynamic moment is destabilizing, and a positive change in angle of attack produces a positive (nose-up) moment. This situation changes at high angles of attack, with the negative slope suggesting good pitch stability from an aftward shift in the center of pressure. Because of an airship’s dominant axisymmetry, lateral airloads from 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 of airship models in the wind tunnel, have been compiled as functions 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

(36) $\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

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

which applies only to a fully developed turbulent boundary layer. While Eq. 36 is a semi-empirical relationship, Figure 38 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 spherical configuration, particularly below the critical Reynolds number.

The Hoerner 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.

Figure 38 presents the measurements plotted in NACA Report 394, authored by Ira Abbott, which documents tests conducted on airship models of the Goodyear Zeppelins in the NACA Langley variable-density wind tunnel. Tests first evaluated the general shape, then added the effects of the gondola, tail surface, struts, and bracing wires.

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, the table below shows a representative allocation of complete-airship drag, which helps with initial drag-coefficient estimates. Of course, the most reliable way to estimate the drag coefficients for an actual airship shape is in a wind tunnel, where a Reynolds number is used to assess drag-coefficient sensitivity.

Component	Drag (%)
Bare hull	50
Gondola	15
Flight surfaces	10
Rigging & cables	10
Miscellaneous	5
Interference	10
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, which is proportional to the wetted surface, grows by less than the square of the increase in 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 with propellers or ducted fans. Estimates of the power required for an airship’s flight follow similar lines to those for a propeller-driven airplane. In simplest terms, an airship reaches maximum airspeed when its engines produce maximum thrust equal to the drag it experiences at that airspeed. That drag depends on the airship’s diameter and length, and, more specifically, on the projected frontal area and the total wetted area of its outer envelope. In general, drag varies with the square of the airspeed, and therefore, power increases with the cube of the airspeed.

Analysis

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

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

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

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

Using Eq. 35, the drag coefficient can be expressed as

(40) $\begin{equation*} C_D = C_{D_0} + \Delta C_D = C_{D_0} + D_1 \left| \Delta C_L \right| + D_2 \left| \delta_E \right| \end{equation*}$

where, from Eq. 34, the lift-coefficient increment is

(41) $\begin{equation*} \Delta C_L = C_1 \, \alpha \left| \alpha \right| + C_2 \, \delta_E \end{equation*}$

The corresponding power required for flight can be written as

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

where $\eta_p$ is the net efficiency of the propulsive system (engine and propeller combined); in practice, this value may vary with airspeed depending on the propeller characteristics.

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 airship’s drag coefficient, based on Eq. 28, 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

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

Inserting the values gives

(44) $\begin{equation*} P_{\rm req} = \frac{1}{2 \times 0.8} \times 1.225 \times 28.0^3 \times 6,600^{2/3} \times 0.051 = 303~\mbox{kW} \end{equation*}$

which is approximately 406 hp (1 hp = 745.7 W).

Power Required Curves

The power-required curves for an airship depend on many factors, partly because, in regular operation, the airship may use dynamic lift for flight; thus, a lift-sharing effect must be considered. The fraction of total weight carried by buoyancy can range from 90% to 95% (as in a blimp) and to 70% or less for a hybrid airship.

Buoyancy Only

With zero dynamic lift, the power-required curves are trivial to compute because the drag coefficient can be assumed constant, i.e., $C_D = C_{D_0}$ . In this case, power will increase proportionally with the cube of the airspeed according to

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

Buoyancy + Aerodynamic Lift

When the airship uses dynamic lift for flight, its drag increases, requiring more power. Assume that there is no dynamic lift from thrust, which means that the lift sharing can be written as

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

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

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

so the lift coefficient is

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

Notice that the lift coefficient decreases with the inverse square of airspeed, ${V_{\infty}}$ . If the aerodynamic lift is assumed to act upward, then $C_L \ge 0$ and $\left|C_L\right| = C_L$ . With no elevator deflection, the drag coefficient will be

(49) $\begin{equation*} C_D = C_{D_0} + D_1 C_L \end{equation*}$

Therefore, because the thrust required equals drag, then

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

or

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

Substituting for $C_L$ gives

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

which reduces to

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

The power required is

(54) $\begin{equation*} P_{\rm req} = \frac{T_{\rm req} \, V_{\infty}}{\eta_p} \end{equation*}$

and so

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

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

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

where

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

and

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

The foregoing 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, the induced power, which increases proportionally with airspeed, as shown in Figure 39. Notice that without aerodynamic lift, i.e., zero static heaviness, the required power is minimal because buoyancy supports the airship’s weight 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 significant drag coefficient. Therefore, the maximum airspeeds are expected to be relatively low compared with those of 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 required power increases with the cube of airspeed, power and fuel demands increase rapidly above these airspeeds.

Therefore, the airship’s speed eventually becomes power-limited: the installed power to produce the thrust required to overcome the airship’s drag is insufficient, thereby limiting the attainable airspeed, as shown in Figure 40. The Hindenburg was among the fastest large passenger airships ever built, with a maximum speed of about 74 kts. The current Goodyear Zeppelin NT semi-rigid airships have a maximum speed of about 67 kts, although normal cruise speeds are lower. Higher 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 at different density altitudes. Power increases with the cube of the airspeed.

If the airship is a blimp, the increased aerodynamic pressure near the nose at higher airspeeds can exceed the internal superpressure that maintains the envelope’s shape, causing the nose to cave inward. Consequently, blimps are generally limited to relatively low maximum airspeeds. Higher speeds require sufficient superpressure and may also require nose battens or other local structural reinforcement to prevent envelope deformation. Thus, factors other than aerodynamic drag and available propulsive power can limit a blimp’s maximum airspeed. Semi-rigid or rigid airships can generally achieve higher airspeeds because their structural framework helps maintain hull shape under increased aerodynamic loads.

Stability Characteristics

Airships, like all aircraft, must be designed with sufficient static and dynamic stability to be flown safely with good handling qualities. In this regard, they must 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, similar to but also different from those of airplanes. If the forces and moments generated by gust disturbances tend to return the airship to its trimmed condition, then it is statically stable. For example, if a disturbance increases the pitch angle and the airship initially responds nose-up, static stability requires a restoring nose-down moment. Static stability refers to the restoring effects that cause the nose to pitch down after a disturbance is removed.

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 over time, i.e., a characteristic known as dynamic response. A statically and dynamically stable aircraft is generally easier to fly. However, an aircraft may be statically stable and dynamically unstable yet still flyable, especially if, as in an airship, its overall dynamic response is sufficiently slow that the pilot can control it with routine flight-control inputs.

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

The c.g. should lie below the center of buoyancy so that the weight and buoyancy forces produce a restoring pendular moment after a pitch or roll disturbance, similar to the pendular stability found on a high-wing airplane. However, the payload distribution must always be arranged so the c.g. position remains within normal flight limits.
The area of the airship’s tail surfaces (empennage), including the horizontal and vertical stabilizers and their control surfaces, plays a significant role in longitudinal and directional stability. If the surfaces are too small, they may not give enough directional stability or control authority. If the surfaces are too large, they increase the empty weight and may cause issues. For example, a tail-heavy airship may need ballast added to 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, making the airship more sluggish in response to control inputs. The significant apparent, or added, mass of airships, an unsteady aerodynamic effect, also contributes to their overall inertial characteristics.

Pitch Response

Moments on an airship are usually referred to its center of volume, which is also the center of buoyancy. For a prolate spheroid, this point is at mid-length, whereas for an actual airship, it may be somewhat forward or aft of that location, depending on the hull shape and the distribution of internal gas volume. The center of gravity of an airship normally lies well below the center of buoyancy, as shown in Figure 41. Hence, for pitch disturbances, the weight and buoyancy forces produce a pendular restoring moment about the center of gravity.

Airships exhibit good pitch stability because the weight and buoyancy forces produce a restoring moment when the center of gravity lies below the center of buoyancy.

However, previous aerodynamic results show that, at lower angles of attack, the aerodynamic moment may be positive, depending on the trim state, indicating that the aerodynamic center of pressure lies ahead of the moment reference point. From a stability-and-control perspective, the change in the slope and sign of the moment curves is noteworthy, as the aerodynamic moment can be destabilizing at low angles of attack. This situation is usually not dangerous because the aerostatic pendular restoring moment is dominant. Still, it means the airship’s pitch stability comes primarily from weight-buoyancy separation rather than from an inherently stable aerodynamic pitching-moment slope.

Critical Airspeed

Airships can experience a form of speed instability as they approach a critical airspeed. This issue arises because 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 must produce downforce to pitch the airship nose-up, as shown in Figure 42. However, if the airspeed is too low, the net vertical force will cause the airship to descend rather than ascend; this speed is called the critical airspeed. Although often called an instability, it is, strictly speaking, a form of control reversal. Normal control effectiveness returns only when the airship exceeds its critical speed. Thrust vectoring, used on many modern airships, can greatly reduce this adverse characteristic by providing direct control forces at low airspeed, when aerodynamic control surfaces are less effective.

Yaw Response

Because of the dominant axisymmetry, the lateral airloads from changes in yaw angle behave similarly to those for pitch. However, the airship has no pendular weight-buoyancy restoring moment about the yaw axis, so directional stability is weaker than pitch or roll stability. At low yaw angles, the aerodynamic center of pressure may lie ahead of the center of gravity, producing a destabilizing yawing moment while also helping the airship begin a turn; see Figure 43. This effect is usually mild and can be compensated for by rudder input or differential/vectoring thrust. At somewhat higher yaw angles, the aerodynamic sideforce distribution may shift so that the resulting yawing moment becomes restoring, thereby providing directional stability.

An airship’s yaw stability is weaker than its pitch or roll stability.

Roll Response

Airships are highly stable in roll because of their high pendular stability, as illustrated in Figure 44. However, unlike airplanes, they perform relatively flat turns, much like seagoing ships, maintaining a flat attitude with little bank angle other than that produced by inertial forces. At higher airspeeds and/or with a tighter turn radius, 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 relatively large moments of inertia of an airship can lead to slow dynamic responses and long settling times, much longer than those of conventional airplanes. Airships tend to have a pronounced phugoid response at lower airspeeds, as shown in Figure 45. For example, even a casual observation of the Goodyear blimp reveals a pronounced porpoising characteristic, known as the phugoid response, when it is in flight. The response lasts for an extended (long) period and is easily controlled by the pilot or the autopilot. At higher airspeeds, the phugoid is well-damped.

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

Like static stability, the dynamic response depends on 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 by strong steel cables or other tethers; see Figure 46. They are designed to remain stationary at a specific location and altitude for extended periods of time. Tethered aerostats have been utilized in various applications since the early 1900s, including military surveillance, telecommunications, scientific research, and advertising. Equipped with multiple sensors, cameras, and radar systems, these aerostats can monitor ground movement, such as troop movements, detect threats and enemy activity, and provide real-time intelligence. Today, tethered aerostats support various telecommunications applications, and lifting antennas and repeaters to higher altitudes can extend wireless networks across wider areas. This technology benefits military theaters, remote areas, or disaster-stricken regions 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 in Figure 47. 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 cable’s weight, which can be calculated from its length and linear density (weight per unit length). The cable also experiences a drag force from the wind flow, which depends on its shape, diameter, and wind speed. The shape formed by the cable is called a catenary.

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

The ordinary catenary equation applies when the tether is loaded by its distributed weight and the horizontal tension component is constant. Therefore, the following derivation neglects aerodynamic drag on the cable and includes only the aerostat drag, $D$ , as the horizontal end load. If cable drag is significant, the horizontal tension varies along the tether, and the governing equations must instead be solved as a more general distributed-load cable problem.

Let the cable have reeled-out length $S$ and weight per unit length $w_c$ . Assume that it is anchored at $(x,y)=(0,0)$ and extends to the aerostat at $(R,H)$ . The catenary may be written as

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

where $c_1$ and $c_2$ are constants determined from the boundary conditions. At the ground anchor, $x=0$ and $y=0$ , so

(60) $\begin{equation*} c_2 = -\frac{D}{w_c}\cosh(c_1) \end{equation*}$

The slope of the tether is

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

At the ground anchor, the vertical component of the tether tension equals the net aerostatic lift remaining after subtracting the aerostat weight and the total tether weight. Therefore,

(62) $\begin{equation*} \sinh(c_1) = \frac{F_b-W-w_cS}{D} \end{equation*}$

and

(63) $\begin{equation*} c_1 = \sinh^{-1}\left( \frac{F_b-W-w_cS}{D} \right) \end{equation*}$

At the aerostat, the vertical component of the tether tension balances the net aerostatic lift of the aerostat alone, giving

(64) $\begin{equation*} \left.\frac{dy}{dx}\right|_{x=R} = \frac{F_b-W}{D} \end{equation*}$

Therefore,

(65) $\begin{equation*} \sinh\left(\frac{w_cR}{D}+c_1\right) = \frac{F_b-W}{D} \end{equation*}$

and the horizontal displacement is

(66) $\begin{equation*} R = \frac{D}{w_c} \left[ \sinh^{-1}\left(\frac{F_b-W}{D}\right) - \sinh^{-1}\left( \frac{F_b-W-w_cS}{D} \right) \right] \end{equation*}$

The height is then obtained by substituting $x=R$ into the catenary equation, i.e.,

(67) $\begin{equation*} H = \frac{D}{w_c} \left[ \cosh\left(\frac{w_cR}{D}+c_1\right) - \cosh(c_1) \right] \end{equation*}$

If the tether angle at the aerostat, $\theta_a$ , is measured from the vertical, then the aerostat force balance gives

(68) $\begin{equation*} \tan\theta_a = \frac{D}{F_b-W} \end{equation*}$

and therefore

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

When aerodynamic drag on the tether is not negligible, it must be represented as a distributed horizontal load. In that case, the horizontal component of tether tension is not constant, and the ordinary catenary solution above is invalid.

Check Your Understanding #6 – Forces on a Tethered Aerostat

A tethered aerostat filled with helium gas is in both vertical and horizontal equilibrium at the end of a 4,000 ft-long cable under tension, as shown in the figure below. For a first estimate, assume the cable is straight and replace the distributed cable weight with an equivalent load carried by the tether system. The aerostat has a volume of 200,000 ft ${^{3}}$ and a maximum diameter of 38 ft. It has a drag coefficient of 1.2 based on the projected frontal area. The aerostat’s non-helium weight is 4,200 lb. The cable weighs 0.25 lb per ft. The wind speed is 25 kts at all heights, and the air density is 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 angle $\theta$ .

Show solution/hide solution.

For this simplified straight-cable model, the total upward buoyancy must balance the aerostat weight, the equivalent cable weight, and the vertical component of the tether force. Therefore,

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

or

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

where ${F_b}$ is the net buoyancy force, $W_a$ is the non-helium weight of the aerostat, and $W_c$ is the equivalent cable weight included in the simplified force balance.

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

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

where

$A_{\rm ref} = \frac{\pi D_{\max}^2}{4}$

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

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

The drag is

$D = 2{,}666~\mbox{lb}$

and the net vertical force available to balance the vertical component of the tether tension is

$F_b - W_a - W_c = 6{,}902~\mbox{lb}$

Therefore,

$\tan \theta = \frac{2{,}666}{6{,}902} = 0.386$

and the angle is

$\theta = \tan^{-1} \left( 0.386 \right) = 21.1~\mbox{deg.}$

Airships of the Future?

Airships occupy a unique niche in aviation history, with a rich legacy of innovation and adventure. Several companies, including Lockheed Martin, Hybrid Air Vehicles, Aeroscraft, and LTA Research, have been actively developing airships. 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 transportation, offering passengers breathtaking views and a sense of nostalgia. Luxury airship travel could attract travelers seeking a distinctive experience akin to ocean cruises, but in the skies.
They can provide stable platforms for aerial observation, surveillance, and monitoring, including environmental research, border patrol, and disaster response. Their low airspeed, long endurance, and ability to loiter or station-keep when winds are within the vehicle’s propulsion and control authority make them well-suited to 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 serve as flying billboards, attract attention, and promote brands or events. They offer a unique, memorable way to reach audiences, especially in crowded urban areas or at 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 reach remote or inaccessible regions could help distribute essential supplies and support rescue operations.
Airships have the potential to be more environmentally friendly than traditional aircraft for some missions, especially when evaluated in terms of fuel consumption or emissions per unit payload distance. This advantage is most likely to be realized in low-speed, long-endurance, or remote-access missions where buoyant lift reduces the power required to remain aloft. 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 spur renewed interest and investment in airship development, thereby shaping their future role in the aviation sector.

Regulatory Frameworks

The regulatory treatment of airships differs in important respects from that of fixed-wing or rotary-wing aircraft, reflecting the unique characteristics of LTA flight. In the U.S., the FAA issues type certification for airships under FAR Part 21. While some airships fall under the general certification criteria of FAR Part 23, many require special class certification or exemptions because of their unconventional design features. Historically, Advisory Circular 21-17 provided guidance on certifying unusual aircraft, including airships; however, a case-by-case approach has largely superseded it. In Europe, EASA has used special conditions for gas airships, including Special Condition SC GAS for large gas airships. Earlier draft material, such as CS-30N for normal and commuter airships, also existed, but CS-23 is an airplane certification specification and is not tailored to lighter-than-air vehicles.

Operationally, airships follow the same general rules as other civil aircraft. Most private or research flights operate under FAR Part 91, while commercial operations may fall under the more stringent requirements of FAR Part 135. Airship pilots must hold the appropriate lighter-than-air category and airship class rating; balloons are treated separately within the lighter-than-air category. Additional aircraft-specific training, endorsements, or type-specific authorization may also be required depending on the aircraft and operation. Training and certification requirements emphasize unique handling characteristics, delayed control response, and ballast management. Emergency procedures, particularly those involving rapid descent or envelope damage, are also a core part of the pilot training syllabus.

Economics of Airship Transportation

Airships offer an unconventional way to transport cargo. Although they are not widely used today, interest has renewed in their potential to reach remote regions and transport large industrial components. To understand their economic prospects, it helps to compare their operating costs with familiar terrestrial modes of transportation, such as long-haul trucking. The cost of transporting goods is often expressed in $US (USD) per ton-mile. If a payload of weight $W$ is carried a distance $D$ , then the total transportation work is $\text{Ton-miles} = W \, D$ .

Long-haul trucking in the United States typically costs 0.10 to 0.15 USD per ton-mile, while rail freight is even lower. Conventional air cargo is much more costly, often exceeding 1.0 USD per ton-mile. For the largest jet freighters, operating costs can easily exceed USD 1.5 per ton-mile, reflecting the extremely high cost of transporting cargo at higher speeds. Modern studies of hybrid airships estimate their operating cost at 0.30-0.40 USD per ton-mile, placing them above trucks but well below conventional aviation.

Airships appear more expensive than trucks primarily because of their low utilization. A tractor–trailer can easily accumulate more than 100,000 miles of productive operation per year. Airships, by contrast, are sensitive to wind and require specialized ground handling, thereby limiting their annual operating hours. Their capital costs are also high: a large cargo airship requires a hangar, a mooring mast, a trained ground crew, and a supply of helium to replenish the gas envelope, which leaks over time. The development cost of designing, certifying, and bringing such an airship to market would likely exceed several hundred million USD. For a fully capable heavy-lift hybrid airship, the total program cost could approach or exceed USD 1 billion. These fixed costs contribute significantly to the per-ton-mile cost and can dominate the economics even when fuel consumption is low.

Nevertheless, airships can become economically competitive where roads, railways, or ports do not exist or are prohibitively expensive to build. In remote regions, for example, building and maintaining a road can far exceed the cost of transport itself. An airship or hybrid airship designed for austere operations may operate from water, snow, open terrain, or a prepared mooring area with less infrastructure than conventional aircraft or ground transportation systems. These infrastructure savings can offset their higher operating costs. Airships can also transport oversized or fragile cargo that cannot be easily moved by road without escorts, detours, or temporary obstacle removal. In such cases, airships may offer a lower overall cost.

Environmental considerations may shape future economics. Airships produce significantly lower carbon dioxide emissions per ton-mile than trucks or aircraft, particularly with hybrid-electric or hydrogen propulsion. If carbon pricing becomes widespread, the lower emissions associated with airships may translate into a noticeable economic advantage. Airships can also reach disaster zones where roads and bridges are damaged, providing another niche in which their unique capabilities outweigh their higher operating costs.

A simple comparison illustrates the situation. Consider transporting 20 tons of cargo over 600 miles. Using a representative trucking cost of 2.3 USD per mile gives

(70) $\begin{equation*} C_{\text{truck}} \approx 600 \times 2.3 = 1{,}380~\text{USD} \end{equation*}$

This corresponds to approximately 0.11 USD per ton-mile. If an airship operates at a projected cost of 0.30–0.40 USD per ton-mile, then transporting the same cargo would cost

(71) $\begin{equation*} C_{\text{airship}} \approx (0.30\text{--}0.40) \times 20 \times 600 = 3{,}600\text{--}4{,}800~\text{USD} \end{equation*}$

This is roughly three times as expensive as trucking in this scenario.

At least for now, airships are unlikely to be economically competitive with trucks on established road networks. Their future value lies instead in circumstances where infrastructure is limited, terrain is rugged, or cargo is exceptionally large or sensitive. In such environments, the savings from avoiding road construction, route surveys, or special handling procedures can outweigh their higher operating cost. The long-term economics of airship transportation will depend on improvements in reliability and utilization, reductions in capital and ground-handling costs, and the degree to which environmental impacts are eventually incorporated into transportation pricing.

Airship Drones

Airship drones are uncrewed aerial vehicles (UAVs) that derive their primary lift through buoyancy rather than aerodynamic forces. Unlike fixed-wing or rotorcraft drones, which rely on wing lift or thrust to remain airborne, airship drones use an envelope filled with a lighter-than-air gas, typically helium, to support their weight. The propulsion system, often consisting of small electric motors with propellers, provides thrust for forward flight, while control surfaces or vectored-thrust systems maintain attitude and maneuverability.

The fundamental advantage of airship drones is their potential for high endurance. Because buoyancy passively supports much or all of their weight, they require little energy to remain aloft. However, station-keeping, repositioning, and attitude control can still require significant power in windy or turbulent conditions. With compatible propulsion, energy storage, lifting-gas retention, and weather conditions, many airships can operate for hours, days, or longer. This endurance potential makes airship drones attractive for persistent surveillance, environmental monitoring, telecommunications relays, and scientific research.

An example of a hybrid airship drone is the Plimp developed by Egan Airships, as shown in Figure 48. The Plimp is a semi-buoyant aircraft that combines the features of a traditional blimp with aerodynamic lift generated by fixed wings. By integrating buoyant and aerodynamic forces, the Plimp can hover and achieve reasonable forward speeds. Its design enables vertical or near-vertical takeoff and landing (VTOL) without heavy propulsion systems or complex rotor arrangements. Plimps are intended for surveillance, communications relays, and cargo transport, offering a different level of operational flexibility than conventional airship drones or fixed-wing UAVs.

The Plimp is a semi-buoyant aircraft that combines the features of a traditional blimp with aerodynamic lift generated by fixed wings.

Airship drones typically operate at low airspeeds, often between 10 and 50 km/h, and at altitudes ranging from a few hundred meters to several kilometers. Some advanced concepts propose high-altitude airship drones capable of operating in the stratosphere, serving as high-altitude platforms (HAPS) for communications and observation. Their payload capacities vary widely and depend strongly on envelope volume, lifting-gas density, structural weight, propulsion weight, and operating altitude. Buoyancy can reduce the propulsive power needed to remain aloft, but it does not automatically give a higher payload capacity than a similarly sized fixed-wing UAV.

Despite their advantages, airship drones face significant engineering challenges. Their large surface areas make them highly sensitive to atmospheric disturbances, such as gusts, turbulence, and adverse weather, which complicate flight control and reduce mission reliability. Helium, the preferred lifting gas, is expensive and slowly leaks, limiting mission duration unless replenishment systems are included. Moreover, airships are relatively slow and unarmored, making them vulnerable to damage in military operations.

Environmental Considerations

Airships offer several notable environmental advantages over conventional heavier-than-air aircraft, particularly in applications that require long endurance and low-speed flight. Unlike airplanes or rotorcraft, airships rely primarily on buoyant lift rather than dynamic lift, substantially reducing the energy needed to remain aloft. This fundamental difference enables significantly lower fuel consumption and associated emissions, particularly at cruise conditions. Some modern designs use hybrid-electric or fully electric propulsion systems, further minimizing carbon dioxide and nitrogen oxide emissions. Fuel consumption or energy use per unit payload-distance can be significantly lower than that of turboprop aircraft or helicopters operating in similar regimes.

Another advantage of airships is their relatively low noise profile. Acoustic emissions are generally low because airships cruise at low speeds and require relatively low propulsive power compared with heavier-than-air aircraft performing similar endurance missions. Many modern airships use ducted fans or other low-speed propulsors, often with thrust-vectoring capability, which can further reduce acoustic disturbance and improve low-speed maneuverability. This makes them potentially suitable for operations near urban centers, environmentally protected areas, or for wildlife monitoring, where minimizing acoustic disturbance is important.

From a ground-operations perspective, airships do not require conventional runways, reducing the environmental impact associated with airport development. However, they still require suitable operating areas, mooring provisions, ground-handling equipment, and trained personnel, especially for larger vehicles. Hybrid airships and some modern designs may operate from relatively unprepared surfaces. Still, this capability depends on the landing system, wind conditions, vehicle size, and ground-support concept. This flexibility can allow airships to access remote or ecologically sensitive areas with less infrastructure than conventional aircraft, but they still require some infrastructure.

Finally, some airship and high-altitude platform concepts propose integrating photovoltaic arrays along the envelope or upper surface. The large available surface area and relatively low loiter power requirements can make solar-electric operation feasible for specific missions, particularly high-altitude station-keeping or long-endurance communications relay. However, solar propulsion is strongly constrained by irradiance, day-night energy storage, altitude, latitude, season, weather, and the photovoltaic system’s available area and efficiency. Such solar-electric airships may serve as atmospheric satellites for persistent surveillance or telecommunications, but only when they meet solar-energy balance and station-keeping requirements.

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, along with their aerodynamic characteristics in forward flight, have been described. With advancements in technology and design, airships are being reintroduced as an alternative mode of transportation that combines efficiency, versatility, and environmental friendliness. New designs incorporating hybrid-electric or hydrogen propulsion systems offer greater potential for clean, sustainable aviation. Airships can consume significantly less fuel per unit cargo weight per unit distance than conventional aircraft, thereby reducing carbon emissions for some missions. This benefit makes airships attractive for long-haul cargo transport, much as container ships traverse the oceans. The reintroduction of airships could also offer a unique, memorable way for passengers to experience recreational travel.

Recent advancements in materials, propulsion systems, and aerodynamics have improved the safety, efficiency, and maneuverability of modern airships. 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 make them well-suited to specific roles in transportation, surveillance, and perhaps tourism.

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 structure and function?
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 safety considerations are 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?
Research and 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 covering 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 film recounts the history of the Goodyear Aircraft Corporation and its production 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, provides extensive information on 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 Hindenburg used hydrogen as its lifting gas. This choice provided excellent buoyancy but also introduced the severe fire risk that ultimately contributed to its catastrophic destruction. ↵
The hull shape of a conventional airship is typically 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, the price of helium gas is about $100 per cubic meter. ↵

License

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Introduction to Aerospace Flight Vehicles Copyright © 2022–2026 by J. Gordon Leishman is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, except where otherwise noted.

Introduction

History

Anatomy of LTA Aircraft

Balloons (Thermal Aerostats)

Stratospheric Balloons

Dirigibles

Blimps

Semi-Rigid Airships

Tethered Aerostats

Hybrid Airships

Buoyant (Lifting) Gases

Hydrogen

Helium

Ammonia

Hot Air

Summary of Buoyant Gases

Why Not a Vacuum Airship?

Principle of Buoyancy

Geometric Characteristics of Aerostats

Projected Frontal Area

Volume

Surface Area

Slenderness Ratio

Center of Buoyancy

Aerostatic Trim

Ballast

Ballonets

Inflation Fraction

Controlling Buoyancy

Pressure Altitude (Gas Ceiling)

Trim Attitude

Center of Gravity

Thrust Vectoring

Other Factors Affecting Performance

Superpressure

Superheat

Envelope Fabrics

Aerodynamic Effects

Dynamic Lift

Lift, Drag & Moment Coefficients

Flow Fields

Lift, Drag & Moment Characteristics

Generalization of Aerodynamics

Comparisons to Drag Measurements

Drag Breakdown

Power Required for Flight

Analysis

Power Required Curves

Buoyancy Only

Buoyancy + Aerodynamic Lift

Maximum Attainable Airspeed

Stability Characteristics

Pitch Response

Critical Airspeed

Yaw Response

Roll Response

Dynamic Response

Tethered Aerostats

Airships of the Future?

Regulatory Frameworks

Economics of Airship Transportation

Airship Drones

Environmental Considerations

Summary & Closure

License

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