Rigid Airships and Blimps: Two structural approaches to cargo transport
The Goodyear blimp is a household name and the most visible instance of applied airship technology today. In some respects, it is the best advertisement for the potential of airship technology to revolutionize future transportation, too. After operating GZ-20 blimps safely for 48 years (1969-2017), Goodyear retired the last of these well-known blimps and replaced them with German Zeppelin NT airships. The Zeppelin NT also has had a flawless safety record since its first flight in 2000.
While the non-rigid, or blimp, structures have dominated the airship industry since the 1940s, this is more a function of demand than structural design. After the jet-powered airplanes took over the passenger transport market, there was little need for giant, ocean-crossing rigid airships that had been built in Germany, Britain and the United States. The rigid airships lacked an easily capturable market niche, and no one had the ambition to pursue it aggressively. The only commercial market left was for “floating billboards” that could also film sporting events. Non-rigid airships like the Goodyear blimps were a less expensive solution than a rigid airship, and adequate for this job.
There is no such thing as a small airship, but most people are unaware of just how much bigger rigid airships were in comparison to the advertising blimps. The photograph of the Graf Zeppelin beside the Goodyear Blimp illustrates the scale difference. The rigid airship is about 4 times longer than the blimp, but has about 50 times more useful lift. In the competitive field of cargo transport, these economies of size are extremely important.
The principal differences between rigid airships and blimp technologies can be explained by an analogy with the automobile wheel. Initially, cars had wooden, spoked wheels with a thin inflated tire to smooth the ride. As materials advanced, the structure provided by the spokes was replaced by a large tire filled with pressurized air. Both approaches work, but the technology of the pneumatic tires proved to be superior. Of course, as technology continues to advance, changes are inevitable. Lighter composite spoked wheels are now challenging the traditional pneumatic car tires.
Blimps resemble car tires; in that they depend on the higher gas pressure inside the envelope to keep it stiff and support the control surfaces and gondola which are attached to the outside. Rigid airships have an internal space-frame structure that, like the spokes of a wheel, holds the airship’s shape, carries all the loads, and protects the lifting gas cells, which are non-pressurized.
Each design has its advantages and disadvantages. In a pressurized blimp, the lifting gas is pushed out of every pinhole. in a rigid airship, the leakage of the non-pressurized gas cells is slower. A blimp can be efficient at a relatively small size because its mass is easily overcome. A rigid airship has to be much larger just to offset its deadweight, which can easily require 50 percent of the total lift. The size crossover point at which blimps and rigid airships meet, achieving similar cost and efficiency, is open to conjecture, The US Navy built the largest blimps ever flown and they would carry about 15 tonnes. The larger rigid airships would provide between 50 and 70 tonnes of useful lift. In the cargo world size matters. As illustrated in the economies of size model, the larger the airship the lower the unit costs of freight.
The economic benefits of size come in two forms. First, the marginal capital cost of building a slightly larger airship are relatively low. Going from a 15-tonne lift rigid airship to a 30-tonne model might cost as little as 25% more in terms of inputs. The other economy is in operations. An airship’s drag, and therefore its fuel consumption, scales with the square of the dimension, while he payload scales faster than the cube, so fuel efficiency improves sharply. Crew costs, too, will tend to scale less than proportionally with payload, and other advantages, such as greater stability in flight, also accrue. So operating cost per ton-km also falls as an airship gets bigger.
Why Blimp Technology Doesn’t Scale Up Well
Blimps face a special scaling problem that arises from the way that hoop stress affects the strength of materials required for the envelopes. “Hoop stress” is a force acting on the wall of a vessel containing a fluid. The origin of the term comes from the wooden stave barrels that were held together by metal hoops. As larger barrels and vats were constructed with larger diameters, the strength of the hoops had to be increased in proportion to the diameter.
In a nonrigid airship, or blimp, the gas wants to form a bubble. Consequently, the most hoop stress forms on the sides of the airship. The formula for hoop stress (approximately), in a “thin-walled” vessel is:
σ = (piDi – peDe)/2t
σ = hoop stress
pi = internal pressure of the vessel
pe = external pressure of the vessel
Di = internal diameter of the vessel
De = external diameter of the vessel
t = thickness of the vessel’s wall
In a blimp, as in a car tire, but not in a rigid airship, there must be a significant difference between pi, the internal pressure on the envelope of the airship, and pe, the external pressure on the airship; again, this pressure difference gives the airship (or the tire) its shape and stiffness. As the diameter of the airship gets larger D, the hoop stress rises proportionally, and the envelope of the airship needs to be made thicker/stronger to resist the forces trying to pull it apart.
Expanding the diameter of the blimp is problematic because the extra thickness of the envelope increases its weight and reduces the benefit of the non-rigid structure. Assuming that strength is a function of the wall thickness, the weight of the envelope scales with roughly the cube of the dimension (the area with the square and the thickness with the dimension; the product of these, which is the weight, scales with the cube). Gross lift also scales with the cube of the dimension, and does not particularly outrun weight. Consequently, blimps lack the tendency to become dramatically more efficient as they become larger. In the words of one engineer, the scaling problem of the blimp becomes like “a dog chasing its tail.”
Heavier envelopes are also harder to fabricate (stiffer materials) and more difficult to transport for assembly of the blimp. In order to reduce the strength of the materials required for a larger diameter blimp, catamaran designs have been created that have two or three lobes. These blimps are usually referred to by the builders (Lockheed-Martin and HAV) as “hybrids” because they are designed to use both aerostatic and aerodynamic lift to fly. The smaller diameters of the two lobes reduces the hoop stress and allows these blimps to lift more than an equivalent single cigar-shaped envelope.
Economies of size also impact the competitive distance of operations. Without being able to gain efficiency by scaling up, blimps will have difficulty becoming a profitable mode of transport for intercontinental shipping.
Scaling-up Rigid Airship Technology
By contrast, rigid airships enjoy dramatic efficiency gains as they scale up, which will lead to incredible competitiveness if only they can be built big enough. The lift of a rigid airship increases with the cube of its dimension, greatly outpacing the weight of the airship’s frame, which scales up with the square of its dimension. In a rigid airship, hoop stress is fairly unimportant because the lifting gas is contained in a series of gas cells within the hull that are non-pressurized.
The downside for a rigid airship was that building a space-frame structure strong enough to resist all the forces that it received in flight was difficult and, above all, heavy. Prior to the war, airship engineers had to depend on observation and slide-rule calculations to work out what they assumed were the stress concentrations. It is unsurprising that the cause of many rigid airship accidents of this era were caused by structural failures. Examples of accidents caused directly or indirectly by structural failure are the Roma, R-38, R-101, USS Macon, USS Shenandoah and many others.
The improvements in materials that are lighter and stronger have gone a long way towards eliminating the structural problems of rigid airships, but advances in engineering tools may be even more important. The last of the giant rigid airships ceased operations before the invention of the strain gauge in 1938. Now precise measurements can be obtained to determine the size and location of stresses. Moreover, the giant size of rigid airships means that ordinary wind tunnels were unable to represent the macro forces operating that that scale. However, computer software can allow this to be done, too.
No one knows what the upper limit is on the sizes of rigid cargo airships. It is clear that a rigid airship within the scale of what has already been accomplished 80 years ago could be economic. The impact of rigid airships two or three times this size will easily compete with jet airplanes, and could give long distance trucking a competitive challenge, too.