The Technological Principles of Airships – Part 2
After aerostatic flight, the next most important technological principle to understand about airships is drag. The drag equation explains why airships fly slower than planes, but more efficiently, and also why airships fly faster than ships sail. It also explains why airships have streamlined, aerodynamic shapes and why commercial airliners fly very high, while airships tend to fly at lower altitudes.
Principle 2. The Drag Equation, Efficient Flight, and the Rewards of Slowness
The drag equation describes the strength of the force of resistance that a vehicle encounters as it moves through a fluid. According to NASA:
Drag = drag coefficient * (density * velocity squared)/2 * reference area [~ the cross-section]
In order to overcome drag, a vehicle must use the power of its engines. In general, the amount of power required for forward motion can be calculated by the drag equation. The drag equation explains why the amount of output required from an aircraft’s engine per mile traveled depends on several factors including the shape, speed and altitude of flight.
Consequence 2.1. Why airships have streamlined, aerodynamic shapes
The first term in the drag equation, the drag coefficient, captures complicated differences in efficiency depending on a body’s shape and materials. The components are form drag, skin friction drag, and– importantly for airplanes– lift-induced drag. Drag coefficients are usually found empirically through wind tunnel tests.
Minimizing drag is an economic question because the cost of drag is higher fuel consumption. Expenses involved in reducing drag need to be weighed against the impact of living with it. Additionally, not all forms of drag are bad. In particular, it is lift-inducing drag that creates the aerodynamic lift employed by heavier than air vehicles. One type of blimp design, referred to as “hybrids,” makes use of lift drag to avoid the need for ballasting the airship after dropping off a load. These designs, by Lockheed-Martin and Hybrid Air Vehicles, employ a wider, flatter shape, like a catamaran, to increase the lift drag. This is achieved by means of a double hull that is like two blimps joined together at their middle.
Many, familiar shapes such as cubes, spheres and pyramids, have high drag coefficients (form drag). Streamlined bodies have far lower drag coefficients. This is why many modes of transport, including cars, airplanes, and some ships, have streamlined shapes. This is illustrated in the figure below by Kirilin (2015). High speed fish have evolved shapes that minimize the resistance of water.
Airships have relatively few features like wings or wheels for their designs to accommodate, so they can have especially streamlined shapes, though they do need fins for stability. The Flying Whales airship company in France has a video that shows a whale morphing into an airship in the sky. The resemblance is not accidental. Whales, too, move in a fluid medium, and need to have a streamlined shape to reduce drag, and fins for stability. Airships might almost be said to float or swim in the air as much as to fly in it.
Consequence 2.2. Why airships are slower than airplanes
The last term in the drag equation (reference area) is the area of the shape of the moving body projected in the direction of movement. Geometrically, that’s not exactly the same concept as the cross-section, but typically the reference area will be very close to the area of the cross-section at the thickest point.
Now, airships have to be very large, and it is especially helpful for lift capacity if they are quite fat. A consequence of this is that, at any given speed, airships will be draggier than airplanes of a similar weight and/or payload. Airships may also experience significant skin friction drag because of their large surface areas. This is another reason why they are slower than airplanes.
Relative to old Zeppelins, modern giant rigid airships might be able to reduce the deadweight of the frame and equipment through better materials and methods. Despite this they are still likely to be similar in size with a lower fineness ratio. Fineness refers to the ratio of the length of the vehicle to its diameter. Zeppelin airships were about 6:1 fineness, but new designs have lower fineness ratios that are closer to 4:1. Shorter-wider structures can be stronger but also encounter more drag because they have larger reference areas.
Considerably wider than airplanes, airships face more drag at any given velocity, and have to go more slowly to keep drag manageable. Airship top speeds are slightly faster than the highway speeds of trucks, e.g., 70 to 100 miles per hour, compared to hundreds of miles per hour for commercial jets.
Consequence 2.3. Why airships are faster than ships: air is much thinner than water
The second term in Equation 1, density, refers to the density of the fluid medium in which a body is moving. The more dense the fluid, the more drag a body moving through it encounters. This is a familiar experience if you compare walking with wading. Wading through water is considerably more difficult than walking on the ground. When you walk on the ground the drag you have to overcome is only air, whereas when you wade, the drag is that of water. Water is about 800 times as dense as air.
This part of the drag equation helps clarify why airships are able to move much more quickly than their waterborne counterparts. Ships and barges, usually move at about 12 to 15 miles per hour. For the same reasons a wader is outpaced by a walker as they move in water, rather than air d consequently facing far more drag.
Hydrofoil boats are the exception that proves the rule. These “ships that fly” use aerodynamic lift to rise most of the way out of the water, so they face much less water drag than other ships do. This reduction in drag is a direct result of using more fuel to increase speed producing lift, the result, similar to airplanes, is that they are far less fuel efficient.
Consequence 2.4. Why being slower than planes is good for fuel efficiency
Going slowly has a benefit that is explained by the third term in the drag equation. Drag is a function of the inverse of the velocity of the moving body, squared. It is not just that slower bodies use proportionally less fuel per minute; they use proportionally less fuel per mile. The square term means that faster travel becomes exponentially costly. Drag is increased by the airship’s huge size and low altitude operations, but this is offset by its slower speed. In fact, a jetliner that displaces only a tiny fraction of the air displaced by a giant airship may have similar drag because the jetliner is traveling so much faster.
If airships slow down a bit more, their drag can be less than that of airplanes with similar payloads. But care must be taken to not confuse physics and economics. The speed of an airplane may come at a large cost in fuel and carbon emissions, but it also generates great productivity. A jet airplane might be able to do five trips in the time that it takes for a cargo airship to do one. This is why passenger airships are likely to compete only to a limited degree with jet airplanes. Most travelers place a high value on their time. For cargo however, speed is less important than cost. Few freight shipments, with the possible exception of a human organ transplant, need to travel at 900 kilometers per hour. Goods regularly cross the Pacific Ocean in 12 hours by cargo jets, just to sit several days in a warehouse.
Airships would probably travel at top speed most of the time, foregoing the extra fuel efficiency they can get by slowing down. The reason is the opportunity cost of airships’ time. Making more trips per year could be more important than fuel savings.
Consequence 2.5. Why airships fly lower than planes
As any aircraft gains altitude, the atmosphere becomes thinner, and drag decreases. Every aircraft has an optimal height and cruise speed that maximizes its economic performance.
The heaviest, thickest air is found at low altitudes. Jet airplanes can reduce their drag by flying at 10,000 meters where the atmosphere is very thin. And this is also necessary for jet aircraft because they travel at such high speeds. Flying this high is unlikely to be an economic option for airships because their aerostatic lift is a function of the weight of air that they displace. At 2,000 meters, the density of air is about 1 kilogram per cubic meter, this drops to 0.4 kilograms at 10,000 meters. So, while a high-altitude airship would have less drag, it would also have only 40% of the total lift. Airships typically cannot sacrifice so much lift, because they need enough lift to offset their deadweight in order to fly at all. This gives airships a ceiling, an altitude above which they cannot fly, and the more weight, such as cargo or ballast, they add, the lower that ceiling is.
Flying lower and slower brings its own tradeoffs. The airship is subjected to more weather because it flies below the clouds, but it does not need to provide oxygen to the crew or cargo. Jet airplanes are constructed as pressure vessels, which are much more expensive to build than rigid airships operating at atmospheric pressure. Jet engines are also very expensive. An airship needs only lower cost diesel or gas turbine engines. Most cargo airships are likely to fly no higher than 2,000 meters. This will make many high mountain ranges impassable for giant cargo airships and force longer routing through some key mountain passes.
The combination of lower altitude and huge size means that a large, busy merchant fleet of giant airships would make a strong visual impression on people below. Whereas jets cruising at 35,000 feet are barely visible to the naked eye, giant cargo airships cruising overhead would probably appear larger from the ground than the sun or moon. Farm hands sweating in the hot sun in fields and orchards would sometimes thank a passing airship for a few seconds of shade.