Sitting on Cloud Nine: Airship Lift and Altitude Control

On the command, “Up Ship!”, the Graf Zeppelin dropped enough water ballast to render the ship 900–1200 pounds light. It rose vertically into the air, and at about 150 feet, started its first engine, on idle. At 300 feet, all engines were idling, and it gradually increased power, and proceeded on its way. Normal cruising altitude was 650 feet. (Dick 48).

Airships are able to leave the ground because of aerostatic lift, the buoyancy imparted to them by the displacement of air by a lift gas that is less dense than air. They are capable of making a vertical ascent, at least if there’s no wind.

In contrast, aircraft take off as a result of aerodynamic lift, a lift force created by the circulation of air around the wing. Unless equipped with pivoted thrust, like a Harrier jet, they need a runway on which to generate enough speed, and therefore enough lift force, to take off. Airships can benefit from aerodynamic lift, but only if specially shaped, or if propelled with nose up or down relative to the direction of travel.

In this article, we will examine how airships in the 1632 universe can generate lift and control their altitude. Warning: Very little of the information in this article is likely to be in “Grantville Literature”—unless the resident balloonist, Marlon Pridmore happens to have it in his head or in his personal library—and it will need to be rediscovered, possibly the hard way.

Milestones in Airship (and Balloon) Lift

Hot air. The first use of hot air for lift of a manned vehicle was on November 21, 1783, in a balloon built by the Montgolfier brothers. Unmanned hot air balloons were used in China many centuries earlier, and in Europe in 1709. The combination of hot air lift with an engine, resulting in a true airship, came much later, in the 1970s. (Escher).

Steam. In 1815, Cayley proposed use of steam instead of heated air. The first balloon using superheated steam is the HeiDAS UH, launched in 2006. (Festo, Stein).

Hydrogen. Hydrogen was discovered in 1766 (by Cavendish) and the first manned hydrogen balloon flight was made by Charles and Robert on December 1, 1783. The hydrogen was generated by the acid-iron process. For this and other methods of producing hydrogen, see Cooper, “Hydrogen: The Gas of Levity” (Grantville Gazette 38).

Coal gas. Coal gas, made by destructive distillation of coal, is a mixture (typically 45% hydrogen, 40% methane, 5% carbon monoxide—Roth 24), and was used by Charles Green on July 19, 1821. It was a popular lift gas until the introduction of helium.

Natural gas. Natural gas, obtained from gas wells, is also primarily methane (90%?), although the mix of hydrocarbon gases varies depending on the field. (It’s perhaps worth noting here that most of the hydrocarbons, other than methane, are denser than air and therefore reduce lift.) Its first practical use for ballooning appears to have been by Carl Myers in 1886 Pennsylvania, who ran it through a heated pipe (to increase lift) and thence into the envelope. (Myers)

Helium. Helium was first used in the Navy C-7 on December 1, 1921.

Ammonia. While ammonia was proposed as a lift gas as early as 1883 ( Baden-Powell, 750), and an ammonia balloon was featured in an 1897 adventure story (George Wright, “Up the Matterhorn in a Boat”) the first true-life manned flight of an ammonia-filled balloon was reportedly on January 7, 1991 (balloonlife.com).

Hybrid (combined aerostatic and aerodynamic lift) airships. The PA-97, a chimera of a Navy ZPG-2W blimp and four old H-34J helicopters, was test flown on April 26, 1986 but crashed in July. A one-sixth model of the Skycat, the “SkyKitten,” was test flown on July 23, 2000. As the “cat” implies, this is a double-hulled craft.

Simple vs. Compound Aerostats

In a simple aerostat, such as the Goodyear blimps, the gas cell envelope is also the hull of the airship, and defines its aerodynamic properties. Unfortunately, if gas leaks, it’s lost completely.

In a compound aerostat, such as the LZ130 Graf Zeppelin, an outer envelope encloses an array of internal gas cells (LZ130 had sixteen.). If the gas leaks from the gas cells of a compound aerostat, it’s still retained by the outer envelope, and thus still provides lift. However, a compound aerostat is more expensive to construct, the leaked gas may reach dangerous concentrations, and maximum lift is limited because there will be air between the inflated gas cells.

Buoyancy

Buoyancy (aerostatic lift) is dependent on the density difference between the lift gas and the outside air; the gross lift is the total weight of air displaced minus the weight of the gas. If the lift gas is lighter than air at ambient temperature, then aerostatic lift can be generated without any expenditure of fuel. For a thermal airship (lift provided by hot air or other gas), fuel is needed to heat the air and thus provide lift. Fuel consumption can be reduced by insulating the envelope—so heat loss to the atmosphere is slower—but this adds weight and cost. (Konstantinov).

Dilute lift gases behave similarly to ideal gases, for which density in kg/m3 can be calculated as equaling

(molecular mass in amu/22.4)*(273/temp oK)*(pressure in atmospheres)(Equation 1).

The buoyancy provided by a lift gas is typically quoted in terms of mass lifted against normal gravity per 1000 cubic feet or per cubic meter of gas. The literature values vary, even for the same gas, and that’s because the actual lift provided depends on the purity of the lift gas, the proportions and molecular weights of any contaminating gases, and the temperature and pressure at which the density of the lift gas was measured. The reference temperature is typically 0, 15, 20 or 25oC, and the reference pressure is 100 or 101.325 kilopascals. Table 1 presents some typical values:

Table 1: Lift Gas Density and Buoyant Lift

Lift Gas

Molec.

Mass amu

Density

kg/m3

Density

lb/1000 cf

Mass Lifted lbs / 1000 cf

Hydrogen

2

0.084

5.2416

71

Helium

4

0.169

10.5456

66

Methane

16

0.676

42.1824

34

Ammonia

17

0.718

44.8032

32

Steam

20-29

0.587

36.6288

40

Hot Air

~29

0.921

57.4704

19

Normal Air 15oC

1.225

76.4743

http://www.flyingkettle.com/conpaper.htm http://www.chem.hawaii.edu/uham/lift.html

Lift varies with ambient conditions; it decreases when the ambient temperature increases (making the outside air less dense, so less of a density difference) and of course the reverse is true. An increase in humidity decreases lifting power (Dick 65), and also increases weight through absorption of water by the envelope fabric (71), so flying in the tropics presents special difficulties.

Choice of Lift Gas

For the 1630s, the most practical lift gases are hydrogen and hot air. The concern with hydrogen is safety; hydrogen-air mixtures in the range of 4–75% are flammable (and 15–59%, explosive), at standard temperature. Such dangerous mixtures could be formed by the leakage of hydrogen when the gas cells are filled, or by inflow of air and outflow of hydrogen into the envelope during flight. Fortunately, hydrogen rises, so escaping hydrogen is likely to move away from the engine pods.

Helium provides about 93% of hydrogen’s lift. But forget it; it’s available only from certain yet-to-be-mapped, let alone drilled, gas fields in the Oklahoma-Texas area. In 1921, helium cost $55–60/1000 ft3 (versus 5–10 for hydrogen) to produce. (Tucker 271). Even in the Twenties, there wasn’t enough helium available to keep two large airships (Shenandoah and Los Angeles ) flying simultaneously (Vaeth 32).

Methane, ammonia and steam are also possibilities. Methane and ammonia both have narrower flammability limits than hydrogen; 5.3–14% for methane and 15–28% for ammonia. Unfortunately, they also provide less lift than hydrogen; 48% (methane) or 44% (ammonia). (Morris IV-5). Also, ammonia is both corrosive and, in high concentrations, toxic. Its principal advantage is easy liquefaction for buoyancy control.

Ammonia may be decomposed, by application of heat, to yield a mixture of hydrogen and nitrogen that provides more lift (76% hydrogen). However, this mixture has a flammability limit almost as broad (7–73%) as that of hydrogen. ( Id. )

As for hot air, unfortunately it only provides about 27% (for a typical temperature) the lift of hydrogen, and of course fuel must be burnt to keep it hot. Initially, the entire gas bag volume must be heated to the “lift” temperature; the fuel required is proportional to the volume. Once the gas bag contents are at the right temperature, keeping it there is a matter of supplying enough heat to compensate for heat losses. The rate at which heat is lost is, at first approximation, governed by Newton ‘s Law of Cooling; it’s proportional to the temperature difference, and to the surface area of the gas bag. The first factor implies that increasing the working temperature, to increase lift, requires a greater fuel consumption rate. And the second one implies that from a burner fuel efficiency standpoint, the more spherical the gas bag, the better. Of course, if the gas bag is also the aerodynamic envelope of the airship hull, this must be weighed against the effect of the shape on drag, and therefore on consumption of fuel for propulsion.

Saturated steam can provide perhaps 56% of the lift of hydrogen, more than twice as good as hot air. (flyingkettle.com) And superheated steam will provide even greater lift. But presumably the burner fuel consumption rate will also be higher. More importantly, steam, especially supersaturated steam, is highly corrosive. (Bormann).

Why Engineers Abhor a Vacuum . . . .

It’s likely that some well-meaning inventor, or a con artist, will propose a “vacuum airship,” i.e., one in which lift is provided by the absence of air rather than by a less-dense-than-air lift gas. In 1670, Francesco Lana-Terzi reasoned that since, according to Archimedes, a body will float in a fluid if the volume of fluid it displaces weighs more than the body itself, an airship could be buoyed up by copper spheres from which the air was evacuated, as a vacuum by definition is less dense than air.

A sphere containing a perfect vacuum would provide about 10% more lift than a hydrogen gas cell of the same volume. Unfortunately, the cell wall would need to be strong enough to withstand the pressure of the air—14.7 pounds per square inch (101,325 newtons/square meter) at sea level—and the weight of the vacuum cell wall would be far greater than the additional lift provided.

We can define a “figure of merit”; the ratio of the additional lift provided by replacing the lift gas with the vacuum, to the additional weight of the vacuum cell wall. That ratio has to be greater than 1:1 for the replacement to make sense.

The derivation is in Appendix 1, but the ratio is equal to

(2/3)*compressive strength of wall material*density of lift gas/(pressure difference*density of wall*safety factor).

With hydrogen as the lift gas, steel as the wall material, and a safety factor of two, (and ignoring the weight of the thin rubberized cloth envelope of the hydrogen airship since it will be a lot less than the steel), the ratio is about 0.008–0.009:1. In other words, you would need a wall material whose ratio of compressive strength to density is more than one hundred times better than that of steel for a vacuum airship to have a gross lift less wall weight equal to that of a hydrogen airship of the same dimensions!

Superheating and Supercooling

Depending on the nature of the airship skin, heat transfer through it may be slow or fast. Hence, the gas inside the airship may be hotter (“superheat”) or colder (“supercool”) than the outside air. Airships have reported as much as 66oF superheat and 9oF supercold. (Robinson 214). To measure superheating/cooling, the Graf Zeppelin had both an air thermometer in the control car and a remote electrical thermometer in the interior of a gas cell. (Dick 196).

The density of hydrogen and helium decrease from 0.075 and 0.151 at 50oC to 0.036 and 0.072 at 400oC. (Konstantinov/Thermal). Thus, superheat increases and supercool decreases lift; but of course these diminish with time as heat transfer progresses. Nonetheless, an airship may time its launch to take advantage of superheat.

Supercooling can be a significant problem; the L59 experienced 9oF of supercooling at night over the Egyptian desert, and its captain estimated that the ship dropped 4% (6600 pounds) of its lift in ballast each night to compensate for evening heaviness (i.e., to maintain cruising altitude). On the other hand, for helium airships trying to land, nighttime supercooling was a blessing as it permitted a descent without venting.

Altitude Effects

The airship can only climb to the altitude at which the buoyant force equals the total weight of the airship. To ascend, it must have excess buoyancy, and it will stop ascending when the reduced atmospheric pressure brings the buoyant and gravitational forces into equilibrium. Hence, buoyancy control (see below) is critical.

As the airship ascends, the outside air pressure and temperature decline, and the air density also declines. Even if the lift gas density remained constant, this would reduce the density difference between the two, and thus reduce buoyancy. However, the lift gas density will also decline.

First, if the lift gas is hotter than the atmosphere, heat will be transferred across the skin, at a rate proportional to the temperature difference, unless and until the difference disappears. This equilibration process will be slower if the envelope is of an insulating type, and faster if it isn’t, but if the airship remains aloft, its lift gas temperature will converge on the ambient air temperature.

Secondly, the gas cells of the airship will be at a pressure that is either equal to that of the ambient air, or differs from it by no more than a fixed amount (overpressure). This means that as the airship ascends, the lift gas pressure will ultimately decline, too.

Airship gas cell management is inspired by ballooning practice. In a zero-pressure balloon, the pressure inside the balloon always equals the pressure of the surrounding atmosphere. (With hot air balloons, this is accomplished with a simple vent hole, and with helium balloons, with ducts.) Hence, if the balloon rises, its volume expands. (The balloon when launched is only partly inflated.) The disadvantage of the zero-pressure design is that outside temperature and humidity changes result in frequent release of lift gas and dropping of ballast and therefore reduce the time aloft.

In a super-pressure balloon, the envelope is completely sealed, and volume is kept constant by maintaining a constant pressure. If so, when the balloon ascends, its internal pressure will be higher than that of the ambient air; the difference is called overpressure. The disadvantage of the super-pressure design is that overpressure places stress on the balloon skin. The tensile strength of the skin will determine the maximum acceptable overpressure; automatic valves release lift gas when needed so this value is not exceeded.

In non-rigid and semi-rigid airships, the shape of the envelope is determined by the lift gas pressure, and overpressure is necessary for the airship to have a constant and aerodynamically sound shape.

In hot air ballooning, overpressure is maintained by pumping air into the envelope with an on-board fan. On hydrogen and helium non-rigid and semi-rigid airships, prior to takeoff, air is pumped into an air bag (ballonet) that lies inside the lift gas envelope, thereby compressing the lift gas. As the airship ascends, air is expelled from the ballonet, allowing the lift gas to expand without changing the total volume of the gas bag and its internal air bag. A typical overpressure for a modern non-rigid or semi-rigid airship would be 0.0045–0.0065 bar; a car tire has an overpressure of about 2 bar. (globalsecurity.org).

The altitude at which the air ballonets are empty, and thus the lift gas volume is at its maximum (for the maximum allowed overpressure), as a result of the reduction in atmospheric pressure with height, is sometimes called the “pressure altitude.”

If the airship descends, the air bags must be re-inflated, and this may be done with engine-driven blowers or, better, by scooping the air from the slipstream of the propeller.

In general, it was found that it was better to have two ballonets, rather than one, so that by differential inflation the trim of the airship could be adjusted. This had the disadvantage of requiring more material to contain the same amount of air. However, some material could be saved by use of an integral ballonet; one side of this ballonet was a part of the outer envelope. (Maintenance of integral ballonets is more complicated.)

It should be evident that the ballonet will have a maximum volume that is determined by the uninflated surface area, and the stretchiness and ultimate tensile strength of the material from which it’s formed. This volume, in turn, will determine the pressure altitude. In the case of the Navy’s B-class airships, it was decided that the ballonet volume should be 25% of the envelope volume, allowing compensation for the change of pressure equivalent to a 7500 foot change in altitude. (Hunsaker 1354). That’s still a fairly common allotment for a non-rigid (26% for the Skyship 600), but I have found both higher and lower values. For example, a WW I French Scout was 37% (2400/6500 m3) (Hunsaker 780), and the Chalaise Meudon-5 was 41% (131,455/320,555 ft3). (CM5). The lowest I have found was 7% for the Wasp RPB drone. I would say that most non-rigids are in the 20–30% range.

Ballonet “slosh”—oscillation of the ballonets as a result of the longitudinal motion of the airship—has been reported, and it apparently had an effect on the handling of the K-class blimps. (Zitarosa).

In a rigid airship, since the outer envelope has a supporting structure, the lift gas could in theory be held in zero pressure gas cells; the envelope would maintain its shape. However one would still have the need to vent gas if the pressure altitude is exceeded, i.e., the gas cells are fully inflated. On the Graf Zeppelin, spring-loaded automatic valves opened if the overpressure exceeded 7-15 mm water—7 mm is 0.000686 bar or 1.43 psf. (Dick 189).

If the gas cells are of the zero pressure type, then to reach a height of 5,000 feet (where the air density is 86% that at the earth’s surface), without venting, they would have to be inflated only to 86% capacity at takeoff. That means, of course, that you can only count 86% of the maximum gas volume in calculating the initial lift if you want that altitude capability (without wasting gas). On the other hand, if you were content with 1,000 feet, the air density is 97% that of sea level, so you can start at 97% inflation.

I should note that there are two basic methods of filling a gas cell or envelope: closed fill-up and displacement fill-up. In closed fill-up, the cell is emptied, then the gas is introduced. In displacement fill-up, the cell is initially inflated with air (or some other non-lift gas) and then the air is pushed out by the lift gas. Since the lift gas is (by definition) lighter than air, it will diffuse to the top of the cell and then push the air down and out. For hydrogen, closed fill-up is the norm. Displacement fill-up would result in dangerous hydrogen-air mixtures during the filling process.

Even if the goal is 86% average inflation, that doesn’t mean that every gas cell is inflated to 86%. The gas cells are typically of different sizes, depending on their location within the hull, and you might achieve 86% by inflating say seventeen of twenty gas cells to 100% and leaving the other three empty.

The Graf Zeppelin usually took off 660–1320 pounds light; its pressure altitude increased roughly 33 feet for each 220 pounds of lightness. Its preferred cruising altitude was 575–820 feet. (Dick 67–8). At the latter altitude, air density averaged 97.65% sea level.

Because fuel is burned during flight, the airship gets progressively lighter, and her pressure altitude increases. At cruising speed, the Graf Zeppelin‘s pressure altitude increased at a rate of 72 feet/hour if lift gas wasn’t being vented.

Aerostatic Gross Lift Calculations

The gross lift provided by the gas cells is the lifting power of the gas (in pounds per thousand cubic feet) multiplied by the actual gas volume (in thousands of cubic feet). (The useful lift is the gross lift less the deadweight, but the estimation of deadweight is outside the scope of this article.)

It’s quite easy to overestimate the gross lift provided by an airship; you must remember to consider (1) the effect of shape on hull volume, (2) the relationship between gas capacity and hull volume, (3) deliberate under-inflation to account for altitude effects, and (4) gas purity and temperature.

Hull volume is dependent, not only on the length and diameter of the airship, but also its precise shape. Table 2 shows how shape affects hull volume for two hypothetical airships, the Royal Anne of canon and a smaller, less elongated airship.

Table 2: Variation of Airship Hull Volume with Shape

“Royal Anne”

650 x 70 feet

‘Flying Fish”

150 x 60 feet

Cylinder with hemispherical caps

2,411,696

367,566

Ellipsoid

1,667,662

282,743

Hemisphere-Tangent Ogive

1,353,257

240,703

Hemisphere-Cone

878,730

169,646

These shapes all have a circular cross-section; the volume will be lower for a given length and maximum diameter if the cross-section (viewed from front) is elliptical. The R100 was “flattened” to expose less surface to side winds during landing and takeoff. (Post).

For a rigid airship, gas capacity is less than hull volume (air displacement). If the airship uses internal gas cells inside an outer envelope, as on the zeppelins, clearly the total volume of the gas cells is going to be less than the nominal envelope volume. If the airship were a cylinder with a length equal to four diameters, and was filled with four spherical gas cells with the same radius r, the volume of the airship hull would be 8*pi*r3, whereas the total volume of the gas cells would be 16/3 * pi*r3, so the maximum gas volume of the compound aerostat would be only two-thirds that of the simple aerostat of the same outer dimensions. In fact, that’s why the zeppelins have gas cells of different sizes; they can be packed more tightly.

Not only is it difficult to pack the gas cells together so that there’s no interstitial space, you wouldn’t want to do it even if you could; you need internal passageways in order for the crew to properly maintain the gas cells, the envelope, and the supporting structures. And if any of the crew, passenger, or machinery compartments are recessed into the hull to reduce drag, they will also reduce the volume available to hold lift gas. Table 3 compares maximum gas cell volume to hull volume for several rigid airships:

Table 3: Gas Cell Volume Relative to Hull Volume

Airship

Gas Cell Volume

Hull Volume

GCV as %HV

Shenandoah

2,115,174

2,289,861

92.4

R38

2,724,000

2,960,000

92.0

Los Angeles

2,599,110

2,764,461

94.0

Akron; Macon

6,850,000

7,401,260

92.6

(Robinson App. E).

Moreover, the gas cells aren’t necessarily full. To avoid venting gas on ascent to cruising altitude, rigid airships (which are complex aerostats) may takeoff with their gas cells only partially inflated, and non-rigid airships (which are simple aerostats) leave the ground with the internal air ballonets inflated. The catch, of course, is that this means that you can’t calculate the airship’s gross lift on the basis of the total volume of the envelope; you must multiply by the fullness of the gas cells for a rigid, or subtract off the volume of air that’s in the ballonets on takeoff for a non-rigid.

Helium rigid airships generally had “flabby” gas cells, no doubt as a conservation measure. On one occasion, the USS Shenandoah took off 91% full (Robinson 105) and another just 85% (86); the latter appears to have been the norm (Hedin 163, Toland 94). The USS Los Angeles was variously recorded as starting flights 80% full (155) and 86% full (161).

For hydrogen rigid airships, I get conflicting answers. Robinson (213) says that “hydrogen ships usually took off 100% full . . . ” and Dick (188) says that “the gas cells were always 100 percent full, or nearly so, at takeoff . . . ” If so, they would vent until they reached cruising altitude. However, Whale asserts that in high altitude air raids on England, the German rigid airships “commenced the flight with gasbags only about 60 per cent full” so the bags could expand without venting, and on Graf Zeppelin flight 366, the gas cells averaged 80.7% inflated at takeoff (Dick 72).

With regard to purity, the gas is at its maximum purity just after its initial manufacture and purification. After that, hydrogen will leak, and air will filter in, progressively reducing lift. The gas was typically analyzed daily for purity as long as it was over 90% pure, otherwise more frequently. Once it fell below 85%, it was necessary to deflate and refill. (Tucker 315; Dick 193).

Keeping Trim

Imagine a child sitting on a seesaw. A force (weight) is applied to the seat. Since the point of action is at some distance from the fulcrum, the seesaw pivots, child going down, other end going up. In physics term, we created a pitching moment, the product of the force and its action point’s distance from the fulcrum (“the moment arm”).

An airship is subject to several different forces, all acting along different lines. Its weight acts downward through the center of gravity (CoG); buoyant force at upward through center of buoyancy (CoB); drag backward through the center of pressure; hull aerodynamic lift, if any, perpendicular to the airflow and through the hull’s aerodynamic center; thrust forward along the propeller axis. And of course the craft’s also subject to unsteady forces, like the wind.

Because of the weight of the engines, etc. in the cars slung below the envelope, the CoG is usually below the CoB; 10 feet on the NS non-rigid. (Bairstow 511). The CoB is also not at the geometric center of the hull; on Navy C-class blimps it was 46.37% of length from the nose. (Burgess 72). The hull’s aerodynamic center (per thin airfoil theory) is at the 25% mark.

Just to complicate matters further, the forces may be distributed in a way that creates additional moments. For example, if the airship is inclined upward relative to its flightpath (positive angle of attack), there will be an upward aerodynamic force on the forebody and a downward one on the aftbody. Even if these added up to zero, they would still try to rotate the ship to a steeper angle. Gas cells and weights are also unequally distributed, and there’s usually more than one propeller.

All forces acting ahead or behind the fulcrum (for airship analysis, the CoB or CoG is used) create pitching moments. While, in steady flight, lift equals weight, and thrust equals drag, if unaligned these create unbalanced pairs of moments (“couples”) and cause rotation. The airship maintains its present pitch (trim)—the angle of its longitudinal axis with the horizon—only if the moments add up to zero.

If that’s not true (inadvertently or deliberately), then the net pitching moment causes the inclination to change. This in turn changes one or more of the component moments. If the effect of the change is to cause a net restoring moment, putting the inclination back as it was, the ship is longitudinally stable. And if it’s to upset the inclination further . . . you’ve lost control! Obviously, you want to design the airship so that there will be restoring moment, assuring longitudinal stability. In analyzing stability, airship designers have to consider all the possibilities: nose up, down or level; airship statically heavy, light, or (this almost never is the case for long) in equilibrium.

Normal trim is considered to be that at which the center of buoyancy is directly over the center of gravity. The airship is “in trim” if this occurs with the airship horizontal. If the propellers are mounted in pods set lower than the CoB they force the nose up, so a counterbalancing aerodynamic force is needed.

Since aerodynamic forces are proportional to the square of the speed, and static forces (gravity and buoyancy) are independent of it, pitch instability occurs if the airship exceeds a critical speed. The critical speed is increased if the airship is equipped with a horizontal tail fin to serve as a stabilizer; if the ship is inclined, the aerodynamic lift force on the fin rotates the ship in the opposite direction to the one on the hull; it creates a restoring moment. Increasing fin area increases pitch stability, but also increases drag and weight. The horizontal fin area on Navy K-class blimps was 992 ft2, and generally speaking this area should be about 35% of the volume divided by the distance from the fin to the CoG (Boeing-Vertol).

La France (1884) was the first airship to use an elevator (D’Orcy 59). Elevators (essentially, tail surfaces that pivot up and down) create additional aerodynamic forces and thus pitching moments; in level flight they are angled to neutralize the other pitching moments. Since they work aerodynamically, elevators are effective only if the airship is in motion. On Navy blimps, the elevator area was about one-quarter of the horizontal fin area. (Burgess, DM386). Please note that up-elevator doesn’t raise the nose, it drops the tail—worth remembering if you’re in a 600-foot long airship and you’re only 300 feet above the ground! (TM50).

Another curious point is that if the airship is below what’s called the “reversing speed,” up-elevator doesn’t encourage ascent. Up-elevator still drops the tail, but only slightly because the moment created by the elevator is small compared to the restoring moment from the weight of the airship, and the inclination of the hull is small. As a result, the upward force on the nose is less than the downward force on the elevators and the airship is pushed downward despite the action of the propellers. The problem is greatest when the airship is trimmed nose heavy. (TM 51).

There’s such a thing as having too much stability. If the restoring moments are too strong, the airship becomes difficult to maneuver; it doesn’t want you to change pitch. Worse, they may cause you to keep overshooting the desired orientation. If you drop the CoG to increase stability (weight then fights a change in pitch), you increase the “reversing speed.”

The pitch of an airship may be deliberately changed by shifting its center of gravity (shifting ballast, cargo, crew or passengers), shifting its center of buoyancy (pumping air between its forward and aft ballonets or transferring lift gas between its forward and aft gas cells), or creating an aerodynamic pitching moment with its elevators. The Zeppelin LZ1 (1900) used a moveable 300 pound lead weight, but unfortunately this jammed (Botting 37). Elevators (used on the LZ2) were more practical.

The Problem of Altitude Control

For a balloon to ascend, there must be positive net buoyancy, and to descend, negative. However, if an airship is in neutral buoyancy (buoyant force=gravitational force) it may ascend or descend by pitching itself relative to the ground, so the thrust from its propellers, exerted parallel to the axis of the airship, has a vertical component. It can ascend or descend in heavy or light condition, too, but the glide angle (between flightpath and ground) won’t equal the pitch and the angle of attack won’t be zero.

As long as its lift gas has not reached its maximum permissible volume, an airship may ascend without venting lift gas. However, if it climbs above its pressure altitude, and therefore vents lift gas, it will have to drop ballast, or otherwise adjust its net buoyancy, to compensate.

On the German commercial zeppelins, pitches greater than five degrees were avoided; “at eight degrees bottles and glasses fall over.” (Dick 208). Hence, if you need to make a steeper ascent, say, to avoid a mountain that just loomed out of the fog, you will need to suddenly and substantially increase net buoyancy, say, by dropping ballast. Or for a fast descent, perhaps to land in a mountain valley, vent gas.

In the course of cruising, the airship may experience changes in buoyancy and weight, and need to neutralize the resulting change in net buoyancy in order to maintain altitude. We have already mentioned that weather conditions may cause the envelope to be superheated (making the ship light) or supercooled (making it heavy). Or the envelope may be made heavier by rain or snow. Or you might encounter a strong updraft or downdraft.

Fuel acts like ballast; as it’s consumed, the airship gets lighter. On the other hand, gas gradually leaks out of the envelope, reducing lift. Chances are that these two opposed effects will not be in balance, which means that buoyancy will have to be adjusted if you want to maintain your altitude. When the German-built USS Los Angeles was delivered to the United States, 850,000 cf (one-third gas capacity) had to be vented to compensate for the 29 tons fuel consumed. (Dick Ch. 8 n.5).

The effect of fuel consumption may be muted by the use of gaseous fuel. Fuel is provided from a ballonet that instead of being filled with air, contains “blau gas,” an artificial gaseous mixture of hydrocarbons (mostly propane) whose density is about the same as that of air. That means that as long as the airship is burning it as fuel, it can just replace the blau gas with ordinary air without a change in buoyancy. (The ballonet shrinks and the volume it formerly occupied is taken up by fresh air.) This technique was used on the Graf Zeppelin (De Syon 130); of its 3.3 mcf of lift gas, 0.75 was blau gas. (Dick 32). The US Navy K-1 blimp had a 51,700 cubic foot propane ballonet for the same purpose.

Still, there are going to be occasions in which the airship needs to adjust its net buoyancy.

Table 4 lists both standard and speculative methods of buoyancy control:

Table 4: Airship Buoyancy Control.

If Airship Is . . .

Comments

Too Light, Decrease Net Buoyancy by . . .

Too Heavy, Increase Net Buoyancy by . . .

Venting Lift Gas

(off-base production of lift gas)

venting wastes gas; carrying reactants for off-base production not weight-effective

Cooling Lift Gas

Heating Lift Gas

standard practice for hot air airships

Re-Ballasting

Dropping Ballast

ballast supply limited, replacement slow or erratic.

Flying Nose Down

(negative dynamic lift)

Flying Nose Up

(positive dynamic lift)

speed-dependent, increased fuel consumption

(Burning Lighter-than-Air Fuel, replaced with air)

Burning Heavier-than-Air Fuel, replaced with air

slow adjustment.

(Compress or Liquefy Lift Gas to Storage)

(Decompress or Evaporate Stored Lift Gas)

not yet practical, except for certain steam airships

Directed Thrust Upward

Directed Thrust Downward

weight, strength, and pitching moment issues

I analyze these options in more detail below.

Buoyancy Control: Manipulating the Supply of Lift Gas

All non-thermal airships are equipped to vent lift gas when the airship is too light or gas pressure has reached a dangerous level. Since the lift gas isn’t free, venting increases operating costs. Venting helium is even more painful than venting hydrogen, because helium is so rare and expensive. At one time, the Hindenburg was intended to use a combination of hydrogen and helium cells; the idea was that the cheaper hydrogen (“anti-ballast”) would be vented when lift had to be reduced. (Dick 93).

An alternative to venting hydrogen is to add it to the fuel feed. That doesn’t solve the problem of permanent loss of lift capability but it at least reduces fuel consumption. However, burning hydrogen is tricky because hydrogen is so volatile. The concept of using hydrogen for both lift and propulsion dates back at least to 1872, when Lenoir tested it in a dirigible scale model (Syon 10). The Germans experimented with it further, but weren’t able to perfect it. (Stocky). However, burning hydrogen did have the advantage that it produced plenty of water, recoverable for ballasting use, in the exhaust. (Dick 102).

Regardless of whether the lift gas is deliberately vented, it will leak out over the course of the flight.

****

It may occur to the reader that the airship might manufacture new hydrogen at an impromptu stopover or even in the air. Unfortunately, this isn’t practical. As I showed in “Hydrogen: The Gas of Levity” (GG38), Table 2, for most field production methods, the weight of the reagents exceeds the weight that would be lifted by the hydrogen they produce. And that’s without even counting the weight of the apparatus, or fuel for generation of heat.

The only exceptions are the hydrolith (calcium hydride) and activated aluminum-water processes. But these use very expensive reactants, and the reactions are very vigorous (translation: you’d have to be crazy to try to carry them out on an airship).

It would be nice if you could electrolyze the water ballast on board to obtain hydrogen and oxygen; you’d simultaneously eliminate the weight of the water and gain the buoyant lift of the hydrogen (the oxygen would be discarded). But the weight cost of the electrolytic apparatus and of the batteries or fuel for generating the necessary power would outweigh the advantage of on-board production.

In 1925, the airship tender Patoka carried a portable hydrogen generator for emergency use. (Robinson 223 n. 54).

Buoyancy Control: Initial Ballast

To increase net buoyancy by dropping ballast, you must have ballast to drop. Buoyancy devoted to carrying ballast isn’t used to carry payload.

In order to cross mountains in Arizona, the USS Macon had to ascend to 6,000 feet. However, its pressure height (the height at which its gas cells were fully expanded) was less than 3,000 feet. Hence it had to both vent helium, and dump 9,000 pounds of ballast and 7,000 pounds of fuel to compensate for the consequent loss of buoyancy.

Ballast may be solid (sand, lead shot, steel pellets) or liquid (water). Water has the advantage that it can be pumped from one end of the airship to the other to adjust trim, used if need be for washing, drinking, or cooling the engines, and replenished from the ocean or from a rainstorm. The ballast could be carried “in rubberized bags (Graf Zeppelin) or metal tanks (Hindenburg). ” (Dick 189). Ballast is precious; on the Graf Zeppelin‘s round-the-world flight, wastewater from the toilets was recycled as ballast (Botting 16).

If the airship is flying under conditions under which water might freeze, denatured alcohol or glycerin may be added. (Although the L-55‘s ballast froze anyway when the zeppelin was forced by enemy fire to climb to 23,500 feet.) The Americans tried using calcium chloride as a cheap antifreeze on the Los Angeles and it corroded many of the keel girders. (Robinson 141).

Ballast has to be dropped quickly in an emergency. The moored USS Shenandoah (gas cell volume 2,115,174 cubic feet; total weight 129,000 pounds) was torn from its mast by a 78 mph gust. Its nose cap was wrenched off, and two of the twenty gas cells deflated. The crew dumped 4200 pounds of water ballast.

The Graf Zeppelin could drop 660 pounds of emergency ballast with a single pull (it had eight such bags), and each of the eight trim ballast bags could discharge 2.2 pounds/second. (Dick 67-8). On the Los Angeles, one 2,240 pound ballast bag could dump 400 pounds in ten seconds. (Robinson 208).

The more ballast the airship takes on board before takeoff, the greater its ability to drop ballast and perform an ascent without resort to dynamic lift, but the less its ability to carry payload.

So, how much is enough? That depends on how often and by how much the airship is expected to change altitude, which can vary from airship to airship and even flight to flight. A military airship that is dependent on high altitude flying to evade defenses will require more than a civilian airship that is going to be hugging the ground. A slow or large airship will need more, proportionately, than a fast or small one, as it will have less potential to benefit from dynamic lift. An airship with the ability to recover ballast from engine exhaust or to collect water from the environment can takeoff with less ballast than one lacking these capabilities. An airship flying under troubled meteorological conditions will want more ballast than one expecting clear sailing, and a long route or one with several stopovers until resupply warrants more than a short, nonstop one.

At a minimum, there should be enough ballast to compensate for the loss of lift in climbing to pressure altitude (for hydrogen, that would imply a ratio of ballast weight to ballonet volume of a non-rigid, or unused gas cell volume of a rigid, of 1.1). I would recommend that for a rigid airship, there be at least enough ballast, above and beyond that needed for this purpose, to compensate for rupture of a gas cell.

Based on historical data (Hunsaker 1355, Dick 67, 71, 112, Robinson 142, 156, 161), I think a reasonable ballast allotment is on the order of 5–10% of the total weight of the airship. Bear in mind that in an emergency, fuel, ammunition, wash water, provisions and even furniture can be dropped overboard.

Buoyancy Control: Re-Ballasting

You can acquire more ballast en route. This has been done in (at least) five different ways.

1. Collecting rainwater; there were rain gutters on the Graf Zeppelin and the Hindenburg. That’s obviously at the mercy of the elements (some flights produced no rain water, Dick 100), and the collectors create drag. On one flight, the Hindenburg collected eight tons rainwater (Dick 117), and on a second, ten tons (125), the latter saving 305,000 cf hydrogen that would otherwise have been vented.

You may also find that you acquire more weight than intended; the Shenandoah passed through heavy rainfall and had to drop ballast to compensate for the water absorbed by the outer cover of its envelope. (Robinson 89). In 1935, the Graf Zeppelin passed through a tropical rainstorm and the rain added seven tons to its weight. (Dick 56). The trick was to pick a light rain squall and just “brush it.” (100).

2. Collecting surface water. During WW I, airships landed on the ocean or a lake, dropped a sea anchor, and collected water. (Lehmann). While the Hindenburg was in development, the Germans tested a water pickup system (pump and hose?) over Lake Constance.

When the US Navy’s N-class airship needed ballast, it halted in mid-air (this was done by flying directly into the wind and balancing the wind force with the engines) and lowered a weighted bag on a winch cable through a trap door on the bottom of the blimp car. The bag could pick up 500 pounds of seawater at a time. (Rodrigues).

The ballast bag used on a WW II Navy blimp was twelve feet long, had “numerous one way openings along its sides,” and could hold 1,800 pounds seawater. It could be used not only to collect ballast but as an anchor. (Stimson).

3. Absorbing moisture from the air. In a test setup, the Zeppelin company found that 8.8 pounds of silica gel, exposed to 141 cubic feet per second airflow, relative humidity 67%, would extract 3.43 gallons water/hour. In practice, the silica gel would need to be transported to a heat source (engine exhaust) to vaporize the absorbed moisture, and this would be condensed and pumped to the ballast tanks while the dried gel was placed back in position. The system weight was expected to total almost 7000 pounds, and to require 5–10 hp for operation, and to produce 330 pounds water/hour. (Dick 99) The idea faded away, in part because there were superior alternatives.

4. Condensing water from the engine exhaust. In theory, the complete combustion of 100 pounds gasoline produces 145 pounds water. (Robinson 82). Three of the five 300 hp engines on the (helium-filled) Shenandoah were equipped with condensers; these recovered 100 to 112 pounds of water ballast from every 100 pounds of gasoline consumed. However, the condensers add weight to the airship, which reduces useful lift. Each condenser weighed 450 pounds (Robinson 82)—1.5 pounds/hp, but bear in mind that there would be additional weight for piping from engine to condenser and condenser to ballast bags. However, the condensers generated back-pressure and consequently water recovery was switched off when the engines were brought up to full power.

The water recovery apparatus on the Akron reportedly weighed 12,528 pounds (2.8 pounds/hp). (Burgess/DM120). The LZ130 (Graf Zeppelin II) system recovered “sufficient water to equal the weight of fuel consumed” and it weighed 11,466 pounds (2.4 pounds/hp). (Dick 156–7).

It may seem as though the later systems were a step backward, but required weight per horsepower increased with engine power. When the Shenandoah-type condensers were placed on the Los Angeles engines (400 instead of 150 hp), they proved troublesome; more powerful engines generated more heat, which warped the condenser heads. (Robinson 141).

The apparatus of the Los Angeles reduced speed 5–10% (Robinson 155). The Akron had “flat panel” condensers intended to reduce drag, but I don’t have particulars. The LZ130 didn’t suffer a speed penalty at all.

Buoyancy Control: Drag Rope (Recoverable Ballast)

A trick that may be useful for small airships is the guide or drag rope (Roth 11), first used on free balloons. For example, Charles Green’s Royal Vauxhall balloon (1836) carried a 300 meter drag rope. (Goebel). The airship pioneer Alberto Santos-Dumont first used a drag rope on a free balloon (17) and later on an airship (No. 7, 45,000 cubic feet) at sea (81).

The drag rope is a long, heavy rope that is paid out when the airship is near the ground, and serves to stabilize the altitude. If the ship descends, say because a cloud passes overhead, more of the drag rope lies on the ground, and thus the weight of the ship is reduced just as if ballast had been thrown overboard—except that the drag rope is recoverable. Or if the ship ascends, because a passenger jumped off, some of the drag rope is lifted into the air and then must be supported by the buoyancy of the ship. An obvious danger with the use of a drag rope is that it can get snagged in a tree.

Buoyancy Control: Temperature Manipulation

Thermal (hot air) airships. These may increase or decrease lift simply by adjusting the burner. However, the greater the size of the airship, the longer it will take for the temperature of the lift gas to change. Moreover, the higher the burner setting, the faster the burner fuel will be consumed, and once that’s gone, the thermal airship has the same aerostatic lift as Newton ‘s apple. Also note that for a thermal airship to adjust altitude in this manner, the gas cell material must be sufficiently elastic to tolerate the full range of internal volumes.

Superthermal Airships. A lift gas that is lighter than air even at room temperature may be artificially superheated to decrease its density and gain altitude, and then allowed to cool to lose altitude. (See discussion of superheating, above.) In Jules Verne’s Five Weeks in a Balloon (1869), the protagonist used both heated and cold hydrogen bags. Of course, heated hydrogen burns (or explodes) at higher state of purity than room temperature hydrogen (the upper flammability limit is about 75% purity at 80oF and 85% at 800oF).

Wikipedia/Buoyancy Compensator reports that the hydrogen cells on the Graf Zeppelin were preheated before takeoff by blowing heated air on them. This isn’t a very efficient heating method (low surface-volume ratio) but presumably running hot air ducts through the hydrogen cells would have added too much weight to the airship.

If you use artificial superheat, you have to worry about how quickly superheat would be lost. This is obviously dependent on both the heat transfer characteristics of the envelope and the size of the airship; large airships have a lower surface area: volume ratio and thus will lose heat to the outside more slowly.

When the Germans thought that the USA might let them buy some helium, they tested the practicality of artificially superheating helium (so they could use less helium to get the same amount of lift). Filling a gas cell with hot air, they found that supplying 100 kilowatts with an electrical heater gave it a superheat of 32oF after eighty minutes, and that with the heater off, it lost 0.9oF superheat in five minutes. (Dick 157). Of course, that didn’t really tell them how much energy it would take to superheat helium to the same extent.

There are obvious risks associated with artificially superheating hydrogen, however, note that the autoignition temperature of hydrogen is 1085oF—so the heater, by itself, isn’t likely to start a fire. But hydrogen’s flammability range increases as the temperature increases (CotD Fig. 1–6). So any artificial superheating of hydrogen would have to be accompanied by very stringent monitoring of hydrogen concentration inside the airship.

Semi-Thermal Airships. It’s possible to build an airship with separate hot air (for altitude control) and non-heated hydrogen or helium (for greater lift) cells. Such an airship wouldn’t need to drop ballast or vent hydrogen unless it needed to make a greater altitude adjustment than a change in hot air temperature permitted. These bags could be completely separate, or you could have concentric envelopes with one gas (probably the heated one) in the inner envelope and the other in the outer one.

The hydrogen-hot air hybrid balloon was invented by Jean-Francoise Roziere; the first such balloon crashed (without catching fire) on June 15, 1785. (Wikipedia/Roziere balloon).

If this design were adapted to an airship, you would of course have to make sure that the hydrogen didn’t mix with the combustion or exhaust gases of the engine (or the hot surfaces, etc. of the burner). You would want to position the hydrogen bag above the hot air bag (hydrogen is light, so it rises) and as far away as possible from it and the engines.

This concern is obviated if you employ a hybrid of hot air and helium for lift. While I don’t believe that this has yet been done to lift an airship, hot air-helium hybrid balloons have circumnavigated the world and set endurance records (Piccard and Jones, 477 hours, 47 minutes in the Breitling Orbiter 3, March, 1999). Unfortunately, it will be a long time before we have useable quantities of helium in the 1632 universe.

It has also been suggested that instead of using a separate burner to heat the helium, one could use aircraft engine exhaust heat. Rapert suggests that even a simple setup provides more than a 30% increase in gross lift.

Buoyancy Control: Dynamic Lift

As a substitute for venting gas, dropping ballast, or collecting new ballast, the airship may deliberately fly inclined; nose up relative to the flightpath to create positive dynamic lift if it’s “statically” heavy, or nose down to create negative dynamic lift if it’s statically light. The USS Shenandoah (2.1 mcf helium), with a useful lift of 24.4 tons, had maximum dynamic lift, 6000 pounds, at 12o up, and is known to have used negative dynamic lift (12o down when 3500–4000 pounds light).(Robinson 92ff). On Flight No. 366, the Graf Zeppelin didn’t have to use any of its ballast (Dick 72), presumably because of artful use of negative dynamic lift and the burning of blau gas as fuel.

Lift is dependent on the angle of attack. The angle of attack is the angle with which the chord (leading edge to trailing edge) of an airfoil (hull, fin, wing) meets the airflow (in still air, this is the flightpath). If the airship initially in horizontal motion is suddenly pitched upward or downward, the apparent wind will at first still be horizontal and the angle of attack will be the angle of pitch. But the forces on the aircraft will change in direction and magnitude, causing it to move in more or less the same direction that the nose is pointed, thus reducing the angle of attack.

Still, if the ship is statically light or heavy, the angle will not become zero. An airship with fixed axis propulsion may move horizontally with nose depressed if it’s statically light, or with nose elevated if statically heavy; the vertical components of the propulsive, gravitational and buoyant forces canceling out.

For a symmetric airfoil, lift should be zero at a zero angle of attack. Aerodynamic theory teaches that with simplifying assumptions (incompressible, inviscid flow; thin airfoil, small angle), the lift should be proportional to the angle of attack. Aircraft wind tunnel and flight data show that for a symmetric airfoil, the lift curve climbs linearly up to about 10–15o. Friction of air with the surface of the airfoil (“viscous flow”) forms a “boundary layer”. Increasing the angle of attack much above the linear range results in the separation of the boundary layer from the hull and thus a potentially catastrophic loss of lift: a stall.

Dynamic lift is proportional to the square of the air speed (Dick 70, Burgess 106). Since it’s generated by horizontal movement, it’s not useful at take off or landing (Burgess 288). Consequently, airships had to “weight off”—come to neutral buoyancy—before landing. And of course dynamic lift doesn’t help you make a purely vertical ascent or descent.

Reliance on dynamic lift has a quite literal downside; if an engine fails (causing loss of speed), you must rapidly drop ballast to avoid a crash. This happened to the L59 when its engines overheated over the Nile valley. (Dick 74). The Zeppelin LZ4 (1908) had the peculiarity that its engines had to be stopped.

While conventional airships don’t have wings, they do have fins. A fin may generate lift even when the hull is at a zero angle of attack if (1) it has a cambered profile, or (2) it is set at an angle (incidence) to the long axis of the airship. From the very scanty data I have (wind tunnel data and some photographs/drawings) my impression is that symmetric, zero-incidence fins were the norm.

Wind tunnel data on airship models suggests that, the fins contribute a substantial part of the lift (with increasing angle of attack, 70–55% for the Akron, 71–60% for the SSZ, 33–42% for the R23)(Klemin; Freeman). Since the lift area of an airship hull is perhaps 20–50 times that of the fins, that implies that the fins are much more efficient lifting surfaces per unit area.

I have used “thin airfoil”/”slender body” theory (an aircraft preliminary design tool) to model the aerodynamics of the fins and hull of an airship—in essence, they are treated as thin, stubby wings. The catch is that airship hulls are typically 9-40% thick (Royal Anne is 10.7% thick), whereas a real wing with 10% thickness (relative to chord) is considered “thick” and 20% is “very thick.” Still, the results were . . . interesting.

For a 1/40th scale model of the USS Akron, I calculated that the fins contributed only 40% of the total dynamic lift. The hull volumetric area-referenced lift coefficients for “hull only” were 364–144% those found in the wind tunnel, and for the fins (estimating, from a drawing, an aspect ratio of 1.26), 77–61%. For hull plus fins, it was 162–99% the experimental value, best fit at higher angles. Disappointing, at least for the lower angles we care about most.

But if you were to use my hull only formula to predict the wind tunnel hull+fins lift coefficients, the results were much better: my values were 108–65% of the experimental, with best performance at lower angles (I matched the experimental at 6o.)

Could this possibly be true for full-size airships? Burgess, Airship Design (1927), page 105, provides the dynamic lift curves for the USS Los Angeles, for different pitches and power levels, and I have compared four of the values (estimated from the figure) with my spreadsheet calculations.

Table 5A: Dynamic Lift for the USS Los Angeles

altitude of 3000 feet

Angle

Power

Speed

(ft/sec)

Reported Lift

(pounds)

My Calculation

Reported as % Calculated

4

80

6,000

8,362

71.8

8

half

70

10,000

12,814

78.0

7

full

95

~16,400

20,459

80.2

10

full

70

~12,200

15,984

76.3

And I found additional data in an obscure design memorandum (Burgess DM44):

Table 5B: USS Los Angeles, Dynamic Lift

(pounds)

altitude (3550 feet by my calculation) at which density is 0.00214 slugs/ft3

Speed: 82 ft/sec (55.9091 mph)

Angle

Observed

Burgess Calc

Hull Only

My Calc

Hull Only

Observed as % My Calc

2

2,200

4,080

4,320

50.9

5

6,360

6,100

8,640

73.6

6

10,100

12,060

12,961

77.9

8

13,800

16,000

17,281

79.9

10

17,000

19,660

21,601

78.7

Speed 59 ft/sec (40.22727 mph)

2

1,100

2,090

2,237

49.2

4

3,200

4,180

4,473

76.7

6

5,300

6,240

6,710

79.0

8

7,200

8,260

8,946

80.5

10

8,700

10,260

11,183

77.8

(Burgess calc is similar to mine except it uses the diameter of the “equivalent ellipsoid”—one with same length and hull volume—and Lamb’s “inertia coefficients”—which require hyperbolic functions to calculate. I don’t think the additional computational complexity is warranted by the slight improvement in accuracy.)

Astonishingly, the formula for hull did a pretty good job of forecasting the lift for the full-size USS Los Angeles, fins, cars and all. And instead of overestimating the lift, it consistently underestimated it! I will save speculation about these results for the Appendix. Here, it suffices to say that it appears that it’s worth quoting my “hull only” formula:

M=7.009 * V2*D2*rad*AoA/100,000 (Equation 2)

with

M, lifted mass (lbs)

V, air speed (mph)

D, diameter (feet)

rad, air density at altitude relative to that at surface,

AoA, angle of attack (degrees)

It’s up to you whether to use the hull only formula “as is,” or to multiply it by a fudge factor—0.75 would be a good choice for an airship similar to the Los Angeles.

****

A lift-induced drag is the price we pay for dynamic lift, and it reduces speed or increases fuel consumption. Theoretically, the lift-induced drag should increase with the square of the angle of attack.

For the additional propulsive power needed to overcome lift induced dynamic drag, we have

P=2.327 * M * V * AoA /100,000/e (Equation 3)

with

P power (hp),

M, V and AoA, as above

e, Oswald efficiency factor for the hull.

The necessary additional engine power will be higher, because the propulsive efficiency is less than 100%. (The derivation of equations 2 and 3 is shown in the Appendix.)

The Oswald efficiency factor corrects for the difference between the real distribution of lift along a wing and the most efficient (elliptic) distribution. The lower the Oswald efficiency, the higher the drag. Aircraft designers have formulae for predicting its value, but they are based on statistical analysis of normal aircraft wings, and I doubt they are useful here. For such wings, it’s in the range of 0.75–9. But an airship hull is like a very thick and stubby wing. I have found data for “lifting bodies” (like the Space Shuttle), and these had efficiency factors in the 0.35–0.67 range (Saltzman’99 Table 3). However, a NASA study (Ardema 5) assumed that an ellipsoidal hybrid airship would have an efficiency of 0.85.

Warning: My induced drag formula is based on thin airfoil theory. Burgess (DM201) reported that with a wind tunnel test of a model of the Akron, the induced drag increased with angle of attack more rapidly than the formula would predict on the basis of the observed lift, both for bare hull and with fins. So it’s quite possible that I’m underestimating the induced drag.

Burgess (105) comments that the maximum dynamic lift is likely to be at about 8o because at higher angles the increased drag reduces air speed—put another way, the airship doesn’t have the excess power to fully compensate for the increased drag that would be experienced if it also maintained speed. For the USS Los Angeles at full power, the maximum dynamic lift was at about 7o, with the air speed being about 95 feet/second.

He also observes that because dynamic lift is proportional to planform area, and buoyancy and weight to volume, for large airships dynamic lift is likely to make a smaller percentage contribution to total lift than for a small one and thus to compensate for the same percentage static lightness or heaviness—unless the power of the airship engines increases faster than the volume.

****

Thus far, I have pretended that the only way a conventional airship (symmetric hull) can generate dynamic lift is by inclining the airship. Well, there’s a second option: use the elevators. Up or down elevator refer to what happens to the trailing edge of the elevator; up-elevator creates negative lift; down, positive. And of course, lift creates drag.

So which is more efficient, generating lift by angling the hull, or by angling the elevator. It all comes down to efficiency, the ratio of aerodynamic lift to induced drag. Burgess (DM60) has collected some interesting model data, from which I have selected a few pairs:

Table 5C: Elevator Effect on Dynamic Lift Efficiency

Airship Model

Hull Angle

Elevator Angle

Lift

Induced Drag

Ratio

Shenandoah

2

0

.080

.003

26.7

0

-10

.085

.003

28.4

4

0

.155

.015

10.3

2

-10

.153

.010

15.3

Class C Blimp

15

0

.757

.195

3.88

10

-10

.751

.161

4.66

It’s clear that you can achieve about the same dynamic lift with less induced drag by generating the lift from the elevator not the hull. And there’s a good reason; drag is inversely proportional to “aspect ratio,” and the aspect ratio of a hull (average diameter/length) is likely to be less than that of the elevators. But it’s not possible to calculate the dynamic lift or associated drag for the elevators without knowing their dimensions, and even then there will be interference from the hull and the stationary portions of the fins.

Still, it seems reasonable to expect that you might reduce drag by as much as a third by artful application of elevator.

Buoyancy Control: Differential Density Fuel System

The next step beyond the blau gas concept (burning a gaseous fuel with a density equal to air so that when replaced with air there is no change in buoyancy) is being able to switch between use of a fuel lighter-than-air and one heavier-than-air so that one can make the ship lighter or heavier at will.

If the Graf Zeppelin were forced to ascend above pressure height and vent gas, becoming too heavy, it burned the heavier-than-air gasoline until buoyancy was equilibrated. (Dick 68).

Unfortunately, there are very few lighter-than-air fuels to burn when too light: hydrogen, methane, ammonia, acetylene and (just barely) ethylene.

Buoyancy Control: Compression and Liquefaction

From time to time, it has been suggested that an airship could convert lift into ballast by compressing or liquefying the lift gas (or air). This has the obvious advantage that the conversion is reversible. So what’s the catch?

Insofar as compression is concerned, the weight of the storage tanks is prohibitive. A high pressure tank must be stronger than a vacuum tank of the same dimensions, because the pressure difference it must resist is greater than atmospheric. So everything I said about the impracticality of vacuum lift must apply even more fiercely to compression. According to Honeywell engineer Donald Horkheimer, even with a high strength titanium alloy, generating 16,329 kg ballast would require (at a reasonable compression ratio and a safety factor of two), a 15,200 kg tank. (My own calculations suggest that this is a bit optimistic, see Appendix 1B.) And that’s not counting the weight of the compressor.

****

For liquefaction, you need power, which of course means increased fuel consumption. With modern (mature tech) liquefaction methods, you can produce one kilogram of liquid air in ten minutes by expending 1–20 kW (depending on the method); 163x methods would probably be less efficient. The power requirement increases rapidly if you want to liquefy more rapidly. (Horkheimer). Hydrogen is the hardest gas to liquefy. Liquefaction might work best on an airship using ammonia as the lift gas, as ammonia is relatively easy to liquefy (Morris IV-6): at atmospheric pressure, cool it to -33.4oC.

That said, water vapor is easy to liquefy. Airships that use steam for both propulsion and lift (thus far, just a design concept) may adjust the reboiling rate so “spent” steam is condensed and accumulated as ballast, or ballast water is vaporized and used as lift gas. (flyingkettle.com).

****

A variation on this idea is to liquefy a gaseous fuel rather than a lift gas In 1937, Burgess (DM254) suggested that isobutane could be used; isobutane has a heating value slightly better than that of gasoline.

While it’s a gas under ordinary circumstances (it boils at -11.5 ° C, 11oF, at atmospheric pressure), the liquid has a vapor pressure of 105 psi at 49oC, (120oF). As a gas, its density is 2.51 kg/m3 (about twice that of air), but as a liquid, it’s 593.4.

Burgess figured that an airship the size of the Macon (400,000 pounds gross lift) would benefit from carrying 20,000 pounds of isobutane and 750 pounds of tank. Its own weight is considered useful lift since it counts as the reserve fuel, so Burgess credits it as having a lift in gaseous form equal to that of the gross weight of the air it displaces (0.076 lb/ft3) without subtracting the weight of the isobutane. And the tanks to hold the liquid isobutane apparently weigh only 750 pounds, which isn’t significantly more than those to hold gasoline.

The fuel ballonet volume would be 132,000 ft3. Initially, the isobutane provides “lift,” in Burgess’ sense, at least as long as outside temperatures don’t fall below 11oF. As gasoline is consumed, or if weather conditions make the airship lighter, the isobutane is condensed and compressed to maintain net buoyancy. (The compression is so it stays liquid even on a fairly hot day, and the vapor pressure is low enough so that the storage tanks aren’t excessively heavy.) The required compression rate was 2200 ft3/min. While operating, the compressor consumes 150 pounds/hour fuel. If the liquid is released from the storage tanks, it will vaporize, but this can be helped along with a heating system using engine exhaust.

When the gasoline is gone, the airship burns the isobutane. That of course makes the ship lighter, but isobutane has a higher hydrogen content than gasoline which is favorable for water recovery. Burgess calculated that the additional weight (compressor, radiators, heaters, blowers, fuel ballonets) to handle the isobutane would be 6000 pounds.

Such a system is more difficult with blau gas; propane has a boiling point of -42oC and it would require compression to more than twice the isobutane pressure to keep it liquid at 49oC. (encyclopedia.airliquide.com).

Buoyancy Control: Directed Thrust

The USS Akron had swiveling, reversible propellers (Allen 37), and thus could generate vertical thrust without any forward motion, like a helicopter. But the swivel mounts add to the weight and complexity of the propulsion system. They are therefore feasible only if the engines are placed within the hull, on the hull axis, rather than in an outboard engine pod (Burgess/DM237), and this will reduce potential gas volume. The materials requirements for the pivoting system would be more exacting than for a normal transmission. The stern propulsion will make the airship tail heavy and this may impose a limit on how powerful an engine can be carried. (Unless perhaps the propeller and engine can be separated, perhaps employing an electrical rather than a mechanical transmission?) With the propeller pivoted, the vertical thrust will be exerted at one end of a long moment arm, resulting in a ferocious pitching moment that it will be difficult to compensate for. (Perhaps you could have both a pusher propeller at the stern and a tractor propeller at the bow, so their moments cancelled out?) Drag is reduced, relative to an outboard system, for normal horizontal propulsion, but pivoted propulsion means pushing through the air broadside and pressure drag will be much higher.

Gas Containment: Materials Selection

The ideal gas containment material for an airship has:

—low gas permeability

—sufficient flexibility

—low density

—high chemical resistance to the lift gas (particularly an issue for steam and ammonia)

—low flammability

—low cost

Bear in mind that if the airship is a simple aerostat, the envelope is in contact with the outside air, and additional factors are important:

—high UV (sunlight) resistance

—low moisture absorption (from rain or moist air)

—high tensile strength (especially if the airship isn’t rigid)

—low drag

Gas tightness, of course, is the sina qua non, but the degree of permeability that can be tolerated depends on (1) the ratio of surface area (determining leakage) to volume (determining gross lift) of the gas cells, (2) how long the airship must remain aloft before the gas can be replenished (itself dependent on airship speed and the distribution of gas plants), (3) the required useful lift at takeoff, and (4) how cheaply the lift gas may be produced.

Thus, the larger the airship, and the closer it is to a spherical shape, the leakier the “fabric” can be. The longer the required time aloft, the greater the total leakage will be and also the greater the amount of ballast that must be carried in order to compensate for the loss in lift. The useful lift is less because gross lift that otherwise could support payload must go to buoying the ballast instead.

To put this in perspective, an ellipsoid with the length (192 feet) and maximum diameter (59.5 feet) of the GZ-20 class of nonrigid Goodyear blimps would have a volume of 355,905 ft3 (10,078 m3) and a surface area of 29,261 ft2 (2,718 m2). Reportedly, about 10,000 ft3 helium is bought, to replenish leakage losses, each month. (goodyearblimp.com).

Calculation is more difficult for a compound aerostat, but the gas cells of some German 1917 zeppelins had a total gas cell surface area of 20–30,000 m2 (Chollet 7). A gas cell with a volume of 900,000 cubic feet might have a surface area of 54,000 square feet (Fulton 48). The total surface area of the USS Akron and USS Macon‘s twelve gas cells was 484,632 square feet and they held 6,856,000 cubic feet gas (Lancaster 1-IV-C; Smith 196). Note that a sphere of that volume would only have a surface area of 174,528 feet, so you can see that the division of the gas into multiple gas cells results in significant multiplication of the amount of “fabric” required.

With all lift gases, leakage is a problem. However, it’s of greatest concern with helium, since its supply is so limited. The USS Shenandoah lost 150,000 cf helium (7.1%) each month, just sitting in the hangar, and later the USS Los Angeles lost 250,000 cf (9.6%) monthly. (Robinson 96). I would expect hydrogen to diffuse out perhaps twice as fast.

Gas Containment: Materials Choices

The potential envelope materials include animal skin, paper, cloth, natural rubber, synthetic rubbers and plastics (as sheets or cloths), and metals.

According to Goodyear engineer Dick, “Throughout most of the rigid airship era, the only acceptable gasproofing material was goldbeater’s skin” (Dick 191), which was glued to lightweight cotton. However, this remark must be placed in context; the rigid airships were large, long distance vehicles, and they had to retain enough lift gas to have adequate buoyancy at the end of a flight of 80 or more hours.

In my opinion, varnished cloth is an adequate envelope material for short-range airships, and its manufacture is within the capabilities of any of the 163x countries that might be contemplating building airships. However, for long-range airships you would probably want to use a material that’s less permeable.

There is some quantitative data (see Appendix) on “permeability” (really, permeation rate for particular thickness rather than permeability for unit thickness), but I must warn the reader that the sources aren’t always as clear as one would like about the thickness and type of the materials used, and the numbers aren’t necessarily consistent. In general, the permeation rate is inversely proportional to the thickness, and if you combine materials with different permeabilities P1 and P2, the combined permeability may be calculated by (1/Pcombo) = (1/P1)+(1/P2). (Barrer 411).

Permeability also depends on the identity of the lift gas. On average, the relative rates of penetration of natural rubber by various gases are as follows:

Table 6A: Relative Permeability of Natural Rubber to Various Gases

Gas

Natural

Rubber (1)

Nitrogen

0.16

Air (78% nitrogen, 21% oxygen)

0.22

Methane

0.39

Oxygen

0.45

Helium

0.65

Hydrogen

1

Carbon dioxide

2.9

Ammonia

8.0

Water Vapor

~50!

(1) Edwards and Pickering, 75 and Black 521 (methane); (2) Comyn 62

Obviously, natural rubber is not the material of choice for steam containment! However, other barrier materials may yield different relative permeabilities. (Barrer 402, Brydson 101ff, Comyn 62).

Nor can you ignore temperature. Rubber is 22 times as permeable to hydrogen at 100oC as at 0oC (Edwards 603). Hence, part of the price you pay for increased lift by artificial superheating is increased leakage.

Goldbeater’s skin was used pre-RoF to hold gold while it was hammered into gold leaf. The German “Skin G” is the outer membrane of the caecum (blind gut) of the large intestine of the ox (other breeds of cattle may be used). The membrane may be visualized as a cylinder 0.5-1 meter long and 0.1 meter in diameter. The skins were graded as #1 if more than 30 inches long, and #2 if 20–30. Of six million cattle, one could expect to obtain 75%–80% useful skins (4.5–5 million). That would break down as 2.75–3 million #1 and 1.75–2 million #2 skins.

Prior to 1930, the German gas cells used a double layer, both glued to a cotton cloth “doublier.” Goldbeater’s skin is of high gas-tightness, but it’s expensive, and it’s of low tensile strength and high moisture-permeability (D’Orcy), and vulnerable to weathering (50 days exposure increased leakage over 16 fold—Judge 330) so it shouldn’t be used, at least without a protective layer, on simple aerostats. (Chollet 8-9).

For the British semi-rigid Nulli Secundus (1907), 110 feet long and 90 feet circumference, the cost of the skins themselves was 12/6 for 100 skins, each 8×30 inches. However, the skins had to be joined by hand and the total cost for the envelope (which reportedly used 200,000 skins) was 2000 pounds sterling. (Turner 276).

To make one large gas cell for a WW I zeppelin required 50,000 skins. In 1920, Goodyear paid $459,650 for 32 gas cells. Adding insult to injury, the useful life is only 2–3 years. (Robinson 60), and is reduced by high temperature or humidity (145).

For the gas cells of the ZR2 (1921), nearly 600,000 skins were needed, and although they cost three cents apiece, the labor brought the assembled cost (skin plus single ply cotton) to almost $200,000. (Risdon).

Do not allow the antiquity of goldbeater’s skins to lead you to assume that it will be easy (if tedious) to assemble the skins into finished envelopes. Even though goldbeater’s skin had been used to make toy balloons as early as 1783 (Chollet 2), when the first zeppelin (Z-1) was constructed (1900), there was “no means of making . . . goldbeaters’ skin sufficiently pliant,” and so it used “gummed cotton” for its gas cells. (Zeppelin).

The special properties of goldbeater’s skin implies that the intestines of cattle are strategic war materials. During WW I, the skins were systematically collected from butchers in German-controlled areas, and it was “forbidden to make sausages” (Chollet 8).

Obviously, large countries are likely to have bigger herds than small ones, and national dietary preferences will also have an impact. (No cattle slaughtering in Mughal India, lest it offend the local Hindus, I expect.)

A logical question is, why can’t we use leather (tanned skin)? It’s true that leather was used in hosing before rubber became generally available. Indeed, in 1909, it was proposed to use chromium salt-tanned leather in balloon-making. The catch, I fear, is that while leather is somewhat waterproof, it’s intended to “breathe.” So it’s likely that only intestinal membranes are suitable for hydrogen containment, although it does appear that the air permeability of leather varies by several orders of magnitude depending on type. (Barrer 410).

Can any other intestinal membranes be used? The inner membrane from the ox (“Skin L”) and the outer membrane from the mature hog (“Skin P”) were German wartime substitutes, used for the outer layer of the gas cells.

Cloth. Cloth is a flexible, strong weave of natural or synthetic fibers, and those fibers can give it considerable tensile strength. Unfortunately, voids between warp and weft defines pores through which gases may pass. Indeed, when used for clothing, it’s considered advantageous for a cloth to be air-permeable.

The tighter the weave, the lower the permeability, but also the higher the weight. The fuzziness of the fibers and the degree of twist in the yarn also has an effect.

As far as I know, the only natural fibers used to weave balloon fabrics have been silk, flax (linen), and cotton, although some consideration has been given to ramie, jute and manila (Lougheed 94ff). Silk is the strongest and lightest, but also expensive, brittle, and able to pick up static electricity (which might spark off the hydrogen). Cotton is the cheapest, and linen is in-between.

Permeability may be reduced by sizing or various coatings. There is an almost certainly apocryphal legend that Conte developed a varnish, whose formula was subsequently lost, that permitted silk to retain hydrogen for weeks (Chollet 2) or even months (Fonvielle 96).

The typical balloon varnish was based on linseed oil. Oiled cotton is sometimes called “oilcloth” or “oilskin.” Varnished cloth is not as tight as goldbeater’s skin, although it can give respectable results—superior, in some tests, to rubberized cloth. A varnished double silk (192 g/m2) was said to have a permeability of 2.7–3.3 liters/m2-day, and an oilskin, if one can believe the results, of 0.5. (Judge 366; cp. Barrer 437).

However, the varnish is subject to cracking when the balloon is folded, and, when stored, it’s subject to spontaneous combustion? (Roth; gasballooning.net).

Other reported coatings include rubber (unvulcanized, dissolved in turpentine), gutta-percha (a natural plastic) in benzene, other natural resins, gelatin, tar, and various synthetic plastics. The Graf Zeppelin‘s gas cells were goldbeater’s skins, but its outer envelope was cotton waterproofed with aluminum-containing dope. (Dick 70).

Cloth is often used as a component of a “mixed balloon fabric,” the textile fibers supplying most of the strength and another layer being responsible for most of the gas impermeability.

Paper. The Montgolfier brothers were paper manufacturers, and their first balloons used paper-cotton laminates. Paper proved to be more a liability, as it cracked easily, and was quite permeable too. I suppose it could have value for a short-term, emergency repair.

Natural Rubber. For the various sources of natural rubber, see Cooper, “Bouncing Back: Bringing Rubber to Grantville” (Grantville Gazette 6). In canon, as of 1635, the Portuguese (Hevea brasiliensis rubber from Brazil ), Spanish (Castilla rubber from Nicaragua ), and USE (Hevea guianensis rubber from Suriname ) have the best access to natural rubber. The best bet for the Russians is probably milkweed, and the Ottomans might take a close look at fig latex.

Other European powers might consider the Funtumia latex of Central Africa.

According to canon, the gas cells of the Royal Anne are made of “cloth sealed with European latex.” Kevin and Karen Evans, “No Ship for Tranquebar, Part Two” (Grantville Gazette 28). I hope that “European latex” means latex vulcanized in Europe, not latex from European plants such as milkweed. To understand my concern, see Cooper, “Bouncing Back: Bringing Rubber to Grantville” (Grantville Gazette 6). Milkweed latex isn’t hopeless, but there are some serious problems that it would have been difficult to overcome quickly.

Rubber has the disadvantages that it requires protection against sunlight (ultraviolet)(Judge 365) and also may be attacked by impurities in the hydrogen. Fillers, such as pigments, or aluminum or mica flakes, can improve its properties.

The French, for their non-rigid airships, which were simple aerostats, favored a mixed fabric consisting of alternating layers of cotton or silk cloth and rubber. When two cloth layers were used, the threads were either parallel or at an angle of 45o to each other.

Rubberized cotton wasn’t quite as good, leakage wise, as goldbeaters’ skin. For example, at 20–22oC, the No. 1 balloon fabric (with 1.65 oz rubber/square yard between plies and 1 on inside face) let through 54.99 liters/square meter per day; the No. 2 (3.11 ounces between), 11.64; the No. 3 (5.51 between), 11.2. (Gibbons 169). “The lowest rate of leakage obtainable for a rubber-proofed fabric is about 5 liters per square meter per 24 hours, whilst for goldbeaters’ skin it is about 0.25 liters (for four layers) and 0.12 (for eight layers).” (Judge 329).

The English chose to glue a rubberized cotton (90g/m2 cotton coated with 10g/m2 rubber film) to goldbeater’s skin. (Chollet 12). This was a case of turning adversity to fortune; they weren’t able to reconstruct the Germans’ secret glue for attaching skin to cotton directly. Robinson (60) reports a total weight of 160 g/m2. I regret to state that mice (German saboteurs?) found the combination very tasty. (211).

In American rigids, the base was HH cotton cloth, weighting 2 oz/yd2. The combination of two cotton layers with one rubber came out to 8.5 oz/yd2 with a 12 liter/m2-day hydrogen leakage. That wasn’t good enough, so we then glued one layer of goldbeater’s skin to HH cloth with rubber cement, and varnished the cloth. This weighed 4.55 oz/yd2, with 2 liter leakage. (Robinson 210). Another report indicates that the choice of varnish made a difference; balloon cloth no. 3 with 4 coats of varnish 1877 limited leakage to 10.86, whereas with varnish 1876 it was 4.5. (Gibbons). A typical useful life for the rubberized cotton used in 1921 was 18-24 months. (Tucker 248).

In 1930, the U.S. developed a cheap, durable gelatin-latex-cotton combination, 5.30 oz/yd2, which was used for the gas cells on the Akron (half) and Macon (all); a similar one was used on the Hindenburg and the Graf Zeppelin II (LZ 130). These did not include any goldbeater’s skin. (Dick 191). I believe that this gelatin-latex coating is described in Carson, USP 1,779,839 (1930). Leakage was reportedly 0.5 liters/m2-day. (NLHC). Another source says balloon cloth no. 3, with “gelatin compound on rubber” is 0.8-1.4. (Gibbons).

Synthetic Polymers (Rubbers and Plastics). Cloth may be impregnated with a plastic in liquid form. The plastic “dopes” first used to waterproof airplane fabrics were based on cellulose nitrate or cellulose acetate, which I expect to be among the first plastics developed in the new timeline. Cooper, “Industrial Alchemy, Part 5: Polymers,” Grantville Gazette 29. The “dope” must include a plasticizer, such as an alcohol. These dopes would probably improve the air-tightness of cloth.

Plastics may also be used in sheet form, and there it’s logical to look at the “barrier plastics, ” like Saran® wrap, used to keep food fresh. With sheets, you of course need to join their edges together in a gas-tight manner.

A third possibility is to spin the polymer into fibers and then weave them into cloth, which are used the same way as natural fiber cloth.

I have tabulated hydrogen and water vapor permeabilities for the elastomers (stretchable polymers) likeliest to be the first ones re-invented in the 1632 universe.

Table 6B: Hydrogen and Water Vapor Permeability of Early Post-RoF Elastomers

Selected elastomer

Timeline (1)

Hydrogen Permeability Coefficient

* 10-8 cc/s/cm2/cm/atm 25oC

Water Vapor Permeability

V=Very High,

H=High, M=Medium,

L=Low

(2)

(3)

(4)

regenerated cellulose (cellophane, Rayon)

1633

0.059

VH

vulcanized natural rubber

1634

38.3

14.6

14.7

M

cellulose nitrate

10.5

12.2

VH

cellulose acetate

6.6

12.2

13.6

VH

polyethylene terephthalate (Mylar)

1635-7

0.44

L

polyvinyl chloride, plasticized (phthalate)

2.6

M

polyvinyl alcohol

0.079

0.15

VH?

polyvinylidene chloride (Saran)

0.05

L

butyl rubber

4.8

L

polysulfide (Thiokol) rubber

1636-8

1.2

0.74

1.01

L

polychloroprene (Neoprene) rubber

10.2

8.4

M

nylon

1637-9

low

H

polyacrylonitrile

low

H

(1) per Cooper, Industrial Alchemy, part 5: Polymers (Grantville Gazette). (2) Knarr 68ff. (3) Barrer Table 97. (4) Cardarelli 734, Comyn 63, Barrer 442ff.

A plastic with high gas impermeability may have disadvantages, such as brittleness, or high moisture absorption. It can be combined with other materials to compensate. The Goodyear blimps are made of polyester coated with neoprene rubber.

Note that some synthetic plastics may be extruded into fibers and woven into cloth, as in the case of nylon, Dacron, etc. Gas-tightness is also important for parachutes, and it’s possible that the aviators in Grantville know something about synthetic canopy fabrics. Silk was replaced with ripstop nylons, with permeability reduced by calendering (MIL-C-7020), or by coating with acrylic (unsuccessful, tear-prone), urethane, or silicone. MIL-C-7020 Type I had a weight of 1.1 oz/yd2, thickness of 0.003, and air permeability of 5 cubic feet/minute air/ft2 cloth. The coated canopies were 0–3 CFM with weights of 38–47 g/m2. Polyester (Dacron) is about equivalent to nylon in weight and permeability, but is more UV resistant and less elastic. (Poynter 74ff).

Metal. The American ZMC-2, 150 feet long and 42 feet in diameter, was a simple aerostat with an Alclad 17ST envelope containing 200,000 cubic feet helium. This was a a duralumin (aluminum 94%-copper 4%-manganese 0.5%-magnesium 0.5%) 17ST alloy bonded with a surface layer of pure (99.7%) aluminum for increased corrosion-resistance, with a specific gravity of 2.96. (NACA-TN-259; Seeley). The Alclad sheets, of 0.095 inch thickness, were riveted together. (Carr). The rate of helium diffusion was about one-half that of a ship with the more typical rubberized fabric envelope. (Fritsche). Over the period 1929-1941, it logged 752 flights and 2264 hours of flight time.

An obvious disadvantage of a metal envelope is that it isn’t flexible and thus can’t adjust lift gas volume to altitude. The helium volume was adjusted by the expansion or contraction of two internal airbags, made of rubberized fabric. These could expand to 25% of the hull volume. (Carr).

Production of aluminum requires lots of electricity, the flux cryolite (either the natural mineral from Greenland or synthetic material made using sodium hydroxide and the very nasty hydrogen fluoride, the latter made from fluorspar), and the aluminum ore bauxite. Cooper, “Aluminum: Will o’ the Wisp?” (Grantville Gazette 8 ).

The other light metals that have been used for structural purposes are magnesium and titanium (specific gravity 4.51) and magnesium (1.74). But I don’t think that light metal production will be on a scale such that a metalclad airship is economically viable until the 1640s at the earliest.

****

Recap. I think the writer may safely assume that it will be reasonably easy to achieve a leakage rate that doesn’t exceed 10 liters/square meter/day, for a reasonable weight. (To put this in perspective, 15 was considered tolerable for the ballonet on a 1921 airship—Tucker 261.) To get much below that will require either the use of goldbeater’s skin, or some combination of experimentation and luck in the development of varnished or rubberized cloths.

Hybrid Airships (Combined Aerostatic and Aerodynamic Lift)

A conventional airship is one with enough aerostatic lift to take it up to cruising altitude. Typically, they have vertically symmetrical bodies, and hence if their angle of attack is zero (level flight), they don’t experience significant aerodynamic lift (the fins might provide a little). However, they may be deliberately flown inclined to generate aerodynamic lift, as we will discuss under “Altitude Control.”

Hybrid airships have been designed that would generate part of their lift (say, at least 20%) aerodynamically even in level flight. These may have a vertical propeller or jet, an asymmetric (“lifting”) body, a pair of flanking “airfoil” wings, or a single “inboard wing” connecting two envelopes. (Liao). They are intended to takeoff “statically heavy,” and hence require a runway to generate enough speed, and thus aerodynamic lift, to leave the ground.

But there are several problems with the concept. It must still be bulky, like an airship, to contain enough lift gas to provide a significant fraction of the lift, which means that it is not going to be easily maneuverable (Burgess 289). This will complicate takeoff and landing. It cannot cruise at low speed to economize on fuel or for more efficient recon because then it won’t have the requisite aerodynamic lift. And it won’t be as fast as a true aircraft because it’s shape is a compromise between aircraft shape (to reduce drag) and airship shape (to increase buoyancy relative to structural weight).

It’s been argued that hybrids will provide a lower cost per ton-mile for shipping than a conventional airplane (Boyd), but I would think that the shipping costs provided by conventional airships would be lower still. On the other hand, hybrids might be faster than the latter.

It won’t be in Grantville literature, but there have been technical analyses of the relative merits of putting wings on a traditional ellipsoidal airship hull, versus use of a deltoid or multihulled lifting body. The former is considered to have superior endurance. ((Buerge; Ardema).

Someone in Grantville may have read McPhee’s 1973 book about the travails of developing the triple-hulled Aereon (1966) and the “deltoid pumpkin seed” Aereon 26 (1970).

However, it should be noted that the “deltoid pumpkin seed” was designed to receive most of its lift from helium, whereas it was tested as a scaled-down model without any lift gas. (McPhee 46, 54).

Conclusion

In Romeo and Juliet, Mercutio tells Romeo to “borrow Cupid’s wings, and soar above the ground.” Later, he speaks of dreams as being “as thin of substance as the air.” (I, iv). The airship soars by virtue of gases that are even thinner than air, and it doesn’t need wings at all.

In this article, I have explained the subtleties of how an airship achieves lift and controls its altitude. But what distinguishes an airship from a balloon is the ability to move forward without the aid of the wind. I will take up the issue of airship propulsion in a later article.

Author’s Note

The Appendices and Bibliography are available from Gazette Extras, http://1632.org/gazetteextras/.

****

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About Iver P. Cooper

Iver P. Cooper, an intellectual property law attorney, lives in Arlington, Virginia with his wife and two children. Two cats and a chinchilla rule the household with iron paws. Iver has received legal writing awards from the American Patent Law Association, the U.S. Trademark Association, and the American Society of Composers, Authors and Publishers, and is the sole author of Biotechnology and the Law, now in its twenty-something edition. He has frequently contributed both fiction and nonfiction to The Grantville Gazette.

 

When not writing (or trying to get an “orange blob” off his chair so he can start writing), he has been known to teach swing dancing and folk dancing, or to compete in local photo club competitions. Iver adds, “I can’t get my wife to read my fiction, but she has no trouble cashing the checks.”

Iver’s story “The Chase” is in Ring of Fire II