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 25^oC , and the reference pressure is 100 or 101.325 kilopascals. Table 1 presents some typical values:

^{http://www.flyingkettle.com/conpaper.htmhttp://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 66^oF superheat and 9^oF 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 50^oC to 0.036 and 0.072 at 400^oC. (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 9^oF 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.

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:

(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:

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 LakeConstance.

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 80^oF and 85% at 800^oF).

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 32^oF after eighty minutes, and that with the heater off, it lost 0.9^oF 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 1085^oF—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 12^o up, and is known to have used negative dynamic lift (12^o 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 10–15^o. 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 6^o.)

Could this possibly be true for full-size airships? Burgess, Airship Design (1927), page 105, provides the dynamic lift curves for the

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