Part 2

*Critical Size of Bag.* Next in importance to the best form to be given the vessel, is the most effective size—something which has a direct bearing upon its lifting power. This depends upon the volume, while the resistance is proportional to the amount of surface presented. Greater lifting power can accordingly be obtained by keeping the diameter down and increasing the length. But the resistance is also proportionate to the square of the speed, while the volume, or lifting power, varies as the cube of the dimensions of the container, so that in doubling the latter, the resistance of the vessel at a certain speed is increased only four times while its lifting capacity is increased eight times. Consequently the larger dirigible is very much more efficient than the smaller one since it can carry so much more weight in the form of a motor and fuel in proportion to its resistance to the air. As an illustration of this, assume a rectangular container with square ends 1 foot each way and 5 feet long. Its volume will be 5 cubic feet and if the lifting power of the gas be assumed as 2 pounds per cubic foot, its total lifting power will be 5 pounds. If a motor weighing exactly 5 pounds per horse-power be assumed, it will be evident that the motor which such a balloon could carry would be limited to 1 horse-power, neglecting the weight of the container.

Double these dimensions and the container will then measure 2 X 2 X 10 feet, giving a volume of 40 cubic feet, and a lifting power, on the basis already assumed, of a motor capable of producing 8 horsepower, and this without taking into consideration that as the size of the motor increases, its weight per horse-power decreases. The balloon of twice the size will thus have a motor of 8 horse-power to overcome the resistance of the head-on surface of 4 square feet, or 2 horse-power per square foot of transverse section, whereas the balloon of half the size will have only 1 horse-power per square foot of transverse section. It is, accordingly, not practicable to construct small dirigibles such as the various airships built by Santos-Dumont for his experiments, while, on the other hand, there are numerous limitations that will be obvious, restricting an increase in size beyond a certain point, as has been shown by the experience of the various Zeppelin airships.

To make it serviceable, what Berget terms the "independent speed" of a dirigible, i.e., its power to move itself against the wind, must be sufficient to enable it to travel under normally prevailing atmospheric conditions. These naturally differ greatly in different countries and in different parts of the same country. Where meteorological tables showed the prevailing winds in a certain district to exceed 15 miles an hour throughout a large part of the year, it would be useless to construct an airship with a speed of 15 miles an hour or less for use in that particular district, as the number of days in the year in which one could travel to and from a certain starting point would be limited. This introduces another factor which has a vital bearing upon the size of the vessel. Refer to the figures just cited and assume further that by doubling the dimensions and making the airship capable of transporting a motor of 8 horse-power, it has a speed of 10 miles an hour. It is desired to double this. But the resistance of the surface presented increases as the square of the speed. Hence, it will not avail merely to double the power of the motor. Experience has demonstrated that the power necessary to increase the speed of the same body, increases in proportion to the cube of the speed, so that instead of a 16-horse-power motor in the case mentioned, one of 64 horse-power would be needed. There are, accordingly, a number of elements that must be taken into consideration when determining the size as well as the shape of the balloon.

*Static Equilibrium.* Having settled upon the size and shape, there must be an appropriate means of attaching the car to carry the power plant, its accessories and control, and the crew. While apparently a simple matter, this involves one of the most important elements of the design—that of stability. A long envelope of comparatively small diameter being necessary for the reasons given, it is essential that this be maintained with its axis horizontal. In calm air, the balloon, or container, is subjected to the action of two forces: One is its weight, applied to the center of gravity of the system formed by the balloon, its car, and all the supports; the other is the thrust of the air, applied at a point known as the center of thrust and which will differ with different designs, according as the car is suspended nearer or farther away from the balloon. If the latter contained only the gas used to inflate it, with no car or other weight to carry, the center of gravity and the center of thrust would coincide, granting that the weight of the envelope were negligible. As this naturally can not be the case, these forces are not a continuation of each other. But as they must necessarily be equal if the balloon is neither ascending nor descending, it follows that they will cause the balloon to turn until they are a continuation of each other, and in the case of a pisciform balloon, this will cause it to tilt downward. Like a ship with too much cargo forward, it would be what sailors term "down at the head."

As this would be neither convenient nor compatible with rapid propulsion, it must be avoided by distributing the weight along the car in such a manner that when the balloon is horizontal, the forces represented by the pressure above and the weight below, must be in the same perpendicular. This is necessary to insure static equilibrium, or a horizontal position while in a state of rest. To bring this about, the connections between the car and the balloon must always maintain the same relative position, which is further complicated by the fact that they must be flexible at the same time.

*Longitudinal Stability.* But the _longitudinal stability_ of the airship as a whole must be preserved, and this also involves its _stability of direction_. Its axis must be a tangent to the course it describes, if the latter be curvilinear, Or parallel with the direction of this course where the course itself is straight. This is apparently something which should be taken care of by the rudder, any tendency on the part of the airship to diverge from its course being corrected by the pilot. But a boat that needed constant attention to the helm to keep it on its course would be put down as a "cranky"—in other words, of faulty design in the hull. A dirigible having the same defect would be difficult to navigate, as the rudder alone would not suffice to correct this tendency in emergencies. Stability of direction is, accordingly, provided for in the design of the balloon itself, and this is the chief reason for adopting the form of a large-headed and slender-bodied fish, as already outlined. This brings the center of gravity forward and makes of the long tail an effective lever which overcomes any tendency of the ship to diverge from the course it should follow, by causing the resistance of the air itself to bring it back into line. However, the envelope of the balloon itself would not suffice for this, so just astern of the latter, "stabilizing surfaces" are placed, consisting of vertical planes fixed to the envelope. These form the keel of the dirigible and are analogous to the keel of the ship. Stability of direction is thus obtained naturally without having constant recourse to the rudder, which is employed only to alter the direction of travel.

The comparison between marine and aerial navigation must be carried even further. These vertical planes, or "keel," prevent rolling; it is equally necessary to avoid pitching—far more so than in the case of a vessel in water. So that while the question of stability of direction is intimately connected with longitudinal stability, other means are required to insure the latter. The airship must travel on an "even keel," except when ascending or descending, and the latter must be closely under the control of the pilot, as otherwise the balloon may incline at a dangerous angle. This shows the importance of an unvarying connection between the car and the envelope to avoid defective longitudinal stability. Assume, for instance, that the car is merely attached at each end of a single line. The car, the horizontal axis of the balloon, and the two supports would then form a rectangle. When in a state of equilibrium the weight and the thrust are acting in the same line. Now suppose that the pilot desires to descend and inclines the ship downward. The center of gravity is then shifted farther forward and the two forces are no longer in line.

But as the connections permit the car to swing in a vertical plane, they permit the latter to move forward and parallel with the balloon, thus forming a parallelogram instead of a rectangle. This causes the center of gravity to shift even farther, and as one of the most serious causes of longitudinal stability is the movement of the gas itself, it would also rush to the back end and cause the balloon to "stand on its head." As the tendency of the gas is thus to augment any inclination accidentally produced, the vital necessity of providing a suspension that is incapable of displacement with relation to the balloon is evident. Here is where the importance of Meusnier’s conception of the principle of triangular suspension comes in. Instead of being merely supported by direct vertical connections with the balloon, the ends of the car are also attached to the opposite ends of the envelope, forming opposite triangles. This gives an unvarying attachment, so that when the balloon inclines, the car maintains its relative position, and the weight and thrust tend to pull each other back in the same line, or, in other words, to "trim ship."

*Dynamic Equilibrium.* In addition to being able to preserve its static equilibrium and to possess proper longitudinal stability, the successful airship must also maintain its dynamic equilibrium—the equilibrium of the airship in motion. This may be made clear by referring to the well-known expedients adopted to navigate the ordinary spherical balloon. To rise, its weight is diminished by gradually pouring sand from the bags which are always carried as ballast. To descend, it is necessary to increase the total weight of the balloon and its car, and the only method of accomplishing this is to permit the escape of some of the gas, the specific lightness of which constitutes the lifting power of the balloon. As the gas escapes, the thrust of the air on the balloon is decreased and it sinks—the ascensional effort diminishing in proportion to the amount of gas that is lost. The balloon, or the container itself, being merely a spherical bag, on the upper hemispherical half of which the net supporting the car presses at all points, the question of deformation is not a serious one. Before it assumed proportions where the bag might be in danger of collapsing, the balloon would have had to come to earth through lack of lifting power to longer sustain it. Owing to its far greater size, as well as to the form of the surface which it presents to the air pressure, such a crude method is naturally not applicable to the dirigible.

Dynamic equilibrium must take into account not only its weight and the sustaining pressure of the air, but also the resistance of the air exerted upon its envelope. This resistance depends upon the dimensions and the shape of that envelope, and in calculations the latter is always assumed to be invariable. Assume, for instance, that to descend the pilot of a dirigible allowed some of the hydrogen gas to escape. As the airship came down, it would have to pass through strata of air of constantly increasing pressure as the earth is approached. The reason for this will be apparent as the lower strata bear the weight of the entire atmosphere above them. The confined gas will no longer be sufficient to distend the envelope, the latter losing its shape and becoming flabby. As the original form is no longer retained, the center of resistance of the air will likewise have changed together with the center of thrust, and the initial conditions will no longer obtain. But as the equilibrium of the airship depends upon the maintenance of these conditions, it will be lost if they vary.

*Function of Balloonets.* In the function of balloonets is realized the importance of the principle established by Meusnier. It was almost a century later before it was rediscovered by Dupuy de Lome in connection with his attempts to make balloons dirigible. That the balloon must always be maintained in a state of perfect inflation has been pointed out. But gas is lost in descents and to a certain extent, through the permeability of the envelope. Unless it is replaced, the balloon will be only partially inflated. In view of the great volume necessary, it requires no explanation to show that it would be impossible to replace the gas itself by fresh hydrogen carried on the car. It would have to be under high pressure and the weight of the steel cylinders as well as the number necessary to transport a sufficient supply would be prohibitive. Hence, Meusnier conceived the idea of employing air. But this could not be pumped directly into the balloon to mix with the hydrogen gas, as the resulting mixture would not only still be as inflammable as the former alone, but it would also contain sufficient oxygen to create a very powerful and infinitely more dangerous explosive. This led to the adoption of the _air balloonet_.

In principle the balloonet consists of dividing the interior of the envelope into two cells, the larger of which receives the light gas while the smaller is intended to hold air and terminates in a tube extending down to a pump in the car. In other words, a fabric partition adjacent to the lower part of the envelope inside and subject to deformation at will. In actual practice it consists of a number of independent cells of this kind, longitudinally disposed along the lower half of the interior of the envelope.

When the balloon is completely inflated with hydrogen, as at the beginning of an ascent, these balloonets lie flat against the lower part of the envelope, exactly like a lining. As the airship rises, the gas expands owing to the reduction in atmospheric pressure at a higher altitude, as well as to the influence of heat. With the increase in pressure, uniform inflation is maintained by the escape of a certain amount of gas through the automatic valves provided for the purpose. Unless this took place, the internal pressure might assume proportions placing the balloon in danger of blowing up. To avoid this, a pressure gauge communicating with the gas compartment is one of the most important instruments on the control board of the car, and should its reading indicate a failure of the automatic valves, the pilot must reduce the pressure by operating a hand valve. But as the car descends, the increased external pressure causes a recontraction of the gas until it no longer suffices to fill the envelope. To replace the loss the air pumps are utilized to force air into the air balloonets until the sum of the volumes of gas and air in the different compartments equals the original volume. In this manner, the initial conditions, upon which the equilibrium of the airship is based, are always maintained.

This is not the only method of correcting for change in volume, nor of maintaining the longitudinal stability of the whole fabric, the importance of which has already been detailed, but experience has shown that it is the most practical. It is possible to give the balloon a rigid frame over which the envelope is stretched and to attach the car by means of a rigid metal suspension, as in the various Zeppelin airships, or to take it semi-rigid, as in the Gross, another German type in which Zeppelin’s precedent was followed only in the case of the suspension. To prevent deformation by this means, the balloon is provided with an absolutely rigid skeleton of aluminum tubes. This framing is in the shape of a number of uniform cylindrical sections, or gas compartments, each one of which accommodates an independent balloon, while over the entire frame a very strong but light fabric constituting the outer or protecting envelope is stretched taut. The idea of the numerous independent balloons is to insure a high factor of safety as the loss of the entire contents of two or three of them through accident would not dangerously affect the lifting power of the whole. The numerous wrecks which attended the landings of these huge non-flexible masses during the early stages of their development led to the provision of some form of shelter wherever they were expected to land. Even now, they are practically unmanageable in the air during a fierce wind and must be allowed to sail under control until the wind has spent itself.

The system of air balloonets has accordingly been adopted by every other designer, in variously modified forms, as illustrated by the German dirigible Parseval, in which but two air bags were employed, one at either end. They were interconnected by an external tube to which the air-pump discharge was attached, and were also operated by a counterbalancing system inside the gas bag, by means of which the inflation of one balloonet, as the after one, for example, caused the collapse of the other.

_Influence of Fish Form of Bag._ But a condition of dynamic equilibrium can not be obtained with the combined aid of the precautions already noted to secure longitudinal stability and that of the air balloonet in maintaining uniform inflation. Why this is so will be clear from a simple example. If a simple fusiform or spindle-shaped balloon be suspended in the air in a horizontal plane, the axis of which passes through its center of gravity, it would be practically pivoted on the latter and would be extremely sensitive to influences tending to tilt it up or down. It would be in a state of "indifferent" longitudinal equilibrium. As long as the axis of the balloon remains horizontal and the air pressure is coincident with that axis, it will be in equilibrium, but an equilibrium essentially unstable. Experiment proves that the moment the balloon inclines from the horizontal in the slightest degree, there is a strong tendency for it to revolve about its center of gravity until it stands vertical to the air current, or is standing straight up and down. This, of course, refers to the balloon alone without any attachments. Such a tendency would be fatal, amounting as it does to absolute instability.

If instead of symmetrical form, tapering toward both ends, a pisciform balloon be tried, it will still evidence the same tendency, but in greatly diminished degree. This is not merely the theory affecting its stability but represents the findings of Col. Charles Renard, who undoubtedly did more to formulate the exact laws governing the stability of a dirigible than any other investigator in this field. His data is the result of a long and methodically carried out series of experiments. In the case of the pisciform balloon, the disturbing effect is due in unequal degree, to the diameter of the balloon and its inclination and speed, whereas the steadying effect depends upon the inclination and diameter, but not on the Speed. The disturbing effect, therefore, depends solely on the speed and augments very rapidly as the speed increases. It will, accordingly, be apparent that there is a certain speed for which the two effects are equal, and beyond which the disturbing influence, depending on speed, will overcome the steadying effect.

To this rate of travel, Renard applied the term "critical speed," and when this is exceeded the equilibrium of the balloon becomes unstable. To obtain this data, keels of varying shapes and dimensions were submitted to the action of a current of air, the force of which could be varied at will. In the case of the La France, the first fish-shaped dirigible, the critical speed was found to be 10 meters, or approximately 39 feet per second, a speed of 21.6 miles per hour, and a 24-horse-power motor suffices to drive the airship at this rate of travel. But the internal combustion motor is now so light that a dirigible of this type could easily lift a motor capable of generating 80 to 100 horse-power. With this amount of power, its theoretic speed would be 50 per cent greater, or 33 miles an hour. But this could not be accomplished in practice as long before it was reached the stability would become precarious. As Colonel Renard observed in the instance just cited, "If the balloon were provided with a 100-horse-power motor, the first 24 horse-power would make it go and the other 76 horse-power would break our necks."

_Steadying Planes._ It is accordingly necessary to adopt a further expedient to insure stability. This takes the form of a system of rigid planes, both vertical and horizontal, located in the axis of the balloon and placed a considerable distance to the rear of the center of gravity. With this addition, the resemblance of the after end of the balloon to the feathering of an arrow is apparent, while its purpose is similar to that of the latter. For this reason, these steadying planes have been termed the _empennage_, which is the French equivalent of "arrow feathering," while its derivative _empennation_ is employed to describe the counteraction of this disturbing effect. In the La France, which measured about 230 feet in length by 40 feet in diameter, the area of the planes required to accomplish this was 160 square feet, and the planes themselves were placed almost 100 feet to the rear of the center of gravity. By referring to the illustrations of the various French airships, the various developments in the methods of accomplishing this will be apparent.

In the Lebaudy balloon, it took the form of planes attached to the framework between the car and the balloon. In La Patrie and La Republique, the resemblance to the feathered arrow was completed by attaching four planes in the form of a cross directly to the stern of the balloon itself. But as weight, no matter how slight, is a disturbing factor at the end of a long lever, such as is represented by the balloon, Renard devised an improvement over these methods by conceiving the use of hydrogen balloonets as steadying planes. The idea was first embodied in La Ville de Paris, Fig. 8, in the form of cylindrical balloonets, and as conical balloonets on the Clement-Bayard. These balloonets communicate with the gas chamber proper of the balloon and consequently exert a lifting pressure which compensates for their weight, so that they no longer have the drawback of constituting an unsymmetrical supplementary load.