Part 4
There are _gases_, if not woods, lighter than air: among them, coal gas and hydrogen. A "bubble" of any of these gases, if isolated from the surrounding atmosphere, cannot sink but must rise. At the same pressure and temperature, hydrogen weighs about one-fifteenth as much as air; coal gas, about one-third as much. If a bubble of either of these gases be isolated in the atmosphere, it must continually rise, just as wood immersed in water will rise when liberated. But the wood will stop when it reaches the surface of the water, while there is no reason to suppose that the hydrogen or coal gas bubbles will ever stop. The hydrogen bubble can be made to remain stationary if it is weighted down with something of about fourteen times its own weight (thirteen and one-half times, accurately). Perhaps it would be better to say that it would still continue to rise slowly because that additional something would itself displace some additional air; but if the added weight is a solid body, its own buoyancy in air is negligible.
Our first principle is, then, that at the same pressure and temperature, any gas lighter than air, if properly confined, will exert a net lifting power of (_n_-1) times its own weight, where _n_ is the ratio of weights of air and gas per cubic foot.
If the pressures and temperatures are different, this principle is modified. In a balloon, the gas is under a pressure slightly in excess of that of the external atmosphere: this decreases its lifting power, because the weight of a given volume of gas is greater as the pressure to which it is subjected is increased. The weight of a given volume we have called the _density_: and, as has been stated, if the temperature be unchanged, the density varies directly as the pressure.
The pressure in a balloon is only about 1% greater than that of the atmosphere at sea level, so that this factor has only a slight influence on the lifting power. That it leads to certain difficulties in economy of gas will, however, soon be seen.
The temperature of the gas in a balloon, one might think, would naturally be the same as that of the air outside: but the surface of the balloon envelope has an absorbing capacity for heat, and on a bright sunny day the gas may be considerably warmed thereby. This action increases the lifting power, since increase of temperature (the pressure remaining fixed) decreases the density of a gas. To avoid this possibly objectionable increase in lifting power, balloons are sometimes painted with a non-absorbent color. One of the first Lebaudy balloons received a popular nickname in Paris on account of the yellow hue of its envelope.
Suppose we wish a balloon to carry a total weight, including that of the envelope itself, of a ton. If of hydrogen, it will have to contain one fifteenth of this weight or about 133 pounds of that gas, occupying a space of about 23,000 cubic feet. If coal gas is used, the size of the balloon would have to be much greater. If hot air is used--as has sometimes been the case--let us assume the temperature of the air inside the envelope such that the density is just half that of the outside air. This would require a temperature probably about 500°. The air needed would be just a ton, and the balloon would be of about 52,000 cubic feet. It would soon lose its lifting power as the air cooled; and such a balloon would be useful only for short flights.
The 23,000 cubic foot hydrogen balloon, designed to carry a ton, would just answer to sustain the weight. If anchored at sea level, it would neither fall to the ground nor tug upward on its holding-down ropes. In order to ascend, something more is necessary. This "something more" might be some addition to the size and to the amount of hydrogen. Let us assume that we, instead, drop one hundred pounds of our load. Thus relieved of so much ballast, the balloon starts upward, under the net lifting force of one hundred pounds. It is easy to calculate how far it will go. It will not ascend indefinitely, because, as the altitude increases, the pressure (and consequently the density) of the external atmosphere decreases. At about a 2000-foot elevation, this decrease in density will have been sufficient to decrease the buoyant power of the hydrogen to about 1900 pounds, and the balloon will cease to rise, remaining at this level while it moves before the wind.
There are several factors to complicate any calculations. Any expansion of the gas bag--stretching due to an increase in internal pressure--would be one; but the envelope fabrics do not stretch much; there is indeed a very good reason why they must not be allowed to stretch. The pressure in the gas bag is a factor. If there is no stretching of the bag, this pressure will vary directly with the temperature of the gas, and might easily become excessive when the sun shines on the envelope.
A more serious matter is the increased difference between the internal pressure of the gas and the external pressure of the atmosphere at high altitudes. Atmospheric pressure decreases as we ascend. The difference between gas pressure and air pressure thus increases, and it is this difference of pressure which tends to burst the envelope. Suppose the difference of pressure at sea level to have been two-tenths of a pound. For a balloon of twenty feet diameter, this would give a stress on the fabric, per lineal inch, of twenty-four pounds. At an altitude of 2000 feet, the atmospheric pressure would decrease by one pound, the difference of pressures would become one and two-tenths pounds, and the stress on the fabric would be 144 pounds per lineal inch--an absolutely unpermissible strain. There is only one remedy: to allow some of the gas to escape through the safety valve; and this will decrease our altitude.
Ascending and Descending
To ascend, then, we must discard ballast: and we cannot ascend beyond a certain limit on account of the limit of allowable pressure on the envelope fabric. To again descend, we must discharge some of the gas which gives us lifting power. Every change of altitude thus involves a loss either of gas or of ballast. Our vertical field of control may then be represented by a series of oscillations of gradually decreasing magnitude until finally all power to ascend is gone. And even this situation, serious as it is, is made worse by the gradual but steady leakage of gas through the envelope fabric. Here, in a word, is the whole problem of altitude regulation. Air has no surface of equilibrium like water. Some device supplementary to ballast and the safety valve is absolutely necessary for practicable flight in any balloon not staked to the ground.
A writer of romance has equipped his aeronautic heroes with a complete gas-generating plant so that all losses might be made up; and in addition, heating arrangements were provided so that when the gas supply had been partially expended its lifting power could be augmented by warming it so as to decrease its density below even the normal. There might be something to say in favor of this latter device, if used in connection with a collapsible gas envelope.
Methods of mechanically varying the size of the balloon, so as by compressing the gas to cause descent and by giving it more room to increase its lifting power and produce ascent, have been at least suggested. The idea of a vacuum balloon, in which a rigid hollow shell would be exhausted of its contents by a continually working pump, may appear commendable. Such a balloon would have maximum lifting power for its size; but the weight of any rigid shell would be considerable, and the pressure tending to rupture it would be about 100 times that in ordinary gas balloons.
It has been proposed to carry stored gas at high pressure (perhaps in the liquefied condition) as a supplementary method of prolonging the voyage while facilitating vertical movements: but hydrogen gas at a pressure of a ton to the square inch in steel cylinders would give an ultimate lifting power of only about one-tenth the weight of the cylinders which contain it. These cylinders might be regarded as somewhat better than ordinary ballast: but to throw them away, with their gas charge, as ballast, would seem too tragic. Liquefied gas might possibly appear rather more desirable, but would be altogether too expensive.
If a screw propeller can be used on a steamship, a dirigible balloon, or an aeroplane to produce forward motion, there is no reason why it could not also be used to produce upward motion in any balloon; and the propeller with its operating machinery would be a substitute for twice its equivalent in ballast, since it could produce motion either upward or downward. Weight for weight, however, the propeller and engine give only (in one computed case) about half the lifting power of hydrogen. If we are to use the screw for ascent, we might well use a helicopter, heavier than air, rather than a balloon.
The Ballonet
The present standard method of improving altitude regulation involves the use of the ballonet, or compartment air bag, inside the main envelope. For stability and effective propulsion, it is important that the balloon preserve its shape, no matter how much gas be allowed to escape. Dirigible balloons are divided into two types, according to the method employed for maintaining the shape. In the Zeppelin type, a rigid internal metal framework supports the gas envelope. This forms a series of seventeen compartments, each isolated from the others. No matter what the pressure of gas, the shape of the balloon is unchanged.
In the more common form of balloon, the internal air ballonet is empty, or nearly so, when the main envelope is full. As gas is vented from the latter, air is pumped into the former. This compresses the remaining gas and thus preserves the normal form of the balloon outline.
But the air ballonet does more than this. It provides an opportunity for keeping the balloon on a level keel, for by using a number of compartments the air can be circulated from one to another as the case may require, thus altering the distribution of weights. Besides this, if the pressure in the air ballonet be initially somewhat greater than that of the external atmosphere, a considerable ascent may be produced by merely venting this air ballonet. This involves no loss of gas; and when it is again desired to descend, air may be pumped into the ballonet. If any considerable amount of gas should be vented, to produce quick and rapid descent, the pumping of air into the ballonet maintains the shape of the balloon and also facilitates the descent.
The Equilibrator
Suppose a timber block of one square foot area, ten feet long, weighing 380 pounds, to be suspended from the balloon in the ocean, and let mechanism be provided by which this block may be raised or lowered at pleasure. When completely immersed in water it exerts an upward pressure (lifting force) of 240 pounds, which may be used to supplement the lifting power of the balloon. If wholly withdrawn from the water, it pulls down the balloon with its weight of 380 pounds. It seems to be equivalent, therefore, to about 620 pounds of ballast. When immersed a little over six feet--the upper four feet being out of the water--it exerts neither lifting nor depressing effect. The amount of either may be perfectly adjusted between the limits stated by varying the immersion.
In the Wellman-Vaniman equilibrator attached to the balloon _America_, which last year carried six men (and a cat) a thousand miles in three days over the Atlantic Ocean, a string of tanks partly filled with fuel was used in place of the timber block. As the tanks were emptied, the degree of control was increased; and this should apparently have given ideal results, equilibration being augmented as the gas supply was lost by leakage: but the unsailorlike disregard of conditions resulting from the strains transferred from a choppy sea to the delicate gas bag led to disaster, and it is doubtful whether this method of control can ever be made practicable. The _America's_ trip was largely one of a drifting rather than of a dirigible balloon. The equilibrator could be used only in flights over water in any case: and if we are to look to water for our buoyancy, why not look wholly to water and build a ship instead of a balloon?
DIRIGIBLE BALLOONS AND OTHER KINDS
Shapes
The cylindrical Zeppelin balloon with approximately conical ends has already been shown (page 68). Those balloons in which the shape is maintained by internal pressure of air are usually _pisciform_, that is, fish-shaped. Studies have actually been made of the contour lines of various fishes and equivalent symmetrical forms derived, the outline of the balloon being formed by a pair of approximately parabolic curves.
The first flight in a power driven balloon was made by Giffard in 1852. This balloon had an independent speed of about ten feet per second, but was without appliances for steering. A ballonetted balloon of 120,000 cubic feet capacity was directed by man power in 1872: eight men turned a screw thirty feet in diameter which gave a speed of about seven miles per hour. Electric motors and storage batteries were used for dirigible balloons in 1883-'84: in the latter year, Renard and Krebs built the first fish-shaped balloon. The first dirigible driven by an internal combustion motor was used by Santos-Dumont in 1901.
Dimensions
The displacements of present dirigibles vary from 20,000 cubic feet (in the United States Signal Corps airship) up to 460,000 cubic feet (in the Zeppelin). The former balloon has a carrying capacity only about equivalent to that of a Wright biplane. While anchored or drifting balloons are usually spherical, all dirigibles are elongated, with a length of from four to eleven diameters. The Zeppelin represents an extreme elongation, the length being 450 feet and the diameter forty-two feet. At the other extreme, some of the English military dirigibles are thirty-one feet in diameter and only 112 feet long. Ballonet capacities may run up to one-fifth the gas volume. All present dirigibles have gasoline engines driving propellers from eight to twenty feet in diameter. The larger propellers are connected with the motors by gearing, and make from 250 to 700 turns per minute. The smaller propellers are direct connected and make about 1200 revolutions. Speeds are usually from fifteen to thirty miles per hour.
The present-day elongated shape is the result of the effort to decrease the proportion of propulsion resistance due to the pressure of the air against the head of the balloon. This has led also to the pointed ends now universal; and to avoid eddy resistance about the rear it is just as important to point the stern as the bow. As far as head end resistance alone is concerned, the longer the balloon the better: but the friction of the air along the side of the envelope also produces resistance, so that the balloon must not be too much elongated. Excessive elongation also produces structural weakness. From the standpoint of stress on the fabric of the envelope, the greatest strain is that which tends to break the material along a longitudinal line, and this is true no matter what the length, as long as the seams are equally strong in both directions and the load is so suspended as not to produce excessive bending strain on the whole balloon. In the _Patrie_ (page 77), some distortion due to loading is apparent. The stress per lineal inch of fabric is obtained by multiplying the net pressure by half the diameter of the envelope (in inches).
Ample steering power (provided by vertical planes, as in heavier-than-air machines) is absolutely necessary in dirigibles: else the head could not be held up to the wind and the propelling machinery would become ineffective.
Fabrics
The material for the envelope and ballonets should be light, strong, unaffected by moisture or the atmosphere, non-cracking, non-stretching, and not acted upon by variations in temperature. The same specifications apply to the material for the wings of an aeroplane. In addition, for use in dirigible balloons, fabrics must be impermeable, resistent to chemical action of the gas, and not subject to spontaneous combustion. The materials used are vulcanized silk, gold beater's skin, Japanese silk and rubber, and cotton and rubber compositions. In many French balloons, a middle layer of rubber has layers of cotton on each side, the whole thickness being the two hundred and fiftieth part of an inch. In the _Patrie_, this was supplemented by an outside non-heat-absorbent layer of lead chromate and an inside coating of rubber, all rubber being vulcanized. The inner rubber layer was intended to protect the fabric against the destructive action of impurities in the gas.
Fabrics are obtainable in various colors, painted, varnished, or wholly uncoated. The rubber and cotton mixtures are regularly woven in France and Germany for aeroplanes and balloons. The cars and machinery are frequently shielded by a fabricated wall. Weights of envelope materials range from one twenty-third to one-fourteenth pound per square foot, and breaking stresses from twenty-eight to one hundred and thirty pounds. Pressures (net) in the main envelope are from three-fifths to one and a quarter _ounces_ per square inch, those in the ballonets being somewhat less. The _Patrie_ of 1907 had an envelope guaranteed not to allow the leakage of more than half a cubic inch of hydrogen per square foot of surface per twenty-four hours.
The best method of cutting the fabric is to arrange for building up the envelope by a series of strips about the circumference, the seams being at the bottom. The two warps of the cloth should cross at an angle so as to localize a rip or tear. Bands of cloth are usually pasted over the seams, inside and out, with a rubber solution; this is to prevent leakage at the stitches.
Framing
In the _Zeppelin_, the rigid aluminum frame is braced every forty-five feet by transverse diametral rods which make the cross-sections resemble a bicycle wheel (page 68). This cross-section is not circular, but sixteen-sided. The pressure is resisted by the framework itself, the envelope being required to be impervious only. The seventeen compartments are separated by partitions of sheet aluminum. There is a system of complete longitudinal bracing between these partitions. Under the main framework, the cars and machinery are carried by a truss about six feet deep which runs the entire length. The cars are boat-shaped, twenty feet long and six feet wide, three and one-half feet high, enclosed in aluminum sheathing. These cars, placed about one hundred feet from the ends, are for the operating force and machinery. The third car, carrying passengers, is built into the keel.
In non-rigid balloons like the _Patrie_, the connecting frame must be carefully attached to the envelope. In this particular machine, cloth flaps were sewed to the bag, and nickel steel tubes then laced in the flaps. With these tubes as a base, a light framework of tubes and wires, covered with a laced-on waterproof cloth, was built up for supporting the load. Braces ran between the various stabilizing and controlling surfaces and the gas bag; these were for the most part very fine wire cables. The weight of the car was concentrated on about seventy feet of the total length of 200 feet. This accounts for the deformation of the envelope shown in the illustration (page 77). The frame and car of this balloon were readily dismantled for transportation.
In some of the English dirigibles the cars were suspended by network passing over the top of the balloon.
Keeping the Keel Horizontal
In the _Zeppelin_, a sliding weight could be moved along the keel so as to cause the center of gravity to coincide with the center of upward pressure in spite of variations in weight and position of gas, fuel, and ballast. In the German balloon _Parseval_, the car itself was movable on a longitudinal suspending cable which carried supporting sheaves. This balloon has figured in recent press notices. It was somewhat damaged by a collision with its shed in March: the sixteen passengers escaped unharmed. A few days later, emergency deflation by the rip-strip was made necessary during a severe storm. In the ordinary non-rigid balloon, the pumping of air between the ballonets aids in controlling longitudinal equilibrium. The pump may be arranged for either hand or motor operation: that in the _Clément-Bayard_ had a capacity of 1800 liters per minute against the pressure of a little over three-fifths of an ounce. The _Parseval_ has two ballonets. Into the rear of these air is pumped at starting. This raises the bow and facilitates ascent on the principle of the inclined surface of an aeroplane. After some elevation is attained, the forward ballonet is also filled.
Stability
Besides proper distribution of the loads, correct vertical location of the propeller is important if the balloon is to travel on a level keel. In some early balloons, two envelopes side by side had the propeller at the height of the axes of the gas bags and midway between them. The modern forms carry the car, motor, and propeller below the balloon proper. The air resistance is mostly that of the bow of the envelope: but there is some resistance due to the car, and the propeller shaft should properly be at the equivalent center of all resistance, which will be between car and axis of gas bag and nearer the latter than the former. With a single envelope and propeller, this arrangement is impracticable. By using four (or even two) propellers, as in the _Zeppelin_ machine (page 68), it can be accomplished. If only one propeller is employed, horizontal rudder planes must be disposed at such angles and in such positions as to compensate for the improper position of the tractive force. Even on the _Zeppelin_, such planes were employed with advantage (pages 66 and 73).
Perfect stability also involves freedom from rolling. This is usually inherent in a balloon, because the center of mass is well below the center of buoyancy: but in machines of the non-rigid type the absence of a ballonet might lead to both rolling and pitching when the gas was partially exhausted.