Produced by James Simmons.
This file was produced from page images at the Internet Archive.
Transcriber’s Note
This book was transcribed from scans of the original found at the
Internet Archive. I have rotated some images. The caption for Figure 20
was illegible in the scanned pages so I used a description from a
paragraph that referred to it.
DIRIGIBLE BALLOONS
INSTRUCTION PAPER
PREPARED BY
CHARLES B. HAYWARD
MEMBER, SOCIETY OF AUTOMOBILE ENGINEERS; MEMBER, THE AERONAUTICAL
SOCIETY;
FORMERLY SECRETARY, SOCIETY OF AUTOMOBILE ENGINEERS; FORMERLY
ENGINEERING EDITOR, "THE AUTOMOBILE"
AMERICAN SCHOOL OF CORRESPONDENCE
CHICAGO ILLINOIS
U.S.A.
COPYRIGHT, 1912, 1918, BY
AMERICAN SCHOOL OF CORRESPONDENCE
COPYRIGHTED IN GREAT BRITAIN
ALL RIGHTS RESERVED
DIRIGIBLE BALLOONS
INTRODUCTION
Of the first attempts of men to emulate the flight of birds, we have no
knowledge, but one of the earliest, perhaps, is embodied in the myth of
Icarus and Daedalus. Xerxes, it is said, possessed a throne which was
drawn through the air by eagles. The Chinese have sometimes been given
credit for the invention of the balloon, as they have for many other
scientific discoveries. It is related that a balloon was sent up at
Pekin in celebration of the ascension of the throne by an emperor in the
beginning of the fourteenth century.
[Illustration: Fig. 1. De Lana Airboat.]
*Early Attempts.* Leonardo da Vinci devoted some time to the problem of
artificial flight. His sketches show the details of batlike wings which
were to spread out on the downward stroke and fold up with the upward
stroke.
Francisco de Lana planned to make a flying ship the appearance of which
was somewhat like that shown in Fig. 1, by exhausting the air from metal
spheres fastened to a boat. The boat was to be equipped with oars and
sails for propulsion and guiding. The method in which he purposed to
create the vacuum in the spheres consisted of filling them with water,
thus driving out the air, then letting the water run out. He thought
that if he closed the tap at the proper time, there would be neither air
nor water in the spheres. His flying ship was never constructed, for he
piously decided that God would never permit such a change in the affairs
of men.
*The First Flying Machine.* In 1781, Meerwein of Baden, Germany,
constructed a flying machine, and was the first, perhaps, to
intelligently take into account the resistance of the air. He took the
wild duck as a basis of calculation, and found that a man and machine
weighing together 200 pounds would require a wing surface of from 125 to
130 square feet. It is of interest to note that Lilienthal, who met his
death in trying to apply these principles, over one hundred years later
found these figures to be correct. Two views of Meerwein’s apparatus are
shown in Fig. 2. The construction involved two wood frames covered with
cloth. The machine weighed 56 pounds and had a surface area of 111
square feet. The operator was fastened in the middle of the under side
of the wings, and over a rod by which he worked the wings. His attempts
at flight were not successful, as his ideas of the power of a man were
in error.
[Illustration: Fig. 2. Meerwein Flying Machine]
*Classification.* All attempts at human flight have gone to show that
there are four possible ways in which man may hope to navigate the air.
He may imitate the flight of birds with a machine with moving or
flapping wings; he may use vertical screws or helices to pull himself
up; he may use an aeroplane and sail the air like an eagle; or, lastly,
he may raise himself by means of a gas bag and either drift with the
wind or move forward by means of propellers.
In these attempts, apparatus of several different types has been
developed. The types are classed in two general divisions based on their
weight relative to that of the atmosphere, viz, the _lighter-than-air
machines_ and the _heavier-than-air machines_. Lighter-than-air machines
are those which employ a bag filled with a gas whose specific gravity is
sufficiently less than that of the air to lift the bag and the necessary
attachments from the earth, and include simple balloons and dirigibles.
Heavier-than-air machines, which will neither rise nor remain in the air
without motive power, include all forms of aeroplanes.
SIMPLE BALLOONS
*Theory.* The balloon-like airship has been more highly developed than
any other type of aerial craft, probably because it offers the most
obvious means of overcoming the force of gravitation. It depends on the
law of Archimedes:
_"Every body which is immersed in a fluid is acted upon by an upward
force, exactly equal to the weight of the fluid displaced by the
immersed body."_
That is, a body will be at rest if immersed in a fluid of equal specific
gravity or equal weight, volume for volume; if the body has less
specific gravity than the fluid in which it is immersed it will rise; if
it has a greater specific gravity it will sink. Therefore, if the total
weight of a balloon is less than the weight of all the air it displaces
it will rise in the air. It is, then, necessary to fill the balloon with
some gas whose specific gravity is enough less than, that of the air to
make the weight of the gas itself, the bags, and the attachments, less
than the weight of the air displaced by the whole apparatus. The gases
usually employed are _hydrogen_, _coal gas_, and _hot air_.
At atmospheric pressure and freezing temperature, the weight of a cubic
foot of air is about .08 pound; the weight of a cubic foot of hydrogen
is about .005 pound, under the same conditions. According to the law of
Archimedes, a cubic foot of hydrogen would be acted upon by a force
equal to the difference, or approximately .075 pound, tending to move it
upwards. In the same way, a cubic foot of coal gas, which weighs .04
pound, would be acted upon by an upward force of .04 pound.
It is evident, then, that a considerable volume of gas is required to
lift a balloon with its envelope, net, car, and other attachments.
Further, it requires almost twice as much coal gas as hydrogen, under
the same conditions, for we have seen that the upward force on it is
only half as great. The lifting power of hot air is less than one-eighth
as great as that of hydrogen at the highest temperature that can
possibly be used in a balloon.
[Illustration: Fig. 3. Montgolfier Balloon]
The general type of lighter-than-air machines may be divided into
_aerostats_ (ordinary balloons, which are entirely dependent on wind
currents for lateral movement, and which are often the chief features at
country fairs) and dirigible balloons or _aeronats_ (air swimmers).
Dirigible balloons employ the gas bag for maintaining buoyancy, and have
rudders to guide them and propellers to drive them forward through the
air in much the same way that ships are driven through the water.
*The First Balloon.* For several years, Joseph and Steven Montgolfier
had been experimenting with a view to constructing a balloon: in the
first place by filling bags with _steam_; then by filling bags with
_smoke_, and finally by filling bags with _hydrogen_. These attempts
were all failures, for the steam rapidly condensed and the smoke and
hydrogen leaked through the pores in the bags. They finally hit upon the
idea of filling the bag with _hot air_, by means of a fire under its
open mouth. Several balloons were burned up, but the next was always
made larger, until, at their first public exhibition on June 5, 1783,
the bag had become over 35 feet in diameter. On this occasion, it rose
to a height of between 900 and 1,000 feet, but the hot air was gradually
escaping, and at the end of ten minutes the balloon fell to the ground.
The Montgolfiers then went to Paris, where, after suffering the loss of
a paper balloon by rain, they sent up a waterproofed linen one carrying
a sheep, a duck, and a rooster in a basket. A rupture in the linen
caused the three unwilling aeronauts to make a landing at the end of
about ten minutes. The Montgolfiers received great honor, and small
balloons of this type became a popular fad. One of these balloons is
shown in Fig. 3, making an ascension.
*Rozier.* The first man to go up in a balloon was Rozier, who ascended
in a captive balloon to a height of about 80 feet, in the latter part of
the year 1783. Later, in company with a companion, he made a voyage in a
free balloon, remaining in the air about half an hour. In these
balloons, the air within was kept hot by means of a fire carried in a
pan immediately below the mouth of the bag, as shown in Fig. 4.
Accidents were numerous on account of the fabric becoming ignited from
the fire in the pan.
[Illustration: Fig. 4. Rozier Hot-Air Balloon]
*Improvements by Charles.* The physicist, Charles, was working along
these lines at the same time. He coated his balloon with a rubber
solution to close up the pores, and was thereby enabled to substitute
hydrogen for the hot air. Shortly after the Montgolfiers’ first public
exhibition, Charles sent up his balloon for the benefit of the _Academie
des Sciences_ in Paris. The balloon, which weighed about 19 pounds,
ascended rapidly in the air and disappeared in the clouds, where it
burst and fell in a suburb of the city. The impression produced upon the
peasants at seeing it fall from the heavens was hardly different from
what could be expected. They believed it to be of devilish origin, and
immediately tore it into shreds. Charles subsequently built a large
balloon quite similar to those in use today. A net was used to support
the basket, and a valve, operated by means of ropes from the basket, was
arranged at the top to permit the gas to escape as desired.
*The Balloon Successful.* The English Channel was first crossed in 1785.
Blanchard, an Englishman, and Jeffries, an American, started from Dover
on January 7 in a balloon equipped with wings and oars. After a very
hazardous voyage, during which they had to cast overboard everything
movable to keep from drowning, they landed in triumph on the French
coast.
An attempt to duplicate this feat was made shortly afterward by Rozier.
He constructed a balloon filled with hydrogen, below which hung a
receiver in which air could be heated. He hoped to replace by the hot
air the losses due to leakage of hydrogen. Soon after the start the
balloon exploded, due to the escaping gas reaching the fire, and Rozier
and his companion were dashed on the cliffs and killed.
EARLY DIRIGIBLES
*Meusnier the Pioneer.* The fact that the invention of the dirigible
balloon and means of navigating it were almost simultaneous is very
little known today and much less appreciated. Like the aeroplane, its
development was very much retarded by the lack of suitable means of
propulsion, and the actual history of what has been accomplished in this
field dates back only to the initial circular flight of La France in
1885. Still the principles upon which success has been achieved were
laid down within a year of the appearance of Montgolfier’s first gas
bag. Lieutenant Meusnier, who subsequently became a general in the
French army, must really be credited with being the true inventor of
aerial navigation. At a time when nothing whatever was known of the
science, Meusnier had the distinction of elaborating at one stroke all
the laws governing the stability of an airship, and calculating
correctly the conditions of equilibrium for an elongated balloon, after
having strikingly demonstrated the necessity for this elongation. This
was in 1781 and Meusnier’s designs and calculations are still preserved
in the engineering section of the French War Office in the form of
drawings and tables.
But as often proved to be the case in other fields of research, his
efforts went unheeded. How marvelous the establishment of these numerous
principles by one man in a short time really is, can be appreciated only
by noting the painfully slow process that has been necessary to again
determine them, one by one, at considerable intervals and after numerous
failures. Through not following the lines which he laid down, aerial
navigation lost a century in futile groping about; in experiments
absolutely without method or sequence.
[Illustration: Fig. 5. Meusnier Dirigible Balloon]
Meusnier’s designs covered two dirigible balloons and that he fully
appreciated the necessity for size is shown by the dimensions of the
larger, which unfortunately was never built. This was to be 260 feet
long by 130 feet in diameter, in the form of an ellipse, the elongation
being exactly twice the diameter. In other words, a perfect ellipsoid,
which was a logical and, in fact, the most perfect development of the
spherical form. Although increased knowledge of wind resistance and the
importance of the part it plays has proved his relative dimensions to be
faulty, a study of the principal features of his machine shows that he
anticipated the present-day dirigible of the most successful type at
practically every point, barring, of course, the motive power, as there
was absolutely nothing available in that day except human effort. As the
latter weighs more than one-half ton per horse-power, it goes without
saying that Meusnier’s balloon would have been dirigible only in a dead
calm.
He adopted the elongated form, conceived the girth fastening, the
triangular or indeformable suspension, the air balloonet and its pumps,
and the screw propeller, all of which are to be found in the dirigibles
of present-day French construction, Fig. 5. It need scarcely be added
that the French have not only devoted a greater amount of time and
effort to the development of the dirigible than any other nation, but
have also met with the greatest success in its use. It was not until
1886, or more than a century after Meusnier had first elaborated those
principles, that their value became known. They were set forth by
Lieutenant Letourne, of the French engineers, in a paper presented to
the _Academie des Sciences_ by General Perrier.
In one form or another, the salient features of Meusnier’s dirigible
will be found embodied in the majority of attempts of later days. His
large airship was designed to consist of double envelope, the outer
container of which was to provide the strength necessary, and it was
accordingly reinforced by bands. The inner envelope was to provide the
container for the gas and was not called upon to support any weight.
This inner bag or balloon proper was designed to be only partially
inflated and the space between, the two was to be occupied by air which
could be forced into it at two points at either end, by pumps, so as to
maintain the pressure on the gas bag uniform regardless of the expansion
or contraction of its contents. Here in principle was the air balloonet
of today. Instead of employing a net to hang the car from the outer
envelope, the former was attached by means of a triangular suspension
system fastened to a heavy rope band, or girth, encircling the outer
envelope. At the three points where the lifting rope members met, a
shaft running the length of the car and carrying what Meusnier described
as "revolving oars" was installed. These constituted the prototype of
the screw propeller, invented for aerial navigation at a time long
antedating the use of steam for marine use. Thus he devised: (1) The air
balloonet to husband the gas supply and thus prevent the deformation of
the outer container or support, as well as to provide stability; (2) the
triangular suspension to attain longitudinal stability; and (3) the
screw propeller for propulsion, beside selecting the proper location for
the latter.
PROBLEMS OF THE DIRIGIBLE
*Ability to Float.* If ability to rise in the air depended merely upon a
knowledge of the principle that made it possible, it undoubtedly would
have been accomplished many centuries ago. As already mentioned,
Archimedes established the fact that a body upon floating in a fluid
displaces an amount of the latter equal in weight to the body itself,
and upon this theory was formulated the now well-known law, that every
body plunged into a fluid is subjected by this fluid to a pressure from
below, equivalent to the weight of the fluid displaced by the body.
Consequently, if the weight of the latter be less than that of the fluid
it displaces, the body will float. It is by reason of this that the iron
ship floats and the fish swims in water. If the weight of the body and
the displaced water be the same, the body will remain in equilibrium in
the water at a certain level, and if that of the body be greater, it
will sink. All three of these factors are found in the fish, which, with
the aid of its natatory gland, can rise to the surface, sink to the
bottom, or remain suspended at different levels. To accomplish these
changes of specific gravity, the fish fills this gland with air,
dilating it until full, or compressing and emptying it. In this we find
a perfect analogy to the air balloonet of the dirigible, which serves
the same purposes. The method by which lifting power is obtained in the
dirigible is exactly the same as in the case of the balloon.
But once in the air, a balloon is, to all intents and purposes, a part
of the atmosphere. There is absolutely no sensation of movement, either
vertically or horizontally. The earth appears to drop away from beneath
and to sweep by horizontally, and regardless of how violently the wind
may be blowing, the balloon is always in a dead calm because it is
really part of the wind itself and is traveling with it at exactly the
same speed. If it were not for the loss of lifting power through the
expansion and contraction of the gas, making it necessary to permit its
escape in order to avoid rising to inconvenient heights on a very warm
day, and the sacrifice of ballast to prevent coming to earth at night,
the ability of a balloon to stay up would be limited only by the
endurance of its crew and the quantity of provisions it was able to
transport. As the use of air balloonets in the dirigible takes care of
this, the question of lifting power presents no particular difficulty.
It is only a matter of providing sufficient gas to support the increased
weight of the car, motor and its accessories, and the crew of the larger
vessel, with a factor of safety to allow for emergencies, in order to
permit of staying in the air long enough to make a protracted voyage.
*Air Resistance vs. Speed.* Unless a voyage is to be governed in its
direction entirely by the wind, the dirigible must possess a means of
moving contrary to the latter. The moment this is attempted, resistance
is encountered, and it is this resistance of the air that is responsible
for the chief difficulties in the design of the dirigible. To drive it
against the wind, it must have power; to support the weight of the motor
necessary, the size of the gas bag must be increased. But with the
increase in size, the amount of resistance is greatly multiplied and the
power to force it through the air must be increased correspondingly. The
law is approximately as follows:
_Where the surface moves in a line perpendicular to its plane, the
resistance is proportional to the extent of the surface, to the square
of the speed with which the surface is moved through the air, and to a
coefficient, the mean value of which is 0.125._
This coefficient is a doubtful factor, the figure given having been
worked out years ago in connection with the propulsion of sailing
vessels. Its value varies according to later experimenters between .08
and .16, the mean of the more recent investigations of Renard, Eiffel,
and others who have devoted considerable study to the matter, being .08.
This is dwelt upon more in detail under "Aerodynamics" and it will be
noted that the values of the coefficient _K_, given here, do not agree
with those stated in that article. They serve, however, to illustrate
the principles in question.
In accordance with this law, doubling the speed means quadrupling the
resistance of the air. For instance, a surface of 16 square feet moving
directly against the air at a speed of 10 feet per second will encounter
a resistance of 16 X 100 (square of the speed) X 0.125 = 200 pounds
pressure. Doubling the speed, thus bringing it up to 20 feet per second,
would give the equation 16 X 400 X 0.125 = 800 pounds pressure, or with
the more recent value of the coefficient of .08, 512 pounds pressure.
The first consideration is accordingly to reduce the amount of surface
moving at right angles. The resistance of a surface having tapering
sides which cut through or divide the molecules of air instead of
allowing them to impinge directly upon it, is greatly diminished; hence,
Meusnier’s principle of elongation. If we take the same panel presenting
16 square feet of surface and build out on it a hemisphere, its
resistance at a speed of 10 feet per second will be exactly half, or a
pressure of 100 pounds.
By further modifying this so as to represent a sharp point, or
acute-angled cone, it will be 38 pounds. There could accordingly be no
question of attempting to propel a spherical balloon.
[Illustration: Fig. 6. Giffard Dirigible]
It is necessary to select a form that presents as small a surface as
possible to the air as the balloon advances, while preserving the
maximum lifting power. But experience has strikingly demonstrated the
analogy between marine and aerial practice—not only is the shape of the
bow of the vessel of great importance but, likewise, the stern. The
profile of the latter may permit of an easy reunion of the molecules of
air separated by the former, or it may allow them to come together again
suddenly, clashing with one another and producing disturbing eddies just
behind the moving body. To carry the comparison with a marine vessel a
bit further, the form must be such as to give an easy "shear," or sweep
from stem to stern.
[Illustration: Fig. 7. De Lome Dirigible]
That early investigators appreciated this is shown by the fact that
Giffard in 1852, Fig. 6, De Lome in 1872, Fig. 7, Tissandier in 1884,
and Santos-Dumont in his numerous attempts, adopted a spindle-shaped or
"fusiform" balloon. In other words, their shape, equally pointed at
either end, was symmetrical in relation to their central plan. However,
that the shape best adapted to the requirements of the bow did not serve
equally well for the stern, was demonstrated for the first time by
Renard, to whom credit must be given for a very large part of the
scientific development of the dirigible. Almost a century earlier,
Marey-Monge had laid down the principle that to be successfully
propelled through the air, the balloon must have "the head of a cod and
the tail of a mackerel." Nature exemplifies the truth of this in all
swiftly moving fishes and birds. Renard accordingly adopted what may
best be termed the "pisciform" type, viz, that of a dis-symmetrical fish
with the larger end serving as the bow; and the performances of the
Renard, Lebaudy, and Clement-Bayard airships have shown that this is the
most advantageous form.
The pointed stern prevents the formation of eddies and the creation of a
partial vacuum in the wake which would impose additional thrust on the
bow. Zeppelin has disregarded this factor by adhering to the purely
cylindrical form with short hemispherical bow and stern, but it is to be
noted that while other German investigators originally followed this
precedent, they have gradually abandoned it, owing to the noticeable
retarding effect.
*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.
[Illustration: Fig. 8. La Ville de Paris Showing Balloonets]
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.
*Location of Propeller.* The final factor of importance in the design of
the successful dirigible is the proper location of the propulsive effort
with relation to the balloon. Theoretically, this should be applied to
the axis of the balloon itself, as the latter represents the greater
part of the resistance offered to the air. At least one attempt to carry
this out in practice resulted disastrously, that of the Brazilian
airship Pax, while the form adopted by Rose, in which the propeller was
placed between the twin balloons in a plane parallel with their
horizontal axes, was not a success. In theory, the balloon offers such a
substantial percentage of the total resistance to the air that the area
of the car and the rigging were originally considered practically
negligible by comparison. Actually, however, this is not the case.
Calculation shows that in the case of any of the typical French airships
mentioned, the sum of the surface of the suspending rigging alone is
easily the equivalent of 2 square meters, or about 21 square feet,
without taking into consideration the numerous knots, splices, pulleys,
and ropes employed in the working of the vessels, air tubes
communicating with the air balloonets, and the like. Add to this
equivalent area that of the passengers, the air pump, other transverse
members and exposed surfaces, and the total will be found equivalent to
a quarter or even a third of the transverse section of the balloon
itself.